Optimal Training Design for MIMO Amplify-and-Forward Two-Way Relay Systems in the Presence of Interference

In this paper, we study the optimal training design for multiple-input multiple-output (MIMO) amplify-and-forward (AF) two-way relay systems in the presence of interference. In order to address the interference issue while accurately estimating the channels, we minimize the total transmit power consumed by two source nodes and a relay subject to the constraint on mean square error (MSE) of the channel estimation, which is a nonconvex problem. To solve this challenging problem, we first derive the optimal structure of the training signals, and then, we convert the original problem into a tractable convex form, from which the optimal training scheme is designed efficiently. We further consider a practical special case, for which the optimal training scheme is designed with a lower complexity and the useful insights into the optimal training design are obtained. Also, to reduce the computational complexity of the optimal training design, we propose an asymptotically optimal training scheme in the high signal-to-interference-plus-noise ratio (SINR) regime with a low complexity. Simulation results demonstrate that the proposed schemes significantly outperform the existing schemes.