  This paper studies dual-hop amplify-and-forward relaying over time-varying
Rayleigh fading channels with differential M-PSK modulation and non-coherent
detection. For the case of "two-symbol" detection, a first order time-series
model is utilized to characterize the time-varying nature of the cascaded
channel. Based on this model, an exact bit error rate (BER) expression is
derived and confirmed with simulation results. The obtained expression shows
that the BER is related to the auto-correlation of the cascaded channel and an
irreducible error floor exists at high transmit power. To overcome the error
floor experienced with fast-fading, a nearly optimal multiple-symbol
differential sphere detection (MSDSD) is also developed. The error performance
of MSDSD is illustrated with simulation results under different fading
scenarios.
