Outage performance of zero-forcing based MIMO two-way relaying with channel estimation error

In this paper, we investigate the effect of imperfect channel state information (CSI) on the performance of a multiple-input multiple-output (MIMO) two-way relay system that employs transmit/receive zero-forcing (ZF) at the sources and analog network coding (ANC) at the relay. In fact, for the transmit/receive ZF, the source nodes require estimation of the CSI that may not be perfect in practice, and hence the channel estimation error (CEE) does exist in the system. By taking this CEE into account, we deduce that the post-processing end-to-end signal-to-noise ratios (SNRs) at the two sources are reduced by an additional noise pertaining to the CEE and the residual self-interference. Based on these SNRs, we analyze the overall system outage probability and the asymptotic outage behavior under a Rayleigh fading scenario. We demonstrate that the CEE has a severe impact on the overall outage performance and it may reduce the system diversity order to zero. Numerical and simulation investigations are conducted with various values of estimation errors and antenna configurations to support the theoretical analysis.