The purpose of this paper is to provide the theoretical approachfor determining the bit error probability in detecting a coherentquaternary phase - Shift-Keyed signal transmitted over a soft-limitedchannel in the presence of the uplink and downlink noise, as well asthe noisy carrier reference signal. The uplink noise Is considered inthe specific way through the envelope variations and the frequencyoffset of the signal remit- ted by the satellite station havinginfluence on the variations of the phase-locked loop parameters inthe receiving ground station. Consequently on the probability densityfunction of the phase error, i.e. the average bit error probability.
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