On performance of multi-antenna relay beamforming with per-antenna power constraints

We analyze the loss due to distributed nature of relay beamforming in an amplify-and-forward relay network. The optimal relay beamforming in both centralized multi-antenna single relay scenario and distributed single-antenna multi-relay scenario are compared in terms of SNR, where individual antenna/relay power budgets are assumed to account for the realistic practical constraints. For centralized relay beamforming, we show that the optimal beamforming for SNR maximization can be obtained by relay per-antenna power minimization along with bi-section search. Comparing the SNR under distributed and centralized relay beamforming, we show that distributed beamforming incurs no loss when relaying is noiseless. For noisy relaying, numerical results show that the loss due to distributed processing is around 1-2dB for two to eight relays (or antennas) at the practical SNR range of interests. Next, we consider the total in-network power minimization of the source and the multi-antenna relay under per-note per-antenna power constraints, disallowing “power sharing” among nodes and/or antennas. We proposed a heuristic iterative approach. Simulation shows that significant power saving can be made for joint in-network power minimization at both source and relay.