ly, the double dither loop (DDL) [8], the product of sum and difference DLL ( DLL) [9], and the modified code tracking loop (MCTL) [10], [11] have been proposed which attempt to mitigate the disadvantages of each config- uration when compared with the other. Another variation, referred to as the complex sums DLL [12], has been suggested for application in environments characterized by severe dynamic range variation where reception is subject to fast fading and scintillation. In this chapter, we focus our attention on the class of non-coherent PN tracking loops that are of interest in SS communication receivers where PN acquisition and tracking (despreading) is performed prior to carrier syn- chronization. Indeed, this is the more common situation in present and past Pseudonoise Code Tracking in Direct-Sequence Receivers SS communication systems in contrast to the other uses of PN modulation where the code is acquired and coherently tracked as a baseband modula- tion, e.g., ranging. Although both linear and non-linear loop analyses are pos- sible, we shall concentrate primarily on the steady state tracking performance results obtained from the linear theory since in most situations the equiva- lent loop signal-to-noise ratio is sufficiently high as to justify this assump- tion. Following the presentation of these results, we shall discuss the acquisition (transient) behavior [4] and slip time (mean time to lose lock) performance [13] of the DLL and TDL, which, by necessity, must both be derived from consideration of the non-linear theory. Finally, the chapter con- cludes with a discussion of quadriphase PN tracking and a summary of other recent contributions. 2.1 THE DELAY-LOCKED LOOP Consider the non-coherent delay-locked loop (DLL) illustrated in Figure 2.1. The input signal x(t) is cross-correlated with advanced and retarded versions of the local PN code generator sequence. The results of these cross-correla- tion operations are then band-pass filtered, square-law envelope detected, and differenced to produce a