A novel tracking jitter computation method for delay locked loops in spread spectrum systems

Kurzfassung

In spread-spectrum navigation systems, the positioning error (or tracking accuracy) is determined from the jitter deviation of delay-locked loops (DLLs). However, jitter simulations are computationally complex, and conventional analytical methods provide only unsatisfactory and incomplete jitter results. Thus, our contribution presents a novel method for the analytical jitter computation by mapping the stochastic differential equation (SDE) of the DLL onto an Ornstein–Uhlenbeck (OU) SDE. Its solution is the well-known OU random process, which is a time-variant Gaussian distribution. The expectation value and the variance of the OU random process yield the jitter deviation. Thus, we derive the analytical time-variant jitter function with its transient response, which was to date unavailable. Contrary to previous jitter computations based on a loop transfer function, our method covers DLLs of any order. We obtain the loop parameters that minimise the jitter deviation analytically without computationally complex simulations. Above all, our method based on OU random processes enables for the first time an efficient joint analytical mean time to lose lock (MTLL) and jitter computation. Therefore, both computationally complex MTLL and jitter simulations become obsolete for many kinds of DLLs