  Most previous researches on bidirectional relay selection (RS) typically
assume perfect channel state information (CSI). However, outdated CSI, caused
by the the time-variation of channel, cannot be ignored in the practical
system, and it will deteriorate the performance. In this paper, the effect of
outdated CSI on the performance of bidirectional amplify-and-forward RS is
investigated. The optimal single RS scheme in minimizing the symbol error rate
(SER) is revised by incorporating the outdated channels. The analytical
expressions of end-to-end signal to noise ratio (SNR) and symbol error rate
(SER) are derived in a closed-form, along with the asymptotic SER expression in
high SNR. All the analytical expressions are verified by the Monte-Carlo
simulations. The analytical and the simulation results reveal that once CSI is
outdated, the diversity order degrades to one from full diversity. Furthermore,
a multiple RS scheme is proposed and verified that this scheme is a feasible
solution to compensate the diversity loss caused by outdated CSI.
