  This paper is concerned with the performance of differential
amplify-and-forward (D-AF) relaying for multi-node wireless communications over
time-varying Rayleigh fading channels. A first-order auto-regressive model is
utilized to characterize the time-varying nature of the channels. Based on the
secondorder statistical properties of the wireless channels, a new set of
combining weights is proposed for signal detection at the destination.
Expression of pair-wise error probability (PEP) is provided and used to obtain
the approximated total average bit error probability (BER). It is shown that
the performance of the system is related to the auto-correlation of the direct
and cascaded channels and an irreducible error floor exists at high
signal-to-noise ratio (SNR). The new weights lead to a better performance when
compared to the conventional combining scheme. Computer simulation is carried
out in different scenarios to support the analysis.
