Capacity Region of the Two-Way Multi-antenna Relay Channel with Analog Tx-Rx Beamforming

In this paper we study the multiple-input multiple-output two-way relay channel (MIMO-TWRC) when the nodes use analog beamforming. Following the amplify-and-forward (AF) strategy, the problem consists of finding the transmit and receive beamformers of the nodes and the relay, and the power allocated to each one, that achieve the boundary of the capacity region. We express the optimal node beamformers in terms of the relay beamformers, and show that the capacity region can be efficiently characterized using convex optimization techniques. Numerical examples are provided to illustrate the results of this paper, and to compare the capacity region achieved by analog beamforming against the conventional MIMO schemes that operate at the baseband.