Mean exit time of a noncoherent DLL for a randomly fluctuating channel delay

The influence of a randomly fluctuating channel delay time on the mean exit time (mean time to lose lock, MTLL) of a noncoherent second-order delay-locked loop (DLL) is investigated. First, we derive a systematic approximation for the MTLL of this pseudo-noise (PN) code tracking loop by applying the singular perturbation method. With this approximation we then find the optimal loop parameters and the corresponding maximum achievable MTLL. Furthermore, this robust design that yields a loop which loses lock as rare as possible is compared to the loop whose parameters were chosen according to the Kalman design for the linearized system.