In this paper, the performance of a non-coherent all-digital delay-lock loop (all-DDLL) for direct-sequence spread-spectrum signals over Nakagami-m fading channels is analyzed. A closed-form expression for the timing error transition probability density function (PDF) of the Chapman-Kolmogorov (C-K) equation is evaluated. The transition PDF is employed to derive the analytical expression for the steady-state tuning error PDF and the mean time to lose lock (MTLL) under the Nakagami-m fading environments, while the numerical results are confirmed by tune-domain computer simulations.
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