Multiple-symbol differential phase detection (DF-DPD) based on decision feedback of past detected symbols is presented for M-ary DPSK modulation. Adopting a Gaussian phase noise assumption, we obtain the a posteriori joint probability density function (pdf) of the outputs of L DPD detectors of orders of 1 to L symbols and derive a DF-DPD algorithm which is based on feeding back the L—1 past detected symbols and minimizing the sum of phase errors of L DPD detectors. A practical implementation of the DF-DPD receiver is presented that uses a single conventional (one-symbol) DPD detector. The bit error rate (BER) performance in an additive white Gaussian noise (AWGN) channel is analyzed taking into account decision error propagation. Performance improvements are evaluated by computer simulations in AWGN and Rayleigh fading channels.
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