### Multi-Antenna Multi-Group Multi-Way Relaying

In this project, we consider a wireless relay network where a half-duplex multi-antenna relay station (RS) assists multiple communication groups. Each communication group consists of multiple half-duplex nodes who exchange messages. Each node has a message and wants to decode the messages from all other nodes in its group. In such a multi-way relay channel, the communication can only be performed through the RS since it is assumed that there are no direct links between the communicating nodes.

Due to the half-duplex constraint, there is a higher number of time-frequency communication resources needed compared to the case when full-duplex nodes exchange messages through a full-duplex RS. Therefore, we propose spectrally efficient communication protocols to perform multi-group multi-way (MGMW) communication using a half-duplex multi-antenna RS. The required number of communication phases is defined by the maximum number of nodes among the groups. In the first communication phase, the multiple access (MAC) phase, all nodes transmit their data streams simultaneously to the RS. After performing signal processing, in the remaining communication phases, the broadcast (BC) phases, the RS transmits to the nodes by ensuring that each node receives the intended data streams from its communication group members.

Three BC strategies are designed, namely, unicasting, hybrid uni/multicasting and multicasting, where each of these strategies ensures that the MGMW communication is completed within the given number of communication phases. Using unicasting strategy, in each BC phase, the RS transmits different data streams to different nodes. Each data stream is intended only for one receiving node. Using hybrid uni/multicasting, for each served group, the RS sends two data streams. One data stream is sent exclusively to only one node and the other data stream is sent to the other remaining nodes in the group. Using multicasting strategy, for each served group, the RS transmits one data stream for all nodes in the group. Considering multicasting strategy, network coding is applied to maintain the number of communication phases the same as for the other BC strategies. The applied network coding can be seen as a form of wireless cooperation between the RS and the nodes. For each group, in each BC phase, the RS performs a linear operation on two chosen data streams of two member nodes in the group and transmits the output to all group member nodes. The chosen data streams are changed in each BC phase such that the data stream of each node is selected at least once. Consequently, each node needs to perform self- and known-interference cancellation to each received data stream using the available side information, namely, its own transmitted data stream or a data stream which has been decoded in one of the previous BC phases.

We consider both non-regenerative RS and regenerative RS for MGMW relaying. A non-regenerative RS performs transceive (transmit and receive) beamforming to the received signals according to the chosen BC strategy and transmits the output to the nodes. We design a unified system model for non-regenerative MGMW relaying valid for all BC strategies and derive the sum rate expression of non-regenerative MGMW relaying for two cases, namely, asymmetric and symmetric traffic. We address transceive beamforming maximising the sum rate of non-regenerative MGMW relaying. Due to the high complexity of finding the optimum transceive beamforming maximising the sum rate, we design generalised low-complexity transceive beamforming algorithms for all BC strategies with three different optimisation criteria, namely, matched filter (MF), zero forcing (ZF) and minimisation of mean square error (MMSE). Also, we introduce BC-Strategy-aware (BCSA) transceive beamforming. BCSA transceive beamforming is designed based on either block diagonalisation (BD) or regularised BD (RBD). It is shown that the sum rate performance of non-regenerative MGMW relaying depends on the chosen BC strategy and the applied transceive beamforming. Using MF, ZF and MMSE, hybrid uni/multicasting performs best followed by unicasting and multicasting strategies. Using BCSA transceive beamforming, multicasting strategy performs best followed by hybrid uni/multicasting and unicasting strategies. BCSA transceive beamforming is able to improve the performance of both hybrid uni/multicasting and multicasting strategies due to the better approach of handling the interference in the network.

A regenerative RS decodes all the received data streams from all nodes in the MAC phase. We consider MMSE with successive interference cancellation for decoding the data streams of all nodes at the RS. After having the information bits, the RS re-encodes the decoded bits and transmits to the nodes according to the chosen BC strategy. Regarding the multicasting strategy, two linear operations are considered, namely, modified superposition coding (mSPC) and exclusive-or (XOR). We design a unified system model for regenerative MGMW relaying valid for all BC strategies and derive the sum rate expression of regenerative MGMW relaying for two cases, namely, asymmetric and symmetric traffic. We propose transmit beamforming minimising the RS’s transmit power while ensuring that each receiving node receives with a rate equal to the rate received at the RS in the MAC phase for each particular data stream. Due to the complexity of finding the optimum transmit beamforming minimising the RS’s transmit power and since in some cases the available RS transmit power is limited, we design generalised transmit beamforming algorithms for all BC strategies with three different optimisation criteria, namely, MF, ZF and MMSE. Also, we design generalized BCSA transmit beamforming. It is shown that multicasting-XOR strategy requires the lowest transmit power at the RS compared to the other strategies. In general, the sum rate performance of regenerative MGMW relaying depends on the chosen BC strategy and the applied transmit beamforming. Due to its better approach of handling the interference in the network, BCSA transmit beamforming is able to improve the performance of regenerative MGMW relaying. In general, multicasting-XOR strategy performs best followed by hybrid uni/multicasting and unicasting strategies. Furthermore, multicasting-XOR outperforms multicasting-mSPC.