MMSE-based precoder design for packet retransmissions in MIMO AF relay systems

Aiming at minimizing mean-squared-error of symbol estimations, a novel progressive retransmission precoder is proposed for multi-input multi-output (MIMO) amplify-and-forward (AF) relay systems. The re-transmission precoder design problem is decomposed into two subproblems: a discrete channel pairing problem and a continuous joint source/relay power allocation (PA) problem. Optimizing the channel pairing requires an exhaustive search over all possible channel pairings. Moreover, for each channel pairing, the joint source/relay PA is a non-convex multi-variable optimization problem. We propose an optimal PA algorithm and a suboptimal iterative PA algorithm. However, the optimal retransmission precoder that depends on the exhaustive search over all possible channel pairings has high computational complexity. Fortunately, we prove that when one hop channel's signal-to-noise ratio (SNR) goes to in nity, the optimal channel pairing should pair current singular values of the other hop channel and the previous subchannel gains in the reversed order. Motivated by reducing the computational complexity, a simpli ed channel pairing searching method is proposed, in which the optimal channel pairing in asymptotic performance is applied to all the SNR regions. Numerical results show that the proposed simpli ed channel pairing and the iterative PA algorithm both always achieve the near-optimal perfor- mance. Compared with conventional retransmission precoder schemes of MIMO AF relay systems, our proposed retransmission precoder can improve the system performance significantly.