Joint source-relay design in multi-antenna multi-relay networks with prefixed receivers

In this paper, we consider the problem of joint source and relay precoder design for multi-antenna multi-relay networks with a prefixed receiver. Prefixed receivers are of practical interest since they enable low complexity at the end-user's receiver as well as backward compatibility. To compute the source and relay precoders, we propose to maximize the worst stream signal-to-interference-plus-noise ratio (SINR) at the output of the receiver subject to source and relay transmit power constraints. The problem is a non-convex optimization problem. To solve it, we propose an iterative alternating algorithm, where, in each iteration, we compute the precoders alternately. We formulate the resulting optimization problems for the computation of the source and relay precoders as second order cone programming (SOCP) and semidefinite relaxation (SDR) problems, respectively. Moreover, we provide sufficient conditions for the convergence of the proposed iterative alternating algorithm to a fixed point. Simulation results show that the performance of the proposed algorithm is close to the performance achieved if the source, relay, and receiver filters are jointly optimized.