Effects of multipath fading on delay-locked loops for spread spectrum systems

A renewal process approach is used to analyze noncoherent delay-locked loops (DLLs) for spread spectrum systems operating over frequency selective and frequency nonselective slow fading channels. The effects of multipath fading are evaluated in terms of the mean-time-to-lose-lock (MTLL) and the root-mean-square (RMS) tracking error. For channels that have a specular component, the following results are observed: (i) the effect of multipath fading is more significant for tracking loops that have large loop signal-to-noise ratios (SNRs); (ii) a smaller early-late discriminator offset Δ, which is bounded by 0<Δ<1, results a better tracking error performance. However, the tracking error is insensitive to Δ, if there is a strong multipath fading effect and/or the tracking loops have small loop SNRs; (iii) a larger Δ (>0.5) may result in a higher MTLL, especially if there is a strong multipath effect. From (ii) and (iii), instead of using the popular choice of Δ=0.5, a larger Δ may be chosen for a DLL that works at low SNRs and/or strong multipath fading environments, where MTLL is an important consideration