Costas loop lock detection in the advanced receiver

The advanced receiver currently being developed uses a Costas digital loop to demodulate the subcarrier. Previous analyses of lock detector algorithms for Costas loops have ignored the effects of the inherent correlation between the samples of the phase-error process. Accounting for this correlation is necessary to achieve the desired lock-detection probability for a given false-alarm rate. Both analysis and simulations are used to quantify the effects of phase correlation on lock detection for the square-law and the absolute-value type detectors. Results are obtained which depict the lock-detection probability as a function of loop signal-to-noise ratio for a given false-alarm rate. The mathematical model and computer simulation show that the square-law detector experiences less degradation due to phase jitter than the absolute-value detector and that the degradation in detector signal-to-noise ratio is more pronounced for square-wave than for sine-wave signals.