mimo ofdm

Adaptation in Multiple Input Multiple OutputSystems with Channel State Information at

Transmitter

JINLIANG HUANG

Licentiate ThesisStockholm, Sweden 2007

TRITA ICT/ECS AVH 07:04ISSN 1653-6363ISRN KTH/ICT/ECS AVH-07/04-SEISBN 978-91-7178-703-3

KTH School of Information andCommunication Technology

SE-16440 StockholmSWEDEN

Akademisk avhandling som med tillstånd av Kungl Tekniska högskolan framläggestill oentlig granskning för avläggande av Teknologie Licentiatexamen i Elektron-ik och Datorsystem fredag den 1 juni 2007 klockan 14:00 i sal E, Forum IT-Universitetet, Kungl Tekniska högskolan, Isajordsgatan 39, Kista.

© Jinliang Huang, Juni 2007

Tryck: Universitetsservice US AB

Abstract

The thesis comprises two parts: the rst part presents channel-adaptivetechniques to achieve high spectral eciency in a single user multiple-inputmultiple-output (MIMO) system; the second part exhibits a programmableand recongurable software-dened-radio workbench (SDR-WB) in the Mat-lab/Octave environment that accommodates a variety of wireless applications.

In an attempt to achieve high spectral eciency, an adaptive modula-tion technique is applied at the transmitter to vary the data rate dependingon the channel state information (CSI). To further enhance the spectral e-ciency, adaptive power allocation schemes are applied in the spatial domainto adjust the power on every transmit antenna. We analyze several powercontrol schemes subject to a peak power constraint to maximize the spectraleciency given an instantaneous target bit-error-rate (BER). A novel powerallocation strategy is proposed to achieve high spectral eciency with rel-atively low complexity. In addition, adaptive techniques that switch acrossdierent MIMO schemes enables even higher spectral eciency by choosingthe scheme with the highest spectral eciency for a given signal to noiseratio (SNR). We propose a new method to switch between spatial multiplex-ing with zero-forcing (ZF) detection and orthogonal space-time block coding(OSTBC). This is done by exploiting closed form expressions of the spectralecienciesdiscrete rate spectral eciency (DRSE)and nding the crossingpoint of the two curves of spectral eciency. The proposed adaptation schemeadds little complexity to the transmitter since it requires only statistical in-formation of the channel, which does not change as time evolves.

Software Dened Radio (SDR) has received more and more interest re-cently as a promising multi-band multi-standard solution for transceiver de-sign. In order to support various wireless applications, we build a pro-grammable and recongurable workbench, namely the SDR-WB, in Mat-lab/Octave environment. The workbench is functionally modularized intogeneric blocks to facilitate fast development and verication of new algo-rithms and architectures. The modulation formats that are currently sup-ported by the SDR-WB are MIMO, Orthogonal frequency-division multiplex-ing (OFDM), MIMO-OFDM, DS-CDMA.

keywords: MIMO, adaptive modulation, power allocation, spectral e-ciency, CSI.

iii

Acknowledgement

I would like to express my sincere gratitude to my advisor, Docent Svante Signell,for giving me a chance to be a graduate student in the Department of ECS andleading me into this wonderland of wireless communications, for his enlighteningguidance and constant support during these years, especially when I experiencedthe toughness of setbacks somewhere along the line.

I owe many thanks to Prof. Mohammed Ismail, Prof. Lirong Zheng and DocentAna Rusu for bringing me into the RaMSiS group. I gratefully acknowledge allmy former and present colleagues in RaMSiS group and ECS lab, Dr. ZhonghaiLu, Dr. Steen Albrecht, Dr. Xinzhong Duo, Dr. Wim Michielsen, Jad Atallah,Sleiman Bou Sleiman, Saul Rodriguez, Dr. Adam Strak, Majid Baghaei Nejad,Martin Gustafsson, Delia Rodriguez, Yajie Qin, Jun Zhu, Dr. Yiran Sun, XiaolongYuan, Roshan Weerasekera, for creating a pleasant working environment. Gratefulacknowledgement to Jinfeng Du for all the inspiring suggestions and discussions inthe work, and also for proofreading the thesis manuscript.

Many thanks to the Swedish Foundation for Strategic Research (SSF) for nan-cially supporting me under the RaMSiS program.

With no less respect, I gratefully thank Lena Beronius, Robert Rönngren, Ag-neta Herling for being patient with me and my long list of questions.

Also, I'm grateful to all my friends in Sweden, without them, life would be asdark as the winter of Stockholm.

Last, but not the least, I'm especially grateful to my parents for their encour-agement and unconditioned support to me in all my decisions.

v

Notation and used symbols

Throughout this thesis, the following notations will be used:

x bold face lower-case letters denote column vectors

A bold face upper-case letters denote matrices

ai the ith column vector of A

aj the jth row vector of A

[A]ji, Aji the (j, i)th element of A

I the identity matrix

(·)∗ the complex conjugate transpose (Hermitian)

(·) the complex conjugate

(·)T the transpose

‖x‖2, ‖x‖ the Euclidean norm of x

‖A‖F the Frobenius norm of A,‖A‖2F = tr(AA∗)

vec(A) the vectorization operator,vec stacks the columns of A into a vector, i.e.

vec(A) =

a1

...an

vii

Notation and used symbols

A† the Moore-Penrose pseudoinverse of AIf the columns of A are linearly independent, thenA† = (A∗A)−1A∗

A−1 the inversion of a non-singular square matrix, A−1A = I

(x)+ maxx, 0

tr the trace of matrix

diag(x1, . . . , xn) a diagonal matrix with x1, . . . , xn on the main diagonal.E(·) the expected value of a random variable

X⊗Y the Kronecker product, X⊗Y =

X11Y . . . X1nY... . . . ...

Xm1Y . . . XmnY

CN (µ, σ2) the circularly symmetric complex Gaussian random variablewith mean µ and variance σ2.

Here follows a list of some commonly used symbols in the thesis:

Nt the number of transmit antennas

Nr the number of receive antennas

Nmin Nmin = minNt, Nr

Nmax Nmax = maxNt, Nr

Ns the number of singular value channels that are used to deliver data

PT the total transmit power

σ2n the variance of Gaussian white noise

Hw the complex valued i.i.d. Rayleigh fading channel

K the Ricean K-factor

ρtx, ρrx the spatial correlation coecients at the transmitter and the receiver

viii

γ0 the system SNR dened as γ0 =PT

σ2n

λi the ith eigenvalue of HH∗

Γk the SNR thresholds for adaptive modulation

ix

Abbreviations and Acronyms

MIMO Multiple Input Multiple Output

SISO Single Input Single Output

OFDM Orthogonal Frequency Division Multiplexing

DMMT Discrete Matrix Multitone

CSI Channel State Information

CSIT Channel State Information at Transmitter

CSIR Channel State Information at Receiver

CRSE Average Continuous-rate Spectral Eciency

DRSE Average Discrete-rate Spectral Eciency

SVD Singular Value Decomposition

OSTBC Orthogonal Space-Time Block Coding

ZF Zero Forcing

SDR-WB Software Dened Radio WorkBench

TAS Transmit Antenna Selection

i.i.d. Independent and Identically Distributed

p.d.f. Probability Density Function

d.o.f. Degree Of Freedom.

xi

Contents

Notation and used symbols vii

Abbreviations and Acronyms xi

Contents xii

List of Figures xiv

1 Introduction 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Contributions and outline . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Overview of MIMO Technology 72.1 Signal model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 MIMO schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3 Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.A Least square method for ZF . . . . . . . . . . . . . . . . . . . . . . . 16

3 Adaptive schemes for MIMO systems with SVD 193.1 Constant-power variable-rate techniques . . . . . . . . . . . . . . . . 203.2 Variable-power variable-rate techniques . . . . . . . . . . . . . . . . 243.3 Further discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.4 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4 Adaptive schemes for MIMO systems with OSTBC and ZF 374.1 DRSEs of MIMO systems with OSTBC . . . . . . . . . . . . . . . . 384.2 DRSEs of MIMO systems with ZF detection . . . . . . . . . . . . . . 424.3 A low complexity adaptation scheme . . . . . . . . . . . . . . . . . . 454.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.A The p.d.f. of the eective SNR of OSTBC in correlated Rayleigh

fading channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504.B Asymptotic p.d.f. of the eective SNR of OSTBC . . . . . . . . . . . 52

xii

5 Software Dened Radio Workbench (SDR-WB) 555.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555.2 Workbench architecture . . . . . . . . . . . . . . . . . . . . . . . . . 555.3 Control ows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595.4 Case study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

6 Conclusions and future work 656.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

Bibliography 67

xiii

List of Figures

1.1 Block diagram of MIMO systems . . . . . . . . . . . . . . . . . . . . . . 21.2 A comparison of capacities with CSIT and without CSIT . . . . . . . . 3

2.1 Capacities of MIMO by using dierent schemes in 2×2 i.i.d. Rayleighfading channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.1 A block diagram of adaptive MIMO . . . . . . . . . . . . . . . . . . . . 203.2 Discrete-rate spectral eciencies achieved by svd and beamforming in

2× 2 i.i.d. Rayleigh channel with target BER 10−3 . . . . . . . . . . . . 243.3 A comparison of the capacity and the spectral eciencies . . . . . . . . 253.4 DRSEs using capacity-optimal WF and continuous-rate optimal WF in

a 4× 4 i.i.d. Rayleigh fading channel . . . . . . . . . . . . . . . . . . . . 273.5 Spectral eciencies of power control schemes in a 4 × 4 i.i.d Rayleigh

fading channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.6 Power allocated to the 1st singular value channel in 4×4 i.i.d. Rayleigh

fading channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.7 Spectral eciencies of power control schemes in a 4× 4 spatially corre-

lated Rayleigh fading channel, with ρtx = ρrx = 0.5 . . . . . . . . . . . . 333.8 Spectral eciencies of power control schemes in a 4 × 4 Ricean fading

channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.9 Comparison of greedy allocation and QoS-based WF in dierent channel

conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.1 A block diagram of adaptive MIMO switching between dierent schemes 384.2 spectral eciencies achieved by OSTBC in 2×Nr i.i.d Rayleigh fading

channel with Nr = 2, 4, 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.3 spectral eciencies achieved by OSTBC in 2 × Nr spatially correlated

Rayleigh fading channel with ρtx = 0.5 . . . . . . . . . . . . . . . . . . . 424.4 spectral eciencies achieved by ZF in 2 × Nr i.i.d. Rayleigh fading

channel with Nr = 2, 4, 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . 444.5 spectral eciencies achieved by ZF in 2×Nr spatially correlated Rayleigh

fading channel with ρtx = 0.5 . . . . . . . . . . . . . . . . . . . . . . . . 454.6 Switching point of ZF-OSTBC in a 2× 2 i.i.d. Rayleigh fading channel 46

xiv

List of Figures

4.7 Spectral eciencies achieved by static adaptation and dynamic adapta-tion in 2×Nr i.i.d. Rayleigh fading channel . . . . . . . . . . . . . . . . 47

4.8 Crossing points of the spectral eciencies in 2×Nr i.i.d. Rayleigh fadingchannel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.9 Spectral eciencies achieved by OSTBC and ZF in 2×2 Rayleigh fadingchannel with dierent correlation coecients . . . . . . . . . . . . . . . 49

4.10 Spectral eciencies achieved by OSTBC and ZF in 2×6 Rayleigh fadingchannel with dierent correlation coecients . . . . . . . . . . . . . . . 50

4.11 The p.d.f. of eective SNR when γ0 = 20dB . . . . . . . . . . . . . . . . 51

5.1 Block diagram of the modularized workbench . . . . . . . . . . . . . . . 565.2 File structure of the workbench . . . . . . . . . . . . . . . . . . . . . . . 575.3 Flowcharts in the run phase . . . . . . . . . . . . . . . . . . . . . . . . 605.4 4× 4 BER in frequency-selctive Rayleigh fading channel . . . . . . . . . 625.5 4× 4 throughputs in frequency-selctive Rayleigh fading channel . . . . . 625.6 Number of bits loaded on sub-carriers . . . . . . . . . . . . . . . . . . . 635.7 2× 2 BER in at Rayleigh fading channel . . . . . . . . . . . . . . . . . 63

xv

Chapter 1

Introduction

1.1 Background

Multiple antenna systemsIn point-to-point wireless links, multiple-input multiple-output (MIMO) systemsthat utilize multiple antennas at transmitter and receiver can considerably increaselink capacity as well as link reliability compared to conventional single-input single-output (SISO) systems [16]. The advantages come from spatial diversity whichare provided by the multiple antennas together with the scattering environmentsurrounding the transmitter and the receiver. If the transmitter and the receiverare equipped with Nt and Nr antennas respectively, the number of scalar channels(sub-channels) that are created by singular value decomposition (SVD) [1] is

Nmin = minNt, Nr (1.1)

in a rich scattering environment1. If separate streams of data are transmittedacross the sub-channels or singular value channels, the link capacity achieved byhaving multiple antennas is Nmin times the capacity of SISO. This is called spatialmultiplexing gain [1, 2, 7]. A denition of the spatial multiplexing gain is givenin [8]:

r = limSNR→∞

R

log SNR , (1.2)

where R is the data rate. On the other hand, one can deliver the same data streamon dierent antennas to explore high diversity gain [4, 5], which is dened as [8]:

d = − limSNR→∞

log Pe

log SNR , (1.3)

1otherwise,Nmin = minNt, Nr, Np, where Np is the number of multipath provided by thescatters [12].

1

Introduction

S/P

mod

mod

MIMO

encoder

MIMO

decoder

demod

P/S

demod

channel

coder

channel

coder

channel

decoder

channel

decoder

Figure 1.1: Block diagram of MIMO systems

where Pe is error ratio. For instance, orthogonal space-time block codes (OSTBC)[4] can provide a diversity gain of 4 in a 2× 2 system.

Furthermore, the spatial multiplexing gain and the diversity gain can be achievedsimultaneously in a given channel, but there is a tradeo between how much gaincan one get [8, 9].

A general block diagram of a MIMO system is illustrated in Figure 1.1, whereMIMO encoder and MIMO decoder accommodate various MIMO schemes, such asSVD and OSTBC that were mentioned previously.

Channel adaptive technologiesIt is well-known that the channel capacity C gives a threshold value that for anyrate R < C, there exists at least one channel encoder and channel decoder thatachieves arbitrarily small error probability. If channel state information (CSI) isavailable at the receiver and the transmitter does not know the channel information,it is best to distribute the transmit power PT equally among the antennas and theergodic capacity is written as [1]:

CCSIR = E

Nmin∑

i=1

log(

1 +PT λi

Ntσ2n

), (1.4)

where λi is the ith eigenvalue of HH∗, σ2n is the noise power. On the other hand, if

the CSI is also available at the transmitter (CSIT), the optimal power allocation canbe derived by applying the well-known waterlling. Let's assume that the channelcoherence time is larger than the interval of updating CSI at the transmitter, hencethe transmitter has perfect CSI and the power allocated on every sub-channel isadjusted based on the instantaneous CSIT. Then the ergodic capacity can be writtenas [1]:

CCSIT = E

Nmin∑

i=1

log(

1 +Piλi

σ2n

), (1.5)

2

1.1 Background

−5 0 5 10 15 20 25 300

5

10

15

20

25

30

35

SNR [dB]

capa

city

[bps

/Hz]

CSITno CSIT

Figure 1.2: A comparison of capacities with CSIT and without CSIT

where Pi is the power allocated on the ith sub-channel obtained by using the well-known waterlling:

Pi =(

ξ − σ2n

λi

)

+

, (1.6)

where (x)+ = maxx, 0 and ξ =1

µ ln 2is the water-level that is given by the

criterionNmin∑

i=1

Pi = PT . (1.7)

The improvement by having the CSIT is shown in Figure 1.2, in which an evidentenhancement is shown at low SNRs.

Unfortunately, these capacities are not achievable in practice due to that theyassume Gaussian signals and innite coding length for the channel encoder. To get aclose performance to the committed capacities shown in Figure 1.2, the transmittermust assign a proper rate and suitable amount of power on every sub-channel basedon the CSIT, e.g. sub-channel gains and noise variance. Furthermore, a powerfulchannel coding scheme have to be applied, e.g., LDPC code. In this work, we do notconsider the channel coding, but focus on adaptive modulation and power schemes.

3

Introduction

Besides the rate and power adaptation, transmitter can also select a suitableMIMO scheme based on the CSIT to obtain either higher rate or lower error ratio[6163].

1.2 Contributions and outlineIn this thesis, we aim at maximizing spectral eciency for a point-to-point wirelesslink equipped with multiple antennas. Adaptive modulation and adaptive powercontrol schemes are considered and a novel diversity/multiplexing switching methodis proposed to further enhance the spectral eciencies.

This dissertation is organized into six chapters. In more detail, the outline ofeach chapter is as follows:

Chapter 2We present the baseband signal models as well as the channel models for bothnarrowband MIMO systems and wideband MIMO-OFDM systems. Three MIMOschemes are briey reviewed, i.e., SVD, spatial multiplexing with ZF detection andOSTBC.

Part of the material was submitted to

Jinliang Huang, Svante Signell, On Diversity Order of Singular ValueDecomposition, accepted by SPWC 2007, London, June, 2007.

Chapter 3In this chapter, adaptive modulation and adaptive power control schemes are re-viewed. A novel power allocation is suggested in the context of peak power con-straint and instantaneous BER constraint, which exhibits near-optimal performancewith relatively low computational complexity.

Most of the material was published in

Jinliang Huang, Svante Signell, A Novel Power Allocation Strategy forFinite Alphabet in MIMO Systems, in Proc. IEEE VTC2006, Mel-bourne, May, 2006.

Chapter 4This chapter presents DRSEs of ZF and OSTBC, based on which an original lowcomplexity adaptation scheme is suggested to switch between ZF and OSTBC inan attempt to explore high spectral eciency.

The results of algorithm switching in an i.i.d. Rayleigh fading channel werepublished in

4

1.2 Contributions and outline

Jinliang Huang, Svante Signell, Adaptive MIMO Systems in 2× 2 Un-correlated Rayleigh Fading Channel, in IEEE Proc. WCNC2007, HongKong, Mar. 2007.

When the channel is spatially correlated Rayleigh fading, the results were sub-mitted to

Jinliang Huang, Svante Signell, On Spectral Eciency of AdaptiveMIMO Systems in 2× 2 Spatial Correlated Rayleigh Fading Channel,accepted by IEEE Sarno2007.

The results of DRSE in both i.i.d. Rayleigh fading channel and spatially corre-lated Rayleigh fading channel can be extended to the case with arbitrary numberof receive antennas, which were submitted to

Jinliang Huang, Svante Signell, On Spectral Eciency of Low-ComplexityAdaptive MIMO Systems in Rayleigh Fading Channel, submitted toIEEE Tran. Wireless Commun.

Chapter 5A recongurable software-dened-radio workbench (SDR-WB) in Matlab/Octaveenvironment is presented and it supports diverse wireless link applications, e.g.OFDM, MIMO, MIMO-OFDM, WCDMA.

Part of the workbench architecture was published in

Svante Signell, Jinliang Huang, A Matlab/Octave Simulation Work-bench for Software Dened Radio, In IEEE Proc. Norchip24, Linköping,Sweden, November 2006.

Part of the simulation results were published in

Jinliang Huang, Svante Signell, The Application of Rate Adaptationwith Finite Alphabet in MIMO-OFDM, IEEE Proc. ICICS2005, Bangkok,Thailand, Dec. 2005.

Chapter 6This chapter summaries the results of this dissertation and points out the possibleimprovements as well as several open problems for future work.

5

Chapter 2

Overview of MIMO Technology

Digital communication using multiple antennas has been receiving much attentionrecently [14] due to its substantial benets on spectral eciency and link reliabil-ity. A number of schemes have been suggested for MIMO systems and they mainlyfall into two categories: spatial multiplexing-based [1, 2] and diversity-based [4, 5].The spatial multiplexing-based schemes, e.g. VBLAST1 [2], SVD [1], are highlyspectrum ecient: they take advantage of spatial diversity of MIMO channels andcreates parallel sub-channels over which separate data streams can be transmitted;whereas diversity-based algorithms dedicate to build up channels with high diver-sity gain, e.g. OSTBC [4, 5]. A hybrid class of scheme that trades o betweenspatial multiplexing gain and diversity gain is also available, e.g. double space-timetransmit diversity (D-STTD) [9].

2.1 Signal model

NarrowbandIn a point to point narrowband MIMO system with Nt transmit antennas andNr receive antennas, the channel is assumed to be at fading. The discrete-timebaseband equivalent signal model can be written as:

y(n) = H(n)x(n) + z(n) (2.1)

where H(n) is an Nr × Nt complex-valued channel matrix. x(n) is an Nt × 1transmitted vector at time n subject to a peak power (PT ) constraint:

Nt∑

i=1

|xi|2 ≤ PT . (2.2)

1Vertical Bell Laboratories Layered Space-Time Architecture

7


y(n) is a Nr×1 received vector. z(n) is the vector of additive white Gaussian noisewith covariance σ2

nINr . The signal-to-noise ratio (SNR) is dened as:

γ0 =PT

σ2n

(2.3)

WidebandOrthogonal Frequency Division Multiplexing (OFDM) [10] can be employed inMIMO systems to increase the data rate by allowing data transmission over awide range of bandwidth [11]. Let M denotes the number of sub-carriers of oneOFDM symbol, then M + ν samples are transmitted at each antenna during oneOFDM symbol, where ν is the length of cyclic prex. The Nt×(M +ν) transmittedsamples for the nth OFDM symbol can be stacked as follows:

xT (n) =[xT

1 (n), . . . ,xTNt

(n)],

where

xTi (n) =

xi(nM − ν + 1), . . . , xi(nM)︸︷︷︸

xo

, xi(nM −M + 1) . . . , xi(nM)︸︷︷︸xo

,

xo is a replica of the last ν samples of xo. Identically, the output samples of thechannel are stacked as

yT (n) =[yT

1 (n), . . . ,yTNr

(n)],

where yTi (n) is the received signal for the nth OFDM symbol at the ith receive

antenna. The channel can be expressed as a vector equation:

y(n) = H(n)x(n) + z(n), (2.4)

where the spatio-temporal channel matrix is composed of (M + ν)× (M + ν) SISOsubblocks

H =

H1,1 · · · H1,Nt

... . . . ...HNr,1 · · · HNr,Nt

∈ C(M+ν)·Nr×(M+ν)·Nt . (2.5)

If the multipath delay spread of the channel is smaller than the length of cyclicprex, the spatio-temporal channel can be reduced to M non-interfering parallel atfading channels by using Discrete Matrix Multitone (DMMT) [12]. The simpliedchannel may be expressed as:

ym(n) = Hm(n)xm(n) + z(n), m = 1, . . . ,M (2.6)

8

2.1 Signal model

wherexm = [x1(nM −M + m), . . . , xNt(nM −M + m)]

is the data vector transmitted on the mth frequency bin, Hm is an Nr ×Nt space-frequency channel evaluated on the mth frequency bin and ym is the received dataon this frequency. With the DMMT approach, any MIMO schemes suggested fornarrowband systems can now be extended to MIMO-OFDM systems by applyingthe coding in space-frequency domain [12,13].

In this dissertation, we will mainly focus on narrowband MIMO systems since anOFDM system can be easily converted into a group of parallel narrowband systems.

Channel modelA number of channel models for narrowband and wideband wireless links have beendiscussed in many works [12,14,15] and [16] gives a complete review of the channelmodels.

Flat fading channelThere are three types of channel under consideration in this thesis: independentand identically distributed (i.i.d.) Rayleigh fading, spatially correlated Rayleighfading and Ricean fading channel.

Let us denote by Hw the i.i.d. Rayleigh fading channel, the entries of which areassumed to be independent zero mean unit variance circularly symmetric complexGaussian random variable, i.e., [Hw]ij ∼ CN (0, 1).

In spatially correlated Rayleigh fading channel, the fading correlation R can beevaluated by:

R = E vec(H)vec∗(H) . (2.7)

The correlation may be separated into two parts [16]: the transmitter spatial cor-relation Rt and the receiver spatial correlation Rr, which are evaluated by:

Rt = E(

hj∗hj)T

, 1 ≤ j ≤ Nr (2.8)

andRr = E hih∗i , 1 ≤ j ≤ Nt (2.9)

respectively. hi is the ith column of H and hj is the jth row of H. They are relatedto R by a Kronecker product:

R = Rt ⊗Rr. (2.10)

Then the channel model is written as:

H = R1/2r HwR1/2

t . (2.11)

9


(·)1/2 denotes any matrix square root that R1/2(R1/2)∗ = R. Furthermore, thetransmitter and the receiver spatial correlation can be modeled by correlation co-ecients ρtx and ρrx as:

[Rt]ji = ρ|i−j|tx , (2.12)

[Rr]ji = ρ|i−j|rx . (2.13)

A semi-correlated fading channel, e.g., a Rayleigh fading channel with spatial cor-relation at the transmitter only, can be obtained by setting ρrx = 0.

In case there exists a line-of-sight (LOS) component between the transmitterand the receiver, the channel is Ricean distributed [23]:

H =

√K

K + 1atx(θtx)a∗rx(θrx) +

√1

K + 1Hw, (2.14)

where the rst term corresponds to the LOS component with an angle of departureθtx and an angle of arrival θrx. atx(θtx) is the normalized transmit antenna arrayresponse vector due to the angle of departure, and arx(θrx) is the normalized receiveantenna array response vector due to the angle of arrival. K is the Ricean K−factordened as the ratio of deterministic to scattered power. The second term is the non-line-of-sight (NLOS) part representing the elements of scattering component, whichcan be assumed to be i.i.d. Raleigh fading in case of a rich scattering environment.

Frequency-selective fading channelA wideband communication system is usually subject to frequency-selective fadingchannel, which can be modeled by a tapped-delay-line model with each tap repre-senting a multipath component [17]. The channel on each tap is at fading and canbe modeled by any of the statistical models mentioned in the preceding section.

An alternative approach is to generate a spatio-temporal representation of thechannel as (2.5), which can be obtained by using a ray-based discrete spatio-temporal channel model [18],

H =NP∑

l=1

βlArx(θrx,l) ·Gl ·ATtx(θtx,l) (2.15)

where

Arx =

arx,1(θrx,l)I(M+ν)

...arx,Nr (θrx,l)I(M+ν)

(2.16)

and

Atx =

atx,1(θtx,l)I(M+ν)

...atx,Nt(θtx,l)I(M+ν)

. (2.17)

10

2.2 MIMO schemes

atx,j(θtx,l) is the jth transmitting antenna gain response due to the angle of de-parture of multipath l, arx,i(θrx,l) is the ith receiving antenna gain response dueto the angle of arrival of multipath l. I(M+ν) is an M + ν identity matrix. βl isthe complex gain of multipath l, NP is the number of resolvable multipaths withdierent delays.

Gl =

0 · · · · · · · · · 01 0 · · · · · · 00 1 0 · · · 0... . . . . . . . . . ...0 · · · · · · 1 0

is the (M +ν)× (M +ν) multipath delay matrix with all ones on the main diagonalor the dth lower subdiagonal. d is the quantised delay dened as d =

⌊τl

Ts

⌋, where

τl is the relative delay of multipath l and Ts is the sample period, which is 50nS incase of WLAN 802.11a.

Furthermore, to introduce time correlation to the channel coecients, Jake'smodel [19] or modied Jake's model [20] can be employed to generate a seriesof time-correlated gains for each multipath component βl and the time-correlatedchannel coecients are obtained by substituting βl into (2.15).

2.2 MIMO schemesSpatial multiplexing based schemes transmit separate streams of data across multi-ple antennas. At the receiver, there exist several decoding schemes, e.g., joint max-imum likelihood (ML) [25], sphere decoding [26], linear receiver with zero-forcing(ZF) [7, 25], linear receiver with minimum mean-square error (MMSE) [7, 25], suc-cessive interference cancellation (SIC) with ZF [7,25], SIC with MMSE2 [7,25] andetc. Additionally, if precoding is feasible at the transmitter, SVD can be adoptedto convert the interfering MIMO channel into a set of parallel sub-channels, orsingular value channels, over which separate data streams are transmitted.

In diversity based schemes, structured codes are applied across space and timedomain [4, 5, 24] to combine the diversity gains provided by the two dimensions.Alternatively, the codes can be employed across the space and frequency domain [13]to combine the diversity gains from space and frequency in MIMO-OFDM systems.In narrowband systems, the most frequently used space-time codes are Alamouticodes [4] for two transmit antennas and generalized space-time block codes for threeor four transmit antennas [5].

Linear receiver with ZF detectionWe can write the channel matrix H in (2.1) column-wisely:

H = [h1,h2, . . . ,hNt ]2this is also referred to as VBLAST.

11


where hi is the ith column of H. Then the received signal can be rewritten as:

y = hixi +∑

j 6=i

hjxj + z (2.18)

which can be viewed as the sum of the desired signal xi together with the interfer-ences xj and the noise. To extract xi out of the received signal, y is projected onto asubspace orthogonal to the one spanned by the vectors h1, . . . ,hi−1,hi+1, . . . ,hNt .The linear operation of the projection can be represented by a di ×Nr matrix Qi,where di is found to be Nr−Nt +1 [7]. The resulting signal after the projection is:

yi = Qiy = Qi(hixi +∑

j 6=i

hjxj + z

︸︷︷︸wi

) (2.19)

Then Maximum Ratio Combining (MRC) is used to maximize the received SNR:

(Qihi)∗Qiyi = ‖Qihi‖22xi + (Qihi)∗Qiwi (2.20)

It is known that this is equivalent to the least square solution [7]

x = H†y = (H∗H)−1H∗y, (2.21)

for an over-determined systemy = Hx

where H is an Nr ×Nt matrix with Nr ≥ Nt. The proof of equivalence is providedin Appendix 2.A.

The SNR of the ith stream can be obtained from (2.20)

SNRi =PT ‖Qihi‖2

Ntσ2n

, (2.22)

If the channel is i.i.d. Rayleigh fading, then ‖Qihi‖2 is Chi-square distributedwith degrees of freedom (d.o.f) equal to 2(Nr −Nt + 1). The capacity that can beachieved by using ZF detection is written as:

Czf = E

Nt∑

i=1

log(

1 +γ0

Nt‖Qihi‖2

), (2.23)

Singular value decompositionThe channel matrix H can be decomposed by using SVD:

H = UΛV∗ (2.24)

12

2.2 MIMO schemes

where U and V are unitary matrices. Λ is an Nr×Nt matrix with √λ1, . . . ,√

λNminon the diagonal and zeros otherwise. λi are the eigenvalues of HH∗ and Nmin =min Nt, Nr.

By premultiplying with V at the transmitter and postmultiplying with U∗ atthe receiver, see (2.25), the channel is converted into a set of parallel sub-channels,coined as singular value channels.

s = U∗y = U∗HVs + w = Λs + w (2.25)

Then the eective SNR on the ith singular value channel is given as:

γi =PT λi

Nminσ2n

(2.26)

The diversity gain on the ith singular value channel is derived in [27,28] as:

di = (Nt − i + 1)(Nr − i + 1). (2.27)

The capacity by using SVD is:

Csvd = E

Nmin∑

i=1

log(

1 +γ0λi

Nmin

), (2.28)

To further enhance the capacity, waterlling can be adopted to calculate the powerto be assigned on every singular value channel and the resulting capacity is givenby (1.5). Application of the waterlling power allocation in adaptive modulationsystems is investigated in Chapter 3.

OSTBCFull diversity full rate OSTBC is only available for MIMO systems with two trans-mit antennas, where the symbols to be transmitted are structured as a 2×2 block [4]:

[s1 −s∗2s2 s∗1

],

where x∗ represents the complex conjugate of x. The signals in the rst row arethe symbols to be transmitted through antenna 1 in two consecutive time slots,and the second row contains the data for antenna 2. The channel is assumed to beconstant over two symbol intervals. Then the relationship of received signal y andsymbols s can be written as [22]:

[y(1)y(2)

]

︸︷︷︸y

=[

h1 h2

h2 −h1

]

︸︷︷︸H

[s1

s2

]

︸︷︷︸s

+[

z(1)z(2)

]

︸︷︷︸z

(2.29)

13


−10 −5 0 5 10 15 20 250

2

4

6

8

10

12

14

SNR [dB]

C[a

paci

ty [b

its/c

hann

el u

se]

waterfillingSVDBFOSTBCZF

Figure 2.1: Capacities of MIMO by using dierent schemes in 2×2 i.i.d. Rayleighfading channel

where hi is an Nr × 1 vector denoting the channel coecients of transmit antennai to all receive antennas and hi is the complex conjugate of hi. At the receiver ofOSTBC, MRC is applied to maximize the received SNR:

s = H∗y =[ ‖H‖2F 0

0 ‖H‖2F

] [s1

s2

]+ H∗z (2.30)

where ‖ · ‖F is the Frobenius norm. The eective SNR γ after the MRC is:

γ =γ0‖H‖2F

2. (2.31)

The diversity gain is 2Nr for every symbol [4] and the capacity achieved by OSTBCis

Costbc = E

log(1 +

γ0

2‖H‖2F

), (2.32)

2.3 CapacityThe capacities achieved by using various MIMO schemes are shown in Figure 2.1.It is observed that the performances of dierent MIMO schemes dier signicantly

14

2.4 Conclusions

from each other. Similarly, the practical spectral eciencies that can be achievedin real systems dier from each other. This motivates our research work on howto adapt the transmission schemes to maximize the spectral eciency. The resultsshown in Figure 2.1 provide us two hints on how to do this:

1. adopt power allocation at the transmitter to vary the transmit power acrossmultiple antennas,

2. switch across dierent MIMO schemes based on the crossing point of thespectral eciencies achieved by the candidate schemes.

The adaptive power allocation requires instantaneous CSIT, which ts in the struc-ture of SVD algorithm, where the instantaneous CSI is available at the transmittereither through a feedback channel in Frequency Division Duplex (FDD) systems orby estimation in receive mode in Time Division Duplex (TDD) systems. Through-out this literature, we assume CSI is obtained at the transmitter via a feedbackchannel in FDD mode. On the other hand, we can switch between the diversitybased scheme and the spatial multiplexing based scheme to make benets from bothalgorithms. For instance, the crossing point of the spectral eciencies of ZF andOSTBC can be used as the switching point between ZF and OSTBC. Furthermore,the crossing point is a function of the channel statistical information which doesnot change as time elapses, so the selection of the MIMO scheme is done once andfor all.

2.4 Conclusions

In this chapter, we presented the base-band signal models for both narrowbandMIMO systems and wideband MIMO-OFDM systems. The associated channelmodels for at fading and frequency-selective fading environment are studied. SinceMIMO-OFDM can be decomposed into a set of interference-free narrowband MIMOsubblocks, we restrict our work to narrowband MIMO systems.

Several MIMO schemes were reviewed, i.e., SVD, OSTBC, Spatial multiplexingwith ZF receiver, and they exhibited distinct performances in terms of capacity,which motivated our work in nding an adaptation technique based on CSI toachieve the maximal spectral eciency.

15


Appendix

2.A Least square method for ZFAn over-determined system is written as:

y = Hx (2.33)where H is an Nr ×Nt matrix with Nr ≥ Nt. The least square method is to ndan estimate x that minimizes

ξ = ‖y −Hx‖2. (2.34)This is solved by multiplying by a pseudoinverse matrix:

x = H†y = (H∗H)−1H∗y (2.35)In this section, it is shown that the pseudoinverse of H (2.35) is equivalent to thelter's solution in (2.20).

Without loss of generality, we look at the ith lter's coecients:c∗i = (Qihi)∗Qi = h∗i Q

∗i Qi, (2.36)

where Qi is composed of orthonormal basis qT1 ,qT

2 , . . . ,qTdi, which spans the

subspace S⊥ that is orthogonal to the one spanned by the vectorsh1, . . . ,hi−1,hi+1, . . . ,hNt.

Note that Q∗i Qi is both hermitian and idempotent: i.e. (Q∗

i Qi)∗ = (Q∗i Qi)2 =

Q∗i Qi, it can be viewed as a projection matrix onto subspace S⊥, with the following

properties:1. Q∗

i Qihi = hi

2. Q∗i Qihj = 0 where j = 1, . . . , i− 1, i + 1, . . . , Nt

By stacking the coecients c∗i :

C =

h∗1Q∗1Q1

...h∗Nt

Q∗Nt

QNt

the product of C and H are:

CH =

h∗1Q∗1Q1

...h∗Nt

Q∗Nt

QNt

[h1, · · · ,hNt ] (2.37)

=

‖h1‖2 · · · 0

... . . . ...0 · · · ‖hNt‖2

16

2.A Least square method for ZF

With properly chosen scaling factors for each row of C, i.e. 1/‖hi‖2, we haveCH = I and hence

C = H†

Due to the uniqueness of pseudoinverse matrix,

C = (H∗H)−1H∗

17

Chapter 3

Adaptive schemes for MIMO systemswith SVD

Adaptive transmission schemes that adjust the transmission parameters relativelyto the time-varying channel enable robust and spectrally ecient data transmissionover the wireless fading channel. The idea of channel-adaptive transmission isto feedback the CSI from the receiver to the transmitter, then the transmissionparameters are adjusted based on the feedback information with respect to thechannel conditions. This technique was rst investigated in [36], but it was short-lived maybe due to hardware constraints. Then it was re-visited in [37], wherevariable-rate, variable-power was suggested to approach channel capacity over aRayleigh fading channel. So far, adaptive transmission schemes have been suggestedfor both SISO [3740] and MIMO applications [35,4145,4749,52] and they mainlyfall into three categories [35]:

maximize the link spectral eciency with xed BER performance subject toa total power constraint [35,4145,47,48],

minimize BER with xed rate subject to a total power constraint [35,49,50],

minimize transmit power with xed rate and xed BER [51,52].

Throughout this work, we target to maximizing the spectral eciency while keepingBER under a predened level.

In adaptive transmission technology, the adaptation of parameters is based onthe CSI, which can be either fed back to the transmitter in frequency divisionduplex (FDD) systems or can be estimated in the receiver mode in time divisionduplex (TDD) systems. We assume that channel estimation is perfect and there isno feedback delay or error. Thus the instantaneous channel information is avail-able at the transmitter and it can be employed to adapt the parameters for everychannel realization. This is applicable for a slowly fading wireless channel wherethe coherence time is larger than the feedback delay. In practice, however, due

19

Adaptive schemes for MIMO systems with SVD

S/P

Channel

Estimation

Link

Adaptation

mod

mod

MIMO

Encoder

(SVD)

1P

tN

P

MIMO

Decoder

(SVD)

demod

P/S

demod

Figure 3.1: A block diagram of adaptive MIMO

to imperfect channel estimation and feedback, the CSIT obtained at the transmit-ter is noise contaminated [5456], and partial CSI can be employed to control theparameters [57,58].

We start our investigation by assuming the rate on every singular value chan-nel is variable but the power is constant; then dierent power control policies areintroduced to further increase the potential rate achievable in multi-antenna sys-tems. A block diagram of the adaptive system is shown in Figure 3.1. Both themodulation order and the transmit power are controlled by the link adaptation unitthrough a feedback channel. In order to minimize the data transmitted over thefeedback channel and the resulting bandwidth, the modulation order and the powerare calculated in the link adaptation unit and directly fed back to the transmitter.

3.1 Constant-power variable-rate techniques

As suggested in [37, 39], the rate on every scalar channel is adjusted by applyingadaptive modulation that dynamically determines the constellation size dependingon the channel gain. In the following, we will review adaptive modulation with con-tinuous rate, i.e., the modulation order can take any nonnegative real value. Thenwe will look into the discrete rate case, where the modulation order is restricted tosome certain integers. The reason for studying the continuous rate modulation isthat it upper bounds the performance of the practical modulation schemes and itis more analytically tractable due to the rate continuity.

20


Continuous rateIn [37], the relationship of the eective SNR (γ), BER (Pb) and the constellationsize (Mk) of MQAM modulation for coherent detection with Gray bit mapping isapproximated as:

Pb ≈ 0.2 exp(−1.5

γ

Mk − 1

), (3.1)

which is tight within 1dB when Mk ≥ 4 and Pb ≤ 10−3.Mk can be rewritten as a function of Pb and γ based on (3.1). If we assume

each of the MQAM symbol uses a Nyquist data pulse, i.e. B = 1/Ts, where Bis the signal bandwidth and Ts is the symbol duration. Then the continuous-ratespectral eciency (CRSE) is derived as:

CR = E log Mk = E log(1 + goγ) , (3.2)where

go =−1.5

ln(5Pb)is the SNR gap [12] between the CRSE and the Shannon capacity. This gap arisesfrom the discrepancies in the coding length and the signal space. Innite chan-nel coding length and Gaussian signals are assumed in Shannon theory whereasuncoded QAM modulation is used here.

Furthermore, the continuous-rate adaptive modulation scheme can be appliedindependently on every singular value channel and the ergodic CRSE of MIMOwith SVD is:

CRsvd = E

Nmin∑

i=1

log(

1 +goγ0λi

Nmin

), (3.3)

Recall the ergodic capacity in (2.28), an analogy can be drawn between the capacityand the CRSE, with the only dierence given by the SNR gap go.

Discrete rateNow, we consider the situation in a real system that the modulation orders can onlybe drawn from a nite set of integers, e.g., Mk = 0, 1, 2, 4, . . .. Let Ak denotes theSNR region for Mk-QAM, i.e., the Mk-QAM is selected if the eective SNR fallswithin Ak. The SNR region Ak is dened as Ak = x : Γk ≤ x < Γk+1 where Γk

denote the region boundaries or SNR thresholds. The key point of the issue now isto determine the SNR thresholds and relate it to the desired BER.

In general, there exist two BER constraints for adaptive modulation systems,i.e., average BER constraint [40]1:

BERi ≤ BERt (3.4)1it is originally dened for rate adaptation in SISO, we extend it to MIMO application by

assuming that the same target BER applies for every sub-channel

21


and instantaneous BER constraint [40]:

BERi ≤ BERt, (3.5)

where BERt is the predened target BER, BERi and BERi are the average andinstantaneous BER on the ith singular value channel, respectively. With averageBER constraint, the average BER over a sucient number of channel realizationsmust be limited by the target BER. The instantaneous BER implies that the BERfor every transmission must be subject to the target BER, which is obviously morerestrictive than the average BER constraint and the corresponding spectral e-ciency is certainly lower than the spectral eciency achieved by applying averageBER constraint. For instantaneous BER constraint, the SNR thresholds can beobtained from (3.1), i.e.,

Γk =Mk − 1

1.5ln

15BERt

(3.6)

For average BER, the optimal solution for the SNR thresholds are hard to nd anda suboptimal solution was suggested in [40], where the SNR thresholds from (3.6)were scaled by a properly selected factor such that the average BER constraint(3.4) is satised. Considering the computational complexity, we only focus oninstantaneous BER constraint hereafter.

However, we should notice that the adaptive modulation scheme with the SNRthresholds suggested for the instantaneous BER can achieve an error ratio that islower than the target BER. This is because for every γ that falls in (Γk,Γk+1), theactual BER is lower than the target BER.

By imposing the SNR thresholds (3.6) to every singular value channel of MIMOsystem with SVD, the discrete-rate spectral eciency (DRSE) can be written as:

DRsvd = E

Nmin∑

i=1

ri

=

Nmin∑

i=1

E Q (γi|Γ)

=Nmin∑

i=1

(K∑

k=1

dk ·∫ Γk+1

Γk

p(γi)dγi

), (3.7)

where ri is the rate allocated to singular value channel i. Q (γi|Γ) is the slicingfunction that outputs ri with input γi conditioned on the modulation order thresh-olds, Γ = Γ1,Γ2, . . . , ΓK. dk = log2 Mk is the number of bits assigned when theeective SNR falls in the interval: [Γk, Γk+1). p(γi) is the p.d.f. of γi.

Let's assume that the channel is i.i.d. Rayleigh fading, i.e., H = Hw. Then thejoint distribution function of the eigenvalues (λ1 ≥ λ2 ≥ . . . ≥ λNmin) of matrixHH∗ is given in [1] as:

p(λ1, λ2, . . . , λNmin) =

C

Nmin∏

i=1

e−λiλNmax−Nmini ·

Nmin∏

i<j

(λi − λj)2 (3.8)

22


whereC =

πNmin(Nmin−1)

ΓNmin(Nmax)ΓNmin(Nmin)with

ΓNm(l) = πNm(Nm−1)/2

Nm∏

i=1

(l − i)!

and Nmax = maxNt, Nr. In a 2× 2 system, the marginal p.d.f. of λ1 and λ2 canbe obtained from (3.8). Further, p(γi) can be derived based on the marginal p.d.f.:

p(γ1) =(

8γ21

γ30

− 8γ1

γ20

+4γ0

)e−

2γ1γ0 − 4

γ0e−

4γ1γ0 (3.9)

p(γ2) =4γ0

e−4γ2γ0 (3.10)

By plugging the p.d.f.s into (3.7), we get the DRSE of SVD with equal powerallocation as a function of γ0:

DRsvd(γ0) =K∑

k=1

∆dke−2Γk

γ0

[(2Γk

γ0

)2

+ 2

], (3.11)

where ∆dk = dk − dk−1 and d0 = 0.Similarly, the DRSE of BF by utilizing only one singular value out of two is:

DRbf (γ0) =K∑

k=1

∆dke−Γkγ0

[(Γk

γ0

)2

+ 2− e−Γkγ0

]. (3.12)

The DRSEs as well as the empirical spectral eciencies attained from theSoftware-Dened-Radio Workbench (SDR-WB) [32] are shown in Figure 3.2. Theresult at each point is averaged over 10, 000 channel realizations and the target BERis set to 0.1%. It is observed that the DRSEs match with the empirical results verywell. Furthermore, we observe that BF outperforms SVD in the low SNR region.This is due to that the 2nd singular value channel is rather weak in the low SNRregion, where it is optimal to put all of the transmit power onto the stronger one(as suggested by waterlling). However, as SNR increases, the spatial multiplexinggain plays a more important role and SVD achieves a higher spectral eciency.

DRSEs of SVD for MIMO systems with more than 2 antennas are providedin [43]. Nevertheless, all of the results shown here and from [43] are obtained basedon the assumption of i.i.d. Rayleigh fading channel and to the best knowledge ofauthor, the DRSE in case of spatially correlated Rayleigh fading channel is stillunsolved.

A comparison is made between the capacity and the corresponding CRSE, DRSEof an uncoded adaptive modulation 2 4×4 MIMO system in Figure 3.3, where the

2the available constellation sizes of MQAM modulation are 2, 4, 16, 64.

23


−5 0 5 10 15 20 25 300

2

4

6

8

10

12

SNR [dB]

spec

tral

effi

cien

cy [b

ps/H

z]

theoretical SVDtheoretical BFempirical SVDempirical BF

Figure 3.2: Discrete-rate spectral eciencies achieved by svd and beamforming in2× 2 i.i.d. Rayleigh channel with target BER 10−3

channel is assumed to be i.i.d. Rayleigh fading and the results are averaged over10, 000 channel realizations. As expected, the SNR gap between the CRSE andthe capacity is a constant that depends on the target BER only, which, in our case,is about 5.5dB for a target BER 0.1%. This coincides with the theoretical result :

10 log10

−1.5ln(5BERt)

.

On the other hand, there exists a gap between the CRSE and DRSE due to thatdiscrete rate is used in practice.

3.2 Variable-power variable-rate techniquesThus far, adaptive modulation is applied independently across the transmit anten-nas assuming equal power allocation. Now, we take into account adaptive powerallocation to further enhance the spectral eciency.

It is well-known that the channel capacity of MIMO system is maximized byutilizing waterlling power allocation [1] if full CSI is available at the transmitter. Itis of great interest to examine the performance of waterlling-based power allocationschemes in practice.

24

3.2 Variable-power variable-rate techniques

−10 −5 0 5 10 15 20 25 300

5

10

15

20

25

30

35

SNR [dB]

spec

tral

effi

cien

cy [b

ps/H

z]

capacityCRSEDRSE

Figure 3.3: A comparison of the capacity and the spectral eciencies

In case of continuous-rate MQAM modulation under instantaneous BER con-straint and average power constraint, the optimum power allocation can be calcu-lated by Lagrange's multiplier [35] and the solution is similar to the waterllingthat maximizes channel capacity. However, the optimality of waterlling does nothold for the discrete-rate modulation case. Table 3.1 summarizes the optimal solu-tions for power and SNR thresholds using discrete-rate QAM signals under dierentconstraints. By imposing the average constraints on BER and power, the optimalsolution for power control and a suboptimal solution for SNR thresholds are derivedin [40], although it was designed for SISO channels using temporal adaptation, itcan be extended to MIMO applications based on the unordered eigenvalue distribu-tion [43]. Substituting instantaneous BER constraint for average BER constraint,the problem is more tractable and closed form expressions were obtained for thepower and the SNR thresholds [43]. However, As far as we know, the optimalsolution subject to an average BER constraint and peak power constraint is notavailable. In this chapter, we investigate more practical control schemes subject toinstantaneous BER constraint and peak power constraint. Although the optimalsolution is found to be an exhaustive search [35], a variety of other power controlschemes have been suggested to reduce the computational complexity, e.g., QoS-based waterlling [44], greedy allocation [53] and uniform power allocation withtransmit antenna selection (TAS).

25


average power peak poweraverage BER Lagrangian [40] a ?instantaneous BER Lagrangian [43] exhaustive search [35]awhere the optimal power allocation is obtained, but optimal solution for SNR thresholds is

not available.

Table 3.1: Optimal power control schemes for discrete-rate QAM signals

Note that the results in Table 3.1 do not hold for spatial multiplexing algorithms,in which the signal to interference and noise power ratio (SINR) after the datastreams are separated is not proportional to the corresponding transmit power andthis non-linearity leads to a more complicated problem [45,46].

Power control policies in discrete-rate modulation schemeSubject to the instantaneous BER constraint, the SNR thresholds of the modulationorder regions are given by (3.6). Then the optimization problem of power controlis stated as:

maxPi

Nmin∑

i=1

K∑

k=1

dk

∫ Γk+1

Γk

p(γi(Pi))dγi(Pi) (3.13)

subject toNmin∑

i=1

Pi ≤ PT

with Pi ≥ 0, i = 1, 2, . . . , Nmin

The optimization involves a mixture of discrete and continuous variables for whichno closed form expression exists. However, we can use exhaustive search to nd theoptimal power allocation together with associated bit-loading that maximizes thespectral eciency [35].

In order to reduce the complexity while achieving a relatively good performanceas exhaustive search, several other power control schemes are considered here, e.g.,direct waterlling [12], QoS-based waterlling [44], greedy allocation [53] and uni-form power allocation with TAS.

Unlike the case of constant power allocation, closed form expression of the DRSEusing adaptive power allocation is not available due to the intractability of Pi.

A direct waterlling methodThe optimal power allocation policy in case of continuous-rate is shown to be thewaterlling method [12,35]:

Pi =(

ξ − σ2n

goλi

)

+

, i = 1, 2, · · · , Ns (3.14)

26


−5 0 5 10 15 20 250

2

4

6

8

10

12

14

16

18

SNR [dB]

spec

tral

effi

cien

cy [b

ps/H

z]

capacity−optimalcontinuous−rate optimal

Figure 3.4: DRSEs using capacity-optimal WF and continuous-rate optimal WF ina 4× 4 i.i.d. Rayleigh fading channel

where ξ is chosen to satisfy the peak power constraint. The number of non-zeropower allocation is Ns ≤ Nmin. This policy is dierent from (1.6) by including anoise-amplifying factor go, where go < 1. This is intuitively reasonable becausethere exists an SNR gap between the CRSE and the capacity and this gap can beviewed as a result of noise amplication. The improvement in DRSE by takinginto account the noise amplication is shown in Figure 3.4. By applying powerallocation given by (3.14), the resulting eective SNR is written as:

γi =Piλi

σ2n

, i = 1, . . . , Ns (3.15)

and the bit-loading is obtained by:

ri = Q (γi|Γ) , i = 1, . . . , Ns. (3.16)

QoS-based waterlling methodIn a sense, the direct waterlling is essentially an SNR quantization where thetransmit power may not make the possibly maximal contribution. A modiedwaterlling method, referred to as QoS-based WF, is proposed in [44] to enhancethe spectral eciency on basis of the direct waterlling. The idea of it is to execute

27


QoS-based waterlling1. Calculate the residual power allocated to every singular

value channel:∆Pi = Pi − Pi

where Pi is the initial power calculated from waterlling(3.14) and

Pi =σ2

nΓk

λi

is the desired power that achieves the SNR threshold Γk.Then the sum of the residual power is:

Pr =Ns∑

i=1

∆Pi

2. Let ∆P = Pr, i = 1

3. Calculate the possibly maximal rate that can be achievedwith ∆P on the ith singular value channel:

ri = Q(

(Pi + ∆P )λi

σ2n

|Γ)

if ri > ri, ∆P = ∆P − σ2nΓk

λi, where Γk corresponds to the

SNR threshold for the updated modulation order.

4. i = i + 1, if i ≤ Ns, go to step 3; otherwise, go to step 5

5. The end.Table 3.2: QoS-based waterlling

the direct waterlling in the rst step, and then collect the residual power from eachsingular value channel that is not used to improve the rate. Lastly, re-distributethe residual power on all singular value channels to achieve potential increase indata rate. A detailed procedure is shown in Table 3.2.

Based on the previous discussions, there are two versions of waterlling, oneis capacity-optimal, the other is continuous-rate optimal, both of which can beadopted here, but the performances are almost the same due to the re-distribution.

Greedy power allocationThe execution of QoS-based waterlling can be divided into two steps: the rststep is to calculate the ideal power allocation over all singular value channels; the

28


Greedy power allocation1. Let ∆P = PT and i = 1

2. Find the maximum rate ri that the singular value channeli can support with ∆P :

ri = Q(

∆Pλi

σ2n

|Γ)

3. calculate the desired power to achieve the rate ri:Pi =

σ2nΓm

λi

where Γm is the SNR threshold for the modulation orderri. Re-calculate the residual power:

∆P = ∆P − Pi

4. i = i + 1, if i ≤ Nmin and ∆P > 0, go to step 2; otherwise,go to step 5

5. The end.Table 3.3: Greedy power allocation

second step is to redistribute the residual power. Notice that power allocation at therst step is optimal only under the assumption of Gaussian signal or continuous-rate QAM modulation. Therefore, an alternative strategy, referred to as greedyallocation, is proposed by considering this discrete eect on the power allocationfrom the beginning.

The idea of greedy power allocation is to assign as much power as possibleonto a singular value channel to achieve the possibly maximal constellation size.Considering that:

λ1 > λ2 > . . . > λNmin ,

the power allocation can be done in an order from the strongest singular valuechannel (i = 1) to the weakest one (i = Nmin). The process is illustrated in Table3.3.

From computer simulations, the CPU time of greedy power allocation is about56% of that of the QoS-based waterlling and the complexity is signicantly re-duced.

Uniform power allocation with TASAlthough greedy power allocation has considerably lowered the computational com-plexity, the power allocation needs to be calculated for every transmit antenna. To

29


Uniform power allocation with TAS1. Initialize the number of selected tx: Ns = Nmin

2. calculate the eective SNR on the smallest singular valuechannel:

γNs=

PT λNs

Nsσ2n

,

if the achievable rate of the smallest singular value channel:ri = Q (γNs |Γ) > 0

go to step 4, otherwise go to step 3

3. Reduce the number of selected antennas:Ns = Ns − 1. If Ns > 0, go to step 2, otherwise go to step4

4. The end.Table 3.4: Uniform power allocation with TAS

further simplify the computation, the transmit antennas with strong gains are se-lected and the power is then uniformly distributed among the selected antennas.The criterion for antenna selection is that the eective SNR on every singular valuechannel must be larger than the smallest SNR threshold Γ1 and the process ispresented in Table 3.4.

Other suboptimal and low-complexity power allocation strategies, like channelinversion (CI) and truncated channel inversion (TCI), are proposed in [21]. WithCI, the power is poured on every sub-channel to maintain the same gain on everysub-channel. The most important advantage of CI is that the eective SNR isidentical for all sub-channels and a uniform constellation size is applied to all sub-channels, which simplies the code design as well as the decoding process. However,CI is subject to substantial rate loss when the sub-channel is invertible, i.e., λi ∼ 0.One way to solve this problem is by using TCI, where a cut-o level λ0 is set forλi so that CI is applied only for sub-channel i whose λi > λ0.

A comparison of power control schemesWe have reviewed four power allocation policies, direct waterlling, QoS-basedwaterlling, greedy power allocation and uniform power allocation with TAS. Theperformance of them are compared in three dierent channel environment: i.i.d.Rayleigh fading, spatially correlated Rayleigh fading and Ricean fading channel.

In a 4 × 4 i.i.d. Rayleigh fading channel, the spectral eciencies achieved byutilizing dierent power control schemes are shown in Figure 3.5. It is observed that

30


−5 0 5 10 15 20 25 300

5

10

15

20

25

SNR [dB]

spec

tral

effi

cien

cy [b

ps/H

z]

uniform power TASdirect waterfillingQoS−based waterfillinggreedy allocationexhaustive search

Figure 3.5: Spectral eciencies of power control schemes in a 4 × 4 i.i.d Rayleighfading channel

the QoS-based waterlling almost achieves the maximal spectral eciency reachedby using exhaustive search. Greedy allocation has a very close performance asQoS-based waterlling in most cases. QoS-based waterlling has about 2 dB gainover the direct waterlling, which comes from the residual power re-distribution.Equal power allocation with TAS, on the other hand, obtain the same performanceas QoS-based waterlling in the low SNR region, but as SNR increases, it onlyattains similar performance as direct waterlling. This is because only one singu-lar value channel is activated at low SNRs, as the case in QoS-based waterlling,whereas at high SNRs, direct waterlling and uniform power allocation with TASare asymptotic to equal power allocation.

Furthermore, the power allocated to the rst singular value channel by usingdierent power control schemes are shown in Figure 3.6. The behavior of greedyallocation follows that of QoS-based waterlling in both low SNR region and highSNR region, except in the middle SNR region where greedy allocation allocates ahigher portion of power than QoS-based waterlling, which explains the discrepancyin spectral eciency between the greedy allocation and QoS-based waterlling. Onthe other hand, uniform power allocation with TAS behaves similarly to the directwaterlling. As SNR increases, the waterlling tends to allocate equal power on allsub-channels.

31


5 10 15 20 25 30 35 400

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

λ1/σ

n2 [dB]

pow

er

direct WFQoS−based WFgreedyuniform power TAS

Figure 3.6: Power allocated to the 1st singular value channel in 4×4 i.i.d. Rayleighfading channel

In case there are not sucient scatters around the transmitter and the receiver,correlation exists between any pair of the transmit and the receive antennas. Underthis condition, the attainable spectral eciencies of dierent power control schemesare shown in Figure 3.7. The spatial correlation is further emphasized by a LOScomponent in a Ricean fading channel and the performance is given in Figure 3.8.We notice that the discrepancy between the QoS-based waterlling and the greedyallocation is vanishing as the spatial correlation increases.

A more noticeable performance contrast is made in Figure 3.9, where ratiosof the spectral eciency achieved by the greedy allocation and that of QoS-basedwaterlling in dierent channel environment are plotted. As the spatial correlationincreases, the performance of greedy allocation is approaching that of the QoS-based waterlling, and even outperforms the latter one at some SNRs in highlyspatially correlated environment.

3.3 Further discussionThus far, all of the power control schemes considered are assumed to have the samepower target for all singular value channels. Specically, the power allocated onthe ith sub-channel, Pi = hi(λi), is independent of i, i.e., ∀i, hi ≡ h. A new class of

32

3.3 Further discussion

−5 0 5 10 15 20 25 300

5

10

15

20

25

SNR [dB]

spec

tral

effi

cien

cy [b

ps/H

z]


Figure 3.7: Spectral eciencies of power control schemes in a 4× 4 spatially corre-lated Rayleigh fading channel, with ρtx = ρrx = 0.5

multi-target power control schemes are proposed in [59], where dierent targets areapplied to channels with dierent fading statistics, i.e., the power allocated ontosub-channel i does not only depend on λi, but also on hi itself.

Waterlling is claimed to be capacity-optimal under the assumption of Gaussiancoding and innite coding length. In practice, however, the M-PSK and M-QAMmodulation are used instead of Gaussian signals and the waterlling turns out notto be optimal any more, as shown in previous discussions. Although the impactcaused by practical modulation schemes are partly compensated by the SNR gapgo, a better solution that explores the optimal power allocation catering to M-QAMand M-PSK modulation is expected. By taking into account the exact modulationschemes, a mercury/waterlling power control strategy is suggested in [60], wherethe gap between Gaussian signal and the practical modulation scheme on eachsub-channel is lled by mercury rst and water (power) is poured on top ofthe mercury. In case of Gaussian signals, the gap is zero and this method boilsdown to waterlling. This method can also be regarded as a multi-target powerallocation scheme: the gap between Gaussian codes and the desired modulationscheme depends on the exact modulation scheme and the modulation order usedby the channel, which tends to dier from sub-channel to sub-channel, then thepower targets of dierent sub-channels are dierent.

33


−5 0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

SNR [dB]

spec

tral

effi

cien

cy [b

ps/H

z]


Figure 3.8: Spectral eciencies of power control schemes in a 4 × 4 Ricean fadingchannel

Although we assume perfect CSI at the transmitter and the receiver, the imper-fection in channel estimation and feedback is inevitable in practice due to hardwareconstraints. This has been extensively studied in [43,54,56].

3.4 Concluding RemarksIn this chapter, we reviewed adaptive power adaptive rate techniques for high datarate transmission. In the case of constant power variable rate, the CRSE and DRSEwere derived for continuous-rate QAM modulation and discrete-rate QAM modula-tion, respectively. DRSE was obtained based on the SNR thresholds that satisedthe instantaneous BER constraint. In case that the power and the rate are bothadaptable, we concentrated on how to achieve a relatively good performance subjectto a peak power constraint and an instantaneous BER constraint with comparablylow complexity. Several power control policies were reviewed (direct waterlling,QoS-based waterlling and uniform power allocation with TAS) and a new powercontrol methodgreedy power allocationwas suggested, which reduced the compu-tational complexity while achieving a comparably good performance compared tothe QoS-based waterlling.

34

3.4 Concluding Remarks

−5 0 5 10 15 20 25 300.9

0.92

0.94

0.96

0.98

1

1.02

1.04

SNR [dB]

gree

dy/Q

oS−

base

d W

F

iid Rayleighspatially correlated RayleighRicean

Figure 3.9: Comparison of greedy allocation and QoS-based WF in dierent channelconditions

35

Chapter 4

Adaptive schemes for MIMO systemswith OSTBC and ZF

In order to achieve the possibly maximal spectral eciency, adaptive modulationand adaptive power techniques are applied to approach the theoretical upper boundof a single MIMO scheme. On the other hand, a new adaptation policy to switchacross dierent MIMO schemes have been suggested to further enhance the spectraleciency promised by multiple antenna systems [62,63], where they switch betweena diversity scheme and a spatial multiplexing scheme based on the BER performanceto explore the highest spectral eciency while maintaining a xed BER. Alterna-tively, there exists another type of adaptation which employs diversity/multiplexingswitching method in an attempt to minimize BER for xed spectral eciency [61].

In this chapter, we will consider applying two MIMO schemes in an adaptivemodulation system: OSTBC and spatial multiplexing with ZF detection. To adoptadaptive modulation into the systems, the eective SNR of every sub-channel isestimated at the receiver and a proper modulation order is selected and fed backto the transmitter through a feedback channel in FDD mode. The variation rate ofthe fading channel is assumed to be lower than the link adaptation rate. Similarlyto Chapter 3, closed form expressions of the DRSEs are obtained for OSTBC andspatial multiplexing with ZF. To improve the potential spectral eciency, a lowcomplexity adaptation scheme is proposed to switch between the diversity schemeand the spatial multiplexing scheme. Unlike [62] and [63] where the switching isbased on the BER performance, we employ the DRSEs here to nd out the switchingpoint for the two schemes. The block diagram of the system is illustrated in Figure4.1, where the modulation order is updated for each channel realization based onthe instantaneous CSI. The scheme is selected based on the statistical informationof the channel.

37

Adaptive schemes for MIMO systems with OSTBC and ZF

S/P

Channel

Estimation

Link

Adaptation

mod

mod

MIMO

Encoder

(OSTBC,

ZF)

1P

tN

P

MIMO

Decoder

(OSTBC,

ZF)

demod

P/S

demod

Figure 4.1: A block diagram of adaptive MIMO switching between dierent schemes

4.1 DRSEs of MIMO systems with OSTBCBecause OSTBC [4] is dedicated for two transmit antennas, we conne our work inthis chapter to a 2×Nr MIMO system, where the channel environment is assumedto be either i.i.d. Rayleigh fading without spatial correlation or spatially correlatedRayleigh fading with correlation at transmitter only.

Similar to SVD, the DRSE of OSTBC can be evaluated by:

DRostbc = E r = E Q (γ|Γ)

=

(K∑

k=1

dk ·∫ Γk+1

Γk

p(γ)dγ

), (4.1)

where the key to evaluating DRSE is to nd p(γ), the p.d.f. of the eective SNR.

DRSEs of OSTBC in i.i.d. Rayleigh fading channelRecall that the eective SNR for a 2×Nr i.i.d. Rayleigh fading channel is writtenas:

γ =γ0‖Hw‖2F

2, (4.2)

where Hw denotes the i.i.d. Raleigh fading channel. Therefore the distribution ofγ depends on the p.d.f. of ‖Hw‖2F , which is Chi-square distributed with p.d.f. [7]:

p(x) =1

(L− 1)!xL−1e−x (4.3)

38

4.1 DRSEs of MIMO systems with OSTBC

Here x = ‖Hw‖2F , 2L is the degree of freedom (d.o.f.), i.e., the number of inde-pendent real-valued random variables, and L = 2Nr in this case. With simpletransformations, p(γ) can be derived from (4.3):

p(γ) =2

γ0(2Nr − 1)!

(2γ

γ0

)2Nr−1

e−2γγ0 , (4.4)

Then the DRSE of OSTBC can be derived by inserting (4.4) into (4.1):

DRostbc(γ0) =K∑

k=1

∆dke−2Γkγ0

2Nr−1∑

j=0

1(2Nr − j − 1)!

(2Γk

γ0

)2Nr−j−1

(4.5)

With the Taylor series expansion: ex = 1 + x + 12!x

2 + 13!x

3 + . . ., it is obvious that

2Nr−1∑

j=0

1(2Nr − j − 1)!

(2Γk

γ0

)2Nr−j−1

= e2Γkγ0 −O (

(2Γk/γ0)2Nr), (4.6)

where O (x2Nr

)denotes the terms of order higher than 2Nr. Therefore, the DRSE

is upper bounded by

DRostbc =K∑

k=1

∆dke−2Γkγ0

(e

2Γkγ0 −O (

(2Γk/γ0)2Nr))

<

K∑

k=1

∆dk = dK (4.7)

The empirical spectral eciencies of OSTBC and the corresponding DRSEswhen Nr = 2, 4, 6 are shown in Figure 4.2, where the target BER is set to 0.1%. Asexpected, the DRSEs match very well with the empirical results that are obtainedfrom the SDR-WB based on 10, 000 channel realizations.

DRSEs of OSTBC in spatially correlated Rayleigh fading channelIn spatially correlated Rayleigh fading channel with correlation at the transmitter,the channel transfer function is written as:

H = HwR1/2t . (4.8)

In case of two transmit antennas, the spatial correlation matrix Rt can be writtenas:

Rt =[

1 ρtx

ρtx 1

], (4.9)

which can be diagonalized as:

Rt = UtΩtU∗t (4.10)

39


−5 0 5 10 15 20 25 300

1

2

3

4

5

6

7

SNR [dB]

spec

tral

effi

cien

cy [b

ps/H

z]

theoretical OSTBCempirical OSTBC

Nr=2

Nr=4

Nr=6

Figure 4.2: spectral eciencies achieved by OSTBC in 2×Nr i.i.d Rayleigh fadingchannel with Nr = 2, 4, 6

where Ut is a unitary matrix. Ωt is a diagonal matrix with ω1 = 1 + ρtx andω2 = 1− ρtx on the main diagonal. The eective SNR is related to H, which is theproduct of Hw and R1/2

t . By substituting (4.8) into (2.31), the eective SNR givenin (2.31) can be rewritten:

γ =γ0

2‖H‖2F

=γ0

2tr

(HwR1/2

t

(HwR1/2

t

)∗)

=γ0

2tr

HwUt︸︷︷︸

Hw

ΩtU∗t H

∗w

=γ0

2tr (H∗

wHwΩt)

=γ0

2

2∑

i=1

ωi‖hwi‖22 (4.11)

40

4.1 DRSEs of MIMO systems with OSTBC

Here tr(A) denotes the trace of A. The third equation comes from (4.10). Thefourth equation follows from tr(AB) = tr(BA). hwi is the ith column vector ofHw and ‖hwi‖2 is the Euclidean norm of it.

Because Ut is a unitary matrix, the distribution of Hw = HwUt is the sameas Hw [1]. Hence, ‖hwi‖22 is Chi-square distributed with the d.o.f. equal to 2Nr,whose p.d.f. is given in (4.3) with L = Nr:

p(xi) =1

(Nr − 1)!xNr−1

i e−xi ,

where xi = ‖hwi‖22. Then γ is the sum of two weighted Chi-square distributedvariables:

γ = γ1 + γ2

where γi = γ0ωixi/2 and it's p.d.f. is given as follows:

p(γi) =2NrγNr−1

i

(Nr − 1)!(γ0ωi)Nre− 2γi

γ0ωi (4.12)

From the theory of probability [31], the p.d.f. of γ is the convolution of the p.d.f.of γ1 and γ2, provided that γ1 and γ2 are independent variables:

p(γ) = be−2γ

γ0ω2

Nr−1∑

i=0

(−1)Nr−i(Nr−1

i

)γi

aMi+1

e−aγ

Mi∑

j=0

PjMi

(aγ)Mi−j −Mi!

(4.13)

where Mi = 2Nr − i− 2 and

a = 2(

1ω1

− 1ω2

),

b =4Nr

(Nr − 1)!2(γ20ω1ω2)Nr

,

Pnm =

m!(m− n)!

(m

n

)=Pn

m

n!=

m!(m− n)!n!

The proof can be found in Appendix 4.A. As ρtx → 0, (4.13) approaches to theresult of i.i.d. Rayleigh fading channel, as can be seen in Appendix 4.B. Further-more, the DRSE of OSTBC with Nr receive antennas can be derived by plugging

41


(4.13) into (4.1):

DRostbc(γ0, ρtx) = b

Nr−1∑

i=0

(−1)Nr−i(Nr−1

i

)

aMi+1

Mi∑

j=0

µMj+11 Pj

MiaMi−j

K∑

k=1

∆dke−Γkµ1

Mj∑

l=0

P lMj

(Γk

µ1

)Mj−l

− µi+12 Mi!

K∑

k=1

∆dke−Γkµ2

i∑

l=0

P li

(Γk

µ2

)i−l

(4.14)where Mj = 2Nr − j − 2 and µi = γ0ωi/2.

The DRSEs of OSTBC when Nr = 2, 4, 6 and the empirical results of spectraleciencies obtained from simulation are shown in Figure 4.3, where we assumeρtx = 0.5 and the target BER is 0.1%. It is observed that the DRSEs coincide withthe empirical results.

0 5 10 15 20 25 300

1

2

3

4

5

6

7

SNR [dB]

spec

tral

effi

cien

cy [b

ps/H

z]

theoretical OSTBCempirical OSTBC

Nr=2

Nr=4N

r=6

Figure 4.3: spectral eciencies achieved by OSTBC in 2×Nr spatially correlatedRayleigh fading channel with ρtx = 0.5

4.2 DRSEs of MIMO systems with ZF detectionBy using linear ZF detection at the receiver, a group of non-interfering sub-channelsare established at the cost of amplied noise power. Applying uncoded adaptive

42

4.2 DRSEs of MIMO systems with ZF detection

modulation on every such sub-channels, the DRSE can be computed as:

DRzf = E

Nt∑

i=1

ri

= E

Nt∑

i=1

Q (γi|Γ)

=Nt∑

i=1

(K∑

k=1

dk ·∫ Γk+1

Γk

p(γi)dγi

), (4.15)

To be consistent with OSTBC, we restrict ZF to a 2×Nr system, in which Nr ≥ 2to guarantee the existence of solution for the linear system.

DRSEs of Spatial-multiplexing with ZF receiver in i.i.d. Rayleighfading channelIt is known from [7] that the sub-channel gain ‖Qihi‖2 (2.22) of the ZF receiver isa Chi-square distributed random variable in case of i.i.d. Rayleigh fading channel.Since the d.o.f. of the Chi-square distributed random variable is 2(Nr −Nt + 1) =2(Nr − 1) [7], The p.d.f. of γi is:

p(γi) =2(2γ/γ0)Nr−2

γ0(Nr − 2)!e−

2γiγ0 , (4.16)

Then the DRSE of ZF can be obtained as:

DRzf (γ0) = 2K∑

k=1

∆dke−2Γk

γ0

Nr−2∑

j=0

(2Γk/γ0)Nr−j−2

(Nr − j − 2)!(4.17)

The DRSEs of ZF are shown in Figure 4.4, where both empirical results fromcomputer simulation and the theoretical results (4.17) are plotted.

DRSEs of Spatial-multiplexing with ZF receiver in spatiallycorrelated Rayleigh fading channelIn spatially correlated Rayleigh fading environment, the eective SNR on the ithsub-stream is distributed as [66]:

p(γi) =σ2

i e−γiσ2i /

γ0Nt

γ0Nt

(Nr −Nt)!

(γiσ

2i

γ0/Nt

)Nr−Nt

(4.18)

where σ2i is the ith diagonal entry of R−1

t . The DRSE can be obtained by substi-tuting (4.18) into (4.15):

DRzf (γ0, σ2i ) =

2∑

i=1

K∑

k=1

∆dke−2Γkσ2

iγ0

Nr−2∑

l=0

1(Nr − l − 2)!

(2Γkσ2

i

γ0

)Nr−l−2

(4.19)

43


0 5 10 15 20 25 30 35 40 450

2

4

6

8

10

12

SNR [dB]

spec

tral

effi

cien

cy [b

ps/H

z]

theoretical ZFempirical ZF

Nr=2

Nr=4N

r=6

Figure 4.4: spectral eciencies achieved by ZF in 2 × Nr i.i.d. Rayleigh fadingchannel with Nr = 2, 4, 6

In a 2×Nr Rayleigh fading channel with transmit spatial correlation given by (4.9),σ2

i = 1/(1− ρ2tx) for i = 1, 2. Then (4.19) can be rewritten as:

DRzf (γ0, ρtx) = 2K∑

k=1

∆dke− 2Γk

γ0(1−ρ2tx)

Nr−2∑

l=0

(2Γk

γ0(1−ρ2tx)

)Nr−l−2

(Nr − l − 2)!(4.20)

In the special case where there is no spatial correlation, ρtx = 0 and (4.20) reducesto (4.17). Therefore, (4.20) holds for:

0 ≤ ρtx < 1.

However, it is not possible to apply the same extension to the DRSE of OSTBCbecause the derivation of the p.d.f. of the eective SNR in the case of spatiallycorrelated channel assumes ρtx 6= 0 and ρtx = 0 would result in a dierent p.d.f..This will be further discussed in Appendix 4.A.

As shown in Figure 4.5, The DRSE turns out to be an accurate estimation ofthe spectral eciencies achieved in practice.

44

4.3 A low complexity adaptation scheme

0 5 10 15 20 25 30 35 40 450

2

4

6

8

10

12

SNR [dB]

spec

tral

effi

cien

cy [b

ps/H

z]

theoretical ZFempirical ZF

Nr=2

Nr=4N

r=6

Figure 4.5: spectral eciencies achieved by ZF in 2 × Nr spatially correlatedRayleigh fading channel with ρtx = 0.5


In conventional adaptive systems [37, 48], the channel is time-varying so that theconstellation size has to be updated over time. The complexity of the systemmainly lies in the link adaptation, where the constellation size is decided based onthe estimated eective SNR and fed back to the transmitter through a feedbackchannel in an FDD system.

Besides adaptive modulation, the proposed adaptation scheme employs algo-rithm switching between OSTBC and ZF to further enhance the spectral eciency.This is facilitated by the closed form expressions of the spectral eciencies derivedfor OSTBC and ZF. Since the DRSE is a function of SNR and the spatial corre-lation coecient (in case of spatial correlation) which are statistical informationthat would not change as time elapses, the selection of the optimal MIMO schemeonly needs to be done once. This adds limited complexity to the current existingadaptive modulation system. Additionally, some extra space is needed to store allschemes, but only the one that is selected is activated.

With the closed form expressions of the spectral eciency derived in (4.5) and(4.17) for i.i.d. Rayleigh fading channel and the target BER is set to be 0.1%, we

45


Nr 2 4 6γsp 18.3dB 7.3dB 4.7dB

Table 4.1: SNR switching point in i.i.d. Rayleigh fading channel

10−5

10−4

10−3

10−2

10−1

8

10

12

14

16

18

20

22

Pb

SN

R [d

B]

Figure 4.6: Switching point of ZF-OSTBC in a 2× 2 i.i.d. Rayleigh fading channel

are able to nd the switching point by solving the equation for γ0:

DRostbc(γ0) = DRzf (γ0). (4.21)

Unfortunately, the equation is intractable and only numerical results can be foundby using Newton-Raphson method [67], which are listed in Table 4.1.

Furthermore, the decrease of the target BER results in a raise of the switchingpoint, as shown in Figure 4.6. This is due to the fact that ZF has a higher spatialmultiplexing gain and the rate is more aected by the decreased target BER.

The selection of the optimal algorithm depends on the SNR only, not the exactchannel realization, which can be regarded as static adaptation. On the other hand,if we compute the constellation size by assuming OSTBC and ZF, respectively, andchoose the one with higher modulation order for every channel realization, a higherspectral eciency is obtained as shown in Figure 4.7. This can be viewed as dy-namic adaptation. The gap between static adaptation and dynamic adaptation ismaximally 2dB which happens at the switching point when Nr = 2. This is due

46


to the fact that the two schemes have similar performance and it really dependson the instantaneous channel gain to decide which one is better. At low SNRs, dy-namic adaptation has almost the same spectral eciency as static adaptation sinceOSTBC outperforms ZF most of the time. The situation is similar at high SNRswhere ZF is favored. However, the price we have to pay for dynamic adaptation isa higher system complexity. As the number of receive antennas increases, the dif-ference between the two adaptation strategies is vanishing to negligibly small. Thisis because OSTBC and ZF have similar performance around the switching pointin the 2× 2 case, the benet we can get from dynamic adaptation is maximal dueto the uncertainty. As Nr increases, the performance of OSTBC diers distinctlyfrom ZF around the switching point, as can be seen in Figure 4.8, and the benetof adaptation becomes negligible.

0 5 10 15 20 25 30 35 40 450

2

4

6

8

10

12

SNR [dB]

spec

tral

effi

cien

cy [b

ps/H

z]

dynamic adaptationstatic adaptation

Nr=2

Nr=4

Nr=6

Figure 4.7: Spectral eciencies achieved by static adaptation and dynamic adap-tation in 2×Nr i.i.d. Rayleigh fading channel

If the channel is spatially correlated Rayleigh fading, the switching point canbe derived from:

DRostbc(γ0, ρtx) = DRzf (γ0, ρtx). (4.22)The solutions for ρtx = 0.5 are derived numerically for Nr = 2, 4, 6 in Table 4.2.

It has been shown in many contributions, e.g. [33,34], that the spatial correlationhas an eect on the capacity. As a result, the spectral eciency also depends onthe spatial correlation. The impact of spatial correlation on the spectral eciency

47


0 5 10 15 20 250

2

4

6

8

10

12

SNR [dB]

spec

tral

effi

cien

cy [b

ps/H

z]

2x2 ZF2x2 OSTBC2x4 ZF2x4 OSTBC2x6 ZF2x6 OSTBC

Figure 4.8: Crossing points of the spectral eciencies in 2 × Nr i.i.d. Rayleighfading channel

Nr 2 4 6γsp 21.8dB 8.8dB 6.6dB

Table 4.2: SNR switching point in spatially correlated Rayleigh fading channel

is shown in Figure 4.9 and Figure 4.10 for 2 × 2 and 2 × 6 systems, respectively,where ρtx is used to quantify the spatial correlation at the transmitter. It is noticedthat OSTBC is more robust to the variation of the spatial correlation compared toZF. The spectral eciency of ZF degrades dramatically as ρtx increases.

The idea of ZF is to project the received signal, consisting of two partsthe inter-ference and the desired signalonto a subspace that is orthogonal to the interferencewhile keeping as much as possible of the desired signal. If high spatial correlationexists at the transmitter, it means the interference is aligned in a direction closeto the desired signal and the eective SNR after the projection would inevitablysuer a lot. The detection of OSTBC, on the other hand, combines the receivedsignal constructively to cancel out the interference, so there is no SNR degradationin the process. The theoretical p.d.f. of the eective SNR is illustrated in Figure4.11 to present the SNR degradation due to spatial correlation. We notice thatthe shape and peak of the p.d.f. does not change much in case of OSTBC as the

48

4.4 Conclusions

0 5 10 15 20 250

1

2

3

4

5

6

7

8

SNR [dB]

spec

tral

effi

cien

cy [b

ps/H

z]

ρtx

=0.9 OSTBC

ρtx

=0.9 ZF

ρtx

=0.5 OSTBC

ρtx

=0.5 ZF

ρtx

=0.1 OSTBC

ρtx

=0.1 ZF

Figure 4.9: Spectral eciencies achieved by OSTBC and ZF in 2×2 Rayleigh fadingchannel with dierent correlation coecients

correlation coecient increases, which means there is only a small variation of theaverage eective SNR. However, the SNR of ZF experiences serious degradation asthe correlation coecient increases.

4.4 Conclusions

Closed form expressions of the spectral eciency of an uncoded adaptive modula-tion system, namely DRSE, are derived for OSTBC and spatial multiplexing withZF receiver. By predening the modulation scheme and the target BER, the DRSEsonly depend on the SNR and possibly the spatial correlation coecient in case ofspatially correlated Rayleigh fading channel. the DRSEs of OSTBC are providedin (4.5) and (4.14) for a 2×Nr MIMO system in i.i.d. Rayleigh fading channel andspatially correlated Rayleigh fading channel, respectively. (4.17) and (4.20) presentthe DRSEs of ZF in i.i.d. Rayleigh fading channel and spatially correlated fadingchannel with transmit spatial correlation. Furthermore, the DRSEs of ZF receiverin the two types of channel can be generalized to (4.20) with 0 ≤ ρtx < 1.

To further enhance the spectral eciency, a low complexity adaptation schemethat switches between OSTBC and ZF is suggested based on the DRSEs. Theswitching points for dierent antenna setups in dierent channel environment are

49


0 5 10 15 20 250

2

4

6

8

10

12

SNR [dB]

spec

tral

effi

cien

cy [b

ps/H

z]

ρtx

=0.1 OSTBC

ρtx

=0.1 ZF

ρtx

=0.5 OSTBC

ρtx

=0.5 ZF

ρtx

=0.9 OSTBC

ρtx

=0.9 ZF

Figure 4.10: Spectral eciencies achieved by OSTBC and ZF in 2 × 6 Rayleighfading channel with dierent correlation coecients

found numerically by the Newton-Raphson method.

Appendices

4.A The p.d.f. of the eective SNR of OSTBC incorrelated Rayleigh fading channel

In this appendix, the p.d.f. of the eective SNR are derived for 2×Nr OSTBC inspatially correlated Rayleigh fading channel with spatial correlation on the trans-mitter side only.

Since γ1 and γ2 (4.2) are independent random variables, the p.d.f. of γ is theconvolution of p(γ1) and p(γ2), where p(γi) is given by

p(γi) =2NrγNr−1

i

(Nr − 1)!(γ0ωi)Nre− 2γi

γ0ωi .

50

4.A The p.d.f. of the eective SNR of OSTBC in correlated Rayleighfading channel

0 10 20 300

0.5

1

1.5

2

2.5

3

3.5

4

4.5x 10

−3

SNR [dB]

p(γ)

OS

TB

C

0 10 20 300

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

SNR [dB]

p(γ

) ZF

ρ

tx=0.1

ρ tx

=0.5

ρ tx

=0.9

ρ tx

=0.1

ρ tx

=0.5

ρ tx

=0.9

Figure 4.11: The p.d.f. of eective SNR when γ0 = 20dB

The p.d.f. of γ can then be obtained:

p(γ) =∫

γ1

p(γ1)p(γ − γ1)dγ1

=4Mre−

2γγ0ω2

(Nr − 1)!2(γ20ω1ω2)Nr

∫ γ

0

(γ1γ − γ21)Nr−1e

2λ1−2λ2γ0ω1ω2

γ1dγ1 (4.23)

For convenience, we repeat the notations here:

Mi = 2Nr − i− 2,

a = 2(

1ω1

− 1ω2

),

b =4Nr

(Nr − 1)!2(γ20ω1ω2)Nr

,

Pnm =

m!(m− n)!

,

(m

n

)=Pn

m

n!=

m!(m− n)!n!

,

51


and the integration can be rewritten as:

p(γ) = be−2γ

γ0λ2

∫ γ

0

(γ1γ − γ21)Nr−1e−aγ1dγ1 (4.24)

Integrating∫ γ

0

(γ1γ − γ21)Nr−1e−aγ1dγ1

=∫ γ

0

Nr−1∑

i=0

(Nr − 1

i

)(γγ1)i(−γ2

1)Nr−1−ie−aγ1dγ1

=Nr−1∑

i=0

(Nr − 1

i

)γi(−1)Nr−1−i

∫ γ

0

γ2Nr−i−21 e−aγ1dγ1

=Nr−1∑

i=0

(Nr − 1

i

)γi(−1)Nr−1−i

e−aγ1

(−a)Mi+1

Mi∑

j=0

PjMi

(−1)j(−aγ1)Mi−j

γ

0

=Nr−1∑

i=0

(−1)Nr−i(Nr−1

i

)γi

aMi+1

e−aγ

Mi∑

j=0

PjMi

(aγ)Mi−j −Mi!

(4.25)

The third equation follows the indenite integral of exponential function, in whichthe exponent a 6= 0. Recall that a = −4ρtx/γ0(1− ρ2

tx), it is equivalent to ρtx 6= 0.Insert (4.25) into (4.24), the p.d.f. of eective SNR is written as:

p(γ) = be−2γ

γ0λ2

Nr−1∑

i=0

(−1)Nr−i(Nr−1

i

)γi

aMi+1

e−aγ

Mi∑

j=0

PjMi

(aγ)Mi−j −Mi!

(4.26)

4.B Asymptotic p.d.f. of the eective SNR of OSTBC

In this appendix, the p.d.f. of the eective SNR of OSTBC is derived as ρtx → 0.By denoting x = aγ, we can rewrite (4.13) as:

p(γ) = be−2γ

γ0ω2 γ2Nr−1Nr−1∑

i=0

(−1)Nr−i(Nr−1

i

)

xMi+1

e−x

Mi∑

j=0

Mi!xMi−j

(Mi − j)!−Mi!

(4.27)

52

4.B Asymptotic p.d.f. of the eective SNR of OSTBC

Recall the Taylor series expansion: ex = 1 + x + 12!x

2 + 13!x

3 + . . ., (4.27) can berewritten as:

p(γ) = be−2γ

γ0λ2 γ2Nr−1Nr−1∑

i=0

(−1)Nr−i(Nr−1

i

)

xMi+1

[Mi!e−x

(ex − xMi+1

(Mi + 1)!−O(xMi+2)

)−Mi!

]

= be−2γ

γ0λ2 γ2Nr−1Nr−1∑

i=0

(−1)Nr−i+1

(Nr − 1

i

)Mi!e−x(

xMi+1

(Mi+1)! +O(xMi+2))

xMi+1

As ρtx → 0,

p(γ) → 2e−2γγ0 (2γ/γ0)

2Nr−1

(Nr − 1)!2γ0

Nr−1∑

i=0

(−1)Nr−i+1

Mi + 1

(Nr − 1

i

), (4.28)

where∑Nr−1

i=0(−1)Nr−i+1

Mi+1

(Nr−1

i

)is shown to be equal to (Nr−1)!2

(2Nr−1)! from computersimulation. Therefore (4.13) is approaching to (4.4) and the resulting discrete-ratespectral eciency (4.14) reduces to (4.5) as ρtx → 0.

53

Chapter 5

Software Dened Radio Workbench(SDR-WB)

As a promising solution for the fast developing radio communications, SoftwareDened Radio (SDR) has received more and more interests recently. The idea ofSDR is to put the AD/DA converters as close as possible to the antennas andoperate as much as possible in the digital domain by software; the hardware at thefront end is parameterized so that they can be operated in the right mode, e.g.frequency band, sampling frequency, etc.

In this chapter, we present a generic workbench for SDR that is supportableto both narrow-band and wideband systems with either single antenna or multipleantennas.

5.1 IntroductionThe SDR-WBmainly deals with the digital signal processing in MATLAB/OCTAVEsimulation environment. In order to accommodate various communications stan-dards, the workbench is functionally modularized into generic blocks with a stan-dardized interface. Furthermore, the numbers, e.g. number of transmit and receiveantennas, are parameterized so that the workbench can be easily recongured.These properties facilitate the modication and extension of the workbench andnew transmission schemes can be easily adopted.

5.2 Workbench architectureThe main function of the workbench is called 'SDR.m', the execution of which isdivided into three phases: setup (initializations of all functions and parameters),run (data transmission) and wrapup (results calculation).

Inside every phase, the modules are called in a specied order. There are vemain modules in the workbench: SOURCE, TX, CH, RX and SINK, as shown in

55

Software Dened Radio Workbench (SDR-WB)

Figure 5.1. They indicate the signal source, the transmitter, the wireless channel,the receiver and the signal sink. Within every module, there exist sub-modules tosplit the task into several sub-tasks and have them accomplished separately by themodels, e.g., BPU_T in TX calls scrambler, channelcoder and interleaver to dealwith all bit processing tasks. Alternatively, modules can call models directly tohandle the basic signal processing. For example, msource in SOURCE generatesrandom data bits to be transmitted.

CH

TX

BPU_T SPU_T DRU_T ARU_T

FCH

RX

BPU_R SPU_R DRU_R ARU_R

SOURCE

SINK

EAU_R

EAU_T

RCH

Figure 5.1: Block diagram of the modularized workbench

The main le structure of the workbench in case of MIMO-OFDM with SVDis illustrated in Figure 5.2. The top level include the main function SDR and thephase functions, namely Setup, Run and Wrapup. On the second level are themodules that are directly called by the top level functions, i.e. SOURCE, TX, RX,CH and SINK. Modules can be further broken down into either sub-modules, e.g.BPU_T, SPU_T, or models, e.g. msource, displayresults.

Kernel functions

The phase functions mentioned in the preceding section, namely, Setup, Run,Wrapup, are kernel functions that dene the data ows of the workbench. Theyare located in a right limited directory that not supposed to be viewed or modiedby the users.

56

5.2 Workbench architecture

SDR.m

SOURCE.m TX.m CH.m RX.m

msourc

e.m

SINK.m

EA

U_T

.m

mqu

antis

er.m

AR

U_

T.m

DR

U_

T.m

SP

U_T

.m

BP

U_T

.m

FC

H.m

RC

H.m

GC

H.m

EC

H.m

scra

mb

ler.m

inte

rleave

r.m

ch

ann

elc

od

er.m

mod

ula

tor.m

de

mu

x.m

enco

de

rSV

D.m

ifftma

pp

er.m

pe

rmu

tato

r.m

pre

am

ble

r.m

F2T

.m

add

CP

.m

iidC

H.m

dsC

H.m

stC

H.m

aw

gn

.m

AR

U_

R.m

EA

U_R

.m

BP

U_R

.m

SP

U_R

.m

DR

U_

R.m

de

scra

mble

r.m

de

inte

rleave

r.m

cha

nn

eld

eco

de

r.m

decod

erS

VD

.m

mu

x.m

dem

od

ula

tor.m

depre

am

ble

r.m

rem

ov

eC

P.m

T2

F.m

dep

erm

uta

tor.m

fftmap

per.m

calc

resu

lts.m

dis

pla

yre

su

lts.m

write

resu

lts.m

Setup.m Run.m Wrapup.m

Figure 5.2: File structure of the workbench

Modules

The SOURCE generates data bits that are to be transmitted. Then the data bits areencoded and mapped into symbols in the TX before they are sent to the antennas.Through CH, the discrete-time signal is received at the RX, where the data bitsare detected. The results such as BER and spectral eciency are computed andshown in the SINK, both in table- and graphical format.

The TX and RX consist of several generic sub-modules: BPU for the Bit Pro-cessing Unit, SPU for the Symbol Processing Unit, DRU for the Digital RadioUnits, ARU for the Analog Radio Units and EAU for the Estimation and Adapta-tion Units, which are dedicated for channel estimation and link adaptation for thepurpose of adaptation.

The CH is made up of four sub-modules: GCH to generate the complex valuedchannel matrix, FCH to feed the transmitted signal through the channel generatedby GCH, RCH to feedback CSI from RX to TX which is used in an adaptive systemthat needs CSI at the transmitter and ECH to obtain perfect channel informationdirectly from GCH.

57


Sub-modules

Sub-modules in TRX

Since TX and RX have a complicated signal processing procedure as shown inFigure 5.2, it is necessary to divide them into sub-procedures that are treatedby sub-modules, i.e., BPU_T,R, SPU_T,R, DRU_T,R, ARU_T,R andEAU_T,R.

BPU_T include all the bit processing units, like data bit scrambler, convolu-tional channel coding and block interleaver.

SPU_T deals with the symbol processing part. It maps the bits into symbolsand operates some application-specic functions, like MIMO encoding.

DRU_T consists of the blocks that are located before the DA converter, suchas OFDM modulation, interpolation and channel ltering.

ARU_T include the frequency translation, power amplier, and transmitterlter. They have not been implemented yet.

EAU_R is composed of two parts, channel estimation and link adaptation.Link adaptation is used in adaptive systems to update the transmission parametersdepending on the CSI from the channel estimation. EAU_T is designed to managethe adaptive transmission based on full or partial CSI.

Sub-modules in CH

GCH calls various models to generate a channel with desired statistics. Then thegenerated channel is called in FCH to compute the received signal. At the receiver,channel information is required to detect the transmitted signal, which is obtainedeither from channel estimation using preamble, or from ECH to get the error-freeCSI. In case of an adaptive system, RCH is applied to feedback the partial or fullCSI from RX to TX.

Models

The basic units of the workbench that perform the signal processing to realize anatomic functionality are called models. All of the models are parameterized to easereconguration. The values of the parameters are pre-dened in a correspondingini-le of the model, where they are systematically organized and can be easilyaltered. For users' convenience, these parameters are alternatively specied in theupmost system-level ini-le such as SDR.ini, so that one doesn't need to go throughthe hierarchy into every ini-le to change the parameter values. Furthermore, allmodels are written independently with each other so that they can be arbitrarilyassembled as long as they make sense.

58

5.3 Control ows

Other functions

Besides the kernel, modules, submodules and models functions, there are othersupporting user-dened functions. For instance, readParam.m helps each mod-ules/models read in the parameter values set in the ini-les; some commonly-usedfunctions which are called by dierent models are modularized into library func-tions, such as root-raised-cosine lter; template les for sub-modules and models areavailable to provide guidelines to users who want to extend or recongure the work-bench. Furthermore, the system parameters for dierent transmission schemes, e.g.,WCDMA, MIMO-SVD, OFDM, MIMOOFDM-GSTBC, are stored in application-specic ini-les.

5.3 Control ows

The applications supported by SDR-WB can be categorized into two classes: thechannel-adaptive transmission schemes (Scenario_CSIT) and non-adaptive schemes(Scenario_Blind).Scenario_CSIT treats the applications that adapt the transmission parameterssuch as rate and power depending on the partial or full CSI.Scenario_Blind does not have CSIT and the transmission parameters are xedregardless of the variation of the wireless channel.As a result, the process of them in the Run phase distinguishes from each other, asillustrated in Figure 5.3. The loop is a parameter of Monte Carlo simulation used inboth owcharts to get an average measure of the performance for each SNR point.In Scenario_CSIT, since the transmission depends on the estimated CSI from thereceiver, the execution of data transmission is placed after the channel estimation.To improve the program eciency and get error-free channel estimation, the chan-nel estimation by using preamble is substituted by ECH. Based on the perfect CSIobtained from ECH, the transmission parameters such as modulation order arecomputed by EAU_R. If the eective SNR is lower than the cut-o threshold, i.e.,γ < γ0, then no data is going to be transmitted and a new channel realizationstarts. Otherwise the transmission parameters are fed back through RCH to TXand a conventional transmission is carried out. The process of Scenario_Blind issimilar to the Scenario_CSIT except that EAU_R and RCH are omitted in thiscase.

Both control ows discussed here assume a quasi-static fading channel, i.e. thechannel remains constant for the current loop and changes independently for thenext channel realization (loop). Therefore, the channel applied in data transmissionis the same as the channel generated at the beginning of the loop. Alternatively,if a delay exists for the two cases, the channel varies within one interval and FCHhas to employ a new channel realization generated by GCH.

59


GCH

ECH EAU_R

TX

FCH

RX

RCH

SOURCE

SINK

0

LOOP?

START

END

No

Yes

Yes

No

GCH

ECH

TX

FCH

RX

SOURCE

SINK

LOOP?

START

END

No

Yes

Scenario_CSIT Scenario_Blind

Figure 5.3: Flowcharts in the run phase

5.4 Case study

Thus far, the transmission schemes that can be simulated by SDR-WB include:SISO, OFDM, MIMO, MIMO-OFDM and WCDMA. Dierent algorithms are avail-able for MIMO technology, e.g., SVD, OSTBC, D-STTD, BF. In this section,

60

5.4 Case study

we present two examples of simulating a MIMO-OFDM system with SVD anda MIMO-STBC in the SDR-WB.

MIMO-OFDMThere are four transmit antennas and four receive antennas, the number of sub-carriers for OFDM is 64, 48 out of which are used to carry the information-bearingsignals. We assume a frequency-selective Rayleigh fading channel generated bya deterministic spatial-temporal channel model [18]. Perfect CSI is available atthe transmitter so that adaptive modulation is applied for every scalar channel.Furthermore, adaptive power control utilizing the uniform on/o power allocationis considered in spatial domain for the sub-channels at the same frequency bin.

SetupIn the setup phase, the system parameters are read from MIMOOFDM-SVD.ini, an application-specic ini-le on the top level. Then the workbenchgoes through all models that are going to be called later in the run phase toinitialize the parameters. A list of models that are called is already given inFigure 5.2.

RunScenario_CSIT is called by Run to control the data ow as shown in Figure5.3 (the left one). In Monte-Carlo simulations, the results are averaged overa large number of channel realizations.

WrapupThe simulation results are computed based on 10, 000 channel realizations,and shown in Figure 5.4, 5.5 and 5.6. Figure 5.4 shows the BER performanceof the system, which is around 10−4, less than the target BER, 10−3. Thethroughput is shown in Figure 5.5, where a large SNR gap exists betweenthe theoretical capacity and the throughput [12]. Figure 5.6 illustrates theaverage number of bits loaded on every frequency index as a function of SNR.There is no dierence between the average number of bits loaded on everyfrequency index since the average sub-channel gain is equivalent to each otherover a large number of channel realizations.

MIMO-STBCIf the CSI is not available at the transmitter, xed transmission is applied regardlessof the channel quality. The control ow is given in Figure 5.3 (the right one) andthe BER performance of MIMO-OSTBC in a 2 × 2 at Rayleigh fading channelassuming 16−QAM modulation is shown in Figure 5.7.

61


0 5 10 15 20

10−4

10−3

SNR [dB]

BE

R

Figure 5.4: 4× 4 BER in frequency-selctive Rayleigh fading channel

0 5 10 15 20 250

5

10

15

20

25

SNR [dB]

Thr

ough

put [

bps/

Hz]

CapacityThroughput

Figure 5.5: 4× 4 throughputs in frequency-selctive Rayleigh fading channel

62

5.4 Case study

05

1015

2025

0

20

40

601

2

3

4

5

6

SNR [dB]#subcarriers

Figure 5.6: Number of bits loaded on sub-carriers

0 5 10 15 20 2510

−6

10−5

10−4

10−3

10−2

10−1

100

SNR [dB]

BE

R

Figure 5.7: 2× 2 BER in at Rayleigh fading channel

63


5.5 ConclusionsThis chapter described a generic simulation workbench for multiple antenna SDRsystems in MATLAB or OCTAVE, for both Windows and Unix/Linux operatingsystems. The workbench is functionally modularized into blocks and sub-blockswith a common interface for the convenience of modication and reconguration.Currently, it accommodates a variety of transmission schemes, including single-carrier multiple-input multiple-output (MIMO), Orthogonal Frequency-DivisionMultiplexing (OFDM), multi-carrier (OFDM) MIMO, Wideband Code DivisionMultiple Access (WCDMA), ltered multitone (FMT).

In future, more features are going to be included to the SDR-WB, e.g., preamblerdesign for MIMO-OFDM, wideband channel models for 802.11n, multiuser scenario,MAC layer design, and etc. New applications such as RFID, UWB OFDM/OQAMand more are going to be realized.

64

Chapter 6

Conclusions and future work

6.1 Conclusions

In this thesis, we investigated adaptive transmission strategies to maximize thespectral eciency in a communication system with multiple antennas. Our par-ticular focus was on the scenario that the receiver has perfect CSI and adapts thetransmitter accordingly by employing a non-delayed feedback channel. The channelused throughout the thesis was assumed to be quasi-static at fading either withspatial correlation or without spatial correlation.

We began our investigation with a description of baseband-equivalent signalmodels for wireless communication systems where both the transmitter and the re-ceiver were equipped with multiple antennas. Three statistical channel models wereprovided to simulate i.i.d. Rayleigh fading channel, spatially correlated Rayleighfading channel and Ricean fading channel, respectively. Moreover, three MIMOschemes were described, namely SVD, spatial multiplexing with ZF and OSTBC.

With SVD, the MIMO channel can be converted into a set of parallel sub-channels over which separate data streams were transmitted. To achieve the highestspectral eciency, adaptive modulation and adaptive power control were employedon every singular value channel subject to a peak power constraint and an instan-taneous target BER. We started with a discussion on adaptive modulation andconstant power, where the SNR thresholds for maintaining the instantaneous BERunder a predened target were obtained and the closed form expression of thespectral eciency, namely DRSE was acquired. Then we extended the discussionsby including adaptive power control policies. In this occasion, waterlling can nolonger provide the maximal spectral eciency, but a modied version of waterllingcan still achieve a relatively high spectral eciency. To reduce the computationalcomplexity of waterlling-based schemes, the greedy allocation was suggested andit can achieve comparable performance to the modied waterlling. To further sim-plify the power control policy, the uniform power allocation with TAS was adoptedand it was found to reach the same spectral eciency as the modied waterlling

65

Conclusions and future work

in low SNR regions.By utilizing adaptive modulation in ZF and OSTBC, we obtained closed form

expressions of the spectral eciencies under dierent channel conditions. With theDRSEs, we were able to nd the crossing point of the two curves numerically andan adaptation strategy switching between ZF and OSTBC was proposed based onthe crossing point. In contrast to conventional adaptation strategies, the proposedadaptation added more exibility to the system design and enhanced the spectraleciency by trading o the two candidate schemes.

Last but not the least, a recongurable versatile SDR workbench that accommo-dates a variety of wireless communication systems was described. The workbenchincluded the transmitter, the wireless channel and the receiver. It has a hierarchicalstructure consisting of generic blocks and each block is parameterized for ease ofreconguration.

6.2 Future workAs stated in Chapter 3, the dynamic power allocation has been evolved from singletarget to multi-target. However, the optimal multi-target power allocation inan adaptive modulation system that maximizes the spectral eciency is still notavailable.

Chapter 4 proposed a novel approach to adapt the transmitter based on the CSI,which exhibited a promising gain in spectral eciency. However, the adaptationis based upon the assumption that the channel is either i.i.d. Rayleigh fading orsemi spatially correlated with correlation on the transmitter side. An immediateproposition for future work is to extend the channel environment to Ricean fadingand spatially correlated Rayleigh fading with correlation on both sides. Further-more, other schemes, e.g. spatial multiplexing with MMSE receiver, D-STTD, canbe considered.

The adaptation strategies in both chapter 3 and 4 assume perfect CSI at the re-ceiver and the transmitter. It is an interesting topic to take into account imperfectCSI and analyze its impact on the system performance. Furthermore, channel cod-ing should be taken into account in future study, where a pronounced improvementin the performance of spectral eciency is expected.

The main functionalities of the SDR workbench is already nished, but moreblocks should be added to cover more cases, for instance, channel models usedin 3GPP and 802.11n should be incorporated. On the other hand, more wirelessapplications can be applied in SDR-WB, e.g. WiMAX, Bluetooth, GSM and etc.

Finally, implementation of the SDR-WB with special focus on adaptation strate-gies is of great interest. FPGA is a promising candidate to implement the basebandsignal processing in the digital domain.

66

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