Multi-Group Multi-Way Relaying: When Analog Network Coding Finds Its Transceive Beamforming

Abstract

In this paper, we introduce non-regenerative multi-group multi-way relaying. A half-duplex non-regenerative multi-antenna relay station (RS) assists multiple communication groups. In each group, there are multiple nodes that want to communicate with each other. Each node has a message and wants to decode the messages only from other nodes in its group. The required number of communication phases for each group is equal to the number of nodes in the group. In the first phase, all nodes transmit simultaneously to the RS and in the following phases the RS applies transceive beamforming and transmits to all nodes. We derive the achievable sum rate of non-regenerative multi-group multi-way relaying for asymmetric and symmetric traffic and for two different cases, namely, with and without analog network coding (ANC). We specially design an ANC-aware transceive beamforming for non-regenerative multi-group multi-way relaying. The ANC-aware transceive beamforming is designed using two criteria, namely, matched filter (MF) and semidefinite relaxation (SDR) of a maximisation of minimum signal to noise ratio problem. From sum rate analysis, it is shown that applying ANC at the RS improves the performance. Regarding the ANC-aware transceive beamforming, the ANC-SDR outperforms ANC-MF at the cost of computational complexity and additional signaling from the nodes to the RS.