Performance of digital code tracking loops for direct-sequence spread-spectrum signals in mobile radio channels

The performance of first- and second-order non-coherent digital delay lock loops (DDLL) for direct-sequence spread-spectrum (DS-SS) signals is investigated in the mobile radio environment. The mobile radio channel is first characterized by Rayleigh fading and Doppler shift. A closed-form expression for the timing error transition probability density function of the Chapman-Kolmogorov (C-K) equation is proposed. The probability density function of the steady-state timing error for the first- and second-order DDLL is obtained by solving the C-K equation numerically, and the results are confirmed by computer simulations. Furthermore, the mean time to lose lock (MTLL) of the first-order loop is evaluated, and some numerical results and simulation results are reported. Finally, the steady-state timing error and MTLL of the first-order loop for DS-SS signals in the log-normal fading environment are also presented, and the results are compared with those of Rayleigh and AWGN channels