Sub-optimal Linear Beamforming Design on MIMO Two-Way Relay Channels

A sub-optimal cooperative beam forming design method of the amplify-and-forward (AF) MIMO two-way relay channels is proposed in this work based on the optimal beam forming design which minimize the sum mean square errors (MSMSE). Suppose the channel state information (CSI) is perfectly known by the receiver and transmitter as well as the relay, global optimal beam forming can be achieved. By analyzing the MSMSE-based optimal method, the results show that effect of the transmit and receive beam forming pairs is to maximize the receive SNR at two communication nodes, and rank of the optimal relay beam forming matrix is no larger than 2 when there is only one data stream at both communication nodes. Based on the analysis, a simplified algorithm is proposed to design the beam forming vectors (matrices). Simulation results show that the system performance of bit error rates (BER) of the simplified method is very close to the optimal one with fast iteration speed and much lower computational complexity.