Parameter Optimization for Amplify-and-Forward Relaying with Imperfect Channel Estimation

Cooperative diversity is a promising technology for future wireless networks. In this paper, we consider a cooperative communication system operating in an amplify-and-forward (AF) mode with an imperfectly-known relay fading channel. It is assumed that a pilot symbol assisted modulation (PSAM) scheme with linear minimum mean square estimator (LMMSE) is used for the channel estimation. A simple and easy-to-evaluate asymptotical upper bound (AUB) of the symbol-error-rate (SER) is derived for uncoded AF cooperative systems with quadrature amplitude modulation (QAM) constellations. Based on the AUB, we propose a criterion for the choice of parameters in the PSAM scheme, i.e., the pilot spacing and the Wiener filter length. We also formulate an optimum power allocation problem for the considered system. The optimum power allocation can be found by means of a gradient search over a continuous range. Numerical simulations are presented to verify the correctness of the theoretical results and the benefits of the parameter optimization. The performance of amplify-and-forward (AF) cooperative systems has been studied in the past from different perspec- tives. However, most of the work on performance analysis of AF systems has assumed that the perfect channel state information (CSI) is available to both the relay and desti- nation terminal. More recently, (1) and (2) have studied the performance of AF cooperative communication systems with channel estimation error by means of Monte Carlo simulations. The accurate SER expression for cooperative communication systems with a pilot symbol assisted modulation (PSAM) scheme employing a linear minimum mean square estimator (LMMSE) is derived in (3). Furthermore, (4) propose a new channel estimation scheme and analyse the mean square error of the channel estimation. To the authors' best knowledge, no research has been conducted to solve the problem of parameter optimization and optimum power allocation for variable gain AF cooperative communication systems with a PSAM scheme. In this paper, we propose to use the asymptotic upper bound (AUB) of the SER to overcome these difficulties. In particular, we derive a tight expression for the AUB of the SER for the AF cooperative communication system with a PSAM scheme. Using the AUB of the SER, we present the criterion for the parameter choice in the PSAM scheme and show that two parameters used in this scheme, i.e., pilot spacing and Wiener filter length, can be chosen in a tradeoff between system performance, pilot overhead, and receiver complexity. With the derived tight AUB, an optimum power allocation problem is also formulated for the AF cooperative communication system. Since the optimization of the power allocation is very complicated, as it is related to many terms, and obtaining an analytical solution is unlikely, we propose to find the optimum power allocation by means of a gradient search over a continuous range. The rest of the paper is organized as follows. In Section II, we describe the system model and some preliminaries of the AF cooperative system with a PSAM scheme. In Section III, we derive an AUB of the SER for an AF cooperative com- munication system with LMMSE. In Section IV, we first deal with the parameter optimization for the PSAM scheme. Then, an optimum power allocation problem is formulated. Various simulation results and their discussions are presented in Section V. Finally, Section VI contains the conclusions. The following notation is used throughout the paper: (·) ∗ , (·) T , (·) H , and (·) −1 denote the complex conjugate, vec- tor (or matrix) transpose, conjugate transpose, and matrix inverse, respectively. The symbol E(·) denotes the expecta- tion operator, |z| represents the absolute value of a com- plex number z, and the complex Gaussian distribution with mean m and covariance P is denoted by CN(m, P). Finally, x ∼C N(m, P) denotes a complex random variable x with distribution CN(m, P).