Diversity combining in bi-directional relay networks with energy harvesting nodes

In this study, the authors consider two multiple-antenna transceivers exchanging information through a relay-assisted network using a single-carrier communication scheme. The authors assume that the propagation delay in different relaying path is negligible and the relay nodes are synchronous. As a result, the end-to-end multipath channel is not frequency-selective (time-dispersive) and hence, the successive arriving signals at the transceivers do not interfere with each other. Otherwise, inter-symbol-interference (ISI) will be inevitable and cyclic insertion and removal matrices will be required to combat ISI. In such a two-way network, the relay nodes harvest energy from the surrounding environment and utilise this energy to forward their received messages using a harvest-then-forward protocol. For different receiver diversity combining techniques, the authors design an optimal relay beamforming to maximise the quality of the received signals at the transceivers subject to the energy casualty constraint at the relay nodes (the energy consumed for transmission of each block cannot exceed the accumulative harvested energy). For each diversity combining technique, a closed-form solution is obtained for the optimal signal-to-noise ratio (SNR) that shows how adjusting the data transmission rate of the transceivers and the amount of energy harvested at the relays affects the received SNR.