Robust Relay Precoding Design for Two Way Relay Systems with Delayed and Limited Feedback

This letter addresses the robust linear precoding design at the relay node in two way relay systems with independent source-relay and relay-source channels. An antenna configuration in which both the two source nodes S1 and S2 and the relay node R are equipped with multiple antennas, is assumed. Due to delayed and finite-rate feedback, only outdated and quantized channel direction information (CDI) of the downlink channel is available at the transmitter of the relay during the broadcast (BC) phase. To tackle the performance degradation caused by the joint effects of channel quantization error and feedback delay, we propose a robust precoding scheme based on minimizing the expected weighted sum mean squared error (WS-MSE) conditioned on the induced channel uncertainties subject to relay power constraints. We also find that CDI-only feedback is sufficient for calculating the robust precoding matrix. Numerical results validate the robustness of the proposed scheme.