Multi-convex optimization for sum rate maximization in multiuser relay networks

A scenario consisting of several single antenna source-destination node pairs communicating through multiple single antenna relays is considered. A two time-slot transmission scheme is considered. In the first time-slot, the source nodes transmit to both the relays and the destination nodes. Both the source nodes and the relays retransmit to the destination nodes in the second time-slot. As the relays cannot decode the received signals, an amplify and forward relaying strategy is assumed. In the present paper, the sum rate maximization problem is tackled. Due to the two transmissions of the source nodes and the two receptions of the destination nodes, there are temporal transmit and receive filters which can be optimized together with the relays´ coefficients aiming at maximizing the sum rate. By partially adapting the filters and by introducing two sets of scaling factors, the sum rate maximization problem is reformulated as a tri-convex optimization problem. An iterative algorithm is proposed which maximizes the sum rate and guarantees a local optimum achievement. The results show that the proposed algorithm outperforms the previously proposed interference alignment scheme in all SNRs.