PSK Performance with Imperfect Carrier Phase Recovery

Methods are given to determine the performance loss caused by imperfect or noisy phase recovery and its use in coherent detection of a PSK signal. Numerical results for both binary and quaternary systems are presented so that these results combined with the characteristics of the phase recovery circuit will enable the "best" practical design of a PSK receiver. lt is assumed that the phase noise associated with the recovered carrier can have a nonzero mean and a Gaussian or a truncated Gaussian-type distribution. The static error of the phase noise is mostly due to offset frequency tracking of the phaselocked loop used to recover the carrier, but may also include an equivalent phase error produced by the comparator dead zone. The random component of the phase noise is due to thermal noise present in the recovery circuit and is also due to the random modulation that may be present on the carrier. Two plausible probability density functions are assumed for the random component of the phase noise to study the sensitivity of the detection results to the detailed characteristics of the phase noise. For small values of static error and phase noise variance and for moderate values of signal-to-noise ratio, it is shown that the two models of the probability distribution give essentially the same results. Since the exact method of determining the performance is rather complex, we also present some simple upper bounds.