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Performance of Analog Network Coding Based Two-Way EH Relay with Beamforming

In this paper, we consider a two-way relay (TWR) system in which two multi-antenna source terminals communicate with the help of an energy harvesting (EH) single-antenna relay utilizing the time switching relaying (TSR) protocol. Assuming beamforming at the terminals and analog network coding (ANC) at the EH based TWR, we derive expressions for the outage probability of the system for Rayleigh fading channels. Using high SNR approximations, we demonstrate that the diversity attained equals minimum of the number of antennas at the source terminals, just as in conventional TWR systems. We further show how system throughput can be maximized by optimizing the fraction of the time allocated for EH, and derive closed-form expression for it in some special cases.