Reduced complexity MMSE beamforming for two-way AF relaying systems with multiple antennas

In this paper, we present a new beamforming design at the relay in AF two-way relaying systems where a relay node with Nr antennas serves two source nodes equipped with a single antenna. In this system, we design low complexity relay beamforming which minimizes the mean squared error (MSE). To this end, unlike conventional designs based on perfect self-interference cancelation at each source whose computational effort grows with an order of O(N6r), we determine the level of SIC in an MSE optimization problem, thereby obtaining a new insightful closed-form solution with complexity of O(N2r. It is also shown that the channel estimation overhead can be reduced by our methods. Finally, simulation results demonstrate that the proposed design method achieves the minimum MSE with reduced complexity.