Frequency Offset Invariant Multiple Symbol Differential Detection of MPSK

Multiple-symbol differential detection (MSDD) of differentially encoded phase-shift keying (PSK) signals in the presence of random frequency variation and additive white Gaussian noise is studied. It is shown that frequency variation distorts the transmitted signal through attenuating its amplitude and introducing a time-varying phase shift to the information symbols. A double differential PSK (DDPSK) modulation scheme is then introduced and a MSDD for detecting DDPSK signals in the presence of frequency offset is proposed. It is shown that the proposed receiver is robust to the distortions caused by the random frequency variation. A lower bound on the error probability of the proposed MSDD receiver is also derived and compared to that of an autocorrelation demodulator for the case where the observation interval approaches infinity.