Closed-form designs for source-relay joint precoder in MIMO AF relaying systems with decision feedback receiver

In this paper, we provide a new design scheme which jointly optimizes the source and relay precoders in multiple-input multiple-output amplify-and-forward relaying systems with minimum mean-squared error (MMSE) decision feedback equalizer (DFE) at the destination node. Instead of conventional optimal designs which require an iterative method, we propose a simple and near optimal closed-form scheme. First, we extend the decomposable property of the error covariance matrix based on linear MMSE receiver to our case. Next, we suggest a new scheme which jointly finds the source and relay precoders with a closed-form solution. Simulation results demonstrate that the performance of the proposed method is less than 1 dB away from the optimal solution with much reduced complexity.