Beamforming Design of AF MIMO Two-Way Relay Channels Based on MSMSE

In this paper, we design the beamforming in multiple-input multiple-output (MIMO) two-way relay channels to minimize the sum mean squared errors (SMSE). Two source nodes communicate to each other with the help of multiple relays each with a single antenna. A scheme for a  centralized model and another scheme for distributed model are proposed, respectively. In the first scheme, relays are assumed to be able to fully cooperate with each other and the multiple relay nodes can be equivalent to a single relay with multiple antennas. Relay beamforming under total power constraint of all relays is unitedly designed with the transmit beamforming and the receive beamforming. In the second scheme, there are no cooperation between relay nodes, and beamforming schemes under relay total power constraint and individual power constraint are designed, respectively. The simulation results show that beamforming at source and relay nodes significantly improve the average bit error rate (BER) performance. Furthermore, with cooperation across different relays, the performance of the centralized scheme is better than the distributed one, but the latter one is much more practical because of the simple structure of the relay nodes.