Modeling and analysis of delay-locked loop tracking with quadrature-spread DSSS signals over fading channels

The paper addresses the modeling and performance analysis of non-coherent delay-locked loop (NC-DLL) code synchronization for quadrature-spread direct-sequence spread-spectrum (DS-SS) signals in fading channels. A discrete-time stochastic difference equation is presented to model the DLL tracking error dynamics as a first-order Markovian process. The stationary probability density function (PDF) of the tracking error is derived iteratively by solving a Kolmogorov-Chapman integral equation. Numerical examples with different network loading assumptions show that the proposed technique, while having some computational complexity, produces more accurate results when compared to simplified Gaussian approximations. Numerical results are given to illustrate the analysis methodology, where DLL tracking error PDFs are obtained for different signal-to-noise ratios and fading conditions based on Rayleigh, Rician and Nakagami-m models.