A distributed algorithm for two-way multiple-relay networks

In this paper we propose an efficient transmission strategy for the two-way relay channel (TWRC) with multiple relays, when these are multiple-input multiple-output (MIMO) transceivers that apply the amplify-and-forward (AF) protocol. Although the optimal beamforming strategy is known, it requires a central node, with channel state information (CSI) of the entire network, to compute all the beamforming matrices, which is impractical. To reduce the overhead, in this paper we present a distributed algorithm for the computation of the relay beamforming matrices. The proposed algorithm divides the problem in two stages. First, each relay computes its own beamforming matrix in parallel using only local CSI. Next, a distributed beamforming is applied to make the signals add up coherently at the nodes. Although the proposed algorithm is suboptimal, we show through simulations that it performs very close to the optimal achievable rate region.