Performance Analysis of Two-Hop OSTBC Transmission over Rayleigh Fading Channels

Hindawi Publishing Corporation EURASIP Journal on Wireless Communications and Networking Volume 2010, Article ID 649541, 8 pages doi:10.1155/2010/649541 Research Article Performance Analysis of Two-Hop OSTBC Transmission over Rayleigh Fading Channels Guangping Li,1 Steven D. Blostein,2 and Jiayin Qin3 1 Faculty of Information Engineering, Guangdong University of Technology, Guangzhou 510006, China 2 Department of Electrical and Computer Engineering, Queen’s University, Kingston, ON, Canada K7L 3N6 3 Department of Electronic and Communications Engineering, Sun Yat-sen University, Guangzhou 510275, China Correspondence should be addressed to Steven D. Blostein, Received 19 March 2010; Revised 5 July 2010; Accepted 26 September 2010 Academic Editor: A. B. Gershman Copyright © 2010 Guangping Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. A two-hop amplify and forward (AF) relay system is considered where source and destination are each equipped with multiple antennas while the relay has a single antenna. Orthogonal space-time block coding (OSTBC) is employed at the source. New exact expressions for outage probability in Rayleigh fading as well as symbol error rate (SER) expressions for a variety of modulation schemes are derived. The diversity order of the system is evaluated. Monte Carlo simulations demonstrate the accuracy of the analyses presented. Results that can be extended to relay systems with a direct source-destination link are also highlighted. To put the results in context, the two-hop system performance is then compared to that of a MIMO point-to-point system. Finally, the new analysis is applied to evaluate two-hop system performance as a function of relay location. 1. Introduction Through exploiting spatial diversity, it is well known that MIMO technology can improve the reliability of wireless communication links [1]. Orthogonal space-time block coding (OSTBC) is a key component of MIMO systems that has attracted tremendous attention. First, OSTBC does not require complicated feedback links to provide channel state information at the transmitter (CSIT). Second, OSTBC methods enable maximum likelihood detection to be performed with low computational complexity [2]. As a result of its practicality, OSTBC has been incorporated into emerging MIMO standards [3]. While MIMO systems offer significant physical layer performance enhancements, a significant problem in initial wireless network deployments is obtaining adequate coverage. The concept of relaying signals through intermediate nodes has been shown to be effective at extending the coverage of networks in a power-efficient manner. In addition, very simple relaying systems have been shown to increase diversity through node collaboration. As a result, the provision for relaying has recently been adopted into recent standards [4]. This paper investigates the effect of simple relaying on MIMO system performance. Previously, end-to-end performance of two-hop relay systems was studied in [5–7], including outage probability and average bit error rate (BER) in a variety of fading environments. However, in [5–7] all assume a single antenna at both source and destination. Recently, a two-hop amplify and forward (AF) relay system in which the source and destination are both equipped with multiple antennas while the relay has a single antenna appears in [8, 9]. In [8], an OSTBC strategy is employed at the source, and end-toend average bit error rate (BER) was investigated. However, the method in [8] is only suitable for systems with the same numbers of antennas at the source and destination. Moreover, an exact expression for outage probability was not given, and the diversity order of the system was not evaluated analytically. In [10], system performance including outage probability and average SER is determined for the special case of multiple antennas at the source and a single antenna at the destination. Although the method used in [10] has been often used in the literature, it cannot be easily generalized to the case of multiple antennas at the destination. 2 EURASIP Journal on Wireless Communications and Networking Relay . .. . .. Source Destination Figure 1: Two-hop relay system model. In this paper, the same system model is assumed as in [8, 9]. First, exact expressions for system outage probability with both exact and ideal relay gain are derived for arbitrary antenna configurations at the source and destination. Exact average SER expressions for different modulation schemes are then derived by calculating the probability density function (PDF) and moment generation method (MGF). Generalizations of results to systems that include a direct link are also briefly indicated where applicable. The diversity order of the system is also evaluated. Monte Carlo simulations confirm the analytical results, compare performance between the proposed relaying system and a MIMO point-to-point system as well as evaluate the two-hop system performance as a function of relay location. where hTRD denotes the ND × 1 Rayleigh fading channel gain ij vector from the relay to the destination, ED = {nD }ND ×T is the ND × T i.i.d noise matrix at the destination where ij nD ∼ CN (0, σD2 ) denotes the noise at the ith receive antenna during the jth symbol period, and xR = GyR denotes the 1 × T signal vector sent by the relay where G is a relay gain. As categorized in the literature, relay gains may be fixed or variable. In this paper, variable relay gain is considered. Relay gains  can be further classified as exact or ideal. We denote G = PR /(PS hSR 2 /NS ) + σR2 as the exact relay gain, where PS and PR are average power constraints at the source and relay, respectively. If we ignore the noise at the relay,  G = PR /(PS hSR 2 /NS ) which is denoted as the ideal relay gain [5] and is amenable to mathematical manipulation. As in most of the literature, the ideal relay gain is used to compute exact average SERs of the proposed system in this paper. Later, it will be observed from simulations that the ideal relay gain provides a tight lower bound on outage probability and average SER in the case of medium-to-high SNR. Substituting xR = GyR into (2) leads to the received signal at the destination given by YD = hTRD GhSR XS + hTRD GnR + ED . (3) Using maximum likelihood (ML) detection of OSTBCs for the case of spatially colored noise given in [11], the received SNR is obtained as follows. Theorem 1. Using the exact relay gain, the received SNR of two-hop AF OSTBC transmission is given by 2. System Model A two-hop relay system is considered where there are NS antennas at the source, ND antennas at the destination, and a single antenna at the relay, as shown in Figure 1. To make the relay as simple as possible, an AF relaying protocol is employed. It is (...truncated)