Multiple symbol differential detection of MPSK in the presence of frequency offset

The conventional multiple-symbol differential detection (MSDD) of differential phase-shift keying (DPSK) signals is studied in the presence of frequency offset. It is shown that in the case of nonzero frequency offset, the performance of the conventional MSDD receiver degrades by increasing the number of observed samples. A double DPSK (DDPSK) modulation scheme is then introduced and it is shown that in the presence of nonzero frequency offset, an MSDD receiver with DDPSK modulation outperforms a conventional MSDD receiver with DPSK modulation, when both receivers use a large number of received samples. Examples lead to a conjecture that the performance of an optimum MSDD receiver with DDPSK modulation and an infinite number of received samples, approaches that of a conventional DPSK demodulator with two received samples.