On codebook design for distributed relay beamforming network

We study the problem of codebook design for quantized distributed relay beamforming under individual relay power constraint in a cooperative relay network. The received SNR is used as the design metric. We study two types of codebook design: phase-only codebook where each relay uses full power, and codebook with power control where relay power and phase need to be jointly considered. For the former, we adopt Grassmannian line packing criterion under equal gain constraint, and compare the performance with that under the generalized Lloyd Algorithm for optimal codebook design. For codebook with power control, the generalized Lloyd Algorithm can be used for the optimal codebook design, but incurs high complexity. We propose a low-complexity suboptimal method, which can directly use the optimal power control solution for perfect channel knowledge under the individual power constraint. Through simulation study, it is found that it is more beneficial to use codebook with power control over codebook without power control when relays are closer to destination, instead of the source.