MEAN TIME TO LOSE LOCK OF THE 1ST-ORDER AND 2ND-ORDER MODIFIED CODE TRACKING LOOP USED IN SPREAD-SPECTRUM SYSTEMS

Pseudonoise (PN) code tracking loops are essential in various direct-s equence spread-spectrum (DSSS) systems for both, communication and nav igation applications. This paper shows how to optimize the so-called m odified code tracking loop (MCTL) of first- and second-order by using the mean time to lose lock (MTLL) as a performance criterion. The stat e equation of the first-order MCTL is related to the Smoluchowski - Kr amers approximation of a second-order system described by the Langevin equation of motion. For such a specific system, the MTLL is known by the work of Kramers. In case of the second-order type II loop (having two perfect integrators), which cannot be described by the Langevin eq uation, the computation of the MTLL is based on the singular perturbat ion method. Optimal parameters maximizing the MTLL under the constrain t of Doppler effects and the channel noise are derived for both type o f loops, resulting in very simple expressions that can be used immedia tely for a practical loop design. Measurements performed for the first -order MCTL verify the theoretical optimal loop parameters and indicat e that the time to lose lock is exponentially distributed. Monte Carlo simulations confirm also very well the theoretical results in case of a second-order loop and hence, show that the application of the singu lar perturbation method yields an excellent approximation of the MTLL.