Cristo Suarez-Rodriguez
email: cristo.suarez-rodriguez@hdr.mq.edu.au

B A Jayawickrama
email: beeshanga.jayawickrama@uts.edu.au

Faouzi Bader
email: faouzi.bader@supelec.fr

E Dutkiewicz
email: eryk.dutkiewicz@uts.edu.au

Michael Heimlich
email: michael.heimlich@mq.edu.au

REM-Based Handover Algorithm for Next-Generation Multi-Tier Cellular Networks

Keywords: Radio Environment Maps, Handover, Heterogeneous Networks

The strongest-cell criterion has been extensively used for handover algorithms during the last cellular-network generations. When network topologies become multi-layered, it results in abrupt behaviors such as the ping-pong effect as a consequence of the power gap between tiers and their irregular deployment. This effect not only affects users' quality of experience but also introduces a significant network overhead. Therefore, we propose an original handover algorithm based on predicted incomplete channel states from a Radio Environment Map to reduce this effect. The proposed algorithm is user triggered, network assisted, and fully backward compatible with LTE-A. Moreover, we evaluate the performance of our proposed algorithm against LTE-A in a two-tier cellular network for different user speeds following the guidelines outlined by the 3GPP on diverse matters (channel, mobility, wrapping, etc.). When applying realistic timing, our results reveal a highly substantial improvement in the number of ping-pong handovers regardless of the handover policy adopted in comparison to LTE-A without sacrificing users' experience; for instance, we obtain at least an order of magnitude decrease in the ping-pong rate at the expense of losing less than 9 percent in spectral efficiency.

I. INTRODUCTION

As a result of the rapidly growing demands of multimedia data-intensive applications such as video streaming, gaming, social networking, etc., current cellular networks, e.g. Long Term Evolution (LTE) and LTE-Advanced (LTE-A), cannot satisfy users' needs any more [START_REF]White paper: Cisco VNI Forecast and Methodology[END_REF]. This has led the 3 rd Generation Partnership Project (3GPP) to design LTE-A Pro, which is meant to pave the way towards a seamless transition to 5G. Among others, 5G is expected to enhance broadband connectivity by using LTE in the unlicensed spectrum below 6 GHz. However, it simultaneously raises a twofold issue: on the one hand, a large portion of the spectrum becomes available for carrier aggregation; however, on the other hand, coexistence across different technologies can also bring higher levels of interference. This represents an opportunity to expand the Heterogeneous Network (HetNet) network layout to a greater extent, combining not only licensed spectrum, as usual, but also unlicensed spectrum to create a multi-tier cellular network.

The ultimate motivation behind the deployment of small cells (micro, nano, pico, femto) underlying the coverage of macrocells is improving the capacity per unit area. Despite its countless advantages with respect to the perceived Quality of Service (QoS) from the users' perspective, Mobile Network Operators (MNO) must overcome a set of challenges like efficient network management or uninterrupted mobility. Traditionally, the LTE handover (HO) algorithm has proven to perform quite well in macro-only scenarios, however it struggles in the presence of small cells due to their non-collocated layout and low transmit power [2]. A comprehensive survey of handover decision algorithms for femtocells in LTE-A is delivered in [START_REF] Xenakis | Mobility Management for Femtocells in LTE-Advanced: Key Aspects and Survey of Handover Decision Algorithms[END_REF]. However, to the best of our knowledge, it is rare to find research works comparing them to decide on which one to consider under certain circumstances.

We introduce the idea of making use of Radio Environment Maps (REM) as a powerful tool for a handover decision algorithm. A REM is basically a heat map of the RSS in R 2 for a specific band. In particular, we are interested in improving mobility performance by reducing the overall number of handovers without sacrificing network capacity. In a multi-tier scenario, this means reducing the number of redundant handovers, also known as ping-pong handovers, between tiers, especially for high-speed User Equipments (UE). Ping-pong handovers are defined as consecutive handovers between the same cells within a short period of time, e.g. less than a second. REMs could potentially address simultaneously a myriad of users ranging from pedestrians to trains. Our proposed algorithm aims at camping users, not only on the strongest cell available but also on the one with the highest Signal-to-Interference-plus-Noise Ratio (SINR) based on the current user's trajectory.

Section II presents an overview of the system model employed. Section III explains the REM-based handover algorithm. Section IV provides numerical performance results of the proposed algorithm benchmarked against LTE-A. Finally, Section V states the main findings of this work as well as a summary.

II. SYSTEM MODEL

In this work, we assume that REMs are stored and managed by the mobile network operator.For example, in [START_REF] Perez-Romero | On the use of radio environment maps for interference management in heterogeneous networks[END_REF] the authors discuss possible implementations in different network entities within an LTE-A network. They introduce a layered architecture that consists of local and global REMs, where the coordination between local REMs can be done through the X2 interface while the coordination between local and global REMs must be done through the S1 one. REMs are essentially geolocation databases that store some Radio-Frequency (RF) relevant parameters. The cost, field measurements mostly, of the maps is not considered in this work. So as to create a map, there are basically two options that can be followed: we can deploy measurement-capable devices that perform measurements (UEs and sensors) and apply spectrum cartography techniques as in [START_REF] Jayawickrama | Improved performance of spectrum cartography based on compressive sensing in cognitive radio networks[END_REF], or we can use a realistic 3D urban electromagnetic wave propagation fused with digital geographical map data (terrain altitude, building contours, etc.) to synthesize coverage maps (up to 5-m resolution) as detailed in [START_REF] Letourneux | 3D coverage analysis of LTE urban heterogeneous networks with dense femtocell deployments[END_REF].

In addition, users must be able to measure the band of interest and report those measurements to their serving cell in a similar fashion to the current LTE-A UE. Moreover, we need UEs to have the capability of positioning using either a Global Navigation Satellite System or an LTE-A networkassisted technique. In the former group is included the GPS, GLONASS or GALILEO positioning systems, whereas in the latter Observed Time-Difference Of Arrival (OTDOA) and Enhanced Cell-ID techniques are used. The impact of these systems on the proposed algorithm is beyond the scope of this work.

We assume a Heterogeneous Network (HetNet) composed of evolved Node B (eNB) and Home eNB (HeNB) in openaccess mode. Both tiers belong to the same MNO, whose allocated frequency bands compose the set F. Additionally, they operate in the same band f ∈ F. As we evaluate the handover performance, from now on, we are solely focused on the downlink. Let C denote the set of cells operating in f , regardless of the tier, and U the set of users. In consequence, the SINR of a user u ∈ U camping on its serving cell s ∈ C can be expressed as

γ s,u = P s |h s,u | 2 c∈C\{s} P c |h c,u | 2 + σ 2 u ( 1
)
where P s is the transmit power of the cell s, P c is the transmit power of the cell c, h s,u is the channel gain from cell s to user u, h c,u is the channel gain from cell c to user u, and σ 2 u is the noise power at user u. Nonetheless, the LTE-A standard defines two different UE measurements: Reference Signal Received Power (RSRP) and Reference Signal Received Quality (RSRQ). Without loss of generality, in our approach a user u only measures the RSS from a cell c ∈ C, defined as RSS c,u = P c |h c,u | 2 . LTE-A caters for mobility with event-triggered reporting, using both intra-and inter-frequency measurements whose values and thresholds are in dBm/dB. The entry condition must be met for at least the Time To Trigger (TTT) period, generally configured by the network and further scaled by the user, depending on its speed to control the ping-pong effect. A relative offset also helps to adjust the timing when the handover is executed: a low value might lead to a tooearly handover while a high value may end up with a too-late handover or even a Radio Link Failure (RLF). Substituting the RSRP for the RSS as aforementioned we can describe this handover policy as follows:

c * = argmax c∈C RSS c,u (t) | RSS TTT s,u < RSS TTT c,u -HHM (2)
where c * corresponds to the strongest cell, RSS TTT c,u

is the RSS c,u during the TTT, and HHM stands for Hysteresis Handover Margin and corresponds to the relative offset. We would like to emphasize the time dependence, which is not normally made explicit since our proposed algorithm to be introduced in the next section will depend specifically on time. From (2) it is clear that the current algorithm promotes cells with higher power/channel gain regardless of any other criteria such as SINR, cell load, UE power consumption, etc. In the remainder of this work, cell detection is assumed to be done under the time constraints specified in 3GPP TS 36. 133 [7], therefore we will only focus on the handover itself.

III. REM HANDOVER ALGORITHM DESCRIPTION

While the LTE-A handover policy has shown itself to be robust enough only in macrocell scenarios, with HetNets it becomes more challenging due to the higher interference under co-channel deployment, Neighbor Cell Lists (NCL) changing rapidly when femtocells appear and disappear, etc. This is especially true for users who pass through an area under the overlapped coverage of different tier cells, because the number of ping-pong handovers increases and, thus, the network signaling. Furthermore, the higher the UE speed is, the more complicated the handover decision stage becomes. Our main objective is to reduce the overall number of pingpong handovers between tiers using the spatial information provided by REMs without compromising the QoS of the users.

The proposed algorithm scheme relies on the same eventtriggered mechanism as does LTE-A, although it is not limited to it. Thus it can be seamlessly adapted to current state-of-theart UEs. As REMs will be only stored on the network side, the proposed algorithm avoids any extra overhead due to the exchange of information between the REM database and the UE. However, users must be requested to send their location along with the measurement reports, as already happens in the Minimization of Drive Test (MDT) in LTE-A [START_REF] Johansson | Minimization of drive tests in 3GPP release 11[END_REF].

Once the measurement report is triggered, our proposed algorithm predicts the user's position in a timespan ∆t, assuming a simple uniform linear motion described by r(t + ∆t) = r(t) + v∆t, where r and v are position and velocity respectively. Even if the trajectory of the user is either accelerated or not linear, provided that the timespan is not too long the trajectory can be approximated by a set of adjacent segments where each follows a uniform linear motion. The endpoint is then introduced in the corresponding REMs to get an expected RSS value for a given cell. In order to reduce the number of queries, there is another algorithmrelated parameter, R, which basically defines a searching radius whose center is the predicted position. An example of this predicted position and the searching radius is depicted in Fig. 1. This parameter allows us to set an upper bound on the number of cells to be considered in the prediction calculations.

At this stage, despite the fact that we could just pick the strongest predicted cell in ∆t, it is preferable to obtain a more unbiased measurement like the SINR. Besides, the expected QoS of the user will depend on the capacity of the channel rather than just the greatest received power. Taking all the previous parameters into account, our proposed policy to determine the strongest cell for handover can be expressed as

c * = argmax c∈B γ c,u (t + ∆t) | RSS TTT s,u < RSS TTT c,u -HHM (3)
where all parameters from (2) remain, and c ∈ B means cells within the searching radius (B ⊂ C). What this policy accomplishes is that a user will hand over to the strongest cell only if that same cell will have the highest SINR in the near future according to the user's trajectory. Note that (1) is a pessimistic evaluation of the SINR since the cell traffic load is not considered (all cells are fully loaded) and hence we could avoid some handovers towards heavily-loaded cells. This effect might increase the spectral efficiency and the global performance but this approach is not the actual focus of this work.

For instance, we can imagine a high-speed user crossing an area under the coverage of a macrocell and several femtocells. Even when the strongest-cell policy might suggest that the best option is handing over to a femtocell, after several seconds the same user will be handing over back to the macrocell. In our approach, we avoid such handovers, remaining camped on the macrocell. If we are dealing with a slowly-moving user, the current strongest cell will most likely have the best SINR in the future since the user will not have left its coverage. Needless to say, this introduces the second condition so as to perform a handover that, eventually, will lead to a reduction in the total number of handovers. The different steps of the proposed algorithm are shown in Algorithm 1.

Algorithm 1 REM-based handover algorithm

12:

BS sends the handover command back to the UE.

13:

end if

14:

end if

15: end procedure

The procedure of the UE REM-HO takes place at the User Equiment and it is identical to what is currently used in the LTE-A standard. Similarly, the second procedure labeled BS REM-HO is run on the operator's side. On the user's side, the values used to trigger the events are not the raw physicallayer measurements but a filtered version using what is known as L3 filtering [START_REF] Holma | LTE Small Cell Optimization: 3GPP Evolution to Release 13[END_REF]. This recursive filter is located in the Radio Resource Control (RRC) layer and is expressed as

F n = (1 -a)F n-1 + aM n (4)
where a = 2 -f c/4 is the filter coefficient with parameter f c, F n is the filtered value (e.g. RSRP, RSRQ, etc.) and M n is the raw measurement provided by the PHY layer. In our case, F n is the RSS while the filter coefficient is optionally signaled by the network (the default value is f c = 4 → a = 0.5). In a similar manner, the RSS values stored in the REMs only represent the effect of path loss and shadowing, since fastfading is averaged out.

IV. NUMERICAL RESULTS

A. Simulation setup

This section provides numerical results for evaluating the performance of the proposed REM-HO algorithm and, for comparison, the standard LTE-HO algorithm in a HetNet. The simulation environment used for carrying out the simulations has been developed entirely using MATLAB. It comprises a scenario generator based on hexagonal grids [START_REF]Hexagonal Grids from Red Blob Games[END_REF] for deploying base stations and users, a radio simulator following WINNER's Phase II Model implementation but using 3GPP 3D channel models [11] (see values in Table I) where we obtain the RSS for each pair BS-UE and, finally, an algorithm workbench where we can test different HO algorithms on the same radio simulation instance. The baseline scenario is based on the European-funded METIS-II project Performance Evaluation Framework User Case 1: Dense urban information society [START_REF]Mobile and wireless communications Enablers for Twenty-twenty[END_REF] that also includes mobility models. We have also included geographical distance-based wrapping following the 3GPP guidelines in [13]. Therefore, we do not have less interference at the border of the network. Table I lists the major simulation parameters. Macrocells, the first-tier network, follow the classic 19-site layout with an Inter-Site Distance (ISD) of 200 m, while picocells, the second-tier network, are deployed following the next Probability Density Functions (PDF) using polar coordinates (r, θ) relative to their macro station [START_REF] Alouini | Area spectral efficiency of cellular mobile radio systems[END_REF]:

p r (r) = 2(r -d min ) (d max -d min ) 2 d min ≤ r ≤ d max (5) p θ (θ) = 1 2π 0 ≤ θ ≤ 2π (6)
where d min is the closest distance admissible between tiers, which is equal to 55 m, and d max corresponds to the cell edge which depends on the angle θ (see details in Fig. 1). The UEs are also scattered according to ( 5) and ( 6) but changing the minimum distance to 35 m instead of 55 m [START_REF]Mobile and wireless communications Enablers for Twenty-twenty[END_REF]. For the baseline scenario, we have deployed 8 picocells and 5 users per macro sector unless otherwise stated. Each UE moves linearly in a direction randomly chosen between [0, 2π), and its speed of motion is constant. During the simulation, the UE's position is updated every 100 ms, and we obtain a channel realization every 10 ms, which corresponds to the LTE-A frame duration. The propagation conditions (Line-and Non-Line-Of-Sight, LOS/NLOS) are assigned at the beginning according to the 3GPP formulae [11] and kept fixed for the rest of the simulation. Similarly, the LTE-HO algorithm has been extracted from [2], including realistic timing such as the intra-frequency measurement period, handover preparation and execution times, etc. The RLF recovery has been bounded to occur within 120 ms, including the RRC procedure delay. In this case, we assume that the target cell is sufficiently strong to be detected in the first correlation attempt [START_REF] Sesia | LTE -The UMTS Long Term Evolution: From Theory to Practice[END_REF]. A UE is said to be out of synchronization when its wideband SINR is below the threshold Q out and to be back in synchronization when above the threshold Q in . An RLF is declared when a UE is out of synchronization for longer than the RLF Time (T310 timer in 3GPP terms, typically 1 s). Subsequently, a handover failure happens if: a) RLF occurs before TTT duration, b) T310 is running when the handover command is sent, or c) the wideband SINR in the target cell is below Q out when the handover-complete message is sent. Finally, the Time of Stay (ToS) is defined as the duration between two consecutive successful handovers. In the event that these handovers are performed between the same two cells in less than the minimum ToS, it is considered a ping-pong handover.

Ping-pong handovers reduce the efficiency of the network so it is crucial to reduce their numbers while keeping a satisfactory QoS. Table II reflects the parameters involved in both handover and RLF. REMs have been built using the worst-case scenario for both macro and picocells, in effect, NLOS, where path loss and large-scale fading can be predicted but small-scale fading cannot due to its nature. If we were able to build REMs from real measurements, this workaround would not be needed since the measurements themselves inherently contain the propagation conditions. Finally, we assess the proposed algorithm and its counterpart by evaluating 4 different sets of configuration parameters as shown in Table III, ranging from less to more aggressive (lower to higher mobility as well), extracted from [2]. We have decided to keep the specific REM-HO parameters constant on purpose so that we can evaluate them later on. R in Algorithm 1 is 200 m to coincide with the ISD and ∆t is 2.5 s, which is a compromise for the different speeds considered (3, 30, 60, 120 km/h). It can be seen that in our proposed algorithm this rate is below 2 percent in any configuration set regardless of the user's speed. The reason behind such a considerable reduction is the incomplete channel states stored in the REMs. Our technique double-checks if a target cell spotted by a user would still be a good choice in ∆t seconds, so avoiding virtually any possibility of hopping over two cells in less than ∆t. The users with the lowest speed suffer from a marginally higher rate because they require more time to cross the same area. An adaptive timespan could be considered according to the user's speed, enunciating an optimization problem.

B. Ping-pong handovers

If we relax the constraint of picking the BS with the highest SINR and we increase the candidate list up to the first K cells with the highest SINR, our proposed technique will tend to behave like LTE-A. As K increases, both algorithms become indistinguishable. For example, in Table IV we have set K equal to 3. Again, the lowest-speed users are the most affected by this change, with rates similar to LTE-A for configuration sets 3 and 4 (see the set details in Table III). The rest of the sets do not increase at the same pace due to the longer TTT.

The decrease in the ping-pong rate has a clear impact on the number of handovers. Table V shows the average number of events where REM-HO events are substantially diminished. The gray rows represent the ratio of ping-pong handovers to the total. The difference in the number of handovers is not only attributed to the ping-pong avoidance; in this regard, our algorithm postpones handovers as long as possible until a strong cell which will stay strong for at least ∆t seconds shows up. This effect is translated into a higher occurrence of RLFs but is still comparable to LTE-A for the most aggressive sets as shown in Table VI. There is a trade-off between the ping-pong rate and the number of RLFs, controlled by the size of the candidate list. As previously mentioned, being less conservative and allowing more cells to be selected can reduce the RLFs while increasing the ping-pongs.

C. Impact on spectral efficiency

Preventing users from handing over also brings a loss in a user's spectral efficiency, as in Fig. 2 and Fig. 3. In these figures we have the average channel spectral efficiency for configuration set 3 (TTT = 80 ms, HHM = 1 dB) for 60 km/h users. In Fig. 2 we keep all the parameters fixed and sweep only ∆t. The obtained loss in spectral efficiency compared to LTE-A can be easily explained. LTE-A picks the strongest cell at any time after TTT seconds whereas we double-check if that cell will maintain its status after ∆t seconds. Therefore, if the timespan becomes smaller, the filtered measurements and the predicted values stored in the REMs will be similar because of the spatial correlation in large-scale fading. For instance, our algorithm almost perfectly overlaps LTE-A when ∆t = 0. Selecting the right ∆t for each speed is key to control the trade-off between the reduction in the ping-pong handovers and the loss in spectral efficiency. As an example, for ∆t = 2.5 s, which corresponds to a prediction distance of 41.67 m, we reduce the ping-pong rate to 0.01% (11.82% for LTE-HO) but, at the same time, we loss approximately 9% of spectral efficiency (1.14 b/s/Hz against 1.25 b/s/Hz). In Fig. 3 we benchmark the performance of the LTE-HO and the proposed REM-HO algorithms under different picocell densities. Although the gap increases with density, it will not go further than approximately 0.1 b/s/Hz. Here we observe the trade-off of using our technique instead of the current LTE-A handover approach. The slight loss of spectral efficiency is due to the smaller overall number of handovers, by around an order of magnitude. However, we ensure an acceptable QoS while introducing a smaller amount of overhead in the network. Regarding the network overhead, the UEs only send a few extra bits of information compared to the LTE-HO algorithm (location and velocity although they are parameters already included in the standard), that we might consider negligible. Besides, the signaling between BSs will depend on the specific algorithm, as detailed in [START_REF] Perez-Romero | On the use of radio environment maps for interference management in heterogeneous networks[END_REF], it is estimated that the REM signaling requirement is about 68 bits/s per cell for an inter-cell interference minimization technique. Yet the update frequency of the databases is not discussed.

V. CONCLUSION

In this work, we have introduced the idea of using REMs in the handover decision-making as a way of predicting QoS. We have also presented a handover algorithm which takes advantage of REMs' spatial information in multi-tier cellular networks by preventing users from handing over too early. We have simulated our proposed algorithm and the LTE-HO algorithm where we have shown a significant reduction in the number of ping-pong handovers independently of the hysteresis margin applied. At the same time, the overall number of handovers is also cut down while maintaining a reasonable channel spectral efficiency. ACKNOWLEDGMENT

Fig. 1 .

 1 Fig. 1. Analyzed scenario for proposed REM handover algorithm.

Fig. 2 .Fig. 3 .

 23 Fig. 2. CDF of channel spectral efficiency for configuration set 3, 60 km/h, 8 picocells and ∆t = {1, 2.5, 5, 10} s.

  procedure BS REM-HO(t, {x, y}, {vx, vy}, ∆t, R, REMc) 7: Predict the user's position in ∆t. {xp, yp} ← {x, y} + {vx, vy} • ∆t

	1: procedure UE REM-HO(RSSc, TTT, HHM) 2: if RSS TTT s < RSS TTT -HHM then t 3: UE sends a measurement report with the target
		cell t, user's location {x, y} and velocity
		{vx, vy}.
	4:	end if
	5: end procedure
	6: if Measurement report then
	8:
	9:	Find all cells within R. c ∈ B where B := (x -xp) 2 + (y -yp) 2 ≤ R	2
	10:	Rank cells according to their expected SINR using
		the values stored in the REMs.
		γc ←	REMc(xp, yp)

k∈B\{c} REM k (xp, yp) + σ 2 11: if t = argmax c∈B γc then

TABLE II HO

 II AND RLF PARAMETERS

	Item	Description
	Qout	-8 dB
	Qin	-6 dB
	RLF Time	1 s
	RLF Recovery Time	120 ms
	HO Preparation Time	40 ms
	HO Execution Time	50 ms
	Minimum ToS	1 s

TABLE V AVERAGE

 V NUMBER OF HANDOVERS PER USER PER SECOND (HO/UE/S) WITH 8 PICOCELLS PER MACROCELL SECTOR AND ∆t = 2.5 S

		Speed [km/h]	Set 1	Set 2	Set 3	Set 4
	LTE-HO	3 30	0.0014 0 0.0034 0.0001	0.0024 0 0.0058 0.0002	0.0056 0.0011 0.0130 0.0011	0.0190 0.0111 0.0213 0.0054
		60	0.0031 0.0001	0.0053 0.0004	0.0168 0.0020	0.0260 0.0056
		120	0.0031 0.0001	0.0050 0.0003	0.0171 0.0031	0.0266 0.0069
	REM-HO (gray rows 1E-4 ×)	3 30	0.0010 0 0.0009 0.0078	0.0013 0 0.0014 0.0234	0.0019 0.0858 0.0028 0.1248	0.0024 0.4600 0.0034 0.4366
		60	0.0005 0	0.0008 0	0.0022 0.0234	0.0026 0.0624
		120	0.0005 0	0.0009 0	0.0031 0.0078	0.0039 0.0234

TABLE VI AVERAGE

 VI NUMBER OF RLFS PER USER PER SECOND (RLF/UE/S) WITH 8 PICOCELLS PER MACROCELL SECTOR AND ∆t = 2.5 S

		Speed [km/h]	Set 1	Set 2	Set 3	Set 4
		3	0.0027	0.0024	0.0020	0.0018
	LTE-HO	30 60	0.0090 0.0145	0.0082 0.0142	0.0042 0.0079	0.0033 0.0061
		120	0.0177	0.0176	0.0117	0.0099
		3	0.0024	0.0022	0.0020	0.0020
	REM-HO	30 60	0.0080 0.0122	0.0076 0.0119	0.0063 0.0106	0.0059 0.0102
		120	0.0148	0.0144	0.0123	0.0116

This paper has been funded by a Cotutelle International Macquarie University Research Excellence Scholarship (iMQRES) -No. 2016188.


Marwa Chafii
email: marwa.chafii@centralesupelec.fr

Faouzi Bader

Jacques Palicot

Enhancing Coverage in Narrow Band-IoT Using Machine Learning

Keywords: Narrow-band Internet of Things (NB-IoT), Coverage Enhancement (CE), Dynamic spectrum access, Reinforcement learning

Narrow Band-Internet of Thing (NB-IoT) is a recently proposed technology by 3GPP in Release-13. It provides low energy consumption and wide coverage in order to meet the requirements of its diverse applications that span social, industrial and environmental aspects. Increasing the number of repetitions of the transmission has been selected as a promising approach to enhance the coverage in NB-IoT up to 164 dB in terms of maximum coupling loss for uplink transmissions, which is a significant improvement compared with legacy LTE technologies, especially to serve users in deep coverage. However, a large number of repetitions reduces the system throughput and increases the energy consumption of the IoT devices, which reduces their battery lifetime and increases their maintenance cost. In this work, we propose a new method for enhancing the NB-IoT coverage based on machine learning algorithms. Instead of employing a random spectrum access procedure, dynamic spectrum access can reduce the number of required repetitions, increase the coverage, and reduce the energy consumption.

I. INTRODUCTION AND MOTIVATIONS

Internet of things (IoT) is becoming an increasingly growing topic due to its promise to change different aspects of our world. As recently predicted by Cisco, there will be 50 billions IoT connected devices by 2020, where each cell supports a massive number of devices (more than 50K connections per cell [START_REF]Cellular system support for ultra low complexity and low throughput internet of things[END_REF]). This rapid penetration of connected devices has the potential to impact the way we live, we work and how we interact with objects. The massive connected world advertised by IoT emerging companies requires a huge transfer of data, devices with long autonomy, as well as an extended coverage and indoor penetration.

In order to meet the requirements of IoT world, the 3GPP has designed the narrow band internet of things (NB-IoT) standard in its recent Release 13 [START_REF]Cellular system support for ultra low complexity and low throughput internet of things[END_REF]. The main design objectives of NB-IoT are increased coverage, long battery life (between 10 and 15 years), and low user equipment (UE) device complexity. To achieve these targets, several techniques have been adopted, including repetitions, power spectral density boosting, single-tone transmission, power saving mode, phase rotated modulations (e.g π 2 -BPSK and π 4 -QPSK) to reduce peak-to-average power ratio in the uplink and so forth.

Other technologies have preceded the proposition of NB-IoT such as the LoRaWan standard [START_REF] Sornin | LoRa Alliance LoRaWAN specification[END_REF] and the ultra narrow band protocol used by Sigfox [START_REF] Anteur | Ultra narrow band technique for low power wide area communications[END_REF], which operate in the unlicensed bands (industrial, scientific and medical (ISM) radio bands). However, cellular IoT standards which operate in a licensed spectrum technologies have been worth the wait. In fact, NB-IoT can be deployed in any of the 2G/3G/4G spectrum (from 450 MHz to 3-5 GHz), since it achieves an excellent coexistence and compatibility performance with legacy cellular systems. NB-IoT needs only a small portion of the existing available cellular spectrum to operate without interfering with it. Hence, NB-IoT provides more reliability and more quality of service (QoS) as it operates in regulated spectrum. Moreover, NB-IoT uses existing cellular network infrastructure, which reduces the deployment costs.

However, since repeating transmission data and control signals has been selected as a major solution to enhance coverage of NB-IoT systems, this leads to reducing the system throughput and thereby a spectral efficiency loss. Another cost of providing deep indoor coverage is lowering the number of supported devices per sector. Hence the interest of studying new techniques of extending the coverage and reducing the number of retransmissions.

In this work, we propose a new method to enhance the coverage based on machine learning. Instead of getting access to the spectrum in a random way, dynamic spectrum access based on reinforcement learning algorithms can help increasing the coverage, decreasing the number of repetitions, and thereby reducing the energy consumption. This problem can be modelled as multi-armed bandit (MAB) framework, as has been proposed for cognitive radio in the literature [START_REF] Jouini | Upper confidence bound based decision making strategies and dynamic spectrum access[END_REF]. It has also been reported that MAB works well in real channel conditions [START_REF] Melian-Gutierrez | Upper Confidence Bound learning approach for real HF measurements[END_REF]. One of the most relevant methods to address MAB problems is upper confidence band (UCB) algorithms, which are efficient and converge quickly when the traffic is stationary and independent and identically distributed [START_REF] Auer | Using confidence bounds for exploitation-exploration tradeoffs[END_REF]. Using this framework, the NB-IoT end device will select the best channel following not only the criterion of availability but also the best coverage condition. This paper is organized as follows: Section II explains the NB-IoT challenges in terms of coverage enhancement and energy consumption, while Section III shows how can dynamic spectrum access and its tools enable to follow the requirements of NB-IoT. Section IV provides simulation results about our proposed solution. Finally, Section V concludes this paper.

II. NB-IOT CHALLENGES

Enhancing the coverage and reducing the energy consumption are among the most relevant key targets of NB-IoT. In this section, we explain the challenges of increasing the coverage and saving energy as well as the recently deployed solutions to fullfill these main requirements.

A. Coverage enhancement

NB-IoT requires 20 dB of maximum coupling loss (MCL) higher than LTE, and then reaches up to 164 dB of MCL in order to serve end devices in deep coverage such as basements. Several modifications have been deployed on the different LTE protocol layers to achieve this significant gain. A major selected technique consists in increasing the number of retransmissions that reaches 128 repetitions for the uplink communications and 2048 for the downlink. These repetitions are combined at the receiver side in order to increase the signal-to-noise (SNR) ratio. Along with repeating the same transmission several times, other techniques have been used to extend the coverage such as cross-subframe channel estimation and frequency hopping. More details on these techniques can be found in [START_REF] Vidit | Reducing the Modem Complexity and Achieving Deep Coverage in LTE for Machine-Type Communications[END_REF].

Threes coverage classes are allowed by a serving cell to an NB-IoT end device:

• CE level 0: normal coverage with MCL≈ 144 dB and 15 kHz sub-carrier spacing. • CE level 1: robust coverage with MCL≈ 154 dB and 15 kHz sub-carrier spacing. • CE level 2: extreme coverage with MCL≈ 164 dB and 3.75 kHz sub-carrier spacing. The choice of the coverage level depends on the channel conditions. The extreme coverage level corresponds to a low power received level, and a normal coverage level corresponds to a high power received level. Each selected coverage class determines the transmission parameters including the number of repetitions. Such a deployment allows the UE to be served in different coverage conditions characterized by different ranges of path loss. Depending on the coverage level, the serving cell indicates to the UE to repeat the transmission {1, 2, 4, 8, 16, 32, 64, 128} times, using the same transmission power on each repetition. Combining the different retransmissions allows a coverage extension.

B. Energy consumption

In addition to the normal connected mode, there are mainly two energy efficient techniques that have been designed in NB-IoT in order to minimize the power consumption in end devices and increase their battery life:

• Idle mode extended discontinuous reception (I-eDRX):

this mode allows a discontinuous reception for maximum of 3 hours, which saves UE battery but still allows it to be reachable by the network through paging messages or downlink control channels. • Power saving mode (PSM): this energy saving mode allows unconnected state for up to 13 days, where UE enters to a deep sleep. Unlike in I-eDRX, UE is unreachable while remains registered in the network. This mode save more energy than the idle mode. As expected, the power consumption of these modes is substantially lower than the power consumed during transmission. Therefore, in a normal environment conditions (MCL of 154 dB), configuration of these power saving techniques allows a battery life of more than 10 years. However, in deep indoor coverage conditions, the targeted level of battery life (more than 10 years) cannot be achievable since the uplink repetitions get large. In addition, the energy consumption and the coverage enhancement mechanism imply high latency as the network waits a long period before being able to transmit its information data.

More techniques that allow both extending the coverage and reducing the number of required repetitions should be investigated to help prolong battery life. We show hereafter that dynamic spectrum access can help enhancing the coverage along with reducing the number of retransmissions and improving the latency.

III. DYNAMIC SPECTRUM ACCESS CAN HELP

Instead of a random access based on slotted ALOHA which selects randomly the channel where to transmit in order to establish connection with the cell, we propose in this work to use a dynamic spectrum access in order to learn the channel which is more likely to be available and in good coverage conditions.

The spectrum learning process can be modelled as a multiarmed bandit (MAB) framework as proposed in [START_REF] Jouini | Upper confidence bound based decision making strategies and dynamic spectrum access[END_REF], [START_REF] Jouini | Decision making for cognitive radio equipment: analysis of the first 10 years of exploration[END_REF]. Depending on the location of UE (outdoor, indoor, basements) and the channel conditions (high or low SNR), the quality of the physical channels changes. Therefore, choosing the channel with the best quality (i.e. coverage level), potentially leads to reliable transmissions, less costly in terms of energy consumption.

A. Multi-armed bandit framework

The MAB problem is a reinforcement learning game where a player have to decide which machine k play (among K machines i.e k ∈ {1, 2, . . . , K}) at each discrete time slot t = 0, 1, 2 . . ., based on informations of their reward. The player plays the machine that has the maximum reward. The rewards associated to each machine k are independent and identically distributed (i.i.d.) and follows a fixed and unknown distribution law d k In general, the reward distributions {d 1 , d 2 , . . . , d K } differ from one machine to another, and the player does not have any knowledge about these distributions.

In our case, the player is the NB-IoT end device, and the machines are the spectrum channels used for cell connection.

In the following we define some concepts related to the MAB framework.

Reward Let r t (k) be the reward of the data transmission for a channel k at instant t. The reward in our scenario takes two values 0 or 1. The reward is equal to 1 if the selected channel is vacant (acknowledgement is received) and in a good coverage.

Note that the quality of the channel is only known when an acknowledgement is received.

Exploitation and exploration dilemma. It refers to a trade-off between the exploitation of the channel with highest mean reward, and exploring the other channels in order to get more information about their payoffs.

Regret. It means the loss represented by the difference between the expected reward associated to the suboptimal channel learned by the end device, and the ideal reward associated to the optimal channel. Since the user does not have any knowledge about the distribution of the reward, he cannot avoid a loss when selecting a channel.

Denote π the learning channels policy. Let µ k = E[d k ] the stationary mean reward of the k th channel, where E[.] denotes the expectation function. The regret of a policy π is defined as

R π t = t.µ * - t-1 l=0 r l , (1)
where µ * stands for the expected value of the reward of the optimal channel. Based on (1), we define the expected cumulative regret as

E[R π t ] = K k=1 (µ * -µ k )E[T k (t)], (2)
where T k (t) being the total number of times channel k has been selected from instant 0 to instant t -1.

The MAB problem can be solved using reinforcement learning algorithms such as UCB approaches. In the following section, we briefly define the use of UCB in dynamic spectrum access.

B. Upper confidence bound algorithm

The policy that we seek should help the NB-IoT device to make a decision on which channel to transmit. We choose to build a policy based on the UCB algorithms since this approach requires few processing resources and memory, and guarantees asymptotically optimal performance. The upper confidence bound index B k (t), is computed at each instant t and for each channel k, and gives an estimation of the expected reward of a channel k. The UCB index is expressed as:

B k (t) = Xk (t) + A k (t), (3)
such that Xk (t) = 1 T k (t) t-1 l=0 r l (k)1 {a l =k} (4)
A k (t) = α ln t T k (t) , ( 5
)
where Xk is the sample mean of the channel k reward, and A k is an upper confidence bias. 1 is the indicator function and a t is the selected channel using the policy π at the t th transmission. Therefore, we have 1 {a l =k} = 1 only if the channel k has been chosen at instant l. The factor α in ( 5) is an exploration coefficient for channel availability and coverage. If α gets larger, the UCB algorithm will explore more channels for better

(B k (t)). (6)

IV. SIMULATION RESULTS

A. NB-IoT Scenario

NB-IoT standard designed by 3GPP is a slotted protocol [START_REF] Ratasuk | NB-IoT system for M2M communication[END_REF]. We assume that the different communications using the studied spectrum are slotted i.e. all devices share synchronized time. We also assume that the end device knows in advance the finite number of dedicated radio frequency (RF) channels.

The NB-IoT supports the following deployment modes:

• In-band mode where NB-IoT is deployed within the LTE bandwidth, and occupies one or multiple physical resource blocks (180 kHz). • Guard-band mode where NB-IoT operates within the guard-band of an LTE carrier • Stand-alone mode where NB-IoT can either occupies one or more GSM carrier (200 kHz), or it can be deployed in an adjacent band to LTE. It is worth mentioning that in the in-band deployment, the channels supported by NB-IoT are well-defined to avoid interfering with resources used by the LTE system such as synchronization, broadcast and control channels. The allowed physical resource blocks (PRB) are provided in Table I. We assume in our scenario that the NB-IoT is deployed in inband mode associated to LTE system bandwidth of 15 MHz. 14 physical channels are then allowed for cell connection as given by Table I.

When the NB-IoT end device turns on, it tries to connect to the cell using the channel that maximizes its reward:

• If the device receives a feedback from the base station, it will update the reward (1 if good coverage level, 0 otherwise) and proceeds to the data transmission. • Otherwise, the reward of the selected channel is updated to 0, and the device waits till the beginning of the next slot to select a new channel. We define µ k vac the expected mean reward associated to the vacancy of the PRBs k, and µ k cov the expected mean reward related to the coverage level of the PRBs k. Table II shows the values used in our learning policy, which are defined in a random way. Without loss of generality, we assume µ1 vac ≤ µ 2 vac . . . µ 14 vac . Note that µ 1 vac = 10% means that channel 1 is available 10% of the time, and µ 1 cov = 50% means that channel 1 has a probability of 50% to be in a good coverage when it is free. µ k vac,cov = 0.05 is associated to the probability that channel 1 is both available and in a good coverage.

B. Best channel selection and cumulative regret

In addition to the cumulative regret defined in Section III-A, the percentage of optimal channel selection is a relevant metric in the analysis of reinforcement learning policies. Since the device should transmit in the optimal channel i.e. that has the highest mean reward, the more is the percentage of optimal channel selection, the better is the policy. Both of these relevant metrics are compared in Fig. 3, Fig. 1, Fig. 4, and Fig. 2 for the following proposed UCB scenarios:

• UCB(vac) means that the policy consider only the vacancy distributions µ k vac and assumes that the different channels have the same coverage properties. The best channel in this case is 14 = arg max k (µ k vac ). This scenario is extremely unlikely to happen, since the coverage level of each RF channel is independent from the probability of its availability.

• UCB(vac,cov) takes into account both the vacancy and the coverage criteria. The policy is then based on the distribution µ k vac,cov . The best channel in this case is different from UCB(vac) case, and it corresponds to 13 = arg max k (µ k vac,cov ). • UCB(vac,cov): In this scenario, the channels do not have the same coverage quality but follow the distributions µ k cov . However, the end device does not take the coverage criterion in the calculation of the UCB index 1 , its calculation is based only on the vacancy distributions µ k vac . The best channel here is 13 since the channels have different coverage and vacancy properties. The exploration coefficient α is set to 1.5 for all the studied scenarios.

Fig. 1 and Fig. 2 show the impact of the coverage constraint on the UCB policies. The major finding resulting from comparing the UCB(vac,cov) policy where the coverage criterion is not considered, and the UCB(vac,cov) policy where the choice of the RF channel is constrained with its coverage quality, is that the former policy does not converge to the optimal channel unlike the latter. This result was expected from the behaviour and the target of each policy. During the first iterations, both algorithms start exploring the physical channels with different objectives: UCB(vac,cov) calculates its UCB index based on the mean reward of vacancy µ k vac , while UCB(vac,cov) takes into account both availability and coverage i.e. µ k vac,cov in its UCB index calculation. In the long run, UCB(vac,cov) tends to choose the channel number 14, which is the most available one, while channel number 13 is the optimal one since it allows both a good availability and a good coverage level. The channel with the highest probability to be free is not necessarily the one with the best coverage. Therefore, the two compared policies behave in a symmetric manner, the best channel selection percentage decreases with time for UCB(vac,cov) and tends to 0% while it converges to 100% for UCB(vac,cov) (see Fig. 1). The resulting cumulative regret increases linearly with time for UCB(vac,cov) and seems insignificant for UCB(vac,cov) compared with the first policy (see Fig. 2). Note that in some other scenarios, the most available channel might be also the one with the best coverage level. Assuming this scenario, even if it is highly unlikely to occur, the policy UCB(vac,cov) would not behave better than the proposed policy UCB(vac,cov).

We compare in Fig. 3 and Fig. 4 the previously analysed UCB(vac,cov) policy, with UCB(vac) scenario. It can be noticed that UCB(vac,cov) still gives the best performance. UCB(vac,cov) converges faster than UCB(vac) and produces the lowest cumulative regret. As an example, if we consider the transmission i.e iteration number t = 10 3 , the best channel selection associated to UCB(vac,cov) reaches 56%, while it is equal to 43% for UCB(vac) which is less than half the percentage achieved by UCB(vac,cov) (16%). Regarding the cumulative regret, Fig. 4 reflects in fact the same performance behaviour. In order to give a numerical insight, let us consider another interval of the data transmission: t = 10 5 . The cumulative regret corresponding to UCB(vac,cov) is only 492, while it reaches 615 for UCB(vac).

Note that for the different scenarios, their behaviour during the first iterations is not regular. This is due to the random selection of the channels during the first round since no knowledge about the vacancy nor the coverage is available during the beginning of the iterations.

C. Coverage extension and reducing repetitions

In the previous section, we have strongly supported that integrating the coverage level constraint into the UCB policy improves the best channel selection percentage and decreases II, using UCB(vac,cov) would rather choose a RF channel (channel number 13 in the provided example) with a good coverage that allows reaching easily the destination, than a RF channel (channel number 14) with an extreme coverage that makes reaching the receiver pretty hard. Moreover, UCB(vac,cov) allows avoiding transmission repetitions by selecting a good quality channel that requires no or few number of repetitions.

When using a random selection procedure, the channel to transmit is chosen in a random way, ignoring its probability of availability or its coverage properties. In the literature, several researchers have been defending the interest of dynamic spectrum access using the vacancy criterion of the channels. Here, we support the relevance of involving the quality of the channels in terms of coverage level in UCB policies, especially for applications that need a long battery lifetime such as NB-IoT. To be convinced of this, let us consider the best and worse case scenarios for the proposed policy UCB(vac,cov):

• Best case scenario for implementing UCB proposed poli-cies: the selected channel by a random selection procedure is the one with the highest required number of repetitions 128 (in an extreme coverage), while the optimal channel in UCB policy requires only 1 (or 0) repetition. This scenario would reduce the latency and save significant amount of energy by avoiding large number of retransmissions.

• Worse case scenario: the randomly selected channel matches the one with the best quality of service. This means that our policy for this typical transmission time, would not save a priori more energy than legacy selection schemes. Hence, our policy promises in the general case a considerable improvement of the quality of the transmission, and meets then the challenges required by NB-IoT applications.

V. CONCLUSION

The emergence of new IoT applications such as NB-IoT requires to fullfill and meet several challenges. Reducing the energy consumption is one of the major features of NB-IoT end devices. This target is inherently correlated to enhancing the coverage, since the fundamental adopted solution is increasing the number of retransmissions, and thereby consuming more energy. In order to enhance the coverage and to reduce the energy consumption, this paper proposes a new solution based on dynamic spectrum using machine learning algorithms. The random selection procedure is replaced by a more efficient selection method that chooses the channels with the highest probability to be available, and with the best coverage and the lowest number of required repetitions. The next step of our work targets the investigation of a multi-player scenario, where several NB-IoT end devices need to access dynamically the network.

  k

Figure 1 :

 1 Figure 1: Impact of considering coverage on best channel selection percentage.

Figure 2 :Figure 3 :

 23 Figure 2: Impact of considering coverage on cumulative regret.

Figure 4 :

 4 Figure 4: Cumulative regret for different scenarios.

Table I :

 I Allowed LTE PRB indices for cell connection in NB-IoT in-band deployment.

	LTE bandwidth	3 MHz	5 MHz	10 MHz	15 MHz	20 MHz
						4, 9, 14,
					2, 7, 12,	19, 24,
	LTE PRB indices for NB-IoT	2, 12	2, 7, 17, 22	4, 9, 14, 19, 30, 35, 40, 45	17, 22, 27, 32, 42, 47, 52, 57, 62, 67,	29, 34, 39, 44, 55, 60, 65, 70, 75, 80,
					72	85, 90,
						95
	vacancy and coverage. Otherwise, when α takes lower values,
	the exploitation is privileged.
	The selected channel a t resulting from UCB algorithm is the
	one with the highest UCB index, i.e.
		a t = arg max

Table II :

 II NB-IoT channel parameters for an LTE Bandwidth of 15 MHz when in-band mode is deployed.

	PRB index	Channel index	µ k vac [%]	µ k cov [%]	µ k vac,cov = µ k vac .µ k cov
	2	1	10	50	0.5
	7	2	20	90	0.18
	12	3	25	55	0.137
	17	4	30	80	0.24
	22	5	35	75	0.262
	27	6	40	60	0.24
	32	7	45	40	0.18
	42	8	50	70	0.35
	47	9	55	65	0.357
	52	10	60	35	0.21
	57	11	65	50	0.325
	62	12	70	40	0.28
	67	13	80	85	0.68
	72	14	90	20	0.18

This is what we mean by the notation cov.

ACKNOWLEDGMENT

This work has received a French state support granted to the Enhanced PHY for cellular Low power communication IoT (EPHYL) project and managed by the National Research Agency under reference Nb. ANR-16-CE25-0002-03.


Marwa Chafii
email: marwa.chafii@centralesupelec.fr

Carlos Faouzi Bader

Jacques Palicot
email: jacques.palicot@centralesupelec.fr

SC-FDMA with Index Modulation for M2M and IoT Uplink Applications

One of the most challenging issues of Internet of Things (IoT) devices is energy consumption. A massive deployment of connected widgets is power hungry. Maximizing the energy efficiency of their batteries reduces the maintenance cost and extends their autonomy and then their utility. To address this issue, this paper proposes the introduction of index modulation on single carrier-frequency division multiple access (SC-FDMA) uplink transmissions for cellular IoT and machineto-machine (M2M) networks. It is shown that the proposed SC-FDMA with index modulation (SC-FDMA-IM) scheme achieves 50% of energy efficiency increase, while improving the bit error rate performance by up to --dB of E b /N0 for the same spectral efficiency performance.

I. INTRODUCTION AND MOTIVATIONS

Machine-to-machine (M2M) communications and more generally internet of things (IoT) communications enable devices to sense their environment, exchange this information among themselves with direct connectivity without human intervention. This data can also be shared actively with humans to allow intelligent decision making. It affects our whole life and our entire ecosystem.

One of the most challenging requirement of countless range of IoT applications, is to achieve energy efficiency high enough to offer ten years of battery lifetime for end devices. Low power wide area (LPWA) [START_REF] Raza | Low Power Wide Area Networks: An Overview[END_REF] technologies have been designed to meet the requirements of M2M and IoT applications in terms of low energy consumption and wide coverage. Unlike traditional cellular technologies, LPWA offers sets of features to low power devices at the expense of low data rates.

The 3rd generation partnership project (3GPP) 1 enters the M2M and IoT market through the recent proposition of LTE Category M (LTE-M) [START_REF] Shariatmadari | Machine-type communications: current status and future perspectives toward 5G systems[END_REF] (also known as enhanced machinetype communications (eMTC)) and Narrow Band-IoT (NB-IoT) [START_REF] Mangalvedhe | NB-IoT deployment study for low power wide area cellular IoT[END_REF] standards in Release-13. In addition to improving the range, reducing the complexity, and the cost of the devices, these cellular solutions adopt two saving power modes in order to prolong the battery lifetime of the devices. The power saving mode (PSM) and the extended discontinuous (eDRx) reception mode enable end devices to enter in a deep sleep mode for hours or days while maintaining their network registration.

In this paper, we propose index modulation (IM) [START_REF] Başar | Orthogonal Frequency Division Multiplexing with Index Modulation[END_REF] as a power saving technique for cellular IoT uplink communications. IM technique consists of selecting a set of sub-carriers for each symbol, the selected sub-carriers will carry on the input data symbols while the rest of the sub-carriers is turned 1 More details on http://www.3gpp.org/.

off (an idea first reported in [START_REF] Pal | Parallel combinatory OFDM signaling[END_REF], [START_REF] Padovani | Coded Phase/Frequency Modulation[END_REF]). Additional information is coded through the choice of sub-carriers indices in a given symbol. Several variants of indexing have been proposed in the literature in order to increase the spectral efficiency [START_REF] Fan | Generalization of Orthogonal Frequency Division Multiplexing with Index Modulation[END_REF], and enhance the bit error rate (BER) performance [START_REF] Xiao | OFDM with interleaved subcarrier-index modulation[END_REF].

Index modulation has been proposed for 5G wireless networks for the design of downlink transmission protocols [START_REF] Başar | Index modulation techniques for 5G wireless networks[END_REF], [START_REF] Hong | FQAM: A Modulation Scheme for Beyond 4G Cellular Wireless Communication Systems[END_REF]. However, we believe that applying IM to the uplink cellular IoT standards is more relevant, since the complexity is offloaded from end devices and kept at the receiver. This application is also motivated by the consideration that IM is more efficient in low modulation orders and for low number of carriers [START_REF] Chafii | DCT-OFDM with Index Modulation[END_REF].

This paper shows that applying index modulation to SC-FDMA for NB-IoT and LTE-M allows an increase of 50% in terms of energy efficiency and --dB gain in terms of E b /N 0 compared with classical SC-FDMA for the same spectral efficiency performance. In [START_REF] Nakao | Single-carrier frequency-domain equalization with index modulation[END_REF], index modulation has been applied to single carrier frequency domain equalization (SC-FDE) system, but the multiple access analysis as well as PAPR and BER performance evaluation for different access modes have not been studied in the previous work. In addition, our study is particularly applied to M2M and IoT applications.

Section II defines the principle of SC-FDMA-IM scheme, while Section III analyses the performance of the proposed scheme in terms of spectral efficiency, energy efficiency, PAPR, and BER for different access modes. Section IV concludes the paper and gives some directives for future works. Let U be the total number of users. User u has m u bits to transmit which are introduced to the index modulation block. IM processing for a user u is based on the following parameters: G u is the number of groups within an SC-FDMA-IM symbol of duration T , n u is the number of subcarriers in each group, and k u is the number of active subcarriers in each group. In our case, k u is supposed to be fixed for every group and during the transmission in order to reduce the complexity. A more flexible selection of the active number of sub-carriers has been proposed in [START_REF] Fan | Generalization of Orthogonal Frequency Division Multiplexing with Index Modulation[END_REF] to increase the performance in terms of spectral efficiency.

II. SC-FDMA WITH INDEX MODULATION

A. SC-FDMA-IM principle

A stream of m u = G(m u 1 + m u 2 ) input information bits is mapped to a SC-FDMA-IM symbol associated to a is the number of bits to be mapped to an index set of actives sub-carriers, and

m u 2 = k u log 2 (M )
is the number of bits mapped to M-ary constellation symbols. The total number of active sub-carriers is denoted K u = k u G u and the total number of the allocated sub-carriers for a user u is N u = n u G u . The index selection is performed by applying a selection procedure such as a look-up table or a combinatorial mapping. More details on IM can be found in [START_REF] Başar | Orthogonal Frequency Division Multiplexing with Index Modulation[END_REF].

Dividing the input information bits m u into G u groups is relevant for the order of the implementation complexity. For G u = 1, the binomial coefficient Nu Ku can take large values which make the implementation of the system computationally unaffordable.

The index modulation procedure is applied for each user u, and then an N u -point-DFT (discrete Fourier transform) is performed on the output vector, which contains symbols from a pre-defined constellation and zeros associated to the inactive sub-carriers. The DFT operation is followed by a sub-carrier mapping in order to establish the access mode of the users, and a N FFT -point-IDFT (inverse discrete Fourier transform) is then applied for each user separately. A similar inverse procedure is performed at the receiver side along with a channel equalization and a minimum distance detection.

B. Multiple access modes

Sub-carrier mapping mentioned in Figure 1 chooses the access mode for different users u ∈ [[1, U ]]. In this work, we investigate the interleaved sub-carrier mapping and the localized sub-carrier mapping. In the interleaved sub-carrier access mode, the DFT outputs of the input data are allocated in equidistant frequency spacings over the entire bandwidth with zeros occupying the unused sub-carriers, whereas consecutive sub-carriers are occupied by the DFT outputs of the input data in the localized sub-carrier access mode. Note that there is difference between the aforementioned unused sub-carriers and the inactive sub-carriers related to index modulation. The unused sub-carriers in the access modes will be used for other users. The inactive sub-carriers resulting

III. PERFORMANCE ANALYSIS

To demonstrate the interest of the proposed scheme for cellular IoT applications, SC-FDMA-IM and SC-FDMA performance are compared in terms of spectral efficiency, energy efficiency, PAPR, and BER for NB-IoT and LTE-M standards in both localized and interleaved modes.

A. Spectral efficiency a) Spectral efficiency expression: Spectral efficiency is a relevant performance metric in communication systems. It relates to the data rate B r that can be achieved within a certain allocated bandwidth W. It is formally defined as:

ξ(bits/s/Hz) = B r (bits/s) W (Hz) . (1)
In SC-FDMA-IM, k u sub-carriers are selected out of n u for each group, and log 2 (M) data bits are assigned to each selected sub-carrier, the effective bit rate for each user u is equal to:

B r u = G u T + T cp log 2 n u k u + k u log 2 (M) . ( 2
)
Knowing that the allocated bandwidth W u to a user u is given by ∆F N u , we get the following spectral efficiency expression:

ξ IM = U u=1 B r u U u=1 W u (3) = U u=1 G u log 2 nu ku + k u log 2 (M) (T + T cp )∆F U u=1 N u (4)
b) Spectral efficiency increase for different numbers of users: We define the spectral efficiency increase as

ρ = ξ IM -ξ 0 ξ 0 , (5)
where ξ 0 is the spectral efficiency of the benchmark classical SC-FDMA.

In order to evaluate the spectral efficiency increase of NB-IoT applications, we consider the parameters shown in Table I. We assume that each user is allocated at least an integer number of resource blocks (RB), such that the length of each RB is 12 sub-carriers. Knowing that the allocated bandwidth counts 6 RB, the possible number µ of users that can have access to the allocated bandwidth at the same time is then µ ∈ [ [START_REF] Raza | Low Power Wide Area Networks: An Overview[END_REF][START_REF] Padovani | Coded Phase/Frequency Modulation[END_REF]]. Adding the assumption that the bandwidth W is allocated equally to each user, the possible number of users becomes µ ∈ {1, 2, 3, 6}. In fact, we can have one user that occupies the whole bandwidth, or 2 users with 3 RB each, or 3 users with 2 RB each, or 6 users with 1 RB each.

Hereafter, we consider that, for each transmission all the users divide their allocated bandwidth W u to the same number of groups. The values of the number of groups for each user depend then on the number of users µ. For each group of sub-carriers, only round(αn u ) 2 are active out of n u , such that α is chosen to be equal to 1 4 in this example. Other values of α can be selected from the interval [0, 1] 3 . Eq. ( 5) becomes:

ρ(µ) = G µ log 2 n µ k µ + k µ log 2 (M) log 2 ( √ M) -1. (6)
Eq. ( 6) is represented in Figure 3 for different numbers of groups when µ ∈ {1, 2, 3, 6}. We can observe that, in general, increasing the number of users reduces the spectral efficiency of SC-FDMA-IM. This can be explained by the fact that, for the same total allocated bandwidth, when we reduce the number of users, the index modulation of each user is applied to a larger bandwidth, which allows groups with larger lengths, the number of possible active sub-carriers combinations gets higher. Hence the increase in terms of spectral efficiency. c) Suitable number of groups: The different curves in Figure 3 indicate that the spectral efficiency depends on the number of groups G µ considered for each scenario µ. Grouping the data bits reduces the number of possible combinations from Nu Ku to G u Nu /Gu Ku /Gu , which reduces the complexity of the detection at the receiver side, since the detection of the used combination of active sub-carriers is performed over each group. From Figure 3, we can observe that the following number of groups achieves the same spectral efficiency than classical SC-FDMA i.e the spectral efficiency increase is set to zero (ρ = 0), while having a small number of sub-carriers (3 or 4) and then reduced complexity:

(G µ , n µ , k µ ) ∈          ({18, 24}, {4, 3}, 1) if µ = 1 ({9, 12}, {4, 3}, 1) if µ = 2 ({6, 8}, {4, 3}, 1) if µ = 3 ({3, 4}, {4, 3}, 1) if µ = 6 . (7)

B. Energy efficiency

In several IoT and M2M applications (especially massive M2M schemes), the spectral efficiency may not be the only most relevant performance criteria. Numerous applications tolerate a spectral efficiency decrease in order to save energy so that the batteries lifetime lasts longer. In order to 3 In [START_REF] Chafii | DCT-OFDM with Index Modulation[END_REF], the authors have proven using Stirling's approximation of the binomial coefficient, that for a large number of sub-carriers, α approaches a spectral efficiency maximizing value given by α

= N →∞ M M+1 .
save energy in SC-FDMA-IM, we will activate the lowest possible number of active sub-carriers while maintaining the same spectral efficiency than classical SC-FDMA and a low implementation complexity. The following configuration is then chosen:

(G µ , n µ , k µ ) ∈          (18, 4, 1) if µ = 1 (9, 4, 1) if µ = 2 (6, 4, 1) if µ = 3 (3, 4, 1) if µ = 6 . (8)
We define the energy efficiency E(bits/Joule) as the total amount of bits normalized by the energy. The energy efficiency increase is then expressed as

R = E IM -E 0 E 0 , (9)
where the index IM relates to SC-FDMA-IM, and the index 0 stands for the benchmark SC-FDMA. Applying the settings of Eq. ( 8), the energy efficiency increase is equal to:

R = G µ k µ log 2 (M) -G µ n µ log 2 ( √ M) G µ n µ log 2 ( √ M) (10)
= -50%.

Thanks to its ability to carry more data while sending less number of bits, the introduction of index modulation reduces the energy consumption by 50% which is a significant improvement, especially for low-power wide-area networks.

Similar analysis of spectral efficiency and energy efficiency can be conducted for LTE-M using the parameters in Table I. It leads to the same significant result of 50% energy consumption reduction following the same aforementioned steps.

C. PAPR performance

In this section, the PAPR performance is studied using the parameter settings reported in Table I. For NB-IoT, we assume that 6 users shares equally the bandwidth µ = 6 (1 resource block for each user). In LTE-M, the user occupies 6 resource blocks. For each user, the grouping is performed so that the total number of sub-carriers per group n and the active number of sub-carriers k within this group are set to (n, k) = (4, 1). These settings insure reaching 50% of energy efficiency increase and a same spectral efficiency as SC-FDMA along with low implementation complexity as given by Eq. ( 8) and Eq. [START_REF] Chafii | DCT-OFDM with Index Modulation[END_REF]. In fact, since only one subcarrier is activated in a group of length 4 sub-carriers, the number of combinations per group is reduced to 4.

The PAPR performance of NB-IoT and LTE-M for localized and interleaved access modes is evaluated through the complementary cumulative distribution function (CCDF) which is the probability that the PAPR exceeds some value γ. The results represented in Figure 4 and Figure 5 show that the introduction of index modulation in SC-FDMA for NB-IoT and LTE deteriorates the PAPR performance for the difference access modes. The resulting difference in terms of PAPR performance becomes less important when we increase the number of sub-carriers (the length of the IDFT). Hence, it is important to apply a PAPR reduction technique to address this issue.

D. BER performance

The BER performance is evaluated in a frequency-selective Rayleigh fading channel represented by the channel impulse response coefficients: h = (h(1), h(2) . . . h(ν)). We assume that all the coefficients are circularly symmetric complex Gaussian random variables with CN (0, 1 ν ) distribution. The associated BER performance results are displayed in Figure 6 for NB-IoT and in Figure 7 for LTE-M. For signal recovery, a minimum mean square error (MMSE) equalization is employed along with a minimum distance detector. In order to provide a mapping between the index set of active subcarriers within a group and incoming bits, a mapping table is implemented in both transmitter and receiver sides. The lookup table selection is given in Table II. The same simulation parameters employed in Section III-C are considered in this part.

We can see that the SC-FDMA-IM scheme achieves a gain of --dB (--dB respectively) in terms of E b /N 0 for BER = 10 -4 for NB-IoT (LTE-M respectively). The index modulation allows more favourable spectrum spacing than the classical modulation, which explains the interesting improvement in BER performance.

IV. CONCLUSION

In this paper, we have introduced the index modulation to the SC-FDMA scheme for uplink M2M and IoT transmissions using LTE-M and NB-IoT standards for both localized and interleaved access modes for multiple users. For the same spectral efficiency as classical SC-FDMA-IM, we have showed that index modulation can lead to a gain of 50% in terms of energy efficiency while maintaining an affordable transceiver complexity. Due to favourable spectrum spacing resulting from index modulation, the BER is improved by up to --dB at the cost of an acceptable PAPR increase. We believe that this significant result encourages more studies about SC-FDMA-IM, especially for IoT and M2M applications.

Figure 1

 1 Figure1depicts the principle of SC-FDMA-IM transceiver. Let U be the total number of users. User u has m u bits to transmit which are introduced to the index modulation block. IM processing for a user u is based on the following parameters: G u is the number of groups within an SC-FDMA-IM symbol of duration T , n u is the number of subcarriers in each group, and k u is the number of active subcarriers in each group. In our case, k u is supposed to be fixed for every group and during the transmission in order to reduce the complexity. A more flexible selection of the active number of sub-carriers has been proposed in[START_REF] Fan | Generalization of Orthogonal Frequency Division Multiplexing with Index Modulation[END_REF] to increase the performance in terms of spectral efficiency.A stream of m u = G(m u 1 + m u 2 ) input information bits is mapped to a SC-FDMA-IM symbol associated to a

Figure 1 :

 1 Figure 1: SC-FDMA-IM transceiver.

Figure 2 :

 2 Figure 2: SC-FDMA-IM access modes. Example when number of users is equal to U = 3 and N FFT = 8

  Figure 2 represents an example of the sub-carrier mapping modes for a number of users equal to U = 3, N FFT = 8, and N u = 4 for each user.

6 Figure 3 :

 63 Figure 3: Spectral efficiency increase of different numbers of users for different numbers of groups.

  SC-FDMA-IM Localized mode SC-FDMA-IM Interleaved mode SC-FDMA Localized mode SC-FDMA Interleaved mode

Figure 4 :

 4 Figure 4: PAPR performance for SC-FDMA-IM in NB-IoT scenario.

  -IM Localized mode SCFDMA-IM Interleaved mode SC-FDMA Localized mode SC-FDMA Interleaved mode

Figure 5 :Figure 6 :

 56 Figure 5: PAPR performance for SC-FDMA-IM in LTE-M scenario.

Figure 7 :

 7 Figure 7: BER performance for SC-FDMA-IM in LTE-M scenario.

Table I :

 I Parameter settings for SC-FDMA-IM

	Parameters	Definition	Value for NB-IoT	Value for LTE-M
	N FFT	IFFT/FFT size	72	256
	∆F	Inter-carrier spacing	3.75 kHz	15 kHz
	T	Duration of block of symbols	1 ∆F
	Tcp	Duration of cyclic prefix	T /8
	RB	Resource Block	12 sub-carriers
	M	M-QAM Constellation	4 for SC-FDMA-IM and 2 for SC-FDMA
	r	Roll-off of the root raised cosine filter	0.3
	L	Upsampling coefficient	4
	ν	Number of path for Rayleigh channel	8
	N iter	Number of iterations	10 6 for PAPR and BER simulations

Table II :

 II Look-up table.

	Incoming bits m 1	Associated index set
	00	1
	10	2
	10	3
	11	4

ACKNOWLEDGMENT

This work has received a French state support granted to the Enhanced PHY for cellular Low power communication IoT (EPHYL) project and managed by the National Research Agency under reference Nb. ANR-16-CE25-0002-03.


Jacques Palicot

Faouzi Bader

Backing to Single Carrier in Tera Hertz Communications for Green Considerations

come   L'archive ouverte pluridisciplinaire

Introduction

Since the 90's, the most predominant communication scheme for broadband wireless communications is the multi-carrier (MC) scheme, more precisely the Orthogonal Frequency Division Multiplexing (OFDM) modulation. This is still the case for the last few years where many actors are studying advanced multi-carriers modulations (FBMC, GFDM, etc.) for fifth generation (5G) communication systems [?]. For systems beyond 5G, the expected date rate will reach Tbps which implies the use of ultra wide bandwidths of several tens of GHz. These bandwidths are not available in the classical bands below 100 GHz. This is the main reason why the community is today focusing and exploring on higher bands like Tera hertz (THz) band. Although there are several EU research projects dealing with wireless communications in high frequency bands, their focus is mainly on frequencies below 90 GHz. As almost all these projects were accepted within H2020 5GPPP framework, with a focus limited to 5G communication rates rather than beyond 5G which is the focus of this paper. Moreover, the radio access technology considered is still mainly based on MC modulation. Among the EU projects focusing on 60-90 GHz communications band, we name, the Flex5Gware 1 project, and the mmMAGIC [START_REF]New Waveforms for 5G Networks[END_REF] http://www.flex5gware.eu/ project2 . This last is concerned with the development and use of SC schemes for millimeter wave communications.

The main justification for the use and the deployment of multi-carrier communication systems is their adequacy and benefits in frequency selective channels by the possibility of generating and implementing a large number of flat small channels. In fact, in such channel environment, the OFDM modulation translates the Inter Symbol Interference effect in a broadband single carrier (SC) into several flat (eventually attenuated) and very narrow band channels. This was the principal interest for the development of the MC communication scheme concept. Associated with a powerful coding and interleaving schemes, in both frequency and time domains, the well known Coded OFDM (COFDM) achieved very interesting results and has been used as a prevailing PHY layer in many standards. Of course some drawbacks related to OFDM (and MC in general) modulation exists and were quickly identified such as, the Inter Carrier Interference (ICI) effect, and the high Peak to Average Power Ratio (PAPR). Despite these limitations, achieved results by means of real implementations and testing were so successful in high selective terrestrial channels that they did not influenced the OFDM standardization and its worldwide commercial success. In some particular situations such as, satellite transmissions or cellular uplink communication mode in Long Term Evolution Advanced (LTE-A) system, MC modulations have been discarded because of the negative effect of the PAPR phenomena.

Transmission at 60 GHz covers less distance for a given power, mainly due to the increased free space path loss (loss over 1 m at 60 GHz is 68 dB, which is 21.6 dB worse than at 5 GHz) band compounded by propagation losses through materials and human body shadowing (losses from a few dB to 30 dB+) [?]. In contrast, oxygen absorption plays a minor role over short range distances even through it peaks at 60 GHz. The above 100 GHz (100-300 GHz) band communications is characterized by a higher degree of absorption than in the 60 GHz band, and by a quasi-optical propagation behavior where the received signal is dominated by line of sight (or along a strong indirect path) and reflexions from strong reflecting materials, and the MIMO precoding generates a flat channel at the receiver side [?]. On the other hand, the non line of sight (NLOS) environments losses are too high for reliable communications, and concrete materials cause additional large signal attenuation and can easily create a blockage. This type of physical communication environment is more conducive for the use of SC modulation scheme. The SC has been proposed in WiFi 802.11ad standard (also named WiGig) [?], and is object to deep researches for millimeter wave communications in [?] for essentially keeping the transceiver complexity and the energy consumption low and affordable for real implementation. Note that with frequencies of order of tens of GHz bandwidth to reach tbps in beyond 100 GHz band, it seems unrealistic to have analogue to digital converters (ADC) with several bits at a reasonable energy consumption. Therefore, all the signal processing for beamforming and classical signal processing at the receiver side should be revisited taking into account a mix of analog and digital design.

The special characteristics of the associated channels, especially from the mm-Wave frequency bands over 60-90 GHz, make SC modulation schemes, unlike the MC scheme, potentially appropriate for communication systems operating in such high communication bands and beyond. This is what emerged from recent studies in [?] and [?], where SC was described as a promising candidate to provide good coverage even when wider bandwidth transmissions (e.g., > 10 GHz) are introduced in these high frequency bands. Another extremely important argument in favor of the use of SC modulation, is the Peak-to-Average Power Ratio (PAPR) that will be lower than MC systems, making possible the use of more energy efficient power amplifier for such high frequency ranges. Combined with simpler modulation/demodulation blocks, the global energy consumption will be significantly reduced. We remind, here, that green radio communication is considered as a strong and an unavoidable argument for next generation systems. Therefore, backing to single carrier modulation will help to meet such essential requirement. The rest of this paper is focusing on this last aspect.

WHY we essentially use OFDM modulation?

To well understand the interest of dividing a broad band into a large number of narrow bands, let's have a look on Figure ??. In this Figure, published in [?], depicts a 3D representation of a frequency selective channel. For a given time, the projection in the frequency direction exhibits holes or deep attenuation that are experiencing variations in time domain due to the mobility effects of the transmitter. If the overall band is split in many small bandwidths (see depicted small squares on the 3D channel representation), we may consider the variation of the channel in each square as flat. Dividing the frequency band in several pieces of small bands to fight the frequency selectivity of the channels is an old idea. One of the pioneer theoretical works is , it was demonstrated that it is possible to replace the parallel modulators bank by a fast Fourier transform (FFT) at both the transmitter and the receiver sides. After this milestone, the scientific community has adopted this major advance and from that time a huge number of researches has been produced in this field. Two others key factors as the advent of very powerful Digital Signal Processors (DSPs) devices with its combination with code schemes associated to the modulation (known as coded OFDM [?]) explained the success of the COFDM in the 90's. In fact, COFDM multicarrier scheme is the key modulation adopted in many wirelesss communication standards as: DAB, ADSL, DVB-T, WiFi, LTE, etc.

3 PAPR issues for energy efficiency

Green radio-communications

Few years ago, the environmental-friendly sustainable development was only the concern of ecological organizations. However, sustainable development has become a globally paramount challenge and an aspiration of longterm civilization development of all human beings since the "Resolution 42/187 of the United Nations General Assembly" in December 1987. The Brundtland Commission of the United Nations (UN) has defined sustainable development as the one that "meets the needs of the present without compromising the ability of future generations to meet their own needs". From then on, several United Nations' conferences (from Rio de Janeiro-1992 to more recently the COP'21 in Paris, 2015) continually confirmed this important issue, for which one of the most obvious aspects and challenges of sustainable development is the earth climate change and the ever-growing CO2. Doubtlessly, making Information and communications technology (ICT) equipments and applications "greener" in terms of energy consumption can not only have a tangible positive impact on environment, but can also help telecommunications operators to attain long-term profitability. Moreover, energyefficient communications and networks can help the world to reduce the dependence on fossil fuel, enable on-demand response and fluent energy resources distribution, and ultimately achieve sustainable prosperity around the world. This evolution was recently stated in many papers and conferences. As illustrated in Figure ?? of [?], the long-term evolution road map of next-generation telecommunications systems from 2G, 3G to 4G/5G is strongly expected to point to the energy-efficiency dominated era from now on.

PAPR considerations 3.2.1 Multi-carrier case

The envelope of a multiplex of modulated signals (for both single-carrier and multi-carrier signals) is not constant. This is always true, for example, for software radio signals like a multiplex of GSM signals (even if each one is actually of constant envelope). The large variations of the multi-carrier transmitted signals lead to a weak power efficiency of the power amplifier and, therefore, intensive energy consumption requiring a growing need for cooling is observed. All the classical multi-carrier systems, as the OFDM, suffer from high power fluctuations. The variations of the signal envelope generate non-linear distortions, when we introduce the OFDM signal into a power amplifier (PA).

Considering the graph of Figure ??, about 30% of the base station power consumption is due to the high power ampli- In [?] we solved this optimization problem and we obtained the following major result that is, no better PAPR compared to OFDM, is possible, without reducing the temporal support of the analyzed waveform. In [?], we proved that all the proposed enhanced multi-carrier waveforms for 5G, like FBMC3 , UFMC [START_REF]The EU project-mmMAGIC[END_REF] , and GFDM5 [?] are all identical or worse than OFDM in terms of PAPR because they not fulfill the condition of having a temporal support smaller than the symbol period.

Conclusion

Single carrier modulations are gaining more and more interest than past few years. The fact that beyond 5G communications targeting wireless applications with Tbps data rate in beyond 100 GHz band, characterized by a higher degree of absorption and by a quasi-optical propagation behavior with line of sight received signal, is very conducive for the use of SC modulations due to the previously mentioned green considerations. Nonetheless, more deep researches have to be conducted to develop advanced signal processing techniques to increase the SC modulation capacity and phase noise robustness, and to reduce the PAPR and the out of band emission.

Figure 1 .

 1 Figure 1. Example of a 3D (Time Frequency Power) varying channel [?]. Each small square could be considered as a flat (eventually attenuated) channel.

Figure 2 .

 2 Figure 2. Evolution from coverage-and capacity-driven telecommunications to energy-efficient green radio communications from [?].

  fier (HPA) and the associated cooling. Depending on in-site implementation technologies this value may reach 50% [?]. This explains the existence of huge scientific literature on HPA efficiency optimization methods. This last problem may be tackled at different levels [?].

Figure 3 .

 3 Figure 3. Example of Power consumption sharing at a Base Station [?].

  In order to reach the magnitude of Tbps, the considered SC modulation should have a high spectrum efficiency. In other words, constant envelope modulations like CPM could be limited due its low spectrum efficiency. As a consequence, modulation having high spectrum efficiency means many symbols in the I/Q plan which, in turn, implies a non-negligible PAPR (depending on the used filtering function) effect. In [?] we proved that the PAPR increases when the roll-off factor oh the Nyquist filter decreases. To decrease this PAPR, some mitigation techniques studied in the multi-carrier context could be adapted and applied in beyond 100 GHz band, i.e., Modified Tone Reservation technique in [?] could be studied.

	PAPR versus spectral efficiency trade-off is obtained with
	an oversampling factor of two together with Interleaved
	Frequency Division Multiple Access (IFDMA) mapping.
	An other scheme is the Constrained Envelope Continu-
	ous Phase Modulation (ceCPM-SC) Constrained envelope
	which is a true single carrier scheme generalizing CPM
	by allowing controlled small envelope variations [?]. Pure
	single-carrier waveforms are relatively robust to channel
	time selectivity compared to multi-carrier waveforms. The
	reason is that single-carrier waveforms have shorter symbol
	durations that are subject to less channel variations across
	time.
	3.2.2 Single carrier case
	Recent conducted researches for millimeter-wave commu-
	nications [?] focused on several SC modulations like, the
	Continuous Phase Modulated Single-Carrier Frequency Di-
	vision Multiple Access (CPM SC-FDMA) which is a gen-
	eralization of SC-FDMA using samples of a Continuous
	Phase Modulation (CPM) signal as generalized coded mod-
	ulation input symbols [?]. The scheme can provide a low
	PAPR signal with very low side lobes, provided the CPM
	parameters like over-sampling factor and sub-carrier map-
	ping have to be suitably selected. It is shown that a good

https://5g-mmmagic.eu/

Filter bank Multi-Carrier

Universal Filtered multi-Carrier

Generalized Frequency Division Multicarrier