Beamforming in Asymmetric Two-Way Relay Systems with Imperfect Channel Estimation

In this paper, we consider a two-way relay system that employs transmit/receive beamforming for bidirectional communication using analog network coding (ANC) protocol in the presence of channel estimation error (CEE). For this set-up, we first obtain the instantaneous end-to-end signal-tonoise ratios (SNRs) with partial self-interference cancellation pertaining to imperfect channel estimation. Then, by considering asymmetric traffic requirements, we derive an accurate expression of overall outage probability (OOP) of the considered system under Nakagami-m fading. We further derive a tight lower bound on OOP that has a simple and compact closed form representation. Moreover, we present an asymptotic OOP expression at high SNR to examine the achievable diversity order with CEE. Numerical and simulation results validate our theoretical analysis and highlight the impact of CEE and different traffic patterns on the system performance with various antenna configurations and fading severity parameters.