Cross-Layer Designs for Link Adaptation

Ministry of Higher Education and Scientiﬁc Research University of Carthage Higher School of Communications of Tunis

A thesis presented in fulﬁlment of the requirements for the degree of Doctor of Philosophy in Information and Communication Technologies

By Ms. Asma Selmi

Defended on the 1st of December 2016 before the committee composed of:

Chair Prof. Ridha Bouallegue Professor at SUPCOM, Tunisia

Reviewers Prof. Mohamed Slim Alouini Professor at KAUST, Saoudi Arabia

Dr. Mohamed Lasaad Ammari Associate professor at ENISO, Tunisia

Examiner Dr. Le¨ılaNajjar Atallah Associate professor at SUPCOM, Tunisia

Supervisor Prof. Mohamed Siala Professor at SUPCOM, Tunisia

Co-Supervisor Prof. Hatem Boujemaa Professor at SUPCOM, Tunisia

Academic year: 2016/2017 Abstract

To pursue the rapidly growing demand for high data rates, new radio communication systems are appealed to efficiently manage power and spectral resources and channel impairments through adaptive techniques. Link adaptation (LA) techniques, namely Adaptive Modulation and Coding (AMC) and Power Control (PC), are used at the physical (PHY) layer to take care of the instantaneous channel quality variations, through appropriate processing prior to data transmission. The channel quality variations could also be handled after data transmission through the use of the Automatic Repeat reQuest (ARQ) protocol at the data link (DL) layer. This thesis focuses on the optimal combination of all of these three LA techniques, since they synergically and nicely complement each other. Such challenge requires the use of cross- layer approaches for throughput efficient LA. In particular, we propose cross-layer designs for a maximized average throughput efficiency (ATE), targeted to single-antenna as well as to multi-antenna systems.

In a first stage, the basic ARQ protocol is optimally combined with both adaptive modulation (AM) and PC techniques. More specifically, the proposed cross-layer allows to jointly select the optimal power level and the appropriate modulation scheme (MS), as a function of the fading channel, to achieve the highest ATE, under an appropriately fixed average transmit power constraint. To do this, a numerical resolution process was developed, which simply relayed on a set of full-fledged throughput efficiency curves corresponding to the MSs supported by the system, to select the optimal transmit parameters. Thanks to a one-shot proposed numerical resolution approach, the proposed combination scheme is found to be generic for any ARQ scheme, regardless of the actual channel statistics and the desired target average transmit power. The performance analysis shows a significant reduction in average transmit power in comparison to a conventional joint AM-ARQ scheme for a preset ATE. Then, we extended this scheme to incorporate coding rate adaptation in addition to constellation size adaptation.

i A type I hybrid ARQ was considered where an error-correction is employed in addition to the error detection. The numerical maximization of the ATE was carried using a Lagrange multiplier parameter, which is intimately related to the desired average transmit power and to the usually unknown channel statistics. To keep the proposed combination scheme independent of channel statistics, we developed an iterative algorithm for blindly estimating and tracking the appropriate value of the Lagrange multiplier, to meet as much as possible the required average transmit power. The proper operation of the proposed tracking loop was validated through a Monte-Carlo simulation approach, modeling in a realistic way channel variations and tracking loop behavior. Then, we studied the convergence behavior and capabilities of the proposed algorithm as a function of the mobile speed.

In a second stage, aiming to improve the offered throughput of a basic ARQ scheme, we wisely redistributed the transmit power budget among potential transmission attempts, such that the resulting throughput is maximized, for a fixed target average power per packet. To this end, a truncated ARQ (T-ARQ) was assumed, and a heuristic algorithm, banking on a dichotomic search, was used for the optimization of the distribution of the available power budget among the different transmissions. This enhanced version of the T-ARQ protocol was then combined with AMC and PC techniques, according to the combination scheme previously developed.

In a third stage, we tackled the problem of QoS-sensitive packet wireless communications. In this context, we developed an efficient cross-layer design that maximizes the ATE by optimally combining AMC, PC and basic ARQ, while fulfilling an error performance constraint in addition to the constraint on the average transmit power. More specifically, both optimal AM switching thresholds and appropriate transmit power are derived as a function of the channel state, while guaranteeing the required QoS in terms of packet error probability.

Finally, we extended the proposed PC-AMC-HARQ cross-layer design, previously developed for SISO systems, to MIMO systems, in order to exploit the spatial multiplexing gain. To this end, we assumed known channel state information (CSI) at both the transmitter and the receiver and decoupled the MIMO channel into parallel eigen-subchannels using singular value decomposition (SVD). For each eigen-mode, the optimal transmit power level as well as the appropriate modulation and coding scheme (MCS) are jointly selected, as a function of the fading state of the subchannel, in order to achieve the highest ATE for the whole MIMO system, for a ﬁxed total average transmit power. We ﬁnally analyzed the achieved ATE improvement for both ordered and unordered eigenvalues cases.

ii Keywords: Link Adaptation, Power Control, Adaptive Modulation and Coding, Error Control, Automatic Repeat reQuest Protocol, Hybrid ARQ Protocol, Forward Error Correc- tion, Throughput Eﬃciency, QoS-based Communications, MIMO, Spatial Multiplexing, Sin- gular Value Decomposition.

iii List of Abbreviations

AM Adaptive Modulation AMC Adaptive Modulation and Coding ARQ Automatic Repeat reQuest ATE Average Throughput Eﬃciency CDMA Code-Division Multiple Access AWGN Additive White Gaussian Noise CSI Channel State Information CRC Cyclic Redundancy Check DL Data Link EMA Exponential Moving Average FEC Forward Error Correction FIFO First-In-First-Out GBN Go Back N HARQ Hybrid Automatic Repeat reQuest HARQ-I Type I Hybrid Automatic Repeat reQuest HSDPA High-Speed Downlink Packet Access HSP High-Speed Packet HSPA High-Speed Packet Access HSUPA High-Speed Uplink Packet Access i.i.d. independent identically distributed

iv IP Internet Protocol LA Link Adaptation LTE Long Term Evolution LOS Line Of Sight MIMO Multiple-Input-Multiple-Output MCS Modulation and Coding Scheme MS Modulation Scheme NLOS Line Of Sight NR Numerical Resolution PC Power Control PDF Probability Density Function OSI Open Systems Interconnection PEP Packet Error Probability PHY Physical PSD Power Spectral Density QAM Quadrature Amplitude Modulation QoS Quality of Service QPSK Quadrature Phase Shift Keying SISO Single-Input-Single-Output SIR Signal to Interference Ratio SNR Signal to Noise Ratio SR Selective Repeat STBC Space-Time Block-Coding STTC Space-Time Trellis-Coding SVD Singular Value Decomposition SW Stop and Wait T-ARQ Truncated Automatic Repeat reQuest TCP Transport Control Protocol UMTS Universal Mobile Telecommunications System WCDMA Wideband Code Division Multiple Access Wi-Fi Wireless-Fidelity

v WiMAX Worldwide Interoperability for Microwave Access WLAN Wireless Local Area Networks

vi Contents

Abstract i

List of Abbreviations iv

Contents vii

List of Figures xi

List of Tables xiv

1 Introduction 1 1.1 Motivation ...... 1 1.2 Contributions...... 2 1.3 Organization ...... 4

2 Link Adaptation Techniques and ARQ protocols 6 2.1 Introduction...... 6 2.2 RadioPropagationEﬀects ...... 7 2.3 PowerControl...... 8 2.4 AdaptiveModulationandCoding...... 9 2.5 Automatic Repeat Request Protocols ...... 10 2.5.1 SW-ARQProtocol ...... 11 2.5.2 GBN-ARQProtocol ...... 11 2.5.3 SR-ARQProtocol ...... 13 2.6 HybridARQ ...... 13 2.7 Cross-LayerDesign...... 14 2.7.1 PHY/DL Cross-Layer Design ...... 16 2.8 Conclusion ...... 16

3 Cross-Layer Design for Link Adaptation in ARQ-based Systems 17

vii 3.1 Introduction...... 17 3.2 GenericSystemModel ...... 18 3.2.1 Transmitter...... 19 3.2.2 WirelessChannel...... 19 3.2.3 Receiver...... 20 3.2.4 Adaptive Modulation and Coding System ...... 20 3.3 Cross-LayerDesign...... 21 3.3.1 ProblemStatement...... 21 3.3.2 Numerical Resolution Process ...... 23 3.4 Numerical and Simulation Results ...... 24 3.4.1 BasicARQThroughputEﬃciency ...... 24 3.4.2 OptimalTransmitPower ...... 25 3.4.3 Average Throughput Eﬃciency Analysis ...... 28 3.5 Conclusion ...... 30

4 Realistic Cross-Layer Design for Link Adaptation in HARQ-based Systems 31 4.1 Introduction...... 31 4.2 SystemModel...... 32 4.2.1 Transmitter...... 33 4.2.2 Receiver...... 34 4.3 Realistic Implementation PC-AMC-HARQ Cross-Layer ...... 34 4.3.1 EMA-based Algorithm for Estimating and Tracking λ ...... 35 4.3.2 ModeofOperation...... 37 4.4 TypeIHARQThroughputEﬃciency...... 38 4.5 Numerical and Simulation Results ...... 39 4.5.1 AMC-SwitchingThresholds ...... 39 4.5.2 Optimal Received SNR Analysis ...... 40 4.5.3 Convergence Analysis of λ ...... 41 4.5.4 Average Throughput Eﬃciency Analysis ...... 43 4.6 Conclusion ...... 44

5 Optimized Power Allocation for Throughput Maximized T-ARQ Com- bined with PC and AM 47 5.1 Introduction...... 47 5.2 SystemModel...... 48

viii 5.3 Optimized Power Allocation for Improved ARQ Protocol ...... 50 5.3.1 Dichotomic Search Approach for Optimal Power Allocation ...... 51 5.4 Combined AMC and PC with Improved ARQ Protocol ...... 52 5.5 Numerical and Simulation Results ...... 53 5.5.1 Performance of Enhanced ARQ Protocol ...... 54 5.5.2 Average Throughput of Joint PC, AMC and Enhanced ARQ Cross-Layer 56 5.6 Conclusion ...... 57

6 QoS-guaranteed Cross-Layer Design for Link Adaptation 58 6.1 Introduction...... 58 6.2 SystemModelandProblemStatement ...... 59 6.2.1 AdaptiveTransmissionSystem ...... 59 6.3 QoS-guaranteed Cross-Layer Design ...... 61 6.3.1 OptimalSwitchingThresholds ...... 62 6.3.2 ModeofOperation...... 64 6.4 Numerical and Simulation Results ...... 64 6.4.1 Average Throughput and Average Transmit SNR ...... 65 6.5 Conclusion ...... 70

7 Cross-Layer Design Combining PC and AMC for HARQ-MIMO Systems 71 7.1 Introduction...... 71 7.2 MIMOSystemsOverview ...... 72 7.3 SystemModelandMIMOChannel ...... 74 7.3.1 Adaptive Modulation and Coding System ...... 75 7.3.2 MIMOFadingChannel ...... 75 7.4 Optimized Link Adaptation for MIMO System ...... 77 7.4.1 Statistics for Unordered Eigenvalues ...... 78 7.4.2 Statistics for Ordered Eigenvalues ...... 80 7.4.3 OptimizedLAScheme...... 81 7.5 SimulationResults ...... 82 7.6 Conclusion ...... 84

8 Conclusion and Future Work 86 8.1 Conclusion ...... 86 8.2 FutureWork ...... 88

ix Bibliography 90

x List of Figures

2.1 Large-scale and small-scale fading effects...... 8 2.2 Power control illustration...... 9 2.3 Adaptive modulation and coding illustration...... 10 2.4 Operation of the basic ARQ protocol...... 11 2.5 SW-ARQpackettrafficdiagram...... 12 2.6 GBN-ARQ packet traffic diagram...... 12 2.7 SR-ARQpackettrafficdiagram...... 13 2.8 Operation of the hybrid ARQ protocol...... 14 2.9 (a) The layered OSI architecture (b) The layered TCP/IP architecture. . . . . 15 2.10 PHY/DL cross-layer perspective...... 15

3.1 Transmissionsystemblockdiagram...... 19 3.2 AMC-switchingthresholds...... 20 3.3 Illustration of the numerical resolution...... 24 3.4 Throughput eﬃciency for ARQ, using QPSK, 16-QAM and 64-QAM modula-

tions (ns =100) ...... 26 3.5 Distribution of the optimal transmit SNR, for λ = 5and5dB...... 26 − 3.6 Evolution of the average transmit SNR as a function of the Lagrange multiplier λ for several Nakagami fading channels...... 27 3.7 Average throughput eﬃciency for AMC-ARQ and PC-AMC-ARQ schemes, Q = 100symbols...... 29 3.8 Average throughput eﬃciency for AMC-ARQ and PC-AMC-ARQ approaches,

for ns =100and1000symbols...... 29

4.1 Transmissionsystemblockdiagram...... 32 4.2 Processingatthetransmitter...... 34 4.3 Processingatthereceiver...... 34 4.4 Illustration of the adaptive algorithm for estimating λ...... 35

xi 4.5 The rationale behind the criterion for steady state determination...... 37 4.6 Mode of operation of the proposed PC-AMC-HARQ-I cross-layer...... 37

4.7 Elementary throughput curves for coded and uncoded modulations, ns = 120. . 40 4.8 Distributions of the received SNR, for λ = 5and5dB...... 41 − 4 4.9 Behavior of the estimated λ and γ¯ˆt, fdTp = 0.005, α = 0.5, ∆λ = 10− , ǫ = 0.7. 41

4.10 Needed packet number for convergence as a function of fdTp, α = 0.5, ∆λ = 4 10− , ǫ = 0.7...... 42

4.11 Needed packet number for convergence as a function of α, fdTp = 0.01, ∆λ = 4 10− , ǫ = 0.7...... 43 4 4.12 Estimated and exact λ, fdTp = 0.1, α = 0.1, ∆λ = 10− ...... 43 4.13 Simulated and theoretical average throughput eﬃciency for PC-AMC-HARQ-I

scheme, ns =120...... 44 4.14 Average throughput eﬃciency for PC-AMC-HARQ-I and AMC-HARQ-I cross-

layer designs, ns =120...... 45 4.15 Average throughput eﬃciency for PC-AMC-HARQ-I and PC-AMC-ARQ cross-

layer designs, ns =120...... 45

5.1 Transmissionsystemblockdiagram...... 48 5.2 Illustration of the dichotomic search based power allocation process...... 52 5.3 Modeofoperation...... 53

5.4 Conventional ARQ throughput, QPSK modulation, T = 3, ns = 100 symbols. . 55

5.5 Enhanced ARQ throughputs, T = 3, ns =100symbols...... 55

5.6 Packet erasure probability, QPSK modulation, T = 3, ns = 100 symbols. . . . . 55

5.7 AMC-PC with conventional and enhanced ARQ, T = 3, ns = 100 symbols. . . 56

6.1 Illustration of the packet error probability...... 60 6.2 AMC-switchingthresholds...... 60

6.3 Transmit SNR as a function of η, P EPtg = 1%, N =3...... 68

6.4 Normalized throughput as a function of η, P EPtg = 1%, N =3...... 68 6.5 Distribution of the optimal transmit SNR for diﬀerent average transmit SNR constraints...... 68 6.6 Optimal transmit SNR as a function of η for diﬀerent PEP constraints. . . . . 69 2 4 6 6.7 QoS-guaranteed scheme for P EP = 10− , 10− and 10− ...... 69 6.8 Performances comparison of the QoS-guaranteed and no QoS-guaranteed schemes. 70

xii 7.1 Transmissionsystemblockdiagram...... 74 7.2 Average throughput as a function of the average transmit SNR, for ordered and unorderedeigenvalues ...... 83 7.3 Average throughput as a function of γ , for 2 2 and 3 3 MIMO systems vs t × × SISOsystem...... 83 7.4 Average throughput as a function of average transmit SNR, for MIMO-HARQ systemswithandwithoutPC ...... 84 7.5 Average throughput as a function of average transmit SNR, for MIMO-ARQ systemswithandwithoutPC ...... 84 7.6 Average throughput as a function of average transmit SNR, for MIMO-HARQ 2x2andMIMO-ARQ2x2systems ...... 85

xiii List of Tables

3.1 SupportedMCSs ...... 24

4.1 SupportedMCSs ...... 39 4.2 802.16e Puncturing pattern deﬁnition for HARQ ...... 39

6.1 Selecting optimal transmission parameters...... 64

7.1 Selecting optimal transmission parameter for eigen-subchannel i . 82

xiv Chapter 1

Introduction

1.1 Motivation

Provisioning higher data rates remains always a key driver in wireless communication networks evolution. The next-generation wireless system, so-called the 5th generation, will, for instance, need to support around 1 Gbps of downlink data rates [1]. To achieve these unprecedented rates, a higher spectrum efficiency is needed, motivating for a further optimization of the used wireless resources. Future wireless communication systems are also expected to suffer from limited bandwidths and power resources, and to face highly time-variant propagation environments and user mobility. In this context, adaptive techniques seem to be among the most promising solutions to better respond to the challenging requirements, through an efficient management of power and spectral resources and channel impairments.

The link adaptation (LA) is one method of tackling the variations in the instantaneous channel quality, through appropriate processing prior to data transmission. There are two link adaptation techniques, namely Adaptive Modulation and Coding (AMC) and Power Control (PC). Recent systems, such as HSPA, employ AMC at the physical (PHY) layer, to maximize throughput, while keeping the transmit power unchanged. In this setup, both modulation and coding schemes (MCS) are dynamically selected, based on switching signal to noise ratio (SNR) thresholds, in order to match the transmission rates to time-varying channel conditions.

On the other hand, systems like UMTS, use PC at the PHY layer, to guarantee a given

1 Chapter 1. Introduction

target signal to interference ratio (SIR), by tracking and compensating instantaneous channel variations, while using a single modulation scheme (typically a QPSK modulation).

In order to reach high reliability at the physical layer, the transmission rate must be reduced by using either small size constellations, or, powerful but low-rate error-control codes, or both. An alternative eﬃcient method to decrease packet loss rate is to rely on the Automatic Repeat reQuest (ARQ) protocol at the data link (DL) layer. This protocol requests retransmissions of erroneously received packets, which helps improving system throughput, relative to the use of forward error correction (FEC) alone at the PHY layer [15]. This method can be seen as a mechanism for handling variations in the instantaneous channel quality after transmission and hence nicely complements link adaptation. A combination of ARQ with FEC, called hybrid ARQ, has been developed, where unsuccessful attempts are used in FEC decoding instead of being discarded.

Aiming at improving the spectral eﬃciency, one may wish to jointly exploit the adaptability of LA techniques to the radio channel conditions and the error-correcting capacity of ARQ. Such challenges require the use of cross-layer approaches, which involve dynamic interactions between the PHY layer and the DL layer to enable the compensation for mismatching of requirements and resources. In this context, instead of considering AMC, PC and ARQ techniques as separate design entities for LA, or combining only two of them, as done in most of the previous research works [4]-[30], we focus in this thesis on the optimal combination of all three techniques, aiming at reducing the energy consumption while maximizing the oﬀered average transmission rate. The main contributions are summarized in the section below.

1.2 Contributions

First, a novel scheme which optimally combines PC with AM, using the basic ARQ protocol is developed in [58]. The considered optimality criterion is to maximize the average throughput efficiency (ATE) for an appropriately fixed average transmit power constraint, for reduced multiple access interference cost. Based on a set of throughput efficiency curves as a function of the received SNR and corresponding to the modulation schemes (MS) supported by the PHY layer, the proposed cross-layer allows to derive the optimal transmit power and the best MS for a given channel state. To do this, we had recourse to a numerical resolution method, which made the proposed approach generic for any ARQ scheme, regardless of the actual

2 Chapter 1. Introduction

channel statistics and the desired target average transmit power. To estimate the performance enhancement brought by this combination scheme, the conventional constant-power adaptive modulation scheme was used as a benchmark.

The numerical maximization of the ATE was carried using a Lagrange multiplier parameter, referred to λ, which is intimately related to the desired average transmit power and to the usually unknown channel statistics. Due to these unknown statistics, we assume in [59], for more realism, that λ is unknown at the transmitter, and that an appropriate feedback from the receiver is used to track it. The proposed iterative algorithm for blindly estimating and tracking λ, referred to as λ-tracking loop, operates in a closed tracking mode, and uses the exponential moving average (EMA) algorithm to estimate the achieved average transmit power. The adaptation of the coding rate is also considered in addition to the constellation size adaptation previously addressed. Hence, a type I hybrid ARQ protocol is considered with a selective repeat (SR) retransmission strategy. We also resort to a Monte-Carlo simulation approach, modeling in a realistic way channel variations and tracking loop behavior. The convergence of the proposed tracking loop is studied in [60] as a function of the mobile speed. To this end, the end-to-end simulations are performed while considering a realistic time-correlated fading channel model based on the Jakes model.

In conventional ARQ protocols, the same power is usually used to retransmit a copy of the same packet, whenever it is needed. However, a packet is often rarely retransmit, especially for advantageous radio-link quality. Hence, we may allocate more transmit power for later transmissions without increasing the average power spent by packet. More specifically, a judicious redistribution of the available budget of transmit power could increase the throughput, without leading to a significant increase of the average power spent by packet. In this context, we propose in [61], not only to select the optimal transmit power level for a given CSI, but also to wisely redistribute this budget of average transmit power per packet among the potential transmissions, such that the resulting throughput is maximized, for a fixed budget of average power per packet (or per symbol). To this end, a truncated ARQ (T-ARQ) protocol is adopted, to limit the maximum number of transmissions. After T unsuccessful transmission attempts, the transmitter discards the current packet and proceeds to a transmission of the next packet waiting in the buffer and ready for transmission. The optimal power allocation is performed through a heuristic algorithm, based on a dichotomic search inspired from [33] for fixed modulation scheme. The enhanced version of the ARQ protocol is then combined with AMC and PC techniques, conforming to what was done in [58]. Obtained results reveal a reduction in

3 Chapter 1. Introduction

average transmit power, which is only pronounced for low average transmit power, compared to the conventional ARQ protocol.

In [62], we develop a power eﬃcient cross-layer design for throughput improved QoS-guaranteed packet wireless communications. In addition to the constraint on the average transmit power, previously considered in [58]-[61], a target Packet Error Probability (PEP) constraint was taken into account. Both optimal adaptive modulation (AM) switching thresholds and appropriate transmit power are derived as a function of the channel state, while guaranteeing the required QoS in terms of PEP. Closed-form expressions of the derived solutions, are also presented, for high received SNR.

Finally, in [63], we generalize the PC-AMC-HARQ cross-layer previously presented in [59] and [60] for SISO systems to MIMO systems. To this end, the MIMO channel is decoupled into parallel eigen-subchannels using the singular value decomposition (SVD) based spatial multiplexing [41], while assuming known perfect channel state information (CSI) at both the transmitter and the receiver. For each eigen-mode, the optimal transmit power level as well as the appropriate MCS are jointly selected, as a function of the fading state of the subchannel, in order to achieve the highest ATE of the whole MIMO system. A constraint on the total average transmit power is considered. The achieved ATE improvement is analyzed for both ordered and unordered eigenvalues cases.

1.3 Organization

The reminder of this thesis is divided into six chapters and is organized as follows. In chapter II, we give a brief overview about link adaptation techniques, namely adaptive modulation and coding and power control as well as automatic repeat request protocols. Chapter III investigates cross-layer design optimally combining AM and PC techniques at the PHY layer with basic ARQ protocol at the DL layer. In Chapter IV, we present a realistic implementation of the PC-AMC combination for hybrid ARQ systems. In chapter V, we address the optimal redistribution of the transmit power budget among potential transmissions of truncated ARQ protocol, and the combination of this enhanced version of T-ARQ with both AMC and PC. Chapter VI is dedicated to the presentation of the developed QoS-guaranteed cross-layer design which combines AMC, PC with an ARQ protocol. Chapter VI is dedicated to the presentation of the extension of the eﬃcient PC-AMC-HARQ cross-layer design to MIMO wireless systems.

4 Chapter 1. Introduction

Finally, chapter VIII draws some concluding remarks and a summary of our ﬁndings.

5 Chapter 2

Link Adaptation Techniques and ARQ protocols

2.1 Introduction

Mobile radio communication is typically characterized by the rapid and signiﬁcant variations in the instantaneous channel quality. Several reasons are behind these variations. Large-scale fading, due to the shadowing and the distance-depend path loss, aﬀect the average received signal strength [2]. Small-scale fading, due to multipath propagation, cause rapid and random variations in the channel quality. Finally, multicell and multiuser interferences impact the interference level at the receiver. All these variations have to be taken into account and desirably exploited.

Link adaptation (LA) is a term used in wireless communications to denote the prior matching of the transmission parameters to the channel variations, to perform optimally under prevail- ing conditions. However, due to the random nature of these variations, perfect adaptation to the instantaneous channel quality is never reached. Therefore, a post transmission processing will be useful to handle instantaneous channel quality variations after data transmission. This can be ensured by the automatic repeat request (ARQ) mechanism [15]-[17], which requests retransmission of packets received in error. A combination of ARQ with forward error correction (FEC), called hybrid ARQ, has been developed [18]-[23], where unsuccessful attempts are used in FEC decoding instead of being discarded. In this chapter, we will give an overview

6 Chapter 2. Link Adaptation Techniques and ARQ protocols

about these techniques for handling variations in the instantaneous radio-link quality. First, we present in Section 2.2 the variations that aﬀect the radio link. In Section 2.3, we give a brief overview about the link adaptation by means of power control (PC). In section 2.4, we present the link adaptation by means of rate control which is also referred to as Adaptive Modulation and Coding (AMC). In section 2.5 and 2.6, we present the ARQ and the hybrid ARQ protocols, respectively. In section 2.7, we present the cross-layer design paradigm. In section 2.8, we give some concluding remarks.

2.2 Radio Propagation Eﬀects

Radio signals generally propagate according to three mechanisms: reflection, diffraction, and scattering. The appropriate channel model depends strongly on the intended application and different models are used for the different applications such as cellular and WLANs. The channel model directly affects the steps of designing, evaluating, and deploying any wireless system in the objective of ensuring adequate coverage and quality of service. As such, the channel model to be adopted should be wisely chosen.

In mobile radio channels, the transmitted signal undergoes diﬀerent channel eﬀects which are multipath propagation, Doppler spread, shadowing and path loss [2]:

Multipath propagation occurs as a consequence of reflections, scattering, and diffraction • of the transmitted electromagnetic wave at natural and man-made objects. Thus, at the receive antenna, a multitude of waves arrives from several directions with different delays, attenuations, and phases. The superposition of these waves results in amplitude and phase variations of the composite received signal.

Doppler spread is caused by moving objects in the mobile radio channel. The changes • in the phases and amplitudes of the arriving waves lead to time-variant multipath propagation. Even small movements on the order of the wavelength may result in a totally diﬀerent wave superposition. When the signal strength varies due to time-variant multipath propagation, the channel is said fast fading or time selective.

Shadowing results from the obstruction of the transmitted waves by objects (for example • hills, buildings, walls, and trees) along the paths of a signal, which results in more or less strong attenuation of the signal strength. Compared to fast fading, longer distances have

7 Chapter 2. Link Adaptation Techniques and ARQ protocols

to be covered to change the shadowing constellation signiﬁcantly. The varying signal strength due to shadowing is called slow fading and can be described by a log-normal distribution.

Path loss indicates how the mean signal power decays with distance between the trans- • mitter and the receiver. In free space Line Of Sight (LOS), the mean signal power decreases with the square of the distance between the transmit and the receive antennas 2 2πd such that the received power at distance d decreases proportionally to w (w is the wavelength). In a mobile radio channel, where often no line of sight (NLOS) exists, signal power decreases with a power higher than two and typically varies between three and ﬁve.

A mobile wireless channel can be characterized by the variations of the channel strength which can be roughly categorized into large-scale fading and small-scale fading (see illustration in Fig. 2.1. For any given position in the space, the received signal is affected by large scale effects such as path-loss, shadowing, diffraction and rain or foliage attenuation. This is more relevant to issues such as cell-site planning and can be avoided through power control at the transmitter. Small-scale effects are caused by rapid fluctuation of the signal due to multipath propagation and movement of either the transmitter or the receiver. They are more relevant to the design of reliable and efficient communication systems [3].

Figure 2.1: Large-scale and small-scale fading eﬀects.

2.3 Power Control

Historically, the dynamic control of the transmit power was used in mobile communication systems based on CDMA, such as cdma2000 and WCDMA, in order to compensate the in-

8 Chapter 2. Link Adaptation Techniques and ARQ protocols

stantaneous channel state variations [4], [5]. The key idea of power control is to dynamically adjusts the transmit power to compensate for variations in the instantaneous channel conditions. The aim of these adjustments is to guarantee a (near) constant signal to interference ratio (SIR) at the receiver such as data are successfully transmitted without a very high error probability. Typically, the PC increases the transmit power when the channel experiences poor radio conditions, and vice versa. This results in a transmit power inversely proportional to the channel quality as illustrates Fig. 2.2. The data rate is then basically constant, regardless of the channel variations, which is a proﬀered property for services such as circuit-switched voice. However, in case of packet-switching mobile communications, there is no need to provide a given constant data rate over the radio link. Even in case of typical constant-rate services such as voice and video, short-term variations in the data rate are not an issue, what is more important is to keep the average data rate almost constant. In such case, an alternative LA technique to PC is the dynamic rate control referred to as adaptive modulation and coding (AMC).

Figure 2.2: Power control illustration.

2.4 Adaptive Modulation and Coding

With dynamic rate control, the data rate is dynamically adjusted to compensate for the varying channel quality and the multiple access interferences by means of adjusting the modulation scheme and/or the channel coding rate (see illustration in Fig. 2.3). When the channel conditions are advantageous and the multiple access interference is reduced, higher-order mod-

9 Chapter 2. Link Adaptation Techniques and ARQ protocols

ulation, 16-QAM or 64-QAM, is used together with a high code rate. On the contrary, when the channel is bad and the multiple access interference is significant, low-order modulation, QPSK, and low-rate coding is used. In all cases, the transmit power remains constant over the time, which implies an efficient utilization of the power amplifier. The proper modulation and coding scheme (MCS) is determined by comparing the signal to noise ratio (SNR) at the receiver to certain predestined AMC-switching thresholds.

Figure 2.3: Adaptive modulation and coding illustration.

2.5 Automatic Repeat Request Protocols

In packet transmission mode, there are mainly two error control techniques: Automatic Repeat reQuest (ARQ) and Forward Error Correction (FEC). In the basic ARQ scheme, the transmitted packets are coded using only an error detection code. The most frequently used error detection codes are the Cyclic Redundancy Check (CRC) codes. At the receiver, a detector error decoding is performed to each received packet. If the receiver detects the presence of errors, it sends to the transmitter a negative acknowledgment message (Ack-) to request the retransmission of the packet. Otherwise, it sends a positive acknowledgment messages (Ack+) to conﬁrm the good receipt of the packet and ask the transmission of the next packet. Retrans- missions take place until the packet is correctly received (untruncated ARQ), or until a preset number of retransmissions is reached (truncated ARQ). The process of this basic ARQ scheme is illustrated in Fig. 2.4. The implementation of this technique is related to the used retransmission strategy. There are three retransmission strategies, namely Stop and Wait (SW) Go

10 Chapter 2. Link Adaptation Techniques and ARQ protocols

Back N (GBN) and Selective Repeat (SR).

Figure 2.4: Operation of the basic ARQ protocol.

2.5.1 SW-ARQ Protocol

In SW-ARQ protocol, the transmitter sends out a packet and waits for an acknowledgment by the receiver. If the acknowledgment is negative, the transmitter retransmits the same packet, otherwise it proceeds to the next packet. This process is illustrated in Fig. 2.5.

2.5.2 GBN-ARQ Protocol

In GBN-ARQ protocol, N packets are sending without analyzing the acknowledgments at the receiver. When a received packet is detected in error, the transmitter restart the retransmission from the wrong packet and remove all the following packets at the receiver (see illustration in Fig. 2.6). The implementation of this protocol requires the use of a buﬀer at the transmitter. This buﬀer is used to store the last N transmitted packets for retransmission in case of error.

11 Chapter 2. Link Adaptation Techniques and ARQ protocols

Figure 2.5: SW-ARQ packet traﬃc diagram.

Figure 2.6: GBN-ARQ packet traﬃc diagram.

12 Chapter 2. Link Adaptation Techniques and ARQ protocols

2.5.3 SR-ARQ Protocol

The SR-ARQ protocol requires the retransmission of only packets declared erroneous at the receiver (see illustration in Fig. 2.7). This protocol requires two buﬀers, one at the transmitter for the retransmission of erroneous packets and the other at the receiver to store the correct packages.

Figure 2.7: SR-ARQ packet traﬃc diagram.

Both type GBN-ARQ and SR-ARQ oﬀer greater throughput eﬃciency than SW-ARQ at the cost of greater memory and processing requirements. Among all ARQ retransmission strategies, SR-ARQ is reported to show the best throughput performance.

2.6 Hybrid ARQ

All CDMA-based communication systems employ a combination of FEC coding and ARQ, called hybrid ARQ (HARQ). Hybrid ARQ was ﬁrst proposed in [21] and several publications on HARQ have appeared since [23]. It rely on FEC codes to correct detectable errors and uses then error detection codes to detect uncorrectable errors. Most current practical HARQ schemes employ convolutional or Turbo codes for error correction and a CRC code for error detection. Whenever a packet is detect in error, the receiver discards it and requests its retransmission (see illustration in Fig. 2.8). This variation of HARQ protocol is known as type

13 Chapter 2. Link Adaptation Techniques and ARQ protocols

I hybrid ARQ.

Figure 2.8: Operation of the hybrid ARQ protocol.

2.7 Cross-Layer Design

One of the biggest problems faced by researchers to accommodate the demanding services and applications for next-generation wireless networks is the availability of strategies at different layers. The layered Open Systems Interconnection (OSI) architecture for networking [38], on which the Transport Control Protocol/Internet Protocol (TCP/IP) architecture is based, is a successful example of a good architectural design. As illustrates Fig. 2.9, these architectures divide the overall networking task into layers, and define a hierarchy of services to be provided by each layer [34]. Each layer in the protocol stack is designed independently. Aiming to meet the challenging demands of future wireless networks, it is desirable to adopt new approaches where protocols can be designed allowing direct communication among nonadjacent layers. This is provided by sharing variables among layers, redefining the layer boundaries, designing protocols within a layer based on the details of another layer, jointly tuning of parameters across layers and so on. Such violations of a layered architecture have been termed as cross- layer design [35]-[37].

14 Chapter 2. Link Adaptation Techniques and ARQ protocols

Figure 2.9: (a) The layered OSI architecture (b) The layered TCP/IP architecture.

Figure 2.10: PHY/DL cross-layer perspective.

15 Chapter 2. Link Adaptation Techniques and ARQ protocols

2.7.1 PHY/DL Cross-Layer Design

Following the spirit of cross-layer design, and in contrast to a local optimization of each of the layers, a joint optimization of the PHY and the DL layers is investigated in this research work. More specifically, we aim to optimally combine AMC and PC at the PHY layer with basic/hybrid ARQ protocol at the DL, which will imply the exchange of layer specific parameters. Particularly, as illustrates Fig. 2.10, the cross-layer design will optimally determine specific opt design parameters at the PHY layer XPHY (e.g. transmit power level, AMC-switching thresholds) based on specific parameters at the DL layer YDL (e.g. throughput efficiency, packet error probability, number of allowed transmissions), that maximize the average throughput efficiency T hr of the system, while satisfying prescribed QoS and/or average transmit power requirements. These reconfiguration strategies will take into account instantaneous channel state information (CSI) at the PHY layer.

2.8 Conclusion

In this chapter, we gave an overview about the two link adaptation techniques namely power control and adaptive modulation and coding. These techniques tries to exploit the channel variations through appropriate processing prior to data transmission. We have also presented the automatic repeat request protocols and their different retransmission strategies namely SW, GBN and SR. These protocols, which can be seen as mechanisms for handling channel variations after data transmission, nicely compliment LA techniques. In fact, the ARQ protocols are typically used in combination with AMC for improved system reliability [27]-[30]. In [24]-[26], AMC and PC have been jointly used without ARQ. However, the combination of the two LA techniques PC and AMC with the ARQ has rarely been addressed in the literature. In the next chapter, we will present our first contribution in the efficient combination of all of these techniques for channel variations handling.

16 Chapter 3

Cross-Layer Design for Link Adaptation in ARQ-based Systems

3.1 Introduction

Power control (PC) [4, 5], adaptive modulation and coding (AMC) [6]-[14] and automatic repeat request (ARQ) protocols [15]-[17] were intensively studied in the literature as separate design entities for channel variation handling. The AMC schemes, which denote the matching of the modulation and coding to time-varying channel conditions, have been widely advocated and adopted at the PHY layer in most state-of-the-art wireless communications standards, such as IEEE 802.11, High-Speed Downlink Packet Access (HSDPA), High-Speed Uplink Packet Access (HSUPA), Long Term Evolution (LTE), LTE-Advanced, IEEE 802.16, etc. [10]-[12]. On the other hand, systems like Universal Mobile Telecommunications System (UMTS), use only PC at the PHY layer, to guarantee a given target signal to interference ratio (SIR), by tracking and compensating instantaneous channel variations.

Some combinations of two of these three techniques were also well investigated. For instance, in [24]-[26] AMC and PC have been jointly used without ARQ. For instance, it was shown in [8] that the Shannon capacity of a ﬂat-fading channel can be achieved by employing both power and rate adaptation while assuming unbounded length coding schemes, which is not applicable for practical systems.

17 Chapter 3. Cross-Layer Design for Link Adaptation in ARQ-based Systems

On the other hand, some cross-layer designs were investigated in [27]-[30], combining AMC at the PHY layer with an ARQ protocol at the DL layer, aiming at improving the spectral efficiency by jointly exploiting the adaptability of AMC to the radio channel conditions and the error-correcting capacity of ARQ. Typically, in [29] the optimal switching thresholds maximizing the average spectral efficiency were derived using an approximate expression of the packet error probability. This expression relies on fitting parameters that depend on the used modulation and coding scheme as well as the packet size.

In this chapter, we develop a cross-layer design that optimally combines both LA techniques AMC and PC at the PHY layer with an ARQ protocol at the DL layer, a combination that has been rarely addressed in the literature. The considered optimality criterion is to maximize the average throughput efficiency (ATE) under a prescribed average transmit power constraint and channel statistics. To do this, an analytic derivation is first carried using the Lagrange multipliers, followed by a numerical resolution process. This numerical resolution approach needs only a set of throughput efficiency curves corresponding to the modulation schemes (or modulation and coding schemes) supported by the system, obtained either by an explicit analytic expression or through Monte Carlo simulations, to determine the appropriate transmission parameters.

The remainder of this chapter is organized as follows. We ﬁrst present our generic system model in Section 3.2. In Section 3.3, we detail the proposed cross-layer design, referred to as PC-AMC-ARQ and present the used numerical resolution process. We provide numerical and simulation results in Section 3.4 and analyze the performance enhancement by comparing the PC-AMC-ARQ cross-layer to the conventional cross-layer combining only AMC and ARQ techniques. Finally, we draws some conclusions in Section 3.5.

3.2 Generic System Model

The point-to-point wireless packet communication link between a single-antenna transmitter and a single-antenna receiver is illustrated in Fig. 3.1, showing the most blocks involved in the transmission and reception processes. This generic system model will be also adopted as a basic transmission system block diagram for upcoming chapters. Arriving from higher stacked protocol layers, the packets to be transmitted by the PHY layer are queued in an inﬁnite buﬀer, then transmitted on a packet-by-packet basis over the wireless channel.

18 Chapter 3. Cross-Layer Design for Link Adaptation in ARQ-based Systems

Figure 3.1: Transmission system block diagram.

3.2.1 Transmitter

At the transmitter, both the signal transmit power Pt, or equivalently the transmit SNR γt, and the MCS are jointly adapted to the channel conditions, based on the channel state information (CSI), η, fed back by the receiver. The channel quality is captured by the instantaneous channel power η = h 2, where h is the channel coeﬃcient. A perfect CSI at the transmitter is assumed. | | The PC selector selects the appropriate transmit SNR, which is deﬁned as the ratio between the average transmit symbol energy Es and the one-sided noise power spectral density (PSD)

N0, and hence related to the transmit power as follows

PtTs γt = , (3.1) N0 where Ts is the symbol duration. Using a set of AMC switching thresholds, the AMC selector selects the appropriate MCS according to the current CSI, as details the subsection 3.2.4. The selected transmission parameters are then used to transmit the current packet ready in the buﬀer.

3.2.2 Wireless Channel

While the proposed LA scheme is applicable to generic fading distributions, we assume an independent identically distributed (i.i.d.) Rayleigh block-fading channel, characterized by its channel power probability density function (PDF), denoted by fη(η) and given by

η fη(η)= e− . (3.2)

19 Chapter 3. Cross-Layer Design for Link Adaptation in ARQ-based Systems

The block-fading assumption accounts for the fact that the packet duration is much smaller than the coherence time of the channel. That is, the channel is assumed to remain invariant over at least one packet and it is allowed to vary from one packet to another.

3.2.3 Receiver

At the receiver, we assume a perfect channel estimates and a perfect error detection. The error detection is performed using a CRC code. When an erroneous packet is detected, the basic ARQ protocol implemented in the DL layer generates a retransmission request Ack . A − selective repeat (SR) retransmission strategy is assumed.

3.2.4 Adaptive Modulation and Coding System

Figure 3.2: AMC-switching thresholds.

For simplicity reasons and without loss of generality, we assume that the PHY layer supports N uncoded modulations presented in Table 3.1. The case of coded modulations will be addressed in the next chapter. A given MCSn, n = 1, 2, ..., N, is characterized by an Mn-ary QAM modulation. For each MCSn, the performance of the ARQ protocol is assessed through the throughput eﬃciency curve, T hrn(γr) in (bit/s)/Hz, as a function of the instantaneous received

SNR γr, deﬁned as the ratio between the average received symbol energy and the one-sided noise power spectral density. The throughput eﬃciency expression is presented in the subsection 3.4.1. The more the selected Mn value is high, the more it provides good performances for high received SNR and weak performances for low received SNR (see Fig.3.4). Hence, for each

γr there is one MCS that outperforms the other modulation and coding schemes. Therefore, as illustrates Fig. 3.2, the received SNR range can be partitioned into N consecutive intervals deﬁned by the switching thresholds T N , where T = 0 and T = + for convenience. { n}n=0 0 N ∞ Whenever the received SNR γr falls within the interval [Tn, Tn+1), the MCSn will be chosen for transmission, since it outperforms all other MCSs. Consequently, the eﬀective throughput

20 Chapter 3. Cross-Layer Design for Link Adaptation in ARQ-based Systems

is given by the maximum of all elementary throughput curves

T hr(γr) = max T hrn(γr) . (3.3) n { }

In conventional constant-power AMC-ARQ cross-layer, the transmit power is kept constant whatever the outcome of the channel. As a consequence, the SNR at the receiver is totally determined by the channel state η, and given by

γr = ηγt. (3.4)

In our case, the transmit power is adapted to the channel state. Therefore, both SNRs at the transmitter and the receiver, will be a function of the channel power and denoted next by γt(η) and γr(η), respectively.

3.3 Cross-Layer Design

In this section, we develop the proposed cross-layer design, which optimally combines PC and AMC at the PHY layer with ARQ protocol at the DL layer. This combination aims to maximize the average system throughput, under an adequately chosen average transmit power constraint, or equivalently an average transmit SNR constraint. First, we present the problem statement. Then, we develop a numerical resolution process to solve the obtained optimization problem.

3.3.1 Problem Statement

The considered optimality criterion is to maximize of the average throughput T hr for a giving average transmit SNR constraintγ ¯t. Note that T hr represents the eﬀective throughput deﬁned in (3.3). This standard constrained optimization problem can be formulated using the Lagrange multipliers method. It amounts to the unconstrained maximization

max T hr λγ¯t subject toγ ¯t =γ ¯tg. (3.5) γt(η) − The Lagrange multiplier λ is indirectly ﬁxed by the target average transmit SNRγ ¯tg. In order to solve the objective function in (3.5), we next replace T hr andγ ¯t by their explicit expressions.

21 Chapter 3. Cross-Layer Design for Link Adaptation in ARQ-based Systems

First of all, the average throughput eﬃciency is given by

+ ∞ T hr = T hr(γr(η))fη(η)dη. (3.6) Z0

Likewise, the constrained average transmit SNRγ ¯t can be expressed as

+ ∞ γ¯t = γt(η)fη(η)dη. (3.7) Z0 Since the throughput is basically a function of the received SNR, we propose, for simplicity reasons, to solve the function in (3.5) with respect to γr(η), which, similarly to (3.4), requires the replacement of γt(η) in (3.7) by

γ (η) γ (η)= r . (3.8) t η

Using (3.6), (3.7) and (3.8), the objective function in (3.5) can be rewritten as

+ ∞ λ max T hr(γr(η)) γr(η) fη(η)dη . (3.9) γr(η) − η Z0

Since the PDF fη(η) is generally non negative, the maximization in (3.9) amounts to the maximization problem λ max T hr(γr(η)) γr(η) , η 0. (3.10) γr(η) − η ∀ ≥ We notice from the equivalent optimization problem in (3.10), that the optimum instantaneous received SNR as a function of the CSI η, does not depend on the channel statistics (i.e. fη(η)). This clearly means that the expected solutions are valid for any generic channel.

However, we also notice that it depends on the Lagrange multiplier λ which is tightly related toγ ¯tg, the constraint imposed on the average transmit power. Hence, we next try to give the general solution in parameterized form.

η By introducing the parameter µ = λ and hence the new function

χ(µ)= γr(λµ), (3.11) the maximization problem becomes

χ(µ) max T hr(χ(µ)) , µ 0. (3.12) χ(µ) − µ ∀ ≥

22 Chapter 3. Cross-Layer Design for Link Adaptation in ARQ-based Systems

Noticing that the new form of the maximization problem does not depend on any parameter and hence has a unique optimal solution, denoted next by χopt(µ), we deduce that the optimal solution of (3.9) has as general parameterized form with respect to η

η γ (η)= χ . (3.13) r,opt opt λ Consequently, the optimal transmit SNR, in parametric form, is expressed as

η γ (η) χopt( ) γ (η)= r,opt = λ . (3.14) t,opt η η

Similarly, the average throughput can hence be rewritten as

+ η T hr = ∞ T hr(χ )f (η)dη. opt λ η Z0 (3.15)

Given the complexity and the non differentiability of the piecewise expression of the effective throughput efficiency (given in (3.3)), the analytic derivation seems not to be the best way to solve the maximization problem in (3.12). Therefore, we propose a numerical resolution process, described in what follows, to solve the obtained optimization problem.

3.3.2 Numerical Resolution Process

The idea of the proposed numerical resolution is illustrated in Fig. 3.3. Let ξ be the upper envelope of the elementary throughputs. It consists in numerically locating the global maximum χ of the diﬀerence between the curve ξ = T hr(χ) and the line ξ = µ , for a given parameter µ.

As shown in the ﬁgure, there can be several local maxima and minima (e.g., maxima M0, M1, and minima m0 m1, for µ = µj), among them the global maximum is located. These extrema correspond to the intersection points of the curve ξ = T hr(χ) with its tangents parallel to the χ line ξ = µ . The abscissa of the global maximum represents the optimal solution χopt of the R+ 1 function in (3.12). The parameter µ takes its values in . When µ is such that the slope µ is larger than the largest slope of the throughput curve (e.g., 1 ), the optimal SNR χ and µi opt 1 the corresponding throughput are always equal to 0. However, when the slope µ vanishes, so that the corresponding solution χopt goes to inﬁnity, the obtained throughput ξ reaches its maximum.

23 Chapter 3. Cross-Layer Design for Link Adaptation in ARQ-based Systems

Figure 3.3: Illustration of the numerical resolution.

3.4 Numerical and Simulation Results

In this section, numerical and simulation results are presented to illustrate the feasibility of the proposed cross-layer. To assess the performance enhancement brought by this combination scheme, we consider the case of adaptive uncoded modulation and we use as a benchmark the conventional constant-power AMC-ARQ scheme. We consider the N uncoded M-QAM, M = 22k, k = 1, 2, ...N, modulations schemes illustrated in Table 3.1.

Table 3.1: Supported MCSs Uncoded modulations MCS1 MCS2 MCS3 QPSK 16-QAM 64-QAM

3.4.1 Basic ARQ Throughput Eﬃciency

The performance of an ARQ protocol is basically assessed by the throughput efficiency defined as the ratio between the number of information bits and the average number of coded bits transmitted during different transmission attempts. Considering an untruncated basic ARQ protocol and a SR retransmission strategy, the throughput expression for a given MCSn scheme

(i.e. Mn-QAM modulation), is expressed as

kb 1 T hrn(γr(η)) = log2(Mn) , (3.16) nb T r

24 Chapter 3. Cross-Layer Design for Link Adaptation in ARQ-based Systems

where kb and nb are, respectively, the number of information bits and the total number of bits per packet (after CRC coding). Considering the assumption of an i.i.d. block-fading channel, the average number of transmission attempts T r can be evaluated as

+ ∞ i 1 T r = P EP (γr(η)) = , (3.17) 1 P EP (γr(η) Xi=0 − where P EP (γr(η)) is the packet error probability given by

P EP (γ (η)) = 1 (1 P (γ (η)))2ns , (3.18) r − − en r where ns is the number of symbols per packet and Pen (γr(η)) is the probability that the inphase/quadrature phase component of an Mn-QAM symbol be erroneously received, given by

√Mn 1 3 Pe (γr(η)) = − erfc γr(η) , (3.19) n √M 2(M 1) n s n − ! where erfc(.) is the complementary error function, deﬁned as

+ 2 2 ∞ −x erfc(x) = e 2 dx. (3.20) √π Zx Using (3.18) and (3.19) in (3.17) the throughput eﬃciency is expressed as

2ns √Mn 1 3 T hr (γ (η)) = log (M ) 1 − erfc γ (η) . (3.21) n r 2 n √M 2(Mn 1) r − n − q In Fig. 3.4, we depict the throughput eﬃciency (3.21) versus the instantaneous received SNR, for ns = 100 and N = 3. Two AMC-switching thresholds, T1 and T2 can be distinguish. The AMC selector chose the appropriate MCS by comparing the power controlled received SNR

γr(η) to those thresholds.

3.4.2 Optimal Transmit Power

The numerical resolution process, applied to the upper envelop of elementary throughput curves in Fig. 3.4, leads to the optimal solutions (3.14), depicted in Fig. 3.5, for λ = 5 and 5 dB. − We can note from this ﬁgure that, when the received SNR γr falls in a region where the slope of the upper envelop is large, the transmitter has to increase the transmit power so that γr

25 Chapter 3. Cross-Layer Design for Link Adaptation in ARQ-based Systems

QPSK 16−QAM 5 T 64−QAM 2

3 T 1

2 Throughput efficiency [(b/s)/Hz] 1

0 0 5 10 15 20 25 30 γr[dB]

Figure 3.4: Throughput eﬃciency for ARQ, using QPSK, 16-QAM and 64-QAM modulations (ns = 100) reachs the next switching threshold. Conversely, when the upper envelop curve has a small slope, the transmitter has to decrease it power such that the same modulation remains valid.

We also notice that the distributions of γt,opt(η) for λ = 5 dB can be deduced from the one for λ = 5 dB by a translation on the x-axis and a scaling on the y-axis (indirect similarity). − Thus, in conformity with (3.14), a single curve is suﬃcient to deduce the distribution curves of γt,opt(η) for any value of λ. It is worth noting that, any decrease in λ leads to an increase in the average transmit power (or equivalently, the average transmit SNR), which results in the ability to transmit most of time with a high constellation size even for poor channel states. For instance, we ﬁnd that in the case when λ = 5 dB, the transmitter may use the 64-QAM − modulation from a channel power η = 15.5 dB, while the same modulation is only used from η = 25.5 dB in the case when λ = 5 dB.

λ = −5 dB : QPSK 7 λ = −5 dB : 16−QAM λ = −5 dB : 64−QAM 6 λ = 5 dB : QPSK λ = 5 dB : 16−QAM λ 5 = 5 dB : 64−QAM

3 Optimal transmit−SNR

0 0 5 10 15 20 25 30 35 40 η[dB]

Figure 3.5: Distribution of the optimal transmit SNR, for λ = 5 and 5 dB. −

26 Chapter 3. Cross-Layer Design for Link Adaptation in ARQ-based Systems

3.4.2.1 Determination of the Lagrange Parameter λ

The Lagrange multiplier λ is indirectly ﬁxed by the constraint on the average transmit SNR.

Using (3.7) and (3.14), we ﬁnd that λ is related toγ ¯t as follows

+ η + χopt( ) χ (µ) γ¯ = ∞ λ f (η)dη = ∞ opt f(λµ)dµ. (3.22) t η η µ Z0 Z0 It is worth noting here that, unlike the solution of the optimal transmit power, the relationship betweenγ ¯t and λ depends on the channel distribution fη(η). Therefore, knowing the channel statistics, the transmitter can numerically determine the target λ by projecting the target transmit SNR on the curve ofγ ¯t as a function of λ. For instance, we depict in Fig. 3.6 the variation ofγ ¯t as a function of λ, in the presence of Nakagami fading channels with normalized channel power, characterized by the PDF

m m m 1 mη f (η)= η − e− , η 0 (3.23) η Γ(m) ≥ where m is the fading ﬁgure and Γ(.) is the Gamma function.

35 γ¯t [dB] m=1 30 m=2 m=3 25

γ¯target

−5 −50 −45 −40 −35 −30 −25 −20 λ1 λ2 λ3 −10 −5 0 λ [dB]

Figure 3.6: Evolution of the average transmit SNR as a function of the Lagrange multiplier λ for several Nakagami fading channels.

However, most of the time the transmitter ignores the channel distribution. Therefore, we propose in the next chapter to iteratively determine the exact λ from the average transmit SNR constraint.

27 Chapter 3. Cross-Layer Design for Link Adaptation in ARQ-based Systems

3.4.3 Average Throughput Eﬃciency Analysis

Next, we examine and compare two link adaptation approaches, namely the conventional approach, used as benchmark and referred to as AMC-ARQ, whereby AMC is exclusively used as link adaptation technique with the ARQ protocol, and the proposed approach, referred to as PC-AMC-ARQ, whereby a combination of PC and AMC is used also in the presence of the ARQ protocol. Although the proposed approach is applicable to generic fading distributions, we assume a single-path Rayleigh fading channel model, with channel power distribution deﬁned in (3.2). This distribution is a special case of the Nakagami-m distribution with m = 1.

First, we compare in Fig. 3.4.3, the average throughputs for the AMC-ARQ and PC-AMC-

ARQ approaches, respectively, for ns = 100. This figure clearly shows that our proposed approach significantly improves the system performance, especially for high and low average transmit SNRs. For example, one can see that the average throughput T hr = 5.9 (b/s)/Hz is reached for an average transmit SNRγ ¯t = 37.6 dB if the AMC-ARQ approach is used alone, while one only needs an average transmit SNRγ ¯t = 30.6 dB, if we use the PC-AMC-ARQ approach. In this case, the obtained gain amounts to a reduction of the average transmit power by around 80%. We also notice that the proposed approach provides a minimum gain of about 2 dB for a target average throughput around 3 (b/s)/Hz. The performance improvement is explained by the fact that power control preserve transmit-power by avoiding transmission when the radio link experiences poor radio conditions (for example γ = 0 dB for η = 10 t,opt − dB). Thus, the preserved power will be exploited when channel conditions improve. Indeed, in case of advantageous radio-link conditions, power control provides a transmit-power higher than the one offered by AMC-ARQ system. Especially, when the SNR at the receiver, in the conventional approach, is slightly lower than the threshold allowing the use of the next modulation, power control at the transmitter provides slightly additional power to reach this upper threshold. Hence, this power increase helps to reach a better modulation scheme and consequently improves the overall system throughput.

Fig. 3.8 compares the performance of PC-AMC-ARQ and AMC-ARQ schemes for diﬀerent packet sizes, namely ns = 100 and ns = 1000. We notice that when the packet length increases, our approach provides a slightly increased gain. Indeed, for a packet length of 100 symbols we gain 1.9 dB in power compared to the AMC-ARQ approach, for a target average throughput T hr = 5 (b/s)/Hz , while we gain in the same conditions 2.2 dB for packet size of 1000 symbols.

28 Chapter 3. Cross-Layer Design for Link Adaptation in ARQ-based Systems

6 5.9 7 dB PC−AMC−ARQ approach 5 AMC−ARQ approach

3 2 dB

1 Average Throughput efficiency [(b/s)/Hz]

0 −10 −5 0 5 10 15 17.3 19.3 20 25 3030.6 35 37.6 40 γ¯t [dB]

Figure 3.7: Average throughput eﬃciency for AMC-ARQ and PC-AMC-ARQ schemes, Q = 100 symbols.

N =100 PC−AMC−ARQ approach s N =100 AMC−ARQ approach s 5 N =1000 PC−AMC−ARQ approach s N =1000 AMC−ARQ approach s

Average throughput efficiency [(b/s)/Hz] 1

0 −10 −5 0 5 10 15 20 25 30 35 40 γ¯t [dB]

Figure 3.8: Average throughput eﬃciency for AMC-ARQ and PC-AMC-ARQ approaches, for ns = 100 and 1000 symbols.

29 Chapter 3. Cross-Layer Design for Link Adaptation in ARQ-based Systems

3.5 Conclusion

In this chapter, we proposed a cross-layer design which effectively combines both AMC and PC LA techniques, at the PHY layer, with a basic ARQ protocol, at the DL layer. The aim of this combination was to maximize the average throughput efficiency under prescribed average transmit power constraint. The optimization problem was first formulated using a Lagrange multiplier parameter λ. An analytic derivation was then carried, followed by a numerical resolution process. We have shown that this numerical resolution approach only needs a set of throughput curves corresponding to the supported MCSs, to determine the appropriate transmission parameters, as a function of the channel conditions. This feature, makes the developed combination scheme easily applicable to any ARQ scheme, regardless the complexity of the relative throughput expression. In fact, due to the complexity of the throughput expressions, in particular the packet error probability (PEP) expressions, most of existing AMC-ARQ/PC-AMC-ARQ combination schemes, rely on approximate PEP’s expressions, to derive the optimal transmit parameters [27]-[32]. Moreover, these approximative expressions are a function of packet size and MCS dependent fitting parameters.

We have also shown that the obtained transmit power distribution curves, for diﬀerent average transmit SNR constraints, can be deduced from one another by a simple translation on the x-axis and a scaling on the y-axis. Hence, a single curve is suﬃcient to deduce the distribution curves for any value of average transmit SNR constraint.

Numerical an simulation results showed that the developed PC-AMC-ARQ scheme offers a significant reduction in average transmit power, for a target ATE, with respect to the conventional AMC-ARQ scheme. We have also shown that this gain, which is always greater than 2 dB, intimately depends on the target average throughput (more gain for low and high average throughput efficiencies) and slightly increases with packet size.

30 Chapter 4

Realistic Cross-Layer Design for Link Adaptation in HARQ-based Systems

4.1 Introduction

In Chapter 3, a cross-layer design which optimally combines adaptive modulation and power control techniques, at the PHY layer, with basic ARQ protocol, at the DL layer, in order to maximize the average throughput eﬃciency (ATE) under a prescribed average transmit power constraint.

In this chapter, we extend this cross-layer to incorporate coding rate adaptation in addition to the constellation size adaptation. To do this, we consider a type I hybrid ARQ protocol where unsuccessful attempts are used in FEC decoding instead of being discarded.

Moreover, we have shown in the previous chapter, that the proposed joint PC-AM-ARQ scheme for a given channel state depends on a Lagrange multiplier, referred to λ, which is intimately related to the desired average transmit power and to the usually unknown channel statistics. Due to these unknown statistics, we here assume, for more realism, that λ is unknown at the transmitter, and that an appropriate feedback from the receiver is used to estimate and track it. The proposed iterative algorithm for blindly estimating and tracking λ, referred to as

31 Chapter 4. Realistic Cross-Layer Design for Link Adaptation in HARQ-based Systems

λ-tracking loop, operates in a closed tracking loop, and uses the exponential moving average (EMA) algorithm to estimate the achieved average transmit power. An end-to-end simulation is performed to validate the accuracy of the proposed tracking algorithm. The convergence behavior and capabilities of the proposed EMA-based tracking loop is studied as a function of the mobile speed.

The remainder of this chapter is organized as follows. We first present the system model in Section 5.2. We detail the realistic version of the cross-layer design in Section 4.3, which operates in tracking mode and optimally combines AMC, PC and type I HARQ. We present the achieved throughput efficiency in Section 4.4, verify the good agreement of the realistic simulation results with the theoretical analytical results in Section 5.5, and finally draw some conclusions in Section5.6.

4.2 System Model

Figure 4.1: Transmission system block diagram.

We consider the transmission system bloc diagram in Fig. 4.2, which is an extended version of the generic bloc diagram previously presented in 3.1. Therefore, in this section, we will highlight only the modiﬁed/added blocs (those with blue frames in Fig. 4.2). We assume that the proposed scheme has a reliable feedback path between the receiver and the transmitter. The channel state information (CSI), given by the channel instantaneous power η, is acquired perfectly at the receive and then fed back to the transmitter. According to the current CSI the transmitter select the most appropriate transmit parameters to be used for next transmission.

32 Chapter 4. Realistic Cross-Layer Design for Link Adaptation in HARQ-based Systems

The packets to be transmitted by the PHY layer are first assumed to be queued in an infinite buffer, then transmitted on a packet-by-packet basis over the wireless channel. The fading conditions are assumed to be slowly time varying from packet to packet according to the Jakes model.

4.2.1 Transmitter

At the transmitter side, the HARQ controller manages an infinite buffer that operates in a first-in-first-out (FIFO) mode. We assume as SR retransmission strategy. Each transmitted packet is encoded for both error detection and correction. When a received packet is found to be in error, it is discarded and another copy of it is sent by the transmitter.

The PC and the AMC selectors are responsible for selecting an optimal transmit SNR γt and an appropriate MCSn, respectively, as a function of the instantaneous channel power η. This choices are intimately related to a parameter λ which depends on the channel statistics and which should appropriately estimated by the transmitter. The role played by this parameter as well as the operation of the corresponding tracking loop block will be detailed later. The transmit SNR, is then a function of η, and denoted by γt(η). The received SNR, denoted by

γr(η), is deﬁned as

γr(η)= ηγt(η). (4.1)

We assume N MCSs supported by the PHY layer. A given MCSn, n = 1, 2, ..., N, consists of a speciﬁc Mn-ary QAM modulation, a rate Rn FEC code and a packet size of Qn symbols. As previously explained in Subsection 3.2.4, the selection of the appropriate MCS is based on a set of AMC-switching thresholds T N , where T = 0 and T =+ . If the received SNR { n}n=0 0 N ∞ γr(η) falls within the interval [Tn, Tn+1), the MCSn will be chosen for transmission.

After selecting the appropriate transmit parameters, the transmitter encode the packet with a detection code, for HARQ error detection purposes. Hence, each packet contains nb bits which comprises its own cyclic redundancy check (CRC) as well as a payload of kb bits. A tail of t bits is then appended to this codeword to terminate the convolutional code trellis. At the output of an error correction code of a rate Rn, a number of (nb + t)/Rn coded bits are obtained. A puncturing technique is used, deleting some bits in the encoder output, in order to reach a code rate of Rn from the low-rate convolutional encoder (see illustration in Fig. 4.2.1). Bits

33 Chapter 4. Realistic Cross-Layer Design for Link Adaptation in HARQ-based Systems

are deleted according to puncturing matrix shown in Table 4.2. Using the selected Mn-ary

QAM modulation, the coded bits are then mapped to ns = (nb + t) / (log2(Mn)Rn) symbols, provided that nb + t is proportional to log2(Mn)Rn.

Figure 4.2: Processing at the transmitter.

4.2.2 Receiver

After perfectly estimating the channel, the receiver fed back the CSI to the transmitter in order to select the appropriate parameters for transmission. When the receiver receives a packet, it performs the inverse process of the transmitter, as illustrates Fig. 4.2.2. After detection and soft Viterbi decoding, an error detection process (using a CRC code) is performed and the corresponding Ack+/- message is fed back to the HARQ controller. Given the short length of the Ack messages and the use of a high degree of FEC protection, an error-free and instantaneous HARQ feedback channel can be assumed. The log-likelihood ratio (LLR) is used as input for the soft Viterbi decoder.

Figure 4.3: Processing at the receiver.

4.3 Realistic Implementation PC-AMC-HARQ Cross-Layer

In Chapter 3, a cross-layer design that optimally combines PC and AMC at the PHY layer with basic ARQ protocol at the DL layer was developed for average throughput eﬃciency maximized system while satisfying an average transmit SNR constraint. However, the obtained solutions intimately depend on the Lagrange multiplier parameter, λ, used to solve the maximization problem. A derived in (3.22), this parameter is related to the prescribed average transmit SNR

34 Chapter 4. Realistic Cross-Layer Design for Link Adaptation in HARQ-based Systems

constraint as follows + η χopt( ) γ¯ = ∞ λ f (η)dη, (4.2) t η η Z0 η where χopt( λ ) = γr,opt is the optimal received SNR solution of the optimization problem (see Subsection 3.3.2). The optimal transmit SNR is deﬁned in (3.14) as

η γ (η) χopt( ) γ (η)= r,opt = λ . (4.3) t,opt η η

In order to numerically determine the λ value from the target average transmit SNR, an unrealistic assumption was assumed, that is the channel statistics, i.e. fη(η), are a priori known at the transmitter. To blindly determine the appropriate λ, without knowing fη(η), we present in this section an iterative algorithm working in a tracking loop mode. The desired λ value is estimated and tracked using an exponential moving average (EMA-based) approach [39].

4.3.1 EMA-based Algorithm for Estimating and Tracking λ

Figure 4.4: Illustration of the adaptive algorithm for estimating λ.

The operation of the λ-tracking loop is illustrated in Fig. 4.3.1. The tracking loop starts with a nominal λ value (λnom), corresponding to a given channel distribution (Rayleigh channel for example). This value will be iteratively adjusted, until the correspondingγ ¯t reaches the target average transmit SNR valueγ ¯target. At the instant t, the estimatedγ ¯t is deﬁned as

γ¯ˆ (t) = (1 α)γ¯ˆ (t 1) + αγ (t),t 1 (4.4) t − t − t,opt ≥ where γ¯ˆt(0) is set toγ ¯target and α is an appropriately chosen smoothing factor (0 <α< 1).

Let ǫ be, the desired accuracy on the estimated average transmit SNR. The proposed adaptive algorithm can be summarized in the following steps :

35 Chapter 4. Realistic Cross-Layer Design for Link Adaptation in HARQ-based Systems

Step 1) Initialize λ = λnom Step 2) repeat while e = γ¯ˆ (t) γ¯ >ǫ do | t − target| Take a channel realization (i.e. η) Preform the numerical resolution process, η Input: µ = λ ,

Output: γt,opt(η) (deﬁned in (4.3)) γ¯ˆ (t) = (1 α)γ¯ˆ (t 1) + αγ (t) t − t − t,opt S = sign(γ¯ˆ γ¯ ) t − target λ λ + S ∆λ ← ∗ t t + 1 ← end while until Steady state

The adjustment step of λ, denoted by ∆λ, must be carefully chosen. In fact, it should be suﬃciently small in order not to wrongly judge that the algorithm reaches the steady state, and suﬃciently large in order not to wrongly judge that the steady state in a transient state.

Values of α close to one have less of a smoothing eﬀect and give greater weight to recent value of γt,opt(η) , while values of α closer to zero have a greater smoothing eﬀect and are less responsive to recent changes.

The tracking loop stops once the algorithm reaches the steady state, as will be discussed in the next subsection.

4.3.1.1 λ-Tracking Loop Convergence Criteria

As illustrates Fig. 4.3.1.1, the estimated λ may accidentally coincide with the target value before it reaches steady state. Especially, if ∆λ was set to a big value. Therefore, we require that the estimated γ¯ˆt must coincides withγ ¯target for K times before judging that the tracking algorithm has converged.

36 Chapter 4. Realistic Cross-Layer Design for Link Adaptation in HARQ-based Systems

Figure 4.5: The rationale behind the criterion for steady state determination.

4.3.2 Mode of Operation

The operating stages of the proposed cross-layer design are summarized in a ﬂowchart given in Fig. 4.3.2.

Figure 4.6: Mode of operation of the proposed PC-AMC-HARQ-I cross-layer.

We can distinguish two loops : an inner loop and an outer loop. The role of the inner loop is to select the appropriate transmission parameters for a given channel state (a given η). Having

η and λ, the optimal transmit power (or equivalently γr,opt) can be determined by performing the numerical resolution process (NR-process), described on Subsection 3.3.2. The appropriate MCS n is then selected by comparing γ to diﬀerent switching thresholds T N , as r,opt { n}n=0 presents Fig. 4.5.1. This inner loop is relatively fast, since it is repeated every time there is a packet to send. The role of the outer loop is to estimate and track the parameter λ. This loop can be considered as a slow loop comparing with the inner loop. In fact, after estimating the adequate λ at the beginning of the transmission, the system needs to update this value only

37 Chapter 4. Realistic Cross-Layer Design for Link Adaptation in HARQ-based Systems

when the channel statistics changes.

4.4 Type I HARQ Throughput Eﬃciency

The throughput expression for hybrid type I ARQ protocol and a given MCSn scheme, can be expressed as

kb Rn T hrn = log2(Mn) . (4.5) nb + m T r Considering the assumption of an i.i.d. block-fading channel, which corresponds to a low

Doppler frequency fd (i.e. low mobile speed), the average number of transmission attempts T r can be evaluated as + ∞ i 1 T r = P EP (γr) = , (4.6) 1 P EP (γr) Xi=0 − where P EP is the packet error probability, tightly upper bounded by

P EP (γ ) 1 (1 P (γ ))nb , (4.7) r ≤ − − E r where PE(γr) is the error event probability of the Viterbi algorithm. For a soft decision decoding, PE(γr) is given by

+ ∞ P (γ ) = min 1, a Q( 2dγ ) , (4.8) E r  d r  d=df X p   where df and ad are respectively the free distance and distance spectra of the code, and where the function Q(x) is deﬁned as

+ 2 1 ∞ u Q(x)= e− 2 du. (4.9) √2π Zx Using the AMC strategy, the eﬀective throughput will then be the maximum of all elementary throughput curves, expressed as

T hr(γr) = max T hrn(γr) . (4.10) n { }

38 Chapter 4. Realistic Cross-Layer Design for Link Adaptation in HARQ-based Systems

In the presence of power control, the SNR at the receiver is aﬀected by both controlled transmit power and channel state η. Hence, for a given channel power PDF fη(η), the average throughput eﬃciency can be expressed as

+ ∞ T hr = T hr(γr(η))fη(η)dη. (4.11) Z0

4.5 Numerical and Simulation Results

This section presents some numerical and simulation results. The performance of the proposed realistic combination of AMC, PC and HARQ-I is compared to two other combination schemes: AMC-HARQ-I and PC-AMC-ARQ. Hence, two categories of MCS schemes are considered for simulations. The ﬁrst one includes N = 3 uncoded Mn-ary QAM modulations, similar to the previous chapter. The second one consists of N = 7 convolutionally coded Mn-ary QAM modulations adopted from IEEE 802.16 standards, as presented in Table 4.1. The coding rate are obtained using the puncturing patterns summarized in Table 4.2.

Table 4.1: Supported MCSs Category I Modulation QPSK 16-QAM 64-QAM Category II Modulation QPSK 16-QAM 64-QAM Coding rate 1/2 3/4 1/2 3/4 2/3 3/4 5/6

Table 4.2: 802.16e Puncturing pattern deﬁnition for HARQ Code rate 1/2 2/3 3/4 5/6 1 1 0 1 0 1 10101 Puncturing matrix 1 1 1 1 1 0 11010

The same packet size, Qn = ns symbols/packet, is assumed for all MCSs. The channel is assumed to follow a Rayleigh fading channel model, which is characterized by channel power PDF deﬁned in (3.2)

4.5.1 AMC-Switching Thresholds

We compare in Fig. 4.5.1 the elementary throughput eﬃciency curves (4.5) and 3.21, for the two categories of MCSs. We can distinguish 2 switching thresholds for uncoded modulations

39 Chapter 4. Realistic Cross-Layer Design for Link Adaptation in HARQ-based Systems

and 6 switching thresholds, T 6 , for coded modulations. The appropriate MCS scheme is { n}n=1 selected by comparing the received SNR γr,opt(η) in (4.3) to these thresholds.

Uncoded Modulations Coded Modulations

6 5

QPSK : R = 1/2 4.5 c QPSK : R = 3/4 T QPSK c 6 5 16−QAM 16−QAM : R = 1/2 c T 4 5 16−QAM : R = 3/4 64−QAM c T 64−QAM : R = 2/3 2 3.5 c 4 64−QAM : R = 3/4 c T 64−QAM : R = 5/6 4 3 c

3 2.5

T 3 2 T 1 2 T 2 1.5 Throughput efficiency [(b/s)/Hz] Throughput efficiency [(b/s)/Hz] T 1 1 1

0.5

0 0 5 10 15 20 25 30 −5 0 5 10 15 20 25 30 γr[dB] γr[dB]

Figure 4.7: Elementary throughput curves for coded and uncoded modulations, ns = 120.

4.5.2 Optimal Received SNR Analysis

By performing the NR-process (conforming to Section 3.3.2) to the upper envelop of the elementary throughput curves in Fig. 4.5.1, we obtain the optimal received SNRs, depicted in Fig. 4.8, for the two MCS categories and for λ = 5 and 5 dB. We can see in this ﬁgure − that, the optimal received SNR remains almost constant, then abruptly rises just above the AMC-switching thresholds T N enabling the use of the next MCS. Put diﬀerently, the { n}n=1 optimal received SNR is always located at the beginning of the throughput saturation zone of each MCS. The goal is to ensure almost the maximum throughput with the minimum transmit SNR. Reaching a throughput saturation zone, the power control unit avoid increasing transmit SNR since it will no longer improve the throughput. The preserved power will be exploited later to reach the next MCS. We can also observe that, in the case of coded modulations, the system jumps some MCSs to directly reach the next transmission mode, such the case of MCS2 and MCS6 as shows Fig. 4.8. This can be explained by the fact that the two thresholds are so close, moreover, power control has preserved enough power allowing to jump two thresholds at a time.

We also notice that the distributions of γr,opt(η) for λ = 5 dB can be derived from the one for λ = 5 dB by a simple translation by ~λ on the x-axis (~λ is the translation vector. Thus, in order − to accelerate the transmit parameters selection process, we only need to store (in a codebook)

40 Chapter 4. Realistic Cross-Layer Design for Link Adaptation in HARQ-based Systems

the set of γr,opt(η) (or respectively γt,opt(η)) values corresponding to a single distribution curve, and then deduce the other curves for any value of λ.

Uncoded Modulations Coded Modulations 30

T6 MCS MCS 7 7 25 T5 64−QAM 64−QAM T2 MCS MCS T4 5 5 20 MCS T3 MCS 4 T1 16−QAM 16−QAM 4 10 [dB] T2 MCS MCS [dB] 3 3 10 r,opt T1 QPSK QPQK γ r,opt γ 5 λ = −5 dB MCS MCS 0 1 1 λ = 5 dB λ 0 = −5 dB λ = 5 dB −5 −5

−10 −10 0 10 20 30 0 10 20 30 η[dB] η[dB]

Figure 4.8: Distributions of the received SNR, for λ = 5 and 5 dB. −

4.5.3 Convergence Analysis of λ

In this subsection, we ﬁrst examine the convergence of the Lagrange multiplier λ, estimated using the proposed EMA-based tracking loop algoritm, as a function of the normalized Doppler frequency fdTp, where fd is the Doppler frequency and Tp is the time in second between two f0v successive packets. The mobile speed v is related to the Doppler frequency by fd = c , where 8 f0 is the carrier frequency and c = 3 10 m/s is the speed of light.

5 60

0 50

-5 40

-10 30 [dB] ] λ dB

-15 [ 20 t ˆ ¯ γ Estimated -20 10

-25 0

-30 -10

-35 -20 0 200 400 600 800 1000 0 200 400 600 800 1000 time time

4 Figure 4.9: Behavior of the estimated λ and γ¯ˆt, fdTp = 0.005, α = 0.5, ∆λ = 10− , ǫ = 0.7.

The convergence of λ is achieved when the adaptive algorithm reaches the steady state as described in the subsection 4.3.1.1. Let’s ﬁx the smoothing factor α to a medium value (let be α = 0.5 for example). We depict in Fig. 4.9 the behavior of both estimated λ and reached

41 Chapter 4. Realistic Cross-Layer Design for Link Adaptation in HARQ-based Systems

average transmit SNR for fdTp = 0.005.

Then, let’s determine, for diﬀerent normalized Doppler frequencies, the number of packets needed to be transmitted to converge to the right λ value. The obtained results, for fdTs = 0.001, 0.005, 0.01, 0.05, 0.1, 0.5, are presented in the histogram in Fig. 4.10. We can notice from these results that the smaller the value of fdTp, the more packets are needed to be transmitted before converging to the right λ. Conversely, the larger the value of fdTp, the less the tracking algorithm needs time to converge. In other words, the faster the mobile, the faster the tracking algorithm converges to the right λ, and conversely. This is logical, since when the normalized Doppler frequency is large, the channel quality (or equivalently η) will change rapidly, allowing the tracking algorithm to cumulate suﬃcient information about the channel quality, and hence determine the adequate λ from the target average transmit SNR.

450

400

350

300

250

200 Number of packets 150

100

0 0.001 0.005 0.01 0.05 0.1 0.5 fdTp

4 Figure 4.10: Needed packet number for convergence as a function of fdTp, α = 0.5, ∆λ = 10− , ǫ = 0.7.

Now, let’s fix the normalized Doppler frequency to a small value, in accordance with the assumption already fixed of a slow time varying channel. Let fdTp = 0.01, for example, which means that each 100 successive packets will experience roughly the same fading. Then, we propose to examine, for different values of smoothing factor α, the number of packets needed to be transmitted before converging to the right λ. We summarize the results in the histogram in Fig. 4.11, for α = 0.1, 0.3, 0.5, 0.7, 0.9. This histogram reveals that, the more α is close to zero, the faster the tracking algorithm estimates the correct λ. Conversely, the more α is close to one, the more time spent to converge to the right λ. This means that the tracking loop converges faster when it is less responsive to recent changes.

We compare in Fig. 4.12 the estimated λ values to the exact values, for fdTp = 0.1, α = 0.1 4 and ∆λ = 10− . We can notice that the two curves are practically superposed. Hence, we

42 Chapter 4. Realistic Cross-Layer Design for Link Adaptation in HARQ-based Systems

1600

1400

1200

1000

800

Number of packets 600

400

200

0 0.1 0.3 0.5 0.7 0.9 α

4 Figure 4.11: Needed packet number for convergence as a function of α, fdTp = 0.01, ∆λ = 10− , ǫ = 0.7. can conﬁrm that the proposed adaptive algorithm for estimating λ from the target average transmit SNR, works properly.

Exact 35 Estimated

25 ] dB [ t

γ 20

0 −70 −60 −50 −40 −30 −20 −10 0 λ[dB]

4 Figure 4.12: Estimated and exact λ, fdTp = 0.1, α = 0.1, ∆λ = 10− .

4.5.4 Average Throughput Eﬃciency Analysis

To confirm the feasibility of the proposed cross-layer design, referred to as PC-AMC-HARQ-I, we compare in Fig. 4.13 the simulated average throughput efficiency to the theoretical one. Monte-Carlo simulation was performed following the flowchart depicted in Fig. 4.3.2. We can notice from Fig. 4.13 the good agreement between simulation and theoretical results.

We compare in Fig. 4.14 and Fig. 4.15 the average throughput curves of the proposed PC- AMC-HARQ-I scheme with both AMC-HARQ-I and PC-AMC-ARQ schemes, respectively, for ns = 120.

Fig. 4.14, which compares PC-AMC-HARQ-I scheme to AMC-HARQ-I scheme, clearly shows

43 Chapter 4. Realistic Cross-Layer Design for Link Adaptation in HARQ-based Systems

4.5 Theoretical 4 Simulated

3.5

2.5

1.5

1 Average Throughput efficiency [(b/s)/Hz]

0.5

0 −5 0 5 10 15 20 25 30 35 γ¯t[dB]

Figure 4.13: Simulated and theoretical average throughput eﬃciency for PC-AMC-HARQ-I scheme, ns = 120. that adding power control signiﬁcantly improves the system performance, especially for high and low average transmit SNRs. For instance, we can observe that to reach an average throughput of T hr = 3 (b/s)/Hz we need an average transmit SNR less than 2dB if we use PC-AMC- HARQ-I scheme instead of AMC-HARQ-I scheme. The performance improvement can be explained by the fact that PC preserves transmit power by avoiding transmission when the radio link experiences poor radio conditions. Thus, the preserved power will be exploited when channel conditions improve.

From Fig. 4.15, we can observe that PC-AMC-HARQ-I scheme provides higher average throughput eﬃciency than PC-AMC-ARQ scheme for low and moderate average SNR, thanks to the FEC. However, at high average transmit SNR, PC-AMC-ARQ-I scheme achieves higher average throughput than PC-AMC-HARQ-I scheme, because its corresponding MCSs support higher data rates. In fact, the highest rate MCS has a rate of 6 (bits/sym.) in uncoded modulations category, which is greater than 5 (bits/sym.) the highest rate in coded modulations category. This means that adopting high-rate modes beneﬁts average throughput at high average transmit SNR. Hence, to improve average throughput over the entire average transmit SNR range, a practical system could also optimally combine MCSs from both uncoded and coded modulations categories.

4.6 Conclusion

In this chapter, we extended the PC-AM-ARQ cross-layer presented in the previous chapter, to incorporate the coding rate adaptation in addition to the modulation scheme adaptation.

44 Chapter 4. Realistic Cross-Layer Design for Link Adaptation in HARQ-based Systems

4.5 PC-AMC-HARQ-I AMC-HARQ-I

4 High gain

3.5

2 3 dB

2.5

1.5

Average throughput efficiency [(b/s)/Hz] High gain 1

0.5

0 -10 -5 0 5 10 15 20 25 30 γ¯t[dB]

Figure 4.14: Average throughput eﬃciency for PC-AMC-HARQ-I and AMC-HARQ-I cross- layer designs, ns = 120.

PC-AMC-HARQ-I PC-AMC-ARQ-I 5

4 with ARQ outperforms

2 with HARQ outperforms Average throughput efficiency [(b/s)/Hz] 1

4.7 dB 0 -10 -5 0 5 10 15 20 25 30 γ¯t[dB]

Figure 4.15: Average throughput eﬃciency for PC-AMC-HARQ-I and PC-AMC-ARQ cross- layer designs, ns = 120.

45 Chapter 4. Realistic Cross-Layer Design for Link Adaptation in HARQ-based Systems

To this end, a type I hybrid ARQ was considered, where an error-correction was employed in addition to the error detection. Then, an eﬃcient combination of type I HARQ with both AMC and PC techniques, was conducted. The aim of this combination was to maximize the ATE under prescribed average transmit power constraint. The numerical maximization of the ATE was carried using a Lagrange multiplier parameter λ, which is intimately related to the desired average transmit power and to the usually unknown channel statistics. Hence, to keep the proposed combination scheme independent of channel statistics, we proposed a tracking loop algorithm, based on the EMA method, for blindly estimating and tracking the appropriate value of λ to meet as much as possible the desired average transmit SNR. The proper operation of the proposed tracking loop was validated through a Monte-Carlo simulation approach, modeling in a realistic way channel variations and tracking loop behavior. The convergence behavior of the proposed algorithm was also assessed as a function of the mobile speed. To this end, simulations was carried using a time-correlated fading channel model based on the Jakes model.

Simulation results, corroborated by analytical results, show that our proposed realistic design offers a significant reduction in average transmit power, for a given average throughput efficiency, with respect to both AMC-HARQ-I and PC-AMC-ARQ designs.

46 Chapter 5

Optimized Power Allocation for Throughput Maximized T-ARQ Combined with PC and AM

5.1 Introduction

In delay-sensitive traffic such as live streaming video, voice over IP, and multimedia telecon- ferencing, only finite delays are tolerated. Therefore, buffers at both ends of transmission link have to be of limited size. Truncated ARQ (T-ARQ) protocols have been adopted to limit the maximum number of retransmissions [17]. After T unsuccessful transmission attempts, the transmitter discard the current packet and proceed by the transmission of the next packet in the buffer. Usually, in conventional ARQ protocols, the same power level is used to retransmit a copy of the same packet, whenever it is needed [15]-[16]. However, a packet is often rarely retransmit, especially for advantageous radio-link quality, allowing to retransmit it with more power without resources waste. This is also valid for subsequent retransmissions that are increasingly rare and can then benefit from more and more power. Hence, a judicious redistribution of the available transmit power could increase the throughput, without leading to a significant increase of the average power spent to transmit a packet.

In order to enhance the spectral eﬃciency, we have proposed in the previous chapters a cross- layer design combining AMC and PC techniques, at the PHY layer, with an ARQ protocol,

47 Chapter 5. Optimized Power Allocation for Throughput Maximized T-ARQ Combined with PC and AM

at DL layer. The proposed combination scheme has proved performance enhancement, with respect to the conventional scheme, whereby only AMC and ARQ are employed for LA. More specifically, the proposed LA scheme selects the optimal transmit power as well as the most appropriate MCS, as a function of the channel state. However, the selected power level remains the same for all consecutive transmission attempts of the same packet. In this chapter, we are looking to efficiently allocate this optimally selected budget in transmit power among potential transmissions, such that the achieved throughput is maximized, while maintaining a fixed average power spent by packet. To perform this optimal power allocation, we adopt a heuristic algorithm, based on a dichotomic search, similar to what was done in [33] for fixed modulation scheme. The performance enhancement of this optimized power allocation ARQ is then assessed while combining with PC and AM techniques.

The remainder of this chapter is organized as follows. We ﬁrst present the system model in Section5.2. We detail the improved version of the ARQ protocol in Section 5.3. The combination of improved ARQ with AMC and PC is then presented in Section 5.4. Numerical and simulation results, as well as their interpretations, are provided in Section 5.5. Finally, Section 5.6 draws some conclusions.

5.2 System Model

Figure 5.1: Transmission system block diagram.

We consider the same generic transmission system block diagram previously presented in Chapter 3. Therefore, the blocks that are relevant to this chapter are reviewed, from another viewpoint. Some assumptions and expressions are also recalled, whenever necessary.

The packets ready for transmission are queued in a ﬁnite transmit buﬀer. Appropriate transmission parameters are selected, at the PHY, based on to the current channel power, η, fed

48 Chapter 5. Optimized Power Allocation for Throughput Maximized T-ARQ Combined with PC and AM

back by the receiver. Perfect channel estimates at the receiver and reliable feedback path are assumed.

At the DL layer, a T-ARQ protocol is considered. When the decoded packet, reaching the receiver, is found to be in error, the T-ARQ generator unit, initiates a selectively retransmission. After T unsuccessful transmissions of a same packet, it is completely erased and the next one waiting in the buﬀer is transmitted. Each transmission is carried using the matched power level, or equivalently the matched transmit SNR γtj , relative to the current attempt j (j = 1,..,T ). Hence, the performance of the T-ARQ protocol will be assessed by the average SNR spent to transmit a given packet through diﬀerent transmissions. All transmissions are assumed to experience roughly the same channel conditions (i.e. same channel power η).

At the PHY, the selection of the appropriate power level, for each transmission attempt, goes through two stages. First, having the current CSI, the optimal average power allocated to transmit a packet Pt(η) (or equivalently the optimal average transmit SNR γtopt (η)) is selected by performing to the same approach previously proposed in Chapter 3. This budget in average transmit power is then optimally redistributed among potential T transmissions, using an heuristic algorithm similar to [33], as we will detail in the next section. Each selected j-th received SNR γrj (η) is related to the jth transmit SNR as follows

γrj = ηγtj . (5.1)

The AMC unit implemented at the PHY layer operates similarly to Subsection 3.2.4. A set of N uncoded modulations are assumed to be supported, without FEC coding. Hence, a given

MCSn (n = 1,..,N) consists of a specific couple Mn-ary QAM modulation and Qn symbols per packet. Similarly the AMC system previously detailed in Subsection 3.2.4, the selection of the appropriate MCSn is performed by comparing the average received SNR γravg (η) to a set of AMC-switching thresholds. In fact, the average received SNR range can be partitioned into N non-overlapping intervals, defined by the switching thresholds T N , where T = 0 { n}n=0 0 and T =+ for convenience. Whenever γ (η) falls within the interval [T , T ), MCS N ∞ ravg n n+1 n is chosen for transmission. The performance offered by a specific MCSn is assessed by its throughput curve, denoted next by T hrn(η), as a function of the average received SNR.

49 Chapter 5. Optimized Power Allocation for Throughput Maximized T-ARQ Combined with PC and AM

5.3 Optimized Power Allocation for Improved ARQ Protocol

Conventional ARQ protocols usually use the same power to retransmit a copy of the same packet, whenever it is erroneously received. We look in this section to wisely redistribute the available budget of average transmit power spent per packet (or per symbol) among the T potential transmissions, such that the resulting throughput is maximized, while fulﬁlling a prescribed constraint on the average power spent per symbol (or equivalently the average transmit

SNR per symbol γtavg (η)). For a given MCSn, it amounts to the following maximization

maximize T hrn(η) subject to γtavg (η) γtopt (η). (5.2) T γt (η) ≤ { j }j=1

The solutions are the set of optimal transmit SNRs γ (η) T . The prescribed budget of { tj }j=1 average transmit SNR per symbol γtopt (η) is selected, in an optimal way, as a function of the channel power η, as previously detailed in Chapter 3 Section 3.3.

We recall the throughout expression which is a function of the selected MCSn, and given by

1 T hr (η) = log (M ) (1 P ep ) , (5.3) n 2 n T r − n where T r is the average number of transmissions of a given packet and P epn is the packet erasure probability. Considering an i.i.d. channel, T r can be evaluated as

T 1 − T r = P EPj, (5.4) Xj=0 where the jth retransmission attempt’s packet error probability P EPj is given by

P EP = 1 (1 P )2Qn . (5.5) j − − ej

The probability that the inphase/quadrature phase component of an Mn-QAM symbol be erroneously received, Pej , is given by

√Mn 1 3 Pe = − erfc γr (η) , (5.6) j √M 2(M 1) j n s n − ! where erfc(.) is the complementary error function.

50 Chapter 5. Optimized Power Allocation for Throughput Maximized T-ARQ Combined with PC and AM

Assuming a maximum number of T transmission attempts, the packet erasure probability

P epn, for a given MCSn, can be evaluated as the product of all retransmission attempts’ packet error probabilities, as expressed as follows

T P epn = P EPj. (5.7) jY=1

We have omitted η from the notations of T r, P epn, P EPj and Pej for simpliﬁcation reasons.

The average SNR spent to transmit a given symbol is the sum of the T transmission attempts’ transmit SNRs weighted by their occurrence probabilities, as expressed as follows

γtavg (η) = γt1 (η)+ γt2 (η)P EP1 + ...

+γtT (η)P EP1P EP2..P EPT 1. (5.8) −

Equation (5.8) reveals that later retransmission attempts may benefit from a high transmit power level, without significantly affecting the average transmit SNR per symbol, since the probability of their occurrence is negligible. Hence, a judicious redistribution of the available transmit power could increase the throughput without exceeding the average power provided per symbol.

Giving the non-linearity and the complexity of the resulting maximization problem in (5.2), we present, in the following, a heuristic algorithm based on a numerical dichotomic search, in order to ﬁnd an optimal power allocation for maximizing the throughput [33].

5.3.1 Dichotomic Search Approach for Optimal Power Allocation

We illustrate in Fig. 5.2 the power allocation algorithm based on a dichotomic search process. The transmit SNR spent during a given transmission attempt j varies between 0 and max a maximum value γj . The more a packet needs retransmissions to successfully reach the destination, the more the probabilities of the latest attempts become negligible. Hence, greater max max max values of γj can be tolerated for advanced attempts, i.e. γj > γi for j > i.

max First, each jth attempt transmit SNR variation range [0 γj ] is discretized using a ﬁrst quantization step ∆j. This initial step is carefully selected to avoid local maxima. All initial

51 Chapter 5. Optimized Power Allocation for Throughput Maximized T-ARQ Combined with PC and AM

Figure 5.2: Illustration of the dichotomic search based power allocation process.

∆j are adapted to the variation ranges of γtj (η), such that ∆j < ∆i for j < i. All possible combinations of quantized values γ (η) (j = 1..T 1) are tested in order to identify which one tj − gives the maximum of throughput. To ensure the use of the whole provided SNR γtopt (η), we choose the last value γtT (η) as a ﬂoat value, derived as

γtopt (η) C γtT (η)= − , (5.9) P (Rd1 )..P (RdT −1 )

where C =γt1 (η)+γt2 (η)P (Rd1 )+..+γtT −1 (η)P (Rd1 )..P (RdT −2 ).

T 1 A given combination γ (η) − is retained only if the resulting γ (η) does not exceed { tj }i=1 tavg

γtopt (η). After each iteration, all searching ranges are reduced around the selected quantized values. All quantization steps are also reduced. The process is repeated till all searching ranges are smaller than a predeﬁned accuracy threshold.

5.4 Combined AMC and PC with Improved ARQ Protocol

In this section, we combine the improved version of the ARQ protocol with the AMC and the PC techniques, as has been addressed in Chapter 3 for a conventional ARQ. The operating stages of this enhanced version of the cross-layer design, are summarized in the ﬂowchart of Fig. 5.3. Having the CSI η, estimated and fed back by the receiver, the optimal average transmit power per symbol (or equivalently γtopt (η)) is identiﬁed through the PC policy, based on the numerical resolution process, described 3.3.2. To perform this process, a required parameter, denoted λ, is estimated beforehand through a tracking loop, as in 4.3.1. The power budget is then wisely

52 Chapter 5. Optimized Power Allocation for Throughput Maximized T-ARQ Combined with PC and AM

distributed among the potential T transmission attempts, by performing the dichotomic search process detailed in 5.3.1. For practical purposes, we consider that a set of optimal allocated power levels, relative to a set of CSIs (η), are stored in a codebook, in order to accelerate the matching of the appropriate γtj (η). By comparing the selected γropt (η) to the AMC switching thresholds T N , the most appropriate MCS is identiﬁed for transmission. If a packet is { n}n=0 n received in error for the jth attempt, it will be retransmitted using the appropriate γtj (η) and the appropriate MCSn. After T unsuccessful attempts, the current packet is erased and the next packet in the buﬀer is prepared for transmission.

Figure 5.3: Mode of operation.

5.5 Numerical and Simulation Results

In this section, numerical results of the enhanced ARQ protocol combined with AM are presented and validated by simulation results. We ﬁrst assess the performance enhancement of the improved ARQ protocol, whereby the provided budget of power per packet is optimally distributed among potential transmissions. We then present the performance of the joint AM-PC, with enhanced ARQ, and compare it with the AM-PC-conventional ARQ previously presented in Chapter 3. For comparison purposes, we consider N = 3 uncoded M-QAM modulations,

QPSK, 16-QAM and 64-QAM. We also consider a ﬁxed number of symbols per packet Qn = ns

53 Chapter 5. Optimized Power Allocation for Throughput Maximized T-ARQ Combined with PC and AM

(n = 1, .., N). Assuming a slow varying Rayleigh fading channel, such that all T transmissions of a given packet experience roughly the same channel power, and which is characterized by its channel power PDF η fη(η)= e− . (5.10)

5.5.1 Performance of Enhanced ARQ Protocol

The throughput of an ARQ protocol is usually evaluated as a function of the transmit SNR per transmission (or equivalently the symbol energy spent per transmission). This could not provide a fair performance evaluation, since the eﬀective average energy spent by symbol is not taken into consideration. Considering a conventional ARQ protocol, where the energy spent per symbol, E, remains the same for all transmissions, the average SNR in (5.8) reduces to

T 1 − j γtavg (η)= γt P (Rd) = γtT r, (5.11) Xj=0

E where γt = N0 , where N0 is the single-sided noise power spectral density.

We present in Fig. 5.4 the throughput given in (5.3), with respect to the average SNR (5.11), for the QPSK modulation. As we can notice, we may have the same average SNR per symbol

γtavg (η), with diﬀerent values of the energy per symbol, but have diﬀerent throughputs at the same time. Thus, the upper envelope of the throughput curve should be considered for maximizing performance.

In Fig. 5.5, we compare the throughput of both improved and conventional ARQ protocols, for N = 3 modulation schemes. It is clearly shown that the optimal power allocation signiﬁcantly improves the performances of the ARQ protocol especially for low and medium SNRs. We can also distinguish from Fig. 5.5 two AMC-switching thresholds (T1 and T2) used to select the adequate MCS for transmission. We examine in Fig. 5.6 the packet erasure probability for both conventional and enhanced ARQ protocols, for MCS1 (i.e. QPSK modulation). We can notice a signiﬁcant reduction in the packet erasure probability. This is due to the allocation of more power to later transmission attempts, which increases the chance of the packet to be successfully transmitted rather erased.

54 Chapter 5. Optimized Power Allocation for Throughput Maximized T-ARQ Combined with PC and AM

1.8

1.6 Conventional Maximized

1.4

1.2

0.8

0.6 Normalizedthroughput [(b/s)/Hz]

0.4

0.2

0 5 10 15 20 γavg[dB]

Figure 5.4: Conventional ARQ throughput, QPSK modulation, T = 3, ns = 100 symbols.

6 64-QAM

Enhanced ARQ

5 Conventional ARQ - Maximized Conventional ARQ

4 16-QAM

2 QPSK Normalized throughput [(b/s)/Hz]

0 0 5 10 15 20 25 30 γavg[dB]

Figure 5.5: Enhanced ARQ throughputs, T = 3, ns = 100 symbols

0.9 Enhanced ARQ Conventional ARQ

0.8

0.7

0.6

0.5

0.4 Packet erasure probability

0.3

0.2

0.1

0 4 6 8 10 12 14 γavg [dB]

Figure 5.6: Packet erasure probability, QPSK modulation, T = 3, ns = 100 symbols.

55 Chapter 5. Optimized Power Allocation for Throughput Maximized T-ARQ Combined with PC and AM

5.5.2 Average Throughput of Joint PC, AMC and Enhanced ARQ Cross- Layer

The average throughput of enhanced ARQ protocol, jointly combined with AMC and PC, is presented in Fig. 5.7, and compared to that of conventional ARQ combined with AMC and PC. The average throughput is given by

+ ∞ T hr = T hr(γropt (η))fη(η)dη, (5.12) Z0 where T hr(γropt (η)) is the eﬀective throughput given by the maximum of all elementary throughput curves, of the N supported MCSs, expressed as

T hr(γr (η)) = max T hrn(η) . (5.13) opt n { }

The average transmit SNR γtopt is given by

+ ∞ γtopt = γtopt (η)fη(η)dη. (5.14) Z0 It can be noticed from Fig. 5.7, that the enhanced ARQ protocol leads to a slight improvement in performances if combined with AMC and PC, with respect to the conventional ARQ. This improvement is more noticeable for low average transmit SNRs. It can be explained by the fact that the more we provide higher average transmit SNR the less the number of transmissions is. Thus, the optimal power allocation is no more needed for high average transmit SNRs, where transmissions succeed from the ﬁrst attempt.

AMC-PC-Conventional ARQ Theo : AMC-PC-Enhanced ARQ Sim : AMC-PC-Enhanced ARQ 5

2 Average throughput efficiency [(b/s)/Hz]

0 -20 -10 0 10 20 30 40

γtopt [dB]

Figure 5.7: AMC-PC with conventional and enhanced ARQ, T = 3, ns = 100 symbols.

56 Chapter 5. Optimized Power Allocation for Throughput Maximized T-ARQ Combined with PC and AM

5.6 Conclusion

In this chapter, we focused on the optimal allocation of the budget in transmit power over T potential transmissions of a truncated ARQ protocol. This optimal power allocation was carried through two stages. First, having the current CSI, the optimal average power allocated to transmit a packet was determined through the PC policy, based on the numerical resolution process presented in Chapter 3. Then, this budget in average transmit power was optimally redistributed among potential T transmissions, using an heuristic algorithm, based on a dichotomic search, as done in [33] for ﬁxed modulation scheme. Provided numerical and simulation results reveal a signiﬁcant throughput improvement, especially for low and medium SNRs, relatively to the conventional ARQ protocol. It was also shown that the improved ARQ protocol leads to a slight average transmit SNR reduction for low average transmit SNR, if combined with both AMC and PC techniques.

57 Chapter 6

QoS-guaranteed Cross-Layer Design for Link Adaptation

6.1 Introduction

In Chapter 3, we have optimally combined PC and AM LA techniques, at the PHY layer, with the basic ARQ protocol, at the DL layer. The considered optimality criterion was the maximization of the ATE under a fixed average transmit power. Nonetheless, no quality of service (QoS) was guaranteed, as required by real-time services. In this chapter, we develop an efficient cross-layer design for throughput improved QoS-guaranteed packet wireless communications. This is still done by an optimal combining of PC, AM and ARQ techniques, in order to achieve the highest average throughput efficiency, while fulfilling a target packet error probability (PEP) constraint, in addition to the constraint on the average transmit power, as previously addressed. More specifically, both optimal adaptive modulation (AM) switching thresholds and appropriate transmit power are derived as a function of the channel state, while guaranteeing the required QoS in terms of PEP. Closed-form expressions of the derived solutions, are also presented, for high received SNR.

The reminder of this chapter is organized as follows. After introducing the system model in Section 6.2, we detail in Section 6.3 the proposed combination scheme, whereby PC, AM and basic ARQ techniques are optimally combined as a function of the channel quality, while fulﬁlling an error performance constraint, in addition to the average transmit power constraint.

58 Chapter 6. QoS-guaranteed Cross-Layer Design for Link Adaptation

Numerical and simulation results, as well as their interpretations, are provided in Section 6.4. Finally, Section 6.5 draws some conclusions.

6.2 System Model and Problem Statement

We consider the same generic system model, previously detailed in Fig. 3.2. Throughout this chapter, we will recall some notations and expressions, whenever it is necessary. Appropriate transmission parameters, namely signal transmit SNR and MCS, are selected at the transmitter, based on to the current CSI η fed back by the receiver and the required error performance in terms of PEP.

6.2.1 Adaptive Transmission System

A set of N MCSs is assumed to be supported by the PHY layer. For simplicity reasons, we only consider the adaptation of the modulation scheme without error correction coding. Hence, an

MCSn, n = 1,..,N, consists of a speciﬁc Mn-ary QAM modulation. For a given MCSn, the

PEP depends on the SNR at the receiver γr, iand s given by

P EP = 1 (1 P (γ ))2Qn , (6.1) n − − en r

where Pen (γr), the probability that the inphase/quadrature phase component of the Mn-QAM symbol be erroneously received, given by

√Mn 1 3 Pe (γr)= − erfc γr , (6.2) n √M 2(M 1) n s n − ! where erfc(.) is the complementary error function. As illustrates Fig. 6.1, requiring a target PEP (P EP ), or equivalently a target symbol error probability (SEP) P = 1 (1 P EP )1/2Qn , tg etg − − tg is equivalent to ensuring a target received SNR γrn for each selected MCSn. We can derive

γrn , n = 1, .., N, by substituting (6.2) into (6.1) then inverting (6.1), as

2(Mn 1) 2 √Mn γr = − erfcinv Pe . (6.3) n 3 √M 1 tg n − For each channel power η, there is one MCS that outperforms the other schemes. Therefore,

59 Chapter 6. QoS-guaranteed Cross-Layer Design for Link Adaptation

Figure 6.1: Illustration of the packet error probability.

Figure 6.2: AMC-switching thresholds. the allowed channel power range can be partitioned into N consecutive intervals defined by the switching thresholds η N , as illustrates Fig. 6.2. Whenever the feedback CSI η falls { n}n=0 within the interval [ηn 1, ηn), the MCSn will be chosen for transmission. The first threshold η0 − represents a cutoff threshold, i.e. no data is transmitted when η < η0. While the last threshold η = + for convenience. The performance of a chosen MCS is assessed by the resulting N ∞ n throughput, which is defined as

T hr = log (M ) (1 P EP ) . (6.4) n 2 n − n

We can note that ensure a target PEP, i.e. P EP = P EP n [1, 2, .., N], keeps the through- n tg∀ ∈ put constant over the whole range between two consecutive switching thresholds (ηn 1, ηn) of − a selected MCSn (see illustration in Fig. 6.4). Therefore, the eﬀective throughput will certainly depend on the choice of the AMC switching thresholds. An optimum selection of these thresholds may obviously maximize the resulting throughput, and this will be the purpose of the next section.

The proposed cross-layer design also supports a PC selector unit at the physical layer. The supported PC policy try to adapt the transmit SNR to the varying channel power η, so that the target SNR γrn , which depends on the chosen MCSn and the corresponding P EPn, is reached at the receiver. The transmit SNR, will then be a function of both η and MCSn, and

60 Chapter 6. QoS-guaranteed Cross-Layer Design for Link Adaptation

deﬁned as γ γ (η)= rn . (6.5) tn η

6.3 QoS-guaranteed Cross-Layer Design

In this section, we develop our proposed QoS-guaranteed LA scheme, which optimally select the AMC switching threshold and the transmit power level, given the channel state, in order to achieve the highest average throughput. To guarantee a given error performance, a PEP constraint is considered in addition to an average transmit power constraint (which was exclusively considered in 3). This standard constrained optimization problem can be solved using the Lagrange multiplier method. It amounts to the following maximization

max T hr λγt N−1 ηn − { }n=0 s.t. P EP = P EP , n [1, 2, .., N]. (6.6) n tg ∀ ∈

The Lagrange multiplier λ is indirectly ﬁxed by the target average transmit SNRγ ¯tg. In order to solve the objective function in (6.6), we next replace T hr and γt by their explicit expressions.

The instantaneous throughput depends on the selected MCSn and remains constant over the whole range between two consecutive switching thresholds (ηn 1, ηn), as illustrated in Fig. 6.4, − since P EPn is ﬁxed. Therefore, the average throughput eﬃciency can be evaluated as

N ηn T hr = T hrn(η)fη(η)dη, (6.7) n=1 ηn−1 X Z where f (η) is the distribution of the instantaneous channel power η and η =+ for conve- η N ∞ nience. Substituting T hrn(η) by its explicit expression (6.4) into (6.7), we obtain

N ηn T hr = log2(Mn) (1 P EPn) fη(η)dη. (6.8) − ηn−1 nX=1 Z

61 Chapter 6. QoS-guaranteed Cross-Layer Design for Link Adaptation

N 1 Likewise, the transmit SNR distribution intimately depends on the set η − , as illustrates { n}n=0 Fig. 6.3. The constrained average transmit SNR can then be evaluated as

N ηn

γt = γtn (η)fη(η)dη. (6.9) ηn−1 nX=1 Z

Replacing γtn (η) by (6.5) into (6.9), we obtain

N ηn fη(η) γt = γrn dη. (6.10) ηn−1 η nX=1 Z

If an MCSn is chosen for transmission, the equivalent PEP must fulﬁll the condition

P EPn = P EPtg. (6.11)

Using (6.8), (6.10) and (6.11), the objective function in (6.6) can be rewritten as

N ηn max log2(Mn) (1 P EPtg) fη(η)dη N−1 − ηn n=0 n=1 " ηn−1 { } X Z ηn f (η) λγ η dη . (6.12) − rn η Zηn−1 #!

In the following subsection, we will derive the optimal switching thresholds, solutions of the maximization procedure in (6.13), then we give a simpliﬁed closed-form expressions of these solutions.

6.3.1 Optimal Switching Thresholds

We construct the Lagrangian of (6.12) as

N ηn L (η0, .., ηN 1, λ)= log2(Mn) (1 P EPtg) fη(η)dη − − n=1 " ηn−1 X Z ηn f (η) λγ η dη . (6.13) − rn η Zηn−1 #

62 Chapter 6. QoS-guaranteed Cross-Layer Design for Link Adaptation

The optimal solutions, ηn∗ ,...,ηN∗ 1, must obey the following equations − ∂L (η0, .., ηN 1, λ) ∗ ∗ = 0, n = 0, ..., N 1. (6.14) η0=η ,..,ηN−1=η − ) ∂ηn − |( 0 N 1 −

Solving (6.14), the general form of the optimal AMC switching thresholds can be written as

λγ r1 if n = 0 log2(M1) (1 P EPtg)  − ηn∗ = λ γr +1 γr (6.15)  n − n if 0 < n < N  Mn+1 log2 (1 P EPtg) Mn −   Considering the constraint on the PEP in (6.11) and the explicit SEP’s expression in (6.2), we can deduce the following equality

√Mn 1 3 − erfc γr √M 2(M 1) n n s n − !

√Mk 1 3 = − erfc γr √M 2(M 1) k k s k − ! n, k [1, 2, .., N], (6.16) ∀ ∈ which reduces to

3 3 A erfc γ = B erfc γ 2(M 1) rn 2(M 1) rk s n − ! s k − ! n, k [1, 2, .., N], A,B R. (6.17) ∀ ∈ ∈

For high received SNR, equation (6.17) yields to the following relationship

M 1 γ = n − γ n, k [1, 2, .., N]. (6.18) rn M 1 rk ∀ ∈ k − Using (6.18) for k = 1 into (6.15), a closed-form expression of the optimal switching thresholds can be formulated as

λγ r1 if n = 0 log2(M1) (1 P EPtg) − γr1 η∗ =  , (6.19) n λ (Mn+1 Mn) M1 1  − × − if 0 < n < N  Mn+1 log2 (1 P EPtg) Mn −  

63 Chapter 6. QoS-guaranteed Cross-Layer Design for Link Adaptation

which gives λγ r1 if n = 0 log (M ) (1 P EP ) ηn∗ =  2 1 − tg , (6.20)  K η if 0 < n < N  n × 0∗ where Kn is deﬁned as  log2(M1) Mn+1 Mn Kn = − . (6.21) log Mn+1 × M1 1 2 Mn − We can also derive the closed-form expression of the controlled transmit power in (6.5), using (6.18), as

γr1 η if n = 1 γtn (η)= . (6.22)  Mn 1 γ (η) if 1

The operating stages of the proposed cross-layer design are summarized in the algorithm in Table 6.1.

Table 6.1: Selecting optimal transmission parameters.

N 1: Having P EPtg, compute the target received SNRs γrn n=1 using (6.3) { } N 2: Having λ (from the constrained γt) and knowing P EPtg and γrn n=1, deduce the optimal N 1 { } AMC switching thresholds ηn∗ n=0− using (6.15) or the closed-form expression in (6.20) { } N 1 3: Having the CSI η, select the adequate MCS MCS by comparing η to η − n { n∗ }n=0 4: Compute the appropriate transmit SNR γtn (η) using (6.5) or the closed-form expression in (6.22)

6.4 Numerical and Simulation Results

In this section, numerical results of the developed QoS-guaranteed cross-layer design are presented and validated by simulation results. The performances of the proposed LA scheme, referred to as QoS-guaranteed AM-PC-ARQ, are compared to two other LA schemes: PC- AM-ARQ proposed in Chapter 3 and the benchmark conventional scheme AM-ARQ, where no QoS is ensured. These performances are assessed basically in terms of average throughput

64 Chapter 6. QoS-guaranteed Cross-Layer Design for Link Adaptation

eﬃciency as a function of average transmit SNR. We assume a Rayleigh block fading fading channel model, with channel power distribution given by

η fη(η)= e− . (6.23)

In the following, we present the explicit expressions of the average throughput and the average transmit SNR, using the optimal AMC switching thresholds expressions derived in Sec- tion 6.3.1.

6.4.1 Average Throughput and Average Transmit SNR

Using the closed-form AMC switching thresholds expression given in (6.20) into the average throughput’s expression (6.8), we obtain

N ∗ Knη0 T hr = (1 P EPtg) log2(Mn) fη(η)dη, (6.24) − ∗ n=1 Kn−1η0 X Z where K = 1 and K =+ , and otherwise K is given by (6.21). 0 N ∞ n

Considering the Rayleigh channel power pdf (6.23), (6.24) becomes as

N ∗ ∗ Kn−1η Knη T hr = (1 P EP ) log (M ) e− 0 e− 0 . (6.25) − tg 2 n − nX=1

Likewise, the average transmit power expression in (6.10) is formulated, using (6.20), as

∗ N Knη 0 fη(η) γt = γrn dη. (6.26) ∗ η n=1 Kn−1η0 X Z Using (6.18) for k = 1 into (6.26), we obtain

N ∗ Knη0 γr1 fη(η) γt = (Mn 1) dη. (6.27) M 1 ∗ η 1 − Kn−1η0 − nX=1 Z

65 Chapter 6. QoS-guaranteed Cross-Layer Design for Link Adaptation

Using the Rayleigh channel pdf in (6.23), (6.27) reduces to

N 1 γr1 − γt = (Mn 1)(E1(Kn 1η0∗) E1(Knη0∗)) M 1 − − − 1 " n=1 − X + (MN 1) E1(KN 1η0∗)] , (6.28) − − where E1(x) is the exponential integral, deﬁned as

+ e t E (x)= ∞ − dt. (6.29) 1 t Zx For comparison purposes, the same case study, considered in Chapter 3 is assumed, where N = 3 M-QAM modulation schemes are used, where M = 22k k = 1, 2, 3 corresponding to a

QPSK, a 16-QAM and a 64-QAM, respectively. We also assume the same packet size Qn = Q for all MCSs. For this special case, the average throughput in (6.25) reduces to

η∗ 4η∗ 16η∗ T hr = 2(1 P EP ) e− 0 + e− 0 + e− 0 . (6.30) − tg Likewise, the average transmit SNR in (6.28) reduces to

γ = γ [(E (η∗) E (4η∗))+5(E (4η∗) E (16η∗)) t r1 1 0 − 1 0 1 0 − 1 0 + 21E1(16η0∗)] , (6.31)

γ Deﬁning β = r1 , β = 4K , and β = 16K , γ in (6.31) can be rewritten as 0 2(1 PEPtg) 1 0 2 0 t −

γ = γ [(E (λβ ) E (λβ )) t r1 1 0 − 1 1 + 5(E (16λβ ) E (λβ )) + 21E (λβ ) (6.32) 1 1 − 1 2 1 2

The Lagrange multiplier λ has to be adjusted such that the equivalent γt in (6.32) equates the target desired value by the constraint γtg.

We observe in Fig. 6.3 and Fig. 6.4 the evolution of the transmit SNR as well as the normalized throughput, respectively, as a function of the channel power η. We can distinguish three AMC switching thresholds η0∗, η1∗ and η2∗ . The ﬁrst threshold η0∗ represents a cutoﬀ threshold below which the transmitter avoid data transmission.

In Fig. 6.5, we compare the selected optimal transmit SNR as a function of the CSI, η, for diﬀerent average transmit SNR constraints. As expected, for the same QoS requirement, the

66 Chapter 6. QoS-guaranteed Cross-Layer Design for Link Adaptation

more the average transmit SNR target is high the more the PC policy allocates high power to maximize the average throughput. Moreover, the more the system requires a low average transmit SNR, the more it becomes prudent to switch from a modulation to another less strong one, which explains the increase of the cutoﬀ threshold η0.

In Fig. 6.6, we observe the optimal transmit SNR as a function of η for the same average transmit SNR and diﬀerent PEP constraints. We can notice that, the more we require good

QoS (ie P EPtg is low), the more PC policy spends power to achieve the QoS requirements.

Conversely, the more we relax the QoS’s constraint (P EPtg becomes large), the lower is the needed energy to meet the demands in terms of QoS.

We depict in Fig. 6.7 the average throughput efficiencies curves of the GoS-guaranteed LA scheme with respect to the average transmit SNR for different QoS requirements (i.e. different

P EPtg). We can see that the more we require a good QoS for transmission, the more we need power to ensure a given transmission rate. For instance, to ensure a transmission with 2 b/s/Hz as normalized throughput, we need to spend 17.6 dB and 16.3 dB of transmit SNR 6 4 (equivalently power) in average to guarantee PEPs of 10− and 10− respectively, while we need only 14.4 dB of average transmit SNR to guarantee the same transmission rate, if 1/100 of packets are tolerated to be in error.

In Fig. 6.8, we compare the performances of QoS-guaranteed scheme to those of the LA scheme proposed in Chapter 3, where no QoS is guaranteed for joint AM-PC-ARQ scheme, as well as the conventional LA scheme, where only AM and ARQ are combined. We can notice that QoS-guaranteed LA scheme provides always better performances than the AM-ARQ scheme especially for high and low average transmit SNR. For instance, we can save more than 5 dB in average transmit power in comparison to the AM-ARQ scheme, while maintaining a PEP 2 no more than 1% (i.e. P EPtg = 10− ). We can also observe that the PC-AM-ARQ schema without guaranteed QoS outperforms our QoS-guaranteed scheme only for medium average transmit SNR. In fact, we can have almost the same performances, for high as well as low average transmit SNR, while guaranteeing a satisfying PEP.

67 Chapter 6. QoS-guaranteed Cross-Layer Design for Link Adaptation

Figure 6.3: Transmit SNR as a function of η, P EPtg = 1%, N = 3.

Figure 6.4: Normalized throughput as a function of η, P EPtg = 1%, N = 3.

350

γ¯t = 20 dB

300 γ¯t = 10 dB

γ¯t = −5 dB

M1 = 4 250 M2 = 16

M3 = 64 No transmission 200 t γ

150

100

0 X X X -10* -5 0 5 10 15 20 25 η η* η* 0 0 0 η [dB]

Figure 6.5: Distribution of the optimal transmit SNR for diﬀerent average transmit SNR constraints.

68 Chapter 6. QoS-guaranteed Cross-Layer Design for Link Adaptation

×104 2 PEP = 10−1

− 1.8 PEP = 10 2

−3 1.6 PEP = 10

M1 = 4 1.4

M2 = 16 1.2 M3 = 64

t 1 γ No transmission

0.8

0.6

0.4

0.2

0 x x x * * η -25 -20η* -15η -10 -5 0 5 10 0 0 0 η [dB]

Figure 6.6: Optimal transmit SNR as a function of η for diﬀerent PEP constraints.

PEP = 10-2

PEP = 10-4 5 PEP = 10-6

Sim PEP = 10-2

Sim PEP = 10-4 4 Sim PEP = 10-6

2 Normalized throughput [(b/s)/Hz]

0 -10 -5 0 5 10 15 20 25 30 35 γ¯t[dB]

2 4 6 Figure 6.7: QoS-guaranteed scheme for P EP = 10− , 10− and 10−

69 Chapter 6. QoS-guaranteed Cross-Layer Design for Link Adaptation

AMC-ARQ no QoS AMC-PC-ARQ no QoS -2 5 AMC-PC-ARQ PEP=10 Sim PEP=10-2

2 Normalized throughput [(b/s)/Hz]

0 -10 -5 0 5 10 15 20 25 30 35 γt [dB]

Figure 6.8: Performances comparison of the QoS-guaranteed and no QoS-guaranteed schemes.

6.5 Conclusion

In this chapter, we developed an efficient LA scheme for throughput improved QoS-guaranteed packet wireless communications. The proposed cross-layer optimally combines the three LA techniques, namely AM, PC and ARQ, in order to achieve the highest average throughput efficiency, while fulfilling a target PEP constraint in addition to the constraint on the average transmit power. Both optimal AM-switching thresholds and appropriate transmit power level were derived as a function of the CSI, while guaranteeing the required PEP. Closed-form expressions of the derived solutions, were also given, for high received SNR.

Provided numerical and simulation results revealed that, QoS-guaranteed PC-AM-ARQ cross- layer obviously needs additional transmit power, compared to no QoS-guaranteed PC-AM-ARQ cross-layer. Nevertheless, we found that it gives always better performances in comparison to conventional AM-ARQ cross-layer, with no guaranteed QoS, used as a benchmark.

70 Chapter 7

Cross-Layer Design Combining PC and AMC for HARQ-MIMO Systems

7.1 Introduction

One of the key techniques for enabling high data rates is the communication over multiple- input-multiple-output (MIMO) channels. MIMO systems were ﬁrst introduced in the physical layer for high-speed packet dada mode (HSP) of 3G. It has been shown that single-user (SU) systems employing m-element antenna arrays at both the transmitter and the receiver can achieve a data rate proportional to m, assuming independent Rayleigh fading between antenna pairs [42]. High reliability can be provided by employing the automatic repeat request (ARQ) protocols in the DL layer [17], yet hybrid ARQ (HARQ) is often used for improved data rates.

By jointly combining MIMO, at the PHY layer, and HARQ, at the DL layer, we may provide both high data-rates and high reliability [44]. While HARQ operating in single-input- single-output (SISO) channels was well-studied, less is known about ARQ operating in MIMO channels.

In this chapter, we extend the realistic SISO cross-layer design investigated in Chapter 3 and Chapter 4 to MIMO systems. Assuming known perfect channel state information (CSI)

71 Chapter 7. Cross-Layer Design Combining PC and AMC for HARQ-MIMO Systems

at both the transmitter and the receiver, the MIMO channel is decoupled into parallel eigen- subchannels using the singular value decomposition (SVD) based spatial multiplexing [41]. For each eigen-mode, the optimal transmit power level as well as the appropriate modulation and coding scheme (MCS) are jointly selected, as a function of the fading state of the subchannel, in order to achieve the highest average throughput eﬃciency (ATE) of the whole MIMO system, while keeping the total average transmitted power under a prescribed constrain. The achieved ATE improvement is analyzed for both ordered and unordered eigenvalues cases.

The remainder of this chapter is structured as follows. We give a brief overview of the MIMO systems in section 7.2. We introduce the MIMO system model in Section 7.3. We present the cross-layer deign combining PC, AMC and hybrid ARQ for MIMO systems in Section 7.4. We provide numerical and simulation results, as well as their interpretations in Section 7.5. Finally, Section 7.6 draws some conclusions.

7.2 MIMO Systems Overview

It is well known that systems with multiple antennas at transmitter and receiver, generally referred to as multiple-input multiple-output (MIMO) systems, can provide dramatic improvements in spectral eﬃciency [49, 50] and reliability [48], without requiring additional transmit power or bandwidth. MIMO technology has been adopted in many wireless systems, such as Wi-Fi, WiMAX and LTE. Several antennas at the transmitter (nT ) and the receiver (nR) are employed to form the MIMO systems whose special case of nT = 1 transmit antennas and nR = 1 receive antennas reduces to the traditional Single-Input Single-Output (SISO) systems. A proper combination of the signals at the receiver, may conduct to the improvement of the signal quality or data rate for each MIMO user [46, 47].

With the advent of MIMO systems, several schemes that benefit particularly well from the added spatial dimensions provided by multiple antennas have been emerged: spatial multiplexing [41, 49, 50] provides higher spectral efficiency, while diversity coding techniques [48] help to increase the reliability of wireless links. Further performance improvements can be obtained by using beamforming to reduce the multipath fading effect through making signals transmitted from different antennas add up constructively [47].

72 Chapter 7. Cross-Layer Design Combining PC and AMC for HARQ-MIMO Systems

7.2.0.1 Spatial Diversity

The transmitted signal over broadband wireless channels generally suﬀers from attenuation due to the detrimental eﬀect of multipath fading, which can severely degrade the reception performance, unless some additional less-attenuated replicas of the transmitted signal are provided. This feature is known as diversity, and is used when there is no knowledge of the channel at the transmitter. In diversity methods, a single stream is transmitted, yet the signal is coded using techniques called space-time coding. Diversity coding exploits the independent fading in the multiple antenna links to enhance signal diversity. Several mechanisms are used to maximize the spatial diversity including delay diversity, Space-Time Block-Coding (STBC) [53, 54] and Space-Time Trellis-Coding (STTC) [48].

7.2.0.2 Spatial Multiplexing

Spatial multiplexing is well known as a very powerful technique for increasing channel capacity at high SNRs [41, 49, 50, 51]. In spatial multiplexing, a high rate signal is split into multiple lower rate streams and transmitted simultaneously from diﬀerent transmit antennas in the same frequency channel. The maximum number of spatial streams is limited to m = min(nT ,nR). At the receiver, spatial multiplexing uses a dedicated detection algorithm to sort out diﬀerent transmitted signals from the mixed corresponding signal. This is feasible as long as the number of receive antennas is greater than or equal to the number of parallel transmitted streams.

Singular Value Decomposition (SVD) based technique is known to achieve the highest capacity by orthogonalizing the MIMO channel [51, 57]. Assuming perfect knowledge of CSI at both the transmitter and receiver, a MIMO-SVD architecture uses the SVD beamforming to split the n n MIMO channel into m parallel independent suchannels in space. This is done R × T through specific transmit pre-coding and receive post-coding processes using pre-filtering and post-filtering matrix deduced from the singular value decomposition of the MIMO channel matrix.

73 Chapter 7. Cross-Layer Design Combining PC and AMC for HARQ-MIMO Systems

Figure 7.1: Transmission system block diagram.

7.3 System Model and MIMO Channel

In this section, we generalize the SISO system model considered in Chapter 3 to MIMO con-

figuration, as illustrates Fig. 7.1. We consider nT transmitting and nR receiving antenna elements. Packets ready for transmission by the PHY layer, are first queued in a transmit buffer, then grouped into frames before being simultaneously transmitted over the transmit antennas. Assuming perfect CSI at the transmitter, an SVD-based processing is applied to the n n MIMO channel in order to decouple it into m = min(n ,n ) parallel subchannels. R × T T R Based on the suchannels´powers η m , the appropriate MCSs´set MCS m as well as the { i}i=1 { i}i=1 optimal transmit power levels´set P m are jointly selected for transmission. Perfect channel { ti }i=1 estimates at the receiver, and reliable feedback path are assumed. The adaptive modulation and coding system as well as the MIMO channel are presented in details in the following subsections.

At the DL layer, a truncated HARQ-I protocol controls packet retransmissions. Each transmitted packet is encoded for both error detection and correction. Whenever a received packet is detected in error, the ARQ generator selectively initiates retransmission requests (negative acknowledgements Ack-), and sends them back to the transmitter. Since only finite delays are tolerated by practical applications, buffers at both ends of transmission link have to be of limited size. Therefore, we truncate the number of transmission attempts for the HARQ protocol to NARQ transmissions. A quasi-static independent flat fading Rayleigh MIMO system is assumed. The quasi-static assumption accounts for the fact that the subchannel powers ( η m ) remain almost the same for all retransmissions of a given packet. { i}i=1

74 Chapter 7. Cross-Layer Design Combining PC and AMC for HARQ-MIMO Systems

7.3.1 Adaptive Modulation and Coding System

A packet consists of a ﬁxed number of symbols ns and a variable number of bits nb. This bit number depends on modulation and coding scheme MCSn selected by the AMC selector unit.

A set of N MCSs are assumed to be supported by the PHY layer. A given MCSn, n = 1, ..., N, consists of an Mn-ary QAM modulation and a rate Rn FEC code. Each packet contains nb bits which comprises its own cyclic redundancy check (CRC) for HARQ error detection purposes as well as a payload of kb bits. A tail of t bits is then appended to this codeword to terminate the convolutional code trellis. At the output of an error correction code of a rate Rn, a number of (nb + t)/Rn coded bits are obtained. Using Mn-ary QAM modulation, these coded bits are then mapped to ns = (nb + t) / (log2(Mn)Rn) symbols, provided that nb + t is proportional to log2(Mn)Rn.

The performance offered by a selected MCSn through a subchannel i is assessed by its throughput curve, T hrn(γri ), as a function of the received SNR γri (i = 1,...,m). As detailed in the previous chapters, for a given γri , there is always one MCS that outperforms the others. There- fore, the received SNR range is partitioned into N non-overlapping intervals, defined by the switching thresholds T N , where T = 0 and T = + for convenience. Whenever the { n}n=0 0 N ∞ received SNR γri falls within the interval [Tn, Tn+1), the MCSn will be chosen for transmission over the i-th subchannel. The i-th subchannel effective throughput is then given by the maximum of all elementary throughput curves,

T hr(γr ) = max T hrn(γr ) . (7.1) i n { i }

7.3.2 MIMO Fading Channel

The MIMO channel is modeled by the n n matrix H = [h ]nR,nT , where h is the channel T × R ij i,j=1 ij coefficient between the jth transmit and i-th receive antennas, assumed to be random and independent identically distributed (i.i.d). The independence of the coefficients hij is held by providing a sufficient spacing between antennas at both ends of the transmission link.

Assuming perfect CSI at the transmitter, the MIMO channel is decoupled into m parallel eigen-subchannels using SVD spatial multiplexing, where m is the rank of the channel matrix H. Throughout the chapter, (.)H and (.)T refer to the Hermitian transpose and transpose,

75 Chapter 7. Cross-Layer Design Combining PC and AMC for HARQ-MIMO Systems

respectively. The channel matrix H veriﬁes

H = UΛVH , (7.2) where the n n matrix U and the n n matrix V are unitary matrices and Λ is a R × R T × T n n diagonal matrix whose diagonal entries σ ,...,σ are the non-negative singular values R × T 1 m of H. Those singular values are either kept in there random order or sorted in an nonincreasing order. When those values are kept in there random order, and since they are independently taken, we can claim that they experience the same probability and same quality in average. When the singular values are nonincreasing ordered, the m subchannels fading will be sorted 2 from the best to the worst. Note that the subchannel power ηi = σi (i = 1,...,m) is the i-th eigenvalue of the complex noncentral Wishart matrix

H HH , if nR nT W = ≤ (7.3)  HH H, if n >n .  R T  A pre-coding is performed to the m 1 M -ary modulated symbol vector X = [x ,x , .., x ]T , × n 1 2 m by multiplying it with the pre-ﬁltering matrix V. At the reception, a post-coding is applied by T H multiplying the received signal vector Y = [y1,y2, .., ym] with the post-ﬁltering matrix U . The equivalent received signal vector is given by

Y˜ = ΛX + W, (7.4) where W is a n 1 additive white Gaussian noise (AWGN) vector whose elements are i.i.d R × zero-mean complex Gaussian with variance N0, the same properties as the initial noise at the input of the receiver. The received SNR of the i-th subchannel, i = 1, 2, ..., m, is aﬀected by both the i-th subchannel power as well as the allocated power to transmit the symbols xi over the i-th subchannel, as expressed as follows

PiTs γri = ηi , (7.5) N0 where Ts is the symbol duration. The transmit SNR over the i-th subchannel, deﬁned as the ratio between the average transmit symbol energy and the noise PSD, is then given by

γri γti = . (7.6) ηi

76 Chapter 7. Cross-Layer Design Combining PC and AMC for HARQ-MIMO Systems

7.4 Optimized Link Adaptation for MIMO System

We look in this section to maximize the average throughput of an n n MIMO system by R × T jointly combining both AMC and PC LA techniques, at the PHY layer, with type I HARQ protocol, at the DL layer. To reduce multiple access interference, a constraint, γtg, on the average transmit power radiated by the whole MIMO system, γt, should be fulﬁlled. It amounts to the following constrained maximization

max T hr s.t. γ = γ . (7.7) m t tg γt { i }i=1

The solution is a set of optimal transmit powers, or equivalently transmit SNRs γ m , as a { ti }i=1 function of the relative instantaneous subchannel powers ηi, i = 1, 2, ..., m.

As the MIMO system is decoupled into m independent eigen-subchannels, using SVD processing, the average throughput of the global MIMO system can be evaluated as the sum of the m elementary average throughputs, given by

m T hr = T hri. (7.8) Xi=1 Similarly, the average transmit SNR of the MIMO system is given by

γt = γti . (7.9) Xi=1

Each eigen-subchannel is treated as a separate SISO system for maximizing the overall average throughput of the MIMO system. We therefore split the constrained maximization problem in (7.7) into a system of m independent maximisation problems, formulated as follows

max T hri λγti s.t. γt = γtg i = 1, ..., m. (7.10) γti (ηi) −

The Lagrange multiplier λ is indirectly fixed by the average transmit SNR γtg prescribed for the whole MIMO system. We can also consider to split this prescribed global constraint into m partial constraints γ m prescribed for the m streams, which amounts to m γ = γ . { tgi }i=1 i=1 tgi tg In this case, two different ways for partitioning γtg could be considered. TheP first way is to

77 Chapter 7. Cross-Layer Design Combining PC and AMC for HARQ-MIMO Systems

evenly divide the global constraint over the m SISO parallel branches, which is appropriate for matrix H whose eigenvelues are randomly chosen. The second way is to consider an adaptive partitioning for channel matrix whose eigenvalues are sorted. In this case, every ith average transmit SNR constraint is weighted with a weighting coeﬃcient αi such as more average transmit power is allocated to the best channel qualities.

To solve each i-th maximization problem we ﬁrst need to substitute both average throughput

T hri and average transmit SNR γti by their explicit expressions. Both expressions need the subchannel powers’ marginal PDF expressions, which are presented in the following subsection for both ordered and unordered eigenvalues cases.

7.4.1 Statistics for Unordered Eigenvalues

When the eigenvalues of the Wishart matrix W, η1,η2...,ηm, are kept in there initial random order, and since they are independently taken (i.e. uncorrelated), their probabilities are equal, u and denoted by flm (η), l = max(nR,nT )). The average throughput and the average transmit SNR of a given i-th eigen-subchannel are a function of this marginal distribution, and expressed, respectively, as + ∞ u T hri = T hri (γri (ηi)) flm (η) dηi, (7.11) Z0

+ ∞ u γi = γti (ηi) flm (η) dηi. (7.12) Z0 u Next, we give the expression of flm (η). The joint PDF of the unordered eigenvalues of the

Wishart matrix W, η1,η2...,ηm, is deﬁned in [41] as

1 P ηi l m 2 f (η , η , ..., η )= K− e− i η − (η η ) , (7.13) η 1 2 m ml i i − k i 1 i

m Kml = m! (m i)! (l i)! . (7.14) " − − # Yi=1 The independence and the randomness order of the eigenvalues implies their equiprobability.

Thus, one need only to compute the marginal distribution of the any i-th eigenvalue ηi, or

78 Chapter 7. Cross-Layer Design Combining PC and AMC for HARQ-MIMO Systems

simply η , to have the marginal distributions of the all ηi, i = 1,...,m. It is derived in [41], by integrating the joint distribution over all the eigenvalues but the i-th one, as

m u 1 2 n m η f (η)= φ (η) η − e− , (7.15) ml m i Xi=1 where φ1,φ2...,φm is the result of applying the Gram-Shmidt orthogonalization procedure to 2 m 1 the sequence 1,η,η ,...,η − , given by [41]

1/2 k! l m φ (η)= L − (η) , k = 0, ..., m 1, (7.16) k+1 (k + l m)! k − −

l m where Lk− (x) is the associated Laguerre polynomial of order k, deﬁned as

k l m 1 x m l d x l m+k L − (x)= e x − e− x − (7.17) k k! dxk Explicit expressions for the two special cases m = 2 and m = 3 are expressed, respectively, as follows [45, eq.9,eq.10] u 1 η l 2 fl2 (η)= Kl−2 e− η − Φ (η,l, 2) , (7.18)

u 1 η l 2 fl3 (η)= Kl−3 e− η − Φ (η,l, 3) , (7.19) where Φ(η,l, 2) and Φ (η,l, 3) are giving, respectively, by

Φ (η,l, 2) = (l 2)!η2 2(l 1)!η + l! (7.20) − − − and

Φ (η,l, 3) = 2η4 (l 1)! ((l 2)!)2 − − − + 4η3 [(h l 1)!(l 2)! l] i − − − + 2η2 (l + 1)! + 2l!(l 2)! 3 ((l 1)!)2 − − − + 4η [lh!(l 1)! (l + 1)!(l 2)!] i − − − + 2 (l + 1)!(l 1)! (l!)2 . (7.21) − −

79 Chapter 7. Cross-Layer Design Combining PC and AMC for HARQ-MIMO Systems

7.4.2 Statistics for Ordered Eigenvalues

We assume that the subchannels’ powers η m are sorted in nonincreasing order, and the { i}i=1 kth-order statistic is denoted by δk. This means that the ﬁrst subchannel experiences always the best subchannel power (δ1) and the last subchannel experiences the worst one (δm). Unlike the case of unordered eigenvalues, ordered subchannel powers’ distributions are not equal. The marginal PDF of a given δk was derived in [45] as

k m 1 flm(δ) = m −  k 1  − + + δ δ ∞... ∞ ... f (δ, η , η , ..., η ) × Λ 1 2 m Zδ Zδ Z0 Z0 k-1 m-k dη ...dη . (7.22) × | 2 {z m } | {z }

A closed-form expression of (7.22) was provided in [45, eq.16,eq.17] for the particular case m = 2, as

f 1 (δ) = 2K [ϕ (l, l 2, δ ) 2ϕ (l 1, l 1, δ ) l2 l2 1 − 1 − 1 − − 1 +ϕ (l 2,l,δ )] , (7.23) 1 − 1

f 2 (δ) = 2K [ϕ (l, l 2, δ ) 2ϕ (l 1, l 1, δ ) l2 l2 2 − 2 − 2 − − 2 +ϕ (l 2,l,δ )] , (7.24) 2 − 2 where k i −δ l −δ δ ϕ1 (l,k,δ)= e δ k! 1 e (7.25) − i=0 i! ! X and k i −2δ l −δ δ ϕ2 (l,k,δ)= e δ k!e (7.26) i=0 i! X

The average throughput and the average transmit SNR are evaluated as a functions of the joint distribution of η m , and given, respectively, by { i}i=1 + + ∞ ∞ T hri = ... T hr (γri (ηi)) fη (η1, ..., ηm) dη1...dηm (7.27) Z0 Z0

80 Chapter 7. Cross-Layer Design Combining PC and AMC for HARQ-MIMO Systems

and + + ∞ ∞ γi = ... γti (ηi) fη (η1, ..., ηm) dη1...dηm. (7.28) Z0 Z0 Since, marginal distribution of a given eigenvalue ηi is derived by integrating the joint distribution over all the eigenvalues but the i-th one, (7.27) and (7.28) reduce, respectively, to

+ ∞ i T hri = T hr (γri (ηi)) flm(η)dηi, (7.29) Z0 and

+ ∞ i γi = γti (ηi) flm(η)dηi. (7.30) Z0

7.4.3 Optimized LA Scheme

To solve the system of m independent maximisation problems in (7.10), we proceed similarly to Section 3.3 for SISO systems. First, we substitute the ith MIMO subchannel’s average throughput and average transmit SNR by their explicit expressions. The system of maximization problems, in (7.10), is rewritten as

+ ∞ max [T hri (γri (ηi)) λγti (ηi)] fl,m(η)dηi , (7.31) γt (ηi) − i Z0

u i where fl,m(η) = fl,m(η), given in (7.15), for undordered eigenvalues and fl,m(η) = fl,m(η), given in (7.22), for ordered eignevalues. Since the PDF fl,m(η) is generally non negative, the maximizations in (7.31) reduce to

max (T hri (γri (ηi)) λγti (ηi)) , i = 1, ..., m. (7.32) γti (ηi) −

Since the throughput is a function of the received SNR, we propose will solve the function in

(7.32) with respect to γri (ηi), which requires the replacement of γti (ηi) by (7.6), which gives

λ max T hri (γri (ηi)) γti (ηi) , i = 1, ..., m. (7.33) γt (ηi) − η i i

81 Chapter 7. Cross-Layer Design Combining PC and AMC for HARQ-MIMO Systems

ηi Then the parameter µi = λ is introduced as well as the function χ(µi) = γri (λµi). The maximization system becomes as follow

χ(µi) max T hri(χ(µi)) , i = 1, ..., m. (7.34) χ(µi) − µ i

Obviously, the system of maximization problems obtained in (7.34) have unique solutions denoted by χ∗(µi). Similarly, to Chapter 3, we adopt the numerical resolution process, developed in 3.3.2 for SISO systems, in order to determine the general solutions of the obtained system maximization problems. The optimal transmit SNRs, solutions of (7.34), are then deduced as follows ηi γr∗i (ηi) χ∗( λ ) γt∗i (ηi)= = i = 1, .., m. (7.35) ηi ηi

We summarize the operating stages of the optimal transmission parameters’ selection, namely the optimal transmit powers and the optimal MCSs, in the algorithm in Table 7.1.

Table 7.1: Selecting optimal transmission parameter for eigen-subchannel i

[Initial step] 1: Having γtg, estimate λ using λ-Tracking Loop (conforming to 4.3.1)

2: Performing Numerical resolution process (conforming to 3.3.2) using µ = λ , Output: i ηi

γr∗i (µi) 3: Compute γr∗i (ηi) using (7.35) 4: Compare γ (η ) to AMC-switching thresholds T N , Output: MCS r∗i i { n}n=0 ni

7.5 Simulation Results

This section presents some numerical and simulation results. We consider the same number of antenna elements at both transmitter and receiver sides, i.e. nR = nT = n where n = 2 and 3. Similar to Chapter 4, we consider that the PHY layer supports two categories of MCSs,

nR,nT summarized in Table 4.1. The channel coeﬃcients hij of the channel matrix H = [hij]i,j=1 are assumed to follow a frequency-ﬂat Rayleigh channel model.

In Fig. 7.2, we can valid the agreement between the average throughput curves for both ordered and unordered eigenvalues.

82 Chapter 7. Cross-Layer Design Combining PC and AMC for HARQ-MIMO Systems

ARQ HARQ-I 18 15

3x3 ordered eigenvalues 3x3 ordered eigenvalues 16 2x2 ordered eigenvalues 2x2 ordered eigenvalues 3x3 unordered eigenvalues 3x3 unordered eigenvalues 2x2 unordered eigenvalues 2x2 unordered eigenvalues 14

12 10

6 5 Average normalized throughput (b/s)/Hz Average normalized throughput (b/s)/Hz 4

0 0 0 10 20 30 -5 0 5 10 15 20 25 30 γt [dB] γt [dB]

Figure 7.2: Average throughput as a function of the average transmit SNR, for ordered and unordered eigenvalues

To conﬁrm the feasibility of the proposed cross-layer design for MIMO systems, we compare in Fig. 7.3 the simulated average normalized throughput to the theoretical one, for MIMO and SISO systems. Monte-Carlo simulations was performed following the operating stages presented in Table 7.1. From Fig. 7.3 we can notice the good agreement between simulation and theoretical results. This ﬁgure also shows that MIMO systems provide an increase of the average throughput proportional to the rank m of the channel matrix H, with respect to SISO systems. For instance, a 2 2 MIMO system provides a maximum average throughput of 10 × (b/s)/Hz which represents twice the maximum average throughput provided by a SISO system.

Theo : MIMO 3x3 - HARQ Theo : MIMO 2x2 - HARQ Theo : SISO -HARQ Sim : MIMO 3x3 - HARQ Sim : MIMO 2x2 - HARQ Sim : SISO -HARQ

5 Average normalized throughput (b/s)/Hz

0 -15 -10 -5 0 5 10 15 20 25 30 35 γt [dB]

Figure 7.3: Average throughput as a function of γ , for 2 2 and 3 3 MIMO systems vs SISO t × × system.

Fig. 7.4 and Fig. 7.5 compare the performance of the proposed cross-layer design with that offered by a conventional cross-layer design where no PC is employed, while considering the HARQ and the ARQ protocols respectively. Both figures clearly show that adding power control significantly improves the system performance, especially for high and low average transmit SNRs. It is also notable that this improvement is more important for schemes employing the

83 Chapter 7. Cross-Layer Design Combining PC and AMC for HARQ-MIMO Systems

HARQ than those employing the basic ARQ.

From Fig. 7.6, we can observe that MIMO-HARQ design provides higher average throughput eﬃciency than MIMO-ARQ design for low and moderate average SNR, thanks to the FEC. However, at high average transmit SNR, MIMO-ARQ scheme achieves higher average throughput than MIMO-HARQ scheme, because its corresponding MCSs support higher data rates. In fact, the highest rate MCS has a rate of 6 (bits/sym.) in uncoded modulations category, which is greater than 5 (bits/sym.) the highest rate in coded modulations category.

MIMO 3x3 with PC MIMO 2x2 with PC SISO with PC MIMO 3x3 no PC MIMO 2x2 no PC SISO no PC

5 Average normalized throughput (b/s)/Hz

0 -5 0 5 10 15 20 25 30 35 γt [dB]

Figure 7.4: Average throughput as a function of average transmit SNR, for MIMO-HARQ systems with and without PC

16 MIMO 3x3 with PC MIMO 2x2 with PC SISO with PC 14 MIMO 3x3 no PC MIMO 2x2 no PC SISO no PC 12

4 Average normalized throughput (b/s)/Hz

0 -5 0 5 10 15 20 25 30 35

γt [dB]

Figure 7.5: Average throughput as a function of average transmit SNR, for MIMO-ARQ systems with and without PC

7.6 Conclusion

In this chapter, we generalized the cross-layer design proposed in Chapter 4, which eﬀectively combines both AMC and PC techniques, at the physical layer, with a hybrid type-I ARQ

84 Chapter 7. Cross-Layer Design Combining PC and AMC for HARQ-MIMO Systems

MIMO 2x2 with PC - HARQ MIMO 2x2 no PC - HARQ 10 MIMO 2x2 with PC- ARQ

4 Average normalized throughput (b/s)/Hz

0 -5 0 5 10 15 20 25 30 35 γt [dB]

Figure 7.6: Average throughput as a function of average transmit SNR, for MIMO-HARQ 2x2 and MIMO-ARQ 2x2 systems protocol, at the data link layer, to the MIMO systems. A throughput analysis was provided for both ordered and unordered eigenvalues statistics. Numerical an simulation results were provided for both 2 2 and 3 3 MIMO systems. × ×

It has been shown that using MIMO systems provides an increase of the average throughput proportional to the rank m of the channel matrix H, with respect to SISO systems. It has also been demonstrated that, adding power control to the conventional AMC-ARQ scheme generalized to MIMO systems, improves the system performance. This improvement is more important with hybrid ARQ protocol than basic ARQ protocol.

85 Chapter 8

Conclusion and Future Work

8.1 Conclusion

Efficient selection of transmission parameters while suffering from limited bandwidths and power resources, and facing highly time-variant propagation environments and user mobility, is always a challenging issue for wireless communication networks evolution. A prior transmission mechanism for handling channel variations is enabled through link adaptation techniques, namely PC and AMC. A post transmission mechanism is the ARQ protocols which help increasing system reliability by retransmitting erroneously received data packet. Those mechanisms nicely and synergically complement each other. In this thesis, we proposed throughput efficient cross-layer designs combining all three LA techniques, namely AMC, PC and ARQ for both SISO and MIMO systems.

First, we have developed a cross-layer design combining adaptive modulation, power control and basic ARQ protocol for SISO systems. More specifically, both most appropriate modulation scheme as well as optimal transmit power were selected, given the channel state information (CSI) feedback by the receiver. The aim of this combination was to offer the maximum of average throughput efficiency (ATE), while keeping the average transmit power under a prescribed adequately chosen value. To do this, an analytic derivation was first conducted using Lagrange multipliers, followed then by a numerical resolution process. Thanks to this one-shot numerical resolution approach, the proposed combination scheme is found to be easily applicable to any ARQ scheme, regardless the complexity of the throughput expression. It was also found to be

86 Chapter 8. Conclusion and Future Work

valid for any generic fading statistics. In fact, it only needs a set of throughput efficiency curves corresponding to the MCSs supported by the system, obtained either by an explicit analytic expression or by even by simulation, to apply the numerical resolution and hence determine the appropriate transmission parameters. The gain offered by adding the power control policy to conventional AM-ARQ cross-layer was studied by comparing the performance of the proposed LA scheme to those of the conventional scheme combining only AM with ARQ. A significant reduction in average transmit power was observed especially for high and low average transmit SNRs.

The proposed cross-layer design was then extended by incorporating coding rate adaptation in addition to constellation size adaptation. A type I hybrid ARQ (HARQ) protocol was considered with an SR retransmission strategy. The transmit parameters selection strategy is closely related to the Lagrange parameter, referred to λ, used to solve the optimization problem. This parameter was derived from the average transmit power constraint intimately related to the channel statistics. In order to maintain the independence of the proposed combination scheme from the channel statistics, we proposed an iterative algorithm for blindly estimating and tracking the λ parameter, following channel statistics variations. This algorithm operates in a closed tracking loop, and uses the EMA algorithm to estimate the achieved average transmit power. An end-to-end simulation was performed to validate the accuracy of the proposed λ-tracking algorithm. The eﬀect of mobile speed variation on the convergence of the proposed EMA-based tracking algorithm was studied. To this end, a Jakes model was used to simulate the time-correlated channel.

Conventional ARQ protocols, usually use the same transmit power level to retransmit the same data packet, whenever it is needed. However, we have shown that allocating more transmit power to later transmissions of a given packet increases its chances for being successfully transmitted, without significantly affecting the average power spent per packet. In this context, we proposed not only to select the optimal transmit power budget for a given CSI as previously addressed, but also to wisely redistribute this budget of average transmit power among the potential transmissions, such that the resulting throughput is maximized, for a fixed budget of average power per packet. To this end, a truncated ARQ (T-ARQ) protocol was adopted, and an optimal power allocation was carried through a heuristic algorithm, based on a dichotomic search. Obtained results revealed that enhanced version of the ARQ protocol, combined with PC and AMC techniques, leads to a reduction in average transmit power for low average SNR, with respect to conventional ARQ protocol.

87 Chapter 8. Conclusion and Future Work

Thereafter, a power efficient LA scheme for throughput improved QoS-guaranteed packet wireless communications was developed. This was done by optimally combining the three LA techniques, in order to achieve the highest ATE, while fulfilling a target PEP constraint in addition to the constraint on the average transmit power. More specifically, both optimal AM-switching thresholds and appropriate transmit power were derived as a function of the CSI. Closed-form expressions of the derived solutions, were also presented, for high received SNRs. A performance analysis was conducted by comparing the QoS-guaranteed approach to both AM-ARQ and PC-AM-ARQ without QoS requirements. Provided numerical and simulation results revealed that ensuring a given QoS certainly requires additional average transmit power with respect to PC-AM-ARQ scheme with no guaranteed QoS. However, the QoS-guaranteed PC- AM-ARQ scheme always outperforms the conventional AM-ARQ scheme (with no guaranteed QoS) used as a benchmark.

Finally, a cross-layer design for throughput eﬃcient MIMO-HARQ systems has been developed. Assuming a perfect knowledge of the CSI at both transmitter and receiver ends, the MIMO channel was decoupled into parallel eigen-subchannels using the SVD-based spatial multiplexing method. For each eigen-mode, the optimal MCS and transmit power pair was determined, as a function of the fading state of the subchannel. The objective was to achieve the highest ATE for the whole MIMO system, while keeping the total average transmitted power under a prescribed constrain. A performance analysis was provided for both ordered and unordered eigenvalues conditions, and then compared to those of SISO cross-layer designs as well as MIMO-HARQ schemes using exclusively AMC LA technique.

8.2 Future Work

The thesis developed eﬃcient cross-layer designs for link adaptation by optimally combining PC, AMC and ARQ techniques. Yet there are still many remaining and emerging link adaptation issues in practical wireless communication systems that could be addressed.

On the ﬁrst hand, thanks to the proposed numerical resolution process, the proposed combination scheme could easily be extended to other more sophisticated HARQ schemes with soft combining. Typically the two categories Chase Combining (CC) and Incremental Redundancy (IR) HARQ protocols, could be considered in conjunction with PC and AMC.

88 Chapter 8. Conclusion and Future Work

Some enhancements of the hybrid ARQ protocol may also be considered. More speciﬁcally, when a data packet is erroneously received, it is interesting to fedback not only the retransmission request but also the quality of the received packet. This quality may be assessed by the underlying log likelihood ratio (LLR). Hence, if the transmitter consider that just a little more eﬀort may help to correctly decode the erroneously received packet, a reduction in the retransmission power will then be recommended.

After generalizing the PC-AMC-HARQ cross-layer to MIMO systems, a trivial extension can be envisioned is to generalize the same cross-layer design to cooperative ARQ (C-ARQ) systems. More precisely, the optimal transmit power levels at both the source (S) and the relay (R) terminals, as well as the most appropriate MCS to be used at S, can be selected as a function of the channel fading states of the S-R and R-D links. The maximization of the average end- to-end (e2e) throughput could be considered while respecting a target source and relay average transmit power constraint. To solve this maximization problem, we can use a 2D numerical resolution drawing on what was proposed for SISO systems.

Finally, it is worth to study and apply the proposed cross-layer designs for LA to the cognitive radio context. In this case, the instantaneous transmit power should be constrained by a maximum allowed value.

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