  Selection combining (SC) at the destination for differential
amplify-and-forward (AF) relaying is attractive as it does not require channel
state information as compared to the semi maximum-ratio-combining (semi-MRC)
while delivering close performance. Performance analysis of the SC scheme was
recently reported but only for the case of slow-fading channels. This paper
provides an exact average bit-error-rate (BER) of the SC scheme over a general
case of time-varying Rayleigh fading channels and when the DBPSK modulation is
used together with the non-coherent detection at the destination. The presented
analysis is thoroughly verified with simulation results in various fading
scenarios. It is shown that the performance of the system is related to the
auto-correlation values of the channels. It is also shown that the performance
of the SC method is very close to that of the semi-MRC method and the existence
of an error floor at high signal-to-noise ratio region is inevitable in both
methods. The obtained BER analysis for the SC method can also be used to
approximate the BER performance of the MRC method, whose exact analytical
evaluation in time-varying channels appears to be difficult.
