Performance Analysis of MPSK Phase Detectors for Carrier Synchronization PLLs at Low SNRs

In this letter, we analyze the performance of a category of phase detectors (PDs) for carrier synchronization phase-locked loops (PLLs) in M-ary phase shift keying (MPSK) receivers working at low signal-to-noise ratios (SNRs). These PDs have the property that their outputs are functions of the inputs' phase only, and thus, their performance is independent of the automatic gain control (AGC) circuits. We deduce closed-form expressions about the linearized gain and equivalent noise variance of these PDs when SNR goes to zero and sum up simple approximate formulas for three typical PDs at all SNRs. We also prove that the modified Mth-power PD performs asymptotically best in this category of PDs as SNR goes to zero.