Low complexity robust recursive beamforming for two-way full duplex relay network

In this study, a two-way full-duplex amplify-and-forward relay network is considered in which two multi-antenna fullduplex user nodes manage to exchange their information via a full-duplex multi-antenna relay. The users and relay can concurrently transmit their symbols in all time slots in the same frequency band, which leads to self-interference (SI) at all nodes. The joint beamforming algorithm is used in which the relay and users beamforming matrices are updated in each time slot to suppress the SI. This algorithm needs the channel state information (CSI) of all previous time slots, so the complexity increases as time lapses. To decrease the complexity, an algorithm is proposed in which the beamforming matrix is computed recursively. Moreover, the channel estimation error is considered when the relay and users have partial CSI. Thus, a robust algorithm, i.e. an algorithm that takes the estimation error into account is proposed to decrease the effect of estimation error. The proposed algorithm has been evaluated in terms of mean square error, achievable sum rate and BER for various values of the estimation error variances and compared with the non-robust algorithm. The results show that the superiority of the recursive robust algorithm in terms of SNR and complexity.