Multiple Symbol Differential Detection of MPSK which is Invariant to Frequency Offset using Maximum-likelihood detection

It is well known that classical differential detection of MPSK signals, wherein the information is encoded as the first order phase difference, is a simple and robust form of communication in environments not subject to frequency variation. For channels that introduce into the carrier a random frequency shift, eg., those associated with moving vehicles, classical differential detection as above may yield poor performance, particularly if the frequency shift is an appreciable fraction of the data rate. In such situations, one must resort to a form of differential detection that encodes the information as higher order (second order for constant frequency shift) phase difference process. 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.