Error probability of digital modulation in satellite mobile, land mobile, and Gaussian channels with narrow-band receiver filter

It is shown how to derive formulas for the error probability for M-ary differential phase shift keying with differential phase detection (DPD) and M-ary frequency shift keying with DPD, limiter-discriminator detection and limiter-discriminator-integrator detection in the satellite mobile channel (SMC) with narrowband receiver filter if such formulas are available for the Gaussian channel. The modification of the formulas involves only a redefinition of the noise power and autocorrelation function. Since the SMC contains as special cases the land mobile (Rayleigh) channel and the Gaussian channel, the derived formulas are valid for these channels as well. In fact the formula for the land mobile channel is in many cases reduced to a closed form, which does not contain an integral. The author computes the error probability for the four systems, and compares their performance assuming a third-order butterworth filter and M=2,4,8 symbols