MMSE-based filter design for multi-user peer-to-peer MIMO amplify-and-forward relay systems

This paper is concerned with linear relay and destination filter design methods for the multi-user peer-to-peer amplify-and-forward relaying systems. Specifically, the relay and destination filter sets are developed which minimize the sum mean-squared-error (MSE). We first present a joint optimum relay and destination filter calculation method with an iterative algorithm. Motivated by the need to reduce computational complexity of the iterative scheme, we then formulate a simplified sum MSE minimization problem using the relay filter decomposability, which lead to two sub-optimum non-iterative design methods. One is based on zero-forcing channel-inversion and the other on minimum-mean-squared-error channel-inversion. Finally, we propose modified destination filter design methods which require only local channel state information between relay and a specific destination node. The simulation results verify that, compared with the optimum iterative method, the proposed non-iterative schemes suffer a marginal loss in performance while enjoying significantly improved implementation efficiencies.