An analysis of delay-locked loop tracking binary Markovian sequence in the presence of multiple access interference and channel noise

Abstract

This paper presents an analysis of delay-locked loops in direct spreading code division multiple access systems with Markovian spreading sequences. The established analysis with piecewise constant approximation is similar to the mean field analysis which estimates macroscopic characteristics of a spatially-distributed probabilistic system from the local interaction between the elements of the system with low computational complexity. The low complexity makes it possible to analyze the behavior of not only second-order archetype delay-locked loops but also higher-order non-coherent delay-locked loops in the presence of both multiple access interference and channel noise. It is found from the presented analysis that replacing i.i.d. spreading sequences with Markovian spreading sequences with non-vanishing negative autocorrelation reduces the phase tracking error of a non-coherent 1Δ delay-locked loop. The time spent for estimating the error by the presented method is about 1/1000 compared with that by the path integral method.