Precoder design for a single-relay non-orthogonal AF system based on mutual information

This paper investigates the precoder design for a non-orthogonal amplify-and-forward (NAF) half-duplex single-relay channel using mutual information (MI) as the main performance metric. Different from precoder design methods using pairwise error probability (PEP) analysis which are valid only at high signal-to-noise ratios (SNR), our precoder design can apply to any SNR region, which is of more interest from both information-theoretic and practical points of view. We develop a MI-based criterion for an arbitrary cooperative length of 2T , which corresponds to the case of using a 2T ×2T precoder. The design criterion is established in a closed-form, which can be helpful in finding an optimal precoder. Then by focusing on the 2×2 precoder design, we analytically show that a good precoder should have all entries that are equal in magnitude, which is different from the optimal precoders obtained thus far using the conventional PEP criterion. Simulation results indicate that the proposed class of precoder outperforms the existing precoders in terms of the mutual information performance.