Spectrum of the product signal of a PN code and its time-shared early and late dithering replica

It is noted that the spectrum of the product signal of a PN code and its replica offset in time has been analyzed by Gill (1965). In the study reported here, a more generalized result is obtained. In particular, the spectrum of the product signal of a PN code and its time-shared early and late replica is given as a function of the dithering rate, the magnitude of the dithers (that is, tau), the code sync error, and the gating function that controls the manner in which time sharing of early and late dithering is accomplished. From this evaluation, the influence of PN self-noise on the performance of a direct sequence spread spectrum communication system with tau-dither code tracking can be quantified.