Statistical Analyses of Digital Delay-Lock Loops Over Nakagami-m Fading Channels

Statistical analyses of a non-coherent digital delay- lock loop (DDLL) for direct-sequence spread-spectrum signals over Nakagami-m fading channels are discussed. Analytical expressions to the characteristics, such as Cramer-Rao lower bound (CRLB), of the timing tracking errors have been proposed based upon the timing error probability density function (PDF) of the Chapman-Kolmogorov (C-K) equation of the first- and second-order loops. Furthermore, mean square tracking errors (MSTEs) against distinct parameters are also simulated, while their corresponding numerical results with CRLBs are confirmed by time-domain computer calculations.