Error probability analysis of two-way amplify-and-forward relaying in the presence of imperfect channel estimations

Two-way relaying is generally designed assuming the availability of perfect channel state information (CSI) at the network nodes. However, perfect CSI is not available in practice. This paper investigates the impact of Gaussian estimation errors on the two-way relaying performance in independent and non identically distributed Rayleigh fading channels. Specifically, we derive the cumulative distribution function (CDF) and the probability density function (PDF) of the two-way relaying output signal-to-noise ratio (SNR) under imperfect CSI, enabling the evaluation of some useful performance metrics such as the average error probability and outage probabilities in practical operating environments. Furthermore, numerical and simulation results are provided and the impact of imperfect CSI on the two-way relaying performance is investigated.