Long-term frequency stability requirements and optimal design of a code tracking delay-lock loop

The classical theory of Kramers on the mean exit time of a Brownian particle in a potential well is applied to calculate the mean time to loss of lock in a code-tracking delay lock loop (DLL), yielding rather simple expressions and insight into the mechanism of loss of lock. The influence of the long-term frequency instability of the code clock and the channel noise on the code tracker is analyzed. Explicit expressions for the required long-term stability are presented. Performance analysis and optimal loop design are applied to an indoor cordless telephone in the 900 MHz band using code-division multiple access (CDMA) direct sequence spread spectrum