Jialong Duan

Xavier Lagrange

Yue Li

Yanhuang Li

Wenjing Shuai

Hao Lin

Bihong Huang

Xiaoran Jiang

Xiao Song

Nan Feng

Miaojing Shi

Keywords: grouping algorithms. . . . . . . . . . . . . . . . 7.1 Comparison of CSI signaling cost of different transmission strategies . . . C-RAN, RRH, Quantization, BBU, Fronthaul, User grouping, Precoding

On the way to this thesis I received lots of help from different people, I would like to take

Résumé

Le réseau d'accès radio centralisé (C-RAN) peut fortement augmenter la capacité des réseaux mobiles. Cependant, la faisabilité de C-RAN est limitée par le débit considérable engendré sur les liaisons de transport, appelées également fronthaul. L'objectif de cette thèse est d'améliorer les performances de C-RAN tout en considérant les limitations du débit sur le frontaul, l'allocation de ressources et l'ordonnancement des utilisateurs.

Nous étudions d'abord les séparations fonctionnelles possibles entre les têtes radios distantes (RRH) et les unités de traitement en bande de base (BBU) sur la liaison montante pour réduire le débit de transmission sur le fronthaul : certaines fonctions de couche basse sont déplacées du BBU vers les RRH. Nous fournissons une analyse quantitative des améliorations de performances ainsi obtenues.

Nous nous concentrons ensuite sur la transmission coordonnée Multi-point (CoMP) sur le lien descendant. CoMP peut améliorer l'efficacité spectrale mais nécessite une coordination inter-cellule, ce qui est possible uniquement si une capacité fronthaul élevée est disponible. Nous comparons des stratégies de transmission avec et sans coordination inter-cellule. Les résultats de simulation montrent que CoMP doit être préféré pour les utilisateurs situés en bordure de cellule et lorsque la capacité du fronthaul est élevée. Nous en déduisons une stratégie hybride pour laquelle Les utilisateurs sont divisés en deux sous-ensembles en fonction de la puissance du signal. Les utilisateurs situés dans les zones centrales sont servis par un seul RRH avec une coordination simple et ceux en bordure de cellule sont servis en mode CoMP. Cette stratégie hybride constitue un bon compromis entre les débits offerts aux utilisateurs et les débits sur le fronthaul. 6.1 M RRHs serve U UEs during N T subframes. . . . . . . . . . . . . . . . . . 6.2 Process of allocating UEs to be served in different subframes with UDA. . . 6.3 An example of the calculation of one element of the reference matrix. . . . 6.4 Sensitivity of the achievable sum rate towards the chosen grouping of UEs for the channel matrix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 Average achievable sum rate vs. RRH power constraint P W (U = 9, Q q = 4). 6.6 Average achievable sum rate vs. RRH power constraint P W (U = 9, Q q = 4). 6.7 Ratio of increasing average achievable sum rate compared with applying "Random user grouping" vs. number of UEs U (P dBm = 46 dBm, Q q = 4). . 6.8 Running time vs. number of UEs U (P dBm = 46 dBm, Q q = 4). . . . . . . . Mobile data traffic is forecasted by Cisco's Visual Networking Index (VNI) to increase 7-fold between 2016 and 2017, reaching 48.3 EB per month by 2021 [1] as shown in Figure 1.1. Meanwhile, the future 5G system is required to support an increase factor of 10-100 times of the transmission user data rate and 10 -100 times more devices with low delay (millisecond level) [START_REF] Osseiran | Scenarios for 5G mobile and wireless communications: the vision of the METIS project[END_REF]. Therefore, operators need to invest more to increase the mobile network capacity, such as building more base stations (BSs).

Recent studies propose a number of techniques to satisfy the data explosion: Heterogeneous Networks (HetNets) that mix implementation of macro and micro base stations (small cells) [START_REF] Hwang | A holistic view on hyper-dense heterogeneous and small cell networks[END_REF][START_REF] Hu | An energy efficient and spectrum efficient wireless heterogeneous network framework for 5g systems[END_REF], Massive MIMO [START_REF] Larsson | Massive MIMO for next generation wireless systems[END_REF][START_REF] Bjornson | Massive MIMO: ten myths and one critical question[END_REF] that explore spatial diversity and serve several User Equipments (UEs) simultaneously by a very large number of antennas in the same timefrequency resource. However, these techniques are all focused on hot spots where the density of users is high. We would like also to improve the system performance in a macro cellular network. The inter-cell interference largely limits the data transmission, especially for the UEs located in the cell edge areas. Advanced algorithms such as Coordinated Multiple-point (CoMP) have been introduced to manage inter-cell interference. Nevertheless, they need tight coordination between different cells, which cannot be satisfied by current radio access network (RAN). Furthermore, the current RAN also faces other great challenges.

At first, the building of more BSs and implementation of the above-mentioned new techniques result in high cost for mobile operators. Both capital expenditure (CAPEX) and operating expenditure (OPEX) will largely increase. However, operators will not get a proportionate increase in revenue. With tough price competition, the overall mobile service revenue is expected with only 1.5 percent annually growth from 2016 to 2026, in contrast to a decade ago, with 10-15 percent growth [START_REF]The 5G Business Potential -Industry digitalization and the untapped opportunities for operators[END_REF]. The Average Revenue Per User (ARPU) is 1.1 Motivation 3 enables many advanced algorithms that were hard to implement in traditional RAN, such as enhanced Inter-cell Interference Coordination (eICIC), CoMP, network coding to name a few [START_REF] Checko | Cloud RAN for Mobile Networks -A Technology Overview[END_REF]. Furthermore, with clouding and virtualization, the BBUs resources can be easily managed and dynamically allocated on demand. This brings statistical multiplexing gains, energy and resource savings, which reduce the cost. C-RAN can be considered as an instance of Network Function Virtualization [START_REF] Mijumbi | Network function virtualization: State-of-the-art and research challenges[END_REF]. The virtualization of BBU resources can further facilitate scalability and integration of different services [START_REF] Agiwal | Next Generation 5g Wireless Networks: A Comprehensive Survey[END_REF]. With BBUs centralized in the BBU pool, the deployment of remote sites with light RRHs and antennas reduces the cost in construction and operation and provides flexibility in network upgrades [START_REF] Peng | Recent Advances in Cloud Radio Access Networks: System Architectures, Key Techniques, and Open Issues[END_REF]. A quantitative analysis in [START_REF] Suryaprakash | Are heterogeneous cloud-based radio access networks cost effective[END_REF] shows that C-RAN can lead to a 10% -15% CAPEX reduction per kilometer comparing with LTE. It also decreases power consumption as less air conditioners are needed to be installed in distributed sites. China Mobile Research Institute forecasts that C-RAN brings 71% powering savings compared with current RAN architecture [START_REF]The Road Towards Green RAN[END_REF] and ZTE estimates 67% -80% depending on the number of cells covered by the BBU pool [START_REF]Green Technology Innovations white papers[END_REF]. A reduction of 50% OPEX is predicted in [START_REF]The Road Towards Green RAN[END_REF].

The potential remarkable benefits of C-RAN motivate both major mobile operators and equipment vendors regarding it as a competitive realization of mobile network supporting future 5G soft and green technologies. The advocates include mobile operators such as China Mobile, Orange, NTT DoCoMo, Telefonica, etc, and equipment vendors such as Huawei, ZTE, Ericsson, IBM, Nokia, Intel, Texas Instruments, etc [START_REF] Checko | Cloud RAN for Mobile Networks -A Technology Overview[END_REF][START_REF] Peng | Recent Advances in Cloud Radio Access Networks: System Architectures, Key Techniques, and Open Issues[END_REF].

However, the commercial deployment of C-RAN also faces a lot of challenges. A main drawback of C-RAN is the high fronthaul optical transportation network cost [START_REF] Bartelt | Fronthaul and backhaul requirements of flexibly centralized radio access networks[END_REF]23]. The current widely used interface protocol for IQ data transmission between RRHs and BBUs is Common Public Radio Interface (CPRI) [24]. The estimated IQ data throughput exceeds 10 Gbps for a 3 sector BS with 20 MHz 4 × 4 MIMO configuration [START_REF] Chanclou | Optical fiber solution for mobile fronthaul to achieve cloud radio access network[END_REF][START_REF] Pizzinat | Things you should know about fronthaul[END_REF]. A BBU pool which is expected to connect 10 -1000 RRHs [START_REF]The Road Towards Green RAN[END_REF] will need vast transmission bandwidth in the fronthaul. The construction cost of optical network is high, e.g. deploying 1 m of optical fiber in urban environments costs up to 100 dollars [START_REF] Bartelt | Fronthaul and backhaul requirements of flexibly centralized radio access networks[END_REF]. The operators who have free/cheap fiber network resources will be more interested in C-RAN.

From a system point of view, a good C-RAN architecture should provide high bit rate with limited cost, in other words, reduced load on the fronthaul. The objective of this thesis is to maximize the user bit rate while taking into account the fronthaul constraints. Moreover, in C-RAN, it is complex to realize user scheduling, resource allocation, advanced coordinated algorithms with centralized BBUs resources and limited fronthaul resources [START_REF] Ha | Coordinated Multipoint Transmission Design for Cloud-RANs With Limited Fronthaul Capacity Constraints[END_REF]. We also try to solve this problem in this thesis.

Introduction

Contributions

This thesis is divided into two parts. In the first part, we propose new functional splits schemes which move part of functions in BBU to RRH in order to reduce fronthaul throughput. As the functional splits are more complex in uplink than downlink, we focus on C-RAN uplink in this study. In the second part, we study the application of advanced coordinated algorithms in C-RAN to improve network capacity. We go deeper into the study of users scheduling and fronthaul resource allocation. A trade-off between load on the fronthaul and throughput on the radio channel is aimed to be optimized. The major contributions of this thesis are summarized as follows.

Performance Analysis of Several Functional Splits in C-RAN Uplink

Various solutions have been proposed to reduce fronthaul throughput. Fronthaul compression techniques, such as applying non-linear quantization [START_REF]The Road Towards Green RAN[END_REF], distributed source coding [START_REF] Park | Robust and Efficient Distributed Compression for Cloud Radio Access Networks[END_REF], compress sensing based compression [START_REF] Rao | Distributed Fronthaul Compression and Joint Signal Recovery in Cloud-RAN[END_REF], spatial filtering [START_REF] Liu | Optimized Uplink Transmission in Multi-Antenna C-RAN With Spatial Compression and Forward[END_REF], are the first steps to reduce fronthaul throughput. Another envisaged solution is to change the functional split between RRHs and BBUs [START_REF] Wubben | Benefits and Impact of Cloud Computing on 5g Signal Processing: Flexible centralization through cloud-RAN[END_REF]. But few papers have done quantitative analyses on the impact of different functional splits.

We propose two new architectures of RRH-BBU functional splits for the C-RAN uplink. In the proposed architectures, the transmission rate between RRHs and BBUs depends on the mobile network load, while that of current architecture is constant. The performance of different functional splits are analyzed quantitatively. This part of work has been published in VTC 2016 Spring [START_REF] Duan | Performance Analysis of Several Functional Splits in C-RAN[END_REF].

Coordinated Transmission Design in C-RAN Downlink with Limited Fronthaul Capacity

C-RAN facilitates the implementation of CoMP and cooperative resource allocation algorithms. These have the potential to largely improve system throughput. However, their high complexity and the corresponding heavy fronthaul load may counteract all the benefits. In this thesis, we study different transmission strategies and resource allocation in a C-RAN downlink system with RRH power constraints and fronthaul capacity constraints. We firstly compare different transmission strategies without and with cooperation between different cells. Then, to improve the performance of distributed MIMO with Zero-forcing, we propose several low complexity user grouping algorithms. In distributed MIMO, several RRHs serve

Comparison of Different Transmission Strategies

At first, we study the maximum throughput of different transmission strategies in a C-RAN cluster with transmission power constraints and fronthaul capacity constraints. Both transmission strategies without cooperation and with cooperation between different cells are considered. This part of work has been presented in WPMC 2016 [START_REF] Duan | Maximum throughput in a C-RAN cluster with limited fronthaul capacity[END_REF].

Improving Zero-Forcing Performance by User Grouping Algorithms

We apply zero-forcing (ZF) for multi-user joint transmission (distributed MIMO) in a C-RAN downlink system. A number of User Equipments (UEs) located in different cells but in the same cluster are assigned to be served into different subframes. The performance of ZF depends on the channel matrix. By appropriately choosing which UEs are served together in the same time frequency resource, the total transmission rate can be improved. With UE data and channel state information shared in BBU pool, C-RAN facilitates the centralized user scheduling. We propose several low complexity user grouping algorithms to maximize the average achievable sum rate. We firstly study the scenario with unlimited fronthaul capacity. This part of work has been published in ICC 2017 [START_REF] Duan | Analysis of different user grouping algorithms in a c-ran downlink system[END_REF].

Then we extend the work to the scenario with limited fronthaul capacity and with multiple antennas on the UE and on the RRH.

Hybrid Transmission

CoMP can improve the spectral efficiency but requires also much higher fronthaul capacity than without coordination. In this paper, we propose a hybrid transmission that divides the User Equipments (UEs) into two parts: some UEs are served in single RRH mode (limited coordinated scheduling) whereas the others are served in distributed MIMO mode (CoMP joint processing). The division is based on the UEs' statistical Channel State Informations (CSIs). We also propose a new fronthaul transmission scheme to let the UEs served in distributed MIMO mode exploit the fronthaul capacity not used for UEs served in single RRH mode. This largely improves system performance when the fronthaul capacity is low.

Introduction

Outline of The Thesis

The rest of the thesis is organized as follows. We give a survey about RAN architecture evolution, functional splits between BBU and RRH, and CoMP in Chapter 2. The Performances of several functional splits in C-RAN uplink are analyzed in Chapter 3. Then we focus on the studies of transmission strategies and resource allocation in C-RAN downlink. The C-RAN downlink transmission model with RRH transmission power constraints and fronthaul capacity constraints is introduced in Chapter 4. Next, Chapter 5 compares the maximum throughput of different transmission strategies without and with cooperation between different cells in a C-RAN cluster. Chapter 6 presents and analyses several proposed user grouping algorithms which aim to improve the performance of Zero-Forcing. Our proposed hybrid transmission strategy is discussed in Chapter 7. This thesis in concluded in Chapter 8 with summarized results and contributions. In this chapter, some possible future study directions are also presented.

Chapter 2 Evolution towards C-RAN

The RAN deals with all radio-related functionality of the overall mobile network. In this thesis, we focus on the physical layer. Here, we firstly do a brief presentation of the physical layer in LTE. Then the evolution of RAN architecture is introduced, from 1/2G RAN to C-RAN. C-RAN facilitates the implementation of CoMP. Another main part of our work is to analyze the performance of CoMP in C-RAN downlink with limited fronthaul capacity. In this chapter, we also do a brief survey on different CoMP algorithms.

LTE Physical Layer

The physical layer in LTE is responsible for coding, modulation, multi-antenna processing, physical time-frequency resources mapping, etc. In 3GPP LTE, Orthogonal Frequency-Division Multiplexing (OFDM) is used as the transmission scheme. In this section, we firstly present OFDM. Then the duplex schemes are introduced. At last, a brief introduction to the physical layer transmission chain is done.

OFDM

OFDM divides frequency-selective wideband channel into overlapping but orthogonal narrowband subcarriers. As shown in Figure 2.1, a data stream is first separated into N sub-streams and then modulated to N parallel narrowband subcarriers. Each subcarrier has approximately 1/N bandwidth of original wideband channel. The transmission on each subcarrier is narrowband. Thus, each subcarrier is non-frequency-selective. OFDM does not need a complex time-domain equalization to adapt to severe time varying channel conditions, such as multi-path channel in an urban area. We use N total to denote the total number of OFDM symbols (including CP) during one subframe. Without oversampling, the sampling frequency for the OFDM symbols is f s = N total /(1ms). For example, N total = 30720 for a LTE configuration with 20 MHz bandwidth. Then we get f s = 30.72 MHz.

A summary of the subcarriers configuration in LTE with different bandwidths is shown in Table 2.1. The corresponding sampling frequencies are also noted. The value of the minimum percentage of null subcarriers is obtained in the case when all the active subcarriers are occupied.

Evolution towards C-RAN

• one word is added to every 15 data words for control and management [START_REF] De La Oliva | An overview of the cpri specification and its application to c-ran-based lte scenarios[END_REF].

• the digitized data are expanded by 10/8 when 8B/10B Forward Error Correction (FEC) code is applied. In the CPRI specification, 64B/66B FEC is also an option.

D DL = 2 × f s × Q q × 16 15 × 10 8 × N TA . (2.2)
We set Q q = 16. Derived from (2.2) and the last column of Table 2.1, the transmission rates from one BBU to one RRH in different LTE downlink configurations are illustrated in Table 2.2. We can observe that the fronthaul bit rate requirement is huge. The downlink maximum user transmission rate in the radio interface for an LTE configuration with 20 MHz bandwith and 4×4 MIMO is 300 Mbits/s. However, the corresponding required fronthaul bit rate is 5.2 Gbits/s. An LTE network does not always work with full capacity. Assuming a 100 Mbits/s average transmission rate, the required fronthaul bit rate is more than 50 times of the data transmission rate in the radio interface.

Centralized RAN Architecture

The first step towards C-RAN is to move BBUs away from RRHs and centralize them in a BBU pool. This makes a centralized RAN as shown in Figure 2.13. A general Centralized-RAN architecture consists of three main parts: 1) a BBU pool with centralized BBUs, 2) RRHs and antennas located at the remote sites, 3) a transport network which provides a connection between BBU pool and RRHs.

Evolution towards C-RAN

Cells Coordination

In mobile networks, transmissions on the same time-frequency resource interfere with each other. Modern mobile-broadband system Long Term Evolution (LTE) has opted for a reuse factor 1 to maximize the data rates for users close to the Base Station (BS). This increases the chance of facing low signal-to-interference ratios (SIR), especially in the cell edge area. The overall system efficiency and UE fairness can be improved if the interference from adjacent cells can be avoided. This can be done by coordination between different cells. Initial activities related to coordination between different cells are done by introducing Inter-cell Interference Coordination (ICIC) in LTE release 8. CoMP is a more advanced way of dealing with Inter-Cell Interference (ICI). The 3GPP activities on LTE release 10 firstly discussed CoMP and the main related features are introduced in LTE release 11 [40]. Both of ICIC and CoMP will be introduced in the following.

Inter-cell Interference Coordination

In Inter-cell Interference Coordination (ICIC), a UE can report back to its serving eNodeB (eNB) if it suffers strong interference on certain sub-carriers. Then, the eNB communicates with neighboring eNBs through X2 interface. The neighboring eNBs would try not to schedule their serving cell-edge UEs on these sub-carriers. ICIC carries out a reconfiguration on a time-scale of the order of seconds or longer. This is to make it slow enough permitting eNBs exchange signaling through X2 interface.

Different Downlink CoMP Technologies

The basic idea of Coordinated Multi-point (CoMP) is to jointly avoid ICI or turn ICI into a useful signal through more tight and dynamic coordination between different cells.

In this thesis, we focus on the downlink CoMP aspects in a macro cellular network. One RRH covers a macro cell. We define a number of cooperative RRHs as a cluster of RRHs. The cluster of RRHs jointly serve the UEs located in the corresponding macro cell applying with CoMP algotithms. Here, we do a brief introduction to different downlink CoMP types and different transmission schemes from BBU pool to RRHs in a C-RAN applying CoMP.

The downlink CoMP strategies can be generally divided into three different types: dynamic point selection (DPS), coordinated scheduling/beamforming (CB/CS) and joint transmission (JT) [START_REF] Irmer | Coordinated multipoint: Concepts, performance, and field trial results[END_REF][START_REF] Lee | Coordinated multipoint transmission and reception in LTE-advanced: deployment scenarios and operational challenges[END_REF]. The three types will be separately presented in the following. the other hand, with shared CSIs, coherent JT can apply closed-loop MIMO techniques, such as Zero-Forcing (ZF), minimum mean square error (MMSE), dirty paper coding (DPC), etc [START_REF] Karakayali | Network coordination for spectrally efficient communications in cellular systems[END_REF]. This provides coherent JT theoretically a high gain over non-coherent JT as compared in [START_REF] Ball | Performance analysis of closed and open loop mimo in lte[END_REF]. However, coherent JT requires tighter RRHs synchronization than non-coherent JT. The needing for full CSIs available in BBU pool also makes coherent JT more complex than non-coherent JT.

Compared with CB/CS and DPS, coherent JT needs a tighter synchronization between different RRHs. Nevertheless, coherent JT can explore more degree of diversity than CB/CS and DPS to improve system throughput.

Different CoMP downlink algorithms for a cluster of cooperative RRHs are summarized in Table 2 [START_REF] Checko | Cloud RAN for Mobile Networks -A Technology Overview[END_REF] 0.05 ppm frequency and 3 µs timing accuracy [START_REF] Checko | Cloud RAN for Mobile Networks -A Technology Overview[END_REF]; 5 µs timing accuracy [START_REF]Timing and synchronization for LTE TDD and LTE Advanced mobile networks[END_REF] 0.05 ppm frequency and 3 µs timing accuracy [START_REF] Checko | Cloud RAN for Mobile Networks -A Technology Overview[END_REF]; 1.5 µs timing accuracy [START_REF]Timing and synchronization for LTE TDD and LTE Advanced mobile networks[END_REF] 5 µs timing accuracy [START_REF]Timing and synchronization for LTE TDD and LTE Advanced mobile networks[END_REF] 0.02 ppm frequency and 0.5 µs timing accuracy [START_REF] Checko | Cloud RAN for Mobile Networks -A Technology Overview[END_REF]

Transmission Schemes from BBU Pool to RRHs

In recent studies, in downlink, two main strategies of forwarding signals from BBU pool to RRHs to realize CoMP are proposed: data-sharing strategy and compression-based strategy [61]. The two transmission schemes and their comparison are introduced in the following.

Data-sharing

In data-sharing strategy, the channel state informations (CSIs) from all RRHs in a cluster to each served UEs are available in each RRH in the cluster. The user data flow of a given UE is transmitted to the corresponding RRH by the BBU pool. The beamformed signals are locally generated in each RRH.

For CB/CS, an RRH only needs the user flow data of its served UEs. By contrast, all the user flow data of the UEs served by the cluster of RRHs need to be available at each RRH. Thus, JT consumes much more fronthaul capacity than CB/CS in data-sharing strategy.

Compression based

We will introduce both Compression after precoding and compression before precoding. But only compression after precoding is applied in this thesis.

In compression-based strategy, each RRH collects only the CSIs from itself to all the served UEs and forwards them to the BBU pool. The joint processing is done in the BBU pool, e.g. the precoding matrices are calculated in the BBU pool [START_REF] Kang | Fronthaul Compression and Precoding Design for C-RANs over Ergodic Fading Channels[END_REF]. The compressionbased strategy can be further divided to two sub-strategies: compression-after-precoding (CAP) and compression-before-precoding (CBP) [START_REF] Kang | Fronthaul Compression and Precoding Design for C-RANs over Ergodic Fading Channels[END_REF]. In CAP (studied in [START_REF] Kang | Fronthaul Compression and Precoding Design for C-RANs over Ergodic Fading Channels[END_REF]), the user flow data are firstly precoded in BBU pool then quantized before transmitted to the corresponding RRHs. In CBP (studied in [START_REF] Kang | Fronthaul Compression and Precoding Design for C-RANs over Ergodic Fading Channels[END_REF][START_REF] Park | Before/after precoding massive MIMO systems for cloud radio access networks[END_REF][START_REF] Kang | Layered Downlink Precoding for C-RAN Systems With Full Dimensional MIMO[END_REF]), the user flow data and quantized precoding matrices are transmitted to the corresponding RRHs and then the user flow data are precoded in RRHs. A RRH only need the user flow data of its served UEs in CB/CS, while the user flow data of all the UEs served by the cluster of RRHs in JT. Furthermore, BBU pool transmits a smaller precoding matrix to each RRH in CB/CS than in JT. Therefore, JT consumes much more fronthaul capacity than CB/CS in CBP, however not significant in CAP.

A simple example of CAP and CBP where 3 UEs are jointly served by 3 RRHs applying D-MIMO is shown in Figure 2.20. For CAP, BBU pool need to transmit quantized corresponding precoded signals to different RRHs. On the contrary, for CBP as illustrated in Figure 2.21, all discrete user data of UE 1, 2 and 3 together with corresponding quantized precoding matrix will be transmitted from BBU pool to different RRHs.

CBP consumes less fronthaul capacity than CAP in CB, however not in JT. Furthermore, when the size of a cluster is large, CBP consume more fronthaul capacity than CAP in JT. In this thesis, we focus on JT instead of CB. Thus, CAP is chosen as the transmission scheme from the BBU pool to RRHs for CoMP in this thesis.

Comparison of the Two Transmission Schemes

Despite the introduction of extra quantization noise, compression-based strategy is more practical than data-sharing strategy in C-RAN. At first, the RRH should be as light as possible in C-RAN to reduce cost. The joint processing is too complex to be done in RRHs. Secondly, the CSIs from all RRHs in a cluster to their served UEs should be available in each RRH. This costs too much resources.

For a traditional transmission strategy without applying CoMP (non-CoMP), each RRH only serves the UEs in its cell and no complex cooperation exists between different RRHs. An RRH only needs to collect the CSIs from itself to its serving UEs and the precoding can also be done locally in the RRH by applying simple linear precoding algorithm. In this way, BBU pool only needs to transmit the user flow data of the UEs served by this RRH to it.

Chapter 3

Performance Analysis of Several Functional Splits in C-RAN

Introduction

In a C-RAN architecture where all baseband processing functions in traditional BBU are put into BBU pool, the burden on fronthaul is high. Several solutions have been proposed in [START_REF]The Road Towards Green RAN[END_REF], such as reducing signal sampling rate, applying non-linear quantization, frequency subcarrier compression and IQ data compression. Another envisioned method to reduce the data throughput between RRHs and BBUs is to change the current functional split architecture between RRH and BBU [START_REF] Wubben | Benefits and Impact of Cloud Computing on 5g Signal Processing: Flexible centralization through cloud-RAN[END_REF]. Part of baseband processing functions in BBU are moved to RRH. This will largely reduce the overheads of the signal transmitted through fronthaul.

This chapter investigates on the performance of different functional splits with a mathematical model. Two new functional split architectures are proposed, which move part of the functions in the physical layer of LTE transmission system from BBU to RRH.

For the downlink, the base station is concerned by the transmission side. The baseband signal is defined in a finite set of discrete symbols. Developing compression scheme is easy as illustrated in Figure 2.21 of Section 2.3.3. For the uplink, the base station is concerned by the receiver side. As the signal received is affected by noise, it is fundamentally analog. The analog received signal should be quantized before being transmitted from the RRH to the BBU. The quantization has an impact both on the quality of the reception and the throughput between the RRH and the BBU. Therefore, we focus on LTE uplink in this chapter. This work has been published in [START_REF] Duan | Performance Analysis of Several Functional Splits in C-RAN[END_REF].

This chapter is organized as follows. In Section 3.2, we firstly give a state of the art about functional splits between RRHs and BBUs. In Section 3.3, the Discrete Fourier Transform Performance Analysis of Several Functional Splits in C-RAN Spread Orthogonal Frequency-Division Multiplexing (DFTS-OFDM) transmission system in LTE uplink is briefly introduced. The current and proposed functional split architectures between RRH and BBU are modeled and presented in Section 3.4. The algorithms applied and numerical configurations in the simulation for numerical estimation of the distortion are proposed in Section 3.5. The simulation results are shown in Section 3.6. At last, this chapter is concluded in Section 3.7.

State of the Art

To reduce the throughput on the fronthaul, some baseband functionalities at the physical layer can be moved from the BBU pool to the RRHs (functional splits in the uppers layers are beyond the scope of this thesis). The fronthaul transmission rates, advantages and disadvantages have been discussed in [START_REF]The Road Towards Green RAN[END_REF][START_REF] Peng | Recent Advances in Cloud Radio Access Networks: System Architectures, Key Techniques, and Open Issues[END_REF][START_REF] Bartelt | Fronthaul and backhaul requirements of flexibly centralized radio access networks[END_REF][START_REF] Wubben | Benefits and Impact of Cloud Computing on 5g Signal Processing: Flexible centralization through cloud-RAN[END_REF][START_REF] Simeone | Cloud Radio Access Network: Virtualizing Wireless Access for Dense Heterogeneous Systems[END_REF]. With more functionalities in the RRHs, it requires more storage and larger calculation capacity available in the remote sites. The multiplexing gain in energy consumption will be reduced. In the same time, this also lowers the coordination level between different cells.

The authors of [START_REF] Bartelt | Fronthaul and backhaul requirements of flexibly centralized radio access networks[END_REF][START_REF] Wubben | Benefits and Impact of Cloud Computing on 5g Signal Processing: Flexible centralization through cloud-RAN[END_REF] studied the implementation of the FFT/IFFT blocks in the RRHs. They found that this can bring 40% reduction of the fronthaul bit rate when combined with the omission of guard carriers and of the cyclic prefix (CP). These studies are based on very simple models that consider a given bit rate budget for each layer.

In [START_REF] Lorca | Lossless compression technique for the fronthaul of lte/lteadvanced cloud-ran architectures[END_REF], a further reduction of fronthaul bit rate is obtained by moving resource demapping for the uplink and resource mapping for the downlink from the BBU pool to the RRHs. The fronthaul bit rate becomes user-traffic dependent. Only the occupied resource blocks need to be transmitted on the fronthaul. This allows the system to exploit the statistical multiplexing gain based on the real time traffic. Furthermore, different physical channels can be distinguished. The authors of [START_REF] Dötsch | Quantitative analysis of split base station processing and determination of advantageous architectures for lte[END_REF] applied higher quantization resolution to channels carrying higher-order modulation and lower quantization resolution to channels carrying lower-order modulation. In [START_REF] Checko | Evaluating c-ran fronthaul functional splits in terms of network level energy and cost savings[END_REF], the authors gave quantitative analysis of multiplexing gains of traffic-dependent C-RAN functional splits. They conclude that the implementation of such functional splits is much beneficial when the traffic is variable bit rate, has low load or is bursty. The requirements on the fronthaul link can be largely relaxed.

All the above studies did not consider the impact of the splits on the overall signal quality. Our objective is to analyse the fronthaul bit rate of different functional splits while maintaining the same quality expressed with the error vector magnitude (EVM).

We simulate a LTE Uplink physical layer with a bandwidth of 20 MHz, which includes 2048 sub-carriers where 1200 of them are active. There are 100 PRBs within one LTE time slot. Modulation scheme 16 QAM is considered. "DAC" and "RF" blocks in the transmitter are not considered as well as "ADC" and "RF" in the receiver. In our simulation, the number of sub-carriers N = 2048 and the length of CP L = 160. As 16 QAM modulation scheme is adapted, there are m = 4 bits per symbol.

Quantization and Frame Arrangement

In order to minimize the quantization error, a digital automatic gain control is applied. A scaling factor F s is determined for each block of N s received I/Q samples. Then the N s received I/Q samples are quantized linearly with Q q bits resolution per complex component based on F s . The scaling factor is sent together with the N s quantized I/Q samples from RRHs to BBUs. In order not to introduce a large extra delay to the transmission system, the value of N s should be a factor of N + L for Method 1, and of total number of sub-carriers occupied during each LTE time slot for Method 2 and 3.

We define the largest absolute value as

V max = max k=0,...,N s -1 {|ℜ(y cp k )|, |ℑ(y cp k )|} (3.7)
where ℜ(y cp k ) and ℑ(y cp k ) denotes the real and imaginary part of y cp k , respectively. The corresponding scaling factor is determined as

F s = ⌈ V max p ⌉ for ⌈ V max p ⌉ ≤ 2 Q s -1 2 Q s -1 for ⌈ V max p ⌉ > 2 Q s -1 (3.8)
where p is the quantization step for V max and Q s is the number of bits used to represent F s .

Then the I/Q samples are linearly quantized to 2 Q q levels ranging from -F s to F s . The n-th quantization level is given by

q n = -F s p + (n + 1 2 ) F s p 2 Q q -1 (3.9)
where n = 0, 1, ..., 2 Q q -1.

Applying the quantization levels obtained, the I/Q samples ŝ s s is linearly quantized as

u I (k) = arg min n |q n -ℜ(y cp k )|, (3.10) u Q (k) = arg min n |q n -ℑ(y cp k )| (3.11)
transmitted. Due to the Forward Error Correction (FEC) code applied in CPRI, a code rate r c needs to be considered.

In LTE uplink with 20 MHz bandwidth, there are totally 2048 sub-carriers including 1200 active ones used for transmission. Therefore, the minimum sampling frequency f s = 2048 × ∆ f = 2048 × 15 kHz = 30.72 MHz. Oversampling is sampling a signal with a frequency higher than the Nyquist rate (minimum sampling rate). Oversampling is applied to improve the performance of system.

D k = N Sc × 1 T s × 2 × Q effk × 1 r c × η (3.14)
where N Sc is the number of active sub-carriers for data transmission, T s is the symbol duration, k = 2, 3, and η is the assumed PRB utilization ratio. The factor 2 in Equation 3.14 results from that both I and Q signals should be transmitted. We also apply FEC code in the transmission, thus the same code rate r c as in Method 1 is included in Equation 3.14. Table 3.3 shows the value assignments of the parameters in our simulation for method 2 and 3.

Error Vector Magnitude

The error vector magnitude (EVM) is used to quantify the performance of aforementioned different methods of receiver. EVM is defined as

EVM = E[|a i k -âi k | 2 ] E[|a i k | 2 ] (3.15)
where a i k are the 16 QAM modulated symbols to be sent in transmitters as shown in Figure 3.1, and âi k are the received symbols before 16 QAM demodulation as shown in Figure 3.3. We have also considered the cases with AWGN in the transmission channel between transmitters and receivers (Section 3.3.2).

If there is no quantization noise,

EVM = E[|a i k -âi k | 2 ] E[|a i k | 2 ] = N 0 E s . (3.16)
From Equation 3.16, we can get EVM = 10

-( E s N 0 ) dB /20
(3.17)

when the number of quantization bits Q q → ∞.

Simulation Results

In our simulation, all the three methods of receiver applied (Method 1 mentioned in Section 3.4.1, Method 2 and 3 mentioned in Section 3.4.2) are tested. The performances in the three different scenarios with and without AWGN have been simulated. Using Equation 3.13 and 3.14, we can get the data transmission rate from RRH to BBU for different methods of receiver applied and quantization resolution Q q .

Fig. 3.8 EVMs for applying method 1 of receiver with different ( E s N 0 ) dB and quantization resolution Q q .

Limitation of EVM On Function of AWGN.

At first, simulations have been done to verify Equation 3.17. We have measured the values of EVM applying Method 1 of receiver with different values of ( E s N 0 )

dB and quantization resolution. The simulation results are illustrated in Figure 3.8.

Table 3.4 EVM on function of (

E s N 0 ) dB . ( E s N 0 ) dB 6 10 15 20
No AWGN EVM (Q q → ∞) 0.5012 0.3162 0.1778 0.1000 0 Using Equation 3.17, we can obtain the values of EVM for different levels of ( E s N 0 ) dB , when Q q → ∞. Thus we get the results as shown in Table 3.4, which are coherent with what we observe from Figure 3.8. D 2 ) with respect to the same value of EVM. The number of PRBs allocated to each transmitter is denoted by NUM RB . Both the scenarios without AWGN and E s N 0 = 6 dB are simulated. It can be observed that, compared with Method 2, Method 3 can save 5% to 10% of the bandwidth between RRH and BBU when each transmitter is only allocated with one PRB without AWGN, and 12% to 15% when E s N 0 = 6 dB. The more PRBs are distributed to each transmitter, the less bandwidth gain Method 3 can be obtained compared with Method 2. This is because the more PRBs are allocated to one transmitter, the more asymmetrical are the serial 12-point IFFT process in receiver and the M-point FFT process in the transmitter.

Performance Comparison Between Method

Conclusion

This chapter introduces two new architectures of functional split between RRH and BBU: Method 2 and 3, which have been modeled and simulated. Digital automatic gain control and linear quantization have been applied. In method 2, removing CP, FFT and resource In the following of this thesis, we concentrate on a C-RAN downlink transmission scenario. This chapter deals with the C-RAN downlink system model. At first, the mathematical model of the system is introduced. Then, we present the transmission model for single RRH mode and CoMP mode. In single RRH mode, each UE is served by only one RRH. There is only limited coordinated scheduling between different RRHs. In CoMP mode, both CS/CB and JT can be applied. We rather apply CAP than "data-sharing" in data transmission scheme from a BBU pool to RRHs for CoMP. This is more realistic. Our system configuration is adapted to a 3GPP 3-sector cellular network [START_REF] Gpp | Evolved Universal Terrestrial Radio Access (E-UTRA) Radio Frequency (RF) system scenarios version 13[END_REF].

We also propose a new RRH clustering mechanism in this chapter. A cluster with large size of RRHs will cause numerous fronthaul overheads and high complexity for CoMP transmission. In general, CoMP is considered to be implemented in a cluster with limited number of RRHs [START_REF] Gong | Joint Scheduling and Dynamic Clustering in Downlink Cellular Networks[END_REF][START_REF] Liu | Semi-dynamic User-Specific Clustering for Downlink Cloud Radio Access Network[END_REF]. The clustering schemes can be categorized to two types [START_REF] Dai | Sparse Beamforming and User-Centric Clustering for Downlink Cloud Radio Access Network[END_REF]: disjoint clustering [START_REF] Papadogiannis | A Dynamic Clustering Approach in Wireless Networks with Multi-Cell Cooperative Processing[END_REF] and user-centric clustering [START_REF] Liu | Semi-dynamic User-Specific Clustering for Downlink Cloud Radio Access Network[END_REF][START_REF] Shi | Group Sparse Beamforming for Green Cloud-RAN[END_REF][START_REF] Jiao | Dynamic user-centric clustering algorithm based on energy efficiency in Cloud-RAN[END_REF][START_REF] Hong | Joint Base Station Clustering and Beamformer Design for Partial Coordinated Transmission in Heterogeneous Networks[END_REF]. In disjoint clustering, we divide the whole network into non-overlapping clusters. The RRHs in each cluster jointly serve the UEs inside their coverage area. This can effectively mitigate inter-cell interference. Nevertheless, the UEs located in cluster-edge still suffer great inter-cluster interference from neighbouring clusters. This disadvantage can be overcome by user-centric clustering [START_REF] Vincent | Key Technologies for 5G Wireless Systems[END_REF]. In this clustering scheme, each UE selects the nearest RRHs to form the cluster which jointly serves it. The clusters for different UEs may be overlapped. In this way, there is no explicit cluster edges. Thus, the UEs fairness can be improved. However, the dynamic selection of clusters and the overlapping of clusters make user-centric clustering much complex than disjoint clustering. [START_REF] Hossain | Cooperative Cellular Wireless Networks[END_REF]. Here we propose a new RRH clustering scheme. It keeps the

Transmission Chain Model

We consider ideal OFDM transmission, which is equivalent to a set of independent narrowband transmissions. Like in most cellular systems, the time is divided into subframes (1-ms subframes for LTE). Each transmission is thus made on a sub-carrier f and during a subframe t. In this thesis, we restrict ourselves on one single sub-carrier. For subframe t, the downlink propagation channel inside the coordinated cluster is defined by a set of matrix 1

H u,v,t ∈ C [N u UA ×N TA ] where H u,v,
N s E(∥X v,t ∥ 2 ) ≤ P, ∀ v ∈ N TP , (4.1)
where N s is the number of OFDM symbols transmitted from an antenna during one subframe.

The N u UA × N s signal Y u,t received by UE u during subframe t is given by

Y u,t = M ∑ v=1 H u,v,t • X v,t + N u,t , (4.2)
where N u,t ∈ C [N u UA ×N s ] is the noise matrix, which consists of i.i.d CN (0, 1) entries. In this thesis, a set of successive N T subframes is called a frame and is denoted by T = {1, 2, . . . N T }. Within a frame, all active UEs are served. The U UEs are thus partitioned into N T disjoint groups N UE,t with t ∈ T and the UEs belonging to the same group are served simultaneously in the same subframe. Thus, t∈T N UE,t = N UE and N UE,i N UE, j = / 0, where i ̸ = j ∀i ∈ T and ∀ j ∈ T . The group of UEs served in subframe t ∈ T is denoted as

N UE,t = {u t 1 , u t 2 , . . . u t N g,t }
, where N g,t is the size of the group during subframe t. The UEs in N UE,t are served together by the M RRHs under the following constraints:

N u RL ≤ N u UA , ∀u ∈ N UE,t , (4.3)
∑ u∈N UE,t N u RL ≤ ∑ v∈N TP N v TP . (4.4)
where N u RL is the number of parallel symbols (layers) transmitted to UE u.

Channel model

We assume the channel to be constant within a coherence time, while they vary in an ergodic way across a large number of coherence periods. We assume the coherence time is longer than a frame. Thus, we omit index t in the channel matrix for simplicity within a frame. The instantaneous channel between RRH v and UE u is modeled as:

H u,v = A(θ u,v )α u,v ρ u,v • Hu,v (4.5)
where the small-scale multipath fading matrix Hu,v ∈ C [N u UA ×N TA ] has i.i.d CN (0, 1) entries, ρ u,v is the shadow fading coefficient, α u,v is the path loss coefficient for downlink from RRH v to UE u and A(θ u,v ) is the antenna gain, which depends on angle θ u,v between the line (RRH v, UE u) and on the antenna orientation of RRH v.

The path loss coefficient is

α u,v = 1 1 + d u,v d 0 η , (4.6)
where d u,v denotes the distance between RRH v and UE u, d 0 is a reference distance and η is the path loss exponent.

The shadow fading coefficients between different RRHs and one UE are correlated. This is made by defining two different independent variables: β u and β u,v with

ρ u,v = β u β u,v , (4.7)
where 10log 10 β u ∼ N (0, σ 2 u ) and 10log 10 β u,v ∼ N (0, σ 2 u,v ).

Discussion on CSI

Channel State Information (CSI) refers to the measured channel properties. There are generally two levels of CSI: instantaneous CSI and statistical CSI [START_REF] Erik | 4G LTE/LTE Advanced for Mobile Broadband[END_REF].

Instantaneous CSI represents the current channel conditions (H u,v ). It corresponds to both small-scale multipath fading part and slow fading part in (4.5).

In this thesis, Statistical CSI refers to the average channel gain. It corresponds to only the term A(θ u,v )α u,v ρ u,v in (4.5). The statistical CSI varies slower than the instantaneous CSI.

When a system is based on FDD, the channel conditions on the uplink and on the downlink are different. The channel can be only measured in the receiver side. For the downlink, a reference signal with constant power is transmitted from the base station to the 4.3 Single RRH Mode 51 UEs to estimate the instantaneous CSIs. Then, the UEs quantize the CSIs and report them back to the base station.

In the case of a system with TDD, the reverse-link estimation is possible. This is due to the reciprocity of the uplink channel and the downlink channel [START_REF] Erik | 4G LTE/LTE Advanced for Mobile Broadband[END_REF]. The downlink instantaneous CSIs can be directly estimated in the base station through uplink. In this way, compared with FDD, there will be less CSI errors caused by quantization and delay. Meanwhile, less transmission resources on the radio interface are consumed. In this thesis, we assume that the system is TDD and all the available CSIs are perfect.

Single RRH Mode

The single RRH mode is defined as when each UE is served by one and only one RRH and each RRH serves only one UE during a subframe. Hence, the size of the set of served UEs in a subframe equals to the number of RRHs, |N UE,t | = M.

For beamforming, we apply Maximum Ratio Combining (MRC). The precoding is done in RRH. We assume the statistical CSIs from each RRH to each UE in C are available in the BBU pool. In each RRH, only the instantaneous CSI between itself and its serving UE is available. The corresponding downlink transmission scheme is shown in Figure 4.2.

After channel coding, the symbols to be transmitted to UE u ∈ N UE,t during subframe t are denoted by S u,t ∈ C [1×N s ] , which are assumed to consist of i.i.d. CN (0, 1) entries. The "UEs mapping" block decides which RRH serves which UE based on the statistical CSIs and distributes the coded symbols to the corresponding RRHs through the fronthaul links. In this mode, no quantization is needed. The mapping strategy is that an UE is served by the RRH corresponding to the highest statistical channel gain.

In RRH v, the output of the precoding is denoted by

X v,t = V v,t S k v,t
, where V v,t is the precoding matrix for the symbols transmitted by RRH v during subframe t and k v,t is the index of the UE served by RRH v during subframe t. The precoding matrix is given as

V v,t = γ v,t H H k v,t ,v (4.8)
where γ v,t is the regulation factor which determines the transmission power of RRH v during subframe t.

In Single RRH mode, no coordinated power control is considered. The beamforming is individually done in each RRH and there is no coordinated beamforming between different RRHs. Each RRH tries its best to do the transmission. The power transmitted by RRH v

C-RAN Downlink Model

Before being transmitted via the v-th fronthaul, the baseband signal sequence Xv,t is quantized. The compressed signals X v,t (after quantization) is:

X v,t = Xv,t + Q v,t , v ∈ N UE,t , (4.15)
where Q v,t is the quantization noise matrix on the v-th fronthaul during t. We assume that the random entries of Q v,t are complex gaussian with variance σ 2 v,t and mean 0 (i.i.d CN (0, σ 2 v,t )), where σ 2 v,t is an optimization variable. A fine quantization corresponds to a low value of σ 2 v,t , but leads to a high bit rate on the fronthaul.

Power constraint. The power transmitted by RRH v is given by [62]

P v,t (V t , σ 2 v,t ) = 1 N s E(∥X v,t ∥ 2 ) = tr (D r t,v ) T V t V H t D r t,v + σ 2 v,t I N v TA (4.16)
which should respect the power constraint

P v,t (V t , σ 2 v,t ) ≤ P. (4.17)
Fronthaul capacity constraint. The rate required on the fronthaul between RRH v and BBUs pool during subframe t can be quantified by [62]

C v,t (V t , σ 2 v,t ) = 1 N s I( Xv,t ; X v,t ) = log det (D r t,v ) T V t V H t D r t,v + σ 2 v,t I N TA ) -N TA log(σ 2 v,t
(4.18) which should respect the fronthaul capacity constraint

C v,t (V t , σ 2 v,t ) ≤ C. (4.19)
Achievable rate for UE u. The precoding matrix V c t,u for the data stream specific to UE u can be obtained by selecting the corresponding columns of V t . The index l u of UE u in N UE,t is given as

l u = {i|N UE,t [i] = u}. The matrix V c t,u is defined as V c t,u = V t D c t,u , where matrix D c t,u ∈ 1 [(∑ u∈N UE,t N u RL )×N u RL ] contains an N u RL × N u RL identity matrix in the rows from ∑ g u i=1 N N UE,t [i] RL -N u RL + 1 to ∑ g u i=1 N N UE,t [i] RL
and all zero elements in the other rows. The corresponding covariance precoding matrix for UE u is defined as

G u = V c t,u (V c t,u ) H , ∀u ∈ N UE,t .
(4.20)

System Configuration

55

The achievable rate for UE u ∈ N UE,t is [START_REF] Kang | Fronthaul Compression and Precoding Design for C-RANs over Ergodic Fading Channels[END_REF][83]

R u = log det I N u UA + H u (∑ k∈N UE,t G k + Ω t )H H u det I N u UA + H u (∑ k∈N UE,t ,k̸ =u G k + Ω t )H H u (4.21)
where

H u = [H 1,u , H 2,u , . . . H M,u ] and covariance matrix Ω t = diag([σ 2 1,t I N 1 TA , . . . σ 2 M,t I N M TA ]).
Fundamental optimization problem. Our objective is to find the quantizations and the precoding matrix that maximize the global transmission rate. The problem of optimizing R(N UE,t ) can be formulated as:

maximize ∑ u∈N UE,t R u over V t , Ω t s.t. C v,t (V t , σ 2 v,t ) ≤ C, ∀v ∈ N TP P v,t (V t , σ 2 v,t ) ≤ P, ∀v ∈ N TP .
(4.22)

System Configuration

Network geometry

We consider a hexagonal three-sectored cellular wireless network as shown in Figure 4.4. The cell radius is denoted by r (the cell range is 2r). Each site is equipped with three RRHs and the distance between two neighbor sites is 3r. Each black arrow represents the antenna orientation for a corresponding RRH. The Cartesian coordinates of RRHs 1, 2 and 3 in the (x, y) plane are

Z 1 RRH = [-3 2 r, 0], Z 2 RRH = [ 3 2 r, 0] and Z 3 RRH = [0, 3 √ 3 2 r].
Each RRH and UE is supposed to be equipped with only one antenna.

Simulation parameters

In the following of this thesis, we let each cluster of RRHs have a size of 3. Therefore, M = 3. We consider a simple cluster including RRH 1, 2 and 3 serving a number of UEs. The set of RRHs is N TP = {1, 2, 3}. The served UEs are uniformly randomly distributed in the area enclosed by the triangle whose three vertices are the positions of the three RRHs.

When possible, we take all parameters from 3GPP reference scenarios defined in [START_REF] Gpp | Evolved Universal Terrestrial Radio Access (E-UTRA) Radio Frequency (RF) system scenarios version 13[END_REF]. Simulations are performed in an urban area LTE downlink scenario where the cell radius r is 500 m, the carrier frequency is 2000 MHz and the base station antenna height is 15 m above average rooftop level.

System Configuration

Antenna radiation pattern

We apply the Base Station antenna radiation pattern in [START_REF] Gpp | Evolved Universal Terrestrial Radio Access (E-UTRA) Radio Frequency (RF) system scenarios version 13[END_REF] where antenna gain is defined as:

10log 10 A(θ u,v ) = -min 12 θ u,v θ 3dB 2 , A m + A 0 where -180 • ≤ θ u,v ≤ 180 • . (4.23)
where θ 3dB = 65 • is the 3 dB beam width, A m = 20 dB is the maximum attenuation and A 0 is the forward antenna gain (in the bore-sight direction of the antenna beam).

In our simulation, we take A 0 = 15 dBi for an urban area and a 2000 MHz carrier frequency [START_REF] Gpp | Evolved Universal Terrestrial Radio Access (E-UTRA) Radio Frequency (RF) system scenarios version 13[END_REF].

Path loss

The propagation from RRH to UE attenuation model for our considered simulation scenario given in [START_REF] Gpp | Evolved Universal Terrestrial Radio Access (E-UTRA) Radio Frequency (RF) system scenarios version 13[END_REF] is

L = 128.1 + 37.6log 10 (d u,v ) dB, (4.24)
where d u,v is in kilometers. This model is designed mainly for a value of d u,v varying from few hundreds meters to kilometers. Comparing Equation 4.24 with the following formula

-10log 10 (α u,v ) = 10log 10 1 + d u,v d 0 η (4.25)
for a comparably large value of d u,v , we can get η ≈ 3.76 and d 0 ≈ 3.92 × 10 -4 km. We will take η = 3.76 and d 0 = 3.92 × 10 -4 km for the following simulation.

Shadow fading

As in [START_REF] Gpp | Evolved Universal Terrestrial Radio Access (E-UTRA) Radio Frequency (RF) system scenarios version 13[END_REF], we take 10log 10 ρ u,v ∼ N (0, 10 dB) in (4.7) and a shadowing correlation factor of 0.5 for the shadowing between sites. As RRH 1, 2 and 3 belong to different sites, we take 10log 10 ρ u ∼ N (0, 5 dB) and 10log 10 ρ u,v ∼ N (0, 5 dB).

RRH transmission power

In this study, we assume the noise has a variance equal to 1 (noise power): the value of each RRH power constraint P is a ratio to the noise power. To make the simulations results more intuitive and comparable with practical system configuration, we convert the unit of power constraint to dBm.

At the UE side, noise figure is 9 dB and the white Gaussian noise power is -101 dBm for a noise temperature of 300 K and a 20 MHz bandwidth. A noise power equal to 1 in previous study corresponds to -101 dBm + 9 dB = 92 dBm. The corresponding RRH power constraint in dBm has a ratio of P to the noise power in dBm and is given by

P dBm = P -92 dBm. (4.26)
As defined in [START_REF] Gpp | Evolved Universal Terrestrial Radio Access (E-UTRA) Radio Frequency (RF) system scenarios version 13[END_REF], for Universal Terrestrial Radio Access (E-UTRA) downlink with a bandwidth of W = 20 MHz, the maximum RRH transmission power is 46 dBm. In our simulation, each RRH power constraint is set as P dBm = 46 dBm.

Fronthaul capacity

In the system model, the unit of fronthaul capacity is bit/channel. For the same reason that of converting the unit of RRH transmission power, we convert the unit of fronthaul capacity to Mbits/s. In LTE downlink with 20 MHz bandwidth, there are 1200 × 14 = 16800 Resource Elements (REs) during one subframe (1 ms), where 1200 refers to 1200 subcarriers and 14 refers to 14 REs for one subcarrier during one subframe. One RE is the equivalent of 1 modulation symbol on a subcarrier. Here we consider one RE as a channel and there are 16800 channels during one subframe. Thus, a transmission rate r bits/channel equals to 16800r bits/ 1 ms = 16.8r Mbits/s in LTE downlink with 20 MHz bandwidth.

In Section 5.5, we do simulations with r = 8 and r = 2. These correspond to a fronthaul capacity of 16.8 × 8 = 134.4 Mbits/s and a fronthaul capacity of 16.8 × 2 = 33.6 Mbits/s, respectively.

RRH Clustering

In this section, we introduce our proposed RRH clustering mechanism. As shown in Figure 4.5, the network is divided into regions of triangular form. Each 3 RRHs on neighbour sites located at the three vertices of a triangle region constitute a cluster, and mainly jointly serve the UEs located inside this region. Meanwhile, the antenna direction of one RRH of a cluster should point to one of the other two RRHs in the cluster. For example, RRH 1, 2 and 3 form a cluster but RRH 1, 2 and 9 do not belong to the same cluster.

Each RRH belongs to two different clusters. For example, RRH 1, 2 and 3 form a cluster while RRH 1, 6 and 7 form another different cluster. To guarantee the coverage of the whole network, each RRH works in each of its two corresponding clusters half of the time. Thus the sum transmission rate got from (4.12) and (4.22) should be divided by 2. During one half Chapter 5

Comparison of Different Transmission Strategies

Introduction

In mobile networks, transmissions on the same time-frequency resource interfere with each other. Early cellular technologies apply static frequency separation between neighbor cells to avoid the interference. This corresponds to a frequency reuse factor higher than 1, which is the number of cells that use different frequencies. However, modern mobile-broadband system Long Term Evolution (LTE) has opted for a reuse factor 1, to maximize the data rates for users close to the Base Station (BS).

In reuse-one deployment, low signal-to-interference ratios (SIR) may occur, especially in the cell edge area, where the power of the useful signal has the same order of magnitude as the interference. C-RAN can facilitate the cooperation among different cells and allows advanced algorithms (e.g. CoMP ) to manage interference.

However, the digitized baseband signals exchanged between BBU pool and RRHs require a large bit rate. This is a main limitation of the feasibility of C-RAN. Therefore, it is important to include fronthaul capacity constraint when evaluating the performance of different advanced cooperation algorithms in C-RAN [START_REF] Vu Nguyen | Cooperative transmission in cloud RAN considering fronthaul capacity and cloud processing constraints[END_REF][START_REF] Simeone | Downlink multicell processing with limited-backhaul capacity[END_REF]. In this chapter, we study the performance of different transmission strategies with RRH power constraints and fronthaul capacity constraints.

This study was published in WPMC 2016 [START_REF] Duan | Maximum throughput in a C-RAN cluster with limited fronthaul capacity[END_REF]. It was made during the first part of the thesis. Hence, only one antenna per RRH and per UE is considered. This limitation is relaxed in the following chapters.

Transmission Rates for Different Transmission Strategies

71

The sum of achievable transmission rates during subframe 1 with fronthaul capacity constraint is

R tot = R 1 + R 2 + R 3 .
(5.3)

Dynamic Point Selection (DPS)

For dynamic point selection (DPS), we assume T = 3, and T = {1, 2, 3}. UE u is supposed to be the only one being served during subframe u, where u = 1, 2, 3. And only the RRH bringing the highest channel gain for UE u does transmission during subframe u.

As the serving RRH transmits signals with maximum power, the achievable transmission rate without fronthaul capacity limitation during subframe u for UE u is

R u = log 1 + P × max (∥h u,1 ∥ 2 , ∥h u,2 ∥ 2 , ∥h u,3 ∥ 2 ) ∀ u ∈ N UE (5.4)
The achievable transmission rate with fronthaul capacity constraint for UE u during subframe u is

R u = min (R u , C) (5.5)
where u = 1, 2, 3.

The sum achievable transmission rate during subframe 1, 2 and 3 with fronthaul capacity constraint is

R tot = 1 3 (R 1 + R 2 + R 3 ).
(5.6)

Round Robin Transmission (RR)

For round robin transmission (RR), we assume T = 3, and T = {1, 2, 3}. UE u is supposed to be the only one being served during subframe u, where u = 1, 2, 3. Only one different RRH transmits during each subframe. Depending on slow fading channel information during subframes 1, 2 and 3, we suppose the association that RRH u serves UE u where u = 1, 2, 3 is the best choice.

As the serving RRH transmits signals with maximum power, the achievable transmission rate without fronthaul capacity limitation during subframe u for UE u is

R u = log 1 + P × ∥h u,u ∥ 2 ∀ u ∈ N UE (5.7)
is due to the high complexity of successive encodings and decodings involved, espectially when the number of UEs is large [START_REF] Somekh | Cooperative Multicell Zero-Forcing Beamforming in Cellular Downlink Channels[END_REF]. In this study, we consider Zero-Forcing (ZF) algorithm [START_REF] Spencer | Zero-forcing methods for downlink spatial multiplexing in multiuser MIMO channels[END_REF] for the parallel data transmission. Applying Zero Forcing algorithm, the precoding matrix is given as:

V = γH H (HH H ) -1 (5.13)
where H is the channel matrix between the 3 RRHs and the 3 UEs, and γ is a normalization factor which is selected to satisfy the RRH power constraint and fronthaul capacity constraint. Water-filling is not considered in this thesis.

We apply precoding matrix V to problem (4.22) in Section 4.4 to calculate the maximum sum transmission rate. Problem 4.22 is a non-convex problem. We apply an adapted Majorization Minimization scheme proposed in [START_REF] Park | Joint Precoding and Multivariate Backhaul Compression for the Downlink of Cloud Radio Access Networks[END_REF] to solve this problem.

Simulation Results

In this section, we compare the performance of different transmission strategies discussed in the previous section. Then, the effect of UE distance from the center of RRH 1, 2 and 3 on the achievable sum rate is tested, with P dBm = 41.4 dBm. The simulation results with C = 134.4 Mbits/s are illustrated in Figure 5.15. ZF-based D-MIMO has a better performance than the others. However, the performance difference between it and single RRH mode becomes smaller and smaller with the increasing of UE distance from center. Single RRH mode has a worse performance than RR in low UE distance from center regime, but better in high regime. The average achievable sum rates of DPS and SU-JT are limited to be less than C.

Comparison of Different Transmission Strategies

When the fronthaul capacity is small (C = 33.6 Mbits/s, see Figure 5.16), RR have the best performance in small UE distance from center regime. The average achievable sum rates of DPS and SU-JT are limited to be no more than 33.6 Mbits/s. The performances of single RRH mode and ZF-based D-MIMO are similar to each other with different values of UE distance from center.

Conclusion

We have studied the performance of different coordinated transmission strategies for a cooperation cluster of 3 RRHs serving 3 UEs with RRH power constraints and fronthaul capacity constraints. Each RRH and UE is assumed to be equipped with only one antenna.

With each fronthaul link capacity C = 134.4 Mbits/s, ZF-based distributed MIMO (D-MIMO) is preferred in RRH high-power regime. When each UE is close to RRH, the performance difference between single RRH mode and ZF-based D-MIMO is small. However, ZF-based D-MIMO needs much more calculation resources, precise channel information feedback from UEs and requires high level of synchronization among coordinated RRHs. It is not interesting to apply ZF-based D-MIMO for only a negligible rate improvement compared with single RRH mode.

When we reduce the fronthaul link capacity to C = 33.6 Mbits/s, round robin selection (RR) has the best performance in RRH high-power regime and in the case that each UE is close to one different RRH. There is no much performance difference between single RRH mode and ZF-based D-MIMO.

Chapter 6

Analysis of Several User Grouping Algorithms

Introduction

In Chapter 5, we compare different transmission strategies without and with cooperations between different cells. Simulation results show that distributed MIMO mode achieves the highest sum transmission rates when the fronthaul capacity is high. We apply ZF in D-MIMO for parallel data transmission. In a C-RAN architecture, the CSIs of the UEs served by a cluster of RRHs can be easily shared. Based on the CSIs, the UEs could be appropriately scheduled in order to further improve the performance of D-MIMO.

ZF is known to have low performance when the ratio of the greatest to the smallest singular value of the channel matrix is large [START_REF] Huang | User Selection for Multiuser MIMO Downlink With Zero-Forcing Beamforming[END_REF]. The more linearly-dependent the channel gain vectors are, the larger this ratio is. We assume the U UEs have a total number of antennas larger than the M RRHs. The U UEs are assumed to be randomly distributed at different positions with different shadow fading. We divide these UEs into several groups with equal size, and each group of UEs is served during separate subframe. By appropriately grouping the UEs, the condition of the channel matrix during each subframe can be improved. However, to determine the best grouping choice to get the maximum sum transmission rate requires an exhaustive search over all possible grouping possibilities.

The method to improve the performance of ZF by selecting a subset of UEs among a number of UEs is widely studied in single-cell multi-user Multiple-Input Multiple-Output (MIMO) [START_REF] Wang | User selection with zero-forcing beamforming achieves the asymptotically optimal sum rate[END_REF][START_REF] Mundarath | A distributed downlink scheduling method for multi-user communication with zero-forcing beamforming[END_REF]. In [START_REF] Huang | User Selection for Multiuser MIMO Downlink With Zero-Forcing Beamforming[END_REF], the sub-optimal greedy user selection algorithms are classified into two categories: 1) capacity-based algorithms and 2) Frobenius norm-based algorithms. The capacity based algorithms choose UEs greedily based on the sum rate variation: such as a UE is added if this increases the sum rate [START_REF] Dimic | On downlink beamforming with greedy user selection: performance analysis and a simple new algorithm[END_REF] [START_REF] Wang | User selection with zero-forcing beamforming achieves the asymptotically optimal sum rate[END_REF]. The Frobenius norm-based algorithms choose UEs greedily based on the variation of the condition of channel matrix, such as maximizing the determinant of the composite channel matrix in [START_REF] Akhlaghi | User Selection and Signaling Over Time-Varying MIMO Broadcast Channels[END_REF]. Another representative of Frobenius norm-based algorithms is the semi-orthogonal user selection (SUS) algorithm proposed in [START_REF] Yoo | On the optimality of multiantenna broadcast scheduling using zero-forcing beamforming[END_REF], where the UEs are greedily selected by choosing the UE whose CSI has the largest projected norm on the channel matrices of the already selected UEs. Capacity based algorithms usually achieve higher sum rate than Frobenius norm-based algorithms, because they can guarantee sum rate increment in each step of user selection, while Frobenius norm-based algorithms can not. However, Forbenius norm-based algorithms are less complex as no calculations of the sum rate is done [START_REF] Huang | User Selection for Multiuser MIMO Downlink With Zero-Forcing Beamforming[END_REF].

In this chapter, we propose several user grouping algorithms to improve the performance of ZF in a C-RAN downlink system with limited fronthaul capacity. This corresponds to a multi-cell MIMO scenario. We apply a practical uniform scalar quantization for the analog data transmitted on fronthaul links as in [START_REF] Liu | Joint Power Control and Fronthaul Rate Allocation for Throughput Maximization in OFDMA-Based Cloud Radio Access Network[END_REF], rather than getting results based on informationtheoretical quantization methods as in [START_REF] Kang | Fronthaul Compression and Precoding Design for C-RANs over Ergodic Fading Channels[END_REF][START_REF] Park | Joint Precoding and Multivariate Backhaul Compression for the Downlink of Cloud Radio Access Networks[END_REF][START_REF] Kang | Layered Downlink Precoding for C-RAN Systems with Full Dimensional MIMO[END_REF]. In D-MIMO mode, we study a cluster of RRHs serving a group of UEs and we apply linear precoding to do joint transmission. Maximizing the sum transmission rate with per RRH power constraint and per fronthaul link capacity constraint is a non-convex optimization problem. Different from [START_REF] Kang | Fronthaul Compression and Precoding Design for C-RANs over Ergodic Fading Channels[END_REF] and [START_REF] Park | Joint Precoding and Multivariate Backhaul Compression for the Downlink of Cloud Radio Access Networks[END_REF] which adopt the Majorization Minimization (MM) scheme to convert the non-convex problem to a series of convex optimization problems, we relax the above mentioned non-convex problem by applying uniform scalar quantization and ZF precoding algorithm and get a closed-form solution.

The remainder of this chapter is organized as follows. In Section 6.2, we introduce the system model and problem formulation. Next our proposed UEs grouping algorithms are described in Section 6.3. The simulation results are presented in Section 6.4. Finally we conclude in Section 6.5.

System Model and Problem Formulation

We apply the system model presented in Section 4.2. Each UE and each RRH are assumed to be equipped with equal number of antennas N UA and N TA , respectively. Thus N u UA = N UA , ∀u ∈ N UE and N v TA = N TA , ∀v ∈ N TP . As shown in Figure 6.1, the U UE are disjointly served by the M RRHs during N T subframes. To simplify the analysis, the number of UEs served during each subframe is the same, N g,t = U/N T = N g,d , ∀t ∈ T . We assume the M RRHs serve the maximum number of UEs in parallel that they can during each subframe, thus N g,d = MN TA /N UA .

where N u RL is the number of parallel symbols (layers) transmitted to UE u. In this paper, we assume N u RL = N UA and the M RRHs serve the maximum number of UEs that they can during each subframe.

We define the achievable sum rate for a certain set of UEs served during subframe t by

R(N UE,t ) = ∑ u∈N UE,t R u , (6.4)
where R u is the achievable transmission rate for UE u.

Here we consider optimizing the achievable sum-rate for all UEs during each subframe which is defined as

R tot = 1 N T N T ∑ t=1 R(N UE,t ). (6.5)
The sum-rate can be optimized over subframes allocation for different UEs, the precoding matrix and the compression noise under fronthaul capacity and RRH power constraints. In the following, we formulate the sum-rate optimization problem.

For a certain set of UEs served during subframe t, problem (4.22) is a non-convex optimization problem. In the following, we apply uniform scalar quantization and ZF algorithm to relax this problem. After the relaxation, we get a closed form expression for the maximum achievable transmission rate.

Uniform Scalar Quantization

In practice, to find the quantization codebooks to achieve the sum rate given in (4.21) with the fronthaul capacity constraints given in (4.18) is very difficult. Inspired by [START_REF] Liu | Joint Power Control and Fronthaul Rate Allocation for Throughput Maximization in OFDMA-Based Cloud Radio Access Network[END_REF], we apply uniform scalar quantization technique for the signals to be transmitted from BBUs pool to RRHs and derive the corresponding achievable sum rate. We generalize the case where each RRH is equipped with only one antenna in [START_REF] Liu | Joint Power Control and Fronthaul Rate Allocation for Throughput Maximization in OFDMA-Based Cloud Radio Access Network[END_REF] to multiple antennas in each RRH.

The interface protocol Common Public Radio Interface (CPRI) is currently used for the data transmission between RRHs and BBUs. It applies separate Inphase (I) and Quadrature (Q) quantization. The baseband signal for the v-th RRH can be expressed as

Xv,t = XI v,t + j XQ v,t . (6.6)
Then the I/Q samples are linearly quantized to 2 Q q,v levels ranging from -η v,t to η v,t , ∀v ∈ N TP . The n-th quantization level in RRH v is given by

q n,v = -1 + 1 2 Q q,v + n 2 2 Q q,v η v,t , (6.7)
where n = 0, 1, . . . 2 Q q,v -1 and η v,t is the scaling factor for the quantized signals transmitted from BBU pool to RRH v during subframe t. With Q q,v bits resolution per complex component, the transmission rate in the v-th fronthaul link is

C v = 2N TA Q q,v bits/channel.
The lower the quantization noise is, the higher transmission rate can be achieved for the UEs on the radio channel. A higher quantization resolution reduces the quantization noise. Taking the fronthaul capacity constraint 2N TA Q q,v ≤ C into consideration, to minimize the quantization noise, we take Q q,v = ⌊ C 2N TA ⌋ as the value of the quantization resolution for the v-th fronthaul link, ∀v ∈ N TP . In other words, the fronthaul is fully used.

We choose the scaling factor η v,t to control the probability of overflow of I/Q samples in a low level. We adapt the "three-sigma rule" applied in [START_REF] Liu | Joint Power Control and Fronthaul Rate Allocation for Throughput Maximization in OFDMA-Based Cloud Radio Access Network[END_REF]. The average power of both Inphase (I) and Quadrature (Q) parts of each element in the k-th row of Xv,t is

V r t,v [k](V r t,v [k]) H /2, where V r t,v [k] denotes the k-th row of V r t,v . Let p = max{ V r t,v [1](V r t,v [1]) H 2 , . . . V r t,v [N TA ](V r t,v [N TA ]) H 2 }. We set η v,t = 3 √ p. (6.8)
The probability of overflow for both I-branch and Q-branch samples is expressed as

P(| XI v,t [i, j]| > η v,t ) = P(| XQ v,t [i, j]| > η v,t ) ≤ 0.0027 (6.9)
where i = 1, 2, . . . N T and j = 1, 2, . . . N s . Each element in Xv,t is linearly quantized as

X I v,t [i, j] = argmin n |q n -XI v,t [i, j]|, (6.10) X Q v,t [i, j] = argmin n |q n -XQ v,t [i, j]| (6. 11
)
where i = 1, 2, . . . N T and j = 1, 2, . . . N s . As mentioned in [START_REF] Liu | Joint Power Control and Fronthaul Rate Allocation for Throughput Maximization in OFDMA-Based Cloud Radio Access Network[END_REF], according to Widrow Theorem, if the number of quantization levels (i.e. 2 Q q,v ) is large, and the signal varies by at least some quantization levels from sample to sample, the quantization noise can be assumed to be uniformly distributed. The

quantization step size is 2 2 Q q,v = 2 1-Q q,v . The corresponding quantization noise variance is σ 2 v,t = (η v,t ) 2 2 2-2Q q,v 6
according to Appendix C in [START_REF] Liang | Joint Power Control and Fronthaul Rate Allocation for Throughput Maximization in OFDMA-based Cloud Radio Access Network[END_REF]. Applying linear quantization with a quantization resolution

Q q,v = ⌊ C 2N TA ⌋, problem (4.22) can be modified to maximize ∑ u∈N UE,t R u over V t , ∀t ∈ T s.t. P v,t (V r t,v , σ 2 v,t ) ≤ P v , ∀v ∈ N TP (6.12)
where

σ 2 v,t = (η v,t ) 2 2 2-2Q q,v 6
, ∀v ∈ N TP (6.13)

η v,t = 3 max{ V r t,v [1](V r t,v [1]) H 2 , . . . V r t,v [N TA ](V r t,v [N T ]) H 2 } (6.14) Q q,v = ⌊ C 2N TA ⌋. (6.15)

Zero Forcing

Applying ZF algorithm, the precoding matrix during subframe t is given as:

V t = γ t H H N UE,t (H N UE,t H H N UE,t ) -1 (6.16)
where

H N UE,t = [H N UE,t [1] ; H N UE,t [2] ; ...; H N UE,t [N g,d ]
] and γ t is a normalization factor which is selected to satisfy the RRH power constraint during subframe t.

Applying Ṽt = V t /γ t , σv,t = σ v,t /γ t , N u UA = N UA ∀u ∈ N UE and (6.16) to (4.21), we get

R u = log det(I N UA + γ 2 t I N UA + γ 2 t H u ΩH H u ) det(I N UA + γ 2 t H u ΩH H u ) , ∀u ∈ N UE,t (6.17)
where dependent. We put the UEs with similar channel gain to the same collection and avoid that they are served on the same time.

σ 2 v,t = γ 2 t ( ηv,t ) 2 2 2-2Q q,v 6 = γ 2 t σ 2 v,
During a given subframe, there is exactly one UE in each collection that is served. Thus the number of UEs in each collection is N d = N T = U/N g,d . As the group of UEs served during the same subframe contains one UE from each collection, the number of collections equals to the number of UEs served during each subframe is N c = N g,d = MN TA N UA . To simplify the analysis, we assume that the value of N TA N UA is always an integer. We denote the i-th collection as M i . Thus,

N c i=1 M i = N UE and M i M j = / 0, ∀i ̸ = j. Let M N c
U be the unordered set of all possible groupings of partitioning U UEs belonging to N c collections into groups with same size N g,d with the above mentioned constraint. The cardinal of M N c U is given by

|M N c U | = U N c ! N c -1 (6.30)
For example, with M = 3, U = 6, N c = 3, we could have M 1 = {1, 4}, M 2 = {2, 6} and M 3 = {3, 5}. In this case, UE 1 and UE 4 are in the same collection, they cannot be served during the same subframe. The same applies also to the UEs in M 2 and M 3 . With this partition of collections, And we have

M 3 6 = {1,
|M N c U | = ( 6 3 !) 3-1 = 4.
We propose an algorithm called "User Division Algorithm" (UDA) to do the first stage process which partitions the UEs to different collections. UDA and the motivation to apply UDA are introduced in Section 6.3.3. For the second stage, we apply separately random selection and GUGA for the two different proposed two-stage UEs grouping algorithms. We call the one which combines UDA and random selection by " Pre Partitioned -Random User Grouping Algorithm" (PP-RUGA); the one which combines UDA and GUGA by "Pre Partitioned -Greedy User Grouping Algorithm"(PP-GUGA). We present the two proposed two-stage UEs grouping algorithms in Section 6.3.4. Among the above mentioned UEs grouping algorithms, PP-RUGA and SUGA are Frobenius norm-based algorithms, GUGA and PP-GUGA are capacity-based algorithms. All the four algorithms are summarized in Table 6.1.

Greedy User Grouping Algorithm (GUGA)

In this section, we describe GUGA algorithm. For each turn, the U UEs are assigned separately to N T different subframes to be served. The GUGA algorithm has a number of iterations which is equal to N T . In each iteration, we assign N g,d UEs to one subframe. Let J be the set of all possible unordered subsets of size N g,d of N UE . The size of J is

|J | = N g,d U = U! (U -N g,d )!N g,d ! . (6.32)
Meanwhile, we denote the set of all possible unordered subsets of size N g,d of the still unassigned UEs at the beginning of the k-th iteration by J (k) . Thus, we have J (1) = J .

Before starting the iterations, we first calculate the value of R(S) for each S ∈ J by (6.4), (6.17) and (6.27), and save them.

In the k-th iteration, we find the set of UEs S ∈ J (k) that has the largest value of R(S) (achievable sum rate of S). This set of UEs is assigned to be served during subframe k and is denoted by S k . Thus, we have

S k = argmax S∈J (k)

R(S). (6.33)

Then we remove the sets in J (k) which contain any element in S k to get J (k+1) , i.e.

J (k+1) = S|S ∈ J (k) and i / ∈ S ∀i ∈ S k . (6.34)
Next we move onto the (k + 1)-th iteration and terminate at the end of the N T -th iteration. At last, the chosen grouping of UEs is given by G = {S 1 , S 2 , ..., S N T }.

Semi-orthogonal User Grouping Algorithm (SUGA)

Semi-orthogonal User Grouping Algorithm (SUGA) is an extension of the user grouping algorithm in [START_REF] Yoo | On the optimality of multiantenna broadcast scheduling using zero-forcing beamforming[END_REF] to the scenario where both RRHs and UEs are equipped with multiple antennas. The basic idea of SUGA is to greedily construct a channel matrix whose rows are as orthogonal as possible to each other.

SUGA is an iterative algorithm which assigns the U UEs to N T contiguous subframes. We denote the set of unallocated UEs as K and the set of allocated UEs during subframe k as S k .

Let

H u = [h T u,1 , h T u,2 , ..., h T u,N UA ],
where h u,i is the channel vector from the RRHs to the i-th antenna of UE u. We initialize n = 1.

For each i-th antenna of each UE u ∈ K, calculate the component of h u,i orthogonal to the subspace spanned by {g 1 , ..., g(n-1)N UA +i-1 }:

g (u-1)N UA +i = h u,i - (n-1)N UA +i-1 ∑ j=1 h u,i gH j ∥g j ∥ 2 g j (6.35) g(n-1)N UA +i = g (u-1)N UA +i . (6.36)
When n = 1, this implies g (u-1)N UA +i = h u,i , where i = 1, 2, ..., N UA . Let ũ be the UE in K that maximizes ∑ N UA i=1 ∥g (u-1)N UA +i ∥ 2 . We remove UE ũ from K, put it in S k and increment n. Next, we select another UE with the same process until N g,d UEs are selected.

Once N g,d UEs are assigned to subframe k, we increment k, reset n = 1, S k = / 0 and allocate another N g,d UEs to the next subframe with the same procedure. After allocating all the U UEs, we get G = {S 1 , S 2 , ..., S N T }, which is the grouping of the UEs.

SUGA is summarized in Algorithm 1. for n = 1 to N UA do 8: for n = 1 to N UA do 14:

User Division

g (m-1)N UA +n = h K[m],n
g (m-1)N UA +n = h K[m],n -∑ (l-1)N UA +n-1 i=1 h K[m],n gH i ∥g i ∥ 2
for i = 1 to N UA do 22: g(l-1)N UA +i = g ( m-1)N UA +i 23:
end for 24:

S k ← S k ∪ {K[ m]} / * Add K[ m] to S k . * / 25: K ← K/K[ m] 26:
end for 27: end for 28: return G = {S 1 , S 2 , ..., S N T } i = 1, 2, . . . N c . Then we select the k-th UE from each collection to be served during the k-th subframe, ∀k ∈ T . PP-RUGA is summarized in Algorithm 3.

N c = MN TA /N UA / * Number of collections * / 2: {M 1 , M 2 , ..., M N c } = UDA(H, M,U, N UA , N TA ) 3: Sort M i into increasing order, ∀i ∈ N TP 4: for k = 1 to U/N g,d do 5:
for l = 1 to N c do 6: Pre Partitioned -Greedy User Grouping Algorithm (PP-GUGA) is a combination of UDA and GUGA. At first, PP-GUGA uses UDA to divide the U UEs into N c = MN TA /N UA collections. Then, it gets the set of all possible unordered subsets of size N g,d of N UE with the constraint that each subset should contain at least and only one UE from each collection: J . To construct one subset of J , we just need to select one UE from each collection. Thus, the size of J is

S k = S k ( kN g,d /M i=(k-1)N g,d /M+1 {M l [i]}) / *
| J | = U N c N c . (6.39)
The second stage of PP-GUGA has the same process as GUGA, expect that we need to replace J in GUGA (see Section 6.3.1) by J . PP-GUGA is summarized in Algorithm 4.

Complexity Analysis

In this subsection, we discuss the complexity of different user grouping algorithms. Let Θ(•) be the complexity of one algorithm.

N c = MN TA /N UA / * Number of collections * / 2: {M 1 , M 2 , ..., M N c } = UDA(H, M,U, N UA , N TA ) 3:
Get the set of all possible unordered subsets of size N g,d of N UE with the constraint that each subset should contain at least and only one UE from M i where i = 1, 2, ..., N c : J 4: Calculate the value of R(S) for each S ∈ J by (6.17) and (6.27) 5: Let J (1) = J 6: for k = 1 to U/N g,d do 7:

S k = argmax S∈ J (k) R(S) / *
J (k+1) = S|S ∈ J (k) and i / ∈ S ∀i ∈ S k 9: end for 10: return G = {S 1 , S 2 , ..., S N T }

GUGA

The main cost of GUGA is the computation of the sum transmission rate of each subset of UEs S in J , where J is the set of all possible unordered subsets of size N g,d of N UE . In this computation, the operation H S (H S ) H -1 costs the most. Each calculation of

H S (H S ) H -1 has a complexity of O(N 2 g,d N 2 UA MN TA ) [98]. GUGA needs to do |J | = U! (U-N g,d )!N g,d ! times this operation. Thus, the complexity of GUGA algorithm is O(N 2 g,d N 2 UA MN TA •U N g,d ). Ap- plying N g,d = MN TA /N UA , we get Θ(GUGA) = O(M 3 N 3 TA U (MN TA /N UA ) ). (6.40)

SUGA

In (6.35), we need at most MN TA -1 times (1 × MN TA ) × (MN TA × 1) × (1 × MN TA ) (column vector)-(row vector)-(column vector) multiplication whose complexity is O(MN PA ) for each antenna of each unallocated UE. To allocate a UE, we need to calculate (6.35) for at most UN UA antennas in UEs' side and choose the one who has the maximum module. Thus, the complexity of allocating one UE is

O(UN UA M 2 N 2 TA ) + O(UN UA ) = O(UN UA M 2 N 2 TA ).
Therefore, the total complexity of SUGA is

Θ(SUGA) = O(M 2 N 2 TA N UA U 2 ). (6.41)

PP-RUGA

In UDA, we need to do MUN UA N TA multiplications and a sorting to MU elements. The complexity for UDA is O(MU log MU) + O(MUN UA N TA ). After applying UDA, the second stage of PP-RUGA is just a randomly allocation of different UEs to be served during different subframes. Thus, the complexity of PP-RUGA is

Θ(PP-RUGA) = O(MU log MU) + O(MUN UA N TA ). (6.42)

PP-GUGA

The first stage of PP-GUGA has the same complexity as UDA. Similar to GUGA, the computation of the sum transmission rate of each possible subset of UEs S in J (see Section 6.3.4) is the main cost of the second stage of PP-GUGA. However, the size of

| J | = (U/N c ) N c is much less than | J |. Note that N c = N g,d . The complexity of the second stage of PP-GUGA is O(N 2 g,d N 2 UA MN TA • (U/N g,d ) N g,d )
. This is higher than that of UDA. Thus, the total complexity of PP-GUGA is

O(N 2 g,d N 2 UA MN TA • (U/N g,d ) N g,d ). Applying N g,d = MN TA /N UA , we get Θ(PP-GUGA) = O M 3 N 3 TA UN UA MN TA (MN TA /N UA )
.

(6.43)

Simulation Results

We apply the system configuration presented in Chapter 4. We consider a simple cluster of M = 3 RRHs serving U UEs. The set of RRHs is N TP = {1, 2, 3}. Each RRH and each UE is equipped with N TA = N UA = 2 antennas. During each subframe, N g,d = 3 UEs are served. Each fronthaul link is assumed to apply the linear quantization with the same number of bits: Q q,v = Q q ∀v ∈ N TP . For each numerical result, an average over 100 times randomly generated U UEs allocated to the studied cluster of RRHs with different large-scale channel gain is performed. For each fixed large-scale channel gain, we take average over 100 times small-scale multi-path fading. We denote the exhaustive enumeration of all possible UEs grouping to solve optimization (6.28) by "Exhaustive algorithm". We call the transmission without applying any user grouping algorithm by "Random UEs grouping". In this section, we compare the average achievable sum rate of applying different user grouping algorithms GUGA, PP-GUGA, SUGA and PP-RUGA with applying "Exhaustive algorithm" and "Random UEs grouping". Fig. 6.5 Average achievable sum rate vs. RRH power constraint P W (U = 9, Q q = 4).

At first, we fix the number of UEs U = 9 and each RRH power P dBm = 46 dBm. The average achievable sum rate of the six algorithms with respect to different fronthaul constraints is shown in Figure 6.5. Secondly, we fix the number of UEs U = 9 and each fronhaul quantization bits Q q = 4. The average achievable sum rate of the six algorithms with respect to different RRH power constraints is shown in Figure 6.5.

It is observed that applying the algorithms which selects an optimal or suboptimal UEs grouping increases the system performance compared to randomly selecting a UEs grouping. Applying GUGA has a similar performance to that of applying "Exhaustive algorithm". Meanwhile applying PP-GUGA achieves a smaller average sum rate than applying GUGA, but higher than SUGA. PP-RUGA also achieves a higher average sum rate than "Random UEs grouping", however smaller than all the other user grouping algorithms.

Then, we fix the RRH power constraint P dBm = 46 dBm and each fronhaul quantization bits Q q = 4. We vary the number of UEs U. The corresponding ratios of increasing average achievable sum rate compared with applying "Random user grouping" realized by applying GUGA, PP-GUGA, SUGA and UDA are illustrated in Figure 6.7. With the increasing number of UEs for grouping, the performances of all the proposed user grouping algorithms Fig. 6.6 Average achievable sum rate vs. RRH power constraint P W (U = 9, Q q = 4). Fig. 6.7 Ratio of increasing average achievable sum rate compared with applying "Random user grouping" vs. number of UEs U (P dBm = 46 dBm, Q q = 4). increase. Applying GUGA increase 50% the average achievable sum rate when U = 30, 40% with PP-GUGA, 25% with PP-SUGA and around 10% with PP-RUGA. However, the increase rate of the average achievable sum rate is gelling lower as U increases, because most of the spatial diversity has been exploited. When we fix the values of M, N TA and N UA , the complexities of the four user grouping algorithms (6.40), (6.43), (6.41) and (6.42) become:

Θ(GUGA) = O(U 3 ) Θ(PP-GUGA) = O(U 3 ) Θ(SUGA) = O(U 2 ) Θ(PP-RUGA) = O(U logU). (6.44)
These correspond to the increase of average running time with respect to the number of UEs U as depicted in Figure 6.8. Note that, although the increasing rate of GUGA is similar to that of PP-GUGA, (6.40) and (6.42) show that GUGA is more complex than PP-GUGA. This is consistent with Figure 6.8.

Conclusion

In this chapter, we proposed four user grouping algorithms denoted GUGA, SUGA, PP-RUGA and PP-SUGA. ZF precoding is used for joint transmission in a C-RAN downlink system with limited fronthaul capacity. For a number of UEs, the algorithms select which UEs are served simultaneously during the same subframe to increase the average achievable sum rate.

GUGA can achieve a similar performance of that of exhaustive enumeration of all possible UEs groupings with a lower complexity. However GUGA is still too complex when the number of UEs U becomes large for a fixed number of UEs served during each subframe. PP-SUGA and SUGA exhibit less complexity with a small loss in performance. PP-GUGA has a better performance than SUGA but a higher complexity. The complexity can be further significantly reduced with PP-RUGA. However, PP-RUGA achieves less average sum rate than all the other three algorithms.

Introduction

In Chapter 5, simulation results show that CoMP should be preferred for UEs located in cell edge areas and when fronthaul capacity is high. The UEs in cell edge area benefit more from CoMP than UEs in cell center area.

CoMP can largely improve system performance but needs more fronthaul capacity [START_REF] Ha | Coordinated Multipoint Transmission Design for Cloud-RANs With Limited Fronthaul Capacity Constraints[END_REF], especially with JT: data of all served UEs have to be shared between different RRHs [START_REF] Dahrouj | Coordinated beamforming for the multicell multi-antenna wireless system[END_REF]. The heavy burden on fronthaul links is the major bottleneck of the feasibility of C-RAN [START_REF] Bartelt | Fronthaul and backhaul requirements of flexibly centralized radio access networks[END_REF]. The extra fronthaul load and CSIs requirement in CoMP may counteract the throughput gain for UEs in cell center area [START_REF] Zhang | Transmission Mode Selection for Downlink Coordinated Multipoint Systems[END_REF].

To improve system performance with limited fronthaul capacity, we propose a hybrid transmission strategy. An example of hybrid transmission is shown in Figure 7.1. The UEs in near RRH area are served in single RRH mode (served by only one RRH), and UEs in cell edge area served in distributed MIMO mode (jointly served by all the RRHs in the cluster).

Single RRH mode corresponds to non-CoMP with limited coordinated Scheduling (CB). The BBU pool just needs to collect the statistical CSIs to decide which RRH serves which UE and which UEs are served at the same time. Distributed MIMO mode is one coherent JT algorithm where we apply Zero-Forcing (ZF) precoding to let a cluster of RRHs jointly transmit signals to a group of UEs.

The performances of CB/CS, JT and non-CoMP with limited fronthaul capacity are compared in a number of studies. Simulation results in Section 5.5 and [START_REF] Seifi | Coordinated single-cell vs multi-cell transmission with limited-capacity backhaul[END_REF] show that non-CoMP outperforms CoMP and CB/CS outperforms JP when the fronthaul capacity is low. To make a trade-off between system performance and fronthaul load, a number of studies has been done to switch between CB/CS, JP and non-CoMP. In [START_REF] Zhang | Downlink Base Station Cooperative Transmission Under Limited-Capacity Backhaul[END_REF], a semi-dynamic hard switching scheme is proposed to decide which UEs are to be served by CB or JT by MIMO, all the U UEs are served in a distributed MIMO mode, in which several UEs are jointly served by all the M RRHs at the same time. In hybrid transmission, part of the U UEs are served in single RRH mode and the rest in Distributed MIMO mode.

For each mode, we have to determine which UEs are served at the same time (during the same subframe). The U UEs are thus partitioned into N T disjoint groups N UE,t with t ∈ T and each group is served in one subframe. Thus, t∈T N UE,t = N UE and N UE,i N UE, j = / 0, where i ̸ = j ∀i ∈ T and ∀ j ∈ T . The group of UEs served in subframe t ∈ T is denoted as

N UE,t =

UEs Scheduling for Distributed MIMO Mode

We partition the U d UEs served in distributed MIMO mode to N T,d groups with same size N g,d = MN TA . Each group of UEs is served during one subframe in T d . We need an heuristic to decide which UEs are served at the same time in order to get a high sum transmission rate.

Here, we apply Semi-orthogonal User Grouping Algorithm (SUGA) adapted from [START_REF] Yoo | On the optimality of multiantenna broadcast scheduling using zero-forcing beamforming[END_REF] and presented in Section 6. {m, n} = argmax i, j Q K,S (i, j) At last, the chosen grouping of UEs is given by G s = {S 1 , S 2 , ..., S |T s | }.

3: M S[n] ← M S[n] ∪ {K[m]}, K ← K/{K[m]} 4: if |M S[n] | = U s /M
In the following, we discuss the complexity of PP-SUGA. UDA in stage 1 does a sorting to U s M elements. Thus the complexity of stage 1 is O(U s M logU s M). In stage 2, SUGA is applied with statistical channel matrix and M UEs served during each subframe. Referring to Subsection 6.3.5, the complexity of stage 2 is O(U 2 s M 2 ). In stage 3, we do a sorting of M 2 elements for each subframe in T s . Thus the complexity of stage 3 is O(N T,s M 2 log M 2 ) =

C eq,v = C + Cv N T,d v ∈ N TP , ∀t ∈ T d . (7.4)
To calculate the corresponding transmission rates for the UEs served in distributed MIMO mode when B-FTS is activated, we replace C with C eq,v in (4.19).

Cost of CSIs

In this subsection, we discuss the cost of CSIs of different transmission strategies. We assume the statistical CSIs to be constant within a period of N L frames, while they vary in an ergodic way across a large number of periods of N L frames. The instantaneous CSIs are updated each frame, and the statistical CSIs are updated every N L frames. The CSI signaling cost of the three transmission strategies is shown in Table 7.1. As N L is usually in a scale of hundreds and statistical CSIs have a small dimension than instantaneous CSIs, the update of statistical CSIs costs much less resources than instantaneous CSIs. Thus, fully single RRH transmission needs the least CSIs while fully distributed MIMO transmission needs the most. Hybrid transmission consumes 100U d U percent instantaneous CSIs of that consumed by fully distributed MIMO transmission.

Simulation Results

In this section, we first evaluate the performance of SUGA and PP-SUGA. Then, we compare the average achievable sum rate of applying fully single RRH transmission, fully distributed MIMO transmission and hybrid transmission. Both S-FTS and B-FTS are evaluated for hybrid transmission. We apply the system configuration presented in Chapter 4. We consider a simple cluster of M = 3 RRHs serving U UEs. For each numerical result, an average over 100 times randomly generated U UEs allocated to the studied cluster of RRHs with different large-scale channel gain is performed. For each fixed large-scale channel gain, we take average over 100 times small-scale multi-path fading.

The average achievable sum rate during one subframe for a set of UEs Ñ served during a set of subframes T is

R = 1 | T | ∑ u∈N R u . (7.5)

Performance of Users Grouping Algorithms

The 60 UEs are separated into two parts: U s UEs served in single RRH mode and U d UEs served in distributed MIMO mode. The separation applies the algorithm introduced in Section 7.3.3. We call "random grouping" the most simple algorithm which consists in randomly dividing a set of UEs into several groups. For example, for distributed MIMO applying , we randomly divide the U d UEs into U d /6 groups, and each group is served during one subframe.

Figure 7.7 compares the performance of PP-SUGA with "random grouping" for UEs served in single RRH mode with different values of U s . Note that the value of C is the capacity constraint for each fronthaul link and there are in total 3 fronthaul links in our simulation scenario.

We observe that, compared with "random grouping", applying PP-SUGA brings about 31% more average sum transmission rate when U d = 18, around 25% when U d = 36 and about 17% when U d = 60. When the fronthaul capacity is larger than 300 Mbits/s, the average sum transmission rate barely increases with the increase of fronthaul constraint: the capacity is limited by the radio interface and not the fronthaul.

Figure 7.8 and Figure 7.9 compares the performance of SUGA with "random grouping" for UEs served in distributed MIMO mode with different values of U d . Figure 7.8 shows the average sum transmission rates for the UEs served in distributed MIMO mode applying SUGA and "random grouping" with respect to different fronthaul capacity constraints. Figure 7.9 shows the corresponding ratios of increasing average achievable sum rates of applying SUGA compared with applying "random grouping". It is observed that SUGA brings significant performance improvement in low fronthaul capacity constraint regime while less significant in high fronthaul capacity constraint regime. SUGA can reduce the quantization noise for a fixed fronthaul capacity constraint, which in turn improves the average sum rate. When the fronthaul capacity constraint is large, the benefit is less significant.

Furthermore, the higher U d is, the higher average sum rate can be achieved. This is because, with a larger number of UEs served in distributed MIMO mode, more diversity can be exploited by SUGA. By contrast, with single RRH mode, the average achievable sum rates continue to increase when the fronthaul capacity constraint is larger than 300 Mbits/s. Fig. 7.9 Ratio of increasing average achievable sum rate compared with applying "Random user grouping" vs. fronthaul capacity constraint C for the UEs served in distributed MIMO mode. This is the incentive for us to share part of the fronthaul capacity for UEs served in single RRH transmission mode to UEs served in distributed MIMO mode.

Performance Comparison of Different Transmission Strategies

In this subsection, we compare the performance of different transmission strategies with different values of U s (U d = U -U s ) from fully single RRH transmission (U s = U) to fully distributed MIMO transmission (U s = 0). The hybrid transmission with 24 UEs served in single RRH mode and 36 UEs served in distributed MIMO mode is denoted by "hybrid 24-36 transmission". Both S-FTS and B-FTS are considered for hybrid transmission.

The simulations results are illustrated in Figure 7.10 and Figure 7.11 is a zoom of the low fronthaul capacity constraint regime. We can observe that the performance of hybrid transmission is always better than fully single RRH transmission. Hybrid transmission has a better performance than fully distributed MIMO transmission in low fronthaul capacity regime while lower in high fronthaul capacity regime. Applying B-FTS (advanced fronthaul transmission for the UEs served in distributed MIMO mode) can largely increase the performance of hybrid transmission compared with applying S-FTS when the fronthaul capacity constraint is low. Hybrid 24-36 transmission with B-FTS has a slightly lower performance than hybrid 36-24 transmission with B-FTS when the fronthaul capacity constraint is less than 200 Mbits/s. This is because with more UEs served in single RRH mode, more fronthaul capacity can be shared to each UE served in distributed MIMO mode. With the increasing of fronthaul capacity constraint, hybrid 24-36 transmission with B-FTS begins to surpass hybrid 36-24 Hybrid Joint Transmission transmission. This is because distributed MIMO mode has a better performance than single RRH mode when fronthaul capacity is high and there are more UEs served in distributed MIMO mode in hybrid 24-36 transmission than in hybrid 36-24 transmission. However, hybrid 24-36 transmission consumes more CSIs than hybrid 36-24 transmission.

Conclusion

In this chapter, we proposed a hybrid transmission strategy in a C-RAN downlink system with limited fronthaul capacity. In this downlink scheme, a cluster of RRHs serves a set of UEs according to two different modes: single RRH mode or distributed MIMO mode. The downlink mode for the UEs is decided in the BBU pool based on the statistical CSIs. Several low complexity user grouping algorithms are proposed to decide which UEs are served at the same time in order to improve the system throughput. Also, a new fronthaul transmission scheme is proposed to exploit the unused fronthaul resources by UEs served in single RRH mode to transmit data in advance for the benefit of UEs served in distributed MIMO mode.

Simulation results show that this strategy improves the system performance for hybrid transmissions when the fronthaul capacity is low. In particular, it outperforms both fully single RRH transmissions and fully distributed MIMO transmissions in low fronthaul capacity regime. With the increasing of fronthaul capacity, more UEs are to be served in distributed MIMO mode to improve system throughput.

Chapter 8 Conclusion

This chapter concludes the major contributions discussed in this thesis and gives possible directions of future work.

Major Contributions

C-RAN has the potential to increase the capacity of mobile networks while reducing operators' cost and energy consumption. Nevertheless, the large bit rate requirement in the fronthaul largely limits the future deployment of C-RAN. This study has been done in two aspects: 1) reduce C-RAN fronthaul throughput on the uplink; 2) design coordinated transmission in C-RAN downlink while considering user scheduling and fronthaul capacity allocation. The main contributions in the two aspects can be summarized separately as follows.

Reducing C-RAN fronthaul throughput on the uplink

This thesis investigates new functional split architectures between RRH and BBU, to reduce the transmission throughput between RRHs and BBUs. Two new architectures are proposed and modeled for the uplink. Part of physical layer functions of the BBU are moved to the RRH. For the proposed architectures, the transmission rate between RRHs and BBUs depends on the mobile network load, while that of current architecture is constant. Unlike most of relative works, we have done quantitative analyses on the impact of different functional splits. Simulation results illustrate that 30% to 40% bandwidth can be saved when all the radio channel capacity is used, and up to 70% bandwidth when half of the radio channel capacity is used.

Conclusion

Coordinated Transmission Design in C-RAN Downlink with Limited Fronthaul Capacity

CoMP can improve the system performance of the mobile network. Its implementation can be facilitated by C-RAN. However, the performance of CoMP is constrained by the high complexity and the limited fronthaul capacity of C-RAN. We design coordinated transmission scheme while considering fronthaul allocation. Low complexity user scheduling algorithms are also developed. This part of work is focused on the downlink. A cellular network model in 3GPP is adopted. A new RRH clustering scheme is proposed. It is a trade-off between disjoint clustering and user-centric clustering. We firstly compare different transmission strategies without and with cooperation between different cells while considering limited fronthaul capacity. Then we propose several user grouping algorithms to improve the performance of distributed MIMO. In distributed MIMO, several RRHs serve a number of UEs in parallel through Zero-Forcing. At last, a hybrid transmission strategy is proposed, in which part of UEs are served by only one RRH and the others served by several RRHs.

Comparison of Different Transmission Strategies

At first, we study the maximum throughput of different transmission strategies in a C-RAN cluster. Both RRH transmission power constraints and fronthaul capacity constraints are taken into account. The transmission strategies non-CoMP (e.g. single RRH mode) and CoMP (e.g. distributed MIMO) are considered. In single RRH mode, each UE is served by only one RRH. In distributed MIMO mode (D-MIMO), a cluster of RRHs serving a group of UEs applying Zero-Forcing (ZF) to do joint transmission. Simulation results show that distributed MIMO has a better performance than single RRH mode with high RRH power constraint, high fronthaul capacity constraint and when the UEs are located at cell edge area.

Improving Zero-Forcing Performance by User Grouping Algorithms

The UEs served by a cluster of RRHs usually have a total number of antennas larger than the RRHs. They are assigned to different subframes for serving. The performance D-MIMO applying ZF can be improved by appropriately choosing which UEs are served together in the same time frequency resource. With UE data and channel state information shared in BBU pool, C-RAN facilitates the centralized user scheduling. We propose several low complexity user grouping algorithms to maximize the average achievable sum rate.

Future Work

Hybrid Transmission

The UEs in cell edge area benefit more from CoMP than UEs in cell center area. The extra fronthaul load and CSIs requirement in CoMP may counteract the throughput gain for UEs in cell center area [START_REF] Zhang | Transmission Mode Selection for Downlink Coordinated Multipoint Systems[END_REF]. We propose a hybrid transmission strategy to improve system performance with limited fronthaul capacity. The UEs in near RRH area are served in single RRH mode, and the UEs in cell edge area served in D-MIMO. This division is based on the UEs' statistical Channel State Informations (CSIs). A new fronthaul transmission scheme is also proposed. It allow the UEs served in D-MIMO exploit the unused fronthaul capacity for the UEs served in single RRH mode. This largely improves system performance when the fronthaul capacity is low. Simulation results show that the proposed hybrid mode and fronthaul strategy outperform both the case where all UEs are served in single RRH mode and the case where all UEs are served in D-MIMO when the fronthaul capacity is limited.

Future Work

This work can be extended in several possible directions for the future work. These directions are summarized as follows.

Coordinated Beamforming (CB)

In this thesis, we have not studied Coordinated Beamforming (CB). Distributed MIMO (D-MIMO) can achieve larger performance gain than CB. However, when we use datasharing or compression-before-precoding (CBP) as the transmission scheme from BBU pool to RRHs, D-MIMO requires much higher fronthaul capacity than CB. Furthermore, the coordination between different cells for D-MIMO is in a signal level whereas that for CB is in a beamforming level. CB is easier to implement than D-MIMO. It would be interesting to compare single RRH mode, D-MIMO and CB with data-sharing or CBP.

Signaling Consumption

When we compare the performance of non-CoMP and CoMP transmission strategies, the channel state informations (CSIs) consumption has not been taken into account. In Frequency Division Duplex (FDD), extra downlink transmission resources are used for the CSIs measurements in the UEs' side. The feedback of CSIs from UEs to RRHs also costs significant uplink resources. Moreover, the transmission of CSIs from RRHs to the BBU Coordination dans les réseaux d'accès radio centralisés avec liaisons de transport à débit limité d'autres termes, une charge réduite sur le fronthaul. L'objectif de cette thèse est de maximiser le débit de l'utilisateur tout en tenant compte des contraintes de fronthaul. De plus, dans C-RAN, il est complexe de réaliser l'ordonnancement des utilisateurs, l'allocation des ressources, les algorithmes coordonnés avancés avec des ressources de fronthaul limitées. Nous essayons également de résoudre ce problème dans cette thèse. Ensuite, nous étendons le travail au scénario avec une capacité de frontal limitée et avec plusieurs antennes sur les utilisateurs et sur les RRHs.

B.2 Les contributions

Transmission hybride

Les utilisateurs en bordure de cellule bénéficient plus de CoMP que les utilisateurs dans les zones centrales. La charge supplémentaire de fronthaul et l'exigence de CSI dans CoMP peuvent amoindrir le gain de débit pour les utilisateurs dans la zone centrale de cellule. Nous proposons une stratégie de transmission hybride pour améliorer les performances du système avec une capacité de fronthaul limitée. Les utilisateurs dans la région proche de RRH sont servis en mode RRH unique, et les utilisateurs en bordure de la cellule servis en mode D-MIMO. Cette division est basée sur les CSIs statistiques.

Dans un schéma typique de transmission sur fronthaul, les données transmises du pool de BBU aux RRHs pendant la sous-trame t sont transmises des RRHs aux utilisateurs sur l'interface radio pendant la sous-trame t + 1. Ce schéma est appelé S-FTS (Synchronous Fronthaul Transmission Scheme). Un nouveau schéma de transmission de fronthaul est également proposé. Il permet aux utilisateurs servis en mode D-MIMO d'exploiter la capacité de fronthaul inutilisée pour les utilisateurs servis en mode RRH unique. On l'appelle B-FTS (Buffered Fronthaul Transmission Scheme).

On étudie un scénario où un nombre fixe d'utilisateurs est servi par une grappe de RRHs. Le nombre des utilisateurs servis en mode RRH unique est désigné par U s et celui servis en D-MIMO mode par U d . Les résultats de la simulation sont montrés sur la

xvi List of figures 3 . 1

 31 Localized DFTS-OFDM transmitter. . . . . . . . . . . . . . . . . . . . . . 3.2 Model of adding white gaussian noise in the transmission channel between transmitter i and receiver. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Localized DFTS-OFDM receiver. . . . . . . . . . . . . . . . . . . . . . . 3.4 Method 1 of functional split between RRH and BBU (used in CPRI). . . . . 3.5 Method 2 of functional split between RRHs and BBUs. . . . . . . . . . . . 3.6 Method 3 of functional split between RRHs and BBUs. . . . . . . . . . . . 3.7 Possible frame structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8 EVMs for applying method 1 of receiver with different ( E s N 0 ) dB and quantization resolution Q q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.9 The relative transmission data rate between Method 1 and 2 with respect to the same value of EVM. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.10 The relative transmission data rate between method 2 and 3 with respect to the same value of EVM. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Downlink of a cluster of RRHs which connect to a BBU pool via finitecapacity fronthaul links in C-RAN. . . . . . . . . . . . . . . . . . . . . . . 4.2 Downlink transmission scheme from BBU pool to RRHs (single RRH mode).4.3 Compression-After-Precoding (CAP) scheme for CoMP ("Q" represents fronthaul compression). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Geometry distribution and clustering of RRHs. . . . . . . . . . . . . . . . 4.5 Clustering of RRHs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Downlink transmission scheme of single RRH mode. . . . . . . . . . . . . 5.2 Downlink fronthaul and radio interface transmission scheme of single RRH mode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Downlink transmission scheme of dynamic point selection. . . . . . . . . . 5.4 Downlink fronthaul and radio interface transmission scheme of dynamic point selection with TDMA mode. . . . . . . . . . . . . . . . . . . . . . . 5.5 Downlink transmission scheme of round robin selection. . . . . . . . . . . 5.6 Downlink fronthaul and radio interface transmission scheme of round robin selection with TDMA mode. . . . . . . . . . . . . . . . . . . . . . . . . . 5.7 Downlink transmission scheme of single user joint transmission. . . . . . . 5.8 Downlink fronthaul and radio interface transmission scheme of SU-JT with TDMA mode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.9 Downlink transmission scheme of distributed MIMO. . . . . . . . . . . . . 5.10 Downlink fronthaul and radio interface transmission scheme of D-MIMO. . List of figures xvii 5.11 Geometry distribution of RRHs and UEs. . . . . . . . . . . . . . . . . . . 5.12 RRH -UE serving association for single RRH mode. . . . . . . . . . . . . 5.13 Average achievable sum rate vs. RRH power constraint P dBm (C = 134.4 Mbits/s, d c = 0 m ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.14 Average achievable sum rate vs. RRH power constraint P dBm with small fronthaul capacity (C = 33.6 Mbits/s, d c = 0 m ). . . . . . . . . . . . . . . 5.15 Average achievable sum rate vs. UE distance from the center of RRH 1, 2 and 3 d c (P dBm = 41.4 dBm, C = 134.4 Mbits/s). . . . . . . . . . . . . . . 5.16 Average achievable sum rate vs. UE distance from the center of RRH 1, 2 and 3 d c with small fronthaul capacity (P dBm = 41.4 dBm, C = 33.6 Mbits/s).

7. 1

 1 An example of hybrid transmission. . . . . . . . . . . . . . . . . . . . . . 7.2 Process of PP-SUGA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Process of separating UEs to twos parts, some served in single RRH mode and the others in distributed MIMO mode. . . . . . . . . . . . . . . . . . . 7.4 Equal fronthaul transmission capacity constraint for the UEs served on Single transmission mode and in distributed MIMO mode. . . . . . . . . . . . . . 7.5 Subframes scheduling of B-FTS. . . . . . . . . . . . . . . . . . . . .

1

 1 and 2.

Figure 3 .

 3 Figure 3.9 shows the relative transmission data rate between Method 2 and 1 ( D 2 D 1 ) with respect to the same value of EVM. The assumed PRB occupation ratio η = 0.5 and η = 1 are considered in both cases. Scenarios without AWGN, E s N 0 = 10 dB and E s N 0 = 6 dB are simulated. It can be observed that, similar results are obtained with adding different levels

Fig. 3 . 9

 39 Fig.3.9 The relative transmission data rate between Method 1 and 2 with respect to the same value of EVM.

3. 6 . 3

 63 Performance Comparison Between Method 2 and 3.

Figure 3 .

 3 Figure 3.10 shows the relative transmission data rate between Method 3 and 2 ( D 3D 2 ) with respect to the same value of EVM. The number of PRBs allocated to each transmitter is denoted by NUM RB . Both the scenarios without AWGN and E s N 0 = 6 dB are simulated. It can be observed that, compared with Method 2, Method 3 can save 5% to 10% of the bandwidth between RRH and BBU when each transmitter is only allocated with one PRB without AWGN, and 12% to 15% when E s N 0 = 6 dB. The more PRBs are distributed to each transmitter, the less bandwidth gain Method 3 can be obtained compared with Method 2. This is because the more PRBs are allocated to one transmitter, the more asymmetrical are the serial 12-point IFFT process in receiver and the M-point FFT process in the transmitter.

Fig. 3 .

 3 Fig. 3.10 The relative transmission data rate between method 2 and 3 with respect to the same value of EVM.

Fig. 5 .

 5 Fig. 5.13 Average achievable sum rate vs. RRH power constraint P dBm (C = 134.4 Mbits/s, d c = 0 m ).

Fig. 5 .

 5 Fig. 5.14 Average achievable sum rate vs. RRH power constraint P dBm with small fronthaul capacity (C = 33.6 Mbits/s, d c = 0 m ).

  Algorithm (UDA) and Motivation to Apply UDA UDA The objective of UDA is to generate N c = N g,d collections of same size N T . In a collection, the UEs are served in different subframes. UDA allocates the UEs that get the highest sum channel gain from N UA antennas of a RRH into the same collection. It firstly calculates a reference matrix Z ∈ R [U×N c ] . Let r = N TA /N UA . Each element of the matrix is Z u,l = uN UA ∑ i=(u-1)N UA +1 lr ∑ j=(l-1)r+1 ∥H(i, j)∥ 2 (6.37) Algorithm 1 SUGA: Semi-orthogonal User Grouping Algorithm Input: H (Channel matrix), M (No. of RRHs), U (No. of UEs), N g,d (No. of UEs served during each subframe), N UA (No. of antennas of each UE), N UE (Set of UEs to be served) Output: G (UEs grouping) Initialisation : Let S k = / 0 (Set of UEs to be served during subframe k), where k = 1, 2, ..., U/N g,d 1: h u,i = [H (u-1)N UA +i,1 , ..., H (u-1)N UA +i,MN TA ], where u = 1, 2, ..., U and i = 1, 2, ..., N UA 2: K = N UE (Set of UEs still unallocated) 3: for k = 1 to U/N g,d do 4: for l = 1 to N g,d do 5: if l = 1 then 6:for m = 1 to |K| do 7:

  for m = 1 to |K| do 13:

  1)N UA +n = g (m-1)N UA +n 16: F = {1, 2, ..., |K|} 20: m = argmax m∈F ∑ N UA i=1 ∥g (m-1)N UA +i ∥ 2 / * Select the UE. * / 21:

Algorithm 3

 3 PP-RUGA: Pre Partitioned -Random User Grouping Algorithm Input: H (Channel matrix), M (No. of RRHs), U (No. of UEs), N g,d (No. of UEs served during each subframe), N UA (No. of antennas of each UE), N TA (No. of antennas of each RRH) Output: G (UEs grouping) Initialisation : S k = / 0 (Set of UEs to be served during subframe k), where k = 1, 2, ..., U/N g,d 1:

  Assign one UE from each collection to be served during subframe k. * / 7: end for 8: end for 9: return G = {S 1 , S 2 , ..., S N T } Pre Partitioned -Greedy User Grouping Algorithm (PP-GUGA)

6. 3

 3 User Grouping Algorithm 93 Algorithm 4 PP-GUGA: Pre Partitioned Greedy User Grouping Algorithm Input: H (Channel matrix), M (No. of RRHs), P (RRH power constraint), U (No. of UEs), N g,d (No. of UEs served during each subframe), N UA (No. of antennas of each UE), N TA (No. of antennas of each RRH) Output: G (UEs grouping) Initialisation : Let the set of all UEs N UE = {1, 2, ..., U}, S k = / 0 (Set of UEs to be served during subframe k), where k = 1, 2, ..., U/N g,d 1:

Fig. 6 . 8

 68 Fig. 6.8 Running time vs. number of UEs U (P dBm = 46 dBm, Q q = 4).

  3.2 to do the UEs grouping. SUGA is an iterative algorithm which assigns the U d UEs disjointly to N T,d subframes. Then UE K[m] is added to M S[n] and removed from K. When the S[n]-th collection is full, RRH S[n] is deleted from S. This adapted version of UDA for Chapter 7 is detailed in Algorithm 5. Algorithm 5 UDA: Users Division Algorithm Input: Q (Statistical channel matrix), M (No. of RRHs), U s (No. of UEs), N UE,s (Set of UEs). Output: {M 1 , M 2 , ..., M M } (UEs collections) Initialisation : K = N UE,s , S = {1, 2, ..., M} (set of collections), M i = / 0 (UEs collection), where i = 1, 2, ..., M 1: for k = 1 to U s do 2:

  then

5 :

 5 S ← S/{S[n]} / * When a collection already has U s /M elements, it should not be assigned with new UEs any more. * / 6: end if 7: end for 8: return {M 1 , M 2 , ..., M M } Stage 2 PP-SUGA realizes stage 2 by using SUGA with the constraint that UEs in the same collection cannot be served during the same subframe. The input to SUGA in Section 7.3.1 is replaced by Q, M, N g,d and N UE,d . At the end of stage 2, we get Gd = { S1 , S2 , ..., SN T,s }. Stage 3 In stage 3, each set is reordered in Gd to decide which RRH serves which UE. A RRH will serve the nearest UE if no shadow fading is considered. It is as dividing M UEs into M collections with size 1. This can be realized by applying UDA: Sk = UDA(Q,M,M, Sk ), where k = 1, 2, . . . |T s |.

Fig. 7 . 7

 77 Fig. 7.7 Average achievable sum rate vs. fronthaul capacity constraint C for the UEs served in single RRH mode.

Fig. 7 . 8

 78 Fig. 7.8 Average achievable sum rate vs. fronthaul capacity constraint C for the UEs served in distributed MIMO mode.

Fig. 7 .

 7 Fig. 7.10 Comparison of average achievable sum rate vs. fronthaul capacity constraint C for different transmission strategies (no zoom).

Fig. 7 .

 7 Fig. 7.11 Comparison of average achievable sum rate vs. fronthaul capacity constraint C for different transmission strategies (zoom).

Figure B. 1 .

 1 Fig. B.1 Comparaison des débits totaux vs. capacité de fronthaul C pour différentes stratégies de transmission.

  . . . 7.6 Fronthaul transmission with previous data transmission for the UEs served in distributed MIMO mode. . . . . . . . . . . . . . . . . . . . . . . . . . . 7.7 Average achievable sum rate vs. fronthaul capacity constraint C for the UEs served in single RRH mode. . . . . . . . . . . . . . . . . . . . . . . . . . 7.8 Average achievable sum rate vs. fronthaul capacity constraint C for the UEs served in distributed MIMO mode. . . . . . . . . . . . . . . . . . . . . . . Ratio of increasing average achievable sum rate compared with applying "Random user grouping" vs. fronthaul capacity constraint C for the UEs served in distributed MIMO mode. . . . . . . . . . . . . . . . . . . . . . . 7.10 Comparison of average achievable sum rate vs. fronthaul capacity constraint C for different transmission strategies (no zoom). . . . . . . . . . . . . . . 7.11 Comparison of average achievable sum rate vs. fronthaul capacity constraint C for different transmission strategies (zoom). . . . . . . . . . . . . . . . . B.1 Comparaison des débits totaux vs. capacité de fronthaul C pour différentes stratégies de transmission. . . . . . . . . . . . . . . . . . . . . . . . . . . Subcarriers configuration in LTE with different bandwidths. . . . . . . . . 2.2 Subcarriers configuration in LTE with different bandwidths. . . . . . . . . 2.3 A summary of CoMP downlink algorithms. . . . . . . . . . . . . . . . . .

	xviii	List of figures
	7.9 List of tables 2.1 Chapter 1 Introduction
	1.1 Motivation

3.1 Summary of different methods of functional splits between RRHs and BBUs. 3.2 Simulation parameters for method 1. . . . . . . . . . . . . . . . . . . . . . 3.3 Simulation parameters for method 2 and 3. . . . . . . . . . . . . . . . . . . 3.4 EVM on function of ( E s N 0 )

  1.2 Contributionsa number of UEs in parallel. At last, a hybrid transmission strategy is proposed, in which part of UEs are served by only one RRH and the others served by several RRHs.

Table 2 .

 2 In LTE, the subcarrier spacing is ∆ f = 15 kHz.The number of subcarriers N ranges from 128 to 2048, depending on channel bandwidth. Figure 2.6 depicts a basic time-frequency resource structure of LTE with 72 subcarriers. The period of one time slot is 0.5 ms, corresponding to 7 OFDMA/DFTS-OFDM symbol intervals for normal CP duration and 6 for extended CP duration. Two time slots make a subframe and 10 subframes form one radio frame. A Resource Element (RE) is the smallest defined unit. It consists of one subcarrier during one OFDMA/DFTS-OFDM symbol interval. The Physical Resource Block (PRB) is the smallest chunk of data transmitted in LTE data transmission. Each PRB is composed of 12 subcarriers along one time slot, which results a bandwidth of 15 kHz ×12 = 180 kHz for each PRB. When a normal CP is used, 12 × 7 = 84 REs form a PRB. When an extended CP is applied,the number of REs in a PRB is 12 × 6 = 72. The number of active subcarriers which are used to transmit data, N c = 12 • N RB , where N RB is the number of PRBs. During one time slot, one RB is distributed to one single User Equipment (UE) while one UE can be allocated with several PRBs. 1 Subcarriers configuration in LTE with different bandwidths.

	2.1 LTE Physical Layer

Table 2

 2

		.2 Subcarriers configuration in LTE with different bandwidths.
	LTE downlink configuration	5 MHz band-width 2×2 MIMO	10 MHz band-width 2×2 MIMO	20 MHz band-width 2×2 MIMO	20 MHz band-width 4×4 MIMO
	Fronthaul rate (Gbits/s)	0.65	1.3	2.6	5.2
	Taking into account the CPRI overheads, the data transmission rate from one BBU to one
	RRH in (2.1) is changed to

Table 2 .

 2 .3. 3 A summary of CoMP downlink algorithms.

	Downlink CoMP algo-rithms	dynamic point selec-tion	coordinated scheduling	coordinated beamform-ing	non-coherent joint trans-mission	coherent joint trans-mission
						Non-
	Acronym	DPS		CS	CB	coherent	Coherent JT
						JT
	User data	all data avail-able in each RRH	a RRH only has the data for its serv-ing UEs	a RRH only has the data for its serv-ing UEs	all data avail-able in each RRH	all data avail-able in each RRH
	CSIs available in BBU pool	yes		yes	yes	no	yes
	Sychonization	0.05	ppm
	requirements	frequency
	between	and 3 µs tim-
	different	ing accuracy
	RRHs

Table 3 .

 3 2 Simulation parameters for method 1.

	PAPAMETER	SYMBOL	VALUE
	Oversampling factor	F os	1
	Minimum sampling frequency	f s	30.72 MHz
	Number of samples for each frame	N s	138
	Number of bits for scaling factor	Q s	16
	Number of bits for reference of PRB	Q r	0
	Code rate of FEC applied	r c	8/10

Table 3 .

 3

2 illustrates the values of the parameters for Method 1 in our simulation.

Data Transmission Rate for Method 2 and 3

The data transmission rate from RRH to BBU for Method 2 is denoted by D 2 , and D 3 for Method 3. The data transmission rate is given by

Table 3 .

 3 3 Simulation parameters for method 2 and 3.

	PAPAMETER	SYMBOL	VALUE
	Number of active subcarriers	N Sc	1200
	Symbol duration (for normal CP)	T s	71.43 µs
	Number of samples for each frame N s k (k = 2, 3)	12
	Number of bits for scaling factor	Q s	16
	Number of bits for reference of PRB	Q r	7
	Code rate of FEC applied	r c	8/10
	Assumed PRB utilization ratio	η	0.5or1

  t is the channel matrix from RRH v to UE u. The channel matrix from M RRHs to UE u is H u,t = [H 1,u,t , H 2,u,t , ..., H M,u,t ]. The whole channel matrix from M RRHs to all UEs is H t = [H 1,t ; H 2,t ; ...; H U,t ] During subframe t, RRH v transmits the signal denoted by X v,t ∈ C [N TA ×N s ] following the power constraints:

Table 6 .

 6 1 Summary of different UEs grouping algorithms.

	Acronym	Meaning	Number of stages	First stage Second stage
	GUGA	Greedy user grouping algorithm		GUGA
	SUGA	Semi-orthogonal user grouping algorithm	1	SUGA
	PP-RUGA	Pre partitioned -random user grouping algorithm			random selection
	PP-GUGA	Pre partitioned -greedy user grouping algorithm	2	UDA	GUGA

  Set of UEs S k having the highest achievable sum rate is chosen to be served during subframe k * /

8:

  {u t 1 , u t 2 , . . . u t N g,t }, where N g,t is the size of the group during subframe t. Let G = {N UE,1 , N UE,2 , . . . N UE,N T } be a set of any arbitrary grouping of UEs. UEs in N UE,t are served together or seperately by the RRHs in N TP on respecting to the constraints: N g,t ≤ MN TA . We denote the number of UEs served in single RRH mode as U s , and the number of UEs served in distributed MIMO mode by U d . Then we have U s + U d = U. Let N UE,s = {u s,1 , u s,2 , . . . u s,U s } be the set of UEs served in single RRH mode. Meanwhile, let N UE,d = {u d,1 , u d,2 , . . . u d,U d } be the set of UEs served in distributed MIMO mode. In Fully Single RRH transmission strategy, U s = U, while U d = U in Fully Distributed MIMO transmission strategy. Let T s = {t s,1 , t s,2 , . . . t s,N T,s } be the set of subframes out of T during which the UEs are served in single RRH mode, where N T,s is the length of T s . Let T d = {t d,1 , t d,2 , . . . t d,N T,d } be the set of subframes out of T during which the UEs are served in distributed MIMO mode, where N T,d is the length of T d . And we have N T,s + N T,d = N T . As mentioned in Section 4.3 and Section 6.2, N g,s = M UEs are served during one subframe in single RRH mode and N g,d = MN TA in distributed MIMO mode.

	(7.1)
	7.3 UEs Scheduling

Table 7 .

 7 1 Comparison of CSI signaling cost of different transmission strategies

	Transmission strategy	CSI signaling cost
	Fully single RRH transmission	statistical CSIs between all the M RRHs and all the U UEs every N L frames
		statistical CSIs between all the M RRHs
	Hybrid transmission	and all the U UEs every N L frames instantaneous CSIs between all the M RRHs
	Fully distributed MIMO transmission	and all the U d UEs in N UE,d each frame instantaneous CSIs between all the M RRHs and all the U UEs each frame
	served on distributed MIMO mode becomes

  Cette thèse est divisée en deux parties. Dans la première partie, nous proposons de nouveaux schémas de division fonctionnelle qui déplacent une partie des fonctions dans BBU vers RRH afin de réduire le débit sur fronthaul. Comme les découpages fonctionnels sont plus complexes sur le lien montant que sur le lien descendant, nous nous concentrons sur le lien montant dans cette étude. Dans la deuxième partie, nous étudions l'application de CoMP sur le lien descendant dans C-RAN pour améliorer la capacité du réseau. Nous approfondissons l'étude de l'ordonnancement des utilisateurs et de l'allocation des ressources de fronthaul. Nous analysons le compromis entre la charge sur le fronthaul et le débit sur la chaîne radio. Les principales contributions de cette thèse sont résumées ci-dessous.B.2.1 Réduction du débit de fronthaul sur la liaison montanteCette thèse étudie les nouvelles architectures de RRH et BBU pout réduire le débit de transmission entre RRH et BBU. Deux nouvelles architectures sont proposées et modélisées sur la liaison montante. Une partie des fonctions dans le couche physique de BBU sont déplacées vers RRH. Pour les architectures proposées, le débit entre RRH et BBU dépend la charge du réseau mobile, tandis qu'il est constant dans l'architecture actuelle. Contrairement à la plupart des travaux précédents, nous avons effectué des analyses quantitatives sur l'impact des différentes divisions fonctionnelles. Les résultats de la simulation illustrent que 30% à 40% de la bande passante peut être économisée lorsque toute la capacité du canal radio est utilisée et jusqu'à 70% lorsque la moitié de la capacité du canal radio est utilisée. Cette partie du travail a été publiée dans la conférence internationale VTC au printemps 2016 [DLG16b]. B.2 Les contributions 131 B.2.2 Conception de transmission coordonnée dans C-RAN avec capacité limitée de fronthaul CoMP peut améliorer les performances du réseau mobile. Cependant, la performance de CoMP est limitée par la complexité et la capacité bornée de fronthaul. Nous concevons un schéma de transmission coordonné tout en considérant l'allocation des resources sur le fronthaul. Cette partie du travail se concentre sur le lien descendant. Un nouveau schéma de constitution de grappes des RRHs est proposé. Nous comparons d'abord différentes stratégies de transmission sans et avec la coopération entre différentes cellules tout en considérant la capacité de fronthaul limitée. Ensuite, nous proposons plusieurs algorithmes de groupement d'utilisateurs pour améliorer les performances du MIMO (Multiple-Input Multiple-Output) distribués, appelés D-MIMO. Dans D-MIMO, plusieurs RRHs servent un certain nombre d'UE en parallèle par Zero-Forcing (ZF). Enfin, une stratégie de transmission hybride est proposée, dans laquelle une partie des utilisateurs sont servies par un seul RRH et les autres servis par plusieurs RRHs.Comparaison des différentes stratégies de transmissionAu début, nous étudions le débit maximal de différentes stratégies de transmission dans une grappe de RRHs de C-RAN. Les contraintes de puissance de RRH et de capacité de fronthaul sont prises en compte. Les stratégies de transmission non-CoMP (par exemple en mode RRH unique) et CoMP (par exemple D-MIMO) sont considérées. En RRH unique mode, chaque utilisateur est servi par un seul RRH. En D-MIMO mode, une grappe de RRHs servent une groupe d'utilisateurs appliquant ZF pour effectuer une transmission conjointe. Les résultats de simulation montrent que D-MIMO a une meilleure performance que le mode RRH unique avec une puissance de RRH élevée, une capacité de fronthaul élevée et lorsque les utilisateurs sont situés en bordure de cellule. Cette partie du travail a été presentée dans la conférence internationale WPMC 2016[START_REF] Duan | Maximum throughput in a C-RAN cluster with limited fronthaul capacity[END_REF].Amélioration zero-forcing par algorithme de regroupement d'utilisateursLes utilisateurs servis par une grappe de RRHs ont souvent un nombre total d'antennes plus grandes que les RRHs. Ils sont servis dans différentes sous-trames temporelles. La performance de D-MIMO appliquant ZF peut être améliorée en choisissant de manière appropriée quels utilisateurs sont servis ensemble dans la même ressource de fréquence et de temps. Avec les données des utilisateurs et les informations d'état du canal (channel Coordination dans les réseaux d'accès radio centralisés avec liaisons de transport à débit limité state information, CSI) partagées dans la grappe de BBU, C-RAN facilite l'ordonnancement centralisé des utilisateurs. Nous proposons plusieurs algorithmes de groupement d'utilisateurs de faible complexité pour maximiser le débit total. Nous étudions d'abord le scénario avec une capacité de fronthaul illimitée et avec une seule antenne sur chacune utilisateur et RRH. Cette partie du travail a été presentée dans la conférence internationale ICC 2017[START_REF] Duan | Analysis of different user grouping algorithms in a c-ran downlink system[END_REF].

  shadow fading coefficient between RRH v and UE u θ u,v angle between the line (RRH v, UE u) and the antenna orientation of RRH v

	136		Nomenclature
	q n		n-th quantization level
	Q q		length of quantization bits
	Q r		number of bits for reference of PRB
	Q s		number of bits for scaling factor
	r c		code rate of FEC applied
	R u t	achievable transmission rate for UE u Nomenclature index of subframe
	T T d T s U u	Roman Symbols a cluster of RRHs set of subframes set of subframes when the UEs are served in distributed MIMO mode set of subframes when the UEs are served in single RRH mode number of UEs served by a cluster of RRHs C C fronthaul capacity constraint index of UE
	U d	d u,v	distance between RRH v and UE u number of UEs served in distributed MIMO mode
	U s	E s	average symbol energy number of UEs served in single RRH mode
	V	f	index of subcarrier precoding matrix
	v	F os	oversampling factor index of RRH
	X	f s	sampling frequency signal transmitted by RRHs
	Y	H	channel matrix signal received by UEs
	M N c Greek Symbols N g,d α u,v path loss coefficient between RRH v and UE u number of RRHs in a cluster number of collections number of UEs served in distributed MIMO mode during one subframe N g,s η assumed PRB utilization ratio number of UEs served in single RRH mode during one subframe N g,t γ normalization factor number of UEs served during subframe t N Sc number of active subcarriers ρ u,v
		N T		number of subframes
	N v TA Other Symbols	number of antennas for RRH v
	N T,d (•) H N TP (•) ⋆ N T,s (•) T C N UE,d Θ(•) N UE,s I n N UE,t N u UA P dBm P N [i] |N | I(X; Y)	hermitian matrix transpose length of T d complex conjugate set of RRHs in the cluster C matrix transpose length of T s set of UEs served in distributed MIMO mode complex field set of UEs served in single RRH mode complexity of an algorithm set of UEs served during subframe t identity matrix of size n number of antennas for UE u RRH power constraint in dBm RRH power constraint the i-th element in set N the cardinal of N
		Q		quantization noise matrix

the mutual information between random variables X and Y 1 two-element set {0, 1}

Acknowledgements

Declaration

I hereby declare that except where specific reference is made to the work of others, the contents of this dissertation are original and have not been submitted in whole or in part for consideration for any other degree or qualification in this, or any other university. This dissertation is my own work and contains nothing which is the outcome of work done in collaboration with others, except as specified in the text and Acknowledgements. de

Nomenclature

List of figures 4.7 Conclusion

The C-RAN downlink system model and configurations for the following of this thesis is presented. We propose a new RRH clustering scheme. It is a trade-off between disjoint clustering and user-centric clustering.

Comparison of Different Transmission Strategies

The achievable transmission rate with fronthaul capacity constraint for UE u during subframe u is

where u = 1, 2, 3.

The sum achievable transmission rate during subframe 1, 2 and 3 with fronthaul capacity constraint is

(5.9)

Single User Joint Transmission (SU-JT)

For single user joint transmission (SU-JT), we assume T = 3, and T = {1, 2, 3}. UE u is supposed to be the only one being served during subframe u, where u = 1, 2, 3. And all the 3 RRH transmit the same signals to UE u during subframe u.

As the serving RRHs transmit signals with maximum power, the achievable transmission rate without fronthaul capacity limitation during subframe u for UE u is

The achievable transmission rate with fronthaul capacity constraint for UE u during subframe u is R u = min (R u , C) (5.11) where u = 1, 2, 3. The sum achievable transmission rate during subframe 1, 2 and 3 with fronthaul capacity constraint is

(5.12)

Distributed MIMO Mode (D-MIMO)

For distributed MIMO mode (D-MIMO), we assume T = 1, and T = {1}. Without losing generality, index t will be omitted in the following of this section. All the 3 RRHs transmit parallel data together to all the 3 UEs. With perfect Channel State Informations (CSI) available at BBU pool, both linear procoding and dirty paper coding (DPC) techniques can be applied for the joint transmission [START_REF] Peng | Recent Advances in Cloud Radio Access Networks: System Architectures, Key Techniques, and Open Issues[END_REF]. DPC can achieve a better performance but is difficult to implement in practical systems. This where

Analysis of Several User Grouping Algorithms

Assign UE m to the set M n 8: The number of all possible UEs groupings with the constraint that UEs in the same collection cannot be served during the same subframe is |M N c U | = |M 3 9 | = 36 (applying (6.30)). We apply the simulation configuration presented in Section 6.2 and set the RRH power constraint to P = 41.86 dBm. Each fronthaul is assumed to have unlimited transmission capacity. In each simulation, we randomly generate U = 9 UEs located at different positions which are served by the cluster of the 3 RRHs with a random channel matrix. For the given channel matrix in this simulation, we calculate the sum rate with each of the |K 3 9 | = 280 UEs groupings using (6.17) and (6.27). Then we order the 280 UEs groupings K 3 9 in increasing order of the average achievable sum rates achieved by them. Next, we do the same process to the |M 3 9 | = 36 UEs groupings. After the reordering, each i-th element of

U is labeled with the number i. M 3 9 is a subset of K 3 9 . Next, we let each element in M 3 9 have the same label as it has in K 3 9 . We perform 5 different simulations, and plot the average achievable sum rate versus the labels of each element in K 3 9 and M 3 9 of each simulation in Figure 6.4. We can observe that there is a wide variation of average achievable sum rate for different UEs groupings in each simulation. The highest average achievable sum rate can be twice as the lowest. Therefore, it is interesting to find a good UE grouping to increase the sum rate. M 3 9 is a set of UEs Conclusion pool for processing generates large fronthaul throughput. In TDD, relying on reciprocity between the uplink and downlink channels, CSIs can be directly gotten in the RRHs' side. However, this still cannot avoid the CSIs transmission on the fronthaul for cooperative processing. Therefore, the evaluation of the performance of CoMP would be more realistic with considering the CSIs consumption.

Imperfect Channel State Information (CSI)

In this thesis, we assume that perfect channel state information (CSI) exists in the BBU pool. However, in practical, it is difficult to obtain perfect CSIs. The performance of CoMP is sensitive to imperfect and outdated CSIs. It is interesting to develop CoMP transmission schemes which are robust to the CSI errors. This can also reduce the need for CSI feedback, which in turn leads to less transmission costs both in radio interface and fronthaul.

Heterogeneous Cloud Radio Access Networks (H-CRAN)

The studies on Heterogeneous networks (HetNets) are hot in recent years. The deployment of low-power nodes (e.g. pico base station, small cell base station) in UEs dense areas is a promising solution to satisfy the high traffic demands. Nevertheless, the coexistence of macro sites and dense low-power nodes results in complex interference environment. Heterogeneous Cloud Radio Access Networks (H-CRAN) has been proposed to facilitate the management of the interference. H-CRAN is a mix of HetNets and C-RAN. The overall interference management in HetNets is much more challenging than in a macro cellular network. To develop low complexity CoMP strategies while considering UEs fairness, limited fronthaul capacity and energy consumption in H-CRAN would be very interesting.

Appendix A

Proof of Theorem 1

For any matrix U, the matrix UU H is positive semidefinite. Therefore, each eigenvalue of H u ΩH H u is non-negative: λ u,i ≥ 0, i = 1, 2, . . . N UA , where λ u,1 , . . . λ u,N UE are the N UA eigenvalues of H u ΩH H u . As H u ΩH H u in (6.24) is a Hermitian positive semidefinite matrix, it is diagonalizable. Thus there exists an invertible matrix P which lets

where

Proof of Theorem 1

Using (A.2) and because det(P -1 ) det(P) = 1, therefore the achievable transmission rate for

= log det(P) det(I N UA +γ 2 t I N UA +γ 2 t P -1 Λ u P) det(P -1 ) det(P) det(I N UA +γ 2 t P -1 Λ u P) det(P -1 )

= log det(P(1+γ 2 t )I

As λ u,i ≥ 0 ∀u ∈ N UE,t i = 1, . . . N UA , it can easily be proved that the maximum value of γ 2 t : We first investigate new functional split architectures between Remote Radio Heads (RRHs) and Baseband Units (BBU) on the uplink to reduce the transmission throughput in fronthaul. Some low layer functions are moved from the BBU to RRHs and a quantitative analysis is provided to illustrate the performance gains.

We then focus on Coordinated Multi-point (CoMP) transmissions on the downlink. CoMP can improve spectral efficiency but needs tight coordination between different cells, which is facilitated by C-RAN only if high fronthaul capacity is available. We compare different transmission strategies without and with multi-cell coordination.

Simulation results show that CoMP should be preferred for users located in cell edge areas and when fronthaul capacity is high. We propose a hybrid transmission strategy where users are divided into two parts based on statistical Channel State Informations (CSIs). The users located in cell center areas are served by one transmission point with simple coordinated scheduling and those located in cell edge areas are served with CoMP joint transmission. This proposed hybrid transmission strategy offers a good trade-off between users' transmission rates and fronthaul capacity cost.