For band-limited pseudonoise signals, a noncoherent digital delay-lock loop (DDLL) equipped with a discrete automatic gain control algorithm under a RAKE scheme over frequency-selective fading channels is studied. Its associated statistical characteristics are analyzed based on the Nakagami-$m$ stochastic process. The transition timing error probability density function (pdf) of the Chapman–Kolmogorov equation is evaluated to drive an analytical expression for the steady-state timing error pdf. The mean time to lose lock and the mean square tracking error with its corresponding Cramér–Rao lower bound (CRLB) under frequency-selective Nakagami-$m$ fading environments are scrutinized, whereas their numerical results are confirmed by time-domain computer simulations. Moreover, the tracking performance of the DDLL in the presence of Doppler shifts is also examined.

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