The Letter shows that the decision feedback multiple-symbol differential detection (DF-DD) schemes proposed by Leib and Pasupathy and by Edbauer are equivalent, and that DF-DD is an approximate realisation of maximum likelihood differential detection (ML-DD) proposed by Divsalar and Simon. A theoretical BER analysis shows that DF-DD can achieve a BER performance almost the same as ML-DD.
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Adachi et al. (1993) studied this question.