Multi-antenna relay network beamforming design for multiuser peer-to-peer communications

We consider a multi-user peer-to-peer relay network with multiple multi-antenna relays for amplify-and-forward relaying. Assuming distributed relay beamforming strategy, we investigate the design of each relay processing matrix to minimize the per-antenna relay power usage for given users' SNR targets. As the problem is NP-hard, we developed an approximate solution through the Lagrange dual domain. Through a sequence of transformations, we obtain a semi-closed form solution which can be determined by solving an efficient semi-definite programming problem. We also considered the semi-definite relaxation (SDR) approach. Compared with the SDR approach, the proposed solution has significantly lower computational complexity. The benefit of such solution is apparent when the optimal solution can be obtained by both approaches. When the solution is suboptimal, simulations show that the SDR approach has better performance. Thus, we proposed a combined method of the two approaches to trade-off performance and complexity. Simulations showed the effectiveness of such combined method.