Digital Code Tracking Loops Over Frequency-Selective Fading Channels

The performance of a noncoherent digital delay-lock loop (DDLL) with a RAKE scheme for direct-sequence spread-spectrum code division multiple access (DS/SS-CDMA) signals over frequency-selective Rayleigh fading channels is discussed. Closed-form expressions for the transition timing error probability density function (PDF) of the Chapman-Kolmogorov (C-K) equations of the first- and second-order loops are derived for driving analytical expressions of the steady-state timing error PDF. Furthermore, the statistics of the tracking error are scrutinized and verified via computer simulations, such as the mean square tracking error (MSTE) and Cramer-Rao lower bound (CRLB).