Double Symbol Error Rates of M-ary DPSK in a Satellite-Aircraft Multipath Channel

Double symbol error rates of
M
-ary differentially coherent phase shift keying (DPSK) systems in a satellite-aircraft multipath channel are evaluated. A joint probability density function (pdf) of two consecutive differential phase errors in the DPSK outputs is newly derived. Numerically calculated results are shown in figures for binary, quaternary, and octonary DPSK systems. It is further shown that the analytical values agree well with the data observed by ATS-5 experimental tests.