Optimization of a two-way MIMO Amplify-and-Forward relay network

In this paper, we address the optimization of a two-way Multiple-Input-Multiple-Output (MIMO) Amplify-and-Forward (AF) relay network. We consider a multiple access broadcast scheme which finishes communication in two time slots. In order to optimally choose the beamforming coefficients of relays, we devise the following criteria: the beamforming coefficient matrices are optimized aiming to minimize the total relay transmission power subject to output Signal-to-Noise-Ratio (SNR) constraint at each transceiver. To design the MIMO equalizer, we impose the Zero-Forcing (ZF) constraint. Since the original optimization problems generated from the criteria are intractable, compromise is essential. So we consider local optimum the problems. Through relaxation, we find that the relaxed optimization problems can be formulated as the Second-Order-Cone-Programming (SOCP) problems which can be solved efficiently using the existing toolboxes. The validity of the proposed algorithm is verified by computer simulations.