  This paper studies dual-hop amplify-and-forward relaying system employing
differential encoding and decoding over time-varying Rayleigh fading channels.
First, the convectional "two-symbol" differential detection (CDD) is
theoretically analysed in terms of the bit-error-rate (BER). The obtained
analysis clearly shows that performance of two-symbol differential detection
severely degrades in fast-fading channels and reaches an irreducible error
floor at high signal-to-noise ratio region. To overcome the error floor
experienced with fast-fading, a practical suboptimal "multiple-symbol"
detection (MSD) is designed and its performance is theoretically analysed. The
analysis of CDD and MSD are verified and illustrated with simulation results
under different fading scenarios. Specifically, the obtained results show that
the proposed MSD can significantly improve the system performance in
fast-fading channels.
