Performance Evaluation of Alamouti STC through Amplify-Forward Cooperative Relay Network over Nakagami-m Fading Channels Saman Atapattu ∗ and Nandana Rajatheva † Telecommunications FoS, SET, Asian Institute of Technology P. O. Box 4, Klong Luang 12120, Thailand satapattu@ieee.org ∗ , rajath @ait.ac.th † Abstract The performance of a cooperative communication wire- less network with a single relay system is studied over Nakagami-m fading channels. The simplest Alamouti space-time block code is transmitted through an amplify- and-forward (AF) relay terminal in a two-hop network. The exact symbol error rates (SER) are analyzed using the mo- ment generating function (MGF) of the total signal to noise ratio (SNR) for a particular signal in the case of M-ary phase shift keying (M -PSK) modulation schemes. Subse- quently, numerical and simulation results are provided to verify the accuracy of the formulation. 1 Introduction In wireless networks, signal fading arising from multi- path propagation is a particularly severe channel impair- ment and transmit diversity is a powerful technique for mit- igating it. The concept of resource allocation strategy with cooperation among users is introduced due to the limitations of radio resources such as bandwidth and power. As a result of these, new forms of spatial diversity schemes have been proposed, whereby diversity gains are achieved via cooper- ation among in-cell users. Such a wireless scenario can be thought of as a virtual antenna array which is referred to as user cooperation diversity [1], [2]. The coded cooperation strategies with specific code structure such as rate-compatible punctured convolutional codes and turbo codes are investigated in [3]. Coopera- tion with space-time coding (STC) is an interesting concept, in order to create a virtual transmit array in a distributed multiple-relay/mobile network. Therefore, STCs are used as a powerful tool of designing cooperative protocols in or- der to maximize the diversity advantage in a fading environ- ment. This concept, known as distributed space-time codes (DSTC), has been analyzed in several recent works, [4], [5] and [6]. The Alamouti code [7], which provides some desir- able properties such as simple decoding and maximum di- versity in a general MIMO system, is employed in [6] with a distributed implementation in a cooperative relay network over Rayleigh fading environment. Cooperation diversity schemes are mainly categorized as either amplify-and- forward (AF) or decode-and-forward (DF) depending on the relay functionality. Among these two, the AF is more attractive in practice due to less processing burden on the relays. Based on signal transmis- sion over relay network, various types of cooperative proto- cols have been analyzed in [8] - [10]. Nabar et al. [10] intro- duce three different time-division multiple-access (TDMA) based transmission protocols with a single relay for space time signal designs. In this work we exploit the protocol I given in [10] with the Alamouti code to analyze the exact SER of an AF-relay assisted cooperative network with maximum ratio combin- ing (MRC) at the destination in Nakagami fading channels. The concept of equivalent single-input single-output (SISO) method of analysis and MGF approach is used. The remainder of this paper is organized as follows. Sec- tion II describes the system model under consideration. In section III, the SER analysis of the system is presented. In particular, exact SERs are analyzed for the M -PSK modula- tion schemes using numerical integration techniques. Sim- ulation results are presented in section IV as a means of ver- ification of the theoretical results. Finally, some concluding remarks are made in section V. Notation. The E(·), V ar(·) and | a | denote the expec- tation operator, the variance and magnitude of the complex value a, respectively. The superscripts T , H and ∗ stand for transpose, conjugate transpose and element-wise conjugate. I T denotes the T × T identity matrix. X → Y signifies the link between terminals X and Y .