Minimum mean squared error design of single-antenna two-way distributed relays based on full or partial channel state information

A maximum mean squared error optimal relay beamformer is proposed here for two-way single-antenna distributed relaying systems. A constrained optimisation problem with respect to the relay beamforming vector is first formulated. It is then shown that the design problem of such a relay beamformer supporting both downlink and uplink transmissions simultaneously can be converted to convex optimisation when full channel state information (CSI) is available at the relays. By employing the Lagrangian multiplier method, a closed-form solution for the relaying vector is obtained. The proposed relay beamforming method is also extended to the situation where only the statistics of the CSI are available. A simulation study is conducted to confirm the merit of the proposed two-way relaying scheme.