Mean Time to Lose Lock for a Coherent Second-Order PN-Code Tracking Loop - The Singular Perturbation Approach

The singular perturbation method is used to approximate the mean time to lose lock (MTLL) for a second-order coherent pseudonoise code tracking delay-lock loop (DLL). Approximate expressions for the MTLL are given. The influence of loop offset due to the Doppler rate is studied, and optimal loop parameters (natural frequency and damping factor) which maximize the MTLL are presented. Upper bounds to the maximum allowable Doppler rates for various operating conditions are given. >

[1]  E. Wong,et al.  On the Convergence of Ordinary Integrals to Stochastic Integrals , 1965 .

[2]  B. Matkowsky,et al.  The Exit Problem for Randomly Perturbed Dynamical Systems , 1977 .

[3]  H. Meyr.  Nonlinear Analysis of Correlative Tracking Systems Using Renewal Process Theory , 1975, IEEE Trans. Commun..

[4]  Z. Schuss,et al.  Loss of Lock Induced by Doppler or Code Rate Mismatch in Code Tracking Loops , 1987, MILCOM 1987 - IEEE Military Communications Conference - Crisis Communications: The Promise and Reality.

[5]  A. L. Welti,et al.  Optimization of a second order PN-code tracking loop using the mean exit time criterion , 1989, IEEE 1989 International Conference on Systems Engineering.

[6]  ANDREAS POLYDOROS,et al.  Analysis and Optimization of Correlative Code-Tracking Loops in Spread Spectrum Systems , 1982, MILCOM 1982 - IEEE Military Communications Conference - Progress in Spread Spectrum Communications.

[7]  C. Gardiner.  Handbook of Stochastic Methods , 1983 .

[8]  Laurence B. Milstein,et al.  Spread-Spectrum Communications , 1983 .

[9]  J.B. Horton,et al.  Digital communications by satellite , 1979, Proceedings of the IEEE.

[10]  Bernard J. Matkowsky,et al.  The Exit Problem: A New Approach to Diffusion Across Potential Barriers , 1979 .

[11]  A. L. Welti,et al.  Optimal design of a modified code tracking loop , 1988, 8th European Conference on Electrotechnics, Conference Proceedings on Area Communication.

[12]  H. Kramers.  Brownian motion in a field of force and the diffusion model of chemical reactions , 1940 .

[13]  A. L. Welti,et al.  Doppler acceleration influence on code tracking in direct sequence spread spectrum systems: threshold calculation and AGC algorithms , 1989, IEEE Global Telecommunications Conference, 1989, and Exhibition. 'Communications Technology for the 1990s and Beyond.

[14]  C. Chester.  Techniques in partial differential equations , 1971 .

[15]  Andrew J. Viterbi,et al.  Principles of coherent communication , 1966 .

[16]  James J. Spilker,et al.  GPS Signal Structure and Performance Characteristics , 1978 .

[17]  Rodger E. Ziemer,et al.  Digital Communications and Spread Spectrum Systems , 1985 .

[18]  Ben-Zion Bobrovsky,et al.  Some results on the problem of exit from a domain , 1992 .

[19]  Marvin K. Simon,et al.  Spread spectrum communications; vols. 1-3 , 1985 .

[20]  Z. Schuss,et al.  A Singular Perturbation Method for the Computation of the Mean First Passage Time in a Nonlinear Filter , 1982 .

[21]  M. V. Day,et al.  Recent progress on the small parameter exit problem , 1987 .

[22]  Jack Kenneth Holmes,et al.  Coherent Spread Spectrum Systems , 1982 .