A recent paper has proved that the classical receiver for coherent detection of differentially encoded M-PSK in AWGN is optimum for the MAP sequence detection criterion. In this letter, we show that asymptotically, as SNR tends to zero, the MAP symbol detection criterion receiver is equivalent to the classical differentially coherent receiver, for M greater than two. An asymptotic relative efficiency figure of merit is defined in order to compare the performances of the classical coherent receiver and the classical differentially coherent receiver.
Kanchumarthy, Venkateshwara R., Choudhari, Tina and Viswanathan, R.. "Performance Analysis of Optimum Receivers for Differentially Encoded M-PSK in Low SNR." (May 2005).