Lock detection in Costas loops

Previous analyses of lock detector algorithms for Costas loops have ignored the effects of the inherent correlation between samples of the phase error process. In this paper, both analysis and simulations are used to quantify the effects of phase correlation on lock detection for the 'square law' and '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. It is shown 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 squarewave than for sinewave signals.