Two-Way AF MIMO Multi-Relay System Design Using MMSE-DFE Techniques

Abstract

Targeting at a better design of the analogue network coding (ANC)-assisted two-way amplify-and-forward (AF) multiple-input multiple-output (MIMO) multi-relay communication systems, we bring in the nonlinear minimal mean-squared error (MMSE)-decision feedback equalization (DFE) receiving technique to jointly optimize the source precoding, relay amplifying, feed-forward and feedback matrices. Under the transmission power constraints at both source nodes and each relay node, the two-way sum mean-squared error (MSE) of the signal waveform estimation of all data streams is minimized. To solve the complicated nonconvex optimization problem with four groups of system parameters, this paper develops an iterative block coordinate descent (BCD) algorithm, which converges to at least a Nash point. On the basis of it, for mitigating the error propagation in MMSE-DFE receivers, a group of permutation matrix variables, determining the detection orders of all data streams, are further introduced in our system optimization. Moreover, in case there is no sufficiently precise channel state information (CSI), we also make an extension of the developed algorithms, yielding a robust design scheme, to handle the channel uncertainties. Numerical simulation results show that, compared with the existing linear MMSE receiving-based algorithm, our proposed nonlinear ones provide improved MSE and bit-error-rate (BER) performance as well as good robustness against the imperfect CSI, indicating a promising application prospect of this research.