Channel Aligned Beamforming in Two-Way Multi-Pair Decode-and-Forward Relay Down-Link Channels

We consider the down-link of multi-pair two-way decode-and-forward (DaF) relay channel with multiple antennas at all the nodes. We propose schemes composed of relay pre-coder and user receive beam-formers to support 2M degrees of freedom when M antennas are employed at the relay. A channel aligning technique, where the channel vectors of a pair are forced to be aligned, is introduced so that we can use, at the relay, the well-known pre-coder like zero forcing (ZF) or the regularized channel inversion (RI) from the cellular down-link channels. Alternation based optimization of the pre-coder and the beam-formers searches the channel aligned vector space to further enhance the performance of the scheme in the low and mid SNR range.