The phase of a vector perturbed by Gaussian noise and differentially coherent receivers

Some results are presented regarding the asymptotic distribution of the phase of a vector perturbed by Gaussian noise. It is shown that for large signal-to-noise ratio, the asymptotic distribution of the phase is of the Tikhonov type. This framework is then used for the synthesis of differentially coherent receiver structures, one for M-ary phase-shift keying (MPSK) and the other for minimum-shift keying (MSK). The first structure bridges the performance gap between coherent and differentially coherent demodulation of MPSK. The MSK receiver uses matched filtering with differential demodulation.<
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