Analysis of Delay tracking Loops in Spread Spectrum systems 

A theory is developed for the numerical calculation of the Mean Time to Loss of Lock (MTLL), 
in tracking loops. 
The loops considered are a range tracking loop in RADAR, 
and non-coherent Delay-Locked-Loop (DLL) for tracking PN sequence in a CDMA system.   
A numerical method is developed for the solution of the Hamilton-Jacobi equation 
which appears in the asymptotic analysis of the loop. 
A method for identifying the caustic curves of the Hamiton-Jacobi equation is presented. 
The MTLL of the non-coherent DLL is calculated for the case of constant clock drift, 
or Doppler shift.   
The MTLL is calculated as a function of loop parameters in the case of constant clock drift rate of chage, 
or Doppler acceleration. An optimal selection rule of loop parameters is given.