Relaying Protocols for Wireless Networks

Thesis for the degree of Licentiate of Engineering

Relaying Protocols for Wireless Networks

Majid Nasiri Khormuji

Communication TheorySchool of Electrical Engineering

KTH (Royal Institute of Technology)

Stockholm 2008

Nasiri Khormuji, MajidRelaying Protocols for Wireless Networks

Copyright c©2008 Majid Nasiri Khormuji except whereotherwise stated. All rights reserved.

TRITA-EE 2008:019ISSN 1653-5146

Communication TheorySchool of Eletrical EngineeringKTH (Royal Institute of Technology)SE-100 44 Stockholm, SwedenTelephone + 46 (0)8-790 7790

Abstract

Motivated by current applications in multihop transmission and ad hoc networks,the classical three-node relay channel consisting of a source-destination pair anda relay has received significant attention. One of the crucial aspects of the relaychannel is the design of proper relaying protocols, i.e., how the relay should takepart into transmission. The thesis addresses this problem and provides a partialanswer to that.

In this thesis, we propose and study two novel relaying protocols. The firstone is based on constellation rearrangement (CR) and is suitable for higher-ordermodulation schemes. With CR, the relay uses a bit-symbol mapping that is differ-ent from the one used by the source. We find the optimal bit-symbol mappings forboth the source and the relay and the associated optimal detectors, and show thatthe improvement over conventional relaying with Gray mapping at the source andthe relay can amount to a power gain of several dB. This performance improvementcomes at no additional power or bandwidth expense, and at virtually no increasein complexity. The second one is a half-duplex decode-and-forward (DF) relayingscheme based on partial repetition (PR) coding at the relay.With PR, if the relaydecodes the received message successfully, it re-encodes the message using thesame channel code as the one used at the source, but retransmits only a fractionof the codeword. We analyze the proposed scheme and optimizethe cooperationlevel (i.e., the fraction of the message that the relay should transmit). We compareour scheme with conventional repetition in which the relay retransmits the entiredecoded message, and with parallel coding, and additionally with dynamic DF.The finite SNR analysis reveals that the proposed partial repetition can provide again of several dB over conventional repetition. Surprisingly, the proposed schemeis able to achieve the same performance as that of parallel coding for some relaynetwork configurations, but at a much lower complexity.

Additionally, the thesis treats the problem of resource allocation for collabo-rative transmit diversity using DF protocols with different type of CSI feedbackat the source. One interesting observation that emerges is that the joint power-bandwidth allocation only provides marginal gain over the relaying protocols withoptimal bandwidth allocation.

Keywords: The relay channel, constellation rearrangement, decode-and-forward, resource allocation.

i

Acknowledgements

I would like to express my sincere gratitude to my supervisor, Prof. Erik Larssonfor his expertise and generous support during the last two years. I would also like tothank Prof. Mikael Skoglund for the valuable research discussions and AssociateProf. Mats Bengtsson for his help with the WINNER project.

I would like to express my appreciations to all my current andformer col-leagues at Communication Theory and Signal Processing Groups. I would like toespecially thank Johannes Karlsson, my officemate and Sha Yao for fruitful dis-cussions on the relay channel.

I would like to thank Dr. Christian Ibars for taking the time to read my collec-tion of papers and acting as the opponent on the thesis. I would also like to thankKarin Demin and Annika Augustsson for helping with administrative issues.

I would like to express my sincere gratitude to my parents andparents-in-lawfor their tremendous support and love. Finally, I would liketo thank my wife forher understanding, patience, and endless love.

iii

Contents

Abstract i

Acknowledgements iii

Contents v

I Introduction 1

Introduction 11 Potential Applications of Relaying . . . . . . . . . . . . . . . . . 1

1.1 Relay-Based Cellular Network . . . . . . . . . . . . . . . 21.2 Wireless Sensor Networks . . . . . . . . . . . . . . . . . 21.3 Relay-Assisted Cognitive Radios . . . . . . . . . . . . . . 2

2 The Classical Relay Channel . . . . . . . . . . . . . . . . . . . . 23 Bounds on Capacity . . . . . . . . . . . . . . . . . . . . . . . . . 3

3.1 Upper bound . . . . . . . . . . . . . . . . . . . . . . . . 33.2 Lower bounds . . . . . . . . . . . . . . . . . . . . . . . . 4

4 Frequency-Division Gaussian Relay Channel . . . . . . . . . . . 54.1 Upper bound on the capacity . . . . . . . . . . . . . . . . 64.2 Achievable rate of DF . . . . . . . . . . . . . . . . . . . 64.3 Achievable rate of CF . . . . . . . . . . . . . . . . . . . 74.4 Achievable rate of linear relaying . . . . . . . . . . . . . 7

5 Slow-Fading Relay Channel . . . . . . . . . . . . . . . . . . . . 86 Resource Allocation for Time-Division Relay Channels . . .. . . 87 Contributions of the Thesis . . . . . . . . . . . . . . . . . . . . . 9References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

II Included papers 15

A Improving Collaborative Transmit Diversity by Using ConstellationRearrangement A1

v

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A12 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . A23 Constellation Rearrangement . . . . . . . . . . . . . . . . . . . . A3

3.1 Design of optimum CR for relaying . . . . . . . . . . . . A54 Receiver Design and Performance Analysis . . . . . . . . . . . . A6

4.1 Optimum Detector . . . . . . . . . . . . . . . . . . . . . A64.2 Suboptimal Detector: Maximum-Ratio Combining (MRC) A8

5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . A106 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A10References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A14

B Receiver Design for Wireless Relay Channels with Regenerative Re-lays B11 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B12 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . B33 Single-Relay Channel . . . . . . . . . . . . . . . . . . . . . . . . B4

3.1 Optimal hard and soft detectors . . . . . . . . . . . . . . B43.2 Soft detector based on statistics of CSI . . . . . . . . . . B73.3 Low- and high-SNR approximations . . . . . . . . . . . . B9

4 Parallel Relay Channel . . . . . . . . . . . . . . . . . . . . . . . B125 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . B146 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B14References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B14

C Cooperative Transmission Based on DF Relaying with Partial Repeti-tion Coding C11 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C1

1.1 Transmission Protocol . . . . . . . . . . . . . . . . . . . C31.2 Channel Model . . . . . . . . . . . . . . . . . . . . . . . C31.3 Performance Measure . . . . . . . . . . . . . . . . . . . C4

2 Transmission Schemes . . . . . . . . . . . . . . . . . . . . . . . C42.1 Baseline Transmission Schemes . . . . . . . . . . . . . . C42.2 DF with Parallel Coding . . . . . . . . . . . . . . . . . . C72.3 Dynamic Decode-and-Forward (DDF) . . . . . . . . . . . C82.4 Proposed Scheme: DF with Partial Repetition . . . . . . . C9

3 Resource Allocation for Collaborative schemes . . . . . . . . .. C113.1 Conventional DF with Repetition Coding . . . . . . . . . C113.2 DF with Parallel Coding . . . . . . . . . . . . . . . . . . C123.3 DF with Partial Repetition (Proposed Scheme) . . . . . . C12

4 Comparisons and Simulation Results . . . . . . . . . . . . . . . . C125 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C15Appendix A Probability ofO(Prαrd + Psαsd, 2β) . . . . . . . . . . . C18Appendix B Probability ofO(Psαsd, Prαrd, δ, β) . . . . . . . . . . . . C18Appendix C Probability ofO1 . . . . . . . . . . . . . . . . . . . . . . C20

vi

Appendix D Probability ofO(Psαsd, Prαrd, δ, β) . . . . . . . . . . . . C21References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C22

D Analytical Results on Block Length Optimization for Decode-and-Forward Relaying with CSI Feedback D11 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D12 System Model and Performance Measure . . . . . . . . . . . . . D23 Baseline Transmission Schemes . . . . . . . . . . . . . . . . . . D3

3.1 Direct (S − D) Transmission . . . . . . . . . . . . . . . . D33.2 Collaborative Transmission without CSI Feedback . . . . D3

4 Block Length Optimization with Perfect CSI at the Source . .. . D45 Collaborative Schemes with One Bit of CSI Feedback . . . . . . .D7

5.1 One Bit Feedback and Selection Combining atD . . . . . D75.2 One Bit Feedback and MRC atD . . . . . . . . . . . . . D8

6 Numerical Results and Discussion . . . . . . . . . . . . . . . . . D9References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D10

E A Spectrally Efficient Transmission Scheme for Half-Duplex DF Re-laying E11 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E12 The Proposed Transmission scheme . . . . . . . . . . . . . . . . E23 Optimized Design forN = 2,M = 1, andr = 2 . . . . . . . . . E7

3.1 Optimum Rotation Angle for Uncoded Transmission . . . E93.2 Outage Probability for Coded Transmission . . . . . . . . E9

4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E11References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E12

vii

Part I

Introduction

Introduction

The classical relay channel [1, 2] has received renewed attention in recent yearsdue to its potential in wireless applications and ad hoc networks [3, 4]. A new con-cept,user cooperation[5, 6] orcooperative diversity[7, 8], has been introduced asa means to enhance the reliability of communication by an additional transmissionof the intended message through another node. The node whichcollaborates withthe main transmitter (user) is calledrelay. Thereby, when the relay cooperates anetwork consisting of the source-destination pair and the relay will be configured.An immediate question which emerges from this setup is how the relay shouldutilize its resources (i.e., power and bandwidth) to enhance the reliability of com-munication. The main theme of this thesis is to partially answer this question. Inwhat follows we first describe some potential applications of relaying. We thenintroduce a formal definition of the classical three-nodes relay channel and somewell known bounds on the capacity of this channel. Finally, we provide a summaryof the contributions in the thesis.

1 Potential Applications of Relaying

Consider a wireless network with some active nodes including a transmitter-receiver pair. Due to the broadcast nature of wireless transmission, some nodes inthe network might overhear the transmitted signal. If the direct communication ofa transmitter-receiver pair fails (for example, due to the channel variations), thosenodes that have a copy of the transmitted signal can help to reestablish the commu-nication between the intended transmitter-receiver pair.The nodes that cooperatein the transmission are calledrelays. Generally speaking, when the relays cooper-ate (i.e., take part in the transmission in order to help the transmitter-receiver pair),multiple paths for conveying the transmitter’s message will be available. In otherwords, a virtual antenna array has been created. Multiple paths in wireless com-munication often translates into diversity gains. From this setup one can envisionvarious applications of having the relays. In the followingwe mention some ofthese applications.

2 INTRODUCTION

1.1 Relay-Based Cellular Network

One immediate application is the deployment of fixed relays in cellular networks[9]. In the uplink (i.e., mobile to base station) transmission, practical constraints onthe size of the handset and the battery life-time preclude the use of Multiple-InputMultiple-Output (MIMO) antenna techniques. MIMO systems are well knownto offer multiplexing gain (i.e., an increase in data rate) and diversity gain (i.e.,an increase in the slope at which the symbol-error-probability decreases with theaverage SNR) [10]. Thus one way to obtain the benefits of MIMO links is touse distributed MIMO by the deployment of the relays. Additionally, relay-basednetworks are more robust to shadow fading (i.e., attenuation of the transmittedsignal due to large obstacles) since the placement of relaysis not as restricted asthat ofcollocated antennasin the conventional MIMO systems.

1.2 Wireless Sensor Networks

Wireless sensors networks [11] are composed of many nodes that are densely de-ployed in the environment. The main purpose of such networksusually is detectionor estimation of a physical phenomenon. The sensors are supposed to work withlow-power and have a sort of intelligence to establish the communication and tomaintain the network. The collaboration among nodes is of crucial importance insuch networks to achieve

• reliable estimation and detection; and

• reasonably long life-time of the network.

In other words, some nodes in the network should take the roleof being relays tomaintain reliable interconnections between the nodes and to save energy.

1.3 Relay-Assisted Cognitive Radios

Cognitive Radio [12] is motivated by the apparent geographical and temporalunder-utilization of the spectrum. The idea is to sense aspectrum holeand try toutilize it in such a way not to harm theprimary user(i.e., licensed user). Clearly,one of main challenges of the cognitive radio is to sense the spectrum. This de-tection problem is intimately related to the cooperative communication in whichthe cognitive users help one another by relaying relevant information to sense thespectrum [13].

2 The Classical Relay Channel

The Discrete Memoryless Relay Channel was introduced by vander Meulen in1971 [1]. Figure 1 shows a block diagram of the relay channel.The channel isdefined using two finite input setsX andXr, two finite output setsY andYr,

3 BOUNDS ONCAPACITY 3

p(y, yr|x, xr)

Encoder

Encoder

Relay

DecoderW WXn

Y n

XnrY n

r

Figure 1: Block diagram of the relay channel

and a pmfp (y, yr|x, xr). Therefore, in Figure 1 we haveXn ∈ Xn, Y n ∈ Yn,Xnr ∈ Xn

r andY nr ∈ Ynr . Moreover, the channel is assumed to be memoryless:

p(yi, yr,i|xi, xir

)= p (yi, yr,i|xi, xr,i)

That is, the received signals at the relay and the destination at time instanti onlydepend on the transmitted signals from the source and the relay at time instanti(i.e.,xi, xri

).1

The goal of the communication channel is to reliably convey the messageWuniformly drawn from the set{1, 2, · · · , 2nR} to the destination inn channel uses.To accomplish this task, one needs to design three main components:

• an encoder to map the messageW toXn;

• a set of relay functions:{fi}ni=1 such that2

xr,i = fi (yr,1, yr,2, . . . , yr,i−1) ;

and

• a decoder to map the received signalY n to an estimate of the transmittedmessageW .

The capacity of the channel is defined as the supremum of all ratesR for whichit is possible to achievePr{W 6= W} → 0 asn→ ∞ [14].

3 Bounds on Capacity

3.1 Upper bound

We next present an upper bound on the capacity. This upper bound is known asmax-flow min-cutor cut-setbound [2] and it consists of two terms:

1Xi , [X1 X2 · · · Xi].2Here we assume causal relaying, that is the transmitted signal at instanti only depends on the

received signals up to time instanti − 1.

4 INTRODUCTION

Broadcast Channel Multiple access channel

XX Y Y

XrYr : Xr

Figure 2: Illustration of the max-flow min-cut upper bound

• Broadcast bound:C ≤ supp(x,xr) I(X ;Y, Yr|Xr)

• Multiple access bound:C ≤ supp(x,xr) I(X,Xr;Y )

Figure 2 schematically illustrates these two bounds. One can easily see the analogybetween the broadcast bound and the receive diversity in which the relay playsthe role of another receiver. On the contrary in the multipleaccess bound, therelay acts as another transmitter by conveying a fresh codeword of the intendedmessage and the relay channel hence mimics the behavior of the transmit diversity.Combing these two bounds we obtain

C ≤ supp(x,xr)

min {I(X,Xr;Y ), I(X ;Y, Yr|Xr)} . (1)

where the supremum is taken over all joint pmfsp(x, xr).

3.2 Lower bounds

We next provide an overview of some well known lower bounds onthe capacity.

Block Markov Encoding

With block Markov encoding [2] (also known as decode-and-forward (DF) [15–18]), the transmission occurs inB consecutive blocks. The relay transmits a freshcodeword by decoding the previous block received at the relay. This scheme relieson the decoding at the relay and hence its performance is limited by the quality ofthe source-relay link. Using DF, the following rate is achievable [2]

R = supp(x,xr)

min {I(X,Xr;Y ), I(X ;Yr|Xr)} (2)

where

• I(X,Xr;Y ) is the multiple access bound on the capacity; and

• I(X ;Yr|Xr) reflectsthe capacity of the source-relay link.

4 FREQUENCY-DIVISION GAUSSIAN RELAY CHANNEL 5

One can readily deduce that DF operates close to the capacityupper bound whenthe quality of the source-relay link is ”reasonably” good.

DF relaying achieves the capacity when the relay channel is physically de-graded, that is

p(y, yr|x, xr) = p(yr|x, xr)p(y|yr, xr).or equivalentlyX → (YrXr) → Y form a Markov chain. This, loosely speak-ing, means that the relay receives a better copy of the transmitted message thanthe destination. Note that by this definition the the broadcast bound simplifies toI(X ;Yr|Xr) and the rate obtained by DF hence coincides with the cut-set bound.

Side Information Encoding

DF relaying requires that the relay decodes the received signal and it therefore re-sults in a performance degradation when the source-relay link is not strong enough.In a situation when decoding is not possible, the relay can transmit an estimate ofthe received signal (Yr) and the destination can perform decoding with the sideinformationY . One can show that the rate [2]

R = supp(x)p(xr)p(yr|xr,y)

I(X ;Y, Yr|Xr)

subject toI(Yr; Yr|Xr, Y ) < I(Xr;Y ) (3)

is achievable. If the relay-destination link supports highdata rate transmission(i.e., I(Xr;Y ) is very large), the destination can recoverYr with low distortionand the rate obtained by this scheme hence approaches the broadcast bound on thecapacity. This scheme is also known as compress-and-forward (CF) [19].

4 Frequency-Division Gaussian Relay Channel

Figure 3 illustrates a Gaussian relay channel with orthogonal receive components[20]. This model is motivated by practical limitations in the radio hardware wherethe relay cannot transmit and receive simultaneously. One solution is that the relayreceives and transmits in different frequency bands. This makes the source-relayand the relay-destination links orthogonal to each other. The received signal at therelay is given by

yr = ax+ zr (4)

wherea is the channel gain between the source and the relay, andzr ∼ N (0, 1)is the additive white Gaussian noise with unit variance. Thereceived signals atdestination are given by

y1 = x+ z1

y2 = bxr + z2

6 INTRODUCTION

+

+

+

Xn

Zn1

Zn2Znr

a

b

Y n1

Y n2Xnr = f(Y nr )

Figure 3: Block diagram of the relay channel with orthogonal receive compo-nent

whereb is the channel gain between the relay and the destination,zr ∼ N (0, 1)and z2 ∼ N (0, 1). We assume thatzr, z1, andz2 are mutually independent.The source and the relay are operating under average power constraints. That isE[X2]≤ Ps andE

[X2r

]≤ Pr.

4.1 Upper bound on the capacity

Using the cut-set bound given by (5), the following upper bound on the capacitycan be obtained [20]

C ≤ min

{1

2log(1 + (a2 + 1)Ps),

1

2log(1 + Ps) +

1

2log(1 + b2Pr)

}

. (5)

which is calculated by choosing independent Gaussian alphabets at the source andat the relay (i.e.,X ∼ N(0, Ps) andXr ∼ N(0, Pr)).

4.2 Achievable rate of DF

Since the transmitted signals from the source and the relay do not interfere at thedestination, we modify the achievable rate obtained by DF given in (2) as

RDF = max

{

supp(x)

I(X ;Y1), supp(x,xr)

min {I(X,Xr;Y1, Y2), I(X ;Yr|Xr)}}

.

(6)

4 FREQUENCY-DIVISION GAUSSIAN RELAY CHANNEL 7

It turns out the optimal choice ofp(x, xr) to maximize (6) isp(x)p(xr) whereX ∼ N(0, Ps) andXr ∼ N(0, Pr). This therefore yields [20]

R = max

{

1

2log(1 + Ps),min

{1

2log(1 + a2Ps),

1

2log(1 + Ps) +

1

2log(1 + b2Pr)

}}

. (7)

Therefore, DF achieves the capacity ifa ≥√

1 + b2(Pr + Pr

Ps).

4.3 Achievable rate of CF

To evaluate the achievable rate using CF, one needs to find theoptimal choiceof p(x)p(xr)p(yr|xr, y) which is a difficult task. However, the achievable rateby employing Gaussian codebook at the source and the relay inconjunction withGaussian quantization can be calculated in closed form. That is X ∼ N(0, Ps),Xr ∼ N(0, Pr), Yr = Y +Nq whereX ,Xr, andNq are mutually independent andNq are chosen to meet the constraintI(Yr; Yr|Xr, Y ) < I(Xr;Y ). This yields thefollowing achievable rate [20]

RCF =1

2log

(

1 + Ps +a2b2PrPs(Ps + 1)

1 + (1 + a2)Ps + b2Pr(1 + Ps)

)

. (8)

From (8), it is clear thatRCF is always greater then the capacity of the direct trans-mission. Note that with CF the relay needs to know the qualityof side information,that is the source-destination channel gain. Finally, we note that

lima→∞

RCF =1

2log(1 + Ps + b2Pr(Ps + 1)

)

limb→∞

RCF =1

2log(1 + Ps + a2Ps)

).

In another words, CF asymptotically achieves the multiple access and broadcastbounds asa→ ∞ andb→ ∞ respectively.

4.4 Achievable rate of linear relaying

With linear relaying [20–23], the relay’s output is a linearcombination of the re-ceived signals at the relay. One of the simplest forms of linear relaying is instan-taneous linear relaying in which the relay transmits an amplified version of thereceived signal, that is

xr =

√

PrE [y2

r ]yr. (9)

8 INTRODUCTION

This scheme is also known as amplify-and-forward (AF). The achievable rate canbe calculated as

RAF =1

2log

(

1 + Ps +a2b2PrPs

1 + a2Ps + b2Pr

)

. (10)

From (10), it is seen thatRAF is always greater than the capacity of the direct linkand it achieves the broadcast bound asb → ∞. By comparing (8) and (10), onecan see thatRCF > RAF .3

5 Slow-Fading Relay Channel

We next consider the relay channel when the channel gains (for examplea andbin Figure 3) are random variables but they stay constant during the transmissionof one block. That is the channels are quasi-static. For thistype of channelsthe classical Shannon capacity [24] might be zero. For example, this is so whenthe channel gains are Rayleigh distributed. Thus other measures such as outageprobability are usually used [25]. The outage probability shows how often thedestination can successfully decode a packet transmitted with a fixed rateβ bitsper channel use and it is defined as

Pout = Pr{R < β} (11)

whereR is the achievable rate obtained by a given scheme.

6 Resource Allocation for Time-Division RelayChannels

When the relay and the source are restricted to use the same frequency bands,due to the practical limitations, the relay cannot transmitand receive simultane-ously. As a remedy, many researchers have assumed a time-division half-duplexmode in which the reception and the transmission occur in non-overlapping times-lots [15, 19, 26, 27]. Note that this is slightly different from the frequency-divisionrelay channel discussed in Section 4. The relay therefore uses a fraction of theavailable timeslot for the listening and the remaining partfor the transmission.Hence, one can optimize the length of the timeslot4 used for listening and fortransmission as well as the conventional power allocation.The works [28–30]consider variable rates transmission protocols for the slowly fading relay chan-nel. The work of [29, 30] formulate criteria for joint power-bandwidth allocation.The former investigates outage probability while the latter studies delay-limited

3There are however some cases such as the full-duplex non-orthogonal relay channel where AF canimprove on CF with Gaussian quantization [20].

4This is also known as bandwidth or dimension allocation as well.

7 CONTRIBUTIONS OF THETHESIS 9

capacity. The work of [31–33] study resource allocation fortheergodicGaussianrelay channel. There is some other related work that only considers optimal powerallocation for the relay channel [34–36].

7 Contributions of the Thesis

The thesis investigates different transmission protocolsfor the slow fading relaychannel. The contributions of the thesis can be divided in two major groups:

• the study of uncoded transmission under a modulation constraint, in whichwe study optimal receivers and mapping optimization at the nodes; and

• the study of coded transmission with an emphasis on DF relaying.

Short summaries of the papers are given in the following:

Paper A: Improving Collaborative Transmit Diversity by Usi ng ConstellationRearrangement

Published at theIEEE Wireless Communications and Networking Conference(WCNC), 2007.

We propose an enhancement to cooperative transmit diversity based onuncoded detect-and-forward, by using so-called constellation rearrangement(CR) [37–40] at the relay. With CR, the relay uses a bit-symbol mapping thatis different from the one used by the source. We find the optimal bit-symbol map-pings for both the source and the relay and the associated optimal detectors, andshow that the improvement over conventional relaying with Gray mapping at thesource and the relay can amount to a power gain of several dB. This performanceimprovement comes at no additional power or bandwidth expense, and at virtuallyno increase in complexity.

Paper B: Receiver Design for Wireless Relay Channels with Regenerative Re-lays

Published at theIEEE International Conference on Communications (ICC),2007.We develop a general framework for design of receivers for the wireless relay

channel. We derive the optimum detectors for various degrees of channel stateinformation (CSI) at the destination. We consider both the case when the destina-tion has access to full knowledge of the CSI and the case when it only knows thestatistics of the channel. High-SNR and low-SNR approximations of the detectorsare presented as well.

10 INTRODUCTION

Paper C: Cooperative Transmission Based on DF Relaying withPartial Rep-etition Coding

To appear in theIEEE Transactions on Wireless Communications, 2008.We propose a novel half-duplex decode-and-forward relaying scheme based

on partial repetition coding at the relay. In the proposed scheme, if the relaydecodes the received message successfully, it re-encodes the message using thesame channel code as the one used at the source, but retransmits only a fractionof the codeword. We analyze the proposed scheme and optimizethe cooperationlevel (i.e., the fraction of the message that the relay should transmit). We com-pare our scheme with conventional repetition in which the relay retransmits theentire decoded message, and with parallel coding, and additionally with dynamicdecode-and-forward (DDF). We provide a finite SNR analysis for all the collabo-rative schemes. The analysis reveals that the proposed partial repetition can pro-vide a gain of several dB over conventional repetition. Surprisingly, the proposedscheme is able to achieve the same performance as that of parallel coding for somerelay network configurations, but at a much lower complexity.

Paper D: Analytical Results on Block Length Optimization for Decode-and-Forward Relaying with CSI Feedback

Published at theIEEE Workshop on Signal Processing Advances in Wireless Com-munications (SPAWC), 2007.

We consider block length optimization for collaborative transmit diversity us-ing a decode-and-forward protocol assuming that the sourceand the relay haveaccess to the magnitudes of all path gains. Moreover, we propose a simple schemewhich requires only one bit of channel state information (CSI) feedback. We an-alyze the outage probabilities of all schemes for both selection combining andmaximum ratio combining (MRC) at the destination. Analytical results show thateven one bit of CSI feedback can provide a significant gain over conventional(non-adaptive) collaborative schemes.

Paper E: A Spectrally Efficient Transmission Scheme for Half-Duplex DF Re-laying

Published at theIEEE Global Telecommunications Conference (GLOBECOM),2007.

We propose a spectrally efficient transmission scheme for the half-duplex relaychannel. In the proposed scheme, the relay combinesN detectedr-dimensionalsymbols and generatesM new r-dimensional symbols, whereM < N , using alinear transformation. The proposed linear transformation preserves the signal en-ergy, and it facilitates decoupled symbol detection at the receiver. We also presentan optimized design for the case of complex scalar modulation (r = 2) withN = 2andM = 1. This design increases the spectral efficiency by 33% compared toconventional decode- or amplify-and-forward relaying.

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