Robust Cross-Layer Scheduling Design in Multi-user Multi-antenna Wireless Systems

Tài liệu tham khảo chuyên ngành viễn thông Robust Cross-Layer Scheduling Design in Multi-user Multi-antenna Wireless Systems

Robust Cross-Layer Scheduling Design in Multi-userMulti-antenna Wireless Systems

submitted byMeilong Jiang

for the degree of Doctor of Philosophyat The University of Hong Kong

in October 2006

Cross-layer design for a multi-user multi-antenna system has been shown to offer high spectralefficiency which benefits from the inherent multi-user diversity and spatial multiplexing gain inwireless fading channels In this thesis, we consider the cross-layer scheduling design under var-ious practical physical layer and network layer constraints for a wireless system with one basestation (with N antennas) and K mobile users (each with a single antenna).

In the first part of the thesis, we study the cross-layer scheduling design with imperfect channelstate information (CSI) at the base station for delay-tolerant applications The CSI imperfectnessmay derive from the CSI estimation error or the CSI outdatedness due to feedback and duplexingdelay With imperfect CSI at transmitter (CSIT), there exists a potential packet transmission errorwhen the scheduled data rate exceeds the instantaneous channel capacity referring to packet out-age Our objective is to maximize the average system goodput, which measures the average b/s/Hzdelivered to the mobiles successfully In practical wireless systems, a discrete set of rates insteadof an infinite continuous rate can only be supported due to the finite choice of error correctionencoders and discrete level constellations To this end, the cross-layer design is formulated as amixed convex and combinatorial optimization problem, with respect to the imperfect CSIT statis-tics and the discrete rate set constraint.

In the second part, we extend the scheduling design for the heterogeneous user applications such asvoice and data services To take delay sensitive users into consideration, we employ both queueingtheory and information theory to model the system dynamics A novel cross-layer heterogeneousscheduler is designed to exploit the spatial multiplexing gain as well as the multi-user selectiondiversity gain while also maintaining the delay constraints of the delay sensitive users.

Numerical results and comparison with various start-of-art scheduling schemes are provided todemonstrate the potential of our proposed schemes Specifically, by considering the CSIT errorstatistics, source statistics and queueing delay into the design, the proposed scheduling schemesprovide significant performance enhancement in terms of system goodput, robustness with respectto imperfect CSIT, and quality of service (QoS) guarantees.

Multi-antenna Wireless Systems

Meilong Jiang

MSEE, Beijing University of Posts and Telecomms.

A thesis submitted in partial fulfillment ofthe requirements for the degree of

I declare that this thesis represents my own work, except where due acknowledgement is made,and that it has not been previously included in a thesis, dissertation or report submitted to thisUniversity or to any other institution for a degree diploma or other qualifications.

Meilong Jiang

I AM DEEPLY INDEBTED to my supervisor, Prof Vincent K.N Lau for having invariablygiven me his patient guidance, stimulating encouragement, and deep insights into my research andmy life as well His enthusiastic attitude and extremely high efficiency has not only had a greatimpact on my Ph.D study, but has also given me great impetus that I would be able to cherish inmy entire life The completion of this thesis would not have been possible without his continualsupport.

I am sincerely grateful to the Graduate School of HKU for having provided the PostgraduateStudentship during the whole Ph.D program I would like to thank Dr N Wong, Prof J Wang,Dr W.H Lam, and Prof Roger Cheng for their insightful guidance, suggestions, and kind helpduring my study I would also like to thank Prof Ricky Kwok, Prof K.L Ho, and Prof Li chunWang for serving on my thesis examination committee.

I truly appreciate the friendship of my friends for having created a pleasant working ment and for their helpful discussions Special thanks go to Mr Tyrone Kwok, Mr Gan Zheng,Mr Carson Hung, Mr David Hui, Doctors-to-be- Xiaoshan Liu , Guanghua Yang and ShaodanMa, Dr Zhifeng Diao, Dr Xiaohui Lin, and Dr Yiqing Zhou for their kind help and insightfuldiscussions Many thanks go to other friends in the lab and research group.

environ-Finally, I would like to express my sincerest gratitude to my parents and my wife Ying Zhengfor their deepest love and constant support.

1.3 Motivation and Problem Statement 5

1.4 Thesis Research and Contributions 6

2.2 Cross-Layer Scheduling and Adaptive Design in Multi-user Wireless Network 13

2.2.1 Adaptive Design in Physical Layer 13

2.2.2 MAC Layer Scheduling Model 15

2.3 Linear Transmit-receive Processing in Multi-antenna Base Station 17

2.3.1 Zero-forcing Processing 18

2.3.2 Transmit MMSE Processing 21

3 Uplink Scheduling Design with Outdated CSI 22

3.1 Overview 22

3.2 Multi-user SIMO System Model 23

3.2.1 Channel Model with Outdated CSIT 23

3.2.2 Multi-user Uplink Physical Layer Model 23

3.2.3 Packet Outage Model 25

3.3 Uplink Space Time Scheduling Design 26

3.3.1 System Utility Function 26

3.3.2 Optimal Solution with Perfect CSI 27

3.3.3 Heuristic Solution with Perfect CSI - Genetic Algorithm 27

3.4 Scheduling with Outdated CSI 28

3.4.1 Performance Degradation of Ideal Schedulers Due to Outdated CSI 28

3.4.2 Proposed Scheme A - Rate Quantization 31

3.4.3 Proposed Scheme B - Rate Discounting 31

3.5 Numerical Results and Discussions 32

4 Cross-Layer Downlink Scheduling and Rate Quantization Design with ImperfectCSIT 37

4.1 Overview 37

4.2 Multi-user MISO System Model 38

4.2.1 Downlink Channel Model 38

4.2.2 Imperfect CSIT Model 40

4.2.3 Multi-user Downlink Physical Layer Model 40

4.3 Problem Formulation of Cross-Layer Scheduling 41

4.3.1 Instantaneous Channel Capacity and System Goodput 43

4.3.2 Cross-Layer Design Optimization 44

4.4 Solutions of the Optimization Designs 45

4.4.1 Combined Scheduling and Rate Quantization Optimization 45

4.4.2 Optimal Inner Scheduling Based on Imperfect CSIT 47

4.4.3 Optimal Transmission Modes Design 50

4.4.4 Summary of the Scheduler Solution 52

4.5 Numerical Results and Discussions 53

4.5.1 Performance of Regular Scheduler with Imperfect CSIT 54

4.5.2 Performance of Proposed Scheduler with Imperfect CSIT 54

5 Performance Analysis of Downlink Scheduling for Voice and Data Applications 65

5.1 Overview 65

5.2 System Model 66

5.2.1 Channel model 67

5.2.2 Multi-user Physical Layer Model 67

5.2.3 Source Model - Voice and Data 69

5.3 Space Time Scheduling for Heterogeneous Users 69

5.3.1 Asymptotic Spatial Multiplexing Gain 69

5.3.2 Scheduling Algorithm 72

5.4 Numerical Results and Discussions 77

5.4.1 Delay Performance of VoIP users 78

5.4.2 Spatial Multiplexing Gains on System Capacity 78

5.4.3 Transient Performance 80

6 Cross-layer Downlink Scheduling with Heterogeneous Delay Constraints 84

6.1 Overview 84

6.2 System Model 85

6.2.1 Multi-user Physical Layer Model 85

6.2.2 Source Model - Delay Sensitive and Delay Insensitive 86

6.3 Formulation of the Cross-layer Design for Heterogeneous Users 87

6.4 Solution of the Cross-Layer Optimization Problem 90

6.4.1 Convex Optimization on (p1, , pK) 90

6.4.2 Combinatorial Search on Admissible Set 91

6.5 Numerical Results and Discussions 91

6.5.1 Delay Performance of the Proposed Scheduler 91

6.5.2 System Throughput Performance 93

6.5.3 Delay and Power Tradeoff 93

7 Conclusions and Future Work 102

7.1 Conclusions 102

7.2 Future Work 103

List of References 105

List of Figures

2.1 Wireless fading channel 9

2.2 System diagram for the cross-layer design framework 14

2.3 Block diagrams of the MAC layer scheduling 16

2.4 Linear downlink transmit strategy with isolated encoding and beamforming 19

3.1 Block diagram of the zero-forcing MUD (multi-user detection) at the base station withnRreceive antennas 24

3.2 Performance degradation of naive cross-layer schedulers (designed for perfect CSI)with outdated CSI 29

3.3 Outage probability of naive scheduler versus various CSI error and SNR 30

3.4 System throughput (b/s/Hz successfully received) versus rate discounting factor whereSNR = 6dB, nR=2, σ2 = 0.05 ∼ 0.1 33

3.5 Performance of maximal throughput schedulers of perfect CSIT, rate quantization andrate discounting with outdated CSIT, ideal (naive) scheduler with outdated CSIT 34

3.6 Illustration of crossover operation in Genetic algorithm 36

4.1 One cell system model of multi-user MISO system 39

4.2 Multi-antenna base station architecture with linear transmit processing 42

4.3 Block diagram of the cross-layer scheduling algorithm 46

4.4 Performance degradation of naive scheduler (scheduler designed for perfect CSIT),no quantization (Q = ∞): system goodput versus SNR in the presence of imperfectCSIT for nT= 4 and K = 10 55

Figure Page4.5 Average system goodput versus SNR for the naive scheduler (designed for perfect

CSIT) with rate quantization (Q = 8) at imperfect CSIT cases, nT = 4 56

4.6 Packet outage probability versus CSIT errors of the naive scheduler (with no tion), the naive scheduler (with rate quantization Q = 8) and the proposed scheduler(with rate quantization Q = 8) for nT = 2 57

quantiza-4.7 Performance comparison of the proposed scheduler, the naive scheduler and the roundrobin scheduler with CSIT error σ2 = 0.05 at nT= 2, 4, 6 59

4.8 Sensitivity of average system goodput to the CSIT errors for the naive scheduler, theproposed scheduler and the round robin scheduler at nT= 4 and Q = 8 60

4.9 Average system goodput versus number of users for proposed scheduler, RXZF uler, TDMA scheduler and opportunistic beamforming scheduler under outdated CSITwith speed= [20, 60] km/h and CSIT delay τ = 300µs (with equivalent error varianceσ2 =[0.015, 0.13] for 5GHz carrier frequency); Transmit antenna nT = 4, receiverantenna for each user nR= 1 (except for linear RXZF scheduler nT= nR = 4);SNR = 15dB 61

sched-5.1 System model of a multi-user wireless system with a base station (nT transmit nas), Kvoicevoice client users and Kdatadata client users 66

anten-5.2 Scheduling and queueing model for voice and data users 70

5.3 Overall space time scheduling algorithm 73

5.4 Scheduling algorithm of the voice and data space time scheduler 75

5.5 Delay performance of VoIP users with background data traffic (BW = 20kHz, nT =4,Kdata=20, Kvoice=2, T0 = 20ms) 79

5.6 Spatial multiplexing gains of voice and data users (BW = 20kHz, Kdata=20, Kvoice=2, T0 = 20ms) 81

5.7 Transient performance of voice users in the presence of bursty data loading BW =20kHz, nT=4, Kdata=20, Kvoice=2, T0 = 20ms 82

6.1 Queueing model and scheduling model 87

Figure Page6.2 Mean packet delay (number of time slots) of two class users versus background data

traffic λ (packets/time slot) (BW = 20kHz, nT=4, ts= 2ms) 92

6.3 Comparison of optimal, heuristic heterogeneous schedulers and Round-Robin uler on Spatial multiplexing gains over nT(BW = 20kHz, K1 = 8, K2 = 8, ts =2ms, SNR = 6 dB and 16 dB) 95

sched-6.4 Minimum transmission power versus first class users delay requirement 96

6.5 Waiting time model consisting of three parts 96

6.6 Flow chart of iterative lagrange multiplier algorithm 101

Cross-layer design for a multi-user multi-antenna system has been shown to offer high tral efficiency which benefits from the inherent multi-user diversity and spatial multiplexing gainin wireless fading channels In this thesis, we consider the cross-layer scheduling design undervarious practical physical layer and network layer constraints for a wireless system with one basestation (with N antennas) and K mobile users (each with a single antenna).

spec-In the first part of the thesis, we study the cross-layer scheduling design with imperfect channelstate information (CSI) at the base station for delay-tolerant applications The CSI imperfectnessmay derive from the CSI estimation error or the CSI outdatedness due to feedback and duplexingdelay With imperfect CSI at transmitter (CSIT), there exists a potential packet transmission er-ror when the scheduled data rate exceeds the instantaneous channel capacity referring to packetoutage Our objective is to maximize the average system goodput, which measures the averageb/s/Hz delivered to the mobiles successfully In practical wireless systems, a discrete set of ratesinstead of an infinite continuous rate can only be supported due to the finite choice of error cor-rection encoders and discrete level constellations To this end, the cross-layer design is formulatedas a mixed convex and combinatorial optimization problem, with respect to the imperfect CSITstatistics and the discrete rate set constraint.

In the second part, we extend the scheduling design for the heterogeneous user applicationssuch as voice and data services To take delay sensitive users into consideration, we employ both

queueing theory and information theory to model the system dynamics A novel cross-layer erogeneous scheduler is designed to exploit the spatial multiplexing gain as well as the multi-userselection diversity gain while also maintaining the delay constraints of the delay sensitive users.

het-Numerical results and comparison with various start-of-art scheduling schemes are providedto demonstrate the potential of our proposed schemes Specifically, by considering the CSIT errorstatistics, source statistics and queueing delay into the design, the proposed scheduling schemesprovide significant performance enhancement in terms of system goodput, robustness with respectto imperfect CSIT, and quality of service (QoS) guarantees.

CDMA code division multiple access

CSCG circularly symmetric complex GaussianCSI channel state information

CSIR channel state information at receiverCSIT channel state information at transmitterD-AMPS digital advanced mobile phone serviceD-BLAST diagonal Bell layered space-timeDFE decision feedback equalizationDFT discrete Fourier transformDS/SS direct sequence spread spectrumDVB digital video broadcastingEV-DO evolution-data optimizedEV-DV evolution-data and videoFDD frequency division duplexFER frame error rate

FFT fast Fourier transform

FH/SS frequency-hopping spread spectrumFTP file transfer protocol

GSM global system for mobile communicationsHSDPA high-speed downlink packet accessi.i.d independent and identically distributedIP internet protocol

ISI inter-symbol interferenceLAN local area network

LDPC low-density parity-check codeLMS least mean square

MISO multi-input single-output

MLSE maximum likelihood sequence estimationMMSE minimum mean square error

NLOS non line of sight

OFDM orthogonal frequency division multiplexingOFDMA orthogonal frequency division multiple accesspdf probability density function

PHY physical layerPLL phase-locked-loop

PRMA packet-reservation-multiple-accessPSD power spectra density

PSK phase shift keying

QAM quadrature amplitude modulationQoS quality of service

QPSK quadrature phase shift keyingRRS round robin scheduler

RXZF receiver zero-forcing

SDMA space division multiple accessSIC successive interference cancellationSIMO single-input multi-output

SISO single-input single-outputSNR signal to noise power ratioSTBC space time block code

TCP transmission control protocolTDD time division duplex

TDE time domain equalizationUDP user datagram protocol

UMTS universal mobile telecommunications system

Notation and used symbols

In this thesis, scalar variables are presented as plain lower-case letters, vectors as bold facelower-case and matrices as bold-face upper cases letters The following is the commonly usednotations and symbols in the thesis.

AijThe ij-th element of the matrix A.

A∗ Complex conjugate transpose (Hermitian transpose) of the matrix A.AT Transpose of the matrix A.

A−1 Inverse of the matrix A.

diag(x1, , xn) A n × n diagonal matrix with diagonal elements {x1, , xn}.tr(A)The trace of the matrix A, T r(A) =PiAii.

(x)+ Is a short notation for max[0, x].

E[x]Statistical expectation of random variable x.

arg maxS(V (S)) The maximizing argument of the function V (·) over the set S.

O(V)The value that is in the same order of V.Pr[A < B]The probability of the event A < B.

|A|The cardinality of the active user set A.

Fχ2(y)The cdf of a chi-square random variable y.

Chapter 1Introduction

1.1 Evolution and Challenge of Wireless Technology

The wireless industry has witnessed its explosive growth since the first generation cellularnetwork was launched in 1979 For example, the first generation analog cellular system (AMPS)has given way to 2G cellular systems (such as GSM, D-AMPS, and IS-95), and nowadays, wehave 3G systems (CDMA2000, UMTS), 3.5G systems (HSDPA,EV-DO,EV-DV), B3G systems(Beyond 3G), and wireless LAN (IEEE 802.11a/b/g) to provide wireless service with higher datarate and mobility More advanced wireless systems targeted for even higher spectral efficiencysuch as Ultrawideband (UWB) systems, and Wi-MAX (IEEE 802.16), as well as Wi-MAN (IEEE802.20) [1] systems are being actively investigated in both academic and industrial communities.

According to a recent report in the Digital Media News for Europe1, the number of worldwidemobile phone subscribers is expected to grow from 2 billion in 2005 to approximately 3.3 billion in2010 The rapid worldwide growth in mobile phone subscribers has demonstrated conclusively thatwireless communication has become a robust and viable voice and data transport mechanism Thedemand for wireless services from the regular low rate voice telephony services to mixed voice/dataand multimedia services with higher data rate and quality of service (QoS) has conversely fuelledthe wireless technique advancement and revolution.

Nevertheless, realizing reliable and efficient communication over the wireless channel has beena very challenging topic since the 1950s and 1960s This is attributed to the hostile nature of the

1http://www.dmeurope.com/default.asp?ArticleID=15236

wireless channel characterized by small-scale fading and large-scale fading [2] For instance, thetransmission of signals over the wireless channels is affected by time-varying channel attenuation,called fading The received signal strength can fluctuate over a wide range of 80dB in the order ofmilliseconds In general, the fading effects of wireless channels impose additional challenges forsignal transmissions aside from the regular channel noise.

In order to satisfy the high data rate requirement and efficiently support multimedia servicesin future wireless systems, many key enabling technologies have been burgeoning in a stable way.Some of them are listed in [3] which include:

• Modulation and multiple access schemes with high spectral efficiency and flexibility such

as orthogonal frequency division multiplex (OFDM), multi-carrier code division multipleaccess (MC-CDMA) and orthogonal frequency division multiple access (OFDMA) [4]

• Multiple antenna technology providing high spectral efficiency referred to as Multiple-Input

Multiple-Output (MIMO) technology

• A scalable network based on IP which seamlessly integrates heterogenous wireless

applica-tions [5]

• Intelligent resource management through cross-layer designs [6, 7]

Among the key enabling technologies, the multiple-antenna technique and the cross-layer signs are the two recent and very promising approaches which deal with the harsh wireless trans-missions [7] Throughout this thesis, we shall exploit the significant performance advantagesbrought about by a combination of these two techniques.

de-1.2 Literature Survey

It was pointed out by Shannon [8] in 1948 that the maximal achievable rate for an error freetransmission of a communication link is limited by the available bandwidth and power The tradi-tional way of increasing the data rate is to increase the bandwidth or power for transmission Yeteither increasing power or broadening bandwidth becomes inadvisable when the required data rate

becomes high and the spectrum is limited Recently, another interesting approach to increasing thebit rate is to make use of multiple transmit and receive antennas It has been shown by the pioneer-

ing works [9,10] that the channel capacity of the MIMO system is proportional to n = min[nT, nR]

where nTis the number of transmit antenna and nRis the number of receive antenna With the tiple antennas, the wireless channel is transformed into a Multiple-Input Multiple-Output (MIMO)

mul-channel where the link capacity gain is contributed by the n spatial mul-channels created Thus it

would be interesting to study the performance of future wireless systems equipped with multipleantennas.

For the point-to-point MIMO link, the performance measure is relatively simple For example,we would like to improve link reliability by exploiting the spatial diversity [11–13] or apply spatialmultiplexing schemes to increase spectral efficiency [14–16] However, for multi-user systems,optimizing the individual link performance is not always the best approach when higher-layerobjectives such as system throughput, fairness and QoS requirement are considered It is thus veryimportant to consider the upper-layer resource allocation together with the adaptive physical layerdesign in a multi-user MIMO wireless system, which is demonstrated to be a method that cancompletely exploit the temporal dimension (scheduling), the spatial dimension (multiple antennas)and the multi-user dimension (multi-user diversity) in the resource space to achieve a good system-level performance [17–19].

Cross-layer scheduling design has attracted intensive attention recently [20–23] In [24, 25], ajoint design of the MAC layer and link layer has been shown to achieve significant gains over theisolated design approach within each layer for single antenna systems This gain is contributed bythe multi-user diversity, which is achieved by scheduling transmissions to users when their instan-taneous channel quality is near the peak Cross-layer scheduling design in multi-antenna systemhas been investigated in [26–28] and the total system throughput is maximized by exploiting thespatial diversity provided by multiple antennas and the inherent multi-user diversity simultane-ously.

As perceived from the existing works mentioned above, channel state information (CSI) isa fundamental requirement for the cross-layer scheduling design With CSI knowledge, channel

adaptive techniques can be applied in both the physical layer and the MAC layer to improve systemperformance CSI is either obtained by channel estimation in TDD systems or CSI feedback to thetransmitter in FDD systems In most of the works mentioned above, perfect CSI knowledge or theperfect CSI feedback is assumed Thus, in the above cases, it is enough to consider the ergodiccapacity as the performance objective since there would be no packet outage with perfect CSI aslong as the error correction code is sufficiently strong.

There are also some recent works on MIMO link capacity with imperfect CSI [29–31] andcross-layer design with limited channel feedback The effect of imperfect CSIT on point-to-pointmultiple input multiple output (MIMO) link capacity has been investigated by [30, 32, 33] It hasbeen found that mutual information degrades significantly due to channel estimation error Theseworks are mainly on point-to-point MIMO case.

In wireless systems with multimedia applications, scheduling is an efficient way to ensurequality of service (QoS) requirements in terms packet delay, throughput requirement and packeterror probability requirement [34, 35] In [36] a cross-layer design for multi-user scheduling atthe data link layer is developed to provide guaranteed quality-of-service (QoS) for multimediaapplications over wireless fading channels, in which the QoS is interpreted in terms of outage ofprobability of each user In [37], the users’ transmission rate and power are adapted based uponchannel state information as well as the buffer occupancy; the objective is to regulate both the long-term average transmission power and the average buffer delay incurred by the traffic Connectionsto the delay-limited capacity and the expected capacity of fading channels are discussed Yet,most of these works are designed for single antenna multi-user systems In a recent work on QoS-based scheduling design in multi-user MIMO system [38], the base station antennas are allocatedto users based on certain priority functions at each time slot The priority functions capture theuser QoS demands quantified in terms of throughput and delay Instead of providing a systematicframework to satisfy the QoS requirements, the scheduling in this work is designed to achieve atradeoff between throughput, delay and fairness with a simple priority-based scheduling scheme.

1.3 Motivation and Problem Statement

It is important to apply the cross-layer design framework in wireless systems However, mostof the existing works assume perfect CSI estimation or perfect feedback and the data rate of thephysical layer of the base station is commonly assumed to be continuously adaptive to the CSIT.These assumptions are not practical in most wireless systems Moreover, the conventional measureof the total system ergodic capacity may not be too meaningful in the presence of imperfect CSITsince there may be capacity outage during the transmission To take into consideration of the

potential packet outage, we define the average system goodput as the optimization objective, which

measures the average total b/s/Hz successfully delivered to the receivers.

In short, there are still lots of open issues in the cross-layer scheduling 2 in user antenna systems Some of them are listed below:

multi-• In practice, the CSIT could never be perfect and this shall greatly affect the scheduler’s

performance What is the effect of CSIT imperfectness on the system capacity with thenaive space-time scheduler (designed for perfect CSIT), and how to obtain robust schedulingperformance by taking the CSIT error statistics into the cross-layer design pose a problem.

• Practical physical layer can only support a discrete set of rates due to the finite choice of

error correction encoders and discrete level constellations Given that we have to support

Q transmission modes and have only imperfect CSIT available, what throughput (specific

channel encoder rate and modulation constellation) to choose and how to determine the righttransmission mode at the base station becomes a challenging problem.

• Most of the existing cross-layer scheduling designs assumed homogeneous user type (pure

delay-tolerant data application), which is not a realistic assumption for modelling next ation wireless multimedia traffic having heterogeneous classes How to design a cross-layerscheduler to exploit the spatial multiplexing gain as well as the multi-user selection diversity

gener-2The cross-layer scheduler in this thesis refers to the multi-user scheduling that exploits the spatial multiplexinggains and the multi-user selection diversity gain through the knowledge of CSIT at the base station.

gain, and at the same time maintain the delay requirements of the delay sensitive users is stillan open problem.

In this thesis, we will focus on the three issues mentioned above and propose schedulers withrobust performance and QoS guarantees (in terms of delay constraints).

1.4 Thesis Research and Contributions

This thesis presents a study on cross-layer (joint MAC-PHY layer) space time scheduling

de-sign in multi-user MIMO wireless systems with a multi-antenna base station and K single-antenna

mobiles We impose different physical layer and network layer constraints which include averagepower, linear transmit processing (Zero-forcing or MMSE beamforming), imperfect CSIT, finiterate set, and heterogenous delay constraints.

Our main contribution is to propose a systematic framework to address the cross-layer ing problem in the presence of outdated CSI or imperfect CSI The objective is to maximize thetotal system goodput (instead of throughput when outage is considered) under average total powerconstraint and linear transmit constraint When heterogeneous applications (with different delayconstraints requirement) are considered, the design utility maximizes the total system throughputsubject to the delay constraint such that all the delay requirements are satisfied.

schedul-After presenting the background knowledge in Chapter 2, we shall first investigate the uplinkcross-layer design for multi-antenna systems with outdated channel state information in Chapter3 We consider a multi-user single-input multiple-output (SIMO) system with one base station

(with NRreceive antennas) and K mobile users (each with single transmit antenna) The

multi-user physical layer is modeled based on information theoretical framework and the cross-layerdesign can be cast as an optimization problem We found that with outdated CSI, there is signif-icant degradation in the spatial multiplexing and multi-user diversity gain due to potential packettransmission outage as well as mis-scheduling Two heuristic but effective schemes, namely therate quantization and rate discounting, are proposed to obtain robust scheduling performance Itis well-known that rate quantization imposes system capacity loss in systems with perfect CSI.

However, we found that the rate quantization in scheduling can enhance the system goodput androbustness in the presence of outdated CSI.

In Chapter 4, the downlink scheduling and rate adaptation are investigated in multi-user input single-output (MISO) systems with imperfect CSIT and finite rate set constraints We pro-pose a systematic analytical design framework to address the design issues regarding rate adapta-tion and robust multi-user scheduling based on information theoretical approach Due to the imper-fect CSIT, there is potential packet outage We formulate the cross-layer design as a mixed convex

multiple-and combinatorial optimization problem to maximize the average system goodput with respect to

the imperfect CSIT statistics and the discrete rate set constraint By applying a tight Chi-squareapproximation on the outage probability, we obtain a closed-form solution for the rate and poweradaptation for any given target packet error probability (PER) Numerical results demonstrate that,by considering the statistic of CSIT errors into the design, the proposed scheduling scheme pro-vides significant performance enhancement.

In Chapter 5 and 6, we shall take a different view by focusing on the design and performanceanalysis of cross-layer schedulers targeted for heterogenous user types with mixed voice and dataapplications Specifically, we consider a wireless multimedia system with a base station (equipped

with nT transmit antennas) and two classes of single-antenna client users (running delay sensitivevoice application and delay insensitive data application) In Chapter 5, we shall propose a low-complexity scheduler for the heterogeneous user applications, in which priority is heuristicallygiven to the delay sensitive voice users Multi-user selection diversity and spatial multiplexing arethereafter exploited among the remaining resource The performance of the proposed schedulerand the interaction between the data users (which are bursty) and the VoIP users (which are delaysensitive) are thoroughly studied It is demonstrated that the proposed heterogeneous schedulerensures a stable quality of service for VoIP users in the presence of burstydata traffic In Chapter6, an analytical cross-layer design framework is proposed for the multi-user multi-antenna sys-tems with heterogeneous delay requirements The proposed scheme optimally exploits the spatialmultiplexing gain and the multi-user selection diversity gain in terms of maximizing the systemcapacity with delay constraints satisfied.

Chapter 2Background

2.1 Wireless Fading Channel - Characterizations and Mitigation

In wireless transmission, a signal can travel from the transmitter to the receiver over ple reflective paths This phenomenon is referred to as multi-path propagation Due to multiplepropagation paths, the received signals consist of multiple delayed and attenuated copies of thetransmitted signal This phenomena actually places fundamental limitations on the performance ofwireless communication systems [2, 39, 40] The degradation categories due to wireless transmis-sion and the typical mitigation techniques to counteract the degradation shall be reviewed in thissection.

multi-As illustrated in Fig 2.1, there are typically two types of fading effect that characterize mobilecommunications: large-scale propagation loss and small-scale multipath fading [39] Large-scalepropagation loss is caused by path loss due to motion over large areas and shadowing due tochanges in terrain or obstacles, which usually fluctuates in a slow way On the other hand, small-scale multipath fading characterizes the variation of the received signal strength It is caused by theconstructive or destructive superposition of the multiple paths depending on the time varying pathattenuation and delay, which usually varies rapidly and dramatically The received signal throughwireless channel typically experiences both types of fading with small-scale fading superimposedon large-scale propagation loss.

In wireless systems, the analysis on fading models plays an important role The large-scalefading (path loss and shadowing) model is used for system planning, power control, link budget and

Varianceabout themean

Timingspreading of

the signal

Timevariance ofthe channel

Frequency selective

Fast fadingSlow fading

Figure 2.1 Wireless fading channel

cell coverage analysis While the small-scale fading (multi-path fading) analysis is often targetedfor physical layer modem design such as coder, modulation, interleaver, etc [2].

2.1.1 Large-Scale Fading

Large-scale fading represents the average signal power attenuation (pass loss) due to motionover large areas and shadowing due to changes of prominent terrain (hills, forests, billboards,clumps of buildings, etc.) between the transmitter and receiver The statistics of large-scale fadingprovide a way of computing an estimate of path loss as a function of distance Combing the path

loss and the shadowing effect, we have the total path loss at a distance d expressed in dB given by:

P L(d) = P L(d0) + 10n log

the signal bandwidth W (approximated by 1/Ts) is larger than the channel coherent bandwidth

(approximated by 1/Td), in which the signal’s spectral components will be affected by the channelin a different (selective) way.

On the other hand, a channel is said to be frequency-nonselective or flat fading if Td< Ts.In this case, all of the received multi-path components of a symbol arrive within the symbol time

duration; hence, the components are not resolvable and there is no channel-induced ISI distortion.However, there is still performance degradation since the un-resolvable phase components mayadd up destructively to yield a substantial reduction in signal-to-noise ratio (SNR).

From the time variance of the channel point of view, a wireless channel can be classified aseither fast fading or slow fading When viewed from the time domain, a channel is referred to as

fast fading whenever Tc< Ts, where Tc is the channel coherence time (a measure of the expected

time duration over which the channel’s response is invariant) and Ts is the symbol time In fastfading channel, the fading character will change several times during a symbol time duration.Fast fading can cause the distortion of the baseband pulse shape because the received signal’scomponents are not all highly correlated throughout time Such distorted pulses typically causesynchronization problems, such as failure of phase-locked-loop (PLL) receivers The fast fadingthus leads to an irreducible bit-error-rate (BER) When viewed in the Doppler shift domain, a

channel is called fast fading if the symbol rate or signal bandwidth W is less than the fading rate

fd(the Doppler frequency shift) Notice that there exists an approximate relationship between the

channel coherence time Tcand Doppler frequency shift fd: Tc≈ 1

Conversely, a channel is referred to as slow fading if Tc> Ts Here, the time duration for whichthe channel behaves in a correlated manner is longer than the symbol time Thus, the channel stateis expected to remain virtually unchanged during the time a symbol is transmitted.

The small-scale multi-path fading in wireless channel will either cause loss in SNR (such as inslow fading or flat fading) or introduce severe signal distortion with irreducible BER floor (suchas in frequency selective fading or fast fading), which turns out to be the major challenge for thehigh-speed and reliable communications in wireless systems.

• Adaptive equalization (e.g decision feedback equalizer (DFE)), Maximum likelihood

se-quence estimation equalizer (MLSE) or Viterbi equalizer

• Spread spectrum (SS) - direct sequence spread spectrum (DS/SS), frequency-hopping spread

spectrum (FH/SS) and Rake receiver

• Orthogonal frequency division multiplexing (OFDM)

• Pilot signal to provide channel sate information

For fast fading distortion

• Robust modulation (incoherent or differentially coherent) that does not require phase

track-ing, and reduce the detector integration time

• Increase the symbol rate by adding signal redundancy

• A polyphase filtering technique used to provide time-domain shaping and duration extension

in OFDM systems

Mitigation to combat loss in SNR

• Diversity techniques including time diversity, frequency diversity, spatial diversity and

po-larization diversity

• Error correction coding

• Spread spectrum and Rake receiver

The mitigation methods mentioned above turn out to be efficient techniques in physical layerto combat the fading effect.

2.2 Cross-Layer Scheduling and Adaptive Design in Multi-user Wireless work

Net-As shown in Fig 2.2, a typical communication system can be modeled by a layered approach(physical layer, MAC layer, network layer, transport layer and application layer) where each layerhas a specific role and performance measure.

The traditional approach of communication system design is based on an isolated procedurewhere the optimization for each layer is obtained by the design within the layer [7] In other words,there is no cross-optimization between layers This isolated approach is valid and reasonable fortime invariant channel However, for the time varying wireless channel, the adaptation techniquesat each layer and cooperation between layers are needed to exploit the time-varying nature of thechannel and enhance the wireless system performance.

In this thesis, we shall investigated the cross-layer scheduling involving physical layer andMAC layer joint design.

2.2.1 Adaptive Design in Physical Layer

The role of the physical layer is to deliver information bits across a wireless channel in anefficient and reliable manner given a limited resource Resource in this context refers to the band-width and transmit power; performance refers to the bit rate (bits per second) and the frame errorrate The design objective is generally to increase the bit rate at a given target frame error rate withfixed bandwidth and power budget MIMO technology and channel adaptive design are two verypromising approaches to dealing with the harsh wireless transmissions and achieve high bit rateand low frame error transmission.

Depending on the level of channel state information available at the transmitter and receiver, wehave different transmission and receiver strategies for the MIMO systems such as space time blockcoding (STBC), spatial multiplexing with layered space time structure (V-BLAST and D-BLAST),beamforming and eigenmode transmission [12, 14, 41, 42] With the availability of perfect CSI atthe MIMO transmitter and possibly at the receiver, the optimal precoder, power adaptation (in both

Physical LayerMAC LayerNetwork LayerTransport LayerApplication Layer

Adaptive modulationRate and power assignmentSource coding and packetization

Congestion optimized routingCongestion distortion optimization

Figure 2.2 System diagram for the cross-layer design framework

the temporal and spatial domains) and rate adaptation can be performed to achieve maximum tem performance [43, 44] In fact, the channel adaptive technologies in multiple antenna wirelesssystems have been shown to contribute significant performance gains and therefore has receivedtremendous attention in the research community more recently [7]

sys-2.2.2 MAC Layer Scheduling Model

A MAC layer usually consists of a request collection sublayer and a scheduling sublayer [7].The request collection sublayer is responsible for the collection of payload transmission requestsfrom the active users On the other hand, the scheduling sublayer is responsible for the prioritiza-tion and the allocation of resource among the competing users Conventional MAC layer designsfor wireless systems follow the isolated approach where there is no cross-optimization across thephysical layer and the MAC layer For instance, a lot of research effort has been devoted to de-signing efficient request collection sublayer Examples are slotted ALOHA, dynamic TDMA, andpacket-reservation-multiple-access (PRMA) The scheduling sublayer is essentially very simple inthe first-come-first-serve sense.

In this work, the MAC layer scheduling algorithm is responsible for the allocation of channelresource at every fading block The system time is partitioned into frames as illustrated by Fig.2.3(a) At the beginning of every frame, the base station estimates the channel matrix from theparticipating mobile users, and passes CSI to the scheduling algorithms in the MAC layer as il-lustrated in Fig 2.3(b) The cross-layer scheduler is typically designed to maximize the average

system throughput or proportional fairness [45] The output of the scheduler consists of an

admis-sible set, A = {k ∈ [1, K] : pk> 0} (the set of user indices with non-zero power allocated at the

current fading block), the corresponding transmission power allocation {pk} and the transmission

rate allocation {rk} for the selected users The scheduled data rates are broadcast on the downlink

common channels to all mobile users and the downlink payload is transmitted at the scheduledrate This MAC layer model shall be used throughout the thesis.

Channelestimation

A fading block

User 1preamble

User 2preamble

User NTpreamble

Downlink payload - user1

Downlink payload - user2

Downlink payload - userN

Scheduling results(user list; rate

(a) System timing of access and frame format

Admissible Set

Space time scheduler

(b) Model of the Scheduling Module

Figure 2.3 Block diagrams of the MAC layer scheduling

2.3 Linear Transmit-receive Processing in Multi-antenna Base Station

Since mobile devices are battery-powered, we would like to push all the multi-user processingcomplexity to the base station Hence, we would like the transmit/receive strategy to satisfy thefollowing constrains.

C1 Linear Processing Constraint at the Base Station: For implementation feasibility, we quire the signal processing at the link layer of the base station transmitter to be linear com-

re-plexity in terms of the number of antenna nTand the number of user K.

C2 Complexity Constraint at the Mobile Devices: For simple mobile implementation, we quire the mobile doesnot need to perform multi-user interference cancellation.

re-C3 Total Average Downlink Transmit Power: We require the total transmit power from all

the nTantennas of the base station to be less than or equal to power constraint P0 i.e.PnT

t=1Pt≤ P0 where Ptis the average transmit power of the t-th antenna over the coding

weight for user k Hence, the received signal at the kth mobile terminal after linear processing at

the base station is given by:

yk = hk

i=1√

where hkis real channel gain vector (1 × nT) between user k and the base station antennas; zkis the additive white Gaussian noise (AWGN); uiis the encoded information symbol for the i-th

We shall investigate two common types of linear processing, namely the zero-forcing (ZF) [46]and minimum mean-square error (MMSE) [47] The calculation of the beamforming weights shall

be based on the estimated CSIT ˆH = {ˆh1, , ˆhK} at the base station The imperfect CSIT at the

base station can be modeled as:

where hkis the real channel gain vector for user k; ∆hkdenotes the nR× 1 CSI error vector The

entries of CSI error ∆hkcan be modeled as i.i.d complex Gaussian variables with zero mean and

variance σ2 The channel estimation error model shall be further elaborated in subsequent chapters.

2.3.1 Zero-forcing Processing

For ZF processing, the linear weights W are selected according to the estimated CSIT ˆhkwith

the orthogonality constraints:

and normalization constraints:

where (·)∗is the complex conjugate transpose operation; A = {k : pk> 0} is the set of admitted

users in the each scheduling slot.

Since there are nTantennas at the base station, at most nT spatial channels can be createdbetween the base station and the mobile stations Hence, we pose a constraint on the cardinality of

the admitted user set A:

CodingandModu 1

CodingandModu 2

CodingandModu KW1= [1, 2NR1]u

Mobile K.

BeamformingMatrixEstimated [h1, , hK]

WnT= [1, 2NRk]W2= [1, 2NR2]

Base Station with Isolated Coding and ZFBF strategyIsolated coding

Figure 2.4 Linear downlink transmit strategy with isolated encoding and beamforming.

where (·)−1 the inverse operation; ekis the nT× 1 vector with k-th element to be one and others

0; ˆHAis the aggregate channel matrix (nT× |A|) of the admitted user set.

If |A| < nT, it means there are more spatial degrees of freedom (contributed by number oftransmit antennas) than the number of equations in (2.4) and (2.5), we could further specify theweight wk by maximizing the received SNR per user Hence, the problem of determining theoptimal beamforming weight is summarized below:

Problem 2.1 Maximize w∗k

khˆk´wksuch that ˆhjwk= 0 ∀j ∈ A, j 6= k and w∗

kwk= 1.Let BA,kbe a nT× (nT− |A| + 1) dimensional matrix with columns spanning the (nT− |A| +

1) dimension orthogonal subspace or null space of the (|A| − 1) dimension interference spacespanned by {ˆhj, j ∈ A, j 6= k} That is:

Observe that constraint (2.8) is satisfied if and only if wkbelongs to the orthogonal subspace

spanned by the columns of BA,k Hence, wk = BA,ku for some (nT− |A| + 1) dimension

complex column vector u The optimization problem in Prob 2.1 reduces to:Problem 2.2 Maximize u∗¡

Notice that the solution involves matrix inversion and SVD However, the size of the matrixinvolving inversion B∗

A,kBA,kis (nT− |A| + 1) × (nT− |A| + 1) which is usually quite small for

moderate values of nT(For example, nT≤ 4 for practical applications) Thus, the complexity of

SVD and matrix inverse is limited.

2.3.2 Transmit MMSE Processing

For MMSE processing, the linear weights W = {wk: k ∈ A} are selected to minimize thetotal normalized mean-square error J given by:

Substituting (2.2) and (2.3) into (2.9) and after some manipulations, the total MSE J is given

J = tr

HW − I

HW − I

+ σ2W∗WΛ2+ Ii

|ˆhkwk− 1|2+X

+ σ2P0+ |A|, (2.10)

where P0 is the total power constraint at the base station Hence, the optimal MMSE weights wkcan be obtained by standard optimization technique in a decoupled manner by:

∂J/∂wk =Ã

wk− ˆh∗

k+ λkwk= 0,

where λkis a Lagrange multiplier for the constraint kwkk2 = 1 and the MMSE weight is given by:

wk =Ã

ihˆi+ λkI!−1

where (A)−1refers to the inverse of matrix A.

The ZFBF beamforming and MMSE beamforming weights obtained in this section shall beutilized in subsequent chapters.

Chapter 3

Uplink Scheduling Design with Outdated CSI 3.1 Overview

In this chapter, we attempt to investigate the effect of outdated CSIT on the uplink direction

of multi-user multi-antenna systems We consider a wireless system with K mobile clients (eachwith a single antenna) and a base station (with nRreceive antennas) The multi-user physical layeris modeled using an information theoretical framework and the cross-layer scheduling design canbe cast as an optimization problem When the CSIT knowledge at the transmitters is perfect,there is significant spatial multiplexing gain and multi-user diversity gain However, as we shallillustrate in this chapter, there is significant degradation in the system performance when the CSITis outdated This is due to the problem of packet outage 1 and mis-scheduling To address these

problems, we propose two simple but effective empirical solutions, namely the rate quantizationand rate discounting For instance, it is well-known that rate quantization imposes system capacity

loss in systems with perfect CSI However, we found that rate quantization can enhance robustnesson system performance with respect to outdated CSIT.

1Note that the potential packet outage is due to the outdated CSIT and hence, the transmitter does not have exactknowledge of the instantaneous capacity There will be packet outage despite the use of powerful error correctioncoding.

3.2 Multi-user SIMO System Model

3.2.1 Channel Model with Outdated CSIT

As shown in Fig 3.1, the channel fading coefficient between the k-th mobile terminal and nRantennas at base station is characterized by the nR× 1 dimension vector hk= [h1,k, , hnR,k]T,

where hr,k∀r ∈ [1, nR], k ∈ [1, K] are modeled as i.i.d complex Gaussian with unit variance.

The received signal at the base station is given by:

where Xkis the transmit symbol from the k-th mobile terminal; Z is the nR×1 dimension Gaussian

noise with covariance given by σ2

zInRand Y is the nR× 1 dimension vector of received symbols

at the base station comprising of nRantennas.

We assume that perfect channel estimation is performed at the base station based on the

dedi-cated pilots from the K mobiles [48] Based on the estimated CSI, the cross-layer scheduler at the

base station determines the user selection, power allocation as well as rate allocation and broadcast

the allocation for the current scheduling slot to the K mobiles with a delay In other words, the CSI

used by the cross-layer scheduler may be outdated when the selected mobiles attempt to transmitthe payload on the scheduling slot Let hkbe the current CSI of user k and ˆhkbe the outdated CSI.We have:

where ∆hkdenotes the nR× 1 CSI error vector The entries of CSI error ∆hkcan be modeled as

i.i.d complex Gaussian variables with zero mean and variance σ2.

3.2.2 Multi-user Uplink Physical Layer Model

In general, the performance of physical layer predominates that of the scheduling algorithmand overall system Before the scheduling problem can be formulated, we need to establish aconvenient physical layer model To isolate the physical layer from implementation details such as