On false lock in suppressed carrier MPSK tracking loops

The problem of false lock in suppressed-carrier minimum phase-shift keying (MPSK) tracking loops (M>4 in particular), such as Mth power phase-locked loop (PLL) and MPSK Costas loop carrier recovery subsystems, is investigated. It is demonstrated that such tracking loops false lock onto the received signal when the received carrier frequency and the reference signal frequency generated by MPSK tracking loops are mismatched by multiples of 1/M of the MPSK symbol rate. False lock margins (FLMs) for the suppressed carrier MPSK tracking loops are obtained for a noiseless system model as well as for a model corrupted by additive white Gaussian noise (AWGN). Numerical results are presented in order to explain the influence of system parameters, such as the time-bandwidth product of MPSK Costas loop arm filters (or the Mth power PLL prefilter), arm filters´ output signal-to-noise ratio and the input signal-to-noise ratio, on the performance of MPSK tracking loops