Joint Source-Relay Optimization for Fixed Receivers in Multi-Antenna Multi-Relay Networks

We jointly optimize the source and relay precoders for multi-antenna multi-relay networks employing 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 consider two different criteria. The objective of the first criterion is 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. Under the second criterion, we minimize the source and relay transmit powers subject to a certain quality-of-service constraint. Both optimization problems are non-convex. To solve them, we propose iterative alternating algorithms, where, in each iteration, we compute the precoders alternately, i.e., for each precoder optimization, we fix all the precoders except the one which is optimized. For both criteria, we formulate the optimization problem for the computation of the source precoder as a second order cone programming (SOCP) problem, for which the optimal solution can be found using interior point algorithms. For each relay precoder, we formulate the optimization problem as a semidefinite relaxation (SDR) problem for which ready-to-use solvers exist. If the solution to the SDR problem is not of rank one, matrix rank-one decomposition or randomization is applied. We also provide sufficient conditions for the convergence of the proposed iterative alternating algorithms to a fixed point. Simulation results show that the performance of the proposed algorithms is close to the performance achieved if the source, relay, and receiver filters are jointly optimized.