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We study amplified-and-forward (AF)-based two-way relaying (TWR) with multiple source pairs, which are exchanging information through the relay. Each source has single antenna and the relay has multi-antenna. The optimal beamforming matrix structure that achieves maximum signal-to-interference-plus-noise ratio (SINR) for TWR with multiple source pairs is derived. We then present two new non-zero-forcing based beamforming schemes for TWR, which take into consideration the tradeoff between preserving the desired signals and suppressing inter-pair interference between different source pairs. Joint grouping and beamforming scheme is proposed to achieve a better signal-to-interference-plus-noise ratio (SINR) when the total number of source pairs is large and the signal-to-noise ratio (SNR) at the relay is low.

On two-way communications for cooperative multiple source pairs through a multi-antenna relay