Low-complexity optimal spatial channel pairing for AF-based multi-pair two-way relay networks

This paper considers a multi-pair two-way relay system with multi-antenna users and proposes a low-complexity optimal spatial channel pairing (SCP) strategy at the relay station (RS) for such a system. The proposed SCP scheme, following the BD-like beamformer at RS, pairs the uplink spatial subchannels of each user pair with the corresponding downlink spatial subchannels by maximizing sum-rate (Max-SR). Furthermore, a new mathematical inequality (arrangement inequalities of a product) is developed and applied to obtain sufficient and necessary conditions for achieving Max-SR-SCP. This also yields a simple low-complexity implementation of the proposed SCP in contrast to the NP-hard complexity of the original Max-SR-SCP problem. Simulation results illustrate that the proposed Max-SR-SCP achieves substantial sum-rate gains over other pairing schemes.