Noncoherent Quantized Digital Delay-Lock Tracking of Binary Signals

The delay-lock discriminator is a nonlinear feedback system which employs a form of cross correlation to estimate the relative delay between a reference signal and a delayed version of that signal which is perturbed with additive noise. Previous treatments of delaylock tracking have assumed that the binary maximal-length code sequences used as the signal are detected in a coherent manner. The present paper is concerned with delay-lock discriminator tracking behavior when noncoherent detection of the received signal is required and when two-bit quantization is employed to reduce the cost of implementation of the cross-correlation network. It is found that the error signal generated by the cross-correlation network is characterized by "clustering" in the absence of noise, however, this mode of error signal behavior gradually vanishes as the noise level is increased and is replaced by an error signal generation characteristic that more closely resembles the behavior that obtains without quantization. The selection of an appropriate threshold value to achieve minimum steady-state errors for the delay-lock discriminator is reduced to the problem of determining the probability density function of the error signal under the condition of exact alignment.