Distributed beamforming and power allocation in two-way multi-relay networks with second-order channel statistics

We investigate distributed beamforming and power allocation for a single-antenna two-way relay network, which consists of multiple, parallel amplify-and-forward relays. The goal is to maximize the smaller of the two signal-to-noise-ratios (SNRs) while maintaining the total transmit power in each time slot below a predefined threshold. While related previous studies have assumed that the two transceivers know perfect instantaneous channel state information (CSI) of the entire network, in this paper, each transceiver only knows its own channel to the relays and the second-order-statistics (SOS) of the channel gains from the other transceiver to the relays. We develop optimal and sub-optimal solutions. The optimal one requires eigenvalue decomposition and iteratively exhaustive search, while the sub-optimal one uses a Taylor series approximation, but gives a near-optimal solution with significantly low computational complexity.