Error performance of physical-layer network coding in multiple-antenna two-way relay systems with outdated CSI

In this paper, we study the impact of outdated channel state information (CSI) on the error rate performance in multiple-antenna two-way decode-and-forward (DF) relay systems, where physical-layer network coding (PNC) is adopted. We consider two variations of relay selection, namely, single best relay selection (S-RS) and multiple successfully-participated relay selection (MSP-RS). Under perfect and outdated CSI assumptions, closed-form expressions for the end-to-end system symbol error probability (SEP) are derived for the S-RS scheme, along with the asymptotic SEP expressions in high SNR regions for the MSP-RS scheme. By both analytical and simulation results, it is clearly shown that a full cooperative diversity gain can be achieved with perfect CSI. The results also manifest that the S-RS scheme can achieve only the transmit diversity gain with outdated CSI. On the other hand, the MSP-RSscheme can achieve a full cooperative diversity gain even if the CSI is outdated at the expense of high complexity.