Overall Outage Analysis of Three-Phase Analog Network Coding with Channel Estimation Errors

In this paper, we investigate the impact of channel estimation errors on the overall outage performance of a two-way multi-relay system that employs three-phase analog network coding (ANC) with opportunistic relay selection. We first represent the two end-to-end instantaneous signal-to-noise ratios (SNRs) with imperfect self-interference cancellation owing to the channel estimation errors. Based on these, we derive a tight closed-form expression for the overall system outage probability over Rayleigh fading channels. We also derive an asymptotic outage expression in high SNR regime, from which the effect of imperfect estimation on the achievable diversity order is examined. The theoretical findings are verified through numerical and simulation results.