2010 Volume 1 Issue 1 Pages 153-165
We analyze stationary phase tracking error of delay-locked loops (DLL) in direct spread code division multiple access (DS-CDMA) using Markovian spreading sequences. The phase tracking error is caused by noise generated inside of DLLs by multiple access interferences. When binary Markovian sequences are used, the noise is not considered as white Gaussian noise. This makes analysis of the tracking error difficult. In this paper, we describe DLLs by stochastic difference equations and derive forward evolutional equations of the probability distribution of the states of DLLs. Applying path integral analysis to the evolutional equations, we obtained stationary distribution. We found from the distribution that Markovian spreading sequences with negative eigenvalue were effective in decreasing stationary phase tracking error of not only a type of DLL in asynchronous CDMA but also DLLs in chip-synchronous CDMA.