Performance of digital delay-lock loops for direct-sequence spread-spectrum signals over Nakagami-m fading channels

In this paper, the performance of a noncoherent 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 timing error PDF and the mean time to lose lock (MTLL) under the Nakagami-m fading environments, while the numerical results are confirmed by time-domain computer simulations.