Steady-state analysis of a class of carrier synchronizers

The paper presents a steady-state analysis of the complete carrier synchronizer when the input is a non-return-to-zero (NRZ) pulse-amplitude-modulated (PAM) signal corrupted by an additive white gaussian noise. The synchronizer consists of the cascade of a bandpass filter (BPF), a non-linearity, and a phase-locked loop (PLL). The bandpass filter is assumed to be a Butterworth design and the non-linearity is of the positive power type. The variance of the phase of the regenerated carrier at the PLL output is expressed analytically as well as by a set of computer generated curves as a function of the BPF bandwidth and order, the power of the non-linearity, and the synchronizer input signal-to-noise ratio. The analysis reveals the optimum choice of the BPF, the non-linearity, and the optimum design of the PLL.