measure of this ability, which is undoubtedly the most informative, is the probability of remaining in lock for a given interval of time. Unfortunately, analytical evaluation of this measure is difficult, and thus an alternate but still informative measure often used is the mean time to lose lock. Although for a carrier tracking loop such as a phase-locked loop (PLL) this perfor- mance measure is well defined [16], its definition for a PN code tracking loop requires some clarification. For our purpose, we shall define out-of-lock to occur when the loop error signal goes beyond its uncorrelated value, or equivalently, the delay error exceeds the range of the discriminator charac- teristic around the lock point, i.e., + T(N + 1)/N. The mean time to loss-of-lock is a special case of the more general prob- lem of finding the n-th moment of the first passage time of the error process in a synchronous control system (SCS). The solutions to problems of this Pseudonoise Code Tracking in Direct-Sequence Receivers nature are typically obtained by assuming that the noise process driving the system is wideband compared to the system bandwidth, in which case the error process can be assumed to be Markovian and its probability density function is a solution to the Fokker-Planck equation. Without belaboring the details, one can show that by applying the appropriate boundary conditions to the time-dependent solution of the one-dimensional Fokker-Planck equa- tion, the first moment of the first passage time (mean time to lose lock) of the error process x(t) in a first-order SCS with symmetrical boundaries +b and symmetrical restoring force h(x) [i.e., h(x) = h(-x)] is given by [16] (2.79) where U(x) is the system potential function which is related to the restor- ing force by (2.80) and K2 is the second-order intensity coefficient in the Fokker-Planck equa- tion. For the DLL, the error process X is the normalized delay error E1 and h(x) is linearly related to the normalized discriminator characteristic by h(x) = = (2.81) Thus, (2