Sum MSE minimization for multipoint-to-multipoint MIMO AF relay systems

In this paper, we consider multipoint-to-multipoint multi-input multi-output relay systems where multiple source-destination pairs simultaneously communicate through a single multiple antenna relay. In this system configuration, we optimize sum mean-squared-error (MSE). This problem is shown to be non-convex, and thus it is quite complex to find an analytical solution. To address this issue, we first introduce the sum MSE minimization scheme based on global channel state information (CSI) at all nodes. Then, a method which reduces complexity and CSI requirements is proposed by utilizing error covariance decomposition and MSE duality between broadcast channel and multiple access channel. Through numerical simulations, we confirm the effectiveness of our proposed schemes.