Multiple Symbol Differential Detection of MPSK Which Is Invariant to Frequency Offset Using Maximum-Likelihood Detection

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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, e.g., 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.