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.

中文翻译：

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用于双向全双工中继网络的低复杂度鲁棒递归波束成形

在这项研究中，考虑了双向全双工放大转发中继网络，其中两个多天线全双工用户节点通过全双工多天线中继设法交换信息。用户和中继可以在同一频带的所有时隙中同时发送其符号，这会导致所有节点上的自干扰（SI）。使用联合波束成形算法，其中中继站和用户波束成形矩阵在每个时隙中更新以抑制SI。该算法需要所有先前时隙的信道状态信息（CSI），因此复杂度会随着时间的流逝而增加。为了降低复杂度，提出了一种算法，其中递归地计算波束形成矩阵。而且，当中继和用户具有部分CSI时，考虑信道估计误差。从而，为了减少估计误差的影响，提出了一种鲁棒算法，即考虑估计误差的算法。针对估计误差方差的各种值，对均方误差，可实现的总和率和BER进行了评估，并与非鲁棒算法进行了比较。结果表明，递归鲁棒算法在信噪比和复杂度方面具有优越性。