Multi-antenna relay network beamforming design for multiuser peer-to-peer communications.
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In this work, we consider a multi-user peer-to-peer relay network with multiple multiantenna relays which employ amplify-and-forward relaying protocol. 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’ Signal-to-Noise Ratio (SNR) targets. As the problem is NP-hard, we develop 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 consider the semi-definite relaxation (SDR) approach. Compared with this SDR approach, the proposed solution has significantly lower computational complexity. The benefit of such a 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 propose a combined method of the two approaches to trade-off performance and complexity. Simulations showed the effectiveness of such a combined method. In the next step, we change the previous objective and constraints to turn the optimization problem into a total power minimization problem for the relay network. We use an approximation by solving this problem in the Lagrange dual domain, and we finally obtain a semi-closed form solution through the dual approach. The use of the SDR approach to solve this problem is also discussed. After analysis, we find the two methods have an advantage over different aspects, thus we propose a combined method for this problem. We eventually compare the two combined methods to see the performance difference in the per-antenna power case and the total relay power case, and discuss reasons for this difference.