Distributed beamforming for two-way relaying networks with individual power constraints

In this paper we study the sum rate maximization problem in a multi-pair two-way relaying network with multiple single antenna amplify-and-forward relays where each relay has its own transmit power constraint. The optimization problem is non-convex and in general NP-hard. First, we propose a monotonic optimization based algorithm. Due to its high computational complexity, this algorithm can only be used as a benchmark. Afterwards, inspired by the polynomial time difference of convex functions (POTDC) method, we develop a sub-optimal solution which has lower complexity but comparable performance. To further reduce the computational complexity, we propose two other algorithms, i.e., the total SINR eigen-beamformer and an interference neutralization based design which are the low SNR and high SNR approximations of the original optimization problem, respectively. Simulation results show that all the proposed suboptimal methods only suffer small losses compared to the global optimal solution especially when there is a sufficient number of relays in the network.