Joint source and relay design for two-hop amplify-and-forward relay networks with QoS constraints

In this paper, we consider the joint design of source precoding matrix and the relay precoding matrix in a two-hop multiple-input multiple-output relay network. The goal is to find a pair of matrices in order to minimize the power consumption and at the same time meet pre-selected quality of service constraints that are defined as the mean square error of each data stream. Using majorization theory, we simplify the matrix-valued optimization problem into a scalar-valued one. We then propose a lower bound and an upper bound of the original problem, both in convex forms. Specifically, the latter is solved by a multi-level water-filling algorithm that is much efficient than directly applying the interior point method. Numerical examples corroborate the proposed studies and also demonstrate the tightness of both bounds to the original problem.