A novel fast calculation algorithm (FCA) for calculating the decision metric of the multiple-symbol differential detection (MSDD) considering the autocorrelation of a received sequence is proposed. In correspondence to the star quadrature amplitude modulation (QAM), the M algorithm is adopted to MSDD over Rayleigh fading channels, in order to reduce the number of search paths. The computational complexity of the decision metric can be greatly reduced by the proposed FCA and the M algorithm. Through computer simulations, it is confirmed that the symbol error rate (SER) performance of the MSDD considering autocorrelation is closer to that of the ideal coherent detection as the length of an observed sequence becomes larger over Rayleigh fading channels.

We propose a novel adaptive multiple-symbol differential detection (MSDD) scheme that has excellent performance over frequency selective fading (FSF) channels. The adaptive MSDD scheme consists of an adaptive noncoherent least mean square channel estimator that can accomplish channel estimation without any decision delay and the MSDD. The M-algorithm is introduced into this detection scheme to reduce the complication of computation due to increasing observed sequence length in the MSDD. Because of the application of the adaptive channel estimator and the M-algorithm, this adaptive MSDD make it possible that channel estimation is accomplished for every symbol along M surviving paths without any decision delay. And the SER performance of this adaptive MSDD is not affected by phase fluctuation introduced by a channel because the MSDD and the noncoherent channel estimator are applied. The adaptive MSDD scheme is applied to typical constellation of 16APSK, the (4,12) QAM and the star QAM. The excellent tracking performance of this adaptive MSDD scheme over FSF channels is confirmed by computer simulations.