Stochastic-Based Analyses of Noncoherent Code Tracking Loops Over Wireless Fading Circumstances

• Published in: IEEE transactions on vehicular technology 2012-01, Vol.61 (1), p.258-274
• Main Authors: WU, Tsan-Ming, TSAI, Tsung-Hua
• Format: Article
• Language: English
• Subjects: Applied sciences; Circuit properties; Circuits of signal characteristics conditioning (including delay circuits); Coding, codes; Cramér-Rao lower bound (CRLB); Delay; digital delay-lock loop (DDLL); discrete automatic gain control (AGC); Doppler shift; Electric, optical and optoelectronic circuits; Electrical engineering. Electrical power engineering; Electrical machines; Electronic circuits; Electronics; Exact sciences and technology; Fading; frequency-selective Nakagami- m fading; Gain control; Information, signal and communications theory; mean time to lose lock (MTLL); Noise; pseudonoise (PN) code tracking; Regulation and control; Signal and communications theory; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Tracking loops; Transmission and modulation (techniques and equipments)
• ISSN: 0018-9545; 1939-9359
• DOI: 10.1109/TVT.2011.2175012

For band-limited pseudonoise signals, a noncoherent digital delay-lock loop (DDLL) equipped with a discrete automatic gain control algorithm under a RAKE scheme over frequency-selective fading channels is studied. Its associated statistical characteristics are analyzed based on the Nakagami- m stochastic process. The transition timing error probability density function (pdf) of the Chapman-Kolmogorov equation is evaluated to drive an analytical expression for the steady-state timing error pdf. The mean time to lose lock and the mean square tracking error with its corresponding Cramér-Rao lower bound (CRLB) under frequency-selective Nakagami- m fading environments are scrutinized, whereas their numerical results are confirmed by time-domain computer simulations. Moreover, the tracking performance of the DDLL in the presence of Doppler shifts is also examined.