MRC-Based Relay Precoding for Cooperative AF Multi-Antenna Relay Networks with CSI

This paper investigates linear precoding designs for a cooperative amplify-and-forward (AF) network with a multi-antenna relay having complete channel state information (CSI). The focus is on both orthogonal AF (OAF) and non-orthogonal AF (NAF) protocols. The precoders at the relay are derived based on the maximum ratio combining (MRC) scheme, followed by an optimal power amplification factor to maximize the end-to-end achievable rate. For OAF, it is a concave optimization problem and the closed-form solution can be obtained using Karush-Kuhn-Tucker (KKT) conditions. However, the optimization problem for NAF is non-convex and getting globally optimal solution in closed-form is more challenging. Our approach is to investigate the achievable rate in different sub-domains of the channel matrix to upper-bound the original problem by a convex optimization problem. It is then shown that the optimal solution to the power amplification factor of the original optimization problem can be obtained in closed-form. The optimal MRC-based relay precoding vector is then established. Numerical results reveal that the proposed system achieves significant end-to-end rate gains over the conventional dual-hop AF multi-antenna as well as cooperative AF single-antenna systems.