A Fundamental Lower Bound on the Performance of Practical Joint Carrier and Bit Synchronizers

In this paper we derive a fundamental lower bound on the linearized mean-square phase and time delay errors resulting from a practical synchronizer operating on a carrier-modulated PAM waveform which is corrupted by stationary Gaussian noise. Our bound applies to a large class of synchronizers and, unlike the linearized performance itself, it is easily evaluated from the modulation format, the baseband PAM pulse shape, the additive noise spectrum, and the synchronizer's closedloop transfer function matrix.