Optimal cooperative beamforming design schemes for AF MOMO two-way relay channels

In this paper, beamforming parameters in multiple input multiple output （MIMO） two-way relay channels （TWRCs） arc designed. We investigate three communicating scenarios, in which, the source nodes are all equipped with multiple antennas. In the first scenario, one pair of source nodes are communicating with each other under the help of a single multi-antenna equipped relay. A centralized scheme is correspondingly de- veloped where the optimal relay beamforming （RaB） is jointly designed with the transmit beamformings （TBs） and the receive beamformings （RcBs） at both source nodes to minimize the sum of mean square errors （SMSE）. In the second scenario, one pair of users in the first scenario is extended to muhi-pair of source nodes. We derive a general expression of the optimal RaB matrix of this scenario in the second scheme, and based on which, a RaB matrix is designed to cancel the inter-pair interference （IPI） and to minimize the intra- pair SMSE. At last, we consider a distributed scenario where multiple single-antenna equipped relays are help- ing the communication between one pair of source nodes. In the scheme associated with this scenario, beam- formings are developed under relay total power constraint and relay individual power constraint, respectively. The simulation results reveal that beamformings at source and relay nodes significantly improve the performance in the sense of average bit error rate （BER）. The proposed multi-pair scheme has made superior progress in BER performance because it not only can cancel the IPIs but also can balance the useful signal and the noise at each user. Moreover, in one-pair scenarios, the performance of the centralized scheme is better than the dis- tributed One, but the latter is nevertheless much more practical.