Further Results Concerning the Effect of Frequency-Selective Fading on Differentially Coherent Matched Filter Receivers

In this correspondence, error probabilities are calculated for binary DPSK communication through frequency-selective channels with predetection diversity matched filter reception. A method due to Bello and Nelin is used to carry out the calculations. Error probabilities are calculated for three different combinations of signaling pulse shape and channel frequency correlation function. One of these cases was investigated previously by Bello and Nelin, but some errors were made in their calculations. It is shown that for each of the three cases, an irreducible error probability exists that is proportional to the
2L
power of the relative data rate (where
L
is the order of diversity) when the data rate is small. Also, when the results for the three cases are suitably compared, it is found that the error probabilities are more sensitive to the shape of the signaling pulse than to the shape of the channel frequency correlation function.