1

Fundamental overview and simulation of MIMO systems for Space-Time coding and Spatial Multiplexing

Hoo-Jin Lee1, Shailesh Patil2, and Raghu G. Raj3

Wireless Networking and Communications Group (WNCG)

Dept. of Electrical and Computer Engineering

The University of Texas at Austin

Austin, TX, 78712-1084, USA

hoojin@ece.utexas.edu 1, patil@ece.utexas.edu 2, raghu.raj@ieee.org 3

Abstract

Multiple-input-multiple-output (MIMO) communication systems use multiple antennas at both the

transmitter and the receiver. Under rich multipath environments with independent multipath fading

between each transmit and receive antenna pair, MIMO wireless communications systems achieve

significant capacity gains over conventional single antenna systems by exploiting the plurality of modes

present in the matrix channel within the same time-frequency slot. Moreover MIMO systems offer

significant diversity advantage over traditional wireless communication systems by exploiting both

transmit and receiver diversity by employing various space-time coding schemes. These have led to MIMO

being regarded as one of the most promising emerging wireless technologies. Our project deals with

MIMO based space-time coding and spatial multiplexing techniques that provide reliable capacity and

link gains, respectively. It is proposed to study, analyze and simulate the above-mentioned techniques. The

simulation results will allow us to compare performance of different space-time coding and spatial

multiplexing schemes.

I. Introduction

Physical limitations of the wireless medium provide a technical challenge for reliable wireless

communication. Techniques that improve spectral efficiency and overcome various channel impairments

such as signal fading and interference have made an enormous contribution to the growth of wireless

2

communications. Moreover, the need for high-speed wireless Internet has led to the demand for

technologies delivering higher capacities and link reliability than achieved by current systems. Multiple -

input multiple-output (MIMO) based communication systems are capable accomplishing these objectives.

MIMO systems are an extension of smart antennas systems. Traditional smart antenna systems

employ multiple antennas at the receiver, whereas in a general MIMO system multiple antennas are

employed both at the transmitter and the receiver. The addition of multiple antennas at the transmitter

combined with advanced signal processing algorithms at the transmitter and the receiver yields significant

advantage over traditional smart antenna systems—both in terms of capacity and diversity advantage.

A remarkable property of MIMO systems is their ability to turn multipath propagation into an

advantage. Indeed under rich multipath environments, with independently fading channels between every

pair of transmitter and receiver antennas, MIMO systems offer capacity increases that vary linearly with

the number of antennas used without increasing premium bandwidth or power [8]. Spatial multiplexing,

initially proposed by Paulraj and Kailath [25] and later practically demonstrated by Foschini [8] in Bell

Labs, is a technology that exploits this feature of MIMO systems to practically achieve the theoretical

capacity limit.

Apart from the capacity improvements mentioned above, MIMO systems can potentially offer

increased diversity advantage over traditional wireless systems. Under the assumption of sufficient

spacing between antenna elements and under rich multipath conditions, it can be shown that space-time

codes can be designed to provide diversity order (which is defined as the number of decorrelated spatial

branches) up toRT NN × , where

TN and RN are the number of transmit and receive antennas,

respectively [2].

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The above description gives but an idea of the potentials of MIMO systems. Indeed research in

this field is proceeding at a very rapid pace. For this reason there is a need for understanding the

fundamentals of MIMO communication systems. In this project we give a foundational introduction to

MIMO wireless communications systems. We implement important algorithms like spatial multiplexing

and space-time coding in a LabView environment and illustrate the advantages and limitations of these

different schemes. All the programs implemented in this project are available as a toolbox with a graphical

user interface (GUI) which can serve as a good educational tool for introducing MIMO systems to novices

in this area and students. Finally the copious references provided herein will direct the reader to the

frontiers of research in this exciting and rapidly growing field.

II. Multi-input Multi-output System Description and Channel Model

In the system design, we consider both discrete Rayleigh and Ricean flat fading MIMO channel

models, where TN and RN are the number of transmit and receive antennas respectively. In the

transmitter, a data stream is demultiplexed into TN independent substreams. Each substream is encoded

into transmit symbols using a modulation scheme (e.g. BPSK, QPSK, M-QAM, etc.) at symbol rate 1/T

symbol/sec with synchronized symbol timing [11].

First we describe the Rayleigh flat fading model. The baseband RN -dimensional received

signal vector TN krkrkrk

R)](),...,(),([)( 21=r at sampling instant k may be expressed as

)()()( kkk nxHr +⋅= (II-1)

where

=

RTR

T

NNN

N

hh

hh

LMOM

L

1

111H ,

=)(

)()(

1

kr

krk

RN

Mr ,

=)(

)()(

1

kx

kxk

TN

Mx ,

=)(

)()(

1

kn

knkn

RN

M .

4

TN kxkxkxk

T)](),...,(),([)( 21=x denotes the transmit symbol vector with equally distributed transmit

power across the transmit power. Here, the superscript T is transposition. H denotes the RT NN ×

channel matrix, whose elements hmn at the mth row and nth column is the channel gain from the mth transmit

antenna to the nth receive antenna, and they are assumed to be independent and identically distributed

circularly symmetric complex Gaussian random variables with zero-mean and unit-variance, having

uniformly distributed phase and Rayleigh distributed magnitude. A circularly symmetric complex

Gaussian random variable is a random variable ),0(~ 2σC?jba + , in which a and b are i.i.d. real

Gaussian distributed as )2/,0( 2σ? . A commonly used channel model in MIMO wireless

communication systems is a block fading (also called quasi-static) channel model where the channel

matrix elements, which are independent and identically distributed (i.i.d.) complex Gaussian (Rayleigh

fading) random variables, are constant over a block and change independently from block to block. Hence,

we drop the index k for the channel gain. The elements of the additive noise vector

TN knknknkn

R)](),...,(),([)( 21= are assumed to be also white i.i.d. complex Gaussian random

variables with zero-mean and unit-variance. From this normalization of noise power and channel loss, the

averaged transmitted power which is equal to the average SNR at each receive antenna is to be no greater

than ? without regard to TN [11, 14, 27, 29].

Now we consider the Ricean fading model for the 2 transmitter and 2 receiver case which we use

in our simulations. The generalization to more than 2 transmit or receive antennas is straightforward. The

Ricean channel model is given by [18]

VF HK

HK

KH

11

1 ++

+= =

+

+

+ 2221

1211

11

1 2221

1211

hhhh

Keeee

KK

jj

jj

φφ

φφ

(II-2)

5

where,

=

2221

1211

φφ

φφ

jj

jj

F eeee

H is a fixed matrix (i.e. fixed for each block of a block fading channel)

consisting of phase elements corresponding to the LOS component and VH is the Rayleigh flat-fading

matrix (as described before) i.e. the matrix element , jih denotes the Rayleigh flat fading channel

coefficient from transmitter i to transmitter j. K is the K-factor of the Ricean distribution which is

proportional to the strength of the line-of-sight (LOS) component.

The Ricean model (II-2) was suggested in [18] as a first order approximation to the Ricean

channel. We have decided to use this model in our simulations because under certain reasonable

assumptions it gives an accurate approximation to the Ricean channel [18]. The assumptions when using

this model are as follows: (i) that the distance between the antennas is sufficiently spaced, (ii) the

subscriber unit is mobile and possibly changing orientations with respect to the base station. Under these

assumptions it is reasonable that the phases of the LOS component arriving at the different receiver

antennas are random and uncorrelated.

In this project we study and simulate the performance of Space-Time coding and multiplexing

schemes. Figure II-1(a) and II-1(b) show a simplified system diagram of Space-time coding and V-BLAST

(Spatial multiplexing receiver) systems respectively. These will be considered in more detail in the

remaining of this paper.

(a) (b)

Figure II-1. System block diagram of (a) Space-time coding and (b) BLAST schemes [5, 11]

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III. Multi-input Multi-output System Channel Capacity

As mentioned already, MIMO systems provide significant capacity gain over single -input single -

output (SISO) channels. According to Shannon capacity of wireless channels, given a single channel

corrupted by an additive white Gaussian noise at a level of SNR, the capacity is

]1[log2 SNRC += [Bps/Hz] (III-1)

In the practical case of time-varying and randomly fading wireless channel, the capacity can be written as

]1[log 22 HSNRC ⋅+= [Bps/Hz] (III-2)

where H is the 11× unit-power complex Gaussian amplitude of the channel. Moreover, it has been

noticed that the capacity is very small due to fading events [9, 26, 29].

In the single -input multiple-output (SIMO) systems, the channel vector H is RN×1 and the

capacity is

]1[log2∗⋅+= HHSNRC [Bps/Hz] (III-3)

where the superscript * is the transpose conjugate. Compared with SISO system, the capacity of SIMO

system shows improvement. The increase in capacity is due to the spatial diversity which reduces fading

and SNR improvement. However, the SNR improvement is limited, since the SNR is increasing inside the

log function (III-4) [9, 26, 29].

For the MIMO system with TN transmit and RN receive antennas, it is shown that the

capacity is derived from

⋅+= ∗]det[log2 HHI

TN N

SNRC

R [Bps/Hz] (III-4)

Here, we can see that the advantage of MIMO systems is significant in capacity. As an example, for a

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large NNN RT == , NN IHH →∗ / , so the capacity is asymptotic to

]1[log 2 SNRNC +≈ [Bps/Hz] (III-5)

Therefore, the capacity increases linearly with the number of transmit antennas. Figure III-3 shows the

capacity for various multiple antenna systems. It is shown that SIMO systems offer smaller capacity gain

than MIMO systems. For example, MIMO system with 2== RT NN provides higher capacity than

SIMO system with 1=TN and 4=RN [9, 26, 27, 29].

Figure III-1. Capacity comparison of several multiple antenna systems

IV. Space-Time Coding Schemes

Space-time codes refer to the set of coding schemes that allow for the adjusting and optimization

of joint encoding across multiple transmit antennas in order to maximize the reliability of a wireless link.

Space-time coding schemes exploit spatial diversity in order to provide coding and diversity gains over an

uncoded wireless link. We first briefly the basics of diversity in the next section and thereafter we

elaborate on the prominent space-time coding schemes proposed in the literature.

IV.I. Overview of Diversity

Multipath fading is significant problem encountered in narrowband wireless communications.

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Fading results in fluctuations in the signal amplitude which degrades the BER performance at the receiver.

Diversity schemes attempt to mitigate this problem by finding independently faded paths in the mobile

radio channel. Usually this involves providing replicas of the transmitted signal over time, frequency or

space. Diversity is the single most important contributor to reliable wireless communications. Figure V-1

illustrates, by way of an example, the improvement in signal quality obtained when using diversity based

schemes. Notice how the deep fluctuations due to multipath fading are mitigated by making use of

independently faded copied arriving at different antennas. We shall now briefly review the 3 types of

diversity schemes that are exploited in wireless communications systems:

(i) Temporal Diversity: Here replicas of the transmitted waveform are provided across time by a

combination of channel coding and time interleaving strategies. The key for this form of diversity to be

useful is that the channel must provide sufficient variations in time. More precisely, this form of diversity

is useful when the coherence time of the channel is small compared to the desired interleaving symbol

duration (since otherwise time interleaving results in large delays).

Figure IV-1. Advantage of Diversity in Multipath Fading Condi tions

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(ii) Frequency Diversity: Here replicas of the transmitted waveform are provided in the form of

redundancies in the frequency domain. For this form of diversity to be useful the coherence bandwidth of

the channel must be small compared to the bandwidth of the signal. This criterion assures that different

parts of the relevant spectrum will suffer independent fades.

(iii) Spatial Diversity: Also known as antenna diversity, this is a very practical, effective and thus widely

used method for reducing the effect of multipath fading. Here replicas of the transmitted waveform are

provided across different antennas of the receiver. For this form of diversity to be effective, the antenna

spacing must be larger than the coherence distance in order to ensure independent fades across different

antennas. There are many traditional types of spatial diversity schemes [19] like selection diversity,

feedback diversity, maximal ratio receiver diversity (MRRD), and equal gain diversity. In the next section

we will find that space-time codes exploit a special type of spatial diversity which we refer to as space-

time diversity.

We emphasize again that the effectiveness of any diversity scheme lays the availability of

independently faded parts of the transmitted signal due to the random nature of the mobile radio channel

so that the probability of two or more relevant parts of the signal undergoing a deep fade is very small.

The constraints on coherence time, coherence bandwidth and coherence distance as stated above ensure

that this condition is met for the respective diversity schemes. The diversity system must then optimally

combine the received diversified waveforms so as to maximize the resulting signal quality. The reader can

refer to [19, 20] and references therein for a broad of overview of traditional diversity combining systems.

Diversity schemes can also be categorized in another way based on whether diversity is applied

at the transmitter or the receiver.

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(i) Receiver Diversity: Traditionally smart antenna systems employ receiver diversity schemes like

Maximum ratio combining [19] in order to improve the received signal quality. The major problem with

these schemes is the cost, size, and power in the remote units tending to be high. Receiver diversity is a

well studied subject [20]. But recently there has been much interest in another form of diversity called a

transmit diversity in the context of space-time coding.

(ii) Transmit Diversity: The idea behind these schemes is to introduce controlled redundancies at the

transmitter which can be exploited by appropriate signal processing techniques at the receiver. Note that

traditional channel coding can be considered a form of transmit diversity, however with the advent of

Space-Time block coding in [1] (which is a form of space time coding) this concept is extended to

encompass spatial diversity schemes. Space-time codes for MIMO in general exploit both transmit and

receiver diversity and as a result provide diversity advantage over traditional wireless systems (as the

latter only exploit receiver diversity). We will describe various space-time coding schemes in more detail

in the next section.

Another advantage of incorporating transmit diversity schemes in modern mobile communication

systems is that we can reduce the complexity of the remote devices and transfer it to the base station.

Portable hand-held mobile units are required to be inexpensive and low-complexity. Although economies

of scale will help in bringing down the cost of mobile units, increasing the complexity of the base station

(via adoption of space-time coding techniques) may be the only other possible trade space for meeting the

requirements of next generation communication systems [1].

IV.II. Space-Time Coding

Space-Time coding schemes primarily exploit a special form of spatial diversity which we refer

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to as space-time diversity. Unlike traditional spatial diversity schemes here information is encoded by

multiple transmitter antennas across both space and time. For the specific space-time codes considered

below we shall see how these codes, under certain conditions, fruitfully exploit this joint coding across

space and time to obtain diversity advantages as high RT NN × where TN is the number of transmit

antennas and RN is the number of receive antennas. Space-time coding can be broadly categorized into

2 classes

(i) Space-Time Block codes: These codes are transmitted using an orthogonal block structure which

enables simple decoding at the receiver.

(ii) Space-Time Trellis codes: These are convolutional codes extended to the case of multiple transmit

and receive antennas.

IV.II.I. Design Criteria for constructing Space-Time codes

In this section we derive optimality criteria which the specific Space-Time codes considered in

this paper are designed to meet. These optimality criteria were first proposed in [21] in the context of

space-time trellis codes. However these optimality criteria use metrics that can be used to evaluate the

performance of general space-time codes.

Consider a mobile communication system with NT transmit and NR receive antennas. The input

bit stream is coded by a space-time coding scheme and then split into NT bit streams. Each stream of data

is then pulse shaped, modulated and then launched into the wireless channel. The symbols TNiis 1= are

transmitted from the NT transmit antennas. All the NT symbols are transmitted in the same time slot and

subsequently mixed in the channel to obtain signal r(k) at the receiver antennas,

12

)()()(..

.

.)(

11

kkHk

s

s

r

r

k

TR Nk

k

Nk

k

nsnHr +=+

=

= (IV-1)

where s(k) is the transmitted signal vector and n(k) is the noise vector.

Suppose that the code word c = TTT Nlll

NN ccccccccc ............ 212

22

121

21

11 is transmitted over l

consecutive time slots (with NT symbols simultaneously transmitted from the NT transmit antennas). The

probability that this code word is erroneously interpreted as e = Mlll

MM eeeeeeeee ............ 212

22

121

21

11 is given

by

))4/(),(exp(),...,2,1,,...,2,1,|( 02

, NEecdNjNihecP sRTji ≤==→ (IV-2)

where

2

1 1 1

2 )(),( ∑∑ ∑= = =

−=R TN

j

l

t

N

i

jt

itij cehecd is the distance between the corresponding received codewords.

This inequality (IV-1) follows by applying the applying the Chernoff bound to a Gaussian approximation

of the distribution of the distance between the received signals corresponding to codewords c and e .

The inequality (IV-1) above can be more compactly represented in terms the error matrix B(c, e)

corresponding to codewords c and e as follows. Let the error matrix B(c, e) be defined as follows

−−

−−

=

TTTT Nl

Nl

NN

ll

cece

cece

..........

..

11

1111

11

B (IV-3)

Then it follows that

∑∑ ∑ ∑== = =

ΩΩ=−=RR R N

jj

Hj

N

j

l

t

N

i

jt

itij cehecd

1

2

1 1 1

2 )(),( BB (IV-4)

13

where ),...,,( ,,2,1 jNjjj Thhh=Ω .

Thus, ))4/(),(exp(),...,2,1,,...,2,1,|( 02

, NEecdNjNihecP sRTji ≤==→

∏=

ΩΩ−=RN

jsj

Hj NEececB

10

* )4/),(),(exp( B (IV-5)

Further we have that, ∑=

=ΩΩTN

ijiij

Hj ecec

1

2,

*),(),( βλBB

where TNii 1=λ are the eigenvalues of ),(),( ecec HBB obtained from diagonalization of ),(),( ecec HBB

==

M

H DVececV

λ

λ

0000.0000.0000

),(),(

1

*BB

where *

,1,2,1 ),...,,( Vjjjj Ω=βββ .

Ricean channel case

Now under the assumption of independent Ricean distributions of 2

,1 jβ we obtain (after

averaging the probability of error (IV-5) with the independent Ricean distributions of2

,1 jβ )

∏ ∏= =

+

−

+≤→

N

ji

s

is

jiM

i isji

NE

NE

K

NEhecP

1

0

0,

1 0, )

41

4exp(

))4/(1(1

)|(λ

λ

λ (IV-6)

where ),...,,( ,,2,1 jNjjj

TEhEhEhK = .

Rayleigh channel case

For the Rayleigh fading distribution case we obtain (by setting Ki,j = 0) that

RT

NN

i isji NE

hecP

+

≤→ ∏=1 0

, ))4/(1(1

)|(λ

(IV-7)

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Let r denote the rank of matrix HBB , then it follows that for the Rayleigh fading case:

TTR

TrN

sNr

ii

NN

i isji N

ENE

hecP−−

==

≤

+

≤→ ∏∏011 0

, 4))4/(1(1

)|( λλ

(IV-8)

The diversity gain and coding gain of a space-time coding scheme is given by TrN and TNr

ii

−

=

∏1

λ

respectively. The rank r of matrix HBB is also called the diversity-order of the space-time code.

Thus we arrive at the following design criteria for space-time codes for Rayleigh flat-fading

channel

(i) Rank criterion: To achieve maximum diversity of TR NN the matrix HBB must have full rank for

any pair of distinct codewords c and e .

(ii) Determinant criterion: For a given target diversity order nm the determinant of HBB must be

maximized in order to maximize the coding gain.

A similar design criterion also holds for the Ricean case [21]. The space-time codes we consider

in the following sections all meet the design criteria mentioned above.

We also infer from (IV-6) and (IV-7) that the worst case performance under a Ricean fading

condition will outperform the worst case performance under a Rayleigh fading condition in terms of BER

performance. Indeed it can also be shown [21] that even for dependent fade coeffic ients, any code that

works well for a Rayleigh channel cannot do worse under a Ricean fading condition (please see [21] for

more details) in terms of BER performance. The intuitive reason for this is clear—for the Ricean channel

the fades are not as deep as the Rayleigh fading case and so we can expect better BER performance for the

Ricean case.

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However, it is important to note that this gain in BER performance for Ricean channels comes at

the expense of capacity reduction because under correlated Ricean fading conditions MIMO systems can

no longer achieve significant capacity gains by exploiting the rich multipath structure of Rayleigh fading

channels.

IV.II.II. Space-Time Block Coding

The field of Space-Time Block coding was initiated by Alamouti [1]. The Alamouti codes

address the case of two transmit and NR receive antennas wherein it provides a diversity order of 2NR

which is equivalent to a NR branch Maximum Ratio Receiver Combining (MRRC) scheme. No knowledge

of channel state information (CSI) is assumed at the transmitter and perfect CSI is assumed at the receiver.

The MRRC scheme realizes spatial diversity gain by using multiple antennas at the receiver in

smart antenna system. We first briefly describe the MRRC scheme and then outline how the Alamouti

scheme performs similar to MRRC.

MRRC scheme

Figure IV-2 shows the channel model. Let the bit stream to be transmitted be indexed

as ,...],...,,[ 10 nsss . Let 0h be the channel between the first transmit antenna and the receiver and 1h be

the channel between the second transmit antenna and the receiver. Uncorrelated Rayleigh fading is

assumed between the transmitter and receiver 000

θα jeh = and 111

θα jeh = , where )1,0(, 10 CNhh ∈

are i.i.d. Complex Gaussian random variables. Thus the received signals at the 2 antennas

are 0000 nshr += and 1011 nshr += , where 10 ,nn are complex Gaussian noise. The receiver estimate

is formed by forming the following decision variable ,

1*10

*00

21

201

*10

*0 )|||(| nhnhshhrhrhy +++=+= (IV-9)

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So, if either 0h or 1h (or both) have not faded, then we can form an accurate estimate of the transmitter

by using a standard ML detector. Note that the probability that signals at both the channels will fade is

very low and so we can improve the average BER at the receiver output. We thus have a diversity of order

two.

Alamouti scheme

Figure IV-3 shows a schematic of the Alamouti scheme. This algorithm consists of three steps.

(i) Encoding and Transmission:

For a given symbol period, T, two symbols signals are transmitted simultaneously from the two

antennas. In the first symbol period the signal 0s is transmitted from the first antenna and signal 1s is

transmitted from the second antenna. During the next symbol period, signal )( *1s− is transmitted from

the first antenna and signal *0s is transmitted from the second antenna. In the encoding described above,

we observe blocks of symbols 0s and 1s are coded across space and time. For this reason Alamouti

codes are called Space-Time Block codes.

Figure IV-2. Two-Branch MRRC [1]

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It is assumed that the channel does not fade across these two symbol periods, that is,

00000 )()( θα jehTthth ==+= and 1

1111 )()( θα jehTthth ==+= .

Figure IV-3. Alamouti scheme [1]

Therefore the received symbols are given by 011000 )( nshshtrr ++== and

1*01

*101 )( nshshTtrr ++−=+= . Alternately we can represent the above equations in matrix form

nsHr += a (IV-10)

where

−

= *0

*1

10

hhhh

aH is the equivalent channel matrix , To ss ],[ 1=s is the transmitted block signal

vector, and To nn ],[ 1=n is the noise vector. Note that aH is an orthogonal matrix which is due to the

fact the transmitted symbol block has an orthogonal structure.

(ii) The combining step

Assuming perfect channel knowledge at the receiver, the vector r of received signal is left-

multiplied by HaH to obtain

18

rHaHs

~= =

~

1

~

0

s

s = s

+

+2

12

0

21

20

0

0

hh

hh+

~n (IV-11)

where nHn~

Ha= .

Thus we have that

~

002

12

0*

110*0

~

0 )( nshhrhrhs ++=+= (IV-12)

~

112

12

0*

100*1

~

1 )( nshhrhrhs ++=−= (IV-13)

where

1*10

*0

~

0 nhnhn += and 1*10

*0

~

1 nhnhn −= (IV-14)

(iii) ML detection

The symbols ~

0s and ~

1s are sent to an ML Detector which amounts to minimizing the

following decision statistic

−++−−

2*01

*101

211000 shshrshshr over all possible values of 0s and

1s . Due to the orthogonality of the transmitted code blocks it can be easily shown that the above is

equivalent to minimizing the following decision statistic for detecting 0s

20

21

20

2

01*

1*00 ||)||||1( shhshrhr ++−+−+ (IV-15)

, and minimizing the following decision statistic for 1s

21

21

20

2

10*

1*10 ||)||||1( shhshrhr ++−+−− (IV-16)

This is a very simple decoding scheme involves decoupling of the signals transmitted from the different

antennas via linear combination at the receiver rather than joint-detection (which is done in space-time

trellis codes described in the next section).

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The Alamouti scheme can be similarly generalized to 2 transmit and RN receive antennas.

Further by the orthogonal property of the transmitted matrix it is easily shown in [3] that the Alamouti

code provides a maximal diversity advantage of TR NN =2 RN . The coding gain provided by this space-

time block coding scheme, which depends on the determinant criterion (mentioned in section IV.II.I), is

dependent on the particular modulation scheme used [3, 21]

The Alamouti is very attractive for practical applications because of the simplicity of decoding

combined with the maximal diversity gain advantage it provides.

Recent work

There has been work in the literature to extend Alamouti codes to the case of more than two

transmit antennas. However it turns out that in such cases it is not possible to design perfectly orthogonal

codes except in the case of real-valued modulations, like PAM. For complex constellation, fully

orthogonal codes cannot be constructed. The reader is referred to [3, 21, 22] for more details.

IV.II.III. Space-Time Trellis Coding

Space-Time trellis codes, which were originally introduced in [21], are convolutional codes

which are extended to the case of multiple transmit and receive antennas. No knowledge of channel state

information (CSI) is assumed at the transmitter and perfect CSI is assumed at the receiver. We define an r-

space-time code to be a space-time code that achieves a diversity order of r (which is the rank of matrix

HBB described in the section IV.II.I). The authors in [21] have proposed different trellis codes for TN =

2 transmitters, for 4-PSK and 8-PSK modulation schemes, and for different number of trellis states.

By analyzing the algebraic properties of these codes it can be shown that these codes satisfy the

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designed criteria derived in section IV.II.I. The space-time codes proposed in [21] satisfy the important

property of being geometrically uniform [21, 24]. From this property it immediately follows that the

proposed codes (like the one described in Figure IV-4) indeed maximize the coding gain for a given

diversity order. The reader is referred to [21, 24] for more details of the derivation.

Apart from maximizing the diversity and coding gain, we also would like to maximize, as much

as possible, the data rate of the transmission and to minimize the trellis complexity (which in turns

minimizes the complexity of the ML decoding algorithm). However there are tradeoffs in achieving these

conflicting goals. For example, diversity can be maximized by sending the same data across all the

different antennas but this would certain minimize the data rate of transmission. Our objective then must

be to maximize the data rate for a given diversity order. The authors in [21] explore fundamentals limits

underlying these tradeoffs and also furnish space-time coding schemes that achieve the above optimality

criterion. We briefly describe this in what follows.

Tradeoffs

We briefly describe some of the main theoretical results proved in [21] regarding the fundamental

limits on the rate, trellis complexity, diversity, constellation size, and their tradeoffs. We do not reproduce

the proofs these as the proofs can be found in [21] but we give some intuition and useful comments that

can allow for better appreciation of these results.

Theorem1: Consider a mobile communication system with n transmit, m receive antennas with a Ricean

fading model. Let rNR be the diversity advantage of this system. Assuming that the signal constellation Q

has 2b elements, the rate of the transmission R satisfies

21

l

rnAR

b l )],(log[2≤ (IV-17)

in bits per second per Hertz, where ),(2

rnA b l is the maximum size of a code of length n and minimum

Hamming distance r defined over an alphabet of size 2bl.

This theorem gives us an upper bound on the maximum achievable rate of any space-time code.

Later a constructive proof is given to show that the upper bound is achievable. From this theorem it is

immediately seen that to obtain a diversity advantage of RT NN , the transmission bit rate is at most b bits

per second per Hertz. For 4-PSK and 8-PSK constellations, for example, diversity advantage of RT NN

places an upper bound on the transmission rate of 2 and 3 bits/s/Hz respectively.

Another implication of Theorem 1, which is explored in the next two lemmas, is that there is a

fundamental tradeoff between constellation size, diversity, and the transmission rate.

Lemma 1: The constraint length of an r-space-time trellis code is at least r-1.

Lemma 2: Let b denote the transmission rate of a multiple antenna system employed in conjunction with

an r-space-time trellis code. The trellis complexity of the space-time code is at least 2b(r-1).

Lemma 2 shows how the trellis complexity is determined by the diversity r in the system and

maximum data rate b.

Code Construction

The authors in [21] construct codes that achieve the upper bound in Theorem 1 thus furnish a

constructive proof of the tightness of the upper bound. The constructive proof is given by demonstrating

codes that achieve this upper bound. Also, as mentioned before, these codes satisfy the design criteria

22

derived in section IV.II.I by virtue of being geometrically uniform. We consider one such space-time trellis

code below by way of an example. The interpretation and implementation of the other codes is very

similar.

Figure IV-4 shows the codes for a 2-space-time code using 4-PSK modulation with 4 states for

TN = 2 transmitters and date rate =2bps/Hz. The Trellis diagram is to be read as follows. The nodes

represent different state in the trellis diagram. The trellis diagram in Figure IV-5 consists of 4 states

(labeled states 0, 1, 2, 3). The symbols to the left of the each node correspond to the encoder state output

for the two transmit antennas (i.e. antenna 1, antenna2 read in this order) when excited by the

corresponding input bits as shown in top of each column. For example, when inputs bits 10 (respectively

for antennas 1 and 2) arrive in state 0, the encoder outputs a 0 on antenna 1 and a 2 on antenna 2. And,

following the state transition arrow corresponding to input 10, we see that the state changes to state 2. For

this 4-PSK scheme, the encoder outputs 0,1,2,3 are mapped to 1, j, -1, -j respectively.

Decoding Space-Time Trellis Codes

Given the received symbols r(k) in equation (IV-1) and assuming perfect CSI at the receiver, the

ML decoder is used to recover the input symbols as follows:

∑−

=

−=1

0

2minarg

TN

kkk

Sk Hsrs (IV-18)

where ],...,,[ 10 TNsssS = and minimization is done over all possible codeword matrices S.

We minimize over all possible codewords to obtain the ML estimate. The Viterbi algorithm is

used to compute the trellis path with the lowest metric. It is important that the complexity of ML decoding

for space-time codes grows exponentially with the number of number of constellations and trellis states.

For an r-space-time trellis coding scheme with a transmission data rate of b bits per second, the

23

complexity of the ML decoding algorithm is of the order )1(2 −rb .

Figure IV-4. Trellis diagram for n=2 with rate 2bps/Hz

IV.II.IV. Comparison of Space-time Block and Trellis codes

Space-time block codes cannot outperform the space-time trellis codes proposed in [21]. The

reason for this is that for space-time trellis codes the coding gain increases as we increase the number of

trellis states. So for a given diversity order trellis codes have more coding gain than space-time block

codes. A detailed proof of this can be found in [21].

Space-time block codes are computationally much more attractive than trellis codes. As

explained before, for Space-time block codes there exist simple ML decoding algorithms which only use

linear processing at the receiver by exploiting the orthogonality of the code design. On the other hand

Input Bits 00

01

10

11

State 0

Output for

Antenna1, Antenna2

00 01 02 03

State 1

Output for

Antenna1, Antenna2

10 11 12 13

State 2

Output for

Antenna1, Antenna2

20 21 22 23

State 3

Output for

Antenna1, Antenna2

30 31 32 32

State #

0

1

2

3

24

space-time trellis code requires computationally hungry trellis search algorithms which make it unsuitable

for most practical applications of MIMO systems.

IV.III. Simulations Results

The space-time coding schemes described above were simulated in LabView. Figure IV-5 shows

a comparison of BER performances of the Alamouti codes for 1, 2, and 3 receive antennas (and of course

for 2 transmit antennas). The x-axis shows the SNR in dB and the y-axis shows the BER. We see that we

get a significant improvement when using Alamouti codes over the case where we have no diversity,

especially for high SNR conditions. As we increase the number of receive antennas the BER performance

improves because the diversity order improves.

We simulated the performance of space-time trellis codes proposed in [21] for 4-PSK for

different number of transmit and receive antennas. Figure IV-6 shows the BER plot for 2 transmit and one

receive antenna for 4, 8 and 16 states. The number of states is associated with the trellis complexity of the

codes. Since the transmission rate (2 bps/Hz) is same for these three cases, by Lemma 2, the rank r

increases for increased trellis complexity which in turn decreases the probability of error as given in

Equation (IV-8). Thus as we increase the number of trellis states the BER decreases. But this comes at the

expense of increase complexity for the ML decoder at the receiver.

Figure IV-7 shows a comparison of BER performance for the case of 2 transmit and 2 receive

antennas with varying number of trellis states (4, 8 and 16 states). As expected the BER decreases as the

number of states increases.

Figure IV-8 shows a comparison of the trellis codes with Alamouti. Indeed, as explained earlier it

25

is guaranteed that Space-time block codes cannot outperform space-time trellis codes. However the

advantage of trellis codes is the simple decoding structure.

Figures IV-9 and IV-10 show the comparison between the performance of Rayleigh vs. Ricean

channel (K=0dB) for both Space-time block and trellis codes respectively. As explained in section IV.I.I.,

we expect an improvement in BER performance for the Ricean channel when compared to a Rayleigh

channel. This is indeed what we observe.

Figure IV-5. Performance of Alamouti Scheme

26

Figure IV-6. Performance of 2x1 Space-Time Trellis codes, 4PSK

Figure IV-7. Performance of 2x2 Space-Time Trellis codes, 4PSK

27

Figure IV-8. Comparison of Alamouti and Space-time trellis codes

Figure IV-9. Rayleigh vs. Ricean comparison for 2x2 Alamouti code, 4PSK

28

Figure IV-10. Rayleigh vs. Ricean comparison for 2x2 Space-time trellis code, 4PSK

29

V. Spatial Multiplexing Schemes

Spatial multiplexing scheme exploits the rich scattering wireless channel allowing the receiver

antennas to detect the different signals simultaneously transmitted by the transmit antennas. That is, spatial

multiplexing method uses multiple antennas at the transmitter and the receiver in conjunction with rich

scattering environment within the same frequency band to provide a linearly increasing capacity gain in

the number of antennas [9, 25, 26]. Hence, the concept of spatial multiplexing is different from that of

space-time coding method, which permits to efficiently introduce a space-time correlation among

transmitted signals to improve information protection and increase diversity gain. The basic spatial

multiplexing scheme is shown below.

Figure V-1. Basic Spatial Multiplexing Scheme with 3 transmit and 3 receive antennas [28]

Diagonal Bell Laboratories Layered Space-Time architecture (D-BLAST) is one of the spatial

multiplexing schemes to approach the theoretical capacity limit of multiple -input multiple-output (MIMO)

systems [9]. However, due to its complex coding procedure, Vertical Bell Laboratories Layered Space-

Time architecture (V-BLAST) has been proposed as a simplified version [10]. In V-BLAST, channel

coding may be applied to individual antennas (sub-layers), corresponding to the data stream transmitted

30

from each transmit antenna, while in D-BLAST coding processing is applied not only across the time but

also to each sub-layer, which implies higher complexity. The simple comparison between D-BLAST and

V-BLAST is shown at Figure V-1.

(a) (b)

Figure V-2. Transmit coding scheme comparison between (a) D-BLAST and (b) V-BLAST [31]

From the above figure, we can see that the essential difference between D-/V-BLAST is the

vector encoding process. In D-BLAST system, redundancy between the sub-streams is introduced by

using specialized inter-sub-stream block coding, and code blocks organized along diagonals in space-time

leads higher spectral efficiencies. On the other hand, in V-BLAST system, demultiplexing followed by

independent bit-to-symbol mapping of each sub-stream, so no coding is required [31]. From these

implemental advantages of V-BLAST, we will focus on the aspect of V-BLAST among several spatial

multiplexing methods.

V.I Receiver Design for Spatial Multiplexing System

The transmitted data stream of spatial multiplexing system is demultiplexed into TN lower rate

streams. After coding and modulation processing, each demultiplexed substream is transmitted

simultaneously from the TN transmit antennas. The substreams are co-channel signals, that is, they have

the same frequency band. At the receiver, each antenna observes a superposition of the transmitted signals,

31

separates them into constituent data streams, and multiplexed them in order to recover the original data

stream [26].

Receivers for spatial multiplexing can be divided into three classes; the maximum likelihood

receiver, the linear receiver, and the successive interference cancellation receiver.

A. Maximum likelihood (ML) Receiver

It is well known that theoretically, maximum likelihood detection algorithm is the optimum

method of recovering the transmitted signal at the receiver. ML receiver is a method that compares the

received signals with all possible transmitted signal vector which is modified by channel matrix H and

estimates transmit symbol vector x according to the Maximum Likelihood principle , which is shown as

2

,..., 1minargˆ k

TNkHxrx

xxx−=

∈ (V-1)

where x is the estimated symbol vector. The ML receiver searches through the all vector constellation

for the most probable transmitted signal vector. However, since the comparison complexity increases

exponentially with the number of transmit antennas, it is very difficult to use the receiver in practice,

which is the main disadvantage of this method. For example, in the case of 4 transmit antennas and 16-

QAM transmission, a total of 65536164 = caparisons per symbol is required to be enumerated for each

transmitted symbol. Therefore, the complexity of ML receiver is high and even prohibitive when many

antennas or high order modulation schemes are used [17, 27, 28].

B. Zero Forcing (ZF) Receiver

Zero-forcing receiver is a simple linear receiver, which uses a straight matrix inversion. Under

the assumption that the channel matrix H is invertible, a transmitted data symbol vector can be estimated

as

32

xHHxHHx * +− == 1)(ˆ (V-2)

where + represents the pseudo-inverse [29]. Note that the inverse only exists if the columns of H are

independent, since it is assumed that the elements of H are i.i.d. From the above equation, we can see that

the ZF receiver can separates the co-channel signals ,..., 1 TNk xxx ∈ . On the other hand, ZF receiver

results in a poor performance in the low SNR regime, when the channel matrix H becomes very ill-

conditioned in certain fading events [17, 27, 29].

C. Minimum Mean-Square Error (MMSE) Receiver

Another linear detection algorithm to the problem of estimating a random vector x on the basis of

observations y is to choose a matrix D that minimizes the Mean Square Error [27]

)][()]ˆˆ[(2 Dy(xDy)xx(x)xx −−=−−= ∗∗Eε (V-3)

The solution of the linear MMSE is given by

rHHHIrDx ⋅+=⋅= − HHNRSNR

1)1

(ˆ (V-4)

where the superscript H denotes the complex conjugate transpose [14]. The ZF receiver perfectly separates

the co-channel signals at the cost of noise enhancement. On the other hand, the minimum mean-square

error (MMSE) receiver can minimize the overall error caused by noise and mutual interference between

the co-channel signals, which is also at the cost of reduced signal separation quality [17, 27].

D. Successive Interference Cancellation (SIC) Receiver

The Successive Interference Cancellation (SIC) algorithm is in general combined with V-BLAST

receiver. Therefore, the SIC receiver is called just as V-BLAST receiver, which is an attractive alternative

to ZF and MMSE receivers. The SIC receiver provides improved performance at the cost of increased

computational complexity. Rather than just jointly decoding the transmitted signals, this nonlinear

33

detection scheme first detects the strongest transmitted signal, cancels the effect of this strongest signal

from each of the received signa ls, and then proceeds to detect the strongest of the remaining transmitted

signals, and so on. Under the assumption that the channel matrix H is known, the basic steps of the SIC

algorithm is summarized as follows [27, 32]

Ordering: Determine the optimal detection order by choosing the row with minimum

Euclidian norm

Nulling: Estimate the strongest transmit signal by nulling out all weaker transmit signals

Slicing: Detect the value of the strongest transmit signal by slicing to the nearest signal

constellation value

Cancellation: Cancel the effect of the detected strongest transmit signal form the

received signal vector in order to reduce the detection complexity for remaining transmit signals

Since the SIC algorithm is combined with ZF receiver or MMSE receiver, it can accordingly be

classified into the ZF V-BLAST receiver and the MMSE V-BLAST receiver.

D-1 Zero Forcing V-BLAST (ZF V-BLAST) Receiver

The Zero Forcing V-BLAST receiver algorithm has been presented in [10]. First, we let the

ordered set ,..., 21 TNkkkS = be a detection order of sub-streams. According to the basic SIC algorithm,

the ZF V-BLAST detection algorithm can be described as a recursive procedure, including determination

of the optimal ordering, as follows [10, 11]

¨ Initialization

211

1

1

)(

1

minarg jj

k

i

G

HG

rr

=

=

=←

+

34

¨ Recursion

As we assumed already, all components of x utilize the same constellation. Therefore, iky with

the lowest post-detection SNR will dominate the error performance of the detection algorithm. Due to

symbol constellation, these post-detection SNRs depend on the order in which the decision statistics are

computed. Thus, an obvious aspect of this system is the maximization of the worst of these post-detection

SNRs. The local optimization of choosing the component with the best SNR at each stage, leads to the

globally optimal ordered set S in this maximum sense. In [10], they proved this optimal ordered set

concept. Since the symbolikx is assumed to have the unit average power, the post-detection SNR

ikρ

for the ik th symbol is calculated as follow

(V-5)

D-2 Minimum Mean-Square Error V-BLAST (MMSE V-BLAST) Receiver

MMSE V-BLAST receiver suppresses both the interference and noise components, whereas ZF

V-BLAST receiver removes only the interference components. That is, the mean square error between the

transmitted symbols and estimate of the receiver is minimized. Thus, MMSE V-BLAST receiver yields

superior performance to ZF V-BLAST in the presence of noise [33, 34]. The detection algorithm is

( )

1

)(ˆ

)(ˆ

)(

21

,,1

1

1

T

minarg1

1

+←

=

=

−=

=

=

=

+∉

+

++

+

ii

k

a

yQa

y

jikkj

i

ki

kkii

kk

ikk

kik

i

i

ii

ii

ii

i

G

HG

Hrr

rw

Gw

L

22

2

i

i

i

k

k

k

a

wσρ =

35

summarized as follows

¨ Initialization

¨ Recursion

where 2σ is the variance of i.i.d complex Gaussian random noise with zero mean. Furthermore, the

detection ordering is determined based on the SINR. As the similar way of ZF V-BLAST, the post-

detection SINR ikρ for the ik th symbol is calculated as follow [34]

(V-6)

V.II Simulation Results

We simulated the average symbol error rate (SER) with 0/ NEs for various antenna

configurations with the modulation of 4-QAM constellation, which is the same as QPSK that we

simulated at the space-time coding schemes. Furthermore, we simulated the several spatial multiplexing

schemes on the Rayleigh and Ricean fading channels for the comparison of the difference of the

( )j

jk

i

)SINR(

1

11

H12H1

1

maxarg=

+=

=←

−HIHHG

rr

σ

( )

( )

1

SINR

)(ˆ

)(ˆ

)(

1,,

1

H12H1

1

T

maxarg1

1

+←

=

+=

−=

=

=

=

+∉

+

−+

+

ii

k

a

yQa

y

jikkj

i

iiii

kkii

kk

ikk

kik

i

ii

ii

ii

i

L

HIHHG

Hrr

rw

Gw

σ

( )( ) 2

11

22

2

1

1

1

∑≠

−

−

+=

iiii

iii

i

klkkk

kkk

kw Hw

Hw

σρ

36

performances.

In Figure V-3, we provide the SERs for the different antenna configuration of 3,2,1=TN

and 3,2,1=RN against 0/ NEs . It can be seen that the diversity order of a system based on the ML

technique is equal to the number of receiver antennas RN , therefore, the SER performance increases by

introducing an extra transmit and an extra receive antenna. However, it should be noted that the SER

performance of a ML receiver system does not lose its diversity order if the number of transmit antennas

increased, but the overall performance deteriorates. For example, we can see the curves of 1×2 and 2×2

antenna configurations. That is, the curves of Figure V-3 shift to the right when more transmit antennas are

added. The reason for this degradation is the increase in the error space with increasing number of

antennas. As the number of transmit antennas is increased, the size of the input vector constellation

increases. Thus, the number of signal vector which can be mistaken for is more, which implies an increase

in the number of possible error vector resulting in performance degradation [17].

Figure V-3. Symbol Error Rate (SER) comparison for various antenna configurations over Spatial

multiplexing scheme by using Maximum Likelihood (ML) receiver technique

37

Figure V-4 shows the SER performance when ZF technique is used at the receiver, which also

use 4-QAM transmit constellation on all antennas. When comparing it with ML receiver system and SISO

system, it is seen that SISO with 1,1 == RT NN , ML receiver with 1,1 == RT NN and MIMO with

2,2 == RT NN show almost the same SER performance representing Rayleigh flat fading. The reason is

that when RT NN = , the 0/ NEs on each stream is chi-squared variable with two degrees of freedom

which is a Rayleigh flat fading. Thus, there is no diversity benefit from the multiple receive antennas [17].

However, when RT NN < , the ZF receiver technique shows the SER performance increase, as shown in

Figure V-3.

Figure V-4. Symbol Error Rate (SER) comparison for various antenna configurations over Spatial

Multiplexing scheme by using Zero Forcing (ZF) receiver technique

38

Figure V-5. Symbol Error Rate (SER) comparison for various antenna configurations over spatial

multiplexing scheme by using Minimum Mean-Square Error (MMSE) receiver technique

In Figure V-5, the SER performance comparison is depicted when MMSE technique is used. The

trend of SER curves is very similar to that of ZF receiver technique. As we already discussed, the MMSE

receiver minimizes the overall error caused by noise and mutual interference between the co-channel

signals, thus it is less sensitive to the channel noise at the cost of reduced signal separation [27]. Therefore,

although the MMSE receiver show a little better performance than ZF receiver, in the high SNR case the

MMSE receiver converges to the ZF receiver [17].

The next two Figures V-6 and V-7 show the SER vs. 0/ NEs of ZF V-BLAST and MMSE V-

BLAST, respectively. As compared to the above V-4 and V-5, these two figures indicate that the ZF and

MMSE receivers with Successive Interference Cancellation (SIC) method present better performance.

Especially for ZF V-BLAST, the improvement is approximately 3dB at the target SER of 10-4 with the

antenna configuration of 2 transmit and 3 receive antennas as shown in Figure V-7. Although the

39

improvement of ZF V-BLAST is not better than that of ML receiver, ZF V-BLAST has less complexity

compared to ML receiver. When we apply MMSE V-BLAST, the improvement compared to only MMSE

scheme is about 3 dB at the target SER of 10-4 with the 2 transmit and 4 receive antenna configuration. As

we already studied, we can see that the improvement is due to the optimal ordering combined with the

successive cancellation of the interference and noise. All of the mentioned spatial multiplexing receivers

are compared in Figure V-8. From the Figure V-8, we can see that the MMSE V-BLAST and ZF V-BLAST

are intermediate and applicable in terms of performance and complexity.

Figure V-6. SER comparison for various antenna configurations over spatial multiplexing scheme by using

Zero Forcing (ZF) receiver with successive interference cancellation receiver technique (ZF V-BLAST)

40

Figure V-7. SER comparison for various antenna configurations over spatial multiplexing scheme by using

Minimum Mean-Square Error (MMSE) receiver with successive interference cancellation technique (MMSE

V-BLAST)

Figure V-8. Comparison of ML, ZF, MMSE, ZF V-BLAST and MMSE V-BLAST receivers with SER

vs. 0/ NEs for various antenna configurations over spatial multiplexing scheme

Finally, the next five figures show the comparison of the spatial multiplexing schemes applied to

Rayleigh and Ricean fading channels. Under the assumption that the all transmit and receive antennas are

41

uncorrelated with each other, the SERs of the spatial multiplexing methods in the Ricean channel indicate

the better performance.

Figure V-9. Rayleigh vs. Ricean comparison for 2x2 ML receiver, 4QAM

Figure V-10. Rayleigh vs. Ricean comparison for 2x2 ZF receiver, 4QAM

42

Figure V-11. Rayleigh vs. Ricean comparison for 2x2 MMSE receiver, 4QAM

Figure V-12. Rayleigh vs. Ricean comparison for 2x2 ZF V-BLAST receiver, 4QAM

43

Figure V-13. Rayleigh vs. Ricean comparison for 2x2 MMSE V-BLAST receiver, 4QAM

44

VI. Conclusions

The increasing demand for the development of wireless communication systems for high data

rate transmission and high quality information exchange leads to the new challenging subjects in the

telecommunication research area. Therefore, The reason that we chose ‘Fundamental overview and

simulation of MIMO systems for Space-Time coding and Spatial Multiplexing’ as a semester project for

EE381k-11 Wireless communication is because of the fact that the MIMO principle is able to provide

future wireless communication systems with significant increased capacity or higher link reliability using

the same bandwidth and transmit power as today.

This project investigated the information theoretical background for MIMO wireless

communication systems. The MIMO capacity formulae were simply explained, which showed the

dramatically increased capacity and reliability as compared with conventional single -input single-output

systems. The basic idea of MIMO system architecture is to usefully exploit the multipath, rather than

mitigate it, considering the multipath itself as a source of diversity which allows the parallel transmission

of a certain number of substreams. The indoor wireless environment is an good example of a rich

scattering environment necessary to obtain the best performance promised by MIMO systems. Several

Space-Time Coding (STC) schemes such as Space-Time Block Coding (STBC) and Space-Time Trellis

Coding (STTC), and Spatial Multiplexing schemes such as V-BLAST exploit the rich scattering wireless

channel allowing the receiver to detect the different signals simultaneously transmitted by the multiple

transmit antennas. STC permits to efficiently introduce a space-time correlation among transmitted signals

that can be exploited to increase information reliability while spatial multiplexing is to increase data rate.

Simulations and measurements were presented to show the capability for several MIMO systems

(STC and Spatial Multiplexing schemes). It could be shown that the reliability and capacity significantly

45

increase with increasing the number of transmit and receive antennas. STBC can realize full diversity gain

and especially, among a number of antenna diversity methods, the Alamouti method is very simple to

implement. Hence, we derived and simulated the performance of the Alamouti coding method and varied

the number of transmit and receive antennas. It was shown that STTC provides better performance than

STBC at the cost of increased receiver complexity. Moreover, we theoretically investigated spatial

multiplexing methods, and then evaluated and simulated the performance V-BLAST, which exhibit the

best trade-off between performance and complexity among spatial multiplexing techniques. In addition,

we derived its several receiver structures such as Maximum Likelihood (ML), Zero-Forcing (ZF),

Minimum Mean-Square Error (MMSE), and Successive Interference Cancellation (SIC) Receivers. By

investigating and simulating each receiver concepts, it was shown that V-BLAST implements a detection

technique, i.e. SIC receiver, based on ZF or MMSE combined with symbol cancellation and optimal

ordering to improve the performance, although ML receiver appears to have the best SER performance.

In this project, the MIMO principle is based on a rich multipath environment without a normal

Line-of-Sight (LOS), that is, the Rayleigh flat fading channel. However, due to movement or other

changes in the environment, LOS situation can arise. Thus, the Ricean channel modeling for MIMO

systems has recently attracted considerable attention and been researched [35, 36]. Therefore, we also

simulated the MIMO system operations in the Ricean channel and achieved the result that the MIMO

systems in a Ricean channel show the better performance than in a Rayleigh channel under the assumption

of uncorrelated antennas. For the case of correlated antennas, future works are necessary.

On the other hand, in order to achieve high gains for a Rayleigh frequency selective fading

channel, the employment of an orthogonal frequency division multiplexing (OFDM) communication

system in MIMO systems has also been actively researched, which is called MIMO-OFDM system [37-

46

40]. It is from the fact that the OFDM system has simple implementation of equalizers and robustness

against frequency selective channels by converting the channel into the flat fading subchannels, that is, a

broadband signal is broken into multiple narrowband tones, in which each carrier is more robust to

multipath [39, 40]. Moreover, space-time coded OFDM (STC-OFDM) and BLAST-OFDM have proposed

to overcome frequency selective fading channels and achieve higher capacity and spectral efficiency in a

rich scattering environment [41-45].

From our study and overview of MIMO systems, it is clear that MIMO systems offer significant

gains in performance over traditional wireless communication systems. For this reason, MIMO technology

is poised to play an important role in the next generation mobile communication systems and standards.

MIMO technology has already been incorporated into wireless LAN standards such as IEEE 802.11 and

HiperLAN/2 and is an optional feature of the 3G UTMS (IMT-2000), a next generation wireless

communications standard. Furthermore, MIMO technology is a strong candidate for 4G along with OFDM.

47

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