Delay-Lock-Loop Mean Time to Lose Lock

A solution to the mean time to lose lock for a first order, pseudo-noise, code tracking loop is derived for both the fulltime delay-lock loop and the time-shared delay lock loop, with both utilizing an early-late gate size of 1/2 chip, and assuming ideal bandpass filters. The result allows a spread spectrum system designer to assess the slip time performance of his code tracking loop by a simple calculation and then a reading of a curve presented in this paper. The results presented here are actually very general and apply to other code loop spacings and types. It also applies to carrier tracking loops and agrees with the carrier loop result of Viterbi [3].