Robust beamforming design under imperfect CSI for two-way relay system with reciprocal channels

This paper presents a collaborative beamforming design under imperfect channel state information (CSI) assumption for a multiple single-antenna two-way relay network with reciprocal channels. In practical scenario, the channel estimation is always inaccurate at relay nodes. Aiming to tackle the performance degradation caused by the imperfect CSI, we propose a robust beamforming scheme with hypothesis of the stochastic error model. By using the weighted sum mean squared error (MSE) as cost function with a mean sum power constraint, an optimization problem is formulated. Due to the intractable expression of the cost function, a lower bound of the cost function is derived via the approximation of the SINR expression. Furthermore, through matrix decomposition the original optimization problem is recast to the form of Rayleigh-Ritz ratio and the closed-form solution for this optimal beamforming vector is obtained. Numerical results have demonstrated the robustness and superiority of the proposed scheme in terms of system sum rate and BER.