Linear Phase-Locked Loop Theory for Cyclostationary Input Disturbances

This paper presents a general method for evaluating the linearized tracking performance of phase-locked loops (PLL´s) estimating the phase of an unmodulated sinusoid corrupted by an additive disturbance which is described in terms of cyclostationary processes. Such disturbances are frequently encountered in carrier modulated systems where the sidebands are responsible for the error in estimating the carrier phase, and in baseband pulse amplitude modulation (PAM) systems where the timing error is caused by the so-called pattern-dependent jitter. The tracking performance has already been determined in the case where the disturbance is band limited [12]. In this paper, a general solution which applies to both cases of carrier extraction and clock synchronization is derived. One might be tempted to replace the disturbance by a stationary process with the same power spectral density, and then evaluate the linearized tracking performance by means of conventional linear PLL theory. It is shown that the mean-square phase error can be severely overestimated by applying this procedure.