Beamforming-Based Physical Layer Network Coding for Non-Regenerative Multi-Way Relaying

We propose non-regenerative multi-way relaying where a half-duplex multi-antenna relay station (RS) assists multiple singleantenna nodes to communicate with each other. The required number of communication phases is equal to the number of the nodes, N. There are only one multiple-access phase, where the nodes transmit simultaneously to the RS, and N − 1 broadcast (BC) phases. Two transmission methods for the BC phases are proposed, namely, multiplexing transmission and analog network coded transmission. The latter is a cooperation method between the RS and the nodes to manage the interference in the network. Assuming that perfect channel state information is available, the RS performs transceive beamforming to the received signals and transmits simultaneously to all nodes in each BC phase. We address the optimum transceive beamforming maximising the sum rate of non-regenerative multi-way relaying. Due to the nonconvexity of the optimization problem, we propose suboptimum but practical signal processing schemes. For multiplexing transmission, we propose suboptimum schemes based on zero forcing, minimising the mean square error, and maximising the signal to noise ratio. For analog network coded transmission, we propose suboptimum schemes based on matched filtering and semidefinite relaxation of maximising the minimum signal to noise ratio. It is shown that analog network coded transmission outperforms multiplexing transmission.