Robust ARQ Precoder Optimization for AF MIMO Relay Systems with Channel Estimation Errors

In this paper, we consider the robust retransmission precoder design for amplify-and-forward (AF) multi-input multi-output (MIMO) relay systems with channel estimation errors. With the objective of minimizing the average mean-squared-error of symbol estimations, we propose a novel progressive retransmission precoder by employing matrix diagonalization and channel pairing. As a consequence, we formulate the precoder design as a joint source/relay power allocation (PA) and channel pairing optimization problem. First, we propose the globally optimal solution, in which exhaustive search is employed for the channel pairing, while with each given channel pairing, an optimal PA algorithm is proposed to solve the nonconvex PA problem by utilizing the necessary conditions for optimality. However, the optimal channel pairing and PA solution is of very high complexity. In order to reduce the complexity, we then propose a suboptimal PA algorithm by iteratively optimizing the PA at the source and the relay, as well as a simplified channel pairing searching method based on the asymptotic optimal solution. It is shown that our proposed robust retransmission precoder improves the system performance significantly, meanwhile, the performance degradation of the low complexity PA and channel pairing algorithm is slight as compared to the optimal PA algorithm and the optimal channel pairing method.