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.