A Multi-User Cooperative Diversity for Wireless Local Area Networks

doi:10.4236/ijcns.2008.13033

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I. J. Communications, Network and System Sciences, 2008, 3, 207-283

Published Online August 2008 in SciRes (http://www.SciRP.org/journal/ijcns/).

A Multi-User Cooperative Diversity for Wireless

Local Area Networks

Jun CHEN

, Karim DJOUANI

LISSI Lab., University Paris 12 and CEDRIC-CNAM Paris, France

Member, IEEE, F’SATIE/TUT Pretoria, South Africa and LISSI Lab., University Paris 12, France

E-mail:

chen_ju@auditeur.cnam.fr,

djouani@univ-paris12.fr

Received on November 12, 2007; revised and accepted on May 3, 2008

Abstract

In this paper, an idea of using space-time block coding (STBC) in multi-user cooperative diversity has been

exploited to improve the performance of the transmission in wireless local area networks. The theoretical

and simulation results show that, using STBC approaches can always achieve the better performance than

existing techniques without introducing the space-time coding. By analyzing the throughput and frame error

ratio (FER) of the two different STBC cooperative schemes, we find the trade-off between throughput and

reliability. The location of the relay is crucial to the performance, which supposes a rule for future cross-

layer design.

Keywords: Multiple-input-multiple-output (MIMO), Cooperation, Space-time Block Coding (STBC).

1. Introduction

Diversity is a powerful technique to mitigate fading and

improve robustness to interference [1], which refers to

the method by conveying the signal to the receiver over

multiple independently signal fading channels. The

conventional view of transmit diversity is that a single

wireless terminal transmits using an array of multiple-

antennas so that the paths from each antenna to the

destination with independently fading. The recent

research work in this area is the space-time coding (STC)

techniques that have been developed for multi-antenna

arrays. STC is an effective coding technique that uses

transmit diversity to combat the detrimental effects in

wireless fading channels [7]. Unfortunately, transmit

diversity methods based on multiple-input-multiple-

output (MIMO) approach are not applicable to many

wireless systems because of the size, complexity, power

or other constraints, as for instance, ad-hoc networks and

sensor networks. On account of these reasons,

cooperation between wireless terminals has been recently

proposed as a means to provide transmit diversity as

which shown in Figure 1, where S, R and D represent

source, relay and destination terminal, respectively. A

new method introduced in [2] and [3] to realize space

diversity gain has been studied under the name of

cooperative diversity. Traditional cooperative diversity

transmits the same signals through two different channels

as Figure 2. In the first time slot, the source

communicates to the relay and to the destination at the

same time; in the second time slot, just the relay

retransmits the signal received at the first time-slot to the

destination. The relay may simply forward the signal

received from the source terminal or retransmit the

estimates of the received symbols, obtained by detection.

We call it as repeat cooperation. In this paper, we present

a paradigm for cooperative diversity, which we term

space-time block coding (STBC) cooperation [21],

integrating user cooperation with STBC.

We summarize here the relevant contributions in the

area of the cooperative diversity. Relay channels and space-

time code form the basis for our study. The classical three-

terminal communication channels originally examined by

van der Meulen [5]. For the channels with multiple

information sources, Kramer and van Wijngaarden [6]

consider a multiple access channel in which the sources

communicate to one destination and share one relay.

Laneman et al. examines the mode of user cooperation

diversity [2,3] and analyzes space time coding

cooperative diversity in nonergodic settings using outage

probability as a performance measure [4]. They

A MULTI-USER COOPERATIVE DIVERSITY FOR WIRELESS LOCAL AREA NETWORKS 267

Figure 1. Single-relay cooperative diversity model.

Figure 2. Time sequence of 2 time slots repeat cooperative

diversity.

Figure 3. Time sequence of 2 time slots multi-user

cooperative diversity.

demonstrated the extent to which space-time coding

cooperative diversity achieves higher diversity order than

repetition-based schemes for larger spectral efficiencies

in theorem. The model they analyzed is a selective

orthogonal amplify and forward (OAF) protocol, where

source transmits the vector of encoded data in the first

time slot and relay retransmits the received vector by

adjusting the power. The non-orthogonal amplify-and-

forward (NAF) scheme was proposed by Nabar et al.

[8,9] for the single-relay channel, where source transmits

all the time but the relay only transmits on even time

slots. They consider three different time-division

multiple-access-based cooperative protocols that vary the

degree of broadcasting and receive collision in either the

amplify-and-forward (AF) or decode-and-forward (DF)

modes. And the results indicate that optimal space-time

code design in the single relay case consists of satisfying

the classical rank and determinant criteria for co-located

antennas. These academic works sustain the possibility,

existence and benefits for deploying space-time coding

cooperative diversity protocols in practice.

This paper examines a new 2×2 full-rate space-time

code (Golden-Code) [12] in the single-relay cooperative

NAF model. For source transmits in both two time slots,

this protocol can achieve a higher throughput than that of

the OAF protocol. And we here consider these two types

of cooperative protocols and compare the performance

between Golden-Code and the classical Alamouti code

[10]. Besides the distinct benefits of the space-time code,

we can see the trade-off between throughput and

reliability during the transmission by analyzing the

results of throughput and frame error rate. At the last part,

we give a basic idea about the selection of relay.

Organization of the paper. This paper continues as

follows: Section 2 outlines the multi-user cooperative

diversity model. Section 3 explains STBC cooperative

diversity. Section 4 shows the performance analysis by

the simulation results. Section 5 summarizes our

conclusions.

2. Multi-User Cooperative Diversity Model

We consider wireless network in which two terminals are

communicating with a base station. The channel between

each terminal and the base station are independent of

each other, and independent of the channel between the

terminals. All channels are subject to flat (frequency non-

selective) fading in order to isolate the benefits of spatial

diversity. Considering the multi-user cooperative

diversity model, signal is to be transmitted from the

source terminal S to the destination terminal D with the

assistance of the relay terminal R. All the terminals are

equipped with single antenna. Throughout the paper we

assume that a terminal cannot transmit and receive

simultaneously. the channels S→D, S→R and R→D are

known to the destination terminal.

The signal transmits procession is like following:

During the first time slot, the source communicates with

the relay and destination. In the second time slot, both

the relay and source communicate with the destination.

Figure 3 shows the detail of the time sequence.

In the AF relaying method [1], the relay simply

amplifies and retransmits the signal received from the

source (the signal received at the relay is distorted by

fading and additive noise). No demodulation or decoding

of the received signal is performed at relay in this case.

The signals received by the destination and relay in

the first time slot can be defined as

sdsdsdsd

nxhwy +=

1 (1)

and

srsrsrsr

nxhwy

(2)

respectively, where w

and w

2sr

are the average signal

energies received by destination over channel S

→

D and

→

R, respectively [9]. h

and h

are the random,

complex-valued and unit-power channel gains between S

→

D and S

→

R. n

∽

CN(0, N

, n

∽

CN(0,Nsr) is the

268 J. CHEN ET AL.

additive noises, and in general w

2sd

≠

2sr

The energy of received signal (3) is given by

(

)

(

)

(

)

srsrsrsrsrsrsr

NhwnExhwEyE +=+=

(3)

In order to retransmit the signal with the same power as

the sender did, the gain β for the amplification is

srsrsr

Nhw +

(4)

Then, the destination receives a superposition of relay

and source during the second time slot:

rdsrrdrdsdsd

nyhvxhwy

(5)

where v

2rd

is the average signal energy received at the

destination through channel R

→

D, the definition of h

and n

are the similar to h

and n

So the equation (5) can be rewritten as:

nxhwvxhwy

rdsrrdsdsd

122

++=

(6)

where

(

)

CNn

∽

with

rdsrrdrd

β+=

As the summary, the transmission function of this

cooperative diversity is y = Hx + n (7)

where

























is the received signal vector and transmitted signal vector,

respectively;













rdsrrdrd

nnhv

(8)

is the noise vector; and H is the 2×2 channel matrix

given by













sdsdrdsrrdsr

hwhhvw

(9)

Assuming that the channel coefficient matrix H is

known or can be estimated, Maximum Likelihood (ML)

decoding can be used at receiver to fully explore the

diversity advantage of the scheme. In equation (9), the

noise of first time slot and second time slot do not have

the same powers, the ML estimation can not be used

directly. One solution is normalizing the received noise

by a parameter

as follows:

















































hwhhvw

sdsdrdsrrdsr

sdsd

ρβρρ

(10)

where

rdsrrdrd

NNhv

(11)

Then, equation (10) can be noted as

Assuming that the channel coefficient matrix

known or can be estimated, the ML estimate of the

transmitted packets is presented as follows:

minarg

xHnx −=

(12)

where

‖·‖

represents the Frobenius-2 norm, and x

takes all possible finite values depending on the signal

constellation.

3. STBC Cooperation Model

STC is a method employed to improve the reliability of

data transmission in wireless systems by using multiple

transmit antennas. It relies on redundant copies of a

signal to the receiver in the hope that at least some of

them may survive the physical path between transmission

and reception. Space time codes may be split into two

main types: Space-time trellis coding (STTC) [16] and

STBC [17]. We are only concerned here with STBC

which acts on a block of data at once (similarly to block

coding) and provide only diversity gain, but are much

less complex in implementation terms than STTC.

Alamouti coding [10] and Golden-Code [12] are typical

examples of STBC.

3.1. Repeat Cooperation

Firstly, we present the model shown in Figure 2, repeat

cooperation transmits the same signals through two

different channels. In the first time slot, the source

communicates to the relay and to the destination at the

same time; in the second time slot, just the relay

retransmits the signal received at the first time slot to the

destination. Then, the transmission function can be noted

as follows:

rdsrrdrdrdsrsrrd

sdsdsd

nnhvxhhwvy

nxhwy

++=

ββ

(13)

The cooperative transmission function can be written

nhxy+=

(14)

where





































rdsrrdrd

rdsrsrrd

sdsd

nnhv

hhwv

3.2. Alamouti Coding Cooperation

Alamouti proposed a simple MIMO scheme that

achieves a full diversity gain [17] with a simple ML

A MULTI-USER COOPERATIVE DIVERSITY FOR WIRELESS LOCAL AREA NETWORKS 269

decoding algorithm. The transmit signals are modulated

using an M-ary modulation scheme, then the encoder

takes a block of two modulated signals s

and s

in each

encoding operation and sends it to the transmit antennas

according to the code matrix:











−













(15)

where * denotes complex conjugate. In this code matrix,

the first column represents the first time slot

(transmission period) in a 2

2 MIMO system [11] and

the second column represents the second time slot. The

first row corresponds to the signals transmitted from the

first antenna and the second row corresponds to the

signals transmitted from the second one. This implies

that the signals are transmitting both in space (across two

antennas) and time (two transmission intervals), that is to

say, space-time coding.

The traditional Alamouti coding is designed for a

two-transmit antenna system. Assuming the cooperative

method using one-relay AF channel, we define d

= (x

) and d

= (x

, x

). Thus, in the first time slot, the

source sends d

, the relay and destination receive the

signal; in the second time slot, the source and relay send

and x

to destination respectively. Then the Alamouti

coding cooperative transmission function can be written as

Y = HX +N

(16)

where

























,yy

are the transmitted and received signal matrix,

respectively; channel matrix H and noise N are given by













sdsrrdsrsdrd

sdsd

hwhhwv

1 2

1 13224

sd sd

rd rdsrrdsdrd rdsrrdsd

n n

Nvh nnnvh nnn

β β

 

 

+ +++

 

3.3. Golden-Code Cooperation

The Golden-Code is a STBC for 2× 2 MIMO system as

Figure 5, the coding matrix for the model is:

Figure 4. Alamouti coding in 2 × 2 MIMO model.

Figure 5. Golden-code in 2 × 2 MIMO model.

(

)

(

)

() ()

1 23 4

1 2

3 4341 2

s sss

x x

Cx x

i ssss

α θαθ

αθα θ

+ +

 

= =

 

 + +

 

 

(17)

where s1, s2, s3, s4

∈

Z[i] are the information signals,

θαθαθθ

iiii −−=−−=

−

=1,1,

and the

factor

is necessary for energy normalizing purposes

[12].

The Golden-Code achieves the diversity multiplexing

frontier [13], and in [12] the Golden-Code was proposed

as a full rate and full diversity code for 2× 2 MIMO

systems.

To the cooperative method using one-relay AF

channel, we define d1 = {(x1,x2)} and d2 = {(x3, x4)}

which are transmitted in first time slot and second time

slot, respectively. The transmission function is similar to

equation (16).

4. Numeral Results

In this section, some simulations are presented to show

the performances of the presented approaches. In the

following simulations, Rayleigh model is used for the

fading channel [20], each channel multi-path is a zero

mean complex Gaussian random variable, and the

distance between all the terminals is assumed to be same.

Transmission energies follow the hypothesis as Table 1.

Table 1. Transmission energies in simulations.

Protocol 1

time slot 2

time slot

Cooperation

=1.0

=0.5

MIMO 2

=0.5

The throughput was defined as the average number of

available frames that were transmitted in a specific time

slot. We performed a random experiment consisting of

10,000 repeated independent trials. The length of each

frame was fixed to N = 600 bits. Considering the multi-

pack reception, the throughput can more than 1.

4.1. The Throughput Comparison between the

Repeat Cooperation and STBC Cooperation

We conducted comparisons between the STBC

270 J. CHEN ET AL.

cooperation and repeat cooperation scheme. Figure 6 and

Figure 7 show the results of throughput versus SNR, for

6Mbps and 12Mbps transmit rates, respectively. We

observe that all the three schemes can achieve the

maximum throughput with a high SNR (> 25dB). With a

special coding method, Golden-Code cooperation

scheme achieves a much higher throughput than the other

two. Considering the coding matrix of Golden-Code,

each row contains all the 4 original signals, which means

the full-rate of the transmission. The cooperative method

transmits 4 available signals ({s1; s2; s3; s4}) during 2

time slots, which means the maximum value of

throughput is 2.

As to amamouti coding scheme, each row of the

coding matrix contains 2 original signals (s

and s

). In

every time slot, the system transmits one signal and the

conjugated signal of the other one, where s

and s

are

surly the redundancy copies of the original signals. That

is why only 2 available signals (s

and s

) can be obtained

at the destination in this scheme while 4 available signals

({

; s

}) can be obtained by using Golden-Code

scheme. Thus, by using two pair of conjugate signals,

Alamouti coding scheme transmits 2 available signals

during 2 time slots of the cooperative period, which

means the maximum value of throughput can no more

than 1 with the increasing of SNR.

Furthermore, as shown in Figure 2, repeat cooperation

transmits one signal during the first time slot and

retransmits the same one in the second. Clearly, repeat

cooperation can just transmit 1 signal during the two

time slots. Thus, its throughput is less than 0.5.

From the simulations, we see that with the help of

STBC gains, the STBC cooperation is outperform repeat

cooperation. And as a reasonable result of analysis and

simulation, the Golden-Code cooperation can clearly

achieve the best throughput among all the three schemes.

This also proves that the design of the space-time code

could impact the performance of the transmission.

Figure 6. Throughput of STBC cooperation and repeat

cooperation schemes (6Mbps).

Figure 7. Throughput of STBC cooperation and repeat

cooperation schemes (12Mbps).

4.2. The FER Comparison between Non-

ooperation, Repeat Cooperation and STBC

Cooperation

The simulation results of FER versus SNR between Non-

cooperation and cooperation schemes demonstrate again

that the use of relay-assisted communication is not

always beneficial when compared to direct transmission

(Non-cooperation scheme) [8]. Figure 8 and Figure 9

reveal that the frame error rate of Non-cooperation

communication is better than that of the simple repeat

cooperation for a high SNR (>35dB).

Further, as expected, cooperation with STBC is

always preferred over Non-cooperation scheme. Thus

from our simulations, we see that, performance using

STBC cooperation improves significantly over Non-

cooperation demonstrating the advantage of using STBC

cooperation. Between the two STBC cooperation

schemes (Alamouti coding and Golden-Code), Alamouti

coding method shows a better performance. As we

discussed, Alamouti coding transmits the redundance

Figure 8. FER versus SNR for Non-cooperation and

cooperation schemes (6Mbps).

A MULTI-USER COOPERATIVE DIVERSITY FOR WIRELESS LOCAL AREA NETWORKS 271

Figure 9. FER versus SNR for Non-cooperation and

cooperation schemes (12Mbps).

Figure 10. FER versus SNR for STBC in cooperation and

MIMO schemes (6Mbps).

signals, a original and a conjugate. This is the reason that

it has a lower error rate in the destination while Golden-

Code just intersperses original signal among all parts of

the transmit signals.

Comparing with the simulation results about the

throughput of these two STBC cooperation schemes, we

see that, Alamouti coding have a lower throughput but a

higher reliability than that of Golden-Code. As a

summary, there is always a trade-off between the

throughput and the reliability.

4.3. The FER Comparison between STB

Cooperation and MIMO Schemes

Figure 10 and Figure 11 show us the FER of cooperation

and MIMO system referring to the different SNRs.

According to the simulation results, the MIMO systems

achieve lower FER than the corresponding cooperative

schemes. This supports that MIMO channels allowing

multiplexing gain [14,15] which is absent in cooperative

relaying channel since time is expended in the latter.

Thus, using MIMO system always obtains the gain of

spatial diversity. And as expected, the Alamouti coding

method has a better performance than the corresponding

Golden-Code method. The simulation result demonstrates

again that there is a trade-off between the throughput and

the reliability.

4.4. Effect via the Movements of the Relay

The main building blocks of a wireless network design

are rate control, power control, medium access

(scheduling) and routing. These building blocks are

divided in layers. Typically, routing is considered in a

routing layer and medium access in a MAC-layer, whereas

power control and rate control are sometimes considered

in a PHY-layer and sometimes in a MAC-layer.

So far, the three stations (S, R, D) were positioned

equidistantly and therefore all the three channels had the

fixed distance. Let us denote the distance between source

and destination as d

; distance between source and relay

as d

and distance between relay and destination as d

Denote SNR

, SNR

as SNR between the source

and destination during the 2 time slots. We have

SNR d

 

∝

 

 

 

∝

 

 

 

∝

 

 

(18)

where v is the path loss exponent. In the following

analysis, we assume that v = 4 for urban environment [18].

In this section, the relay is moved, so the distance

between the relay and source, the relay and destination

will change at the same time. The effects on the signal

quality when moving the relay between the source and

destination using Golden-Code cooperation with 6Mbps

and 12Mbps transmission rate are shown in Figure 12

and Figure 13, respectively. In the simulations, the

distance between the sender and the destination is set to

one, and therefore the SNRs shown in the X-axis is only

valid for the direct link S

→

Figure 11. FER versus SNR for STBC in cooperation and

MIMO schemes (12Mbps).

272 J. CHEN ET AL.

Figure 12. Benefit results when the relay is located between

the source and the destination (6Mbps).

Figure 13. Benefit results when the relay is located between

the source and the destination (12Mbps).

The best performance is achieved when the relay is

situated in the middle of the source and destination,

which means the better channel quality at S

→

R and R

→

D. And this can be a rule for a relay-selection method at

MAC-layer using the information of PHY-layer.

5. Conclusions

This paper describes STBC cooperation in wireless

communication, a technique that allows single-antenna

mobiles to share their antennas for obtaining some

benefits of multiple-antenna systems. The diversity is

realized by using a third station as a relay and the STBC

methods for information coding. We analyze the

performance of two different types of STBC cooperative

methods (Alamouti coding and Golden- Code) through

the theoretical study and simulations, there is the trade-

off between throughput and reliability during the

transmission. The results show that using the STBC

cooperative diversity can always increase the

performance. Through the analysis of the two methods

with the corresponding MIMO systems, we know that the

performance of MIMOs is always better than that of

cooperation with allowing multiplexing gain. The

location of the relay is crucial to the performance.

The best performance was achieved when the relay is

in the middle of source and destination. And in general

the relay should not be to far from the line between the

two terminals.

We believe several areas of future research on

cooperative communication will be fruitful. Firstly, the

generalization of the one hop space-time coded

cooperation to multi-hop case. Most of the research work

about cooperative communication concerns the single-

hop (single-relay or multi-relay) transmission. Nowadays,

multi-hop ad-hoc network can be found in everywhere,

and the protocol adapted to multi-hop environment

always derives from that of the single-hop. Secondly, the

integration and interaction with higher layer network

protocols can be explored. Recently, the need for

protocol adaptation and code cooperation of wireless

communication system suggested a new concept of

protocol architecture, named cross-layering architecture.

Different protocols implemented at different protocol

layers may be designed to have mutually cooperative

reactions, based on sharing the information between the

different layers. Obviously, a cross-layer approach that is

based on metrics computed at physical layer as SNR and

minimal distance in the decoding process is under

investigation. Such approach will be of a certain interest

for MAC and Network levels, taking advantage of the

information measured or estimated at the physical layer.

Our contribution will concern, mainly, link adaptation

and frames scheduling at MAC level. Lastly,

generalization of the STBC approach to meshed network

while considering multi-channel cooperation, radio

resources management and link adaptation will be our

crucial objective in perspective.

6. Acknowledgement

This work comes within the framework of a project

supported by the Agence Nationale de la Recherche/

R’eseau National de Recherche en T’el’ecommunications

under name RNRT/RADIC-SF/COMSIS and reference

ANR-05-RNRT- 014-01.

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