Precoding design for space-time codes and relay selection with a novel scheme for multiple relay systems

In this paper, we consider the joint design of precoding matrices at both the source and relay nodes in a multi-relay system based on perfect and imperfect channel information, and propose the novel relay selection scheme based on log-likelihood ratio (LLR). Moreover, the symbol error rate (SER) for relay selection system based on proposed scheme is analyzed. At first, we design the combined precoding matrices based on respectively the maximum signal-to-noise ratio (SNR) with perfect channel state information (CSI) and the minimum SER of the single-relay system with imperfect CSI. Using decomposition of matrices, the joint design problems are solved with a two-step method, i.e., the first step is to determine the optimal direction of the precoding matrices, and the second step is to transform the optimization problem into two kinds of independent sub-problems which can be solved in lower complexity. Then, different from traditional relay selection based on signal-to-noise ratio, the relay node with the maximum LLR is chosen. Simulation results show the proposed selection scheme based on LLR is superior to the scheme based on SNR in the SER performance. Furthermore, the multi-relay system using the precoding matrices joint space-time coding technology can improve SER performance of the system effectively compared with only space-time coding or only precoding system.