An Efficient Adaptive Distributed Space-Time Coding Scheme for Cooperative Relaying

Abstract

A non-regenerative dual-hop wireless system based on a distributed space-time coding strategy is considered. It is assumed that each relay retransmits an appropriately scaled space-time coded version of its received signal. The main goal of this paper is to investigate a power allocation strategy in relay stations, which is based on minimizing the outage probability. In the high signal-to-noise ratio regime for the relay-destination link, it is shown that a threshold-based power allocation scheme (i.e., the relay remains silent if its channel gain with the source is less than a prespecified threshold) is optimum. Monte-Carlo simulations show that the derived on-off power allocation scheme performs close to optimum for finite signal-to-noise ratio values. Numerical results demonstrate a dramatic improvement in system performance as compared to the case that the relay stations forward their received signals with full power. In addition, a hybrid amplify-and-forward/detect-and-forward scheme is proposed for the case that the quality of the source-relay link is good. Finally, the robustness of the proposed scheme in the presence of channel estimation errors is numerically evaluated. Comment: submitted to IEEE Transactions on Wireless Communications (24 pages)

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arXiv:0812.1203v2 [cs.IT] 8 Dec 2008
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An Efficient Adaptive Distributed Space-Time
Coding Scheme for Cooperative Relaying
Jamshid Abouei, Hossien Bagheri, and Amir K. Khandani
Coding and Signal Transmission Laboratory (www.cst.uwaterloo.ca)
Department of Electrical and Computer Engineering, University of Waterloo
Waterloo, Ontario, Canada, N2L 3G1
Tel: 519-884-8552, Fax: 519-888-4338
Emails: {jabouei, hbagheri, khandani}@cst.uwaterloo.ca
Abstract
A non-regenerative dual-hop wireless system based on a distributed space-time coding strategy is
considered. It is assumed that each relay retransmits an appropriately scaled space-time coded version
of its received signal. The main goal of this paper is to investigate a power allocation strategy in relay
stations, which is based on minimizing the outage probability. In the high signal-to-noise ratio regime
for the relay-destination link, it is shown that a threshold-based power allocation scheme (i.e., the relay
remains silent if its channel gain with the source is less than a prespecified threshold) is optimum. Monte-
Carlo simulations show that the derived on-off power allocation scheme performs close to optimum for
finite signal-to-noise ratio values. Numerical results demonstrate a dramatic improvement in system
performance as compared to the case that the relay stations forward their received signals with full
power. In addition, a hybrid amplify-and-forward/detect-and-forward scheme is proposed for the case
that the quality of the source-relay link is good. Finally, the robustness of the proposed scheme in the
presence of channel estimation errors is numerically evaluated.
∗This work is financially supported by Nortel Networks and the corresponding matching funds by the Natural Sciences and
Engineering Research Council of Canada (NSERC), and Ontario Centers of Excellence (OCE).
∗The material in this paper was presented in part at the 42nd Conference on IEEE Information Sciences and Systems (CISS),
Princeton University, Princeton, NJ, March 19-21, 2008 [1].

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Index Terms
Cooperative relaying, space-time coding, outage probability, multi-hop wireless networks.
I. INTRODUCTION
A primary challenge in wireless networks is to mitigate the effect of the multipath fading.
Exploiting techniques such as time, frequency and space diversity are the most effective methods
to combat the channel fading. Due to the dramatic reduction in the size of wireless devices
along with the power and the cost limitations, it is not practical to install multiple antennas on
mobile stations. A heuristic solution to this problem is to use a collection of distributed antennas
belonging to multiple users [2]–[4]. This new diversity scheme, referred to as cooperative
diversity (also known as cooperative relaying), has attracted considerable attention in ad hoc
and sensor wireless networks in recent years. In particular, this approach is considered as an
option in many wireless systems; including IEEE 802.16j mobile multihop relay-based (MMR)
networks. Unlike conventional relaying systems that forward the received signal in a relay chain,
cooperative relaying takes one step further; i.e., multiple relay nodes work together to achieve
a better performance.
Cooperative relay networks have been addressed from different perspectives; including capacity
and outage probability analysis [2]–[7], resource allocation (e.g., power allocation [8]), coding
[9], relay selection [4], [10], etc. Central to the study of cooperative relay systems is the problem
of using distributed space-time coding (DSTC) technique as well as efficient power allocation
schemes in regenerative and non-regenerative configurations [5], [11]–[18].
The first study on using DSTC scheme in cooperative relay networks was framed in [5] where
several relay nodes transmit jointly to the same receiver in order to achieve full spatial diversity
in terms of the number of cooperating nodes. Reference [5] analyzes the outage capacity in the
high signal-to-noise ratio (SNR) regime. Nabar et al. [11] analyze the pairwise error probability
of an amplify-and-forward (AF) single-relay system which relies on a DSTC scheme. In [12],
the authors investigate the high SNR uncoded bit-error rate (BER) of a two-relay system using

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a switching scheme for QPSK modulation. Scutari and Barbarossa [14] analyze the performance
of regenerative relay networks with DSTC where the error on the source-relay link propagates
into the second phase of the transmission in the relay-destination link. They show how to
allocate the transmission power between source and relay to minimize the average BER. The
BER of single and dual-hop non-regenerative relay systems with DSTC has been analyzed in
[15] where different transmission policies are investigated in order to maximize the end-to-end
SNR. The BER of regenerative relay networks using the DSTC scheme, along with different
power allocation strategies over non-identical Ricean channels is analyzed in [17]. Zhao et al.
[8] introduce two power allocation algorithms for AF relay networks to minimize the outage
probability without the DSTC scheme.
In this paper, we consider a dual-hop wireless system consisting of a source, two parallel relay
stations (RS) and a destination. Assuming that each relay knows its channel with the source,
the RSs collaborate with each other by transmitting a space-time coded (STC) version of their
received signals to the destination. In such configuration, if the instantaneous received SNR of
the relays are unbalanced, the performance of the system degrades substantially. To overcome
this problem, an adaptive distributed space-time coding (ADSTC) method is proposed, in which
instead of transmitting the noisy signal at each relay with full power, the RS retransmits an
appropriately scaled STC version of the received signal. The main goal is to optimize the scaling
factor based on the channel-state information (CSI) available at each relay to minimize the outage
probability.
The above scheme is different from the power allocation algorithms studied in [8]; primarily
we utilize an ADSTC scheme based on the CSI available at each relay, while in [8], no DSTC
scheme is used. In our scheme, no information is exchanged between the relay stations. This
is to be contrasted with the algorithms proposed in [15], in which the relays need to exchange
some information with each other in order to establish which relay transmits. In addition, our
scheme is different from the power allocation strategies in [19]–[21], in which the best relays

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are selected based on the feedback from the destination.
In the high SNR regime for the relay-destination link, it is shown that a threshold-based
power allocation scheme (i.e., the relay remains silent if its channel gain with the source is
less than a prespecified threshold) is optimum. Numerical results indicate that the derived on-
off power allocation scheme provides a significant performance improvement as compared to
the case that the RSs forward their received signals with full power all the time. To further
improve the system performance when the quality of the source-relay link is good, a hybrid
amplify-and-forward/detect-and-forward scheme is proposed.
In the proposed scheme, we assume that perfect channel knowledge is available at the receiver.
In practice, however, the performance of the system is degraded due to the channel estimation
error. In the last part of this paper, we address this issue and evaluate the robustness of the
proposed scheme in the presence of channel estimation errors.
The rest of the paper is organized as follows. In Section II, the system model and objectives
are described. The performance of the system is analyzed in Section III. In Section IV, the
simulation results are presented. The effect of channel estimation errors on the proposed scheme
is evaluated in Section V. Finally, conclusions are drawn in Section VI.
Notations: Throughout the paper, we use boldface capital and lower case letters to denote
vectors and matrices, respectively. ? a ? indicates the Euclidean norm of the vector a. The
conjugate and conjugated transposition of a complex matrix A are denoted by A∗and A†,
respectively. The n × n identity matrix is denoted by In. A circularly symmetric complex
Gaussian random variable (r.v.) is represented by Z = X + jY ∼ CN(0,σ2), where X and
Y are independent and identically distributed (i.i.d.) normal r.v.’s with N(0,σ2
represents the link from node A to node B. Finally, P{.} and E[.] denote the probability of the
given event and the expectation operator, respectively.
2). Also, A → B

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II. SYSTEM MODEL AND OBJECTIVES
In this work, we consider a cooperative relay system consisting of one base station (BS),
multiple relay stations randomly located within the network region, and multiple mobile stations
(MSs) (Fig. 1-a). All the nodes are assumed to have a single antenna. The relay stations are
assumed to be non-regenerative, i.e., they perform some simple operations on the received signals
and forward them to the MSs [15]. Also, it is assumed that no information is exchanged between
the relays. In this set-up, each pair of the relay stations cooperate with each other to forward
their received signals from the source to the destination1(Fig. 1-b).
The channel model is assumed to be frequency-flat block Rayleigh fading with the path loss
effect. Let us denote the channel coefficients of the links S → RSiand RSi→ D as Lsriand
Lrid, i = 1,2, respectively. In this case, the channel gain between S and RSiis represented by
gsri? |Lsri|2= Γsri|hsri|2, where Γsri? 10−Υsri/10is the gain associated with the path loss
Υsri[dB], and the complex random variable hsriis the fading channel coefficient. Similarly,
the channel gain of the link RSi → D is represented by grid ? |Lrid|2= Γrid|hrid|2, where
Γrid? 10−Υrid/10and hridare the gain associated with the path loss Υrid[dB] and the channel
fading coefficient, respectively. Under the Rayleigh fading channel model, |hsri|2and |hrid|2are
exponentially distributed with unit mean (and unit variance). Also, the background noise at each
receiver is assumed to be additive white Gaussian noise (AWGN). For this model, communication
between S and D is performed based on the following steps: i) Data Transmission: This is
performed in two phases and through two hops. In the first phase, the source broadcasts the
symbols x[1] and x[2] (normalized to have unit energy) to the RSs in two consecutive time slots
and over one frequency band. The received discrete-time baseband signal at RSiis given by
ui[k] =
?
PsLsrix[k] + nri[k], i = 1,2,
(1)
where k = 1,2, represents the transmission time index, Psis the transmit power of the source
1In the sequel and for the sake of simplicity of notations, the BS and the MS are denoted by the source (S) and the destination
(D), respectively.