  This paper considers the performance of differential amplify-and-forward
(D-AF) relaying over time-varying Rayleigh fading channels. Using the
auto-regressive time-series model to characterize the time-varying nature of
the wireless channels, new weights for the maximum ratio combining (MRC) of the
received signals at the destination are proposed. Expression for the pair-wise
error probability (PEP) is provided and used to obtain an approximation of the
total average bit error probability (BEP). The obtained BEP approximation
clearly shows how the system performance depends on the auto-correlation of the
direct and the cascaded channels and an irreducible error floor exists at high
signal-to-noise ratio (SNR). Simulation results also demonstrate that, for
fast-fading channels, the new MRC weights lead to a better performance when
compared to the classical combining scheme. Our analysis is verified with
simulation results in different fading scenarios.
