Error probability of PSK satellite communication system in the presence of noise and noisy carrier reference signal

A PSK satellite communication system consisting of earth transmitter station, uplink, satellite station, downlink and earth receiver station is considered in this paper. The synchronization reference signal is extracted by the first-order nonlinear PLL and, by assumption, this extraction is not ideal. The uplink noise influence is considered through the frequency offset of signal remitted by the satellite station (the narrowband process phase derivative fluctuations), while the downlink noise is taken into consideration through the error probability expression. The steady-state p.d.f. of phase error p(φ) for the observed system is determined as well as the total error probability P_c