The purpose of this paper is to provide the theoretical approach for determ
ining the bit error probability in detecting a coherent quaternary phase-sh
ift-keyed signal transmitted over a soft-limited channel in the presence of
the uplink and downlink noise, as well as the noisy carrier reference sign
al. The uplink noise is considered in the specific way through the envelope
variations and the frequency offset of the signal remitted by the satellit
e station having influence on the variations of the phase-locked loop param
eters in the receiving ground station, consequently on the probability dens
ity function of the phase error, i.e. the average bit error probability. Th
e downlink noise is also taken into consideration. The determined results a
re based on the non-linear phase-locked loop model with primary emphasis on
the degradations in the system performance produced by the imperfect carri
er signal extraction. Copyright (C) 1994 John Wiley & Sons, Ltd.