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Variable-Rate Two-Phase Collaborative Communication

Protocols for Wireless Networks

Hideki Ochiai

Department of Electrical and Computer Engineering, Yokohama National University

79-5 Tokiwadai, Hodogaya-ku, Yokohama, Japan 240-8501

Patrick Mitran and Vahid Tarokh

Division of Engineering and Applied Sciences, Harvard University

33 Oxford Street, Cambridge, MA 02138

Abstract

The performance of two-phase collaborative communication protocols is studied for wireless

networks. All the communication nodes in the cluster are assumed to share the same channel and transmit

or receive collaboratively in a quasi-static Rayleigh flat-fading environment. In addition to small-scale

fading, the effect of large-scale path loss is also considered. Based on a decode-and-forward approach, we

consider various variable-rate two-phase protocols that can achieve full diversity order and analyze the

effect of node geometry on their performance in terms of the outage probability of mutual information.

For the single relay node case, it is shown that if the collaborator node is close to the source node, a

protocol based on space-time coding (STC) can achieve good diversity gain. Otherwise, a protocol based

on receiver diversity performs better. These protocols are also compared with one based on fixed-rate

repetition coding and their performance trade-offs with node geometry are studied. The second part deals

with multiple relays. It is known that with N relays an asymptotic diversity order of N +1 is achievable

with STC-based protocols in the two-phase framework. However, in the framework of collaborative STC,

those relay nodes which fail to decode remain silent (this event is referred to as a node erasure). We

show that this node erasure has the potential to considerably reduce the diversity order and point out the

importance of designing the STC to be robust against such node erasure.

Index Terms

Collaborative (cooperative) communication, relay channel, space-time coding, spatial diversity,

wireless networks.

The material of this paper was in part presented at IEEE Fall Vehicular Technology Conference, Los

Angels, CA, September 2004. This work was in part supported by the Telecommunications Advancement

Foundation (TAF).

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I. INTRODUCTION

In many wireless networks, the power consumption of communication nodes is a critical issue. In

addition, typical wireless channels suffer from signal fading which, for a given average transmit power,

significantly reduces communication capacity and range. If the channel is slow and flat fading, channel

coding does not help [1,2] and spatial diversity may be the only effective option that can either reduce

the average transmit power or increase communication range. Results on space-time coding (STC) [3,

4] have shown that the use of antenna arrays at the transmitter and receiver can significantly reduce

transmit energy. However, for many applications with low-cost devices such as wireless sensor networks,

deployment of multiple antennas at each node is too costly to implement due to severe constraints on

both the size and power consumption of analog devices.

The recently proposed collaborative (or cooperative) diversity approaches [5–14] demonstrate the

potential to achieve diversity or enhance the capacity of wireless systems without deploying multiple

antennas at the transmitter. Using nearby collaborators as virtual antennas, significant diversity gains can

be achieved. These schemes basically require that the relay nodes share the information data of the source

node, and this data sharing process is generally achieved at the cost of additional orthogonal channels (in

frequency or in time). In a companion paper [15], we have shown that for a given fixed rate and under

suitable node geometry conditions, there are collaborative coding schemes that can nearly achieve the

same diversity as if all the relay node antennas were connected to the source node, without any additional

orthogonal channels or bandwidth. The construction of such codes, however, appears to be challenging.

Among many approaches in the literature, Laneman [5,6] analyzes several low-complexity relaying

protocols that can achieve full diversity, under realistic assumptions such as half-duplex constraint and

no channel state information (CSI) at the transmitting nodes. It has been shown that in the low-spectral-

efficiency regime, the SNR loss relative to ideal transmit diversity system with the same information

rate is 1.5dB[5]. Multiple-relay cases are also considered in [6] and bandwidth-efficient STC-based

collaborative protocols are proposed.

Collaborative diversity protocols are largely classified into amplify-and-forward and decode-and-

forward schemes [5]. In the following, we will restrict our attention to decode-and-forward schemes

since these may provide some salient advantages. First, there is no error propagation if the relay transmits

information only when it decodes correctly. Otherwise, the relay remains silent and thus an unnecessary

energy transmission can be saved1. Second, the information rate per symbol does not need to be the same

for each phase. In other words, the relative duration of each phase can be changed according to node

geometry.

1Even though perfect detection of the codeword is not feasible in practice, one can design a cyclic redundancy-check (CRC)

or error detectable low-density parity-check (LDPC) code such that for a given system outage probability, the effect of error

propagation is negligible. Many existing communication networks have this structure.

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R∗

T

T1

T2

R1

R2

(a)

(b)

phase-I phase-II

Fig. 1. Two-phase communication. (a) baseline system. (b) two-phase protocol.

It is the latter property that we shall focus on in this work. Suppose that we wish to transmit data with

information rate R∗bits per second and T is the frame period, also in seconds. Then the total information

transmitted during this period is R∗T bits (per frame). The baseline frame design that achieves this is

shown in Fig.1 (a). Alternatively, we may split the time interval into two phases of duration T1 and

T2where T = T1+ T2and each phase is operated with information rate R1and R2, respectively, as

depicted in Fig.1 (b). We assume that for both phases, the same information (but with different coding

rate) is transmitted. If R1and R2are chosen such that R1T1= R2T2= R∗T, then in principle there

is no loss of total transmission rate compared to the baseline system. Let the fraction of the relative

time period for each phase be denoted by δ1? T1/T = T1/(T1+ T2), and δ2? T2/T = 1 − δ1. Then,

the information rate during each phase is R1= R∗/δ1and R2= R∗/δ2. Therefore, during each phase,

information should be transmitted employing larger constellation sizes than the baseline system2.

For ideal AWGN and interleaved fading channels under an average signal-to-noise power ratio (SNR)

constraint over the entire communication process, two-phase protocols do not necessarily achieve a gain

and may even result in performance loss compared to the baseline system. However, for quasi-static or

block Rayleigh fading channels, it is not the constellation size but diversity that is the dominant factor

for the outage behavior. Thus, if additional diversity can be achieved by two-phase methods, the resulting

outage probability of the mutual information may more than offset any loss due to constellation size and

yield a reduction in required SNR. (This is somewhat analogous to coded modulation which increases the

signal constellation size in order to achieve coding gain. In our case, however, we shall achieve diversity

gain.)

In practical collaborative wireless communication networks, node geometry is an important factor.

Intuitively, if the collaborative relay node is close to the source node, it may be efficient for the relay

2The fraction δ1 and δ2, or equivalently, the coding rate R1 and R2 are determined based on the node location, not on each

realization of fading channel coefficient as done in [15,16].

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to act as a transmit antenna. In this case, STC based protocols such as [6] may be efficient. On the

other hand, if the relay is close to the destination, it should operate as a receive antenna. To capture

this geometrical effect, we model the wireless network channel as an aggregate of large-scale path-loss

and small-scale fading [17]. The large-scale path-loss is the decay of signal power due to the transmitter

receiver separation, and is a function of the distance between the two terminals. On the other hand, the

small-scale fading is a consequence of multipath which may vary randomly according to any physical

change of surroundings. The overall system model is detailed in Section II.

In this paper, motivated by the rate-flexible nature of decode-and-forward protocols and the importance

of node geometry, we extend the work of Laneman [5,6] to a variable-rate framework with particular em-

phasis on path-loss gain effect of relay nodes, achieved due to the relay’s proximity to source/destination

nodes. Several low-complexity protocols are considered, including a simple multi-hopping protocol, the

bandwidth-efficient STC-based protocol of [6], as well as its receiver diversity counterpart (SectionIII).

Their performances with a single relay node are theoretically analyzed in terms of achievable diversity

gain for a given information rate based on outage probability of mutual information. For this purpose,

convenient simple analytical tools are developed in Section IV.

The main objective of the paper is, for a given relative location of the relay node, to determine a suitable

protocol and minimize the total required power of the transmitting nodes. To that end, optimal power

control factors and relative phase durations for the relay node are derived for each protocol considered.

Associated with these protocols, closed-form expressions for diversity gain are derived in SectionV, where

it is shown that by suitably choosing the protocol and controlling the transmission rate, as a function

of node geometry, the achievable diversity gain can be significantly improved. Also, it will be shown

that under severe path-loss, even a simple multi-hop protocol benefits relative to direct transmission. For

example, a significant gain is attained if the relay is located midway between the two communicating

nodes.

In the analysis of STC-based collaborative protocols, we presume two types of STC which we denote

as perfect and imperfect STC. A perfect STC refers to an STC with partial decodability, i.e., the (full)

information can be retrieved from a subset of the transmitting nodes, whereas an imperfect STC refers to

a system in which the receiving nodes fail to decode if any one of the transmitting nodes that constitute

the STC fails to transmit. This partial erasure of an STC antenna branch may happen if the relay nodes

fail to decode correctly. (This event will be referred to as a node erasure.) In SectionVI, we show that

the diversity order of an imperfect STC with N collaborative relays is at most 2, whereas that of a perfect

STC can achieve diversity order of N + 1 as in [6].

Throughout this paper, our main focus is on the achievable diversity gain for a given information rate.

The diversity-multiplexing trade-off [18] of the relay channels is also of practical importance, but this is

beyond the scope of this paper. Some results in this direction are explored in [5,6,16]. As related work,

the effect of node geometry is also considered in [12,19,20], but in a fixed-rate framework. Also, we do

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S

D

R

θ

HS,R

HR,D

HS,D

dS,R

dR,D

dS,D

GS

GD

Fig. 2. Two-phase communication.

not address specific design issue of coding as many existing channel/STC techniques in the literature are

applicable to our framework without major modification. Note that some practical design of collaborative

codes (with implicit variable-rate coding) is proposed in [21] and its outage behavior is evaluated in [13].

The use of incremental redundancy such as [22] may be of further potential in this framework. Finally,

we note that variable-rate coding for multiple-access channels has been recently studied in [23].

II. SYSTEM AND CHANNEL MODEL

Fig.2 illustrates the basic model which is considered throughout the paper. It is assumed that the three

nodes source(S), relay(R), and destination(D) are located in the two dimensional plane as in Fig.2 where

θ is the angle of the line S − R − D and dA,Bdenotes the Euclidean distance between nodes A and B.

We suppose that S wishes to transmit the message to D and that R has agreed to collaborate with S a

priori.

For simplicity, we assume that all the channel links are composed of large-scale path loss and

statistically independent small-scale quasi-static frequency non-selective Rayleigh fading. Consequently,

the complex channel coefficients HS,D, HS,R, and HR,D in Fig.2 are uncorrelated and circularly

symmetric complex Gaussian random variables with zero mean and unit variance. They are assumed

to be known perfectly to the receiver sides and unknown at the transmitter sides. Perfect timing and

frequency synchronization are also assumed, even though accurate acquisition of synchronization among

distributed nodes may be challenging in practice.

The path loss between two nodes, say A and B, is modeled by

PL(A,B) = K/dα

A,B,

(1)

where K is a constant that depends on the environment and α is the path-loss exponent. For free-space

path loss, we have α = 2 and K = GtGrλ2/(4π)2, where Gtand Grare antenna gains at transmitter

and receiver, respectively, and λ is the wavelength [17]. Although the path-loss exponent and the constant

factor K may vary for each channel link, throughout the paper it is assumed that α and K are identical

for all channel links.

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