Proposal Thesis Update 25

7/29/2019 Proposal Thesis Update 25

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PhD Proposal

Design of Adaptive MIMO Wireless

Communications Systems

Mabruk Gheryani

Supervisor: Dr. Yousef R. Shayan

May 24, 2007


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Abtract

Design of Adaptive MIMO Wireless

Communications Systems

Mabruk Gheryani, PhD

Concordia University, 2007

Since the discovery of MIMO channel capacity, a lot of research works have

been done in this field. Space-time (ST) codes are the most promising technique for

MIMO systems. However, in most applications, the channel state information (CSI)

is assumed to be known to the receiver but unknown to the transmitter. To furtherimprove the system performance, the transmitter shall adapt the transmission rate

based on the level of CSI fed back from the receiver. Our overall goal in this study

is to develop adaptive MIMO schemes that can adapt the transmission rate based on

the level of CSI and meanwhile satisfy the given quality of service (QoS).

First, a tight upper bound of error probability at high signal-to-noise ratio is

derived for full-rate linear dispersion code and the bound is verified by simulation

results. For the low signal-to-noise ratio, a upper bound is also found without strictmathematical proof. The theoretical results demonstrate the relationship between

the error probability, the constellation size and the space-time symbol rate.

Secondly over a Rayleigh fading channel, the probability density function of

signal-to-interference-noise ratio of a MIMO transceiver using full-rate linear disper-

sion code and linear minimum-mean-square-error receiver is derived. With these

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theoretical results as a guideline, we study the design of adaptive systems with dis-

crete selection modes. An adaptive algorithm for the selection-mode adaptation is

proposed. Based on the proposed algorithm, two adaptation techniques using con-

stellation and space-time symbol rate are presented, respectively. To improve the

average transmission rate, a new adaptation design is developed, which is based on

joint constellation and space-time symbol rate adaptation. Simulation results and

theoretical analysis are provided to verify our new design.

As future work, new beamforming techniques and adaptation strategy will

be further investigated. Additionally, overall adaptation design for a concatenated

system will be studied.

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Contents

Abstract i

List of Tables v

List of Figures vi

Notations and Abbreviations vii

Chapter 1 Introduction 1

1.1 Research Background . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Literature Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.3 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 Organization of the proposal . . . . . . . . . . . . . . . . . . . . . . . 5

Chapter 2 Performance Analysis of linear dispersion codes 62.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.3 Performance Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.4 Simulation Results and Discussions . . . . . . . . . . . . . . . . . . . 13

2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Chapter 3 New Adaptive MIMO System using full rate linear disper-

sion code with Selection Modes 16

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.2 Adaptive Transceiver . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.2.1 The Adaptive Transmitter . . . . . . . . . . . . . . . . . . . . 17

3.2.2 The Statistics of SINR with the MMSE Receiver . . . . . . . . 17

3.3 Design of Adaptive Transceiver . . . . . . . . . . . . . . . . . . . . . 25

3.3.1 Adaptation Using Variable Constellations . . . . . . . . . . . 26

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3.3.2 Adaptation Using Variable ST Symbol Rate . . . . . . . . . . 32

3.4 Joint Adaptation Technique . . . . . . . . . . . . . . . . . . . . . . . 38

3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Chapter 4 Conclusions and Remaining Works 44

4.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.2 Remaining Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Bibliography 47

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List of Tables

3.1 adaptive constellation with ST symbol rate =1, 2, 3 and 4 . . . . . . 31

3.2 adaptive ST symbol rate when constellation size=BPSK, QPSK, 8PSK

and 16QAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.3 Joint Adaptive Of ST symbol rate and Constellation Size . . . . . . . 40

4.1 Schedule for the remaining tasks. . . . . . . . . . . . . . . . . . . . . 46

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Notations and Abbreviations

X: upper bold letter for matrix

x: lower bold letter for column vector

XH: hermitian of X

XT: transpose of X

: Kronecker product

diag[x]: a diagonal matrix with x on its main diagonal

tr(X): trace ofX

det(X): determinant of X

vec(X): a column vector formed by stacking the column vectors of X in order

: Euclidean norm

{x}: a set ofx

P(x): probability of event x

E(x): expectation of x

AWGN: additive white Gaussian noise

BER: bit error rate

BLAST: Bell-labs layered space-time

CSI: channel state information

FDFR: Full Diversity Full Rate

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Chapter 1

Introduction

1.1 Research Background

In the future wireless communications, one major challenge is to design an flexible

system that can adapt the transmission rate to the channel condition while the target

quality of service (QoS) is also satisfied [1].

Recent significant advances in wireless communications is the so-called multiple-

input-multiple-output (MIMO) technology [2][3]. It makes use of multiple transmit

and receive antennas to improve the data rate and performance over fading channels.

Since the advent of MIMO technology, tremendous research and development efforts

in academia and industry have been invested, and this investment is ever increasing.

To date, MIMO technology has been widely used in modern wireless communica-

tion systems, such as WLAN and 3G cellular systems, and is recognized as the most

important enabling technology for future wireless communication systems.

Information theory have demonstrated that a significant gain in capacity over

fading channels can be obtained in MIMO systems [2][3]. Furthermore, the use of

multiple antennas increases the diversity to combat fading [4][5][6].

To realize the promised theoretical capacity and diversity of MIMO wireless

channels, we propose to develop new adaptive MIMO wireless communication schemes

with maximal data rate for various level of CSI feedback while target QoS is satisfied.

1.2 Literature Survey

After the discovery of capacity of MIMO systems, a lot of research efforts have been

put into this field[2][3]. To exploit the significant capacity and diversity, space-time

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(ST) codes are the most promising technique for MIMO systems. In most appli-

cations, the channel state information (CSI) [7]is assumed to be known or can be

estimated at the receiver but unknown to the transmitter.

To further improve system performance, the receiver feeds back CSI to the

transmitter. With a perfect CSI feedback [7], the original MIMO channel is convertedto multiple uncoupled single-input-single-output (SISO) channels via single value de-

composition (SVD). To maximize the system throughput, the so-called water-filling

(WF) principle is performed on the multiple SISO channels. Numerous schemes have

been proposed based on this optimal solutions. For example, over time-invariant

MIMO channels, it is known that the optimal performance (ergodic capacity) is at-

tained by power water-filling across channel eigenvalues with the total power con-

straint [2]. Also, for time-varying MIMO channels, the optimal performance is ob-

tained through power water-filling over both space and time domains with the average

power constraint [8]. The space-time WF-based scheme and the spatial WF-based

scheme for MIMO fading channels were compared in [9]. The comparison shows that

for Rayleigh channels without shadowing, space-time WF-based scheme gains little in

capacity over spatial WF-based scheme. However, for Rayleigh channels with shad-

owing, space-time WF-based scheme achieves higher spectral efficiency per antenna

over spatial WF-based scheme. A WF-based scheme using imperfect CSI in MIMO

systems was studied in [10]

The feedback bandwidth for the perfect CSI is often very large in all the above

WF-based schemes. To save feedback bandwidth, various beamforming techniquesare also investigated intensively. In these schemes, complex weights of transmit an-

tennas are adjusted according to the CSI feedback. For example, an optimal eigen-

beamforming STBC scheme based on channel mean feedback was proposed in[11].

A MIMO system based on transmit beamforming and adaptive modulation was pro-

posed in[12], where the transmit power, the signal constellation, the beamforming

direction, and the feedback strategy were considered jointly. The analysis of MIMO

beamforming systems with quantized CSI for uncorrelated Rayleigh fading channels

was proposed in [13].

The above schemes often need near-perfect CSI feedback for adaption calcula-

tion. In practice, feedback channel has narrow bandwidth, the feedback CSI is often

not prompt and the CSI estimation is not accurate. All these factors make the CSI

at the transmitter imperfect. In this case, adaptive schemes with selection modes are

often more preferable, which require only partial CSI at the transmitter.

For the MIMO communication system, the structures of most existing ST cod-

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ing designs mainly fall into two categories, either trellis structure or linear structure.

ST codes with trellis structure, such as the space-time trellis codes (STTCs) [5] and

space-time turbo trellis codes (ST Turbo TCs)[14][15][16], can achieve full diversity

and large coding rate. However, their computational complexity grows exponentially

with respect to the number of states and transmit antennas, they are often designedby hand and the trellis structure is not flexible for rate adaptation. ST codes with

linear structure can also be referred to as linear dispersion codes (LDCs), such as

STBC[6][17], Bell-labs layered space-time (BLAST) architectures [18][19][20][21][22].

The LDC allows a variety of decoders including simple linear techniques, higher data

rate and flexibility. However, the error performance of these high-rate LDCs is often

less satisfactory.

To achieve better performance, the idea of concatenated coding schemes is

often applied to MIMO communications recently. By combining two or more relatively

simple constituent codes, a concatenated coding scheme can achieve large coding gain

with a moderately complex decoding. Additionally, such a coding structure also allows

flexible and simple design. In MIMO communications, a ST code is concatenated with

a conventional outer code serially. Such a concatenated coding system often possesses

many advantages: On the one hand, the outer code can provide large coding gain

and time diversity; on the other hand, the inner space-time code provides guaranteed

spatial multiplexing and diversity [23]. Together, they enable a variety of design

targets in performance, bandwidth efficiency, complexity, and tradeoffs among them

[24]. Although any structure of ST codes can be a potential candidate for the innerST modulation, a particular desirable choice is linear dispersion codes (LDCs) instead

of ST codes with trellis structure. This is because the LDC is simple, flexible with

relatively low complexity.

For such a concatenated MIMO system[25], several discrete parameters are

available for adaptation, such as constellation size (i.e., bit-loading), active transmit

antennas and coding rate of the outer code. For example, adaptive modulation with

antenna selection combined with STBC was discussed in [26]-[27]-[28]-[29] [30]. The

advantage of this scheme using STBC is to simplify the design of an adaptive mod-

ulation system. However, this scheme is not flexible for different rates which is the

key requirement in the future wireless communications.

To achieve these requirements, LDCs are applied in our system. The ST symbol

rate of the LDC together with the other parameters can be adjusted for flexible rate

and throughput improvement.

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1.3 Objectives

The overall goal of this study is to develop adaptive MIMO schemes that can improve

the average transmission rate according to the level of CSI and meanwhile satisfy the

given quality of service (QoS). To accomplish our goal, the following tasks will be

carried out.

1. Derive Upper Bound Of Linear Dispersion Code

In general, it is difficult to find the codeword error probability. However, the

pair-wise error probability (PEP) can be used in the codeword design. That is,

the Euclidean distance between the received signals associated with any pair of

codewords shall be maximized by minimizing the PEP between any pair of code-

words. In this task, the upper bounds of error probability for high signal-to-noise

ratio (SNR) and low SNR are obtained, respectively. The bounds demonstratethe relationship between error probability and, space-time symbol rate and the

constellation size. The relationship will be a guideline for adaptation. The task

has been accomplished and will be described in Chapter 2.

2. New adaptive MIMO system with selection modes

In this task, Over a Rayleigh fading channel, the probability density function

of signal-to-interference-noise of a MIMO transceiver using full-rate linear dis-

persion code and linear minimum-mean-square-error receiver is derived. With

these theoretical results as a guideline, new adaptation design with selection

modes is studied. New parameter, i.e., ST symbol rate is introduced to improve

transmission rate together with constellation for the given QoS. This task has

been accomplished and will be described in Chapter 3.

3. New beamforming technique

When more CSI is available at the transmitter, beamforming techniques can be

applied. In this task, new beamforming techniques will be studied for MIMO

adaption.

4. New adaptation strategy

With the adaptation techniques, more efficient new strategy shall be studied

for MIMO adaptation.

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5. Overall adaptation for concatenated system

In this task, we will study the design for overall MIMO concatenated system.

Especially, when turbo principle is applied to the concatenated system, design

for overall adaptive system will be studied.

1.4 Organization of the proposal

The rest of the proposal is organized as follows.

In Chapter 2, For full-rate linear dispersion code, tight upper bounds of the

pair-wise error probability at high SNR and low SNR are obtained and verified. The

theoretical results show the relationship between the error probability and the con-

stellation size and the space-time symbol rate, which will provide guidelines for adap-

tation.In Chapter 3, first we study the probability density function of signal-to-

interference-noise for a MIMO transceiver using full-rate linear dispersion code and

linear minimum-mean-square-error receiver over a Rayleigh fading channel. With the

statistics as a guideline, we study design of the adaptive transceiver with selection

modes. Two adaptation techniques using constellation and space-time symbol rate

are studied, respectively. To improve the average transmission rate, a new adaptation

design is proposed, in which constellation and space-time symbol rate are considered

jointly. Theoretical analysis and simulation results are provided to verify the new

design.

Finally, in Chapter 4, we will conclude our proposal and present the research

schedule for the remaining tasks.

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Chapter 2

Performance Analysis of linear

dispersion codes

2.1 Introduction

The rich and mature knowledge on the conventional outer codes lets us focus on

the adaptive design of the inner ST modulator. Although any existing space-time

code can be a potential candidate for the inner space-time modulation, a particu-

lar desirable choice is linear dispersion codes (LDCs). This is because it subsumes

many existing block codes as its special cases, allows suboptimal linear receivers with

greatly reduced complexity, and provides flexible rate-versus-performance tradeoff

[20]. Hence, in our research, we focus on the LD space-time modulator in the adap-

tive MIMO transmission system. Below, we first introduce our system model and

then provide the performance analysis for the inner ST modulator. The analytical

results will provide design guideline for the adaptive system with selection modes.

2.2 System Model

In this study, a block fading channel model is assumed where the channel keeps con-

stant in one modulation block but may change from block to block. That is, thechannel is not necessarily constant within a coding frame which often consists of a

large number of modulation blocks. Furthermore, the channel is assumed to be a

Rayleigh flat fading channel with Nt transmit and Nr receive antennas. Lets denote

the complex gain from transmit antenna n to receiver antenna m by hmn and collect

them to form an Nr Nt channel matrix H = [hmn], known perfectly to the receiver

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but unknown to the transmitter. The entries in H are assumed to be independently

identically distributed (i.i.d.) symmetrical complex Gaussian random variables with

zero mean and unit variance. The Adaptive MIMO Transmission System is shown in

Figure 2.1.

MLAnt-Nt

ConstellationMapper S/P

M1

1Ant-1

MLOr

MMSE1

Nt

Nt

Ant-1

Ant-Nr

De-Mapper

Binary

Info.

source

Binary

Info.

Out

2Q

L /T

Feedback

Selection

Mode

Figure 2.1: Adaptive Transmission System Model

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In this system, the information bits are first mapped into symbols. After that,

the symbol stream is parsed into blocks of length L. The symbol vector associ-

ated with one modulation block is denoted by x = [x1, x2, . . . , xL]T with xi

{m|m = 0, 1, . . . , 2Q 1, Q 1}, i.e., a complex constellation of size 2Q, such as2Q-QAM). The average symbol energy is assumed to be 1, i.e., 12Q

2Q1m=0

|m|2 = 1.Each block of symbols will be mapped by the ST modulator to a dispersion matrix

of size Nt T and then transmitted over the Nt transmit antennas over T channeluses.An Nt T codeword matrix is constructed as [20].

X =Li=1

Mixi +Li=1

Nixi (2.1)

Where Mi, Ni are the dispersion matrices for the i-th symbol. For simplicity, the

following model will be considered in this study, i.e.,

X =Li=1

Mixi (2.2)

where Mi is defined by its L Nt T dispersion matrices Mi = [mi1, mi2, . . . , miT].The so-obtained results can be extended to the model in (2.1). With a constellation

of size 2Q, the data rate of the space-time modulator is Rm = QL/T bits per channeluse and the data rate of the overall system is R = Rm bits per channel use. Hence, one

can adjust ST symbol rate L/T, constellation size Q, to meet different requirements

on data rate and performance. Since the ST modulation is linear, suboptimal linear

receivers can be used for demodulation [20][21]. It can also be observed that the

space-time mapping schemes used in the existing layered space-time architectures,

e.g., [18]-[19], are LD modulation. Hence the proposed adaptive MIMO Transmission

System with LD ST modulation subsumes existing layered space-time schemes as

special cases. At the receiver, the received signals associated with one modulation

block can be written as

Y = PNt HX + Z = PNt HLi=1

Mixi + Z (2.3)

where Y is a complex matrix of size Nr T whose (m, n)-th entry is the receivedsignal at receive antenna m and time instant n, Z is the additive white Gaussian

noise (AWGN) matrix with i.i.d. symmetrical complex Gaussian elements of zero

mean and variance 2z , and P is the average energy per channel use at each receive

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antenna. It is often desirable to write the matrix input-output relationship in (2.3)

in an equivalent vector notation. Let vec() be the operator that forms a column

vector by stacking the columns of a matrix and define y = vec(Y), z = vec(Z), and

mi = vec(Mi), then (2.3) can be rewritten as

y =

P

NtHGx + z =

P

NtHx + z (2.4)

where H = ITH with as the Kronecker product operator and G = [m1, m2, . . . , mL]will be referred to as the modulation matrix. Since the average energy of the signal

per channel use at a receive antenna is assume to be P, we have tr(GGH) = NtT.

Denoting hi = Hmi as the i-th column vector ofH, the above equation can also bewritten as

y =P

Nt

Li=1

hixi + z (2.5)

2.3 Performance Analysis

After we define our system model as in (2.5). we will start to find the upper bound on

the probability of error. Basically, most of the LD codes have follow (2.5) with differ-

ent design for modulation matrix.The average pairwise error probability conditioning

on H is give byPe(pairwise/H) = P(dEi < dEi+1/si+1 sented) (2.6)

where dEi is the Euclidean distance related to the signal vector si and equal to

dEi = x

SN R

NtHsi (2.7)

We can start from [20] to find the upper bound. In [20]the average pairwise

error probability is obtained by choosing x as Gaussian in (2.5). Then, the error

result is averaged between an independent x and x by applying a union bound tothis average pairwise probability of error which yields an upper bound on probability

of error of a signal constellation.

Pe 2RT1E

detI+ HHH1 (2.8)

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where E[ ]is the expectation over the channel matrix H and = SNR2Nt . Now,we need to find the distribution of the modified H. The modified H depends on Hand G.In the Full Diversity Full Rate(FDFR) design [24][22], the entries of G should

satisfy GGH = INtT to preserve the channel capacity. So that, the entries of the

modified H is still CN(1, 0),Note also that

det

INrT + HHH = det IL + HHH

Lets define

W =

HHH NrT < LHHH NrT L (2.9)

and

n = max(NrT, L), m = min(NtT, L), L = min(NtT, NrT)W is an m m random non-negative definite matrix and thus has real non-

negative eigenvalues.The distribution law of W is called the Wishart distribution

with parameters m and n. The unorder eigenvalues have the joint density function

[2] [32][33][34]

P (1....m) = (m!Km,n)1 exp

i

i

i

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where

k+1() =

k!

(k + n m)!

12

Lnmk () k = 0,...m 1

where Lnmk () is the associated Laguere Polynomial of order k [35] defined as

Lnmk () =k

c=0

(1)c k + n m

k c

cc!

Equation (2.13) can be written as,

f() =1

m

m1k=0

k!

(k + n m)![Lnmk ()]

2 (2.14)

Substituting (2.10) into (2.11) we have that

Pe 2RT1

m

0

(1 + )m

m1k=0

k!

(k + n m)![Lnmk ()]

2d (2.15)

Lets define

K1(k) =k!

(k + n m)!(k + n

)

22kk!

K2(i) =(2i)!(2k 2i)!

i![(k i)!]2(k + n)

K3(d) =(2)d

d!

2k + 2n 2m2k d

(2.16)where n

= n m + 1. Then, we can write (2.12) as

Pe 2RT1

m

m1

k=0K1(k)

k

i=0K2(i)

2k

d=0K3(d) I (2.17)

where I is the intgration part define as

I =0

(1 + )m exp()nm+dd

I = ()m0

(u + )m exp()nm+dd (2.18)

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where u = 1. To compute the above integration,we make use of the result in [35].

0

x(x + u) exp(x) dx

= 21u

+2 (+ 1) exp

12u

Wp,s

1

where W( ) is the Whittaker function defined by Gradshteyn and Ryzhik

[35] then

I = ()m ()dn+2m

2 exp

2

(d + n

)Wp,s

1

(2.19)

where p = (dn

2

) and s = (d+n2m+1

2

)

Substituting (2.19) into (2.17) we have,

Pe 2RT1 ()m exp

2

m1k=0

K1(k)k

i=0

K2(i)

2kd=0

K3(d)(d + n

) ()2mnd

2 Wp,s

1

(2.20)

The above exact upper bound probability of error does not show the diversity

advantage which is the important measure of code performance. We instead examine

the performance at High SNR.

Then, (2.17) can be further upper bounded by

Pe 2RT1

m()m

m1k=0

K1(k)k

i=0

K2(i)2kd=0

K3(d)0

exp()n2m+dd (2.21)

Lets define the integration by I

I =0

exp()n2m+dd

I = (d + n 2m) (2.22)

Substituting I into (2.21) we get the upper bound at high SNR

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Pe Kk,i,d2QL1

m

SNR2Nt

m(2.23)

where

Kk,i,d =m1

k=0 K1(k)k

i=0 K2(i)2k

d=0 K3(d)(n 2m + d)2.4 Simulation Results and Discussions

In this section, we verify our derivation by simulation. In the simulation, Nt = Nr =

T = 2, BPSK and QPSK constellations were assumed. At the receiver, the optimal

maximum-likelihood (ML) detector was applied.

5 10 15 20 2510

9

108

107

106

105

104

103

102

SNR(dB)

e

High SNR Upper bound for BPSK&QPSK LD 2TX & 2RX with ML receiver

SIM BPSK

SIM QPSK

UP BOUND BPSK

UP BOUND QPSK

Figure 2.2: Simulation result and the associated upper bound at high SNR.

In Figure 2.2, the simulation results and the associated theoretical upper

bounds derived at high SNR are compared. Additionally by experiments, we also

find that, if we divide the exponential in the upper bound for high SNR by 2, it

approximates to the upper bound for low SNR. The simulation results and the asso-

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0 2 4 6 8 10 12 14 16

103

102

SNR(dB)

UPPER BOUND FOR LOW SNR FOR 2X2 BPSK& QPSK LDC USING ML Receiver

SIM QPSK

UP BOUND FOR LSNR QPSK

SIM BPSK

UP BOUND FOR LSNR BPSK

Figure 2.3: Simulation result and the associated upper bound at low SNR.

ciated theoretical upper bounds are shown in Figure 2.3. In summary, we have upperbound for both high SNR and low SNR as follows.

Pe Kk,i,d

2RT1

m

SNR2Nt

mfor high SNR

Kk,i,d2RT1

m

SNR2Nt

m/2for low SNR

(2.24)

As can be seen from the Figures, both upper bounds fit well with simulation results.

The simulation results and the associated theoretical bounds have the same slopes.

Some observations related to the above performance analysis will be useful

for future study. The first observation is that from (2.23), the Pe(Q,L,SNR) is

monotonically increasing with respect to ST Symbol rate and the constellation size.

This means that if we increase number of layers, the Pe will increase. We have the

same observation for constellation size.

The second observation is described as follows. The above upper bound shows

that the diversity order of the FDFR MIMO scheme is m = min(NrT, L), where

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L = min(NtT, NrT). For example, if Nr Nt and T Nt then the diversity orderwill be NtT. When we set Nt = Nr and T = Nt then the diversity order will be NtNr.

To satisfy full rate and full diversity, the minimum value for T is Nt and

L = NtT must be satisfied. For given Nt, If T is increase, L will be increased so

that the symbols interference from other layers will be increased and the associateddiversity will be reduced. By these facts, the optimum value for T is Nt.

As mentioned before, the error probability of an FDFR LDC is a function of ST

symbol rate and constellation size. With this fact, we can maximize the transmission

rate by adjusting the ST symbol rate and constellation size jointly while maintaining

the target QoS as described in the next chapter.

2.5 Conclusions

In this chapter, our adaptive MIMO system model with linear dispersion code is

introduced. For full-rate linear dispersion code, a tight upper bound of the pair-wise

error probability at high signal-to-noise ratio is derived and verified by simulation

results. For the low signal-to-noise ratio, a upper bound is also found by experiments

without strict mathematical proof. The theoretical results show the relationship

between the error probability and the constellation size and the space-time symbol

rate. The relationship will provide guidelines for adaptation.

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Chapter 3

New Adaptive MIMO System

using full rate linear dispersion

code with Selection Modes

3.1 Introduction

For the reasons mentioned in Chapter 1, we study the adaptive system with discrete

selection modes in this chapter. With the upper bound of pair-wise error probability

obtained in the last chapter as a guideline, we design an adaptive MIMO system with

discrete selection modes. The associated MIMO transceiver uses an LDC as the ST

modulator and the minimum mean square error (MMSE) detector at the receiver for

simplicity. As mentioned before, different from existing adaptive systems, the new

design adds a new adaptive parameter referred to as ST symbol rate. As can be seen

from the following discussions, by adding this new parameter, the overall throughput

of the system is increased.

3.2 Adaptive Transceiver

In this section, we will introduce our adaptive MIMO transceiver, which uses a LDCas the ST modulator and the MMSE receiver.

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3.2.1 The Adaptive Transmitter

In our design example, the ST modulation is LDC with dispersion matrices given by

M(k1)Nt+i = diag[fk]P(i1) (3.1)

for k = 1, 2, . . . , N t and i = 1, 2, . . . , N t, P is the permutation matrix of size Nt and

given by

P =

01(Nt1) 1INt1 0(Nt1)1

(3.2)where fk denotes the k-th column vector of F. F = [fmn] is a Fast Fourier Transform

(FFT) matrix and fmn is calculated by

fmn =

1

Nt exp(2j(m 1)(n 1)/Nt) (3.3)

3.2.2 The Statistics of SINR with the MMSE Receiver

As a suboptimal receiver for the LDC, linear minimum-mean-square-error detector is

more attractive due to its simplicity and good performance [36][37].

However, the performance analysis in this case is still deficient. Most of the

related works address only the V-BLAST [18][38] scheme, a special case of the full-rate

LDC. For example, the case of two transmit antennas was analyzed in [39] and the

distribution of the angle between two complex Gaussian vectors was presented. Thelayer-wise signal to interference plus noise ratio (SINR) distribution for V-BLAST

with successive interference cancellation at the receiver was provided in [40].

The main goal of this section is to study the statistics of SINR for full-

rate LDCs [20]-[24] using linear minimum-mean-square-error(MMSE) receiver over

a Rayleigh fading channel, which will benefit future studies, such as error-rate prob-

ability.

We consider a general system model as shown in Section 2.2. In our study,

Nr

Nt is assumed. For simplicity, we choose T equal to Nt and L equal to NtT.

Equation (2.4) can also be written as

y =

P

Nthixi +

P

Nt

j=i

hjxj + z (3.4)

In the sequel,the i-th column ofH , denoted as hi, will be referred to as thesignature signal of symbol xi.

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Without loss of generality, we consider the estimation of one symbol, say

xi. Collect the rest of the symbols into a column vector xI and denote HI =[h1,.., hi1, hi+1,..., hL] as the matrix obtained by removing the i-th column from

H.

A linear MMSE detector is applied and the corresponding output is given by

xi = wHi y = xi + zi. (3.5)

where zi is the noise term of zero mean. The corresponding wi can be found as

wi =

hih

Hi + RI

1hi

hHi

hih

Hi + RI

1hi

(3.6)

where RI = HIHHI + 2zI. Note that the scaling factor 1hHi (hihHi +RI)1hi in the coef-ficient vector of the MMSE estimator wi is added to ensure an unbiased estimation

as indicated by (3.5). The variance of the noise term zi can be found from (3.5) and

(3.6) as

2i = wHi RIwi (3.7)

Substituting the coefficient vector for the MMSE estimator in (3.6) into (3.7), the

variance can be written as

2i =1

hH

iR1

Ihi

(3.8)

Then, the SINR of MMSE associated with xi is 1/2i .

i =1

2i=

P

Nt

hHi R

1I hi (3.9)

In our system model, all the symbols has the same SINR, i.e., 1 = 2 = .........L =

By using singular value decomposition (SVD), (3.9) can be written as

= P

NthHi U

1UHhi (3.10)

where UH is an N2t 1N2t 1 unitary matrix and the matrix is (N2t 1)(N2t 1)with nonnegative numbers on the diagonal and zeros off the diagonal. Lets define

h = UHhi

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where 1F1(.,.,.) is Kummers confluent hypergeometric function [35] and defined as

1F1(a,b,x) =n

(a)n(c)n

xn

n!

where ()n = (+n)() .Lets define

K =()NrNt

(NrNt)()NrNt1 exp(

)

Then equation (3.17) can be written as

P/() = Kn

(NrNt r)n(r)n

n

n!

n

(1 + )

r

exp() (3.18)Now, we can find the probability density function (PDF) of as follows.

P() =0

P/()f() d (3.19)

f() was given in [2] and can be written as

f() =1

r

ri=1

i()2NrNtr exp() (3.20)

where

k+1() =

k!

(k + NrNt r)!

12

LNrNtrk ()

k = 0,...r 1

where LNrNtrk () is the associated Laguere Polynomial of order k [35]. Equation

(3.20) can be written as

f() =1

r

r1

k=0k!

(k + NrN

t r)!

[LNrNtrk ()]2 (3.21)

Lets define

K1(k) =k!

(k + NrNt r)!(k + n

)

22kk!

K2(i) =(2i)!(2k 2i)!

i![(k i)!]2(k + n)

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K3(d) =(2)d

d!

2k + 2NrNt 2r2k d

where n

= NrNt r + 1. Then we can write (3.19) as

P() =Kr

r1k=0

K1(k)k

i=0

K2(i)2kd=0

K3(d)0

(1 + )r NrNtr+d

1F1(NrNt r, NrNt, )exp()d (3.22)

The term (1 + )r can be written as

(1 + )

r

=

rr

v=0r

v vrvThen equation (3.22) can be written as

P() =K

r

r

n

nK(n)r

v=0

K(v)K1(k)k

i=0

K2(i)2kd=0

K3(d)

r1k=0

0

NrNtr+d+v+n exp() d (3.23)

with

K(n) =(NrNt r)n

(r)nn!

and

K(v) =

rv

vrThe general form of the integration of (3.23) can be found in [35]

0

x exp(x)dx = !1

where

= NrNt r + d + v + n

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Then (3.23) can be written as

P() =K

r

r

n

nK(n)r

v=0

K(v)r1k=0

K1(k)k

i=0

K2(i)

2kd=0

K3(d)NrNt+rdvn1(NrNt r + d + v + n)! (3.24)

Further,

P() =K

rr

rNrNt+1

r1k=0

K1(k)k

i=0

K2(i)2kd=0

K3(d)

dr

v=0 K(v)v

n K(n)(NrNt r + d + v + n)! (3.25)Lets define

K(v, d) = (NrNt r + d + v)!(NrNt r + d + v + 1)(d + v r + 1)

(d + v + 1)(NrNt + d + v + 1)`K(v)

and

`K(v) =

rv

Then (3.25) can be written as

P() =K

rNrNt1

r

r1k=0

K1(k)k

i=0

K2(i)

2kd=0

K3(d)dr

v=0

K(v, d) (3.26)

This is the PDF of SINR for our system over Rayleigh fading channels.

We verify our derivation by simulation. In the simulation, Nt = Nr = T = 2

and Nt = Nr = T = 4 were assumed. In Figure 3.1 and Figure 3.2, the theoreticalPDFs of the SINR in (3.26) and results by Monte Carlo simulation were compared

for 2 2 and 4 4 channels, respectively at P/2z = 20dB. Simulation results matchto the analytical result very well.

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0 10 20 30 40 50 60 70 80 900

5

10

15x 10

4

Monte Carlo Simulation

Theoretical PDF

2

10

Figure 3.1: Comparison between the theoretical PDF of SINR and Monte CarloSimulation when Nr = Nt = 2 at P/

2z = 20dB

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0 10 20 30 40 50 600

1

2

3

4

5

6

7x 10

4

Monte Carlo Simulation

Theoretical PDF

2

10

Figure 3.2: Comparison between the theoretical PDF of SINR and Monte CarloSimulation when Nr = Nt = 4 at P/

2z = 20dB

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3.3 Design of Adaptive Transceiver

The general idea of adaptive technique with selection modes is to choose from a set of

available adaptive transmission rates. Based on some certain strategy, the transmitter

is informed with necessary information that will be used to increase or decrease the

transmission rate depending on the channel condition (i.e., CSI). For adaptive system

with the selection modes, the SNR will be considered as a proper metric. In this case,

the adaptive algorithm is proposed as follows.

1. Find the SNR at the receiver;

2. Find the BERs associated with the SNR for each mode for the BER curves

obtained from experiments.

3. Select a proper transmission mode with the maximum rate while maintainingthe given target BER.

We can describe the selection of transmission modes as follows.

opt = arg maxn

(BERn() BERtarget)] (3.27)

where n, 1, 2, . . . , N is a transmission mode, BERn() is the BER of the adaptivescheme using the transmission mode n for given SNR . opt is the optimal trans-

mission mode with the maximum data rate for given SNR while the target BERis satisfied. Let Rn denote the rate of the transmission mode n. Without loss of

generality, we assume R1 < R2 < .. . < RN.

Below, we consider the average transmission rate with the above algorithm.

Let n denote the minimum SNR for the given transmission mode n and target

BER, i.e.,

n = arg min [BERn() BERtarget)] (3.28)

Then, the average transmission rate is

R =N

n=1

Rnn+1n

p()d (3.29)

where p() is the probability density function (pdf) of the SNR and N+1 = .The solution for the above optimization problem can be solved using Lagrange multi-

pliers. However, due to the structure of both the objective function and the inequality

constraint an analytical solution is extremely difficult to find as can be seen from SINR

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distribution given in the last section. Therefore, we will find the optimal SNR regions

by using simulation results.

In our simulations, we assume the same system model as Section 2.2 with

Nt = Nr = 4. First, we will start our adaptation using the constellation size while

each set has fixed ST symbol rate. Secondly, we will change the ST symbol ratewith fixed constellation size. Finally, we will adapt these two parameter jointly to

maximize the throughput while maintaining the target BER which is equal 103 in

our design example.

3.3.1 Adaptation Using Variable Constellations

Although the system design for continuous-rate scenario provide intuitive and use-

ful guidelines[12], the associated constellation mapper requires high implementation

complexity. In practice, using discrete constellation is preferable. That is, Q takesonly integer number Q = 1, 2, 3,..... For a given adaptive system, we can adjust the

constellation size to maximize the transmission rate at the same time satisfying the

target BER. The above algorithm is applied to the case. Although any constellation

can be used, we only use BPSK (Q = 1), QPSK (Q = 2), 8PSK (Q = 3) and 16QAM

(Q = 4) as examples. Simulation results are shown in Figure 3.3 - Figure 3.6, where

each Figure has its own ST symbol rate.

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4 2 0 2 4 6 8 10 12 14 16

104

103

102

101

100

SNR(dB)

BER

8PSK1layer

QPSK1layer

BPSK1layer

16QAM1lyaer

Figure 3.3: Adaptive Constellation Size when ST symbol rate=1

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2 0 2 4 6 8 10 12 14 16 18 20104

103

102

101

100

SNR(dB)

BER

BPSK2layer

QPSK2layer

8PSK2layer

16QAM2layer


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5 0 5 10 15 20 25 3010

4

103

102

101

100

SNR(dB)

BER

BPSK3Layer

QPSK3layer

8PSK3layer

16QAM3layer


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0 5 10 15 20 25 30 35

103

102

101

100

SNR(dB)

BER

BPSK4layer

QPSK4layer

8PSK4layer

16QAM4layer


We can find the SNR region for each constellation by curve-fitting technique or

simply by reading the SNR points corresponding to a target BER. The BER versus

SNR relationship can be approximated by the following expression.

BER = aRm,Q exp(bRm,QSN R) (3.30)

where Rm and Q are the ST symbol rate and the constellation size respectively,

and aRmQ and bRmQ are constant which can be found by curve-fitting technique. We

summarize our simulation results in Table 3.1. Note that, LT

Q in Table 3.1 is the

minimum SNR for the given transmission mode.

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Table 3.1: adaptive constellation with ST symbol rate =1, 2, 3 and 4

MODE Constellation size ST symbol rate Total Rate bits/ch use LT

Q

1 BPSK 1 1 11=-0.63092 QPSK 1 2 12=-0.1893

3 8PSK 1 3 13=3.384

4 16QAM 1 4 14=11.7479MODE Constellation size ST symbol rate Total Rate bits/ch use 2Q

1 BPSK 2 2 21=0.83852 QPSK 2 4 22=1.40583 8PSK 2 6 23=5.38864 16QAM 2 8 24=15.4452

MODE Constellation size ST symbol rate Total Rate bits/ch use 3Q1 BPSK 3 3 31=3.10142 QPSK 3 6 32=4.48333 8PSK 3 9 3

3=8.9696

4 16QAM 3 12 34=26.5898MODE Constellation size ST symbol rate Total Rate bits/ch use 4Q

1 BPSK 4 4 41=8.15092 QPSK 4 8 42=14.28123 8PSK 4 12 43=24.25334 16QAM 4 16 44=30.8208

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3.3.2 Adaptation Using Variable ST Symbol Rate

In other existing schemes, only the orthogonal designs, such as Alamouti scheme, are

applied as the ST modulation. In this case, the most convenient adaptive parameter

is the constellation size. For our adaptive scheme, the application of LDC makes

another adaptive parameter available, i.e., ST symbol rate. In this section, we fix the

constellation size but adjust the ST symbol rate for adaptation. Additionally, one

advantage of using ST symbol rate is that it is easier to change ST symbol rate than

constellation size for adaption. The same algorithm can be applied to ST symbol

rate.

Note that, this system with 4 transmit antennas can have 16 choices of ST

symbol rates, i.e., ( 14 164 ). For convenience and less complexity, we use 4choices, i.e., L

T= 1, 2, 3, 4. In the following context, the integer of L

Tis referred as

layer. The simulation results are shown in Figure 3.7 - Figure 3.10.

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2 0 2 4 6 8 10

104

103

102

101

100

SNR(dB)

BER

BER BPSK 4X4

3Layer

4layer

1layer

2layer

Figure 3.7: Adaptive ST symbol rate when Constellation Size is BPSK

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2 0 2 4 6 8 10 12 14 16 18 2010

6

105

104

103

102

101

100

SNR(dB)

BER

BER 4PSK 4X4

2layer

3layer

4layer

1layer

Figure 3.8: Adaptive ST symbol rate when Constellation Size is QPSK

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0 5 10 15 20 2510

4

103

102

101

100

SNR(dB)

BER

BER 8PSK 4x4

1layer

2layer

3layer

4layer

Figure 3.9: Adaptive ST symbol rate when Constellation Size is 8PSK

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0 5 10 15 20 25 30 3510

4

103

102

101

100

SNR(dB)

BER

BER 16QAM 4X4

3layer

1lyaer

2layer

4layer

Figure 3.10: Adaptive ST symbol rate when Constellation Size is 16QAM.

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We summarize these results in Table 3.2 In Table 3.2. LT

Q In Table 3.2 is the

minimum SNR for the given transmission mode.

Table 3.2: adaptive ST symbol rate when constellation size=BPSK, QPSK, 8PSK

and 16QAMMODE Constellation size ST symbol rate Total Rate bits/ch use

LT

Q

1 BPSK 1 1 11=-0.63092 BPSK 2 2 21=0.83853 BPSK 3 3 31=3.10144 BPSK 4 4 41=8.1509

MODE Constellation size ST symbol rate Total Rate bits/ch use i21 QPSK 1 2 12=-0.18932 QPSK 2 4 22=1.40583 QPSK 3 6 32=4.4833

4 QPSK 4 8 4

2=14.2812MODE Constellation size ST symbol rate Total Rate bits/ch use i31 8PSK 1 3 13=3.3842 8PSK 2 6 23=5.38863 8PSK 3 9 33=8.96964 8PSK 4 12 43=24.2533

MODE Constellation size ST symbol rate Total Rate bits/ch use i41 16QAM 1 4 14=11.74792 16QAM 2 8 24=15.44523 16QAM 3 12 34=26.58984 16QAM 4 16 4

4

=30.8208

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3.4 Joint Adaptation Technique

As shown in the above two techniques, adaptation by adjusting either constellation

size or ST symbol rate can increase the average transmission rate satisfying the given

QoS as compared to non-adaptive MIMO schemes. However, we can further improve

the average transmission rate by applying a joint adaptation. The idea of the joint

adaptation is to choose the best combination of constellation size and ST symbol

rate. For the given target-BER, a scheme with the joint adaptation can improve the

average transmission rate significantly as compared to that with only one of the above

two techniques.

Our adaptation in this case works as follows.

maxN

n=1 n()(Qn, (L

T

)n) for BERTarget

where (Qn, (LT)n) is the specific rate associated with a specific fading region and

where n() is the probability of n in the region n. We will used the joint adap-tation technique by choosing the best one from the available curves, which has the

maximum throughput. The simulation results are shown in Figure 3.11.

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0 5 10 15 20 25 30 35

106

105

104

103

102

101

100

SNR(dB)

BER

BER BPSK,QPSK,8PSK,16QAM and 1,2,3,4 ST symbol rate for uncoded LDC with MMSE IC

1layer

1layer

2layer

3layer

4layer2layer

4layer

2layer

4layer

3layer

2layer

1bitBPSK1

2bitQPSK1

4bitQPSK2

6bitQPSK3

6bit8PSK2

9bit8PSK3

8bitQPSK4 8bit16QAM2

12bit8PSK4

16bit16QAM4

Figure 3.11: Joint Adaptive of ST symbol rate and constellation size

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We note from Figure 3.11 that we can reduce the gap between the selection

modes further by adding more choices of the transmission rates. We conclude the

result in Table 3.3, where LT

Q is the minimum SNR for the given transmission mode.

Table 3.3: Joint Adaptive Of ST symbol rate and Constellation SizeMODE Constellation size ST symbol rate Total Rate bits/ch use

LT

Q

1 BPSK 1 1 11=-0.63092 QPSK 1 2 21=-0.18933 QPSK 2 4 22=1.40584 QPSK 3 6 23=4.48335 8PSK 3 9 33=8.96966 8PSK 4 12 34=24.25337 16QAM 4 16 44=30.8208

From Figure 3.11, we observe the following observations:

If the ST symbol rate is reduced, the slope of the associated BER curve becomessteeper, which suggests a larger diversity;

If the constellation size is reduced, the BER curve will go down but with thesimilar slope, which suggests the diversity keeps the same but the coding gain

is enlarged.

There exists a tradeoff between diversity gain and multiplexing gain [23]. However,

this tradeoff can not provide insight for the adaptive system with discrete constel-

lations. From the above observations, we find that we can improve data rate by

using the two adaptive parameters jointly. Specifically, in some cases, we can adjust

constellation size to improve rate and performance; which in the other cases, we will

adjust ST symbol rate, i.e., multiplexing gain, for adaptation. To proceed, we have

the following proposition.

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Proposition 1: The average data rate in the adaptive system with selection

modes can be improved by adding more possible selection modes providing higher

data rate than the corresponding original mode at the same SNR region.

Proof: Let us define the SNR regions of our adaptive system using one set of

selection modes as follows.

1 1 < < 2 associated with R1

2 2 < < 3 associated with R2.

.

i

i1 < < i associated with

Ri

as shown in Figure 3.12 a. If we add more possible selection modes, the SNR regions

will be changed as follows.

1

1 < < Xi1 associated with R

1

2 Xi1 < < Xi2 associated with R

2

i Xij1 < < Xij associated with R

i

as shown in Figure 3.12 b.The total average rate for original scheme can be written as

R =i

Ri

i2

i1

Pn()d

The total average rate when for the scheme with more selection modes can be

written as

A =i

(Ri

ixi1

n()d+ R

i

i2

ix

n()d)

It is obvious thatA > R

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RiR1 R2 R3

1 2 3 i

RiR1 R2 R3

1 2 3 ix2x1 xi

Figure (a) adaptive constellation size only

Figure (b) adaptive constellation size and ST Symbol Rate

Figure 3.12: Fading Regain for adaptive constellation size

In Figure 3.13, we compare the average spectral efficiency (ASE) for the three

adaptation techniques. As can be seen from Figure 3.13, The ASE of the adaptive

scheme with the joint adaptation outperforms the other two schemes significantly

from 0dB to 25dB. At high SNR (larger than 25 dB), three schemes have the same

performance. As can been seen from the Figure, if there are more available rate

choices, the ASE can be improved further.

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5 0 5 10 15 20 25 30 35 400

2

4

6

8

10

12

14

16

18

20

SNR[dB]

Average

SpectralEfficiencybps/channeluse

ASE Joint Adaption (Q,L/T)

ASE changing constellation size(BPSK,QPSK,8PSK,16QAM with L/T=4

ASE changing ST symbol rate(L/T=1,2,3,4) with 16QAM

Figure 3.13: Average spectral efficiency comparison for the three adaptive schemes.

3.5 Conclusions

In this chapter, first we studied the statistics of signal-to-interference-noise for a

MIMO transceiver using full-rate linear dispersion code and linear minimum-mean-

square-error receiver over a Rayleigh fading channel. The associated probability den-

sity function of the signal-to-interference-noise is derived, which will benefit the future

study, such as error-rate probability. With the statistics as a guideline, we study the

design of the adaptive transceiver with selection modes. An adaptive algorithm forthe selection-mode adaptation is proposed. Based on the proposed algorithm, two

adaptation techniques using constellation and space-time symbol rate are studied,

respectively. To improve the average transmission rate, a new adaptation design is

proposed. In the new design, constellation and space-time symbol rate are considered

jointly. Theoretical analysis and simulation results are provided to verify our new

design.

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Chapter 4

Conclusions and Remaining Works

In this chapter, we will conclude the proposal and present with their scheduled.

4.1 Conclusions

We have studied MIMO adaptive systems based on partial channel state information.

This proposal gives an introduction of MIMO adaptation with selection modes and

the research results will provide background for further research.

In the proposal, our adaptive MIMO system model with linear dispersion code

is introduced. A tight upper bound of the pair-wise error probability at high signal-

to-noise ratio is derived and verified by simulation results. For the low signal-to-noise

ratio, a upper bound is also found without strict mathematical proof.

Statistics of signal-to-interference-noise ratio has been studied for the adaptive

system with full-rate linear dispersion code and linear minimum-mean-square-error

receiver. The associated probability density function of the signal-to-interference-

noise is derived, which will benefit the future study, such as error-rate probability.

With these theoretical results as guidelines, an adaptive algorithm for the

selection-mode adaptation is proposed. Based on the proposed algorithm, we have

introduced three novel adaptation techniques for the adaptive system with full-rate

linear dispersion code and linear minimum-mean-square-error receiver.The first technique is an extension of commonly used adaptation technique for

SISO systems. We have identified the signal-to-noise ratio regions for which specific

constellations can be applied. This technique is called as adaptive constellation. The

second new technique for adaptation of full-rate linear dispersion code is promising.

The technique is called as adaptive space-time symbol rate. Finally, to further im-

prove the average transmission rate, we introduced a novel adaptive procedure which

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takes advantages of both adaptation techniques. This technique is called as joint

adaptation.

Theoretical analysis and simulation results are provided to verify our new de-

sign. The contributions of this study are summarized as follows.

A tight upper bound of the pair-wise error probability at high signal-to-noiseratio is derived for full-rate linear dispersion with maximum likelihood receiver

and verified by simulation results. For the low signal-to-noise ratio, a upper

bound is also found without strict mathematical proof.

Probability density function of the signal-to-interference-noise ratio is derivedfor full-rate linear dispersion with linear minimum-mean-square-error receiver,

which will benefit the future study

The development of a novel adaptive full-rate linear dispersion with linearminimum-mean-square-error receiver. An adaptive algorithm for the selection-

mode adaptation is proposed. Based on the proposed algorithm, two adaptation

techniques using constellation and space-time symbol rate are studied, respec-

tively. To improve the average transmission rate, a new adaptation design is

proposed. In the new design, constellation and space-time symbol rate are

considered jointly

In the following section, the future works will be discussed.

4.2 Remaining Works

Five tasks are identified as listed in Section 1.3. The first two tasked has been

accomplished and the related research results have been presented in Chapter 2 and

3.

In the first remaining task, we will study the beamforming technique. To per-

form beamforming, when perfect channel information is available at the transmitter,

one needs to perform singular value decomposition on the channel matrix H. Thisis also called eigen-beamforming since it uses eigenvectors to find the linear beam-

former that optimizes the performance. Inspired by existing beamforming schemes,

we will propose a new beamforming technique called minimum eigenvector beam-

forming or beamforming-nulling (BN). With this technique, the feedback bandwidth

for channel state information can be reduced and the loss of channel capacity as

compared to the optimal water-filling scheme can also be minimized.

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Table 4.1: Schedule for the remaining tasks.ID Task Name Schedule

1. New Beamforming Techniques 2007/3 - 2007/102. New Adaptation Strategy 2007/4 - 2007/73. Overall Concatenated System 2007/8 - 2007/124. Wrap-ups 2007/11 - 2007/125. Thesis Writing 2008/1 - 2008/4

The second remaining task is to propose the strategy for the new adaptive

system. The basic task of any adaptive strategy is how to inform channel state

information to the transmitter coordinating the receiver together and thus adapt to

the channel variations. Related to this issue, we will study different strategies that

can be used in adaptive MIMO wireless communication systems.

The third remaining task is to design the overall adaptation for a concatenatedsystem. In this task, we will study the adaptation in concatenated MIMO transmis-

sion systems. Instead of exhaustive error-rate simulation, the technique of EXIT

Chart will be used for joint adaption between the coding rate, constellation and ST

symbol rate.

The remaining three tasks are scheduled in Table 4.1 and the associated Gantt

chart is also shown in Figure. 4.1.

ID Task Name

2007

Q1

1 New Beamforming Techniques

2 New Adaptation Strategy

3 Overall Concatenated System

2008

Q2 Q3 Q4 Q1 Q2

4

5 Thesis Writing

Wrap-ups

Figure 4.1: Gantt chart for the remaining tasks.

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Bibliography

[1] 3rd Generation Partnership Project Release 4, 3GPP Technical Report vol.4.0.0,

Mar.2003.

[2] I. E. Telatar, Capacity of multi-antenna Gaussian channels, Eur. Trans. Tele-

com., vol 10, pp. 585-595, Nov. 1999.

[3] G. J. Foschini, M. J. Gans, On limits of wireless communications in a fading

environment when using multiple antennas, Wireless Personal Communications,

vol. 6, no. 3, pp. 311-335, 1998.

[4] D. Gesbert, M. Shafi, D. S. Shiu, P. Smith and A. Naguib, From theory to

practice: An overview of MIMO space-time coded wireless systems, IEEE J.

Select. Areas Commun., Special Issue on MIMO Systems, pt. I, vol. 21, pp. 281-

302, Apr. 2003.

[5] V. Tarokh, N. Seshadri, and A. Calderbank, Space-time codes for high data rate

wireless communications: Performance criterion and code construction, IEEE

Trans. Inform. Theory, vol. 44, pp. 744-765, Mar. 1998.

[6] S. Alamouti, A simple transmitter diversity scheme for wireless communica-

tions, IEEE J. Select. Areas Commun., vol. 16, pp. 1451-1458, Oct. 1998.

[7] D. Gesbert, R. W. Heath,and S. Catreux,V. Erceg Adaptive Modulation and

MIMO Coding for Broadband Wireless Data Networks, in 2002 IEEE Commu-

nications Magazine vol. 40, pp. 108-115 , June 2002.

[8] Z. Luo, H. Gao,and Y. Liu,J. Gao Capacity Limits of Time-Varying MIMO

Channels, IEEE International Conference On Communications vol.2, Mar.2003.

[9] Z. Shen, R. W. Heath, Jr., J. G. Andrews, and B. L. Evans, Comparison of

Space-Time Water-filling and Spatial Water-filling for MIMO Fading Channels,

47


57/60

in Proc. IEEE Int Global Communications Conf. vol. 1, pp. 431 435, Nov. 29-Dec.

3, 2004, Dallas, TX, USA..

[10] Z. Zhou and B. Vucetic Design of adaptive modulation using imperfect CSI in

MIMO systems, 2004 Eelectronics Letters vol. 40 no. 17 August 2004

[11] S. Zhou and G. B. Giannakis, Optimal Transmitter Eigen-Beamforming and

Space-Time Block Coding Based on Channel Mean Feedback IEEE Transactions

on Signal Processing, vol. 50, no. 10, October 2002

[12] P. Xia,and G. B. Giannakis, Multiantenna Adaptive Modulation With Beam-

forming Based on Bandwidth- Constrained Feedback IEEE Transactions on

Communications, vol.53, no.3, March 2005

[13] Bishwarup Mondal and Robert W. Heath, Jr., Performance Analysis of Quan-tized Beamforming MIMO Systems IEEE Transactions on Signal Processing ,

vol. 54, no. 12, DECEMBER 2006

[14] Y. Liu and M. Fitz, space-time turbo codes, 13th Annual Allerton Conf. on

Commun. Control and Computing, Sep. 1999.

[15] D. Cui and A. M. Haimovich, Design and performance of turbo space-time

coded modulation, IEEE GLOBECOM00, vol. 3, pp1627-1631, Nov. 2000.

[16] D. Tujkovic, Recursive space-time trellis codes for turbo coded modulation,Proc. of GlobeCom 2000, San Francisco.

[17] V. Tarokh, H. Jafarkhani, and A. R. Calderbank, Space-time block code from

orthogonal designs, IEEE Trans. Inform. Theory, vol. 45, pp. 1456-1467, July

1999.

[18] G. J. Foschini, Layered space-time architecture for wireless communication in

fading environments when using multiple antennas, Bell labs. Tech. J.,vol. 1, no.

2, pp. 41-59, 1996.

[19] H. El Gamal and A. R. Hammons Jr., A new approach to layered space-time

coding and signal processing, IEEE Trans. Inf. Theory, vol. 47, pp. 2321-2334.

Sep. 2001.

[20] B. Hassibi and B. Hochwald, High-rate codes that are linear in space and time,

IEEE Trans. Inform. Theory, vol. 48, pp. 1804-1824, July 2002.

48


58/60

[21] R. W. Heath and A. Paulraj, Linear Dispersion Codes for MIMO Systems

Based on Frame Theory, IEEE Trans. on Signal Processing, vol. 50, No. 10, pp.

2429-2441, October 2002.

[22] X. Ma and G. B. Giannakis, Full-Diversity Full-Rate Complex-Field Space-

Time Coding, IEEE Trans. Signal Processing, vol. 51, no. 11, pp. 2917-2930,

July 2003.

[23] L. Zhang and D. Tse, Diversity and multiplexing: A fundamental tradeoff in

multiple antenna channels IEEE Trans. Inform. Theory, vol. 49, pp. 1073-96,

May 2003.

[24] Z. Wu and X. F. Wang, Design of coded space-time modulation, IEEE Interna-

tional Conference on Wireless Networks, Communications and Mobile Computing,

vol. 2, pp. 1059-1064, Jun. 13-16, 2005.

[25] G. D. Forney Jr., Concatenated Codes, M. I. T. Press, Cambridge, Mas-

sachusetts, 1966.

[26] Youngwook KO and Cihan Tepedelenlioglu, Space-time block coded rate-

adaptive modulation with uncertain SNR feedback IEEE Signals, Systems and

Computers, vol.1, pp 1032- 1036, Nov. 2003

[27] Bengt Holter, Geir E. mien, Kjell J. Hole, and Henrik Holm, Limitations in

spectral efficiency of a rate-adaptive MIMO system utilizing pilot-aided channel

prediction IEEE 2003. VTC, vol. 1, pp 282- 286 , April 2003

[28] Guillem Femenias, SR ARQ for Adaptive Modulation Systems Combined With

Selection Transmit Diversity 2005 IEEE Transaction on Communications, vol.

53, no. 6, pp 998-1006, June 2005

[29] Marie-Hlne Bourles-Hamon and Hesham El Gamal,On the design of adaptive

space-time codes 2004 IEEE Transaction on Communications, vol. 52, no. 10,

October 2004

[30] Andreas Mller, Joachim SpeidelAdaptive modulation for MIMO spatial mul-

tiplexing systems with zero-forcing receivers in semi-correlated Rayleigh fading

channels Proceeding of the 2006 international conference on Communications

and mobile computing pp. 665 - 670, 2006

49


59/60

[31] Zhendong Zhou, B. Vucetic, M. Dohler, Yonghui Li MIMO systems with adap-

tive modulation IEEE Transactions on Vehicular Technology vol.54, pp.1828-

1842, Sept.2005

[32] Robb J. Muirhead, Aspects Of Multivariate Statistical Theory, New York: John

Wiley and Sons Inc.1982

[33] T. W. Anderson, An Introduction to Multivariate Statistical Analysis,2th ed.

New York: John Wiley and Sons Inc.1984

[34] Anant M. Kshirsagar, Multivariate Analysis,Volume 2. New York: Marcel

Dekker,Inc.1972

[35] I. S. Gradshteyn ,I. M. Ryzhik,A. Jeffrey,and D. Zwillinger, Table of Integrals,

Series, and Products,6th ed. San Diego, Calif. : Academic Press 2000

[36] R. Lupas and S. Verdu, Linear multiuser detectors for synchronous code-division

multiple-access channels, IEEE Trans. inform. Theory, vol. 35, pp. 123-136, Jan.

1989.

[37] H. V. Poor and S. Verdu, Probability of error in MMSE multiuser detection,

IEEE Trans. inform. Theory, vol. 43, pp. 858-871, May 1997.

[38] G. D. Golden, G. J. Foschini, R. A. Valenzuela, and P. W. Wolniansky, Detec-

tion algorithm and initial laboratory results using V-BLAST space-time commu-nication architecture, Electron. Lett., vol. 35, pp. 14-16, Jan. 1999.

[39] S. Loyka , V-BLAST outage probability: analytical analysis, 2002 Proc. IEEE

Vehicular Technology Conference (VTC), vol.4 pp.1997-2001, Sept. 2002.

[40] R. Bhnke, Karl-Dirk Kammeyer, SINR Analysis for V-BLAST with Ordered

MMSE-SIC Detection, International Wireless Communications and Mobile Com-

puting Conference, pp. 623 - 628, July 2006.

[41] Marvin K. Simon ,Mohamed-Slim Alouini, Digital Communication over FadingChannels,2th ed. , Hoboken, New Jersey : Wiley and Sons, Inc.2005

[42] G. E. Roberts and H. Kaufman, Table Of Laplace Transforms,Volume 2.

Philadelphia: W. B. Saunders Company.1966

T. Rapaport, Wireless Communications: Principles and Practice, 2nd ed. Pren-

tice Hall, 2001

50


60/60

[43] J. Proakis, Digital Communications, 4th ed. New York: McGraw-Hill.

[44] T. M. Cover and J. A. Thomas, Elements of Information Theory, New York:

Wiley, 1991.

[45] B. Vucetic and J. Yuan, Space-Time Coding, John Wiley & Sons Ltd, England,2003.

[46] S. Lin, D. J. Costello, Error Control Coding: Fundamentals and Applications,

Prentice Hall, New Jersey, 1983.

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