Design of Amplify and Forward MIMO Relay Networks with QoS Constraint

In this paper, we design the optimal precoding matrices for amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay networks. Specifically, we consider a dual-hop relay network and minimize the total power consumed by source and relay under predetermined quality of service (QoS) constraints, i.e., mean square error (MSE) constraints. By using majorization theory, we simplify the matrix-valued problem into a scalar-valued one. Since the problem is non-convex, we then propose two convex suboptimal problems that provide the upper and lower bound of the original objectives. Numerical results demonstrate that the lower bound and the upper bound are tight in high signal-to-noise ratio (SNR).