Two-Way Amplify-and-Forward Relaying with Gaussian Imperfect Channel Estimations

In this letter, we study the effect of channel estimation errors on the reception reliability of two-way relaying. For a network with two users that exchange information with each other through multiple amplify-and-forward relays, we investigate a single-relay selection scheme. Since the communication is two-way, the selection scheme aims at optimizing the worse performance of the two communication tasks between the pair of users. The signal-to-noise ratio (SNR) at the users' nodes of the relaying network is formulated and upper bounded. Then, the probability density function (PDF) of the upper bounded SNRs are determined. Subsequently, expressions for the error probabilities are obtained. Furthermore, an approximate PDF of the output instantaneous SNRs are derived, based on which simple and general asymptotic expressions for the error probabilities are presented and discussed. Numerical and simulation results are provided to verify the analysis and compare the performance of the two-way relaying network for different operating conditions and scenarios.