Robust distributed beamforming for two-way wireless relay systems

In this paper, a robust optimal distributed relay beamforming scheme is presented for two-way wireless relay systems with two sources (one base station and one mobile terminal) and multiple relays, each having a single antenna. Considering that the perfect channel state information (CSI) between the mobile terminal and the relays is usually not available, the new beamforming problem, based on the minimization of the sum MSE (mean squared error) subject to a total relay power, is formulated such that only the CSI between the base station and the relays is required. The constrained beamforming optimization problem is then solved by the Lagrangian multiplier method, leading to a closed-form solution for the distributed relay beamforming. Monte Carlo simulations show that the proposed scheme performs better than the conventional relaying method in terms of both sum rate and the bit-error-rate (BER).