Maryline Helard

and Daniel ROVIRAS (CNAM Paris) -for kindly accepting the invitation to my HDR and honoring me with their participation, leading to a very interesting and rich scientic discussion. Being a part of Innov'COM/Sup'Com (since 2005) and CEDRIC/

C n , R n

The sets of vectors of length n, with complex and real elements.

C p×n , R p×n

The set of matrices with p rows and n columns, with complex and real elements.

N

The set of positive integer elements.

log(•)

The natural logarithm.

log 2 (•)

The base 2 logarithm.

x *

Complex conjugate of the complex value x.

|x|

The absolute value of a scalar.

x

The oor operator, i.e. the smallest integer less than x.

x

The ceil operator, i.e. the smallest integer greater than or equal to x.

|Ω|

The cardinality of the set Ω, i.e. the number of elements in the nite set Ω. ∩

The intersection operator.

∪

The union operator.

E{•}

The expectation operator.

[•] T

The transpose operator.

[•] H

The complex conjugate (Hermitian) transpose operator.

X -1

The inverse of matrix X.

I n

The identity matrix of size n.

n

The square zero matrix of size n.

n×m

The zero matrix of size n r × n t . v

Euclidean norm of vector v. v * Nuclear norm of vector v. v F Frobenius norm of vector v. Re{x} Real part of the complex value x. Collaboration with THALES Communications with Dr. Sylvain Traverso on carrying out some testbed experiments in order to convince evidences of some multicarrier waveforms feasibility using realworld environment imposing some RF imperfections: RF power amplier nonlinearities, IQ imbalance and mirror-frequency interference and phase noise. I provided results concerning CP-OFDM, WOLA-OFDM and BF-OFDM, and Dr. Traverso provided ltered-OFDM's results. Invited Speaker Title: Special Session: Post-OFDM waveforms for 5G The teaching activities 1 are separated in lectures (L), directed works (DW) and labworks (LW). Total in HDW 756

Im{x}

Teaching during PhD

Teaching description (i) Computer networks administration

The purpose of this lecture is to give a sound understanding of computer network conguration, with a strong emphasis on the management and administration of the network. I taught interconnection, routing (RIP, OSPF and BGP), network access control (VLAN, ACL, Firewall), NAT, administration through SNMP and HPOpenView platform. Through networking labs, I gave students the opportunity of learning further conguration details and acquire practical knowledge. I was in charge of these labworks and I built LW exercises using several tools for computer networks management and supervision.

(ii) TCP/IP Networking In this course, I taught to students the fundamentals of computer networking, with a strong emphasis on TCP/IP and the internet model. Indeed, I taught TCP/IP architecture, the internet protocol version 4 (IPv4), addressing and the transport layer (TCP and UDP). In the laboratory works, students exercise practical congurations, like setting up a network, packet captures and protocols analysis. I was in charge of the labworks and I entirely produced their handout.

(iii) Digital data transmission I taught to undergraduate students the fundamentals of digital data transmission. I focussed on techniques of PHY and MAC layers. The contents of this course was: data transmission chain overview, baseband and passband modulations, channel coding, ...

(iv) Introduction to telecommunications

This course aimed at developing the fundamental principles of telecommunication systems and their recent technological innovations. Specically, Its goal was just to give a synthetic panorama of the telecommunication sector by describing the main elements constituting such a system and the main techniques, in an introduction level.

(v) Radiowave propagation

This course gave the fundamentals of electromagnetic waves and prorogations. I taught Maxwell's equations, propagation, uniform plane waves and waveguide.

(vi) Communication Systems

In this labwork, I taught to students the design of transceiver chain through MATLAB or circuit hardware and real signals, gathering all their knowledge in analog modulaions. The transmission was accomplished through radio-frequency link. They implemented AM and FM modulator/demodulator using electronic devices. Using MATLAB, they implemented channel encoder, digital mapping, multi-tone modulator, propagation channel and the whole receiver chain.

Total in HDW 1704

Teaching description (ii) Radiocommunications

In this course, students were given a system overview of how radiocommunication systems are built up.

The main emphasis is on digital radiocommunication and the lowest layer, physical layers, and how the radio channel aects design choices. Advanced technologies, like OFDM and MIMO, were taught and their performance were studied under many radio channel models and in presence of hardware imperfections.

I am in charge of this course (30 HDW per year in average). I have produced the slides and 5 DWs.

Concerning LW, I have entirely built labworks exercises on MATLAB.

(iii) Digital communications

The course gives a fundamental description to the principles and systems for digital transmission of information over channels with Gaussian noise, including detailed analysis of digital carrier modulation formats including assessment of signal-to-noise ratio, bit error rate, and power and bandwidth eciency for

Works supervision experience

Up to now, over 80 highly qualied students in their project graduation. These projects concern undergraduate and graduate levels for dierent specialities. Specically, they are related to hardware/software developments including transmission/reception to remote management of industrial and medical systems.

These projects have adopted new technologies integration (GPS, RFID, CPL,....) and tele-informatics over communication networks. They have been very benecial to my students who have gone on to secure highly sought-after positions in industry. At ISI/University of Tunis ElManar, undergraduate and graduate students are asked to perform an internship, most often in industry but it can be in an academic laboratory, in order to obtain their, respectively, Licence (L3) or Engineer degree (M2).

Teaching at CNAM-Paris

Since 2018, I have mainly taught graduate engineering students at CNAM-Paris. I teach LW in Digital Communications 1, Digital Communications 2 and Information theory for alternating graduate students (M1) in the following specialities :

-Systemes Electroniques, Telecommunications et Informatique (SETI).

-Systemes Electroniques et Signalisation Ferroviaire (SESF).

In these LW for alternating students, I try to create a link between the theory studied in lecture and some of the practice aspects that students face in their work by giving them some labworks exercises in the design and evaluation of various components of a digital transceiver through MATLAB or circuit hardware and real signals. My teaching time at CNAM averages 150 HDW per year that are summarized in Table 2.3.

Research topics

Green wireless communication technologies have received increasing attention due to concerns over the explosive increase in power-consumption in the information and communications technologies (ICT) sector and, correspondingly, increasing carbon dioxide (CO2) emissions. Indeed, ICT currently consumes 3% of the world-wide energy and generates about 2% of the world-wide CO2 emissions [START_REF] Fettweis | Ict energy consumption ? trends and challenges[END_REF]. Therefore, energy eciency in signal processing hardware has been in high demand in order to achieve this green goal, in particular to contribute to the reduction of both user equipment energy consumption resulting in longer battery lifetime, and the base station energy consumption resulting in power saving and reduced environmental pollution.

Note that the most important part (50-80%) of the total power budget is actually consumed by the transmit power amplier (PA) which has to be operated near its saturation region, generating however severe nonlinear amplitude-to-amplitude (AM-AM) and amplitude-to-phase (AM-PM) distortions. These undesirable impairments are very harmful, yielding in-band distortions and out-of-band (OOB) radiation, which cause signal distortion and adjacent channel interference, respectively.

In the lights of these facts, my research activities have focused, in one hand, on developing a deep understanding how the radio-frequency (RF) PA aects the performance of wireless communication systems. In another hand, I have been interested in developing new digital processing (DSP) based solutions aiming at mitigating RF PA impairments jointly with increasing energy-eciency. In addition, it is important that these solutions are of low-complexity in order to enable real-time operation.

The dierent research topics, which are summarized in Figure 3 Advanced Multi-carrier Waveforms (MWFs) with high energy-eciency for future WCSs

The need for reducing the energy-consumption has been accentuated by the trends of accommodating, in addition to enhanced mobile broadband (eMBB), new service regimes that arise with new emerging applications like machine-type communications (mMTC) (also known as Internet of Things (IoT)), and ultra-reliable and low latency communications (URLLC). Indeed, future generations of wireless communications will have to cope with high degree of heterogeneity in terms of services and requirements.

Regarding physical layer specications, the major innovation with respect to former standards is to seek new multicarrier waveforms (MWFs) in order to address the major limitations of the traditional CP-OFDM in challenging new spectrum use scenarios, like asynchronous multiple access, as well as the support of mixed numerology. This latter refers to dierent parameter settings in the MWF such as subcarrier spacing (SCS), symbol duration and cyclic prex (CP) length.

Besides this, the post-OFDM MWFs still suer from high PAPR of the modulated signal that would lose their good property in presence of PA. Therefore, high power eciency and PA with perfect linearity are of paramount importance when considering a wireless system with a massive number of low-cost and low-power MTC/URLLC devices, meaning that each device has to become more energy-ecient if not the total energy consumption shall increase.

As far as I am concerned, it is important to study the performance of wireless communication systems In addition, the upcoming wireless communication systems are expected to support a wide range of services with diverse requirements. Therefore, multi-carrier WF based massive MIMO and mixed numerologies transmission are proposed as solutions. In this regard, I have been interested in studying the capability of massive MIMO to deal with the spatial multiplexing of users who are sharing the same bandwidth and are using dierent numerologies.

Indoor Localization: from matrix completion to deep learning Besides the above topics, I have been also involved in some works that aim at developing solutions for indoor localization. In fact, many applications in wireless sensor networks (WSN), such as surveillance, equipment monitoring and control, target tracking and health monitoring, require the location of sensor nodes. Here, we have considered the problem in which some unkown sensor nodes determine their own location (position) using the coordinates of a small number of sensors, called anchor nodes, whose positions are known (obtained by GPS or by installing them at points with known coordinates). In particular, we have adopted advanced approaches, such as matrix completion and machine learning, to develop accurate solutions for indoor localization with an important focus on reducing the computational complexity.

PhD thesis

Introduction and context

The aim of my PhD was the investigation of new linearization techniques applied to power amplier for broadband radio-communications. In this context, we used feedforward neural networks (NN) based baseband adaptive predistortion techniques. Indeed, we have considered three power amplier models.

The rst PA is a stationary memoryless travelling wave tube amplier (TWTA), whose output signal can be expressed as

z = F a (ρ) exp(jF p (ρ) exp(φ)) (3.1)
where ρ and φ are, respectively, the modulus and phase of the input signal. The memoryless TWTA can be modeled using Saleh's model [START_REF] Saleh | Frequency-independent and frequency-dependent nonlinear models of twt ampliers[END_REF] whose AM/AM and AM/PM characteristics can be represented as

F a (ρ) = α a ρ 1 + β a ρ 2 F p (ρ) = α p ρ 2 1 + β p ρ 2 , (3.2)
where α a and β a are the parameters controlling the nonlinear level, and α p and β p are phase displacements. The second PA model is a nonstationary memoryless TWTA whose parameters (α a , β a , α p and β p ) are time-varying. The third one is an amplier with memory modeled, according to Hammerstein, by a memoryless amplier followed by a linear lter [START_REF] Wang | Compensation of nonlinear distortions with memory eects in ofdm transmitters[END_REF] [6]. Indeed, we have presented new NN structures which give the best performance for the three power amplier models. Equally important, many NN training algorithms have been deployed and tested in order to identify the most adequate for adaptive predistortions. This comparison has been conducted through computer simulation for 64 carriers and 16-quadrature amplitude modulation (QAM) OFDM system. It is based on some quality measure (mean square error (MSE), symbol error rate (SER)), the required training time to reach a particular quality level, and computation complexity. The chosen adaptive predistortions (NN structures associated with an adaptive algorithm) have the fastest convergence toward the best performance while performing the lowest computational complexity.

Contributions of the thesis

Neural Network Predistortion for stationary memoryless TWTA The basic idea proposed is to identify the PA inverse transfer functions with a feed-forward neural network (see Figure 3.2). Therefore, by using the indirect learning structure, we aim at obtaining direct estimation of the inverse of the AM/AM and AM/PM nonlinearity characteristics. In order to do that, two processes, referred to as and compared, starting by one hidden layer with 2 neurons, then increasing progressively the number of neurons, before testing a network with two hidden layers, and again increasing progressively the number of neurons on the two layers. Note that activation functions of hidden layers are hyperbolic tangent, while the ones of the output neurones are linear.

Symbol error rate (SER) metric is a typical performance measure to quantify the capability of the proposed predistortion structures to reduce HPA distortions. Then, Figure 3.8 shows the SER performance versus signal to noise ratio (SNR) of many NNDDP's congurations for an OFDM system in presence of a stationary memoryless TWTA operated with an IBO of 8 dB. PD(2, x, 2) represents a NN with one hidden layer of x neurons, PD(2, xy, 2) represents a NN with two hidden layers of x and y neurons, respectively. From these results, we note that all the NNDPDs can reduce the SER compared to the one without any predistorter. Moreover, a satisfactory performance can be obtained with a NN with one hidden layer of nine neurones, which is referred to as DPD(2,9,2).

Neural Network Predistortion for nonstationary memoryless TWTA Here, we assume that the PA parameters are time-varying requiring an improved DPD structure. In this regard, We have studied an adaptive predistortion architecture that performs simultaneously the estimation of the inverse PA characteristics in a postdistortion stage and in a simple predistortion one, as shown by Figure 3.3.

It is worth to mention that the initial DPD (i.e., NN coecients) can be performed oine, and will be adapted online, regarding the variation of the PA characteristics, using an iterative algorithm. Therefore, this latter has to be selected with a very wise way because it should provide satisfactory performance with a reduced complexity. Thus, I have tested and implemented many advanced algorithms [7] with the NNDPD selected above. Among these algorithms, we nd gradient descent (GD) back-propagation [START_REF] Sutton | Two problems with backpropagation and other steepest-descent learning procedures for networks[END_REF],

GD with momentum (GDm) [START_REF] Ning Qian | On the momentum term in gradient descent learning algorithms[END_REF], conjugate gradient (CGF) [START_REF] Fletcher | Function minimization by conjugate gradients[END_REF], quasi-Newton (BFG) [START_REF] Shanno | Conditioning of quasi-newton methods for function minimization[END_REF] and Levenberg-Marquardt (LM) [START_REF] Marquardt | An algorithm for least-squares estimation of nonlinear parameters[END_REF]. We can observe, from these results, that LM algorithm performs better than all the other algorithms. distorter is composed of a linear lter followed by a memoryless neural network, with one hidden layer of nine neurons, and with two linear output neurons. Using this mimetic scheme (LN-NLN), we realize separately the memory predistortion with the linear network and the compensation of the memoryless PA nonlinearities with the nonlinear neural network. A comparative study of these two structures has been done in terms of performance and complexity. To ensure a good comparison between the dierent structures, we have chosen the same length of the tap delay line (4 memory cells). The LM algorithm, which has given the best performance with the lowest computational complexity, has been considered. The realistic level of memoryless nonlinear distortions is considered by operating the PA with an IBO of 7 dB. From these results, we note that the two memory NN structures (FCNN and LN-NLN) are able to reduce considerably the SER compared to the one without any predistortion. Moreover, one can note that the mimetic structure (LN-NLN) performs slightly better than the FCNN structure when they are both trained with LM. We deduce from Table 2 that the computational complexity of the mimetic structure (LN-NLN) is much lower than the fully connected one (FCNN) with an approximate ratio of more than 80% in learning phase and nearly 40% in the generalization phase. and mass-market applications, a major issue in the design and implementation of radio equipment is the cost-eciency in terms of implementation size, cost and power consumption. On one hand, the cost and size of individual radio equipment are strongly limited leading to various Dirty-RF impairments impacting the good properties of the above mentioned technologies. On another hand, facilitating very dense deployments of wireless communication links to connect over trillion wireless devices will result in increasing the power consumption of the ICT sector for more than 14% of estimated world-wide power consumption by 2020 causing 1.4 Giga ton CO2, nearly 2.7% of the global carbon footprint [13] [14].

Thus, I have been dealing with the promising 5G technologies, where low latency, good reliability and high data rate are of paramount importance while a particular attention has been given to the aspect of energy consumption. The main focus has been on the radio access network, in particular on the power amplier, which is known for dominating energy consumption in the radio transmitter.

In the following, we present the dierent research activities, which are illustrated in Figure 3.12 with their related funding. The structure of the second part of this manuscript will follow the research axes presented here.

Advanced Multicarrier Waveform design solutions for 5G and Beyond

I have been interested in investigating advanced MWFs to address the major limitations of the traditional CP-OFDM in challenging new spectrum use scenarios, like asynchronous multiple access, as well as the support of mixed numerology which allows the service to choose between a set of supported subcarrier spacing (SCS) and symbol duration. Indeed, I have had major contributions in the ANR WONG5 project in which notable waveforms have been introduced. Post-OFDM MWFs are basically based on ltering or/and windowing processing in either time or frequency domain [START_REF] Medjahdi | Wola processing: A useful tool for windowed waveforms in 5g with relaxed synchronicity[END_REF]. Indeed, a rst class of these MWFs gathers the ones that adopt a per-subcarrier pulse-shaping to reduce out-of-band (OOB) radiation and increase relaxed synchronization requirements: oset quadrature amplitude modulation based lter-bank multicarrier (FBMC-OQAM) [START_REF] Bellanger | Physical layer for future broadband radio systems[END_REF] [17] and ltered multi-tone (FMT) [START_REF] Cherubini | Filter bank modulation techniques for very high speed digital subscriber lines[END_REF] have been heavily studied.

Generalized frequency division multiplexing (GFDM) [START_REF] Michailow | Generalized frequency division multiplexing for 5th generation cellular networks[END_REF] employs a circular convolution [START_REF] Abdoli | Weighted circularly convolved ltering in ofdm/oqam[END_REF] to directly apply the ltering operation on a time-frequency block [START_REF] Fettweis | Gfdm -generalized frequency division multiplexing[END_REF]. Another class of sub-band ltering-based waveforms (i.e. apply ltering at sub-band level over single or multiple resource blocs (RBs)) has been investigated, where the universal ltered multicarrier (UFMC) [START_REF] Cho | Asynchronous multi-user uplink transmissions for 5g with ufmc waveform[END_REF], ltered-OFDM (f-OFDM) [START_REF] Zhang | Filtered ofdm systems, algorithms, and performance analysis for 5g and beyond[END_REF] and fast Fourier transform FBMC (FFT-FBMC) [START_REF] Zakaria | Theoretical analysis of the power spectral density for t-fbmc signals[END_REF] and block-ltered OFDM (BF-OFDM) [START_REF] Gerzaguet | Block-ltered ofdm: A new promising waveform for multi-service scenarios[END_REF] are the most studied.

Time-domain windowing can also be a useful tool to achieve the desired enhancements, which permit to prevent steep changes between two OFDM symbols so as to conne OOB emission. In this regard, I have studied an advanced windowing based multicarrier approach called -weighted overlap and add based OFDM (WOLA-OFDM) [26], which has been introduced to the 5G-NR as a low-complexity candidate method (it has nearly computational complexity as the classical CP-OFDM). In addition, WOLA-OFDM allows transparent design where transmitter (Tx) and receiver (Rx) units use independent waveform processing techniques, which will comply with the 3GPP agreement [START_REF]3rd Generation Partnership Project (3GPP)[END_REF]. This work has been published in [C24].

Furthermore, some alternatives make the use of both ltering and windowing, such as windowed cyclic prex-based circular-OQAM (WCP-COQAM) [START_REF] Lin | Multi-carrier modulation analysis and wcp-coqam proposal[END_REF] where a circularly pulse shaping lter combined with a time-domain windowing is applied. In this regard, we have investigated a new MWF design that is based on the WOLA processing and the circular convolution approach [START_REF] Medjahdi | Wola processing: A useful tool for windowed waveforms in 5g with relaxed synchronicity[END_REF] with the Post-doc of Dr.

Nonlinear distortion characterization and machine learning based mitigation techniques for energy-ecient 5G MWFs

Despite the mentioned MWFs advantages, all of them still suer from the high PAPR of the modulated signal. This feature has a signicant impact on the power-eciency of the PA, which is an intrinsic nonlinear device. Indeed, the PAPR issue leads to the PA saturation and, consequently, output signal can be aected by in-band and out-of-band distortion eects [START_REF] Guerreiro | On the optimum multicarrier performance with memoryless nonlinearities[END_REF]. Therefore, the outstanded MWFs lose rapidly their good frequency localization property when a RF PA is employed. To deal with the high power peaks of MWF signals and avoid the nonlinear and saturation operating regions of the PA, a large back-o can be considered, which results in reduced power-eciency and a large amount of the consumed power is dissipated as heat, since the PA is operated far from its saturation point. Therefore, I have been interested in studying the performance of the future wireless communications exploiting MWFs in presence of RF PA impairment, especially when the power-eciency is high, by using both analysis and evaluation through practical scenarios. Equally importantly, I have been interested in developing new and reliable digital signal processing based solutions coping with the expected 5G requirements, with a particular focus on mitigating RF PA impairments while reducing the power-consumption, through a set of new algorithms and advanced techniques. Since 2009, my contributions to researches regarding this topic have been performed in several research projects, such as the FP7 EMPHATIC, the CMCU-PHC-Utique C3, the PHC-TASSILI ATOME5+ and the ANR WONG5 projects. Some of these contributions have been achieved with the PhD students I have co-supervised (see Figure 3.12). In the following, I will give short description for each investigate issue.

Theoretical characterization of nonlinear distortion eects in MWFs based systems

A theoretical characterization of nonlinear distortion eects, in OFDM and FBMC transmission systems, has been addressed during the PhD of Hanen Bouhadda and with my personal contribution, supported in part by the C3 project and in part by EMPHATIC project, receiving fund by, respectively, the PHC-Utique and the FP7 EC ICT. In this investigation, we have adopted Bussgang's theorem showing that the in-band distortion eects on the decision variables can be characterized by means of a complex gain and an additive Gaussian term with zero-mean and suitable variance. Then, we have introduced analytical expressions for the gain and the variance, where a new approach has been developed leading to performing these expressions for any simulated or measured PA model. Consequently, closed-form analytical expressions have been derived and illustrated to evaluate the bit-error-rate (BER) performance using OFDM with rectangular pulse shaping as well as well-localized lter-bank based multicarrier (FBMC) running under an additive white Gaussian noise (AWGN) or a frequency-at fading Rayleigh channels. These works have been, respectively, published in [J05] and [J07].

Then, in the framework of the WONG5 project, we focussed our attention on developing an universal approach to make this study feasible for any 5G MWF. In collaboration with Prof. Daniel Roviras, Dr. Hmaied Shaiek and Dr. Yahia Medjahdi, we have presented further discussions and comparisons on dierent waveforms: CP-OFDM, WOLA-OFDM, UFMC, f-OFDM and FBMC/OQAM and we have provided insights on the impact of in-band NLD caused by RF PA. This investigation has been presented in [J14] where simulation and theoretical results are shown to be in agreement for dierent MWFs and various IBO values.

Machine Learning for green communications: High PA Eciency and Linearity

In order to improve PA linearity and eciency, two complementary solutions have to be deployed in MWF based systems. These latter are grouped into two categories including PAPR reduction and PA linearization.

Concerning PA linearization, digital predistortion (DPD) has drawn most of the attention among all the studied methods. Although its simplicity, it has proven to be eective providing a good tradeo between eciency, linearity and implementation complexity and has been the main focus of my conducted works. My previous conducted studies on the eld of DPD were limited to SISO-OFDM systems. We pursued my investigations on DPD based energy-eciency solutions considering MIMO technology and post-OFDM MWFs. Furthermore, We have been interested in designing DPD using machine learning approaches. In particular, We have developed some low-complexity and highly-ecient neural network (NN) architectures to deal with DPD and its issues. A rst issue encountered in DPD is that its eciency can be aected by the RF crosstalk generated between transmission/reception paths when MIMO techniques are considered. To overcome this problem,

We introduced, in papers [C08] and [C10], crossover neural network predistorter (CO-NNPD) models to compensate simultaneously for RF crosstalk and PA nonlinearities while taking into account the memory eect in MIMO-OFDM systems.

Due to the similarity between OFDM and post-OFDM MWFs, it is natural to consider employing DPD to compensate amplitude and phase nonlinear distortions of MWF signals. However, some of the post-OFDM MWFs, like the FBMC-OQAM, have a dierent signal structure compared with OFDM. Therefore, directly applying the DPD schemes of OFDM systems to FBMC-OQAM systems may be not very eective. To deal with this issue, we considered the investigation of the PA nonlinearity eects mitigation in FBMC-OQAM systems. First, we showed that the classical DPD scheme performs worse with the FBMC-OQAM system when compared to the OFDM one. Such degradation can be explained by the fact that this DPD, which aims to compensate simultaneously the amplitude and phase nonlinearities, is not able to compensate perfectly the phase error. Indeed, AM/AM distortion can only be perfectly tackled when the PA is operated far from the saturation, otherwise the predistorted amplier exhibits a residual AM/AM distortion that aects the correction of the AM/PM distortion. In the regard to get ecient DPD, my eorts were deployed to build a new NN based DPD scheme around the concept of separating the compensation of the phase and amplitude distortions. By using the proposed scheme, it was shown that OFDM and FBMC-OQAM systems reach the same performance showing that a higher attention must be paid for phase correction in ltered MWFs like FBMC. This work has been published in [C19].

On the other hand, the MCM techniques suer from high PAPR which is one of the most crucial issues that need to be solved eectively with a reasonable complexity. Indeed, when a PA for other post-OFDM MWFs (published in [C38]), like WOLA-OFDM, UFMC and f-OFDM, that have been good promising candidates for the futures wireless systems. In addition, a global power amplier eciency evaluation with PAPR reduction has been presented in [C39] for post-OFDM MWFs.

Joint approach for PAPR reduction and PA linearization In conventional systems, PAPR reduction and linearization techniques have been optimized separately and applied independently.

I started focusing on their association aiming at avoiding mutual eects in order to enhance interoperability. I have introduced a joint approach for PAPR reduction and PA linearization that consists in a really synergistic combination of the two operations in order to improve power amplier eciency and linearity. Its key idea was to synthesize only one correction signal in a Ping-Pong manner between PAPR reduction and DPD. The proposed Ping-Pong joint optimization approach provides signicant improvement, compared to conventional association schemes, in fullling OOB requirements and preserving low in-band distortion while preserving excellent energy-eciency of the system. The proposed approach, which was a part of the ANR WONG5 project, has been rst patented [P01] and then published in [J11].

Experimental tesbed of post-OFDM Multi-carrier Waveforms toward 5G and beyond networks It has been encouraged to concentrate on more careful and thoughtful design, evaluations, realizations and comparison of CP-OFDM waveform and its most promising enhancements, i.e., WOLA-OFDM and BF-OFDM especially in experimental testbed. In the framework of the ANR WONG5 project, I was in charge of the development of an experimental testbed to study the capability of new multicarrier waveforms to accommodate 5G requirements. Testbed experiments were done with an implementation of CP-OFDM and its most promising enhancements, i.e., WOLA-OFDM and BF-OFDM, with congurable universal software radio peripherals (USRPs)based software dened radio prototype. These experiments were done in a realistic laboratory-like environment, where capabilities of the selected waveforms to accommodate 5G requirements are evaluated while focusing on the optimization of the energy eciency. On one hand, I have provided details and deign guidance to improve energy-eciency and robustness of the studied waveforms through new approaches of DPD and PAPR reduction in the presence of real RF PA. In particular, I focused on the mitigation of in-band and OOB non-linear distortions and their eects on power spectrum density (PSD) and bit-error-rate (BER), respectively. It has been demonstrated

that the combination of PAPR reduction and DPD allows the transmitter to signicantly improve the spectrum localization without sacricing the in-band and OOB waveform quality, while achieving high power-eciency, thus operating the PA very close to its saturation region, as well. On another hand, I addressed the impact of the lack of synchronism between transmitters on the performance of the selected waveforms, which is of special relevance for future 5G MTC applications.

Experimental results show that BF-OFDM and WOLA-OFDM would permit the accommodation of 5G requirements when RF PA issues are tackled. In some specic scenarios, ideal spectrum utilization can be realized by these waveforms, using only one tone as guard band while keeping good energy-eciency. This work was the subject of one conference paper [C41] and one peer-reviewed journal [J10].

Massive MIMO Networks: Energy and Hardware eciency

Massive MIMO, also known as large-scale multi-user (MU) MIMO, has been recognized as the most promising technology for future generations of wireless communications because it is the most ultimate enablers of enhanced energy-eciency (EE) and spectral-eciency (SE). Within the H2020 MSCA ADAM5 project, I have been interested in two investigation issues related to massive MIMO systems.

Linear Precoding for Energy-Ecient Massive MIMO The deployment of massive MIMO systems is attractive if the RF chains consist of inexpensive hardware components. Moreover, it is important to study the realistic massive MIMO systems with non-ideal hardware components, which may induce hardware impairment. Therefore, in the framework of the H2020 MSCA ADAM5 project, I am paying particular attention to this aspect of SE and EE in massive MIMO as well as hardware impairment mitigation to meet future WCS's requirements. Especially, the main focus was in the RF PAs which represent the dominating energy-consumption (50 -80%) in the RF chains. Indeed, signals generated by massive MU-MIMO precoders suer from the high PAPR, independently of whether single-carrier or multi-carrier transmission is adopted. Accordingly, the nonlinearity of the RF PA, which is the main hardware impairment and is expected to be lowcost and energy-ecient component to enable cost-and energy-ecient massive MU-MIMO BS deployments, yields harmful in-band distortion and OOB radiation. tioned algorithm compared to the ones proposed in literature, its computational complexity is still needed to be eectively reduced. Therefore, via the MSc internship of Miss Samar Chebbi, we are investigating approaches to complement traditional machine learning (ML) methods, like the meta-learning (learning to learn) approach, with the aim to obtain lower complexity. It consists in developing a meta-learning model capable of being generalized with a new channel conguration that has never been learned during learning, avoiding the adaptation of the model.

Inter-Numerology Interference Analysis and Cancellation for Massive MIMO-OFDM

The extremely diverse service requirements is an important challenge for the upcoming 5G wireless communication technologies. OFDM-based massive MIMO and mixed numerologies transmission are proposed as solutions. In the framework of the ADAM5 project, I have investigated with Xinying Cheng, a PhD student I co-supervise with Prof. Daniel Roviras, the use of spatial multiplexing of users, sharing the same bandwidth, whose associated numerologies are dierent. We rst introduced a precoding design that aims to manage the mixed numerologies spectrum sharing (SS) transmission.

Then, we analysed the inter-numerology interference (INI) and derive the theoretical expressions of its radiation pattern in massive MIMO-OFDM downlink systems. We demonstrate that by using the proposed precoding scheme and considering two groups of users using two dierent numerologies, INI appears only in frequency selective channels. Besides, the transmission of users using numerology with large subcarrier spacing (SCS) is always with the best quality, only users using the numerology with small SCS suer from INI. In that case, INI increases due to the dierence in SCS, channel Matrix Completion Based Indoor Localization Here, we consider the case where few number of sensors (anchor nodes) whose coordinates are known by installing them at known positions, and the rest unkown nodes, have to determine their own coordinates using measured inter-sensor distances and anchor nodes coordinates. Since, in IoT, sensors are not capable of high-power transmission which would be unable to make measurements with all nodes, the trilateration would not be able to oer good performance. Then, as a rst contribution, we have proposed an approach based Indicator (RSSI) ngerprints. This work has been published in a peer-reviewed journal [J12] where we have shown that, when considering the trade-o between localization accuracy and computational complexity, our proposed method outperforms other popular approaches.

Part II

Scientic contributions

Chapter 4

Multicarrier Waveform Design for 5G and Beyond

Introduction

The future/fth generation (5G and beyond) mobile communications are expected to enhance, signicantly, major key performance indicators (KPIs), such as spectral eciency, power consumption, latency, connection density, low cost terminals and mobility. Moreover, the future standard should support various new service regimes with dierent and often diverging requirements, presenting serious challenges on 5G

commercial deployments [START_REF] Gerzaguet | Block-ltered ofdm: A new promising waveform for multi-service scenarios[END_REF]. The IMT-2020 1 vision denes the usage scenarios into three broad groups of use cases as enhanced mobile broadband (eMBB) where applications require ultra large bandwidth and spectral eciency, massive machine type communications (mMTC) (also known as Internet of Things (IoT)) where a tight requirement for device battery life and complexity, and ultra-reliable and low latency communications (URLLC). These versatile services require critical capability objectives such as 20Gbits/s peak data rate, 10 6 devices/km 2 connection density, ultra high energy eciency, low cost terminals, 1ms latency and mobility up to 500km/h [START_REF] Lien | 5g new radio: Waveform, frame structure, multiple access, and initial access[END_REF]. Nevertheless, these challenges are dicult to be addressed by the traditional cyclically prexed orthogonal frequency division multiplexing (CP-OFDM) and its low peak-to-average power ratio (PAPR) variant discrete Fourier transform spread OFDM (DFT-s-OFDM), which have consequently shaped the success of the today's 4G LTE 2 .

Thus, the CEDRIC/LAETITIA team of the CNAM University, where I am associate researcher, has been interested in studying advanced multi-carrier waveforms (MWFs) to overcome the major limitations of the CP-OFDM in challenging new spectrum use scenarios, like asynchronous multiple access, mixed numerology, which allows the service to choose between a set of supported subcarrier spacing (SCS) and symbol duration, while improving their power consumption, signicantly. Indeed, within the research projects PHYDYAS [START_REF]Phydyas-physical layer for dynamic spectrum access and cognitive radio[END_REF] and EMPHATIC, spurred on by the work of Prof. Maurice Bellanger, the CEDRIC/LAETITIA team developed recognized expertise in new MWF design, initially on lter-bank based multi-carrier modulations (FBMC) [START_REF] Bellanger | Specication and design of a prototype lter for lter bank based multicarrier transmission[END_REF], then other waveforms like the fast Fourier Transform FBMC (FFT-FBMC) [START_REF] Zakaria | Theoretical analysis of the power spectral density for t-fbmc signals[END_REF], studied within the framework of the ANR WONG5 project. summarizes author's contribution related to equalization for FBMC-OQAM. Finally, the outputs of these contributions are resumed in Section 6.5.

Fundamentals of the 5G MWF design 4.2.1 Preliminary concepts

In a typical communication system, the transmitter maps every modulated information point from the message space into the signal space whereas the receiver does the reverse operation [START_REF] Sahin | A survey on multicarrier communications: Prototype lters, lattice structures, and implementation aspects[END_REF]. The signal space is the time-frequency plane where time and frequency constitute its coordinates [START_REF] Gabor | Theory of communication. part 1: The analysis of information[END_REF]. The waveform denes the physical shape of the signal that carries the modulated information. When considering a multicarrier scheme, the structure in signal space relies on N simultaneously-transmitted subcarriers, regularly spaced by ν 0 in frequency. The transmitted signal is given by

x(t) = +∞ m=-∞ N -1 n=0 X mn f mn (t), (4.1)
and the received symbol Xm0n0 , located in time index m 0 and subcarrier index n 0 can be found by the projection of the received signal y(t) onto the corresponding receive function g m0n0 (t) as

Xm0n0 =< y(t), g m0n0 (t) >= t y(t)g * m0n0 (t)dt, (4.2)
where -X mn denotes the m-th transmitted symbol of the n-th subcarrier, which represents the random part of the waveform. One may choose X mn from a set of a modulation symbols or a part of it, e.g., its real or imaginary part [START_REF] Du | Classic ofdm systems and pulse shaping ofdm/oqam systems[END_REF].

f mn (t) and g m0n0 (t) denotes, respectively, the synthesis function, which maps X mn into the signal space, and the analysis function. They are obtained by a prototype lter, respectively p tx and p rx , translated in both time and frequency, constructing two Gabor systems [START_REF] Du | Classic ofdm systems and pulse shaping ofdm/oqam systems[END_REF] [36] [37] [START_REF] Jinfeng | Pulse shape adaptation and channel estimation in generalised frequency division multiplexing[END_REF] when they are given by equations (4.3) and (4.4), respectively.

f mn (t) = p tx (t -mτ 0 )e j2πnν0t , (4.3)
and

g m0n0 (t) = p rx (t -m 0 τ 0 )e j2πn0ν0t , (4.4)
where τ 0 denotes the symbol spacing in time.

Note that pulse shaping lters (known as prototype lters) have an important eect on the signal characteristics since they dene how the energy is spread over the time and frequency domains. Thus, the amount of energy transferred from the transmitter to the receiver is determined by both transmit and receive lters [START_REF] Sahin | A survey on multicarrier communications: Prototype lters, lattice structures, and implementation aspects[END_REF]. The coordinates of the lters form a two-dimensional structure in the time-frequency plane are known as lattice [39] [40]. In addition, they identify the structure of the multicarrier scheme, i.e., orthogonal, bi-orthogonal, or non-orthogonal [START_REF] Kozek | Nonorthogonal pulseshapes for multicarrier communications in doubly dispersive channels[END_REF] [39] by nding out the correlation between the points in the lattice. Dierent shapes can be associated to the lattice geometry, either regular or hexagonal [START_REF] Han | Hexagonal multicarrier modulation: A robust transmission scheme for time-frequency dispersive channels[END_REF].

Moreover, additional dimensions, like space domain, can be included in the lattice.

The Baseline for 5G MWF Discussion: CP-OFDM and MWF design requirements

CP-OFDM is the dominant multicarrier modulation scheme that is currently being deployed in many standards such as the downlink of 4G LTE and the IEEE 802.11 family [START_REF] Hwang | Ofdm and its wireless applications: A survey[END_REF]. In OFDM systems, the spectrum is used in a very ecient manner due to the orthogonally overlapped subcarriers, allowing exible frequency assigning.

The new radio for 5G and beyond is expected to support a variety of new services beyond the user centric communications to more machine type communications, as discussed in Section 7.1. Looking at the 5G requirements and asking the question if OFDM still suitable? Let us talk about strengths and weaknesses of OFDM. First of all, the best strength is its simplicity. It is FFT based which is very ecient and its single tap equalization for frequency selective channel that is really awesome. Second, it is fast, it supports wide bandwidth and MIMO. OFDM naturally supports MIMO in a way it is almost designed with MIMO. It is also very resilient, handling the interference in a multipath environment by ensuring circularity of the channel (thanks to the CP) and by enabling easy frequency-domain equalization (FDE). However, a major weaknesses of OFDM is related to the fact that it is power-hungry. It has high PAPR and it needs a linear or linearized power amplier; with new methods like digital predistortion (DPD) [7] and envelope tracking (ET) [START_REF] Yan | Multi-carrier envelope tracking power amplier[END_REF], we can make it much better but this could be the strongest drawback for multicarrier schemes. Another critical issue is related to the fact that it is noisy, which is very important for a lot of 5G use cases. It has very large side lobes (i.e., high out-of-band (OOB) emissions), called low spectrum agility. Actually, with the FFT we got basically about at most 30 dB attenuation in the side lobes and we really need at least 60 or 70 dB or more, if we want to intersperse trac within 5G mMTC. We need those side lobes to be really low to avoid adjacent channel interference (ACI). Typically, OOB emissions are reduced by various windowing/ltering approaches along with the guard band allocation [START_REF] Medjahdi | On the road to 5g: Comparative study of physical layer in mtc context[END_REF] to meet the spectral mask requirements of the various standards. 3GPP LTE standard uses 10% of total bandwidth as guard bands to handle this problem, decreasing unfortunately the spectral eciency. Finally, it is also very sensitive to carrier frequency oset (CFO). Furthermore, a big downfall of OFDM is the uplink interference [26]. In fact, with the OFDMA, we need all the signals coming up to the base station are lined-up. Although the use of the CP, it cannot be too big for spectral eciency purpose. It cannot be able to support asynchronous communications in a connected network with millions, if not billions, of devices in 5G mMTC. Moreover, it seriously suers from its limited exibility and the unfriendly coexistence with dierent numerologies for various channel conditions and use cases.

In the diagram depicted in Figure 4.1, we can rearrange these strengths and weaknesses and want to group them as can be better shared between all 5G use cases. For eMBB, we see the ability to retain and really improve upon the needs to support MIMO and to be a wide bandwidth even wider bandwidth like 100MHz. Furthermore, it needs to solve the sensitivity to CFO, UL access and its power-hungriness. For mMTC, there is a lot of issues: we need to make sure that it is still simple and even make it simpler. It also needs to solve the large side lobes, asynchronous UL access and the power-hungry problems. Finally, for URLLC, we denitely need to solve sensitivity and the large side lobes.

Major MWF candidates for 5G and beyond

Filtering approach is used to enhance the capability of multi-carrier techniques to support asynchronous access to fragmented spectrum. The ltering-based MWF can either be subcarrier-wise or subband-wise.

In the following, I give a brief description of the major studied ltered MWFs.

Subcarrier-Wise Filtering

FBMC-OQAM FBMC has been proposed as an alternative to CP-OFDM oering better frequency localization and exible access to the available resources. Indeed, contrary to OFDM's rectangular lter, FBMC uses well-frequency localized lters (like PHYDYAS [START_REF]Phydyas-physical layer for dynamic spectrum access and cognitive radio[END_REF] or IOTA [START_REF] Medjahdi | On the impact of the prototype lter on fbmc sensitivity to time asynchronism[END_REF]) to oer excellent spectral containment (i.e., better adjacent channel leakage performance). The duration of the prototype lters is usually a multiple of the FFT size (L = KN ), where K is called the overlapping factor. Here, we exploit polyphase lter-banks [START_REF] Demmer | Filter-bank ofdm transceivers for 5g and beyond[END_REF] for pulse shaping, reducing side lobes eectively and having better spectrum agility.

Furthermore, Nyquist constraints on the prototype lter combined with oset-quadrature amplitude modulation (OQAM) have to be used in order to ensure orthogonality between adjacent symbols and adjacent subcarriers while keeping maximum spectral eciency. OQAM is used wherein it is actually not orthogonal in complex domain but it is orthogonal in real domain so it provides staggering of "in-phase" and "quadrature-phase" components in both time and frequency domains, and imaginary intrinsic interference is occurred which is orthogonal to the real transmitted symbols. Moreover, no more than one subcarrier is required as guard band to support eectively asynchronous (i.e., non-orthogonal) transmissions [START_REF] Medjahdi | On the road to 5g: Comparative study of physical layer in mtc context[END_REF]. Nevertheless, the equalization is more dicult without the use of CP. Furthermore, the biggest challenges is that the MIMO integration and pilot design with FBMC-OQAM are not straightforward as in CP-OFDM due to the non-orthogonality in the complex domain [START_REF] Lin | Flexible congured ofdm for 5g air interface[END_REF].

In this dissertation, we consider FBMC-OQAM with PHYDYAS prototype lter with K = 4, the most commonly used. Note that new form of FBMC, which is called Lapped-OFDM, uses the sine prototype lter with K = 2. Interested readers are referred to [START_REF] Bellanger | Lapped-ofdm as an alternative to cp-ofdm for 5g asynchronous access and cognitive radio[END_REF] for more details.

GFDM

Similar to FBMC, generalized frequency division multiplexing (GFDM) [START_REF] Fettweis | Gfdm -generalized frequency division multiplexing[END_REF] [19] applies subcarrier-wise ltering. However, GFDM performs a time-frequency ltering over data blocks. A data block contains a set of symbols transmitted over a group of N A consecutive sub-carriers over N B time-slots and thus is composed of N T = N A × N B symbols. From this implementation perspective, it is equivalent to a DFT-s-OFDM 3 signal [START_REF] Sahin | Flexible dft-s-ofdm: Solutions and challenges[END_REF], which also explains lower PAPR compared to CP-OFDM. Since the lters for pulse shaping are circularly convoluted over a data block, GFDM is a nonorthogonal transmission scheme because of symbols overlap in both time and frequency, generating inter and intra data blocks interference.

Note that a CP is appended in each block in order to avoid inter block interference. Furthermore, GFDM requires successive interference cancellation (SIC) algorithms at the receiver, making its complexity quite high. Similar to FBMC-OQAM, MIMO integration and pilot design is not straightforward. Moreover, the block-wise transmission causes latency making it not suitable for short burst transmission.

It is worth to mention that a new transceiver design is needed for subcarrier-wise ltering based MWFs (FBMC and GFDM), and there is no backward compatibility with 4G LTE.

Subband-Wise Filtered MWF UFMC

Alcatel-Lucent Bell Laboratories [START_REF] Vakilian | Universal-ltered multi-carrier technique for wireless systems beyond lte[END_REF] is the major proponent of the universal ltered multicarrier (UFMC) [START_REF] Wild | 5g air interface design based on universal ltered (uf-)ofdm[END_REF], which is also referred to UF-OFDM in the literature. UFMC can be seen as a compromise between ltred-OFDM (detailed in next subsection) and FBMC, where a ltering operation is applied to a group of successive subcarriers instead of the subcarrier-wise ltering of FBMC. The key-idea of UFMC is that each resource block (RB) has its corresponding transmit lter with a passband larger than the FBMC prototype lter one, leading thus to a shorter impulse response. In typical UFMC systems, each symbol at the output of the IFFT is ltered and zero padding (ZP) [START_REF] Muquet | Cyclic prexing or zero padding for wireless multicarrier transmissions?[END_REF] is then used to absorb the lter transient response. Here, no CP is used and the transitions regions (i.e., ramp-ups and ramp-downs) provide a soft ISI protection. Then, the symbols are not circularly convoluted with the channel leading to a more complicated receiver [START_REF] Schaich | Waveform contenders for 5g -suitability for short packet and low latency transmissions[END_REF]. This latter uses a FFT of twice the size of IFFT used at the transmitter.

It is worth to point out that the circular convolution can be obtained by collecting additional samples corresponding to the length of the ZP and using an overlap-and-add process [START_REF] Muquet | Cyclic prexing or zero padding for wireless multicarrier transmissions?[END_REF]. Then, the FFT size becomes identical to the IFFT used at the transmission side.

UFMC has shorter lter lengths compared to subcarrier-wise ltering making it more suitable for short packet and low-latency transmissions. Furthermore, UFMC is suitable for all existing OFDMrelated techniques like MIMO, channel estimation/equalization, pilot design, synchronization, PAPR reduction [START_REF] Medjahdi | On the road to 5g: Comparative study of physical layer in mtc context[END_REF].

f-OFDM

In ltered-OFDM (f-OFDM) [START_REF] Zhang | Filtered-ofdm -enabler for exible waveform in the 5th generation cellular networks[END_REF], the ltering granularity is more exible than UFMC. Further details on several lters are given in [START_REF] Farhang-Boroujeny | Ofdm versus lter bank multicarrier[END_REF]. The partition in the time-frequency grid is adjusted based on the dierent channel conditions and use cases.

FFT-FBMC

FFT-FBMC scheme has been proposed within the WONG5 project [START_REF] Zakaria | Theoretical analysis of the power spectral density for t-fbmc signals[END_REF], which aims at overcoming the FBMC intrinsic interference [57] [58]. FFT-FBMC utilizes a data precoding process in a subcarrier-wise manner using an IFFT [START_REF] Zakaria | Theoretical analysis of the power spectral density for t-fbmc signals[END_REF]. Then, with the aid of the subcarrier-wise IFFT/FFT precoding/decoding and the CP insertion, the interference coming from the same subcarrier can be removed using a simple equalization. Furthermore, a new transmission strategy is adopted, together with a well-frequency localized prototype lter, in order to avoid the interference coming from adjacent subcarriers [START_REF] Zakaria | Theoretical analysis of the power spectral density for t-fbmc signals[END_REF].

In FFT-FBMC proposal, a data stream of M N/2 is divided into M blocks of N/2 data complex samples. Then, each block of N/2, corresponding to each subcarrier k ∈ {0, 1, ..., M -1}, is fed to a N -IFFT operation. The N/2 data samples are alternately fed to the rst and last N/2 bins of the N -IFFT. When the subcarrier index k is odd (resp. even), the symbols are fed to the rst (resp. last) N/2 bins. After that, a CP is appended to the N -IFFT output that feds to a FBMC modulator of M carriers in the given subcarrier k.

Most importantly, the complex orthogonality is guaranteed in FFT-FBMC and single-tap equalization can be performed, as shown in [START_REF] Zakaria | Analysis of the t-fbmc equalization in selective channels[END_REF]. Indeed, M N/2 channel frequency response coecients, weighted by coecients depending on the used prototype lter, represent the equivalent equalizer coecients.

BF-OFDM

Block-Filtered OFDM (BF-OFDM) is a precoded lter-bank multi-carrier modulation that has been studied in [START_REF] Demmer | Block-ltered ofdm: A novel waveform for future wireless technologies[END_REF] [61] [START_REF] Gerzaguet | Comparison of promising candidate waveforms for 5g: Wola-ofdm versus bf-ofdm[END_REF]. As in FFT-FBMC, the precoding stage is performed by means of IFFT and the ltering operation is applied with a polyphase network (PPN). Nevertheless, this precoding strategy results in a complex receiver scheme. In order to tackle this issue, BF-OFDM slightly increases the transmitter complexity in order to rely on a low-complex CP-OFDM like receiver through the insertion of a lter pre-distortion stage at the transmitter side [START_REF] Gerzaguet | Block-ltered ofdm: A new promising waveform for multi-service scenarios[END_REF]. Here, each data block of N/2 samples is pre-equalized before going to the IFFT precoding operation. The pre-equalizer coecients depend on the frequency response of the used prototype lter. Note that the BF-OFDM receiver is just a simple OFDM one (i.e., only a FFT is used).

Contributions to related MWF design

Despite the eectiveness of the previously mentioned MWF class to handle most of the 5G challenges, they are not suitable for low-latency communications and short packet transmission due to the long prototype lters (i.e., long ramp-up/down of MWF signal leads to a loss in spectral eciency). In addition, the complexity of these ltered MWFs makes them not very attractive to 5G and beyond. Besides, timedomain windowing based CP-OFDM processing, can also be a useful tool to advance the 5G waveform development.

Therefore, we have been interested in investigating new MWFs based on advanced windowing techniques. In the framework of the WONG5 project, we rst investigated a MWF based on new windowing approach, introduced recently and called Weighted Overlap and Add (WOLA) processing [START_REF]Waveform candidates[END_REF]. The studied low-complexity waveform WOLA-OFDM, which is presented in [C24], allows transparent design where transmitter (Tx) and receiver (Rx) units use independent waveform processing techniques, complying with the 3GPP agreement [START_REF]3rd Generation Partnership Project (3GPP)[END_REF]. Then, a new MWF approach based on the WOLA processing and a circular convolution approach has been introduced via the supervision of the Post-doc of Dr. Through the collaboration with the WONG5's partners, THALES, CEA-Leti and CentraleSupelec, we have carried out, in [J09], an exhaustive analysis and objective comparison of these studied MWFs with several other 5G MWFs in order to identify the most suitable waveform conguration to any 5G use case according to its critical requirements. Our WOLA approach has been shown to be very eective in MWF design enabling exible multiple access to fragmented spectrum with relaxed synchronicity.

In the following, I give an overview of the studied MWFs based on WOLA processing and a summary of its performance assessment and comparison.

WOLA-OFDM

Since a large part of OOB emission of CP-OFDM is caused by the discontinuity between adjacent OFDM symbols in time-domain, a natural and straightforward way to reduce these indiserable OOB emissions is to avoid the traditional usage of rectangular pulse shape. Then, windowing schemes to smooth the time-domain signal transitions seem promising approaches. Therefore, the WOLA-OFDM has gained a great interest along this line of study due to its low computational complexity. At the transmitter side, the time-domain WOLA-OFDM symbol is cyclically extended with cyclic prex and cyclic sux.

Then, the smooth transition of the last samples of a given symbol and the rst samples of the next symbol is provided by a time-domain windowing. Here, the Meyer root raised-cosine (RRC) [START_REF] Gaspar | Frequency-shift oset-qam for gfdm[END_REF] has been considered, which combines the RRC time-domain pulse with the Meyer auxiliary function. In order to have similar overhead as in CP-OFDM, to comply within standards, adjacent symbols are overlapped in the edge transition regions (see Figure 2 in [26]). Furthermore, WOLA-OFDM presents a spectral eciency (SE) loss of W T X samples, cyclic sux length, per packet compared to CP-OFDM.

The WOLA-OFDM SE expressed in bit per second per Hertz is given by equation (4.5).

η WOLA = SN S(N + N CP ) + W T X η S→∞ ----→ S N + N CP , (4.5)
where S is the total number of transmitted symbols, η is the modulation eciency (including both modulation order and coding rate) and N the number of active subcarriers. When S is large, the WOLA-OFDM SE tends to the one of CP-OFDM.

In addition to the transmit windowing, the WOLA processing, initially introduced by Qualcomm Incorporated [START_REF]Waveform candidates[END_REF], is applied to aid the suppression of asynchronous inter-user interference (i.e. adjacent non-orthogonal signals). It is performed through two steps: First, the receiver takes N + 2W RX samples (W RX denotes the window edge size), which correspond to the samples of one WOLA-OFDM symbol.

Then, these samples are windowed. In the second step, the overlap and add processing (see Figure 3 in [26]) is applied to minimizes the windowing eects on the useful data, creating the useful N samples from the N + 2W Rx ones.

It is worth emphasizing that the applied receive window is independent of the one applied at the transmitter, complying with the 3GPP agreement [START_REF] Gerzaguet | Block-ltered ofdm: A new promising waveform for multi-service scenarios[END_REF].

WOLA-COQAM

We have been interested in investigating the combination of the WOLA processing with a ltering approach. Such combination can be very promising to handle most of the 5G challenges previously mentioned. Here, we consider a subcarrier-wise ltering, due to its good frequency localization, together with a burst truncation in order to reduce the SE loss caused by long prototype lter, making the transmission suitable to low-latency communications. In addition, a circular convolution [START_REF] Abdoli | Weighted circularly convolved ltering in ofdm/oqam[END_REF] [65] is adopted to maintain smooth transition at the burst edges while removing the overhead signal. Then, the circular-OQAM

(COQAM) signal, dened in a block interval m ∈ [0, KN -1], is expressed as, x COQAM [m] = N -1 n=0 2K-1 k=0 a k [n] g (m -kN/2) e j 2π N n(m-D 2 ) e jφ n,k , (4.6)
where, the lter g stands for circular convolution (see Figure 1 in [START_REF] Medjahdi | Wola processing: A useful tool for windowed waveforms in 5g with relaxed synchronicity[END_REF]) with the prototype lter g of length KN = D + 1. More precisely, g is obtained by the periodic repetition of duration KN of g [START_REF] Siohan | Multi-carrier modulation analysis and wcp-coqam proposal[END_REF], so that,

g (m) = g (mod [m, KN ]) (4.7)
Note that the prototype lter g is originally designed for FBMC-OQAM systems. This means that the input data symbols a k [n] are real-valued, since the orthogonality only applies to the real eld. The phase term φ n,k at subcarrier n and symbol index k can be expressed as π 2 (n + k). It is introduced on both transmitter and receiver side, in order to make the intrinsic interference purely imaginary-valued thus orthogonal to the useful data which is real-valued. A CP is then added in order to avoid multi-path channel interference. Thanks to circular convolution, the continuity of CP-COQAM signal is maintained inside a given CP-COQAM block. Then, a windowing is needed to enhance the spectral containment by smoothing the inter-block discontinuities. Finally, the WOLA processing, previously explained, is also applied to suppress inter-user interference resulting from the mismatched FFT capture window. It is worth to mention that the rst window part [0, 2W RX ] applied at the receiver must be symmetrical w.r.t the point W RX , 1 2 , correctly recover the weighted data samples.

Summary of MWFs performance assessment and comparison

In this section, I provide a summary of the comparative performance study of the major MWF candidates for 5G and beyond. In addition to the MWFs described above (FBMC-OQAM, GFDM, UFMC, f-OFDM, FFT-FBMC, BF-OFDM, WOLA-OFDM and WOLA-COQAM), other promising MWFs, studied in literature, have been considered in this comparative study in order to give a complete and clear picture of the ongoing MWF discussions and put in perspectives the main advantages and drawbacks of these solutions. These MWFs are : ltered multi-tone (FMT) [START_REF] Cherubini | Filter bank modulation techniques for very high speed digital subscriber lines[END_REF] and windowed cyclic prex based circular-OQAM (WCP-COQAM) [START_REF] Siohan | Multi-carrier modulation analysis and wcp-coqam proposal[END_REF]. Note that CP-OFDM is kept as a MWF reference basis. I classify and compare all of these MWFs regarding a given system model and several KPIs, such as OOB emissions, robustness to time and frequency synchronization errors, transceiver complexity and end-to-end PHY latency.

The tradeo between frequency localization and time localization should be well optimized in order to address dierent challenges future mobile access networks will have to face. Indeed, frequency localization is important to allow relaxed synchronization transmissions across adjacent subbands with better adjacent channel leakage performance. On the other hand, the time localization is critical for low latency applications where longer lter/window durations are not suitable for URLLC.

All ltered and windowed MWFs granted lower OOB emissions compared to CP-OFDM (see Figure On another hand, GI-less MWFs provide bad BER performance in multipath fading channel and complex receivers are required since the traditional FDE is not straightforward. Moreover, the MIMO deployment, which is a key technology for high throughput, is not feasible in MWFs like FBCM-OQAM and GFDM because of the non-orthogonality in complex domain.

In order to evaluate the capability of the studied MWFs to support asynchronous transmissions, we consider a scenario with two co-existing users sharing the available frequency as shown in Finally, when coming to the complexity 5 , WOLA-OFDM provides the lowest level, it is almost the same as CP-OFDM. However, the computational complexity required by UFMC is excessively high about 200 times the CP-OFDM/WOLA-OFDM complexity. The other MWFs have tolerable computational complexity, compared to the CP-OFDM/WOLA-OFDM, it is approximately 2 times for BF-OFDM and FFT-FBMC, 3 times for FBMC-OQAM and 9 times for GFDM. A summary of the main advantages/disadvantages of these major MWF candidates is provided in

Contributions to related equalization for FBMC-OQAM

As explained above, FBMC-OQAM is shown to oer the best spectral localization among all the post-OFDM MWFs, thanks to the adopted lter-bank approach, providing then the best performance in supporting asynchronous and mixed numerologies transmissions. Besides, it oers high spectrum efciency since it avoids the use of CP and large guard bands. Furthermore, the orthogonality in real domain is guaranteed thanks to the use of the OQAM modulation. Consequently, it is sensitive to ISI and then it does not full the robustness requirements when a frequency selective channel is considered.

To overcome this problem, via the Hayfa Fhima's PhD, I co-supervised with Prof. Daniel Roviras, we had been interested in studying advanced equalization schemes to handle this FBMC-OQAM's issue.

One can remark that FBMC-OQAM is based on a non second order circular (NSOC) modulation [START_REF] Picinbono | Widely linear estimation with complex data[END_REF] and its signal is a cyclo-stationary one [START_REF] Dayana | Co-operative cyclo-stationary feature detection with universal ltered multi-carrier spectrum sensing for cognitive radio network[END_REF][START_REF] Lazov | Cyclo-stationary process analysis within telecom applications[END_REF]. Then, an application of widely linear (WL) [START_REF] Gerstacker | Receivers with widely linear processing for frequencyselective channels[END_REF] and FREquency SHift (FRESH) [7072] processing makes a lot of sense. Indeed, these latter have been shown to enhance the performance of the traditional linear equalizers. In this regard, we have studied three dierent MMSE equalizer schemes, referred to as linear (LE), widely linear (WLE) and widely linear FRESH (WL FRESH) equalizers. For the developed equalizers, both symbol spaced (SSE) and fractionally spaced (FSE) processing have been evaluated, in synchronous DL/UL and asynchronous UL scenarios, with mixed numerologies transmissions.

In the following, I give a brief description of the studied equalizers as well as their expressions followed by their performance comparison. In order to assess their performance, we consider a system with two users using the same kind of modulation, either rectilinear (R) or quasi-rectilinear (QR) while using dierent numerologies. Let us recall that R modulations correspond to mono-dimensional modulations such as M-pulse amplitude modulation (M-PAM), whereas QR modulations are complex modulations corresponding, after a simple de-rotation operation, to a complex ltering of a R modulation [START_REF] Dayana | Co-operative cyclo-stationary feature detection with universal ltered multi-carrier spectrum sensing for cognitive radio network[END_REF].

Basics of LE, WLE and WL FRESH equalizers

Since the LE [START_REF] Fhima | Analysis of widely linear equalization over frequency selective channels with multiple interferences[END_REF], [START_REF] Chevalier | New insights into optimal widely linear array receivers for the demodulation of bpsk, msk, and gmsk signals corrupted by noncircular interferences-application to saic[END_REF], [START_REF] Ikhlef | An enhanced mmse per subchannel equalizer for highly frequency selective channels for fbmc/oqam systems[END_REF], uses only the information carried by the autocorrelation matrix of the received signal y p (l), it results in a vector w LE ∈ C 1×Le (L e is the equalizer length) which is given by

w LE = r xeyp R -1 yp , (4.8)
where r xeyp = E[x e (n)y H p (l)], which has a dimension of 1 × L e , is the inter-correlation vector between the transmit sample x e (n) and the equalizer input; and R yp = E[y p (l)y H p (l)] ∈ C Le×Le denotes the auto-correlation matrix.

In WLE [START_REF] Fhima | Performance of linear and widely linear equalizers for fbmc/oqam modulation[END_REF], [START_REF] Chevalier | New insights into optimal widely linear array receivers for the demodulation of bpsk, msk, and gmsk signals corrupted by noncircular interferences-application to saic[END_REF], [START_REF] Fhima | Widely linear equalizer performance with multiple independent interferences[END_REF], we exploit the information carried by both the auto-correlation and pseudoautocorrelation matrices. Indeed, in the case of an improper modulation, it has been shown that the pseudo-autocorrelation matrix contains energy. Therefore, taking into consideration the pseudoautocorrelation matrix in the design of the equalizer would result in better performance [START_REF] Picinbono | Widely linear estimation with complex data[END_REF] than the classical LE. Then, the WLE vector, wW L ∈ C 1×2Le , can be given by

wW L = r xeỹp R -1 ỹp , (4.9)
where the inter-correlation vector r xeỹp ∈ C 1×2Le uses the equalizer input in its widely linear version (i,e, ỹp (l) = [y T p (l), y * p (l)] T ). Besides, R ỹp ∈ C 2Le×2Le is the new auto-correlation matrix considering the WL signal ỹp (l). This matrix can be represented by

R ỹp = E[ỹ p (l)ỹ H p (l)] = R yp C yp C * yp R * yp , (4.10)
where C yp = E[y p (l)y T p (l)] represents the pseudo-autocorrelation matrix (∈ C Le×Le ) of the signal y p .

When coming to WL FRESH equalizer, it exploits the cyclo-stationarity properties of rectilinear and quasi-rectilinear signals (i.e., the correlation between the spectral components of the signal) [START_REF] Dayana | Co-operative cyclo-stationary feature detection with universal ltered multi-carrier spectrum sensing for cognitive radio network[END_REF][START_REF] Lazov | Cyclo-stationary process analysis within telecom applications[END_REF][START_REF] Chevalier | Reception lter impact on widely linear fresh receiver performance for saic/maic with frequency osets[END_REF][START_REF] Chauvat | Widely linear fresh receiver for saic/maic with frequency osets[END_REF]. It means that the auto-correlation and the pseudo-autocorrelation matrices of the received signal, called R I (t, τ ) and C I (t, τ ), are periodic in time [START_REF] Chauvat | Widely linear fresh receiver for saic/maic with frequency osets[END_REF]. Hence, they can be represented as Fourier series expansions, given as follows [START_REF] Fhima | Study and implementation of widely linear (wl) receiver for lter bank based multicarrier (fbmc-oqam) modulations over frequency selective channels[END_REF] R (4.12)

I (t, τ ) = αi R αi I (τ )e j2παit
Here, R αi I (τ ) and C βi I (τ ) are dened, respectively, as the non-conjugate and conjugate cyclic correlation functions. Likewise, α i and β i are called the Second Order (SO) non conjugate and conjugate cyclic frequencies of the signal, which are given by

     α i = i T 1 for i ∈ Z β i = ±2δ f + i T 1 for i ∈ Z,
where δ f stands for the guard band between the user of non interest (UNOI) and the user of interest (UOI) and T 1 is the symbol duration corresponding to UNOI.

For the sake of simplicity and without loss of generality, we consider only one set of couple of cyclic frequencies (±α 1 , ±β 1 ), where the greater amount of energy is located. Therefore, the corresponding WL FRESH equalizer is depicted by Figure 4.8 where observation vector is zp

(l) = [z T 1 (l), z T 2 (l), z T 3 (l), z T 4 (l), z T 5 (l), z T 6 (l)] T , where z i (l) = [z i (lT 0 ), z i (lT 0 -T e ), ..., z i (lT 0 -(L e -1)T e )]
T , for i = 1, .., 6. z i (l), i ∈ {1, 3} are the frequency shifted versions of the received signal y p (l); this shift is done via the use of the cyclic frequencies +α 1 , 0 and -α 1 , respectively. Likewise, z i (l), i ∈ {4, 6} represents the frequency shifted version of the received signal complex conjugate y * p (l) and that is done by the use of the following conjugate cyclic frequencies +β 1 , 0 and -β 1 . Therefore, the studied WL FRESH equalizer is given by

wWLFresh = r xezp R -1 zp , (4.13)
where r xezp ∈ C 1×6Le is the inter-correlation vector corresponding to the Fresh version of the equalizer input (i.e., zp (l)). Besides, R zp = E[z p (l)z H p (l)] is a matrix ∈ C 6Le×6Le , and it is dened as the auto- correlation matrix of the signal zp (l).

Application to rectilinear signal case

In order to clearly show the performance of the studied equalization schemes, we started rst by using M-PAM modulation, representing a class of rectilinear modulations. Here, we consider two users, UOI and an interferer user (UNOI) sharing the same frequency band with a guard band of δ f . The UNOI's symbol duration is twice the UOI one (i.e., T 1 = 2T 0 ). Also, the pulse shaping lters of the two users (UOI and UNOI) are chosen to be rectangular ones.

β 1 = 2δ f + 1 T1 .
As expected [69] [73], we note, from results depicted in

β i = ±2δ f + i T 1
and since the WLE exploits the energy contained at the null conjugate frequency; i.e.,

β i = 2δ f + i T 1 = 0 ⇔ δ f = i 2 T 1
. As T 1 = 2T 0 , then it performs better when δ f = i 4 T 0 .

We move now to the WL Fresh equalizer where another interesting and new remark can be added. The WL FRESH equalizer has also notches when δ f = i 8T0 = i 4T1 . This can be explained in the same manner as previously. Indeed, as the most energetic conjugate SO cyclic frequencies are equal to

β i = ±2 δ f + i T1 ,
after frequency shifting equal to ±β 1 , the most energetic conjugate cyclic frequencies become located at

frequencies β i ± β 1 = ±4δ f + i T1 which are null for δ f = i 4 T 1 = i 8 T 0 .

Application to FBMC-OQAM

We consider a FBMC system having two users (UOI and UNOI) with quasi-rectilinear (QR) modulation of type OQAM, with two dierent numerologies. The system with Numerology 1 is considered as the UOI and it has M 1 = 64 sub-carriers, whereas the second system (UNOI) with the second numerology has twice the number of UOI's sub-carriers, meaning M 2 = 2 × M 1 = 128. ∆t is the time shift between the two user signals, describing the asynchronism between the UNOI and UOI. δ f denotes the guard band between the two users. The modulation is chosen to be 64-OQAM.

Down-Link "DL" case

In this case, we consider that the BS serves simultaneously the two users (i.e., ∆t = 0). We activate only 5 SCs for the UOI (using numerology 1) and 8 SCs for the UNOI (using numerology 2). The δ f is chosen to be equal to the one UOI sub-carrier spacing (δ f = F e M 1

). Since only the UOI subcarriers in the edge of the band are aected, we study the performance of the dierent equalizers in rejecting the interference caused by the UNOI. The BER performance of the studied equalizers in symbol spaced mode (SSE) mode We note from these results that the WL FRESH equalizer outperforms both the LE and WLE whereas the worst behavior is provided by the LE. This is true for both SSE and FSE cases. When the number of samples per symbol, P , increases, the WLE and WL Fresh equalizer performances increase, and the WL Fresh gives always the best performance.

Up-Link "UL" case

In this case, users (UOI and UNOI) can communicate asynchronously with the BS (i.e., ∆t can be dierent from 0). 5.2 Sensitivity of (OQAM or QAM)-based OFDM systems to phase estimation error

In OQAM based OFDM systems, like FBMC-OQAM, the subcarrier orthogonality is satised only in the real domain. Specically, each subcarrier is modulated in OQAM where the real and imaginary values are time staggered by half a symbol duration [START_REF] Farhang-Boroujeny | Ofdm versus lter bank multicarrier[END_REF]. In such system, emitted data is real (real or imaginary part of the complex symbols) and an imaginary intrinsic-interference occurs in the transmission process.

This interference, which is caused by the data symbols transmitted in the neighborhood area in the time-frequency domain, is imaginary and orthogonal to the useful real emitted data. Then, the detection process is easily performed when the channel is at fading or slowly selective [START_REF] Rostom | Ser analysis by gaussian interference approximation for fbmc system in the presence of phase error[END_REF]. Contrary to classical OFDM systems, the performance of FBMC-OQAM is more sensitive to phase error which can be occurred by the amplication of the transmitted signal using nonlinear PA or by channel estimation error. Thus, we have been interested in providing an universal theoretical analysis for the impact of phase error on the BER performance of MWFs based on either QAM or OQAM processing. In particular, we have derived the exact BER of M-OQAM/QAM by considering the Gaussian intrinsic-interference approximation.

These BER expressions can be evaluated without any numerical integration method.

The received data at subcarrier n 0 and instant m 0 , is expressed, in OFDM case, by r m0,n0 = h m0,n0 (a I m0,n0 + ja Q m0,n0 ) + w m0,n0 ,

where a I m0,n0 and a Q m0,n0 denote, respectively, the in-phase and the quadrature components of the trans- mitted complex symbol, w m0,n0 is the Gaussian noise term with variance σ 2 w and h m0,n0 = αe jθ is the complex channel coecient, which is assumed to be slow-varying Rayleigh at-fading, where the amplitude α follows the Rayleigh probability density function with an average fading power ν = E[α].

While in FBMC-OQAM case, it is expressed by r m0,n0 = h m0,n0 (a m0,n0 + ju m0,n0 ) + w m0,n0 ,

where a m0,n0 and u m0,n0 denote, respectively, the real-valued transmitted data and the intrinsic-interference. Given a channel estimate h = αe j θ , where the phase estimate error ψ = θ -θ and assuming a perfect amplitude estimation α = α, because this latter represents the same contribution as in the classical OFDM. Then, the in-phase (a I m0,n0 ) and quadrature (a Q m0,n0 ) components or real-valued (a m0,n0 ) data and intrinsic-interference (u m0,n0 ) could interfere when, respectively, OFDM or FBMC-OQAM are considered.

The input of the decision device, in OFDM case, is given by r = (a I cos(ψ) -a Q sin(ψ)) + w h .

(5.3)

While in FBMC-OQAM case, it is given by r = (acos(ψ) -usin(ψ)) + Re w h .

(5.4)

For concise expressions and without loss of generality, the subscript of subcarrier and time index are removed.

Lemma 1: the BER conditioned on α, u and ψ for M-QAM/OQAM (OFDM/FBMC) is given by

BER M -QAM (α, u, ψ) = ξ i=1 w i Q [a i cos(ψ) -äi usin(ψ) + b i ] α σ w (5.5) where ξ = 1 2 log 2 (M ) l=1 2 l-1 √ M
2 , äi denotes the sign of a i and the coecients w i , a i and b i are listed in [J08].

Proof: is given in paper [J08] Note that, in OFDM case, u ∈ {- 2 ) e jϕm,n where ϕ m,n = π/2(m + n) -πmn and the delay term D = L -1 depends on the length of the prototype lter p tx [t]. According to [START_REF] Siohan | Analysis and design of ofdm/oqam systems based on lterbank theory[END_REF], the prototype lter is designed such that the intrinsic-interference term is orthogonal to the useful data, i.e., ju m0,n0 is pure imaginary-valued. Let

√ M + 1, - √ M + 2, ..., -1, 1, ..., √ M -2, √ M -1}
us call +∞ -∞ f m,n (t)f * m0,n0 (
t) as χ ∆m,∆n (where ∆m = m 0 -m and ∆n = n 0 -n), which can be calculated assuming null data except the considered symbol (m 0 , n 0 ) where a unit impulse is applied [START_REF] Rostom | Ser analysis by gaussian interference approximation for fbmc system in the presence of phase error[END_REF]. Then χ ∆m,∆n can be derived as

χ ∆m,∆n = +∞ -∞ p tx (t)p tx (t -∆nT /2) × e j 2π
T ∆p( D 2 -m) e jπ(∆m+m0)∆n e -j π 2 (∆m+∆n) ,

where p tx (t) is the prototype lter impulse response.

Since the most part of the energy of the impulse response is localized in a restricted set around the considered symbol (denoted by Ω m0,n0 ), the intrinsic-interference ju m0,n0 can be expressed as

ju m0,n0 = (m,n)∈Ωm 0 ,n 0 a m,n χ ∆m,∆n (5.7)
The coecients ju m0,n0 represent the sum of many independent and identically distributed random variables. They are depicted by Table I in [START_REF] Zayani | Ber analysis of lter-bank multicarrier with oset quadrature amplitude modulation systems with phase estimation error[END_REF] where the PHYDYAS prototype lter with overlapping factor set to K = 4 is considered. Here, we note that the resulting interference term is a sum of at least twenty independent random variables where the distribution of each of these variables depends on the modulation order. Based on the central limit theorem, the probability distribution of the intrinsic-interference can be approximated by a zero-mean Gaussian random variable with a variance σ 2 u = (log 2 (M ) 2 -1)/3.

Theorem 1: The closed-form BER expression for an uncoded M-(QAM or OQAM) over Rayleigh fading channel is given by

BER rayleigh M -OQAM (ψ) = 1 8 ξ i=1 w i   1 - 1 √ π κ j=1 β j a i cos ψ -äi 2σ 2 u x j sin ψ + b i (a i cos ψ -äi 2σ 2 u x j sin ψ + b i ) 2 + 2σ 2 w   (5.8)
where

β j = (2 κ-1 κ! √ π)/(κ 2 [H κ-1 (x j )]
2 ) and x j are, respectively, the weights and zeros of the κ-order

Gauss-Hermite polynomial (H κ (x) = (-1) κ e x 2 d κ dx κ e -x 2
). The tables containing the values of β j and x j respectively. We clearly observe a degradation of the BER performance when a phase rotation error occurs, showing that the eect of the intrinsic-interference is harmful even at low SNR. The analytical curves are obtained by using equation (5.8) and compared to the ones obtained by simulations. We observe from these gures a good agreement between both simulated and theoretical performance curves which are very close. It is worth to mention that the quadrature order of the Gauss-Hermite approximation in equations (5.8) was κ = 20. According to these results, one can note the eectiveness of the Gaussian intrinsic-interference approximation in the evaluation of FBMC-OQAM performance in presence of phase error and when a Rayleigh fading channel is considered.

PA NLD characterization and theoretical performance analysis for 5G MWFs

In order to derive a statistical characterization of the decision variables at the input of decision devices, we rst describe the input and output signals of the nonlinear power amplier. The MWF modulated symbol stream (given in equation (4.1)) has a complex envelop x(t) = x I (t) + jx Q (t) that can be written, using the polar coordinates, as

x(t) = ρ(t)e jφ(t) ,

(5.9)

where ρ(t) and φ(t) are the modulus and phase of x(t), respectively. As a general formulation, the amplied signal at the output of a memoryless nonlinear PA can be expressed as z(t) = F a (ρ(t))e jFp(ρ(t)) e jφ(t)

= S(ρ(t))e jφ(t) , (5.10) where F a (.) and F p (.) denote the AM/AM and AM/PM conversions, respectively, and S(ρ(t)) = F a (ρ(t)) exp(jF p (ρ(t)))

(5.11)

is the complex soft envelop of the amplied signal z(t).

For any MWF signal, when the number of subcarriers, N , is suciently large, the input signal x(t) is assumed to be a zero mean complex Gaussian random process. According to the Bussgang theorem [START_REF] Bussgang | Recrosscorrelation functions of amplitude-distorted gaussian[END_REF],

z(t) can be written as

z(t) = K 0 x(t) + d(t), (5.12)
where d(t) is an additive zero-mean (non-Gaussian) noise having variance σ 2 d and uncorrelated with x(t) and K 0 is a constant complex gain. According to [START_REF] Dardari | A theoretical characterization of nonlinear distortion eects in ofdm systems[END_REF], the NLD parameters K 0 and σ 2 d can be computed theoretically as

K 0 = 1 2 E ∂S(ρ) ∂ρ + S(ρ) ρ (5.13)
and

σ 2 d = E(|d(t)| 2 ) = E |S(ρ)| 2 -|K| 2 E(ρ 2 ) (5.14)
Note that the analytical computation of the NLD parameters, K 0 and σ 2 d , depends on the S(ρ). In [START_REF] Dardari | A theoretical characterization of nonlinear distortion eects in ofdm systems[END_REF],

only closed-form expressions for SEL model have been introduced, which are expressed as

K 0 = 1 -e -A 2 sat σ 2 + 1 2 π A 2 sat σ 2 erf c A 2 sat σ 2 , (5.15)
and

σ 2 d = σ 2 1 -e -A 2 sat σ 2 -K 2 0 , (5.16)
where σ 2 denotes the input signal power and A sat is the saturation amplitude at the output of the SEL model. Nevertheless, for more complicated expressions of S(ρ) (e.g., SSPA and TWTA models) or measured PA, the derivation of closed-form expressions for the NLD parameters is not straightforward and no such expressions have been introduced in literature. Therefore, via the supervision of Mrs Hanen's PhD, we investigated a new approach, based on polynomial approximation of the PA characteristics, that allows an universal derivation of K 0 and σ 2 d for any modeled or measured PA. This work was supported by the PHC-Utique C3 project.

The proposed approach aims at approximating the complex soft envelop S(ρ) of the amplied signal by using a polynomial model with odd and even coecients, which can be written as

z(t) = L l=1 a l x(t)|x(t)| l-1 = e jφ L l=1 a l ρ l , (5.17)
where the new expression of S(ρ) can be given by L l=1 a l ρ l . The above theoretical expressions of K 0 and σ 2 d (equations (5.15) and (5.16)) involve the computation of the expectation of ρ l (l is a positive integer). This expectation is equivalent to calculate the l-th derivation of the moment-generating function (MGF) [START_REF] Raich | Orthogonal polynomials for power amplier modeling and predistorter design[END_REF].

Lemma 2: The NLD parameters K 0 and σ 2 d can be given by

K 0 = a 1 + π 8 L l=2,leven (l + 1)a l σ l-1 l-2 2 i=0 (2i + 1) + 1 2 L l=3,lodd (l + 1)a l √ 2σ l-1 l -1 2 ! (5.18)
and

σ 2 d = L l=1 |a l | 2 2 l σ 2l l! -2|K 0 | 2 σ 2 + 4π 2 L l,n=1,l =n,(l+n)odd Re[a l a * n ]σ l+n l+n-1 2 i=0 (2i + 1) + 2 L l,n=1,l =n,(l+n)even Re[a l a * n ] √ 2σ l+n ( l + n 2 )! (5.19)
Proof: is given in paper [J05] It is worth to mention that K 0 and σ 2 d are function of the standard deviation of the PA input signal σ that depends on the PA operating point (input back-o (IBO)) and can be written as σ = Asat √ 10 IBO/10 .

Considering that the nonlinearly amplied signal passes through a radio channel, the demodulated data at time instant m 0 and subcarrier n 0 is given by

r m0,n0 = K 0 h m0,n0 (a m0,n0 + ju m0,n0 ) + h m0,n0 d m0,n0 + w m0,n0 , (5.20)
where h m0,n0 indicates the channel coecient corresponding to the subcarrier m 0 and instant n 0 .

Remark 1: the instantaneous signal-to-noise ratio (SNR) after equalization remains the same for OFDM and FBMC-OQAM, as explained in [J07]. It can be expressed as

γ = |K 0 | 2 |h| 2 σ 2 |h| 2 σ 2 d + σ 2 w (5.21)
Note that, in case of FBMC-OQAM, σ 2 = 2P a , P a is the average power of the information-bearing real symbol a.

BER AW GN = 2( √ M -1) √ M log 2 (M ) erf c 3 log 2 (M )|K 0 | 2 σ 2 (M -1)(σ 2 w + σ 2 d ) (5.22)
Proof: is given in paper [J05].

Theorem 2: With nonlinear PA, the closed-form BER expression of an uncoded (QAM or OQAM based) OFDM over quasi-static frequency-at Rayleigh channel is given by

BER Rayleigh = a(1 - 2 √ π +∞ n=0 +∞ k=0 (-1) k+n ( √ b) 2n+1 k!n!(2n + 1) ( σ 2 w ν ) k+1 (γ c ) n+k+3/2 n + k + 3/2
2 F 1 (k + 2, n + k + 3/2; n + k + 5/2; 1),

Adaptive Digital Predistortion for PA linearization

Baseband adaptive digital predistortion (DPD) is the most promising solution to compensate of the nolinearities and memory eects of the PA. The DPD consists in adding a processing unit before the PA such that the resulting system DPD plus PA is linear (up to the PA saturation). The DPD's characteristics are the inverse of the ones of the PA. Specically, the DPD applies an expansion, in the PA compression zone, on the input signal in order to compensate the loss of gain and it must also apply a phase shift of opposite quantity of the one introduced by the PA. Typically, the DPD is adaptive, i.e., capable to update the coecients of the DPD following the time-varying PA characteristics.

The common adopted hardware implementation combines a digital signal processor (DSP) and a eld programmable gate array (FPGA) to realize the adaptive DPD architecture (see Figure 5.3). The DPD function is performed by the FPGA that provides implementation structure highly parallelized while the adaptation process is realized by the DSP which is more adequate for complex algorithm derived in sequential form. In Figure 5.3, the DPD architecture requires a feedback loop to take a part of the amplied signal and to demodulate it. After a synchronization and a power normalization processes, the new input and output signals permit to update the DPD function. The feedback loop contains a coupler, an attenuator, a mixer and analog to digital converters (ADC). Here, we consider the indirect learning architecture (ILA) which has been shown to be the most promising one.

The DPD is expected to provide good linearization performance and low cost. The DPD complexity cost represents both the computational complexity of the DPD function and the identication processing, which depends on the updating algorithm and the number of coecients of the DPD function. For the sake of simplicity and without loss of generality, we consider, in the following, the simplied DPD architecture given in Figure 5.4.

Several mathematical models have been proposed for DPD modeling, which serve for PA modeling.

These mathematical models, which are derived from the Volterra Series model, are Memory polynomial (MP) [START_REF] Lei Ding | A robust digital baseband predistorter constructed using memory polynomials[END_REF], generalized memory polynomial (GMP) [START_REF] Morgan | A generalized memory polynomial model for digital predistortion of rf power ampliers[END_REF], Laguerre-Volterra model [START_REF] Lavrador | A new volterra series based orthogonal behavioral model for power ampliers[END_REF], Kautz-Volterra model [START_REF] Dooley | Behavioral modeling of rf power ampliers using adaptive recursive polynomial functions[END_REF] and dynamic-deviation-reduction (DDR) Volterra model [START_REF] Zhu | Dynamic deviation reduction-based volterra behavioral modeling of rf power ampliers[END_REF]. The review of the dierent methods for predistortion is not the main object of this dissertation and the interested reader is referred to [START_REF] Baudoin | Digital predistortion, Digitally Enhanced Mixed Signal Systems[END_REF].

Volterra based models are able to compensate both nonlinearity and memory eects of NL PA. Nevertheless, other techniques exist for synthesizing NL systems. Among them we have chosen a Neural Network (NN) implementation of the DPD, which has great capability to learn any arbitrary nonlinear input-output relationships from corresponding data [7]. Indeed, we have widely investigated DPD based on real-valued multi-layer perceptron (MLP) whose input signal consists of Cartesian in-phase and quadrature phase (I /Q) components. This NN structure is capable to compensate eectively both nonlinearity and memory eects [START_REF] Tarver | Design and implementation of a neural network based predistorter for enhanced mobile broadband[END_REF] In order to assess the performance of the proposed architecture (Figure 5.5), the MIMO multiplexer adopted is the space time block coded (STBC) 2 * 2 proposed by Alamouti [START_REF] Alamouti | A simple transmit diversity technique for wireless communications[END_REF]. Note that the crosstalk is the result of interferences occurring between the dierent paths in the same low-size integrated circuit.

This crosstalk can be linear or nonlinear, in the rst case, it will be tackled by the receiver equalizer. But in the second case the crosstalk, which is generated before the PAs (i.e., amplied in nonlinear manner), is much more harmful and it cannot be eliminated by the receiver. Then, the PA output aected by the memory crosstalk can be modeled as

z 1 = f 1 (y 1 + F (y 2 )) z 2 = f 2 (y 2 + F (y 1 )) (5.24)
where f 1 and f 2 are the PA transfer functions corresponding, respectively, to antenna 1 and antenna 2, F Figure 5.7 shows the performance of several NN predistorter congurations on the considered STBC-MIMO-OFDM system with a Saleh's TWT amplier [START_REF] Saleh | Frequency-independent and frequency-dependent nonlinear models of twt ampliers[END_REF] operated at an IBO of 7dB, in presence of memory crosstalk. We present the BER performance of the conventional/memoryless CO-NNPD (studied in [C08]) compared to the proposed MCO-NNPD (TD5,n 1 -n 2 ,4), where TD5 denotes the tap delay line of length 5 while n 1 and n 2 represent the number of neurones in, respectively, the rst and second hidden layers.

The BER performance of linear PA case serves as a benchmark.

Classical/First DPD scheme

The rst technique is the one studied in [7] for OFDM systems (see Figure 5.4). It consists in two neural network (NN) units. The rst one, NNDPD, realizes directly the predistortion function by applying deformations on the transmitted signal such that the resulting system is linear. The second, NNupdate, is updated regularly, using a training algorithm, according to the variation of the PA. Then, the coecients of the NNupdate are transferred to the NNDPD using a simple copy. The NNDPD response can approximate simultaneously the inverse transfer functions of the nonlinear PA (AM/AM and AM/PM).

The NN structure considered was a feedforward multilayer perceptron (MLP) neural network, which has two inputs, namely the I and Q components of the input signal, two linear output neurons that are the predistorted signals (I and Q) and one hidden layer with ten nonlinear neurons. The activation function, f a (.) used for the hidden layer is an hyperbolic tangent, while the output layer is linear. It is well known that each neuron in the network is composed of a linear combiner and an activation function which gives the neuron output as

x out l,j = f a N l -1 i=0 w l,j,i x in l-1,i + b l,j , (5.25)
where w l,j,i is the weight which connects the i-th neuron in layer l -1 to the j-th neuron in layer l, b l,j is the bias term, and x in l-1,i denotes the i-th component of the input signal to the neuron.

The weights of the NNupdate are adjusted using Levenberg-Marquardt (LM) algorithm, which has shown, in [7], to exhibit a very good performance with both a lower computational complexity and a

(t+1) l,j,i = w (t)
l,j,i -J T J + µI J T e, (5.26) where e is the error vector, J is the Jacobian matrix which contains the rst derivatives of e w.r.t. the weights and biases, and µ is the training rate.

The symbol error rate (SER) performance of the classical DPD scheme over OFDM and FBMC-OQAM systems in presence of amplitude and phase distortions with a Saleh's TWTA operated at an IBO of 6dB are depicted in Figure 5.9.a. One can also note that this DPD scheme can reduce considerably the SER compared to the performance without any DPD correction. Nevertheless, it performs worse with FBMC-OQAM modulation when compared to the OFDM one. Such degradation can be explained by the fact that this DPD, which aims to compensate simultaneously the amplitude and phase nonlinearities, is not able to compensate perfectly the phase error. Indeed, the predistorted amplier exhibits a residual AM/AM distortion, which can only be perfectly compensated as far as the input power is lower than the saturation power, aects the correction of the AM/PM distortion.

Proposed/Second DPD scheme

With that technique (Figure 5.8) the predistortion aims to compensate separately amplitude distortion and phase distortion by using two NNs. The rst one (NN1) identies the inverse AM/AM conversion and the second one (NN2) identies the inverse AM/PM conversion. The two NNs have the same structure as the ones used in the rst scheme, where each one has ve neurons in the hidden layer in order to keep the same computational complexity. The transfer functions and training algorithm are also the same as described above.

The SER performance of the proposed DPD scheme for OFDM and FBMC-OQAM are given in Figure 5.9.b. Comparing the dierent curves, we clearly note an excellent match between the performance provided by the second predistortion scheme for both OFDM and FBMC-OQAM systems. We can note from these results that this DPD scheme is able to compensate perfectly the phase error due to the nonlinear PA.

PAPR reduction techniques for 5G MWFs

In MWF based communication systems, the PAPR reduction remains one of the most challenges that need to be tackled eectively. Numerous PAPR reduction techniques have been proposed for the classical OFDM, such as clipping [START_REF] Ryu | Papr reduction using soft clipping and aci rejection in ofdm system[END_REF], Tone Reservation (TR) [START_REF] Behravan | Tone reservation to reduce the envelope uctuations of multicarrier signals[END_REF], Selective Mapping (SLM) [START_REF] Bauml | Reducing the peak-to-average power ratio of multicarrier modulation by selected mapping[END_REF], Active Constellation Extension (ACE) [START_REF] Yang | Ace with frame interleaving scheme to reduce peak-to-average power ratio in ofdm systems[END_REF], Partial Transmit Sequence (PTS) [START_REF] Muller | Ofdm with reduced peak-to-average power ratio by optimum combination of partial transmit sequences[END_REF], Tone Injection (TI) [START_REF] Chen | Papr reduction of ofdm signals using cross-entropy-based tone injection schemes[END_REF], and block coding [START_REF] Wilkinson | Minimisation of the peak to mean envelope power ratio of multicarrier transmission schemes by block coding[END_REF]. Review of these techniques is out of the scope of this dissertation and interested readers are referred to [START_REF] Seung | An overview of peak-to-average power ratio reduction techniques for multicarrier transmission[END_REF] and [START_REF] Jiang | An overview: Peak-to-average power ratio reduction techniques for ofdm signals[END_REF].

However, a direct application of the aforementioned PAPR reduction techniques proposed for OFDM to ltered MWFs is not eective due to their overlapping structure. Therefore, we have been interested in investigating improvements of these classical methods to be able to take into account the overlapping structure of the ltered MWFs. Indeed, contrary to the classical symbol-wise optimization methods, the proposed schemes optimize the PAPR with taking into account the whole interval upon which the ltered MWF symbol got spread. In this regard, two methods have been considered in our study, TR and SLM, which are the most promising ones. The performance of the proposed improved TR/SLM schemes are assessed through FBMC-OQAM since it has the most pronounced overlapping symbol structure.

Dispersive SLM based PAPR reduction in FBMC-OQAM systems

The dispersive SLM (DSLM) algorithm is summarized bellow,

Step 1-Initialization: Given M complex input symbol vectors {X m } M -1 m=0 and U uniformly distributed phase rotation vectors {Φ (u) } U -1 u=0 ∈ {-1, 1} of length N . We initialize m = 0

Step 2-Phase rotation: Compute U phase rotated version of the m-th symbol X m , obtaining {X (u)

m = X m Φ (u) } U -1 u=0 .
Step 3-FBMC-OQAM modulation: Apply FBMC-OQAM modulation for all pattern of the m-th symbol vector with taking into account K -1 previous symbols, where K is being the adopted prototype lter length, to obtain x m (t) (u) U -1 u=0

Step 4-PAPR calculation: Compute the PAPR of the modulated signals x m (t) (u) U -1 u=0 on [mT, mT + KT ] interval time, giving U PAPRs.

Step 5-Selection: Select the vector which gives the lowest PAPR to this symbol,Φ (um) , and send

X (um) m = X m Φ (um) .
Step 5-Increment: Increment m by 1 and go to Step 2.

The performance of the above algorithm is depicted in Figure 5.10. One can note that the provided PAPR reduction is quite similar to that of the OFDM with the classical SLM. Nevertheless, for high values of U there is a performance gap between OFDM and FBMC-OQAM. Without taking into account the memory eect of FBMC-OQAM (step 3 of the proposed algorithm), this gap should be signicantly larger.

Dispersive TR based PAPR reduction in FBMC-OQAM systems

In the TR scheme, iterative clipping and ltering approach is considered. The total N subcarriers are partitioned into R peak reduction tones (PRTs) and N -R data subcarriers. Symbols in PRTs are chosen such that time-domain FBMC-OQAM signal has a low PAPR. These PRTs do not carry any useful Unlike to the traditional TR, which adopts symbol-wise optimization, the proposed dispersive TR (DTR) takes into account the overlap of the past symbols, when optimizing the PRTs entries for the m-th symbol. Again, the considered prototype lter is the PHYDYAS one with an overlapping factor K = 4.

The DTR algorithm is as follows

Step 1-Initialization: Given a PRT location set B, generate M complex input symbol vectors {D m } M -1 m=0 and put zeros in the PRT locations (i.e., C m is initially set to zero). We initialize m = 0. The input symbols in frequency domain can be expressed as

X m [n] = D m [n] + C m [n] = C m , if n ∈ B D m , if n ∈ B c , (5.27)
Step 2-FBMC-OQAM modulation: Apply FBMC-OQAM modulation for all pattern of the m-th symbol vector with taking into account K -1 previous symbols, obtaining x m (t).

Step 3-Peak-cancelling signal optimization: Compute the optimal values of of PRTs subject to

argmin Cm [ x m (t) + (C m ) ] , m ∈ [mT, mT + KT ] , (5.28)
where denotes FBMC-OQAM modulation. Note that the optimal C m ) can be obtained by solving equation (5.28) using convex optimization algorithms such as Quadratically constrained quadratic programs (QCQP), gradient search [START_REF] Hwang | Peak power reduction method for multicarrier transmission[END_REF], projection onto convex sets (POCS) [START_REF] Gatherer | Controlling clipping probability in dmt transmission[END_REF], etc.

Then, the input symbol vector is updated as

X m = D m + C m (5.29)
Step 4-Increment: Increment m by 1 and go to Step 2.

From results in Figure 5.11, one can observe the strong capability of the proposed DTR method in reducing the PAPR of FBMC-OQAM. Its performance are quite close to those obtained by classical TR for OFDM.

Ping-Pong Joint Optimization (P2JO) for PAPR reduction and PA linearization

As explained above, the two complementary techniques of PAPR reduction and PA linearization have to be deployed in order to improve both PA linearity and eciency. In conventional systems, these solutions are optimized separately and applied independently. Indeed, designers start focusing on their association aiming at avoiding mutual eects in order to enhance interoperability, achieving an optimal performance. In literature, dierent schemes have been studied where PAPR reduction is followed by predistortion [START_REF] Abel | A joint approach for papr reduction and predistortion by adding signal in cognitive radio[END_REF] [107] [START_REF] Nader | Peak-power controlling technique for enhancing digital pre-distortion of rf power ampliers[END_REF], These schemes showed attractive improvements in eciency and linearity when both digital pre-processing techniques are combined. Furthermore, in [START_REF] Nader | Peak-power controlling technique for enhancing digital pre-distortion of rf power ampliers[END_REF], authors proposed a method to control the DPD-avalanche [START_REF] Landin | Peak-power controlled digital predistorters for rf power ampliers[END_REF] by limiting the peaks generated from the digital predistorter.

Another approach has been widely studied in [START_REF] Landin | Peak-power controlled digital predistorters for rf power ampliers[END_REF] [110] [START_REF] Braithwaite | Descent-based coecient estimator for analog predistortion of a dual-band rf transmitter[END_REF] [112] [START_REF] Piazza | Generalized direct predistortion with adaptive crest factor reduction control[END_REF], it consists in including PAPR control as a constraint in the estimation of the predistortion parameters.

In the framework of the ANR WONG5 project, we have been interested in investigating new solution to tackle this issue. In this regard, we have introduced a new and promising concept to optimize jointly PAPR reduction and PA linearization that aims at creating a good synergy between the two techniques in order to provide optimal performance. The proposed approach synthesises, in a Ping-Pong manner, only one correction signal that takes into account the PAPR reduction and PA linearization allowing then better trade-o between PA eciency and linearity, compared to classical combinations studied in literature. In this work, the clipping control based tone reservation (CC-TR) method, which is commonly used and is adopted in DVB-T2 systems [START_REF]Channel Coding Digital Video Broadcasting (DVB): Framing Structure and Modulation for Digital Terrestrial Television Broadcasting System(DVB-T2)[END_REF], is considered for PAPR reduction. It can obtain a moderate PAPR reduction with little degradation of bit-error-rate (BER) performance [START_REF] Li | An improved tone reservation scheme with fast convergence for papr reduction in ofdm systems[END_REF]. While for PA linearization, the neural network based DPD is an excellent for the PA linearization [7]. The proposed Ping-Pong Joint Optimization (P2JO) approach takes benet from the fact that a common vision of PAPR reduction and PA linearization techniques is possible since they can be formulated as adding signal techniques, thanks to Bussgang theorem [START_REF] Bussgang | Recrosscorrelation functions of amplitude-distorted gaussian[END_REF].

Classical combination of PAPR reduction and DPD by adding signal

Let us consider x as the signal issued from a MWF modulation (Figure 5.12). After scaling the signal to the desired PA back-o, using γ 0 , we can generate a PAPR reduction signal c papr using CC-TR technique [116] [117]. Then, the low-PAPR signal, expressed as y papr = y 0 + c papr ,

(5.30)

will serve to generate a predistortion signal c dpd . Then, the signal at the input of the PA can be given by y = y papr + c dpd (5.31)

We recall that we consider the CC-TR to generate the PAPR reduction signal where many iterations are needed for a given OFDM symbol. While, we execute only one time the considered neural network to obtain the predistortion signal. This combination scheme, considered in [START_REF] Abel | A joint approach for papr reduction and predistortion by adding signal in cognitive radio[END_REF] [110] as a dynamic joint approach for PAPR reduction and predistortion, will be considered, in this work, as the classical combination and will serve as a reference to show how our proposed approach will achieve better trade-o between PA linearity and eciency.

S d

Identity matrix of order N with zeros at positions in R S r

Identity matrix of order N with zeros at positions in R c γ 0 Scaling factor to control the PA Back-o

Proposed P2JO algorithm

The key idea is to synthesize the additional signal c for PAPR reduction and predistortion in a Ping-Pong manner and iteratively (Figure 5.13). In this technique, we:

1) add the PAPR reduction signal scaled by a factor µ 1 ≤ 1, 2) add the predistortion signal scaled by a factor µ 2 ≤ 1,

3) repeat steps 1) and 2) until we reach the desired performance.

Using this approach, we create a good synergy between the two operations in order to avoid mutual eects leading to a better trade-o between PA eciency and linearity. Table P2JO describes the proposed P2JO algorithm and Table 5.1 contains a list of parameter denitions to be used in the algorithm.

It is worth to mention that the proposed algorithm has been published in patent [P01].

P2JO performance assessment

In order to study the capability of the proposed approach, an uncoded OFDM system with N =256 subcarriers and using 16-QAM modulation with Gray mapping. The number of reserved tones is set to be 32, randomly selected over the bandwidth of the OFDM signal. The oversampling factor is set to 4 that guarantees a good PAPR approximation [START_REF] Ochiai | Performance analysis of deliberately clipped ofdm signals[END_REF]. The considered PA is the Saleh's TWTA. The optimal clipping threshold A sat is dened according to [START_REF] Li | An improved tone reservation scheme with fast convergence for papr reduction in ofdm systems[END_REF]. For the P2JO algorithm, we recall that, for PAPR reduction, we consider the CC-TR method, where its peak-cancelling signal, during each iteration, is extremely smaller than that of the original clipping noise. In order to keep a maximal performance of power eciency and push the predistortion to oer its best performance, µ 1 should be adaptive when considering optimized TR PAPR reduction methods with adaptive peak-cancelling signal level, like in [START_REF] Li | An improved tone reservation scheme with fast convergence for papr reduction in ofdm systems[END_REF] [START_REF] Jiang | Curve tting based tone reservation method with low complexity for papr reduction in ofdm systems[END_REF]. Three values of µ 2 have been considered, 10 -2 , 3 × 10 -2 and 5 × 10 -2 , to clearly show how we can take into consideration the mutual eect between TR PAPR reduction and DPD by the proposed iterative Ping-Pong approach. In the following, µ%P2JO refers to the use of the P2JO P2JO: The P2JO approach 1: Set the minimum EV M min , the reserved tone set R, the initial clipping level A sat and the maximal iteration number maxIter. 2: Set i = 0, the time-domain signal of the 0 th iteration y 0 = x, where x is the original OFDM symbol. 3: TR : calculate the clipping noise, using the OFDM signal at iteration i and its clipped version (mathbf ȳi ), as w i = calculate the peak-cancelling signal c papr,i = IF F T (S r × F F T (w i )) 4: DPD : calculate the predistortion signal c dpd,i = y dpd,iy i where y dpd,i is the predistorted version of y i signal. 5: Update the signal y i+1 = y i + µ 1 c papr,i + µ 2 c dpd,i 6: Calculate the amplied signal z i+1 = S(|y i+1 |)exp(∠y i+1 )

7: Calculate X i+1 = S d × F F T (y i+1 ) 8: Calculate the error vector magnitude EV M i+1 = E[X i+1 -X 0 ] E[X 0 ] , if EV M min < EV M i+1 < EV M i & i < maxIter , set i = i + 1
and go to step 3). otherwise, choose y i+1 as the transmitted signal and terminate the loop. 9: End. algorithm where µ 2 = µ × 10 -2 . It is worth to note that, when µ 2 = 1,the P2JO converges to the same performance obtained by the classical approach. Figure 5.14 shows the BER performance of the µ%P2JO in presence of nonlinear Saleh's TWTA operated at outpout back-o (OBO) of 2.5dB, 3dB and 3.5dB and an AWGN channel. 'classical TR+DPD' and 'w/o corr' denotes, respectively, the classical approach and the OFDM system without any correction. One can note that the µ%P2JO outperforms the classical scheme in all cases, we note for a BER of 4 × 10 -3 , a SNR gain of 1dB, 2.5dB and 11dB at, respectively, OBOs of 3.5dB, 3dB and 2.5dB. In order to show the impact of µ 2 on the P2JO performance, Figure 5.15 shows BER performance of 1%P2JO, 3%P2JO and 5%P2JO. We can clearly see that the more µ 2 is decreased, the more the performance is improved. This can be explained by the fact that the mutual eect between TR PAPR reduction and DPD is better considered when µ 2 is lower. To have a clear comprehension of the P2JO algorithm convergence speed, Figure 5.16 shows EVM performance versus iteration number for dierent values of OBOs. It can be observed that, when lower value of µ 2 is considered, the EVM decreases slowly and ensures a better convergence towards a lower EVM. At OBO of 2.5dB, 1%P2JO converges to an EVM of 9% in 100 iterations, while 5%P2JO converges to an EVM of 11.3% in only 20 iterations.

To study the eect of the proposed approach on the OOB emission, the PSD and the adjacent channel power ratio (ACPR) are considered. As depicted in Figure 5.17, the OOB emission reduction in the neighboring channels based on µ%P2JO outperforms those of the classical approach. Furthermore, Table 5.2 gives the ACPR performance of the P2JO approach compared to the classical one with Saleh's TWTA operating at OBOs of 2.5, 3, 3.5 and 4 dB. As can be observed, the schemes based on 1%P2JO provide an ACPR gain of 2dB compared to the classical approach. Most importantly, a real-time SDR implementation is ensured by considering a specic computer conguration, interested readers are referred to [START_REF] Zayani | Experimental testbed of post-ofdm waveforms toward future wireless networks[END_REF]. The link performance results were provided for two scenarios : DL and UL following the experimentation cases. modied TR and SLM techniques that are more adequate to BF-OFDM than the classical ones. The key idea is, when reducing the PAPR of the current symbol x(i), we take into consideration the tail of the previous optimized symbol x(i -1). We move to DPD, it is based on the well-known polynomial model based inverse learning architecture (ILA) [7]. Figure 5.21 compares measured BER of dierent MWFs when the RF PA is operated at an IBO of 3 and 6dB. Again, we can note that WOLA-OFDM and BF-OFDM provide almost the same performance as the classical CP-OFDM when PAPR reduction is performed by SLM/TR. At an IBO of 6dB, BER performance provided by all waveforms is very close to the one performed in linear case. It is worth mentioning that BER oor related to the demonstrator noise oor is not observable for BER > 10 -5, which represents a signicant BER range for wireless communications standards. Scenario 2 denes an asynchronous UL transmission case. We addressed the impact of the lack of synchronism between transmitters on the performance of the selected MWFs, which is of special relevance for future 5G mMTC applications. We provided further discussions and comparisons of the selected waveforms CP-OFDM,WOLA-OFDM and BF-OFDM, with corresponding parameter selections. Here, we consider a scenario with two co-existing users sharing the available frequency band as illustrated in MHz bandwidth. A guard-band δ f between the two users is separating the frequency bands of both users and a timing oset is given to create asynchronism. In order to well assess the performance of these From results illustrated in Figure 5.22, we clearly show that the inter-user interference level depends on the chosen MWF. CP-OFDM exhibits the worst performance due to its bad frequency response localization. Furthermore, we note that the interference level decreases slowly as the spectral distance between the victim subcarrier and the interferer ones increases.

We move to WOLA-OFDM, we can observe better performance compared to CP-OFDM. Its achieved interference level, in the middle of the bandwidth, is lower (approximately -34dB) compared to CP-OFDM scheme. These good results are related to the WOLA processing applied at the receiver that is able to suppress inter-user interference resulting from the mismatched FFT capture window.

Concerning BF-OFDM, it provides better protection to the edge subcarriers (in the vicinity of interferer subcarriers) compared to both CP-OFDM and WOLA-OFDM. In such region, the NMSE varies from -16dB when δ f = 4.883KHz to -24dB when δ f = 39.06KHz for BF-OFDM scheme while it varies from -14.2dB to -23dB for WOLA-OFDM scheme when the same band is considered. However, the gain of BF-OFDM for the inner subcarriers is marginal compared to CP-OFDM. This is a direct consequence of the BF-OFDM receiver which is no more than the classical CP-OFDM receiver (i.e., a simple FFT). Thus, BF-OFDM could be more interesting than WOLA-OFDM when few number of RBs will be considered for the UOI.

Outputs

The outputs related to work on NLD characterization and mitigation techniques to enhance the energyeciency of 5G MWFs are summarized bellow.

Chapter 6

Massive MIMO: Energy Eciency and Hardware Eciency

Introduction

To support the exponential growth in data trac demand and simultaneously oer ubiquitous connectivity, researchers have been interested in designing new revolutionary wireless communication technologies.

One of the most promising solutions to increase spectral, energy and hardware eciencies by orders-ofmagnitude is massive MU-MIMO [START_REF] Björnson | Massive MIMO networks: Spectral, energy, and hardware eciency[END_REF], which is also known as large-scale MU-MIMO. However, massive MU-MIMO precoders exhibit signals with high PAPR, independently of whether single-carrier or multicarrier transmission are adopted [START_REF] Mollen | Waveforms for the massive mimo downlink: Amplier eciency, distortion, and performance[END_REF]. Accordingly, the nonlinearity of the radio frequency (RF) PA, which is the main hardware impairment and is expected to be low-cost and energy-ecient component to enable cost-and energy-ecient massive MU-MIMO BS deployments, yields harmful in-band distortion and out-of-band emissions. Furthermore, massive MU-MIMO should support mixed numerologies spectrum sharing (SS) transmissions, expected for 5G and beyond. Therefore, I have been interested in investigating: 1) the PAPR reduction problem as well as the compensation of PA nonlinearities in massive MU-MIMO based systems, leading then to highly energy-ecient systems and 2) the introduction of new precoding schemes to make massive MU-MIMO much more exible, satisfying the extremely diverse service requirements.

This chapter exposes the main researches I conducted, within the H2020 MSCA ADAM5 project, to tackle the aforementioned massive MU-MIMO issues. Section 6.2 summarizes the technical contributions related to PAPR reduction problem. Several new methods, which have been developed, will be presented and compared in terms of performance and complexity. In Section 6.3, I move toward PA nonlinearity compensation in massive MU-MIMO. A new approach will be presented and compared to the most studied ones in literature. Section 6.4 is devoted to the work developed via the supervision of Xinying Cheng's PhD on the analysis and cancellation of inter-numerology interference (INI) in massive MIMO systems.

Finally, Section 6.5 summarizes the outputs of these contributions.

Low-Complexity Linear Precoding for PAPR reduction in Massive MU-MIMO-OFDM Downlink Systems

In order to improve the PA eciency, which leads to the global system energy-eciency improvement, MU precoders that generate signals with low-PAPR would be of great interest. This will enable low-cost, lowsize and power-ecient hardware implementations in massive MU-MIMO-OFDM systems. Indeed, some previous works have studied low-PAPR precoders for massive MU-MIMO-OFDM [START_REF] Studer | Par-aware large-scale multi-user mimo-ofdm downlink[END_REF] [126] [START_REF] Bao | An admm approach for papr reduction for large-scale mimo-ofdm systems[END_REF]. All of these methods exploit the excess DoFs and the large null-space oered by the massive MIMO downlink channel to perform low-PAPR precoding. These methods can achieve substantial PAPR reduction but with scarifying high computational complexity. In [J15], we present an approach to perform jointly MU Precoding and PAPR reduction, which was formulated as a simple convex optimization problem and solved online via gradient descent (GD) approach. Specically, we design peak-canceling signals (PCSs) to be added to the frequency-domain precoded data signals, with the goal of reducing the PAPRs of their time-domain counterpart signals. Most importantly, the added PCSs have to lie in the nullspaces of their associated MIMO channel matrices such that they do not cause any MU interference (MUI) and OOB radiation. Furthermore, we introduced the MU-PP-GDm [J15] algorithm that aims to minimize alternately the objective functions with respect, respectively, to the MU precoding and PAPR reduction. This process is repeated over many iterations to achieve the desired MUI and PAPR performance. The MU-PP-GDm, which can be seen as an alternate approach using gradient-iterative method based linear precoding, has been shown to achieve satisfactory PAPR performance with lower computational complexity than the other previous works [START_REF] Studer | Par-aware large-scale multi-user mimo-ofdm downlink[END_REF] [126] [START_REF] Bao | An admm approach for papr reduction for large-scale mimo-ofdm systems[END_REF], especially when the number of users is suciently high. In addition, to optimize the tradeo between performance and complexity, we have studied linear precoders based on matrix polynomials (M-POLY) approaches for both data and PCSs precoding [SJ1]. The key idea is to approximate the matrix inverse by a matrix polynomial decomposition with J terms, where the approximation accuracy can be guaranteed with very few terms.

This approach was rst studied for large-scale MIMO in [START_REF] Zarei | Low-complexity linear precoding for downlink large-scale mimo systems[END_REF] and then widely studied, for massive MIMO downlink related-power/spectral eciency [START_REF] Sifaou | Power ecient low complexity precoding for massive mimo systems[END_REF] [130] [START_REF] Benzin | Low-complexity truncated polynomial expansion dl precoders and ul receivers for massive mimo in correlated channels[END_REF] and security [132] [133], where the polynomial coecients are optimized using tools from random matrix theory [START_REF] Hachem | Deterministic equivalents for certain functionals of large random matrices[END_REF].

In order to assess the performance of the dierent proposed precoding schemes, we assume the downlink of a typical single-cell massive MIMO-OFDM where the BS is equipped with M t transmit antennas and serves M r single-antenna user terminals (UTs) over a frequency-selective channel, where M t M r .

Let N denotes the total number of OFDM tones and s n ∈ C Mr×1 , which is chosen from a complex-valued constellations A, denotes the signal vector containing the information symbols associated with the n-th subcarrier for M r users, where n = 1, ..., N indexes the OFDM tones. The PAPRs of the generated timedomain signals are high, hence a performance degradation in presence of power-ecient RF PAs. To overcome this problem, the BS generates frequency-domain peak cancelling signals (PCSs) to reduce the PAPRs of the time-domain transmitted signals and to prevent severe PA distortions. These PCSs should be constrained to lie in the null-spaces of the MIMO channel matrices such that they do not damage neither the transmission quality of the M r users through the N subcarriers (i.e., guaranteeing excellent MUI and capacity) nor the spectrum purity. In typical OFDM systems, a guard-band is considered in order not to disturb the transmission in adjacent bands. Then, we specify some unused subcarriers at both sides of the used band. These latter will serve to ensure that the proposed low-PAPR precoder does not generate any spectrum regrowth and to obtain a good approximation of the PAPR of the oversampled time-domain OFDM sysmbols. Therefore, the set of tones available are divided into two sets χ and χ c , where the subcarriers in set χ are used for data transmission and the subcarriers in its complementary set χ c are used for guard-band. Moreover, we set s n = 0 Mr×1 for n ∈ χ c such that no signal is transmitted on the guard-band. The frequency-domain signal vector, x n ∈ C Mt×1 , ∀n, transmitted by the BS over the n-th subcarrier through the M t antennas, is given by

x n = √ αW n s n + βV n r n , (6.1)
where r n ∈ C Mt×1 denotes the PCS vector for the n-th subcarrier. W n ∈ C Mt×Mr and V n ∈ C Mt×Mt are, respectively, the data and PCS precoding matrices for the n-th OFDM subcarrier. It is worth pointing out that the design of the precoded signals {x n , ∀n}, which collects the precoded data d n = W n s n and PCS c n = V n r n vectors, is the main scope of this section.

The PCS precoding matrix V n has rank M t -M r , i.e., M t -M r dimensions of the M t -dimensional space spanned by the M t BS antennas are exploited for PAPR reduction, which represent the projection onto the null-spaces of the MIMO channel matrices. The data and PCS precoding matrices are normalized

as tr{W n W H n } = M r and tr{V n V H n } = M t -M r , ∀n.
Note that α is a normalization factor designed to obtain an average transmit power, allocated to the information-carrying signal for each user, equal to P u (i.e., it can be written as α = Pu Mr ). β is dedicated to control the power allocated to all PCS signals, which can be optimized to perform an optimal trade-o between PAPR reduction and signal-to-noise ratio (SNR) gap.

After precoding, the M t -dimensional vectors {x n , ∀n} are reordered to M t transmit antennas for OFDM modulation, according to the following one-to-one mapping

x t 1 , ..., x t Mt T = [x 1 , ..., x N ] . (6.2)
Here, the x t mt ∈ C 1×N denotes the frequency-domain vector to be transmitted though the m t -th antenna. The time-domain signals {a t mt , ∀m t } are obtained by applying an inverse discret Fourier transform (IDFT) to {x t mt }. Then, a cyclic prex (CP) is added to the time-domain samples of each antenna in order to avoid inter-symbol interference (ISI).

For the sake of clarity and without loss of generality, we specify the wireless channel's input-output relation in frequency-domain only. Therefore, the vectors collecting the signals received by the M r users at the n-th subcarrier can be expressed as

y n = G n x n + b n , n ∈ χ (6.
H n = Lc l=1 H t l e -j2πln N . (6.4)

Computing peak-canceling signals (PCSs)

In this subsection, we discuss how to design the optimal frequency-domain PCSs {r n }, in equation (6.1), to perform the best PAPR reduction performance. The key idea consists in tting, iteratively, these PCSs to their associated time-domain clipping-noise signals. These latter are computed by clipping the time-domain signals {a t mt }, at each antenna. Thereby, we compute rst the precoded data {W n s n , ∀n} that satisfy G n W n s n = s n , ∀n ∈ χ. Then, we compute the clipped signals {a t mt } as follows

āmt (k) = a mt (k), if |a mt (k)| < λ λe jφ(k) , if |a mt (k)| > λ , (6.5)
where a mt (k) = |a mt (k)|e jφ(k) , φ(k) is the phase of a mt (k) and λ denotes the clipping threshold. In order to have the best PAPR reduction, λ has to be deend as follows [START_REF] Jiang | Curve tting based tone reservation method with low complexity for papr reduction in ofdm systems[END_REF] λ = σ 2 a ln N |χ|

(6.6)
where σ 2 a denotes the variance of the modulated signal at each antenna.

Finally, the original frequency-domain clipping-noise associated to the m t -th transmit antenna is e t mt = DF T (ā mt -a mt ). Here, the vector e n , associated to the n-th subcarrier, is collected from the M t vectors e t 1 , e t 2 , ..., e t Mt .

In order not to damage the transmission quality (i.e., perfect MUI), the added PCSs {r n } are constrained to lie in the null-spaces of their associated MIMO channel matrices such that they do not disturb the signals received by M r users through the |χ| active subcarriers. In addition, r n has to respect the out-of-band constraint such that it has to be set to zero on the guard-band, as shown by the following equation

r n = e n , n ∈ χ r n = 0 Mt×1 , n ∈ χ c . (6.7)
Thereby, the precoded version c n = V n r n is added to the precoded data instead of e n , as shown in equation (6.1), where V n represents the n-th MIMO channel null-space.

Due to the reconstruction of the precoded PCSs from their projections onto the MIMO channel nullspaces and the active data subcarriers in χ, it is obvious that the considered PCSs, at each iteration, can be smaller than their associated clipping noises when the traditional clipping and control (CC) method is employed in massive MIMO-OFDM systems. Hence, a regularization factor is needed in order to generate the optimal PCSs, leading then to a fast convergence toward the optimal solution. The regularization factor can be calculated using least-square approximation (LSA), as explained in [START_REF] Li | An improved tone reservation scheme with fast convergence for papr reduction in ofdm systems[END_REF]. It is dened as

p n = mt |c n ||e n | mt |c n | 2 , n ∈ χ (6.8)
Using such regularization factor, the amplitudes of PCSs, c n , generated by LSA, almost equal to those of the original clipping noise e n . Then, we transmit p n V n r n instead of V n r n . Obviously, it may reduce the number of iterations to achieve the optimal PAPR reduction.

Linear Data and PCS Precoders for low-PAPR massive MIMO-OFDM

In this section, I describe two developed algorithms that consist of iterative CC method with the peakcanceling signals constrained in the null-spaces of the associated MIMO channel matrices. The goal is to design signals {x n } which satisfy the MU precoding (i.e., in-band and out-of-band constraints) and meanwhile their time-domain signals have low PAPR. It is worth noticing that the proposed formulation can perform the PAPR reduction problem and the MU precoding, jointly (1st algorithm) or separately (2sd algorithm). Note that MU precoding and PAPR reduction are using two orthogonal spaces (beamforming space for data transmission and null-space for PAPR reduction). Therefore, we developed two algorithms that are summarized in subsection 6.2.3 and 6.2.4 ,respectively.

6.2.3 1st Algorithm: Gradient-iterative method based MU-PP-GDm algorithm

In order to reduce the computational complexity required for data and PCS precoders, the algorithm MU-PP-GDm, which is introduced in [J15], adopts gradient-iterative method for data and PCS precoding.

Here, the null-spaces of channel matrices {V n } are computed using the singular value decomposition (SVD) as explained in [J15], where the

{V n } are of dimension M t × (M t -M r ) instead of M t × M t .
Furthermore, MU-PP-GDm aims at computing r n such that V n r n is very close to e n . thereby, it is equivalent to nd the solution rn according to the following simple convex optimization problem, in equation (6.9), with taking into consideration in-band and out-of-band constraints.

minimize {rn} G(r n ) = V n r n -e n 2 2 , n ∈ χ subject to s n = H n d n , n ∈ χ e n = 0 (Mt-Mr)×1 , n ∈ χ c (6.9)
In this algorithm [J15], the joint MU precoding and PAPR reduction is achieved by alternately repeating the PAPR reduction process using the CC method, restoring the restrictions on the PAPR reduction signal components using null-spaces of MIMO channels and performing MU precoding. To make the problem tractable, the equality constraint

s n = H n d n , is relaxed as minimize {rn, dn} J(d n , r n ) = F (d n ) + G(r n ), n ∈ χ subject to dn = 0 Mt×1 , n ∈ χ c rn = 0 (Mt-Mr)×1 , n ∈ χ c (6.10)
The search directions of the steepest descent method at the iterate d

n and r (l) n are determined by the negative gradient of J at, respectively, d

n (denoted by -∇ l d J(d

(l) n , r (l)
n )) and r

(l) n (denoted by -∇ l r J(d (l+1) n , r (l)
n )), where

∇ l d J(d (l) n , r (l) n ) = 2 L dn H H n H n d (l) n -s n , n ∈ χ (6.11)
and

∇ l r J(d (l+1) n , r (l) n ) = 2 L rn V n H V n r (l) n -e (l+1) n , n ∈ χ (6.12)
where L dn = 2σ 2 max (H n ) and L rn = 2σ 2 max (V n ) are the Lipschitz constants [START_REF] Golub | Matrix Computations[END_REF] for, respectively,

H n d n -s n 2 2 and V n r n -e n 2 2 .
The details of the proposed MU-PP-GDm is summarized in Table Algorithm1. It is followed by a computational complexity analysis of that algorithm. The complexity is expressed in terms of the number of oating point operations (FLOPs). Here, we consider one FLOP as one scalar complex multiplication [START_REF] Hunger | Floating point operations in matrix-vector calculus[END_REF] and neglect the computational complexity of matrix and vector additions. Specically, we consider the number of complex multiplications required at the BS for generating τ precoded data and PCS vectors, where τ is the number of transmit symbols generated in one channel coherence interval.

Algorithm1: The MU-PP-GDm algorithm

Given a set of N modulated complex symbols {s n }.

1: Initialize x (1) n = 0 Mt×1 , e (1)
n = 0 (Mt-Mr)×1 , dx (0) n = 0 Mt×1 , Lx n = 2σ 2 max (H n ), Le n = 2σ 2 max (V 0 n
), and set the maximal iteration number N iter and the momentum term µ 2: for l=1,...,maxI ter do

3: dx (l) n = 2 Lx n H H n H n x (l) n -s n + µdx (l- 1) n , ∀n ∈ χ 4: x (l+1) n = x (l) n -dx (l) n , ∀n ∈ χ 5: a t(l+1) mt
= IF F T x t(l+1) mt , ∀m t = 1...M t 6: e t(l+1) mt = F F T āt (l+1) mt -a t(l+1) mt 7
: r t(l+1) n = r t(l) n -2 Lr n V n H V n r (l) n -e (l+1) n
, ∀n ∈ χ

8: p n = k |Vnr (l+1) n ||e (l+1) n | k |Vne (l+1) n | 2 , ∀n ∈ χ 9: x (l+1) n = x (l+1) n + p n V n r (l+1) n
, ∀n ∈ χ 10: end for 11: return {x n = x (Niter+1) n } Hence, using the MU-PP-GDm algorithm only matrix-vector multiplications are performed and no matrix inversion or matrix-matrix multiplication is required. One can observe that the precoded data vector d n can be expressed as

d (l) n = H H n s n , l = 1 H H n (H n d (l-1) n ), 2 ≤ l ≤ N iter , (6.13)
where l denotes the iteration index. Hence, it requires τ |χ|M t M r (2N iter -1) FLOPS to compute the precoded data vectors for τ |χ| data symbols. Concerning PCS precoding, τ |χ| M t (M t -M r) + M 2 t + 2M t N log(N ) complex multiplications are required at each iteration. Thereby, the overall complexity required by MU-PP-GDm to compute both data and PCS precoded vectors is given by equation (6.14).

C M U -P P -GDm = τ N iter 2M t N log(N ) + 2|χ|M 2 t -2|χ|M t M r (6.14)

2sd algorithm: disjoint MU precoding and PAPR reduction

Contrary to the 1st algorithm, which performs jointly MU precoding and PAPR reduction, this algorithm aims at performing, rst, MU precoding and then PAPR reduction over the iterative CC method. The algorithm is summarized in Table Algorithm2.

Algorithm2: disjoint MU precoding and PAPR reduction Given a set of N modulated complex symbols {s n ∈ C Mr×1 }.

1: Set d n = 0 Mt×1 , n = 1, ...,
a t(l) mt = IF F T x t(l) mt , ∀m t = 1...M t 6: e t(l) mt = F F T āt(l) mt -a t(l) mt 7: r (l) n = e (l)
n , for n ∈ χ and r

(l) n = 0 Mt×1 , for n ∈ χ c 8: p n = m t |Vnr (l) n ||e (l) n | m t |Vnr (l) n | 2 , ∀n ∈ χ 9: x (l+1) n = x (l)
n + p n V n r (l)
n , ∀n ∈ χ 10: end for 11: return {x (N iter+1) n

}

Looking at the proposed algorithm, it computes the precoded data vectors in Step 2, the clippingnoises in Steps 5 and 6 and its constrained version in Step 7. Finally, it updates, in Step 9, the transmitted frequency-domain precoded vectors {x n } by adding the scaled precoded PCS vectors {p n V n r n }. One can note that its computational complexity is dominated by Steps 2, 5, 6 and 9. In the following three subsections, we analyze the computational complexity of the proposed algorithm using dierent data and PCS precoder designs, to compute {W n s n } (Step 2) and {p n V n r n } (Step 9).

Computation of

Wn using M-POLY as in (6.20) dn is computed using Horner's implementation as in (6.28) Computation of Vn using matrix inversion as in (6.17) Complexity is given in (6.18) is given in (6.31)

A. RZF data and OPNS PCS precoders (RZF-OPNS)

For data precoding, the regularized zero-forcing (RZF) precoder is the most widely used solution for the optimization problem in (6.35), which is given by

W n = H H n H n H H n + ξ 1 I Mr -1 , ∀n (6.15)
where ξ 1 is a regularization constant.

It can be seen that the computational complexity required, in one channel coherence interval, for data precoding using RZF is comprised of the complexity required for computing one precoding matrix and τ precoded data vectors, for each active subcarrier. Generating such precoding matrix requires, for |χ| active subcarriers, 2M t M 2 r + M 3 r |χ| FLOPs. Then, τ |χ|M t M r FLOPs are required to perform the vector-matrix multiplications and to generate τ |χ| precoded data vectors. Finally, the total computational complexity required by RZF data precoder is

C RZF = 2M t M 2 r + M 3 r + τ M t M r |χ| (6.16)
Concerning PCS precoder at the n-th subcarrier, the PCS is designed to lie into the null-spaces of the estimated channels between all M r users and the BS. Then, the OPNS V n is given by

V n = I Mt -H H n H n H H n -1 H n , ∀n (6.17)
which has rank M t -M r and exists only if M r < M t .

To compute the precoding matrices {V n } for all activated subcarriers in χ, which are computed one time in one coherence interval, we require 3M t M 2 r + M 3 r |χ| FLOPs. In the loop of the proposed algorithm, the computing of τ PCS precoded vectors entails 1) the computing of the clipping noises {e n } by the operation clipping and control and the N -point IDFT, which has a complexity of 2M t N log(N ) FLOPs and 2) the projection of {e n } onto the channel null-space matrices {V n } that requires |χ| matrixvector multiplications with a complexity of M 2 t |χ| FLOPs. Hence, the total complexity is

C OP N S = N iter |χ|M 2 t + 2M t N log(N ) , (6.18)
where N iter denotes the maximal iteration number.

The overall complexity of the algorithm when using RZF and OPNS for, respectively, data and PCS precoding is given by equation (6.19).

C RZF -OP N S = |χ| 5M t M 2 r + 2M 3 r + τ M t M r |χ| + N iter M 2 t |χ| + 2M t N log(N ) (6.19)
B. M-POLY based data and PCS precoders (POLY-POLY-Horner)

In order to mitigate the high computational complexity imposed by the previous methods, while achieving good performance, we propose to replace the matrix inversion and matrix-matrix multiplication by matrix polynomial decompositions (M-POLY) to compute the precoded data and PCS vectors.

The proposed M-POLY data precoder, W n , for the n-th subcarrier has the form

W n = 1 √ M t HH n J i=0 w i Hn HH n i , (6.20)
where Hn = 1 √ Mt H n and w = [w 0 , ..., w J ] T contains the real-valued coecients of the M-POLY data precoder, which have to be optimized. It has been shown in [128] [133] that, for M r , M t → ∞, the optimum coecients w do not depend on the fast channel uctuations and can be computed using results from random matrix theory and free probability theory [138] [139]. The optimal coecient vector w minimizes the average mean square error (MSE) between transmitted and received data corresponding to all users. Using the solution provided in [START_REF] Zarei | Low-complexity linear precoding for downlink large-scale mimo systems[END_REF], a closed-form expression for the optimum coecients is dened as

w opt = γΞ -1 Φ, (6.21)
where the elements of matrix Ξ and vector Φ are, respectively, given by

[Ξ] m,n = B 1 B 2 ξ (m+n) + (1 -B 1 B 2 )ξ (m) ξ (n) + B 2 σ 2 b ξ m+n-1 , (6.22)
and

[Φ] m = ξ (m) , (6.23)
where B 1 and B 2 are dened as B 1 = T r(KP) and B 2 = T r((KP) -1 ). Here, P denotes the diagonal power allocation matrix and ξ (m) represents the m-th order moment of the sum of the eigenvalue of matrix Hn HH n , which is dened in closed-form by [ [128], Theorem 2]

ξ (m) = m-1 i=0 m i m i + 1 δ i m , (6.24)
when M r , M t → ∞ with their ratio δ = M r /M t being constant. Finally, γ is a normalization factor such that T r(W n W H n ) = 1 holds.

For the PCS precoding, the proposed M-POLY precoder is given by

V n = I Mt -HH n Q i=0 v i Hn HH n i Hn , (6.25)
where v = [v 0 , ..., v Q ] are the real-valued coecients of the M-POLY PCS precoder, which have to be optimized. The optimization goal is the minimization of asymptotic average PCS (PAPR reduction process) leakage caused to all users. The corresponding optimization problem is formulated as [START_REF] Zhu | Linear precoding of data and articial noise in secure massive mimo systems[END_REF] minimize

{v} βE T r(G n V n V H n G H n ) subject to T r(V n V H n ) = 1/δ -1. (6.26)
The solution of the formulation in (6.26) is provided in [ [START_REF] Zhu | Linear precoding of data and articial noise in secure massive mimo systems[END_REF] Theorem 2] and the optimal coecient vector v opt is given by v opt = Σ -1 Θ, (6.27) where [Σ] m,n = ξ m+n+1 + ξ m+n and Θ = [ξ 2 + ξ, ..., ξ Q+2 + ξ Q+1 ], where is chosen such that T r(V n V H n ) = 1/δ -1 One can note that coecient vector w opt and v opt does not depend on channel estimates, and hence, can be calculated o-line using equations (6.21) and (6.27).

One ecient way to calculate the precoded data and precoded PCS vectors, via the M-POLY precoding scheme, is when using Horner's rule [START_REF] Muller | Design and analysis of low-complexity interference mitigation on vector channels[END_REF]. First, the precoded data vectors, {d n }, can be obtained as where, we rst multiply s n with matrix HH n , then we multiply the result with the channel matrix Hn and nally add s n to the resulting vector. This operation is performed J times and the resulting vector is multiplied by HH n . It can be shown that in order to compute all the precoded data vectors associated to all activated subcarriers, it results in a total complexity of τ (2J + 1)M t M r |χ|.

d n = HH n √ M t w 0 s n +
Using the same way as in (6.28), we can compute {c n } using equation (6.29).

c n = r n -v 0 HH n Hn r n + v 1 v 0 HH n Hn (r n + ...) , (6.29)
where, c n is eciently calculated by rst multiplying r n with the channel matrix Hn , then the re- sulting vector is multiplied with HH n . After adding r n to the latter resulting vector, we repeat these operations Q times. This leads to a complexity of 2(Q + 1)M t M r |χ|. Therefore, with taking into consideration of computing the clipping noises by the clipping and control approach and the N -point IDFT, the computational complexity to compute τ precoded PCS vectors, over N iter iterations, is τ N iter (2M t N log(N ) + 2(Q + 1)M t M r |χ|).

Hence, the overall complexity needed by the proposed algorithm when using the M-POLY approach to compute both the precoded data and PCS vectors is given by equation (6.30).

C P OLY -P OLY = τ [(2J + 1)M t M r |χ| + N iter (2M t N log(N ) + 2(Q + 1)M t M r |χ|)] (6.30)

C. M-POLY data and OPNS PCS precoders (POLY-OPNS)

An alternative to the above mentioned methods is to compute the precoded data vectors using M-POLY as given by equation (6.28) and compute the precoded PCS vectors using the OPNS precoder as explained in subsection (6.2.4). Thereby, the overall computational complexity required by this POLY-OPNS precoding scheme is given by equation (6.31).

C P OLY -OP N S = |χ|(3M t M 2 r + M 3 r ) + τ (2J + 1)M t M r |χ| + N iter (2M t N log(N ) + |χ|M 2 t ) (6.31)

Performance Evaluation

In this section, we carry out simulations to illustrate the performance of the considered low-PAPR massive MU-MIMO-OFDM system. We consider an uncoded OFDM with N = 512 subcarriers (i.e., the number of DFT/IDFT points) and use a spectral map χ, in which |χ| = 128 subcarriers are used for data transmission. We recall that we specify some unused subcarriers at both ends of the used band. These latter serve, in one hand, to ensure that the proposed low-PAPR precoder does not generate any spectrum regrowth. In another hand, it corresponds to L = 4-oversampling in the time-domain in order to measure the PAPR levels accurately. A 16-QAM with Gray mapping is considered. Note that we adopt the suboptimal power allocation P = K -1/2 and instead of transmitting {s n }, we transmit {Ps n }. Moreover, the wireless channel is assumed to be frequency-selective as modeled in (6.4) with L c = 8 taps. All presented results are averaged over 1000 channel realizations.

Complexity-Performance Tradeo of M-POLY Data and PCS Precoders

We start by evaluating the performance of the studied M-POLY data and PCS precoders in order to identify the values of J and Q (see equations (6.20) and (6.25)) that ensures a good complexity-performance tradeo. To this end, we consider a massive MU-MIMO-OFDM system with M t = 500 antennas at the BS and serving M r = 100 single-antenna users to be in a case where the precoding complexity is an issue. In Figure 6.1, we depict the normalized mean square error (NMSE) for the studied M-POLY data and PCS precoders for dierent values of J and Q. One can note that the performance of the M-POLY precoders quickly improves as the number of terms of the two polynomials J and Q increase. Moreover, they can achieve a NMSE of -35dB when J = 5 and Q = 3, which can be a sucient performance needed in practical systems. It is worth to point out that choosing larger values for J and Q gives better performance, however doing so requires more computational complexity. Furthermore, This latter is more sensitive to Q than to J because of the computing of the precoded PCSs depends on the number of iterations as shown by equation (6.30). That is why we vary J from 0 to 10 while Q from 0 to only 3. .2 shows more directly the relationship between the user performance and M-POLY orders J and Q. Hence, we show the bit error rate (BER) versus the signal-to-noise ratio (SNR) for the studied M-POLY data and PCS precoders for dierent values of J and Q and compare them to those of RZF-OPNS precoders. Indeed, we assume that the channel is perfectly known, in order to be in a regime where the RZF-OPNS based data and PCS precoders are perfect (i.e., the RZF achieves excellent transmission quality and the OPNS does not leak any interference) and it serves as a reference. Again, we can see that the M-POLY precoders quickly approaches the performance of the RZF-OPNS precoders as the polynomial orders J and Q increase, and they achieve similar performance to the RZF-OPNS precoders when J = 5 and Q = 3. The proposed M-POLY precoders never outperform the RZF-OPNS ones, which is natural since M-POLY precoding is an approximation of RZF-OPNS.

In the following, we will use these polynomial orders (J = 5 and Q = 3) to, rst, compare the computational complexity of the M-POLY data and PCS precoders with the other studied precoders.

Then, we evaluate its performance in terms of PAPR reduction and hence its capability to make us able to operate the power ampliers with lower IBO. This will enhance the amplier eciency and then the global energy eciency of the studied massive MU-MIMO-OFDM system.

Computational complexities comparison

We start by comparing the computational complexities of the four studied data and PCS precoders, the 'RZF-OPNS', 'MU-PP-GDm' and 'POLY-OPNS' precoders with that the proposed 'POLY-POLY-Horner' precoder based on the Horner's implementation rule.

According the aforementioned closed-form expressions (see section 6.2.2) and the conguration given in section 6.2.5, it is possible to numerically assess the complexities of the studied data and PCS precoders.

In particular, Figs. 6.3 and 6.4 show the computational complexity (in GigaFLOPs) versus the number of users in the cell. Here, the number of BS antennas was assumed to be constant M t = 500, the number of iterations is xed to N iter = 5 and the channel coherence interval is xed to τ = 1 and τ = 10 in Figs. 6.3 and 6.4, respectively. For the given setting, the performance gains in terms of PAPR reduction of the studied precoders are substantial and almost similar. Regarding these results, one can note that the M-POLY data and PCS precoders have a substantial lower computational complexity than the other precoders for M r < M t /5. However, even for larger M r the POLY-POLY-Horner based precoders still have lower computational complexity than the precoders based on matrix inversion like 'RZF-OPNS' and 'POLY-OPNS'. Furthermore, they are preferable as they do not incur the stability issues that may arise in the implementation of the large-scale matrix inversions required for RZF and/or OPNS. It is worth to mention that the 'MU-PP-GDm' algorithm that adopts an alternate data and PCS precoding becomes more interesting (i.e., it has lower computational complexity) than the POLY-POLY-Horner based precoders when the number of users is very large. The break-even point, where 'MU-PP-GDm' outperforms the M-POLY based precoders, is at M r < M t /5.

Performance Evaluation : PAPR reduction

In this subsection, we discuss the convergence rate of the two proposed algorithms based on a sequential design, where the RZF-OPNS, POLY-OPNS and POLY-POLY-Horner are considered, and an alternate design spanned by the MU-PP-GDm approach. Figure 6.5 shows the average PAPR versus the number of iterations for dierent numbers of users. In order to simplify the presentation of results, we plot only the performance of the 'POLY-POLY-Horner' which are similar to the ones given by RZF-OPNS and POLY-OPNS. From these results, we can rst note that POLY-POLY-Horner based precoding yields a larger PAPR reduction gain than the MU-PP-GDm. It can achieve, with only 5 iterations, an average PAPR of 2.8dB, 3dB and 4.5dB when the number of user is, respectively, M r = 25, M r = 100 and M r = 250. Moreover, The PAPR reduction gain is reduced when the number of users is increased and this result is expected because of the null-space, onto which the PCSs are projected, is reduced. This is a substantial PAPR reduction gain with low computational complexity spanned by few number of iterations, motivating then the use of low-cost and low-size radio frequency (RF) components in future wireless massive MU-MIMO-OFDM systems. In the following, we address how this translates to multiuser radio link performance under nonlinear PA units.

Performance Evaluation : multiuser radio link bit error rate (BER)

Here, we evaluate and analyze the multiuser radio link bit error rate (BER) of the proposed POLY-POLY-Horner based precoding and the conventional RZF precoders without PAPR reduction, in the case where both exhibit the same antenna transmit power. Figure 6.7 shows the uncoded BER performance versus the SNR. The RZF precoder with ideal PA units (denoted by RZF ideal PA) is regarded as a benchmark. In order to clearly show the gain achieved by reducing the PAPR of the transmitted signals,

we assume that the PAs are ideally linearized, they behave as soft envelope limiter (SEL), such that only the distortions caused by the saturation exist. It can be clearly seen that the performance of the involved low-PAPR precoder surpasses that of the classical RZF, in all cases. The benet of using the low-PAPR precoder is especially clear from moderate to relatively high SNR. With an IBO of 1dB, the proposed low-PAPR precoder achieves a SNR gain of 4.5dB, compared to the RZF, at BER of 2 × 10 -2 with only 5 iterations. When increasing the IBO, e.g. 3dB, the proposed low-PAPR precoder has signicantly better performance, very close to those of ideal massive MIMO-OFDM, from moderate to high SNR.

Accordingly, the loss of performance due to in-band distortions cannot be compensated by increasing the number of transmit antennas but it needs advanced signal processing techniques (e.g., low-PAPR precoders).

PA-aware Massive MIMO DL systems

In addition to PAPR reduction, a digital predistortion (DPD) technique based PA linearization is primordial. In this regard, some approaches have been introduced, in recent literature, which aim at compensating for PA nonlinear behaviour in massive MIMO systems [START_REF] Abdelaziz | Digital predistortion for hybrid mimo transmitters[END_REF] [142] [START_REF] Yao | A digital predistortion scheme exploiting degrees-of-freedom for massive mimo systems[END_REF]. Nevertheless, the implementation of high-precise DPDs is not suitable for massive MIMO systems due to the large number of DPD modules, which are computationally impractical. In [START_REF] Yao | A digital predistortion scheme exploiting degrees-of-freedom for massive mimo systems[END_REF], a low-complexity architecture based DPDs have been proposed, which updates the precoder to compensate the gap in performance due to the low-precision related DPDs. In [START_REF] Brihuega | Digital Predistortion in Large-Array Digital Beamforming Transmitters[END_REF], authors proposed a DPD based solution that requires only one DPD component per user to linearize an arbitrary number of PAs enabling then the reduction of the complexity associated to the linearization of the dierent used PAs. Nevertheless, the associated computational complexity is still unsatisfying, limiting its practical application in massive MU-MIMO.

In this regard, I have been interested in investigating an extremely low-complexity solution, that parameter (i.e., W coecients) by copying the new estimate parameter of R. Here, the model parameter R is estimated using an iterative algorithm, where the search direction of the steepest descent method at the iterate R k is determined by the negative gradient of the cost function Rrx 2 . Then, the precoder matrix is adjusted as

R k+1 = R k -λ × 2 (R k r k -x k ) r H k (6.34)
where λ is the updating rate.

Proposed Joint MU Precoding and Energy-Eciency enhancement Algorithm

The key idea is to compute the precoded symbols x that satisfy Hy = s. Here, we formulate a simple convex optimization problem by minimizing the mean square error (MSE) between the intended signal s and the amplied precoded signal y through the channel H as follows

minimize ẋ E s -HF (x) 2 subject to E x 2 ≤ P t (6.35)
The problem in (6.35) is not straightforward to address directly because of the nonlinear operation induced by PAs. Since PA input signals are complex Gaussian, one can decompose the nonlinear signal at the PA output into a linear function of the PA input and an uncorrelated distortion term, by using the well-known Bussgang theorem [START_REF] Shaiek | Analytical analysis of ser for beyond 5g post-ofdm waveforms in presence of high power ampliers[END_REF]. Then, we can write the amplied signal in (6.32) as y = Qx + d (6.36) where Q = diag ([q 1 , q 2 , ..., q Mt ]) is the M t × M t square diagonal matrix with elements of {q mt } on the diagonal. Note that q mt is the m t -th PA complex gain and d mt stands for the added zero-mean distortion noise with variance σ 2 d . As we explained in [J05], these NLD parameters (q mt and σ 2 d ) can be analytically computed for any measured or modelled PA.

Substituting (6.36) in (6.33), we have r = HQx + Hd + z (6.37)

Then, the optimization method in (6.35) can be rewritten as

minimize ẋ J(x) = HQx + Hd -s 2 2 subject to x 2 2 ≤ P t (6.38)
The considered optimization problem leads to ecient, yet exible implementation for massive MU-MIMO based systems by avoiding the use of DPDs and enabling low-complexity rst order algorithm that only requires matrix-vector multiplications [J16]. The search directions of the steepest gradient descent (GD) method at the iterate x (l+1) is determined by the negative gradient of the cost function J at x (l) , which is given by ∇ x J(x (l) ) = 2Q H H H HQx (l) + Hd (l) -s (6.39)

The precoded vector is adjusted as given by (6.40). Here, the gradient descent with momentum (GDm) is considered.

x (l+1) = x (l) -∆x (l) (6.40)

where ∆x (l) = λ∇ x J(x (l) , d (l) ) + µ∆x (l-1) . The proposed algorithm, referred to as MU-PNL-GDm, is summarized as follows Algorithm: The MU-PNL-GDm algorithm Given a set of M r modulated complex symbols s.

1: Initialize x (1) = 0 Mt×1 , d (1)
n = 0 (Mr)×1 , ∆x (0) = 0 Mt×1 , and set the maximal number of iterations maxIter, the learning rate λ and the momentum coecient µ 2: for l=1,...,maxI ter do 3: ∆x (l) = 2λQ H H H HQx (l) + Hd (l) -s + µ∆x (l-1) 4: x (l+1) = x (l) -∆x (l) 5: Adjustment of the power of x (l+1) to the desired IBO. 6: d (l+1) = F (x (l+1) ) -Qx (l+1) 7: end for 8: return x (maxIter+1)

Performance assessment and comparison

Table 6.2 shows the MUI and complexity comparison for three dierent values of IBO (0dB and 3dB).

According to these results, one can note that ILA1 can only outperform the EZF (see paper [J16]) in the case when we operate the PA quite far from its saturation region (i.e, IBO=3dB). Otherwise, for low values of IBO, it has the worst MUI performance. The PA input and output are assumed to obey the memoryless modied Rapp model [START_REF] Nokia | R4-163314[END_REF] with parameters G = 16, V sat = 1.9, p = 1.1, A = -345, B = 0.17 and q = 4 [START_REF] Nokia | R4-163314[END_REF]. One can note that by using DPD in the classical way does not have a great interest when the IBO is low. Note that ILA2 and the proposed MU-PNL-GDm, which exploits the excessive DoFs in massive MU-MIMO, provide very good and satisfying performance achieving gains of about 15 and 10dB over the classical ILA1 and EZF, for IBO=0 and 3dB. It is worth to mention that the achieved gain is more pronounced when IBO goes lower. Most importantly, we note that the proposed MU-PNL-GDm scheme requires about 55% of the computational complexity needed by ILA2, when achieving the same MUI performance.

Analysis and Cancellation of Inter-Numerology Interference in Massive MIMO-OFDM Downlink Systems

An essential step, which brings more exibility in the communication system, is the mixed numerologies proposed in 5G New Radio (NR) [START_REF] Zaidi | Waveform and numerology to support 5g services and requirements[END_REF]. Mixed numerologies structures are also included in the 3GPP

NR standardization and are widely studied in literature [START_REF] Lien | 5g new radio: Waveform, frame structure, multiple access, and initial access[END_REF] [147] [START_REF] Zhang | Subband ltered multi-carrier systems for multi-service wireless communications[END_REF] [149] [START_REF] Yazar | Reliability enhancement in multi-numerology-based 5g new radio using ini-aware scheduling[END_REF]. Although, the usage of mixed numerologies signicantly improves the system exibility, there is a lot of interference between users using dierent numerologies and the occurred inter-numerology interference (INI) aects the system

Proposed transmission strategy

We assume a DL scenario, where the M r users can be divided into N U M groups using N U M numerologies, represented by index num, where num = 1, ..., N U M . N num and CP num represent, respectively, the IFFT/FFT size and CP size of group num. For the sake of simplicity and without loss of generality, we present, in this section, results corresponding to two users (M r = 2) belonging to two dierent numerologies (num ∈ {1, 2}). Consequently, we have two channel frequency responses corresponding to the two numerologies, denoted by H(num) ∈ C Mr×Mt×Nnum . Besides, synchronization is achieved over the least common multiplier (LCM) methods [START_REF] Choi | A transceiver design for spectrum sharing in mixed numerology environments[END_REF] [148] [START_REF] Zhang | Mixed numerologies interference analysis and inter-numerology interference cancellation for windowed ofdm systems[END_REF], where

N 1 = N × N 2 , CP 1 = N × CP 2 ,
where N = 2 i and i is an integer. x

mt and x

(2,n) mt are OFDM-modulated symbols on the m t -th transmit corresponding, respectively, to user 1 and user 2. The length of x (1) is N times the length of x (2,n) and all symbols are aligned.

To enable exible management of INI, a new transmission strategy is considered, where we consider two ZF based linear precoding branches [START_REF] Spencer | Zero-forcing methods for downlink spatial multiplexing in multiuser mimo channels[END_REF], one for each numerology. Looking at branch one (dashline block) in Figure 6.9, the rst line of matrix S (1) is the data information vector s (1) for user 1 in numerology 1, while the second line is set to zero aiming to protect user 2. Also, in the second branch (solid-line block), matrix S (2) contains data vector s (2) for user 2 and null-vector is prepared for user 1. Then, each data stream is precoded using ZF, which is designed to cancel completely the Intra-NI between users using the same numerology. Nevertheless, INI between users using dierent numerologies can be occurred and the received signal of user 1 (y 1 ) and the n-th received signal of user 2 (y 2,n ) can be, respectively, given by y

1 [n 1 ] = s 1 [n 1 ] + ini (2,1) [n 1 ] + b 1 [n 1 ], n 1 = 1, ..., N 1 , (6.41) and y 2,n [n 2 ] = s 2,n [n 2 ] + ini (1,2) n [n 2 ] + b 2,n [n 2 ], n 2 = 1, ..., N 2 , (6.42)
where ini (2,1) is INI from numerology 2 to numerology 1 while ini (1,2) n represents INI from numerology 1 to n-th numerology 2 symbol. b 1 and b 2,n are receiver noises whose entries are i.i.d circularly-symmetric complex Gaussian distribution with zero-mean and σ b 2 variance. Thus, the goal is to derive theoretical expressions for these INIs, which will be given in the following.

INI Analysis

Corollary 1: No INI is occurred by large numerology to small one in MN SS massive MU-MIMO-OFDM. An immunity is given to small numerology whether the IFFT/FFT sizes, SCS, channel selectivity, power allocation are, thanks to the ZF based proposed transmission strategy. Thus, we have ini (1,2)

n = 0 n = 1, ...,
ini (2,1) = N n=1 ini (2,1) n , (6.44)
where ini (2,1) n denoted the INI caused by the n-th symbol in numerology 2. Its expression, at the n 1 -th subcarrier in numerology 1 is expressed as ini (2,1) n

[n 1 ] = N1 n 1 =1 N2 n2=1 E n (n 1 , n 1 )Z(n 1 , n 2 ) Mt mt=1 hf (1) 1,mt [n 1 ]v (2,n) mt [n 2 ], (6.45)
where:

v (2,n) mt
is the frequency-domain precoded vector corresponding to antenna m t , as shown in Figure 6.9, hf mr,mt is the channel frequency response between transmitting antenna m t and user m r ,

E n ∈ C N1×N1 =      G (2) 1 W (2) 1 f or n = 1, G (2)
2 ID (2) n W

(2) 3

f or n = 2, ..., N.

(6.46) Z = G (2) 2 W
(2) Remark 1: In a constant channel (i.e., hf

2 ∈ C N1×N2 , G (2)
1 = 0 N1×CP1 DFT N1 ∈ C N1×(N1+CP1) , G (2) 2 = DFT N1 ∈ C N1×N1 , W (2) 1 = IDFT N1 0 CP1×N1 ∈ C (N1+CP1)×N1 , W (2)
3 = IDFT N1 ∈ C N1×N1 , ID (2) n
=    0 T1×(N1/2) 0 T1×(N1/2) I T2 0 T2×(N1-T2) 0 T3×(N1/2) 0 T3×(N1/2)    ∈ C N1×N1 , for matrix ID (2) n , we have                                T 1 = N 1 -(N -n + 1)(N 2 + CP 2 ), T 2 = N 2 + CP 2 + D f or n = 2, ..., N -1 N 2 + CP 2 f or n = N, T 3 = (N -n)(N 2 + CP 2 ) -D f or n = 2, ..., N -1 (N -n)(N 2 + CP 2 ) f or n = N.
,mt [n 1 ] = hf (2) 1,mt [n 2 ] (1) 1
)), transmission of user 1's data is performed with excellent performance. Then, we have ini (2,1) n

[n 1 ] = 0 (6.48) Proof: see [J17].
In contrast to SISO and classical MIMO systems, massive MIMO is able to support mixed numerologies and no INI is generated when the channel is at-fading. This nding is valid only for massive MIMO when the proposed transmission strategy is employed.

Remark 2: Channel selectivity and dierence between N 1 and N 2 increase the ini (2,1) .

In frequency-selective channel case, vector hf (1) 1,mt can be obtained through the interpolation of vector hf (2) 1,mt , where N -1 values are added between every two points. Accordingly, we have hf

(1) 1,mt [(n 2 -1)N + 1] = hf (2) 1,mt [n 2 ], (6.49)
where n 2 = 1, ...N 2 . Therefore, the dierence between hf 1,mr [n 2 ] is closely related to the channel selectivity and the dierence between N 1 and N 2 . The higher selectivity and dierence between N 1 and N 2 are, the higher dierence between the two channel frequency responses, leading to greater interference. Remark 3: Power allocation for dierent users has a direct inuence on the power of interference ini (2,1) .

Here, a simple power allocation scheme is adopted. The power allocated to the m r -th user (p mr ) is proportional to the inverse of its path-loss √ κ mr . Then, the greater large-scale fading in user m r leads to greater transmitting power for that user. This means, if user 2 is farther away from the BS, i.e. κ 2 < κ 1 , user 1 receive more INI because of the increased transmitting power for user 2. For example, when considering two users, instead of transmitting s 1 , we transmit s 1 = s 1 -ini (2,1) . This change permits to improve the transmission of user 1 while it does not damage the transmission of user 2.

Note that In the cancellation process, the estimated ini (2,1) of equation (6.45) can be computed over only several subcarriers on numerology 2 (over a window of length L subcarriers), having the most amount of energy.

Figure 6.10 shows the BER performance of user 1 with and without INI cancellation. One can note that the performance of user 1 is signicantly declined when the path-loss of user 2 increases. For example, we can compare κ 1 /κ 2 = 0 dB and κ 1 /κ 2 = 26 dB. When E b /N 0 = -3 dB, user 1 can achieve Chapter 7

Indoor Localization: From Matrix Completion to Deep Learning

Introduction

In addition to our contributions related to communication technology toward 5G and its emerged applications, I have been interested in researches concerning localization, which is among the most challenging issues related to IoT/mMTC. The position information can be used for target tracking, surveillance applications, guiding autonomous vehicles, etc. The outdoor localization is performed by global positioning system (GPS) which is not adequate for indoor environment. Therefore, several indoor localization methods have been developed where the receive signal strength indicator (RSSI) from wireless access point (anchor node) has attracted lots of attention due to its easy acquisition. These methods are mainly based on Trilateration [START_REF] Yang | Quality of trilateration: Condence-based iterative localization[END_REF] and Fingerprinting [START_REF] Shu | Gradient-based ngerprinting for indoor localization and tracking[END_REF].

Using trilateration, a node (object) determines its coordinates via a geometric method that exploits inter-sensor distances and the coordinates of anchor nodes (installed at known positions). However, it does not achieve good localization precision when it is applied to a few number of available measurement distances to neighboring nodes. This is related to the fact that IoT sensors are not capable of high-power transmission which would not allow measurements with all anchor nodes. As a rst contribution, we investigated the matrix-completion approach to enhance the performance of the trilateration by completing the matrix containing the inter-nodes distances. The developed work is synthesized in Section 7.2.

Fingerprint based localization can achieve high accuracy but needs to pay heavy computational complexity for similarity evaluation of the measured ngerprint to a ngerprints' database constructed oine, making it not adequate for a real-time localization. As a second contribution, we developed a localization framework based on a deep convolutional neural network (CNN) where the localization problem is formulated as radio image-related region classication. In Section 7.3, I give an overview of classical similarity evaluation methods and their performance and then I emphasise the development of the CNN framework. Finally, the outputs of these contributions are resumed in Section 7.4. where ω is the set of known entries.

Let us dene n is the total number of sensor nodes (anchor and unknown nodes) placed in the indoor environment with m nodes with known positions named 'Anchor nodes' and (n-m) sensors with unknown positions. We denote by U i the i-th unknown node, where i = 1, 2, ..., (n -m) and A j the j-th anchor node, where j = 1, 2, ..., m. X, which is the (n × n) Euclidean distance matrix, can be partitioned as given by equation (7.4).

X

= X 11 X 12 X 21 X 22 , (7.4)
where: X 22 contains the exact distances between each pair of anchors. Its entries are {d Aj A j = ||C Ai -C Aj || 2 }, which are the pairwise distance between anchor node (A j ) and anchor node (A j ). Note that C Aj ∈ R

h ij = h ji =    1 if (i, j) ∈ ω 0 otherwise , (7.6)
Let us denote the objective function as

J( X) = f ( X) + λ × l( X), (7.7)
where f (

X) = ||H ( X -X)|| 2 F and l( X) = ||(1 -H) X|| * .
It is worth to point out that the formulated optimization problem can be eectively solved via iterative gradient descent (GD) method and its variants. Then, we developed a simple and ecient algorithm based on many optimization approaches, which are described in the next Subsection. The developed algorithm is summarized in Table 7.1, where V (t) is the update matrix and index t refers to the number of update iteration. Here, we discard the class of algorithms that are computationally very expensive for high dimensional data sets, e.g. the second-order Newton's method [7]. In the following, I give the expression of V (t) related to each method.

Gradient descent (GD)

Gradient descent is an iterative method that aims to nd local minimum of dierentiable cost functions [START_REF] Ruder | An overview of gradient descent optimization algorithms[END_REF]. It is the most common rst-order optimization algorithm in machine learning and deep learning.

GD is based on updating each element of matrix X(t) in the direction to optimize the objective function J( X(t) ). The new parameter V (t) can be adjusted as

V (t) = α∇(J( X(t) )), (7.9)
where α denotes the learning rate from range (0, 1) and ∇(J( X(t) )) refers to the gradient of the cost function with respect to the matrix entries. Its computation is detailed in [START_REF] Njima | Beyond stochastic gradient descent for matrix completion based indoor localization[END_REF] and the update matrix is given by

V (t) = α × (2 × H ( X(t) -X (t) ) + λ × (1 -H) ( X(t) • (( X(t) ) T • X(t) + × I) -0.5 )), (7.10)
where is a regularization parameter.

Note that this update matrix contains two components, referred to as

U (t) = α×(2×H ( X(t) -X (t) ) and W (t) = λ × (1 -H) ( X(t) • (( X(t) ) T • X(t) + × I) -0.5
)). In the following, the update of U (t) will be done using GD while the update of W (t) will be performed using some advanced methods.

Nesterov accelerated gradient (NAG)

To update W (t) with NAG [START_REF] Ruder | An overview of gradient descent optimization algorithms[END_REF], we use the following rule W (t) = µ × W (t-1) + λ × ∇(l( X(t) -µ × W (t-1) )), (7.11) where µ is an updating rate factor. The mathematical derivation are detailed in [START_REF] Njima | Beyond stochastic gradient descent for matrix completion based indoor localization[END_REF], obtaining W (t) = µ × (1 -H) ( X(t-1) • (( X(t-1) ) T • X(t-1) + × I) -0.5 ) + λ × (1 -H) ( Ŷ(t) • (( Ŷ(t-1) ) T • Ŷ(t-1) + × I) -0.5 ), (7.12) Adaptive Gradient (Adagrad) Adagrad [START_REF] Ruder | An overview of gradient descent optimization algorithms[END_REF] update rule is as

W (t) = 1 √ G (t) + × I E (t) , (7.13)
where

E (t) = δl( X(t) )
δ X(t) = (1 -H) ( X(t) • (( X(t) ) T • X(t) + × I) -0.5 ), (7.14) and the memory of squared gradients over time

G (t) = t i=1 (E (i) ) 2 , (7.15)
It is worth to point out that no learning rate is needed. convergence speed. Adam is better compared to other algorithms considering the tradeo between the localization accuracy and convergence speed. Indeed, it has the fastest convergence speed toward the lowest EDM reconstruction error, performing the best localization accuracy. Its localization mean error is 1.2 m and 2.6 m when, respectively, σ c = 2 and σ c = 5. As mentioned before, these results have been done on 10 simulations and the variance is about 0.1 m for each value of sigma shadowing. Therefore, we recommend Adam for such indoor localization schemes.

RSSI Fingerprinting based Indoor Localization

RSSI ngerprinting technique is based on two phases: oine and online. During the oine phase, a radio map is constructed. For known positions named 'reference positions', RSSI measurements received from all access points (APs) are associatred to real coordinates of the location, constructing the 'training database' or the 'radio map'. In the online phase, the test ngerprint is used to estimate the user's location. This technique can be of great interest, especially when used with advanced approaches like similarity evaluation and Neural Networks (NN).

Similarity Evaluation based Indoor Localization

This method consists in comparing the test ngerprint to the whole training base, in order to associate it to the average position of the K-Nearest Neighbors (KNN) [START_REF] Li | A feature-scaling-based k-nearest neighbor algorithm for indoor positioning systems[END_REF]. Therefore, dierent similarity evaluation metrics together with dierent methods of combining the locations of neighbors are possible. In this subsection, we give a comparative study of several combinations of these similarity evaluation and position estimation methods in performing good localization accuracy.

Similarity Evaluation

Numerous similarity evaluation metrics have been tested, which can be divided into to categories: The two coecients of penalty are combined to a single penalty, given by P pen = T +N P penT × P penN . Then, the size of each realization is of (M × T × 2) (Figure 7.3). Constructed radio images needed to be classied and organized, so each image is labeled q, q = 1, 2, ..., Q. Then, N realizations of each sensor node should belong to the associated class. Images are organized into Q folders labeled class1, class2, ..., classQ, each contains the appropriate 3D radio images.

To nd a sensor's position, after acquiring RSSI values and doing the preprocessing of the data, a radio image is constructed having the same dimension and structure of those used for training. This image The implementation of a multi-standard communication system with very wide spectral bands, all with low energy consumption, reduced size and low cost, is not without consequences for the terminal. Indeed, building compact and low-cost radio equipment implies non-ideal hardware (HW) quality. Then, various RF impairments could take place in the used radio transceiver, such as oscillator phase noise, mirrorfrequency interference due to IQ mismatch, Tx Leakage due to an adjacent antenna and non-linear distortion due to power amplier (PA). We are talking about radio imperfections generated by the radio frequency (RF) chain, known as "Dirty-RF" [START_REF] Gunturi | Mitigation of narrowband interference in dierentially modulated communication systems[END_REF]. In addition, crosstalk between antennas may occur, aecting then the transmission quality. These imperfections, which are often neglected, have detrimental eects on massive MIMO communications with multi-carrier waveforms.

In my previous works [J16], the study was limited to the PA non-linearities. A rst objective is to study the impact of Dirty-RF on massive MIMO performance with taking into account the optimization of the multi-carrier waveform as a function of the propagation channel (delay spread, time-varying,...) and, on the other hand, of the type of non-linear imperfections caused by the RF chain. The second objective is the development of reliable digital signal processing based solutions to mitigate RF impairments on both the transmitter and receiver sides of 6G communication systems. This will enable extensive use of low-cost and low-power components.

Optimization and adaptation of MWFs toward future wireless communications 6G

As explained in Chapter 4, all the MWF design-related research works are motivated by the fact that perfect orthogonality, recommended by all the pioneering works on OFDM, is not sucient to guarantee excellent performance, in presence of time and frequency dispersions, commonly encountered in cellular radio-mobile systems. Taking this fact into account, a part of research works [START_REF] Jung | Pulse shaping, localization and the approximate eigenstructure of ltv channels[END_REF] have focused on optimizing the localization in time and frequency of the adopted waveforms, with however relaxing the perfect orthogonality of these waveforms. Nevertheless, satisfying both of antagonistic constraints of perfect orthogonality and good localization is not without impacts on the system performance which remains quite low and disappointing to fulll the requirements of practical radio-mobile networks. Furthermore, the frequency localization metric remains a purely intuitive criterion and does not lead to increased robustness against channel dispersions. Another part of research works aim at reducing the inter-symbol interference and inter-carrier interference, often in a context of identical waveforms at emission and reception. However, doing that has a dramatically impact on the limitation of degrees of freedom in the optimization of practical communication systems. Few works deal with dierent waveforms in transmission and reception, with, however, a preservation of a strict orthogonality, referred to as biorthogonality [START_REF] Han | Wireless multicarrier digital transmission via weyl-heisenberg frames over time-frequency dispersive channels[END_REF]175177].

In 2018, I collaborated with a research team in Mediatron laboratory of Sup'Com school, which have proposed a new approach of waveform optimization [178181]. The proposed approach, referred to as POPS (Ping-pong Optimized Pulse Shaping), permit an eective optimization of waveforms for any channel propagation statistics, with relaxing the constraints of identical waveforms in emission and reception. In my research project, the POPS approach will be judiciously used to perform the adaptive waveform communications (AWC).

In this regard, a rst research activity will be about the modeling of articial imperfections, in terms of time and frequency dispersions, caused by the new 5G+/6G applications. A second part consists in optimizing batteries (or dictionaries) for each service of interest, with taking into account the considered channel statistics. Then, I intend to study the real-time estimation of propagation statistics, during communication, with the application of the most suitable waveform pairs. In this context, I will study the reduction of pilot contamination in massive MIMO systems, in order to simplify the coherent detection of pilot symbols (referred to as Pilot Aided Channel estimation-PACE), known at the receiver side. If the pilots are suciently close in time and frequency (applied to OFDM), the impulse response of the transmission channel can be reconstructed in two-dimensions (2D) through interpolation. In the context of massive MIMO, the principle of channel estimation via interpolation can be extended to spatial domain, leading to a 3D implementation in the grid of PACE pilots.

On the other hand, the pilot contamination problem in massive MIMO, adopting time-division duplex (TDD), can limit their expected capacity performance. For channel reciprocity, in TDD mode, the channel state information (CSI) is obtained at the base station (BS) when transmitting in the uplink. The channel coherence interval is generally not very large to enable the use of orthogonal pilot sequences in dierent cells. The non-orthogonal pilots of adjacent cells contaminate the pilots of the cell of interest. Thus, the channel estimation at each BS contains the channel information of mobile terminals (MTs) in the other cells, together with the ones of its own users. Consequently, when the BS combines linearly the received signal in order to decode the transmitted symbols of its own MTs, it also combines linearly the symbols of users of adjacent cells, leading to an inter-cell interference. This latter does not vanish by increasing the number of BS antennas, even to innity [START_REF] Farhang | Filter bank multicarrier for massive mimo[END_REF][START_REF] Farhang | Pilot decontamination in cmt-based massive mimo networks[END_REF]. One goal will be the implementation of 3D PACE for the channel estimation in massive MIMO applied to MWFs. Then, we will investigate the pilot decontamination in massive MIMO, with dierent MWFs, by extending the blind equalization techniques studied in SISO to multi-cell massive MIMO [START_REF] Savaux | Ofdm/oqam blind equalization using cna approach[END_REF] in order to reduce the eects of channel estimation error caused by the pilot contamination. Moreover, we will investigate the impact of the pilot distribution on the PAPR. In order to overcome this problem, we are investigating a new advanced approach to complement traditional machine learning (ML) methods, the meta-learning [START_REF] Cheng | Analysis and cancellation of mixed-numerologies interference for massive mimo-ofdm ul[END_REF] (learning to learn) approach, which allows lower complexity. The aim is to develop a meta-learning model capable of being generalized with a new conguration that has never been learned during learning (like a new channel matrix, for example).

Specically, we propose to use two neural networks (NN precoder and Meta-NN, as shown by Figure 8.2). The rst one, the NN Precoder, which can be generalized for any data streams (s i ∈ C Mr × 1) for a given channel conguration, is used to generate the precoded data vector (x i ∈ C Mt × 1) such that when nonlinearly amplied and then propagated through the channel, the received data symbols is very similar to the transmitted ones. Note that the NN-Precoder is executed N times per channel coherence time interval, T c (see Figure 8.2). The second NN, the Meta-NN, is used to generate the weights of the NN-Precoder corresponding to a channel conguration. Meta-NN, which can be generalized for any channel conguration, is then executed only one time per channel coherence time. Doing that, we avoid the adaptation of the NN-Precoder and the corresponding computational complexity when the channel changes and we use instead a generalization of the Meta-NN. Preliminary results have been obtained

showing that the proposed meta-model provides the same BER performance as the algorithm, proposed in [J16], but with a lower computational complexity of one order of magnitude.

In this regard, I initiated a collaboration with researchers from the CEDRIC/VERTIGO team, specialists in the eld of machine learning. This collaboration was initiated by the supervision of the Samar Chebbi's master internship (ongoing) and should be pursued by the supervision of a PhD.

ML-aided Multi-carrier Waveform parameters selection for

Future Heterogeneous Network towards 6G

The studied MWFs have shown to overcome the limitations of the today's OFDM technique in supporting asynchronous communications and enabling exible accommodation of various applications/services with dierent requirements. From the exibility perspective, ultra reliability, low latency, high security, high spectral eciency, high energy eciency, and low complexity are some example requirements of dierent service types. Therefore, dierent optimizations need to be done for meeting some of these requirements together while providing complete satisfaction for all users simultaneously. The aim is to develop machine learning approach to help base stations to decide on the waveform parameters of each user using channel information (random maximum excess delay, random maximum Doppler eect, and random service type (eMBB, uRLLC, or mMTC)). The MWF parameters can be the numerology parameters (the subcarrier spacing CP duration, slot duration, maximum allowed bandwidth,... ), the number of numerologies, the waveform processing technique (windowing, ltering, ...). Three performance metrics (SINR, spectral eciency, and exibility) will be considered.

Knowledge-driven Machine Learning for radio access management optimization in Massive MIMO systems

In communication systems, mathematical models for performance's optimization are often available making then the adoption of deep learning more exible than a purely data-driven approach. Indeed, the optimization of these theoretical models is sometimes incompatible with real-time wireless communications, i.e., the complexity and the time to do so might not be compatible with fast time-varying wireless communication scenarios (e.g., user joins/leaves the network, the channel realizations change, time-varying hardware impairments, and so on); In this regard, my project is to study new approaches of machine learning which capitalize on the availability of these theoretical models to reduce the amount of empirical data required and thus the learning complexity. The key idea is to complement purely data-driven machine learning, such as knowledge-driven machine learning [START_REF] Zappone | Model-aided wireless articial intelligence: Embedding expert knowledge in deep neural networks for wireless system optimization[END_REF].

The objective is to develop knowledge-driven machine learning approach, to complement purely datadriven ML, in order to solve radio access problems in networks with massive connectivity and dierent QoS requirements, which is essential in beyond 5G and the future 6G. The work will be dedicated to the eld of radio resource management for real-time energy-eciency maximization in multi-user massive MIMO networks. The goal is to allocate the transmit powers of the users to maximize the network's bit/Joule energy-eciency, which is dened as the ratio between the system sum achievable rate and the total network power consumption. Here, power amplier imperfection will be considered, where a model to formulate the energy-eciency optimization problem is available, but the presence of interference-related PA distortion makes it too complex to be globally solved at an aordable computational complexity. This is especially problematic when the optimization is performed in fast time-varying channel because it causes a considerable complexity overhead that prevents the use of real-time implementations.

System-wide optimisation: Machine learning and distributed intelligence

As a long-term perspectives, I intend to investigate eective ML approaches to achieve global system optimization. A possible global optimization may include the resource allocation policy at the base stations. Routing strategy to be applied to the dierent ows crossing the network, scheduling policies in the switches, and transport protocol parameters can also be jointly optimized for the specic context. Nevertheless, such multi-dimensional optimization, which is an interesting task, is impossible to solve directly in real-time using traditional optimization methods. Therefore, I believe that ANN based knowledge-driven deep learning can indeed help the development of an innovative scalable approach to the above problem. This multi-level model is a very advanced topic.

Conclusion

All of the aforementioned research perspectives represent, in one hand, the evolution of some existing works and, on the other hand, investigating new directions, characterizing my future research activities.

These six proposals include developments concerning signal processing for 6G multi-carrier and multiantenna communications, optimization of energy eciency, hardware imperfection problems, resource allocation and machine-learning.

  : Innov'Com laboratory, Sup'Com/University of Carthage, Tunis. Research: Energy-Ecient Multicarrier waveforms based systems: From PA linearityeciency trade-o optimization to machine learning. Since 2010 Associate researcher : CEDRIC laboratory/CNAM-Paris Research: Energy-Ecient Multicarrier waveforms based systems: From PA linearity-Wafa Njima Title: Indoor localization for IoT-sensor systems Date: 2015-2019 (defended in December 2019) Supervision: 40% Funding: Co-tutelle Sup'Com and CNAM Results: 2 journal papers, 3 conference papers Hanen Bouhadda Title: Theoretical BER performance analysis of non-linearly amplied PHC-TASSILI ATOME5+ Title: Energy-Eciency improvement for multi-carrier waveforms based massive MIMO Funding: CMCU PHC-TASSILI Dates: 2019-2022 Role: Supervision of PhD students Partners: CEDRIC/CNAM-Paris, France and LTT, University of TLEM-chine learning based energy-ecient massive MIMO with very low computational complexity. In this regard, I am interacting with Dr. Marin Ferecatu and Dr. Nicolas Audebert, specialist in data science and machine learning, via the supervision of the Samar Chebbi's MSc internship. Collaboration with the LTT laboratory, University of TLEMCEN I am currently collaborating with Prof. Tarek Bendimerad via the PHC-Utique ATOME5+ project on the supervision of the Meryem Benosman's PhD. Visiting Researcher CEDRIC laboratory/CNAM-Paris, Jan. -Oct. 2018 I have been interested in the development of an experimental testbed to study the capability of the most promising multi-carrier waveforms to accommodate the requirements of the futures wireless communications. In this visit, which was granted by the ANR WONG5 project, I collaborated with Prof. Daniel Roviras, Dr. Hmaied Shaiek and Dr. Cristophe Alexandre. In addition, my collaboration with Prof. Michel Terre took place with the supervision of Wafa Njima's PhD. Following this visit, we have been granted by CMCU PHC-TASSILI for the project ATOME5+. Visiting Researcher CEDRIC laboratory/CNAM-Paris, May -Sep. 2016 I have had the opportunity to collaborate with Prof. Daniel Roviras's team to investigate new multi-carrier waveform design addressing the major limitations of the traditional CP-OFDM in challenging new spectrum use scenarios. During this visit, which was granted by the ANR WONG5 project, I participated with Prof. Daniel Roviras and Dr. Hmaied Shaiek in the supervision of Dr. Yahia Medjahdi's postdoc. Invited professor CNAM-Paris, Feb. -Apr. 2016 In the department of Electronique, Electrotechnique, Automatique, Mesures (EPN03) of the CNAM school, I have been invited for three months. During this visit, I have jointly worked with Prof. Daniel Roviras and Dr. Hmaied Shaiek on widely linear equalization for FBMC-OQAM systems via the supervision of Hayfa Fhima's PhD. Moreover, I participated, with Prof. Michel Terre, in the supervision of Wafa Njima's PhD. Collaboration with CEA-Leti, Grenoble In 2016, I was studying the WOLA-OFDM waveform. I collaborated with the Jean-baptiste Dore's team to investigate and compare the performance of the WOLA-OFDM waveform and the one proposed by CEA-Leti, the BF-OFDM. Our collaboration is pursuing, in 2020, with Dr. Dore and Dr. Benoit Miscopin on the study of new outphasing techniques to enhance the eciency-linearity tradeo of RF transmitters. Collaboration with the CentraleSupélec, Renne with Prof. Yves Louet on (1) the evaluation of global power amplier eciency with PAPR reduction for post-OFDM MWFs and (2) Impact of selective channels on post-OFDM waveforms for 5G MTCs. These works were done in the framework of the ANR WONG5 project.

  Collaboration with MEDIATRON laboratory of Sup'Com school, Tunis with Prof. Mohamed Siala and Prof. Fatma Abdelke on the characterization of a new design of PHYDYAS waveforms, namely POPS-PHYDYAS, which is based on the mix of the POPS algorithm and the PHYDYAS waveform. this collaboration took place via the Zeineb Hraiech's PhD. Invited professor CNAM-Paris, Mar. -Jun 2014 in the framework of the PHC-Utique C3 project, I participated in the supervision of Hanen Bouahadda's PhD. The scientic topic was the study of the performance of FBMC-OQAM systems in presence of PA nonlinearities. Visiting Researcher CEDRIC/CNAM-Paris, Sep. -Nov. 2013 In the FP7 EMPHATIC project, the LAETITIA/CEDRIC team was interested in improving the energy-eciency of FBMC-OQAM which was a good candidate to 5G. In this regard, I was invited in the LAETITIA team to investigate new signal processing solutions for PA linearization and PAPR reduction addressing the reduction of FBMC-OQAM systems power-consumption. 1.6.2 Scientic seminars and conferences I participated in the organization of two special sessions in international conferences. Moreover, I was an invited speaker in a special session on 5G MWFs radio access technology. In 2016, I organized an international school on advanced MWFs and 5G networks. I have been also involved as Technical Program Committee member for the IEEE IWCMC 2019 Advances in 5G and Beyond Symposium. In addition, I gave two seminars in French laboratories.

  I spent most of my time in preparing my PhD, I tried to maintain a teaching activity in order to pursue an academic career because of my interest in scientic research and my unmitigated passion for teaching. From 2005 to 2009, I was temporary lecturer at ISI/University of Tunis ElManar. The studies at ISI comprise two graduations, i.e. Licence and Engineer. The Licence level comprises 3 years denoted (L1, L2 and L3) and the Engineer level 3 years, i.e. ING1, M1 and M2. I had the opportunity to teach to undergraduate students (L1, L2 and L3) courses involving some fundamentals of telecommunications and networking. Indeed, I started teaching to students in undergraduate level the course radiowave propagation and Introduction to telecommunications for L1, Digital data transmission and TCP/IP Networking for L2 and Computer networks administration for L3. I taught a labwork for ING1 entitled Communication systems. My teaching time was about 190 HDW per year. It is worth to mention that I kept some of these fundamentals courses in my next statutory teaching period where some evolutions have been naturally appeared. Table 2.1 summarizes my teaching experience as temporary lecturer. 1 The amount of hours are given in hour of directed works (HDW), i.e. 1 hour of lecture = 1.5 HDW and 1 HDW = 1 HLW.

2. 3

 3 Statutory teaching at ISI/University of Tunis ElManar since 2009 Since 2009, I have taught undergraduate and graduate engineering courses at ISI/University of Tunis ElManar. I recall that the studies are divided into two main parts, 3 years in undergraduate level (Licence) and 3 years in a Telecommunications and Networking engineering speciality (1st year (ING1), 2sd year M1 and 3rd year M2). I have mainly taught in the department of Communication Systems and Networking (CSN), where I am committed to create a synergy between teaching and research considering that they are complementary activities continually supporting each other. Since creating such synergy requires a good background on telecommunications and networking fundamentals, I have kept some of the courses that I taught during my PhD with of course some evolutions. After a solid background on these fundamentals is formed, I devote a signicant eort to combine research and teaching, whenever possible, by bringing research into the classroom by teaching recent results to students, especially for graduate level. For example in the courses radiocommunications and advanced digital communications that I teach for graduate engineering level (M1 and M2), I try to assign some creative projects to students, which permit them to implement the studied new algorithms and concepts. My teaching time per year at ISI/University of Tunis ElManar averages 228 HDW. In 2015/2016, I was in sabbatical where I was released from my regular teaching and responsibilities to focus entirely on my research/scholarly interests. During this year, I spent time in organizing a winter school and visiting the CNAM school to participate in some research programmes. Teaching hours are illustrated in

( i )

 i Advanced digital communications In 2014, I introduced a lecture on advanced digital communication techniques for the engineer students in last year. I have taught to the students advanced topics in digital communications. Students have been provided with up-to-date knowledge of the technologies studied for modern communication systems and the principles underlying their design. The course has covered two main areas, advanced multi-carrier waveforms and new MIMO technologies. I teach 30 HDW, per year, of lectures.

  amplitude-shift keying (ASK), phase-shift keying (PSK), frequency-shift keying (FSK), and Quadrature-Amplitude Modulation (QAM). Line codes (NRZ, RZ, AMI, Manchester) and PSD of line codes were addressed. Moreover, I taught matched lter receivers and receiver design, transmission bandwidth, Nyquist pulses, sampling and inter-symbol interference, Gaussian noise, and related error analysis in symbol detection, coding, convolutional codes, decoding,... I am in charge of this course and I have produced slides. I teach (42 HDW per year). I produced the labworks in MATLAB. (iv) Wireless networks protocols This course described fundamental concepts and principles on wireless network technologies such as the IEEE 802.11 wireless LANs and Bluetooth wireless PANs. Concepts regarding WLAN and the IEEE 802.11.x protocols were taught in detail starting from the very basic data communication concepts up to the analysis of the MAC and routing protocols. Laboratory experiments include tools and techniques to monitor, measure, and characterize the performance of wireless LANs as well as the use of network simulation tools to model and evaluate the performance of IEEE 802.11. (v) Computer networks administration From 2009 to 2015, I was in charge of this course, which I taught during my PhD (see description in the previous section), and I have evolved the handout. In particular, I added chapters on trac control via RMON and its corresponding labworks. I taught 2 groups for which 30 HDW per year. (vi) TCP/IP Networking This course is the evolution of the one I taught during my PhD. I am in charge of this course, where some chapters are added such as internet protocol version 6 (IPv6) and routing algorithms, link state and distance vector routing.

Furthermore, I am

  handling, with colleagues (Prof. Daniel Roviras and Dr. Cristophe Alexandre), a labworks for alternating graduate students (M2, nal year), as a practical application project, in radiocommunications where I teach to students hands-on experiences in the design, implementation and evaluation of some techniques deployed in recent generations of wireless communication systems through software dened radios (SDRs). In the academic year 2018-2019, I taught lecture in Basics of digital communications 2 (BDC-II) to students in the International Master of CNAM. This course focused on passband digital communications. The concepts addressed in this course, which was taught in English, are: (1) Study the QAM, PSK, FSK and PSD of modulation formats, (2) Design an optimal coherent receiver for an arbitrary digital modulation format in Gaussian noise, (3) Analyze the bit, symbol, and frame error probabilities for any arbitrary digital modulation format and (4) Equalization techniques (ZF, MMSE) for frequency selective channels.

Figure 3 . 1 :

 31 Figure 3.1: Research topics.

  .1, are described in the following. Machine Learning for energy-ecient communications During my PhD (2005-2009), I was specially studying PA linearization techniques. Indeed, I started working on the development of digital predistortion (DPD) schemes based on neural network techniques to linearize RF transmitters using the cyclically prexed-orthogonal frequency division multiplexing (CP-OFDM) technology. This latter, which has been largely adopted by physical layer (PHY) of today's long term evolution advanced (LTE-A), is very sensitive to PA nonlinear distortions since its time-domain signal has large peak-to-average power ratio (PAPR).

  exploiting new MWFs with a particular attention to the energy consumption. Therefore, my research interests, in this topic, are in two folds: (1) Identifying the most suitable post-OFDM waveforms to the future wireless communications requirements by analyzing their performance in terms of spectraleciency, energy-eciency, OOB radiation, user asynchronicity and complexity. (2) developing new DSP solutions, to mitigate RF impairments, that are more adequate to post-OFDM waveforms, through a set of algorithms and advanced techniques, Massive MIMO systems : Energy-eciency and Hardware-eciency One of the most ul-timate wireless communication technology is massive multiple-input multiple-output (MIMO), where the base stations (BSs) have to be equipped with hundreds of individually controllable RF chains. Here, energy-ecient hardware becomes indispensable to motivate corresponding energy and cost-ecient massive MIMO BS deployments. Therefore, my research activities have been widened to develop DSP solutions for massive MIMO enabling the use of low-end power ampliers that are allowed to operate close to saturation. In particular, I have developed downlink transmission schemes to address the PAPR reduction problem and the mitigation of nonlinear PA distortions in massive MIMO based wireless communications. Furthermore, I have been interested in investigating advanced optimization approaches and machine learning tools in order to improve the energy and hardware eciencies in massive MIMO systems.

  Training and Generalization, have to be performed. During the training process (Figure 3.2(a)), indirect learning architecture (ILA) is applied to obtain direct estimation of the inverse of the AM/AM and AM/PM nonlinearity characteristics. Using the ILA, the PA output signal is used as NN input while PA input signal is considered as desired signal. The error calculated between the NN input and output signals is sent to a learning algorithm that adjusts the NN coecients to make the error getting lower at each iteration. It is worth mentioning that the training process can be performed oine since the PA is stationary. Concerning the generalization process, coecients of the trained NN are recopied on the NNDPD that achieves the predistortion.

Figure 3 . 2 :

 32 Figure 3.2: Block diagrams for training and generalization of DPD with PA.Figure 3.3: Simultaneous DPD updating.

Figure 3 . 3 :

 33 Simultaneous DPD updating.The neural predistorter was a multi-layer perceptron, which has two inputs, namely the I and Q components of the input signal complex envelope. The NN has N h hidden layers and an output layer with two neurones that are the predistorted signals I and Q. Dierent structures have been deployed

Figure 3 .

 3 Figure 3.4 shows, for all methods, the mean square error (MSE) versus the iterations number averaged over 100 simulations. One can note that the MSE in LM decreases much faster toward the best performance compared the other algorithms. It is important to study the computational complexity of the dierent algorithms.

Figure 3 . 4 :

 34 Figure 3.4: MSE vs. iterations number for the dierent studied algorithms.

Figure 3 . 5 :

 35 Figure 3.5: Computational complexity required vs. the MSE goal.

Figure 3 . 6 :

 36 Figure 3.6: Fully connected NN predistorter structure.

Figure 3 . 7 :

 37 Figure 3.7: Linear network + nonlinear network predistorter structure.

Figure 3 .

 3 Figure 3.9 shows the SER performance versus SNR in systems with a linear PA along with nonlinear memory PA without predistortion and a nonlinear memory PA with NN memoryless predistortion, FCNN predistortion, and LN-NLN predistortion.

Figure 3 .

 3 10 and 3.11 represent AM/AM curves of the amplied signal versus input signal without predistortion and predistorted signal versus input signal for two studied predistortions (memoryless NN PD and LN-NLN).

Figure 3 . 8 :

 38 Figure 3.8: SER vs. SNR of OFDM system with predistorter: a 16-QAM modulation is used over 64 subcarriers and IBO=8dB.

Figure 3 . 9 :

 39 Figure 3.9: SER vs. SNR for 16-QAM OFDM with 64 subcarriers at IBO=7dB.

Figure 3 .

 3 Figure 3.10: AM/AM curves for memoryless NNDPD.

Figure 3 .Figure 3 .

 33 Figure 3.11: AM/AM curves for LN-NLN DPD.

Figure 3 . 12 :

 312 Figure 3.12: Research activities and their related funding.

First, I have

  developed a PAPR-aware downlink transmission scheme in an OFDM-based massive MU-MIMO. Linear precoding of data and peak-cancelling signals (PCSs) were employed to reduce the PAPRs of the transmitted signals by exploiting the excess degrees-of-freedom (DoFs) provided by equipping the base station (BS) by a large number of transmit antennas. Specically, we designed PCSs to be added to the frequency-domain precoded data signals, with the goal of reducing the PAPRs of their time-domain counterpart signals. Most importantly, the added PCSs have to lie in the null-spaces of their associated MIMO channel matrices such that they do not cause any multiuser interference (MUI). In this regard, an ecient algorithm was developed, which was based on dierent data and PCSs precoders, and the corresponding achievable PAPR reduction and biterror-rate (BER) performance are analyzed. Moreover, to optimize a tradeo between performance and complexity, linear precoders based on matrix polynomials (M-POLY) and gradient-iterative approaches (published in [J15]) are studied for both data and PCSs precoding. Simulation results reveal that these latter provide similar performance as the regularized zero-forcing (RZF) and orthogonal projection null-space (OPNS) based data and PCSs precoders, while they need much lower computational complexity. The substantial PAPR reduction provided by the proposed algorithm oers interesting insights for the design of energy-ecient massive MU-MIMO-OFDM systems. This work has been submitted to the peer-reviewed IEEE Open Journal of the Communications Society (OJ-COMS) [SJ2].Second, I have investigated the compensation of the PA nonlinear distortion (NLD) in massive MIMO downlink systems. I have introduced a PA-aware precoding approach that exploits the high-dimensional DoFs, allowed by equipping the base station (BS) by a high number of antennas, and performs the precoded signals that when amplied and passed through the channel, guarantee excellent transmission quality. Specically, we formulate the proposed PA-aware precoding approach as a simple convex optimization problem which enables ecient, low-complexity, and reliable algorithm implementations. The simulation results demonstrate the strong potential of the proposed approach in terms of improving the link quality and reducing the required computational complexity. This work has been published in[J16]. Meta-Learning model for PA NLD mitigation in Massive MIMO systems Despite the better performance, in terms of BER and computational complexity, provided by the aforemen-

  scheme was improved and a new INI cancellation scheme was introduced. Our analysis has shown that the INI theoretical model matches the simulation results, and the introduced INI cancellation eciently mitigates the INI and enhances the performance of massive MIMO-OFDM systems. This study was applied to downlink and uplink scenarios that have been published in two peerreviewed journals [J17] and [J18], respectively.

  on matrix completion theory to enhance the trilateration based indoor localization. Specically, the proposed indoor localization scheme is formulated as a simple optimization problem which enables ecient and reliable algorithm implementations. Many approaches, like Nesterov accelerated gradient (Nesterov), Adaptative Moment Estimation (Adam), Adadelta, Root Mean Square Propagation (RMSProp) and Adaptative gradient (Adagrad), have been implemented and compared in terms of localization accuracy and complexity. This work has been published in a peer-reviewed journal[J13] where we demonstrated that the Adam optimizer outperforms all other methods in terms of localization accuracy and computational complexity. Deep Convolutional Neural Network (CNN) for Indoor Localization in IoT-Sensor Systems In order to reduce the complexity of the ngerprinting approach, we have been interested in developing a localization framework that shifts the online prediction complexity to an oine preprocessing step, based on Convolutional Neural Networks (CNN). Motivated by the outstanding performance of such networks in the image classication eld, the indoor localization problem is formulated as 3D radio image-based region recognition. It aims to localize a sensor node accurately by determining its location region. 3D radio images are constructed based on Received Signal Strength

1

  International Mobile Telecommunication for 2020 and beyond 2 Long-Term Evolution In this context, I have been involved in many research projects and have supervised some PhD/Master students with the CEDRIC/LAETITIA team. I was in charge of 1) the energy-eciency enhancement of the studied waveforms, 2) the study and proposition of new MWF design adapted to 5G critical MTC systems and 3) the development of an experimental testbed to evaluate the capability of the notable MWFs to accommodate 5G requirements.This chapter aims to provide a complete picture of the ongoing 5G MWFs I studied and overviews the main researches I developed in work on MWF design. It is organized as follows: Section 6.3 presents preliminary concepts and reveals the 5G waveform design requirements. Section 6.4 provides a brief description of major MWF candidates for 5G and beyond. Author's contribution related to MWF design is presented in Section 5.5. A summary comparison of the MWFs key features is given. Section 5.6

Figure 4 . 1 :

 41 Figure 4.1: 5G MWF design Requirements.

  Yahia Medjahdi I co-supervised with Prof. Daniel Roviras. The proposed MWF called WOLA based circular oset quadrature amplitude modulation (WOLA-COQAM) [C26] has shown better performance than the classical windowed based MWFs conrming the capability of WOLA processing in supporting asynchronous multi-user access.

4. 2 )

 2 . The subcarrier-wise ltering based MWFs, like FBMC-OQAM and FMT, provide the best frequency localization, especially in the far-end PSD, compared to the other MWF candidates. They provide the fastest spectrum decaying and only one subcarrier guard is necessary to achieve very low PSD levels, as depicted in Figure4.3. Note that Lapped-OFDM has lower PSD performance than the aforementioned MWFs due to the shorter prototype lter (K = 2 instead of K = 4 in FBMC-OQAM). Although GFDM is based on subcarrier-wise ltering approach, it does not have excellent frequency localization due to the abrupt transition between GFDM blocks caused by the rectangular window shape in the time domain.WCP-COAM and WOLA-COQAM, despite the time-domain transition between signal blocks, provides better OOB emissions performance compared to GFDM thanks to the performed time-domain windowing.Furthermore, subband-wise ltered MWFs lead to a better time localization with the cost of increasing the OOB emissions compared to the subcarrier-wise ltered MWFs. BF-OFDM and FFT-FBMC provide very good spectral connement thanks to the adopted lter-bank approach. The performance of UFMC and f-OFDM, where a lter is applied to a group of subcarriers, are very similar. We move now to low-complexity MWF based on time-domain windowing, the WOLA-OFDM, oers satisfactory OOB emissions performance (about 20dB compared to CP-OFDM), but its far-end PSD performance remains moderate. Spectral eciency 4 , which is highly aected by the window/lter duration, the shape of the lter, and extra overheads, depends on wether short or long packet sizes. Indeed, well frequency-localized MWFs (FBMC-OQAM and FMT) provide the worst SE performance, in case of very short packet transmissions, due to the long prototype lters. However, this class of MWFs reduces the need for guard bands and 4 SE analysis corresponding to the major 5G MWFs is given in[J09]

Figure 4 . 2 :

 42 Figure 4.2: PSD comparison.Figure 4.3: PSD edge comparison.

Figure 4 . 3 :

 43 Figure 4.2: PSD comparison.Figure 4.3: PSD edge comparison.

Figure 4 . 4 :

 44 Figure 4.4: Asynchronous scenario.

Figure 4 . 5 :Figure 4 . 6 :

 4546 Figure 4.5: Per-subcarrier NMSE against TO.

(4. 11 )

 11 C I (t, τ ) = βi C βi I (τ )e j2πβit .

Figure 4 .

 4 Figure 4.7 shows the performance of the dierent equalizers, i.e., LE, WLE and WL FRESH, in terms of guard-band values. Results are obtained for frequency selective channel whose coecients are chosen randomly and kept constant during the transmission of 10 4 symbols and E b N 0 = 20 dB. For the Fresh equalizer the SO non conjugate and conjugate cyclic frequencies are chosen to be α 1 = 1 T1 and

Figure 4 . 7 ,Figure 4 . 7 :

 4747 Figure 4.7: MSE Performance system with respect to GB (δ f ) in SSE mode: the UNOI symbol dura- tion is twice the UOI one (T 1 = 2T 0 ).

Figure 4 . 8 :

 48 Figure 4.8: Widely linear Fresh equalization scheme.

Figure 4 . 9 :

 49 Figure 4.9: BER performance over a frequency selective channel with 8 taps.

  [START_REF] Ning Qian | On the momentum term in gradient descent learning algorithms[END_REF].a and 4.9.b, respectively.

Figures 4 .Figure 4 . 10 :Figure 4 . 11 : 5 NLD

 44104115 Figure 4.10: Equalizers performances in term of MSE when UOI and UNOI are synchronous.

Figure 5 . 1 :

 51 Figure 5.1: BER performance of FBMC-OQAM in presence of phase oset, Rayleigh at fading channel

Figures 5 .

 5 Figures 5.1.a and 5.1.b provide the FBMC-OQAM BER performance with 16-OQAM and 64-QAM,

Lemma 3 :

 3 With nonlinear PA, the closed-form BER expression of an uncoded M-(QAM or OQAM) based OFDM over AWGN channel (h m0,n0 = 1) is given by

( 5 .

 5 23) (a) AWGN channel,M = 16, φ 0 = π/6. Rayleigh channel, IBO = 6dB, φ 0 = π/3.

Figure 5 . 2 :

 52 Figure 5.2: BER vs E b /N 0 for M-ary (QAM or OQAM) based OFDM, N = 64, PA: Saleh's TWTA model.

Figure 5 . 2 .

 52 Figure 5.2.a and 5.2.b show the BER performance of a non-linearly amplied FBMC-OQAM and OFDM signals transmitted over, respectively, AWGN channel and at-fading Rayleigh one. We can clearly note a very good agreement between the Monte-Carlo simulation results and those obtained analytically (equations (5.22) and (5.23)) for both FBMC-OQAM and OFDM systems. It is worth to mention that the innite series, in equation (5.23), can be truncated to n = 10 and k = 50 terms with negligible loss in precision.

Figure 5 . 3 :

 53 Figure 5.3: DPD architecture.

Figure 5 . 4 :

 54 Figure 5.4: Simplied DPD architecture.

Figure 5 . 5 :

 55 Figure 5.5: CO-NNPD and nonlinear crosstalk in MIMO-OFDM transmitter.

Figure 5 . 6 :

 56 Figure 5.6: MCO-NNPD based on a MLP neural network.

  denotes the memory crosstalk which represents the ltered part of the signal from the other branch. Here a low-pass lter with four poles is considered as {0.3162, 0.153, 0.1, 0.07}. The proposed NN structure is illustrated in Figure5.6. It has two inputs (x 1 and x 2 ) where each one is scattered to I and Q components and then connected to a tap delay line on each branch. All the outputs of the two tap delay lines are fully connected to all neurones of the rst NN hidden layer. Then, we have four outputs representing the I and Q components of the output signals (y 1 and y 2 ). The training algorithm adopted was the Levenberg-Marquardt (LM) one (see equation(5.26)).

Figure 5 . 7 :

 57 Figure 5.7:BER vs E b /N 0 , STBC MIMO OFDM system, BPSK modulation, 512 subcarriers, IBO of 7dB, Rayleigh channel.

Figure 5 . 8 :

 58 Figure 5.8: Second DPD scheme

Figure 5 . 9 :

 59 Figure 5.9: SER vs SNR for OFDM/FBMC system, IBO=6dB, 64 subcarriers, AWGN channel

  w

Figure 5 .

 5 Figure 5.10: CCDF of PAPR comparison of DSLM and classical SLM schemes in FBMC-OQAM with N = 64 and U = [2, 4, 8].

Figure 5 .

 5 Figure 5.11: CCDF of PAPR comparison of DTR and classical TR schemes in FBMC-OQAM with N = 64 and PRT set R = [4, 8, 16].

  information and are orthogonal to the data subcarriers, making the data recovery trivial.

Figure 5 . 12 :

 512 Figure 5.12: Principle of classical combination of PAPR reduction and predistortion by adding signal. Figure 5.13: Ping-Pong Joint Optimization by adding signal.

Figure 5 . 14 :

 514 Figure 5.14: BER performance of an OFDM system with R = 32 for 16-QAM, Saleh's TWTA.

Figure 5 .

 5 Figure 5.15: BER performance of an OFDM system with R = 32 for 16-QAM, Saleh's TWTA.

Figure 5 . 16 :

 516 Figure 5.16: EVM vs iteration number of an OFDM system with R = 32 for 16-QAM, Saleh's TWTA.

Figure 5 . 17 :

 517 Figure 5.17: PSD of an OFDM system with R = 32 for 16-QAM at OBO=3dB, Saleh's TWTA.

5. 7 Figure 5 . 18 :

 7518 Figure 5.18: Overall architecture.

Figure 5 . 20 :

 520 Figure 5.20: PSD performance of dierent WFs using TR (R=16) and DPD.

Figures 5 .

 5 Figures 5.19 and 5.20 depict measured PSD performance comparison of the studied MWFs when SLM and TR are, respectively, performed with DPD. One can clearly see the signicant gain providedby WOLA-OFDM and BF-OFDM compared to CP-OFDM, especially for IBO of 6dB. We can also note that BF-OFDM outperforms WOLA-OFDM due to the better spectrum containment provided by the subband ltering used by BF-OFDM. Further, BT-Gaussian based BF-OFDM[START_REF] Demmer | Block-ltered ofdm: A novel waveform for future wireless technologies[END_REF] provides slightly better performance than PHYDYAS based BF-OFDM. For an IBO of 6dB, the CP-OFDM PSD performance is almost as the one in linear case. As explained in chapter 4, its PSD localization is worse compared to WOLA-OFDM and BF-OFDM.

Figure 4 . 4 .

 44 Figure 4.4. The user of interest (UoI) occupies 7 resource blocks (RBs), about 1.1 MHz bandwidth from 2.0020 to 2.0031 GHz. The interferer user occupies, on each side of the user of interest, 7 RBs of 1.1

Figure 5 . 21 :

 521 Figure 5.21: BER performance of dierent WFs using SLM and DPD, 16-QAM.

Figure 5 .

 5 Figure 5.22: scenario 2: NMSE performance of different WFs when ∆t = 106µs and δ f = 4.883KHz.

3 ) 2 b

 32 where b n ∈ CN 0 Mr , σ 2 b I Mr denotes the Gaussian noise vectors with σ represents the noise variance at one user. Note that G n = K 1/2 H n ∈ C Mr×Mt is the MIMO channel matrix associated with the n-th OFDM subcarrier. Thereby, K = diag{κ 1 , ..., κ Mr } denotes the path-losses from the BS to the M r users. Furthermore, the wireless channel is assumed to be frequency-selective and modeled as a tap delay line with L c taps. The time-domain channel response matrices H t l , l = 1, ..., L c , have i.i.d. circularly symmetric Gaussian distributed entries with zero mean and unit variance. The frequency-domain MIMO channel associated to the n-th OFDM subcarrier, H n ∈ C Mr×Mt , is obtained as

Figure 6 . 1 :

 61 Figure 6.1: NMSE of M-POLY precoding (with different J and Q) for M t = 500, M r = 100, N iter = 5 and 16-QAM.

Figure 6 . 2 :

 62 Figure 6.2: BER of RZF-OPNS precoding and M-POLY precoding (with dierent J and Q) for M t = 500, M r = 100, N iter = 5 and 16-QAM.

Figure 6

 6 Figure 6.2 shows more directly the relationship between the user performance and M-POLY orders J and Q. Hence, we show the bit error rate (BER) versus the signal-to-noise ratio (SNR) for the studied M-POLY data and PCS precoders for dierent values of J and Q and compare them to those of RZF-

Figure 6 . 3 :

 63 Figure 6.3: Computational complexity of dierent linear precoders for a system with M t = 500, N iter = 5 and τ = 1.

Figure 6 . 4 :

 64 Figure 6.4: Computational complexity of dierent linear precoders for a system with M t = 500, N iter = 5 and τ = 10.

Figure 6 . 5 :Figure 6 . 6 :

 6566 Figure 6.5: Convergence rate of PAPR of selsh and collaborative approaches (with dierent M r) for M t = 500.

Figure 6 . 7 :

 67 Figure 6.7: BER of M-POLY precoders (with dierent IBO) for M t = 500, M r = 100 and 16-QAM, in presence of ideally linearized PA.

Figure 6 . 9 :

 69 Figure 6.9: System model of the massive MIMO OFDM downlink with two dierent numerologies: M t transmit antennas at the BS, two single-antenna terminals, two blocks illustrate two dierent numerologies with OFDM of N 1 and N 2 subcarriers.

(6. 47 )

 47 Interested readers are referred to [J17].

  [n 1 ] and hf[START_REF] Zayani | Ecient precoding for massive mimo downlink under pa nonlinearities[END_REF]

Table 6 . 3 :

 63 NMSE (dB) of user of interest with interfering numerology and dierent channels

Figure 6 . 10 :

 610 Figure 6.10: BER performance with and without INI cancellation on user 1: N 1 = 1024, N 2 = 256, κ 1 /κ 2 = 0, 20, 23 and 26 dB.

Figure 7 . 1 :

 71 Figure 7.1: Algorithm details considering the sensor network consisting of 7 sensor nodes from which 3 are anchors [J13]

( 1 )

 1 deterministic methods including the Euclidean distance and the Manhattan distance, (2) probabilistic methods including the Gauss distance and the Kernel method. Let us note by o = (o 1 , o 2 , ..., o D ) the test ngerprint containing received RSSI from D APs and o l = (o l1 , o l2 , ..., o lD ) the training ngerprint corresponding to D APs at position l.The Euclidean distance: It is based on the Minkowski distance of order p[START_REF] Honkavirta | A comparative survey of wlan location ngerprinting methods[END_REF] and the similarity metric is dened asS(o, o l ) = D d=1 (o d -o ld ) 2 ,(7.26)where o j denotes the received RSSI from the d-th AP at a test location and o lj is the he received RSSI from the d-th AP at the l-th training location.The Manhattan distance: The similarity metric is dened as[START_REF] Moreira | Wi-ngerprinting in the real worldrtls@um at the evaal competition[END_REF] S(o, o l ) = D d=1 |o d -o ld |,(7.27)The Gauss method: The similarity metric depends on the detected APs[START_REF] Njima | Comparison of similarity approaches for indoor localization[END_REF]. To compare a test ngerprint o to a training ngerprint o l , we can consider three cases: 1) the AP is detected in the training and test phases, 2) the AP is not detected in the test phase and 3) the AP is not detected in the training phase. In case 1, the probability of the training ngerprint to match the test ngerprint is given by P exp = M M is the number of detected APs in the training and test phases and σ 0 is an adjustable parameter. In case 2 and 3, coecients of penalty are considered for, respectively, T APs not detected in test phase and N APs not detected in training phase. These coecients are, respectively, given by

(7. 31 )

 31 Then, the probability of similarity, P , computed for each training ngerprint is dened asP (o, o l ) = P pen × P exp (7.32) Note that D = M + T + N .The Kernel method: A probability of similarity is assigned to each training ngerprint using the Kernel Gaussian. The probability of similarity is given by[START_REF] Roos | A probabilistic approach to wlan user location estimation[END_REF] P (o, o l ) of the position, which is expressed using latitude and longitude as c t = (lat t , long t ), corresponding to the t-th test ngerprint. This position is computed by combining the positions corresponding of training ngerprints corresponding to the K-nearest neighbors. Three combination methods are used: 1) simple average which consists in averaging the coordinates of the neighbors' locations. 2) weighted average, where we assign a weight to each neighbor's location as given by k .w(k) k w(k) ,(7.35) where the weight can be assimilated to the distance between test and training ngerprints w(k) = 1/S(o, o l ) or their probability of similarity w(k) = P (o, o l ). And 3) using Nadaraya Watson Kernel

Figure 7 . 3 :

 73 Figure 7.3: The structure of the radio images [J12].

8. 1

 1 Optimization of Energy-Eciency toward future wireless communications 6GWhile the 5G is rolling out, academic and industrial researchers have started work on the sixth generation of the radio-mobile network. 100 times faster than 5G, with improved coverage and available everywhere including in space, 6G[START_REF] Docomo | g evolution and 6g[END_REF], whose emergence is expected in ten years, should also nalize the reliability of 5G services (eMBB, mMTC, URLLC) with taking into consideration very low latency and energy consumption. Furthermore, 6G should meet the requirements of future emerging applications (autonomous cars, connected devices also autonomous,...), which require high level of autonomy and have a great awareness of the environment and knowledge of the activities and needs of users. Autonomous and intelligent communication systems have the potential to improve overall system performance and reduce the workload associated with conguring and managing communication systems. 6G will oer new digital technology perspectives. Nevertheless, the complexity of the future 6G will exceed the current technology capabilities as well as conventional optimization approaches. Then, a fundamental evolution towards technologies like multi-carrier waveforms and massive MIMO is of paramount importance. In this regard, my research project is to reinforce the development of the composite of two timely concepts, Massive MIMO, exible multi-carrier waveforms, the most promising direction in 6G wireless communications, where energy-eciency, low latency, good reliability and high data rate are of crucial importance.The contribution of my previous work in this context is obvious, leading then to a fruitful contribution. 8.1.1 Study of Hardware Imperfection in Multi-carrier/Multi-antenna based 6G systems

8. 2

 2 Meta-Learning for Energy-Eciency enhancement in Massive MIMO systemsIn the framework of the H2020 MSCA ADAM5 project, we have developed algorithms [J15, J16] to improve the energy-eciency related to power amplication in massive MIMO systems. Several optimization methods have been deployed and compared in terms of performance and complexity. All these methods oer good performance but their complexities remains a major problem to be solved, especially when the channel is fast time-varying and the number of users is large enough.

Figure 8 . 2 :

 82 Figure 8.2: Meta-model for energy-eciency enhancement in massive MIMO systems.

  Linear precoding for energy-ecient Massive MIMO downlink systems Date and place: January 2020 at ETIS, ENSEA, Cergy-Pontoise university,

	Seminars Guest Editor for Special Issue in International Journals Title: France Hindawi Wireless Communications and Mobile Computing, Special Issue: Interference Mitigation for
	Massive IoT Deployments
		Title: RF transmitters with high power eciency and linearity ::digital pre-
	distortion and PAPR reduction:: Date and place: December 2019 at CEA-Leti, Grenoble, France. 1.8 Committee Member
	2012-2018	General Secretary of the Tunisian Association for Scientic Innovation and Technology
		Title: Experimental testbed for Multicarrier Waveforms performance evalua-(TASIT)
	tion Date and place: June 2018 at CentraleSupelec, Renne, France. PhD Qualication Committee Member at Innov'COM laboratory of Sup'Com school Teaching activities 2013-present 1.9 Certications 1.6.3 Awards Articial Intelligence Certication, CentraleSupelec, Paris, France, 2019. I have been awarded a H2020 Marie Sklodowska-Curie Individual European grant for my ADAM5 project proposal. CISCO CCNA Exploration Certication, Sup'Com, Tunisia, 2009. 2.1 Introduction
	1.7 Scientic Outreach 1.10 Publications
	Participation to PhD defense committee
	Krishna Bulusu: Performance Analysis and PAPR reduction techniques for lter-bank based multi-
	carrier systems with nonlinear power ampliers
	Date and place: 29/04/2016, CNAM-Paris
	Role: Examinator
		radio access technology
	Event: 14th International Symposium on Wireless Communication Systems Reviewer for International Journals (4 per year in average)
	(ISWCS), Bologna, Italy, 2017. IEEE Communication letters
	General Chair IEEE Wireless Communication letters Title: Winter school: International School on Advanced Waveforms for 5G IEEE Transaction on Wireless Communications
	Networks IEEE transaction on Communications Date and place: 21-23 January 2016, Tunis, Tunisia. EURASIP Journal on Advances on Signal Processing Website: http://www.supcom.mincom.tn/isw5g2016/. EURASIP Journal on wireless Communications and Networking
	Hindawi Wireless Communications and Mobile Computing
	Special Session submitted to Springer Wireless Personal Communications, 2020. Title: PAPR reduction and power amplier linearization for energy-ecient
	Organizer [J17] X. Cheng, R. Zayani, H. Shaiek and D. Roviras, "Inter-Numerology Interference Analy-5G waveforms Event: 13th International Symposium on Wireless Communication Systems (ISWCS), Poznan, Poland, 2016. Reviewer for International Conferences IEEE International Conference on Communications (ICC) sis and Cancellation for Massive MIMO-OFDM Downlink Systems", in IEEE Access, vol. 7,
	IEEE International Symposium on Wireless Communication Systems (ISWCS) pp. 177164-177176, 2019. doi: 10.1109/ACCESS.2019.2957194.
	Title: Post-OFDM waveforms for 5G radio access technology IEEE International Symposium on Signal, Image, Video and Communications (ISIVC) [J16] R. Zayani, H. Shaiek and D. Roviras, "Ecient Precoding for Massive MIMO Down-Event: 14th International Symposium on Wireless Communication Systems (ISWCS), Bologna, Italy, 2017. link under PA Nonlinearities", in IEEE Communications Letters.

IEEE International conference on Wireless Communications and Mobile Computing (IWCMC) Technical Program Committee member for International Conferences IEEE International conference on Wireless Communications and Mobile Computing (IWCMC 2019 Advances in 5G and Beyond Symposium).

1.10.1 Submitted international peer-reviewed journals [SJ1] R. Zayani and D. Roviras, "Low-Complexity Linear Precoding for Low-PAPR Massive MU-MIMO-OFDM Downlink Systems", submitted to IEEE Open Journal of the Communications Systems (OJ-COMS), 2020. 1.10.2 Published international peer-reviewed journals [J19] X. Cheng, R. Zayani, H. Shaiek and D. Roviras, "Analysis and Cancellation of Mixed-Numerologies Interference for Massive MIMO-OFDM UL", in IEEE Wireless Communications Letters 2020. [J18] H. Fhima, R. Zayani, H. Shaiek, D. Roviras, B. S. Chang and R; Bouallegue, "Comparison of Linear, Widely Linear and Fresh Equalizers for FBMC-OQAM systems with dierent Numerologies", doi: 10.1109/LCOMM.2019.2924001. [J15] R. Zayani, H. Shaiek, D. Roviras, "PAPR-aware Massive MIMO-OFDM Downlink", IEEE Access 2019. Chapter 2 In this chapter, I describe my teaching activities that have been dedicated to a variety of students: classes at the undergraduate or graduate engineering level at ISI/University of Tunis ElManar, and also for alternating graduate engineering students (in partnership with industry) at CNAM-Paris during or after business hours. This has allowed me to work with students from a variety of backgrounds who were very diverse both culturally and linguistically. My courses are mainly concerned with digital communications, radio-communications and networking. Section 2.2 summarizes the teaching classes I gave during my PhD while Section 2.3 and Section 2.4 detail my teaching activities since I have been Associate Professor.

Table 2 .

 2 1: Teaching activities during PhD.

	Period	Topic	Level Volume (HDW)
	2005-2009	Computer networks administration (L/DW/LW )	L3	168
	2005-2009	TCP/IP Networking (L/DW/LW)	L2	336
	2006-2009	Digital data transmission (L/DW )	L2	63
	2007-2009	Introduction to telecommunications (L/DW)	L1	42
	2005-2009	Radiowave propagation (L/DW)	L1	84
	2006-2009	Communication systems (LW)	ING1	63
	2005-2009

Table 2 .

 2

	2.
		Table 2.2: Statutory teaching activities.
	Period	Topic	Level Volume (HDW)
	Since 2009	Radiocommunications (L/DW)	M1	294
	Since 2009	Digital communications (L/DW/LW)	M1	294
	2009-2011	Wireless networks protocols (L/DW/LW)	M1	84
	2009-2015	Computer networks administration (L/DW/LW )	L3	360
	Since 2009	TCP/IP Networking (L/DW/LW)	L2	672
	Since 2009

Table 2 .

 2 3: Teaching activities at CNAM. R. Zayani et al., Computer networks administration, L3 level, published locally at ISI/University of

	Period	Topic	Level Volume (HDW)
	Since 2018-2019	Basics of digital communications 2 (L/DW)	M1	42
	Since 2018	Digital communications 1 (LW)	M1	98
	Since 2018	Digital communications 2 (LW)	M1	52.5
	Since 2018	Information theory (LW)	M1	35
	Since 2018	Radiocommunications (Practical project)	M2	60
	Since 2018	Total in HDW		287.5
	2.5 Teaching Material

I have produced course material for multiple educational levels (a package with slides, tutorials and labworks): -R. Zayani, Digital communications, M1 level, published locally at ISI/University of Tunis ElManar. -R. Zayani, Radiocommunications, M1 level, published locally at ISI/University of Tunis ElManar. -R. Zayani, Basics of digital communications 2, M1 level, published locally at CNAM-Paris. -In 2006, I initiated laboratory works in networking ('Atelier réseaux') for undergraduate students (L3 level). I tried to provide to students a global mastering in computer networks. These labs cover various practical experimentations, such as, setting up a computer network, installation, address conguration, troubleshooting, applicative protocol trac analysis (FTP, Telnet, SSH, DHCP, ...), network security policies conguration (VLAN, ACL, Firewall, ...), network management and supervision (SNMP, RMON, HPOpenView) and system administration : Windows, Linux. Laboratory equipment management I have prepared the LW material containing a package with experimentation descriptions that have been dispatched between a group of teachers. The management of the laboratory and equipment was also in my charge. Participation to ISI engineer curriculum committee I was involved the ISI engineer curriculum committee for two times, in 2010 and 2016. These reforms aim at providing innovative training engineer programs with themes of excellence and to create the expertise adequate to the new digital world. Participation to engineer degree projects committee I have participated in many committees and have acted as an examiner on several undergraduate and graduate engineering's degree projects. Chapter 3 In this chapter, I summarize my research activities. Section 3.1 gives an overview of my research topics, a summary of my PhD is given in Section 3.2 and Section 3.3 summarizes my research interests and developed expertise since I have been Associate Professor.

  Although it requires the most signicant number of computation per epoch (because of the Hessian approximation), it requires the lowest computational complexity (Ntops) for a given MSE goal. Moreover, the gain performed by the LM algorithm gets higher as the error goal goes lower.

	Neural Network Predistortion for PA with memory In new generations of wireless communi-
	cations which use OFDM as modulation scheme, memory eects of PA can no longer be ignored due
	to the broadband input signal. Consequently, the NNDPD structure should be improved by adding a
	tap delay line to deal with this imperfection (memory eect). Indeed, we have introduced two NNDPD
	structures. They are the following: (1) A fully connected multi-layer NN (FCNN) predistorter with
	memory (see Figure 3.6). The tap delay input is connected to nine neurons in the hidden layer. The
	output neurons are real and imaginary parts. The fully connected NN aims at simultaneously mitigat-
	ing memory and PA nonlinear eects. (2) A neural network mimetic structure (see Figure 3.7), which
	combines a linear network (LN) and a memoryless nonlinear neural network (NLN). The LN-NLN pre-

Table 3 .

 3 1 summarizes the results of the comparative study of the two-mentioned structures in terms of complexity. The variables Nlearnops and Nrunops are the number of oating operations that each structure requires to learn per epoch and to run, respectively, per OFDM sample.

Table 3 .

 3 1: Complexity comparison of NN predistorter structures.

	Structure Nlearnops LRatio Nrunops RRatio
		LN	57		LN	25
	LN-NLN	NLN	5059	1	NLN	64	1
		Total	5116		Total	89
	FullyCNN	32981	6.45	145		1.63
	3.3 Research interests since 2009
	In this section, I summarize researches I have been leading since 2009. Most of my researches has been fo-

cused on energy-ecient digital signal processing techniques related to new PHY technologies based future generation of wireless communications (5G and beyond). Such promising technologies include enhanced multicarrier waveforms (MWFs) that enable a exible accommodation of various applications/services with dierent requirements, and massive MIMO that employs linear precoding and combining schemes and oers signicant gains in terms of spectral-and energy-eciencies compared to the traditional MU-MIMO. In massive MU-MIMO, impairments such as fading, noise, and interference vanish for very large number of BS antennas. In order to introduce such technologies within 5G based heterogeneous

  Then, f-OFDM is more suitable for the use of dierent numerologies (such as bandwidth, sub-carrier spacing, CP duration, and transmission time interval)[START_REF] Zhang | Mixed numerologies interference analysis and inter-numerology interference cancellation for windowed ofdm systems[END_REF] compared to UFMC with the cost of increased complexity. Contrary to UFMC, f-OFDM maintains the CP leading to a better immunity against the ISI and lower complexity at the receiver. Furthermore, f-OFDM diers to UFMC by adopting identically IFFT/FFT sizes and matched ltering at the receiver. f-OFDM has the advantage of having well frequency-localization, providing low OOB emissions, allowing asynchronous

transmission, supporting dierent numerologies and oering high SE (i.e., requiring less number of guard tones). Although f-OFDM cannot oer excellent spectral containment as per-subcarrier ltered MWFs due to the shorter lter length utilization, it has the advantage to be compatible to MIMO and does not require any SIC algorithm. Nevertheless, its main drawback, compared to the classical CP-OFDM, is the complexity.

Table 4

 4

.1.

5

Complexity analysis corresponding to the major 5G MWFs is given in

[J09]

Table 4 .

 4

				1: The major 5G MWF candidates
	MWF	Design features	Advantages	Disadvantages
	CP-OFDM	no	lter-	Simple FDE, Easy MIMO integration, Flex-	High OOB emission, Sensitive to asyn-
		ing/windowing,	ible frequency assignment, Low implemen-	chronous transmissions, high power con-
		orthogonality in	tation complexity	sumption
		complex domain
	WOLA-OFDM	Tx/Rx window-	All advantages of CP-OFDM, Lower OOB	High power consumption
		ing, orthogonality	emissions compared to CP-OFDM, Good
		in complex do-	robustness against TO and CFO
		main
	UFMC	RB Tx ltering,	Good frequency localization, Shorter lter	No immunity to ISI due to lack of CP,
		orthogonality in	length compared to subcarrier-wise oper-	Higher receiver complexity due to increased
		complex domain	ations (i.e., FBMC-OQAM and GFDM),	FFT size
				Feasible MIMO integration
	f-OFDM	SB Tx/Rx lter-	Flexible ltering granularity, Better fre-	Very high implementation complexity, High
		ing, orthogonality	quency localization, Shorter lter length	latency for long bursts
		in complex do-	compared to subcarrier-wise operations
		main		(i.e., FBMC-OQAM and GFDM), Compat-
				ible with MIMO
	FFT-FBMC	RB Tx/Rx lter-	Very good frequency localization, Good	Higher complexity implementation than
		ing, orthogonality	robustness against TO and CFO, Lower	CP-OFDM/WOLA-OFDM
		in complex do-	implementation complexity (compared to
		main		FBMC-OQAM, GFDM and f-OFDM),
				Compatible with MIMO
	BF-OFDM	RB Tx ltering,	Very good frequency localization, Good	Lower robustness against TO and CFO
		orthogonality in	robustness against TO and CFO, Lower	than FFT-FBMC and WOLA-OFDM
		complex domain	implementation complexity (compared to
				FBMC-OQAM, GFDM and f-OFDM),
				Receiver-like OFDM, Compatible with
				MIMO
	WCP-	SC Tx/Rx lter-	Flexible design, Low latency for long	Higher latency for short bursts, Challeng-
	COQAM	ing, orthogonality	bursts, Good immunity to ISI due to cir-	ing MIMO integration and pilot design,
		in real domain	cular convolution	Higher implementation complexity than
					CP-OFDM
	WOLA-	SC Tx/Rx lter-	All advantages of WCP-COQAM, Good ro-	Higher latency for short bursts, Challenging
	COQAM	ing, Rx window-	bustness against TO and CFO	MIMO integration and pilot design, High
		ing, orthogonality		implementation complexity
		in real domain
	FBMC-OQAM	SC Tx/Rx lter-	Best frequency localization (i.e., lowest	MIMO integration and pilot design are not
		ing, orthogonality	OOB emissions), Good spectral eciency	straightforward, No immunity to ISI due to
		in real domain	(no guard band or CP), Robust against	lack of CP, High implementation complex-
				Doppler eect, Suitable for asynchronous	ity
				transmission
	GFDM	SC Tx/Rx lter-	Flexible design, Low latency for long	Higher latency for short bursts, MIMO in-
		ing, no orthogo-	bursts, Reduced PAPR (depending on the	tegration and pilot design are not straight-
		nality		block size)	forward,High implementation complexity

  . Most importantly, this NN structure is able to compensate, together with the memory PA nonlinearity, other hardware imperfection like I/Q imbalance, DC oset[START_REF] Wang | Augmented real-valued time-delay neural network for compensation of distortions and impairments in wireless transmitters[END_REF]. In

	the following, I give enhanced DPD architectures that, in one hand, are able to take into consideration
	crosstalk between antennas in MIMO systems (Subsection 5.4.1) and, in another hand, are more adequate
	to OQAM based MWFs (Subsection 5.4.2), like FBMC-OQAM, which are more sensitive to phase error
	than classical OFDM.
	5.4.1 Crossover Neural Network Predistorter for the compensation of mem-
	ory crosstalk and PA nonlinearity in MIMO-OFDM systems

Via the supervision of Hanen Bouhadda's master internship, we have proposed a new crossover NN predistorter with memory (MCO-NNDPD) architecture capable to compensate both PA nonlinearity and memory crosstalk eects in MIMO-OFDM transmitters.

Table 5 . 1

 51

		: P2JO Parameters
	i	Current iteration index
	maxIter	Maximum number of iteration
	A	Clipping level

Table 5 .

 5 2: ACPR [dB] performances of an OFDM system with R = 32

	OBO [dB]	4	3.5	3	2.5
	1%P2JO	-30.13	-28.78	-26.98	-24.88
	5%P2JO	-29.08	-27.83	-26.12	-24.20
	CL TR+DPD	-28.37	-26.91	-24.82	-22.84
	w/o corr.	-21.13	-20.53	-19.28	-18.24

  N , the maximal iteration number N iter 2: Compute the precoded data vector d n = W n s n ,

		∀n ∈ χ
	3: Initialize x (1) n = d n ,	∀n
	4: for l=1,...,maxI ter do

5:

Table 6 .

 6 1 summarizes the three studied methods in, respectively, subsections 6.2.4.A, 6.2.4.B and 6.2.4.C.

Table 6 . 1 :

 61 Summary of the three studied methods for data and PCS precoders.

		Data precoding			PCS precoding				Total	complex-
												ity
	RZF-OPNS	Computation of Wn using ma-	Computation of Vn using ma-	is given in (6.19)
		trix	inversion	as	in	(6.15)	trix	inversion	as	in	(6.17)
		Complexity is given in (6.16)		Complexity is given in (6.18)
	POLY-POLY-	Computation	of	Wn	us-	Computation	of	Vn	us-	is given in (6.30)
	Horner	ing	M-POLY	as	in	(6.20)	ing	M-POLY	as	in	(6.25)
		dn is computed using Horner's im-	cn is computed using Horner's im-
		plementation as in (6.28)			plementation as in (6.29)
	POLY-OPNS

Table 6 .

 6 2: Complexity and MUI [dB] performance comparison: 16-QAM, M t = 100, M r = 10,

			IBO=0dB			IBO=3dB
	Scheme	Niter	MUI	Complexity	Niter	MUI	Complexity
	EZF	-	-25.41	127800	-	-29.87	127800
	ILA1	-	-23.39	137200	-	-35.03	137200
	ILA2	3	-43.11	206100	2	-44.65	179400
	MU-PNL-GDm	6	-40.11	118800	5	-42.15	99000
	performance. In [151], authors investigated the INI problem in SISO-OFDM system and underlined its
	causes related system parameters, such as subcarrier spacing (SCS), number of activated subcarriers,

power, etc. Furthermore, a theoretical model was developed in

[START_REF] Zhang | Mixed numerologies interference analysis and inter-numerology interference cancellation for windowed ofdm systems[END_REF]

as a function of frequency spacing between numerologies, overlapping windows and channel frequency response, in SISO Windowed-OFDM system. Recently, authors in

[START_REF] Rajagopal | Multi-user MIMO with exible numerology for 5g[END_REF]

[START_REF] Choi | A transceiver design for spectrum sharing in mixed numerology environments[END_REF]

dealt with mixed numerologies spectrum sharing (SS), where users are sharing the same time/frequency resources. Unlike in non-overlapping mixed numerologies system, it is impossible to avoid interference using windowed/ltered waveforms. In this regard, a new transceiver design considering a mixed numerologies SS system for classical MIMO-OFDM was introduced in

[START_REF] Choi | A transceiver design for spectrum sharing in mixed numerology environments[END_REF]

. To the best of our knowledge, no previous work has studied the INI issue in massive MU-MIMO-OFDM system in the open literature. Furthermore, it is still not yet clear how massive MU-MIMO-OFDM systems behave when mixed numerologies SS transmission is considered. Again within the framework of the H2020 ADAM5 project and via the supervision of Cheng's PhD, I co-supervise with Prof. Daniel Roviras, we have been interested in investigating this INI issue for massive MU-MIMO-OFDM in downlink and uplink scenarios. Through this investigation, new and interesting ndings have been highlighted, having great dierence to the ever proposed SISO-OFDM and classical MIMO-OFDM systems. Indeed, a new transmission/reception strategy has been proposed for DL/UL scenario enabling exible management of MN SS transmission. Moreover, a theoretical INI model has been built for each scenario, which could be a valuable tool to guide 5G system design and parameter selection. Besides, ecient INI cancellation schemes have been developed making massive MU-MIMO-OFDM very attractive to future WCSs [J17][J18].

  Where the total INI is the summation of INI caused by N modulated symbols in numerology 2 and is expressed as

N.

(6.43)

Proof: see [J17]. Corollary 2: By using the proposed transmission strategy in MN SS massive MIMO-OFDM, users using large numerology (i.e. larger IFFT/FFT size) are not totally protected.

Table 6 .

 6 4: NMSE values before and after INI cancellation

	User of					user1 (N 1 = 1024)
	Interest
	Interfering		user2(N 2 = 512)					user2(N 2 = 256)
	User
	κ 1 /κ 2 (dB) original (dB)		corrected		original (dB)	corrected
						(dB)					(dB)
	20	-22			-300				-18	-300
	23	-19			-300				-14	-300
	26	-16			-300				-11	-300
		-12 10	-11	-10	-9	-8	-7	-6	-5	-4	-3	-2

  6.4.3 INI cancellationAs explained above, the transmission corresponding to any numerology is aected only by INI coming from smaller numerology (i.e., users using smaller IFFT/FFT size). Therefore, the proposed INI cancellation scheme aims at adding correcting signal to each numerology's data such that, after precoding and propagating through the channel, the reception is with the best quality. With the aid of the derived INI expressions, it is straightforward to calculate in advance the total INI coming from all other users using smaller numerology and calibrate the transmitted data (i.e., pre-cancel the INI). Specically, the computation of INI always starts from numerology with the smallest IFFT/FFT size. Numerology with the largest IFFT/FFT size can be corrected by suppressing INIs from all the other numerologies.

  3 denotes the location coordinates of anchor node j. 7. INDOOR LOCALIZATION: FROM MATRIX COMPLETION TO DEEP LEARNING108 Given the real Euclidean distance matrix is of low rank (r << n) and taking into account that observations can be aected by noise, the constraint in (7.3) can be relaxed and the optimization problem ||.|| F is the Frobenius norm, || X|| F =

	can be given by
	min X λ × || X|| * + ||H ( X -X)|| 2 F ,	(7.5)
	where λ is a tunable parameter, n i=1	n j=1 |x ij | 2 , and H is n × n
	a matrix whose entries are

X 11 is the (n -m) × (n -m) distance sub matrix between each pair of unknown nodes. X 12 and X 21 , where X 12 = X 21 T , are the distance sub matrices between each pair of anchors and unknown nodes.

It is worth to mention that X 11 , X 12 and X 21 are obtained from RSSI measurements using the log normal shadowing propagation model given by equation(7.2). CHAPTER

Table 7 .

 7

	1: The proposed algorithm for matrix completion
	1. Input: X, H, number max of iterations
	2. Initialization: X(0) , t
	3. while t <number max of iterations
	Update X:
	X(t+1) = X(t) -V (t) ,	(7.8)
	t = t + 1
	end
	4. Return

X

7.2.3 Optimization through GD and its variants for Matrix Completion

In this work several optimization methods were deployed and tested to solve the given optimization problem (i.e., nd the update matrix V (t) at each iteration), Gradient descent (GD), Nesterov accelerated gradient (NAG), Adaptive Gradient (Adagrad), Root Mean Square Propagation (RMSProp), Adadelta and Adaptive Moment Estimation (Adam). Interested readers to these algorithms are referred to

[START_REF] Ruder | An overview of gradient descent optimization algorithms[END_REF]

. CHAPTER 7. INDOOR LOCALIZATION: FROM MATRIX COMPLETION TO DEEP LEARNING109

Acknowledgements I would like to thank the three reviewers -Marie-Laure BOUCHERET (ENSEEIHT/INPT, Toulouse), Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

ISI/Tunis ElManar University in 2009

This dissertation is submitted to Conservatoire National des Arts et

Contents

does not require any DPD, in order to enable ultra-low latency and highly energy-ecient massive MU-MIMO communications. Moreover, the proposed solution should take into consideration both PAPR reduction and DPD. Then, we have introduced, in [J16], a PA-aware precoding approach that exploits the high dimensional DoFs and designs the precoded signals that, when amplied and passed through the channel, guarantee excellent transmission quality. Furthermore, a new formulation have been proposed for the PA-aware precoding approach. It consists in a simple convex optimization problem which enables ecient, low-complexity and reliable algorithm implementation. The developed algorithm is referred to as MU-PNL-GDm.

In order to evaluate the performance of the proposed approach, we adopted a single carrier massive MU-MIMO system where the BS has M t RF PAs and serves M r users. The resulting amplied signals are given by y = [f 1 (x 1 ), f 2 (x 2 ), ..., f Mt (x Mt )] T = F (x) (6.32) where f mt (.) denotes the nonlinear amplication operation of the m t -th PA. Finally, the input-output relationship of the MU-MIMO dwnlink system with nonlinear PAs can be denoted as r = Hy + b (6.33)

The AM/AM and AM/PM conversions are modelled by the modied Rapp model [START_REF] Nokia | R4-163314[END_REF] proposed by the 3GPP for the New Radio (NR) evaluation.

Existing PA linearization techniques: DPD Concept and Solutions

Two indirect learning architectures (ILAs) based on DPD, that were studied in [START_REF] Yao | A digital predistortion scheme exploiting degrees-of-freedom for massive mimo systems[END_REF], are considered for the used massive MU-MIMO system (see Figure 6.8). The rst ILA, referred to as ILA1, the DPD-PA . Using this classical ILA1, a high-precise, i.e. high complexity, DPD structure is required to extend the operation of the PA into weakly nonlinear region, but its practical application for massive MIMO is limited due to the associated computational complexity. In order to enable the use of low-complexity DPD, an improved ILA is proposed [START_REF] Yao | A digital predistortion scheme exploiting degrees-of-freedom for massive mimo systems[END_REF], which referred to as ILA2. The key idea consists in nding the appropriate MU precoder for the adopted DPD. Therefore, the classical ILA1 is modied by incorporating the channel matrix and adaptive ZF precoder (R) in the feedback path as shown in Figure 6.8.(b) and we update the precoder

Matrix Completion based Trilateration for indoor localization

In order to enhance the trilateration method, a high number of pairwise distances between sensors is required. However, obtaining the complete matrix of distances, called Euclidean distance matrix (EDM),

is not straightforward, leading to an incomplete pair-wise distance information. Then, a matrix completion approach is of paramount importance to recover the real EDM from the incomplete one, making the trilateration more interesting and precise. The proposed scheme employs mathematical concepts based on sparse representation and matrix completion theories. Specically, the proposed indoor localization scheme is formulated as a simple optimization problem which enables ecient and reliable algorithm implementations.

System model

In order to assess the performance of our approach, we considered a system (Figure 7.1) where each sensor node uses two steps to compute its position: 1) Rene and complete the Euclidean distance matrix and

2) Compute the coordinates by using the classical trilateration process.

The Euclidean Distance Matrix, referred to as X, contains the distance information between each pair of sensor nodes, which can be built through RSSI measurements.

The value of RSSI can be calculated in dBs as R ml = p e -κ ml + x σc ,

where p e denotes the transmission power, x σc is a Gaussian random variable with zero mean and variance σ 2 c , which describes the random shadowing eects, and κ ml represents the path-loss in dBs which can be obtained using the the log normal shadowing propagation model [START_REF] Michael | Path-loss and shadowing (large-scale fading)[END_REF], given by

where κ 0 is the path-loss value at a reference distance d 0 , is the path-loss exponent, f is the used frequency in MHz, and d is the distance between the m-th and l-th nodes.

Due to the limitation of radio communication range, some RSSI measurements corresponding to dierent sensor nodes are missing. Thus, the matrix X is incomplete (only a small number of X entries are available) and can be aected by noise, leading then to an ineective localization precision. This incomplete EDM can not eectively serve for localization and it should be completed.

Problem formulation

Let us dene the matrix X true as the complete real EDM. Our goal is to reconstruct the complete distance matrix from incomplete and noisy data. The problem of recovering a low rank matrix from a small number of known entries is known as minimizing the matrix rank. Due to the non convexity and non linearity of the matrix rank [START_REF] Fazel | Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization[END_REF], its minimization cannot be solved numerically. Inspired from the theory of Compressed Sensing (CS), Candes and Recht proposed to replace the rank function by the nuclear norm [START_REF] Emmanuel | Exact matrix completion via convex optimization[END_REF]. The optimization problem can be formulated as

Root Mean Square Propagation (RMSProp)

RMSProp [START_REF] Hinton | Neural networks for machine learning lecture 6a overview of mini-batch gradient descent[END_REF] uses only recent past gradients computed in a restricted time. Here, we compute the local average of previous (E (t) ) 2 as

Then, we apply the update

Adadelta Adadelta [START_REF] Hinton | Neural networks for machine learning lecture 6a overview of mini-batch gradient descent[END_REF] update rule is as follow:

we compute gradient E (t) as in equation (7.14).

we compute the local average G(t) of previous (E (t) ) 2

we compute new term accumulating prior updates ( Momentum : acceleration term)

Then, we apply the update

Adaptive Moment Estimation (Adam)

The Adam [START_REF] Kingma | A method for stochastic optimization[END_REF] update rule consists of the following steps.

Compute second gradient moment with local accumulation ( Adadelta/RMSProp)

Compute the rst gradient moment

Compute bias-corrected rst moment and second moment estimate

Update parameters For evaluating the studied solutions based on GD and its variants combined with the trilateration process, we dene the following Localization error metric To verify that trilateration guarantees better localization accuracy when more distance information is provided, we rstly, apply the trilateration with observed distances only. We can easily notice that it introduces the worst localization accuracy compared to tested combinations in both noisy and noiseless environments (Figure 7.2). The localization accuracy is much better when we use a complete EDM than using only the observed distances. Moreover, to apply the trilateration process, at least 3 detected anchors are needed. If this is not the case, the sensor node cannot be localized. This problem can be solved when using a compete EDM containing all pairwise distances. Therefore, the combination of matrix completion technique and trilateration is highly recommended.

The performances of GD and NAG in terms of localization accuracy are very close. So that, their CDF are superimposed for each sigma shadowing value. Adagrad exhibits worse performance than the other optimization methods. This is due to the fact that, it accumulates the squared gradients in the denominator. So, the sum of positive terms keeps growing and the learning rate becomes very small, thus making the algorithm no longer able to ensure updates in order to reach a lower minimum.

Instead of accumulating all past squared gradients, RMSProp and Adadelta use a window of size (ρ) of accumulated past gradients. RMSProp improves a little bit the localization error compared to those introduced by Adagrad in a noiseless environment. But, the result is still worse than those obtained by GD and NAG. The performances of RMSProp and Adagrad are quite close in a noisy environment. They exhibits almost the same CDF performance (Figure 7.2).

Adadelta performs slightly better than GD and NAG for sigma shadowing = 0 and 2. We notice that Adadelta is more aected by noise than other algorithms. Indeed, it provides the best localization accuracy when σ c = 0 and its performance decreases when σ c is higher. In this latter case, Adam, GD and NAG are better than Adadelta in terms of EDM reconstruction error, localization accuracy and

where

Performance assessment

Dierent combinations of the aforementioned similarity evaluation and position estimation metrics are tested. The location error loc error corresponding to all the combinations are given in Table 7.2. The location error is given by loc error = (lat est -lat r ) 2 + (lon est -lon r ) 2 , (7.38) where lat est and lon est are the estimated coordinates, and lat r and lon r are the real coordinates of the test ngerprint.

Looking to these results, one can note that the Nadaraya estimator has almost the worst performance in estimating the real coordinates. Furthermore, the weighted average is the best position estimation metric with deterministic similarity evaluation metrics (Euclidean and Manhattan distances) and the simple average is the best with the probabilistic metrics (Gauss and Kernel methods). Most importantly, the best results in terms of mean location error is obtained when using the Manhattan distance for similarity evaluation and the weighted average of K-nearest neighbors for the position estimation. It is worth to mention that these results were obtained for K = 5-Nearest Neighbors, which is identied to be the most suitable for the tested conguration.

Deep CNN for Indoor Localization

We deal with the issue of indoor localization in the context of IoT networks as a 3D radio imagengerprint-based location recognition problem. Motivated by the outstanding performance of CNN in image classication problems, it is used with taking into account the correlation between dierent RSSI measurements to predict the position of a given node. We propose to split the studied environment into regions, "classes", limited in space, and we construct radio images from measured RSSI ngerprints, which are used as the CNN input data to predict the region index to which belongs the desired node. is fed to the trained model in order to predict the region to which the sensor node belongs. For this, probabilities are assigned to each class, and the predicted class is the one that corresponds to the highest probability.

Deep CNN Architecture Overview

The deep CNN includes specialized NN layers, where each layer ensures a specic function. Here, the structure of the CNN designed for region recognition consists of convolutional layers and pooling layers followed by one or more fully-connected layers. The CNN takes radio images as input and the classes' labels as outputs. The architecture of a CNN is given in Figure 7.4.

In the training phase, the backpropagation algorithm is used. The weights w are updated iteratively in order to reduce the cross-entropy loss function, between the initial prediction (estimated class) and the label (real class). The aforementioned optimisation methods have been adopted, such as the classical SGD [START_REF] Ruder | An overview of gradient descent optimization algorithms[END_REF], RMSProp [START_REF] Hinton | Neural networks for machine learning lecture 6a overview of mini-batch gradient descent[END_REF] and Adam [START_REF] Kingma | A method for stochastic optimization[END_REF]. SGD is the most common rst order optimization algorithm in machine learning and deep learning. RMSProp and Adam are rst order gradient-based optimization of stochastic objective function algorithms. They are advanced methods used to optimize the learning process registered by SGD employing an adaptive learning rate.

Comparison of the Indoor Localization Accuracy of Dierent Approaches

The proposed indoor localization method based on CNN using RSSI ngerprinting is evaluated and compared to standard methods, like trilateration and classical MLP neural networks. All methods use the RSSI information to localize a specic sensor node. For the trilateration technique, it is based on pairwise distances between APs and the node to be localized, requiring at least three known pairwise distances. Traditional MLP NN, referred to as "Classic NN", which is a neural network composed of F c fully connected (FC) layers. Many architectures have been deployed and tested in order to identify the best one, providing the best localization accuracy. Using the "Classical NN", the best localization accuracy 84.75% is obtained with F c = 2 hidden layers with, respectively, 100 and 200. The number of output neurones is 120 corresponding to the number of regions/classes. Then, a deep CNN is deployed

Outputs

The outputs related to work on indoor localization are summarized bellow.