Multi-User Two-Way Relay Networks with Distributed Beamforming

We consider a two-way relay network consisting of multiple pairs of single-antenna users and multiple distributed single-antenna relays. The two communication peers in each pair of users transmit simultaneously to the relays in the first time slot, and the relays rebroadcast the received sum signal weighted by a complex gain, in the second time slot. For multi-user systems, the signal arriving at the users contains not only self interference from the back-propagation of user signals, but also inter-pair interferences from other pairs of users. In this paper, we use zero-forcing (ZF) to cancel the inter-user interference, assuming that channel-state information for all relay-peer connections are known at every relay, but no data exchange occurs between relays. We also derive two closed-form expressions for zero-forcing beamforming weights, corresponding to two different relay power constraints, which can be implemented in a distributed manner. The first approach uses standard ZF to null out every inter-pair interference and the second approach sets the total inter-pair interference to zero. We also derive a closed-form upper bound of the achievable sum-rate and show that both methods achieve the same multiplexing gain when the number of relays N is sufficient for perfect zero-forcing, namely 2K² + K, where K is the number of user pairs. For the case of insufficient number of relays, we also propose two solutions for beamforming weights, i.e., based on diagonal loading and use of the pseudo-inverse, and compare their advantages and weaknesses.