Linear MMSE Transceiver Design with Quality-of-Service Constraints in Amplify-and-Forward MIMO Relay Systems

This paper addresses the linear transceiver design with quality of service (QoS) constraints in an amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay system. Taking both the direct and the relay links into account and using the minimum-mean-squared-error (MMSE) receiver at the destination, we jointly design the source/relay precoders such that the transmitted power is minimized and QoS constraints are satisfied. The optimization problem such formulated, however, is a highly nonlinear formulation of the source and relay precoders, and the optimum solution is difficult to derive. To solve the problem, we then propose to use a constrained structure for the precoders, and derive mean-squared-error (MSE) upper bounds. Using the primal decomposition method, we can then translate the original optimization problem into two scalar-valued convex optimization problems. The closed-form solutions for the precoders can then be derived by corresponding Karush-Kuhn-Tucker (KKT) conditions. Using the solution, we further provide a sufficient condition to determine if the system is proper to be operated in the cooperative mode or not. Simulations show that the proposed precoded MIMO relay system can significantly reduce the transmission power, compared to a non-cooperated one.