Precorrelation filter design for spread-spectrum code tracking in interference

Optimal design of a precorrelation filtering system for use in noncoherent direct-sequence code-tracking loops in the presence of colored noise is described, utilizing a linearized theory of loop operation. The design produces a bias-free loop with an odd S-curve, for which the rms tracking error is minimized. As a byproduct, one arm of the tracking loop provides an optimized signal for data-detection purposes. Widely applicable performance calculations, including rms tracking jitter, mean time to lose lock, and average detection signal-to-noise ratio, are given and illustrated, based on nonlinear models of loop operation.