Optimal Training Signal Design for Estimation of Correlated MIMO Channels in Two-Way Amplify-and-Forward Relay Systems

In this study, we design a training signal for a correlated two-way amplify-and-forward (AF) relay channel, where the relay system consists of two sources and one relay, and each terminal is equipped with multiple antennas. In the system, given that a mean square error (MSE) exists at each source, we minimize the sum of the two MSEs. In particular, we first derive a linear minimum MSE channel estimator with an arbitrary training signal. Second, we formulate the training signal design problem to minimize the sum of the MSEs of the two sources. Finally, we present the optimal structure of the training signal. The optimal training signal is obtained numerically, and a suboptimal training signal is obtained in a closed form. The simulation results show that the MSE performance of the closed-form training signal is almost the same as that of the optimal training signal.