Noncoherent digital delay-lock loops for direct-sequence spread-spectrum signals over Weibull fading channels

The Weibull distribution is a flexible statistical model for describing multipath fading channels in both indoor and outdoor radio propagation environments. The performance of noncoherent first- and second-order digital delay-lock loops (DDLLs) for direct-sequence spread-spectrum systems over Weibull fading channels is analyzed. Closed-form expressions for timing error transition probability density functions (PDFs) of Chapman-Kolmogorov (C-K) equations are derived, which are employed to drive the analytical expressions for the steady-state timing error PDF and the mean time to lose lock (MTLL). Moreover, the tracking performance of the DDLL in the presence of Doppler shifts is also examined.