Precoding techniques for MIMO AF relaying systems with decision feedback receiver

In this paper, we provide new precoding schemes which jointly optimize the source and relay precoders in multiple-input multiple-output amplify-and-forward relaying systems with minimum mean-squared error decision feedback equalizer (DFE) at the destination node. Instead of conventional schemes which resort to an iterative method, we propose simple precoding schemes based on a closed-form solution. To this end, we first extend the decomposable property of the error covariance matrix for a linear receiver to relaying systems with DFE receivers. Then, we suggest two closed-form solutions which successively identify the source and the relay precoders. To improve the performance, a mode selection which adaptively chooses one of the two closed-form precoding schemes according to the channel conditions is introduced. Then, we propose a simple eigenvalue based mode selection algorithm, and analyze its selection probability behavior for Rayleigh fading channels. Simulation results demonstrate that the performance of the proposed method is almost identical to the iterative solution with much reduced complexity.