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

IEEE Journal on Selected Areas in Communications

Volumn 8, Issue 5, 1990, Pages 809-818

  Welti, Arnold L ^a   Bobrovsky, Ben Zion ^a,b  

^a ETH ZURICH   (Switzerland)

^b TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

COHERENT-TRACKING LOOP; DELAY-LOCK LOOPS; DOPPLER RATES; MEAN TIME TO LOSE LOCK (MTLL); PSEUDONOISE CODED COMMUNICATION; SINGULAR PERTURBATION METHOD;

MATHEMATICAL TECHNIQUES--PERTURBATION TECHNIQUES; PROBABILITY--RANDOM PROCESSES; SIGNAL FILTERING AND PREDICTION;

RADIO COMMUNICATION;

EID: 0025448416     PISSN: 07338716     EISSN: None     Source Type: Journal    
DOI: 10.1109/49.56387     Document Type: Article

References (28)

1. B. Z. Bobrovsky and Z. Schuss, “Jamming and maneuvering induced loss of lock in a range tracking loop,” Swiss Fed. Inst. Technol., Zürich, IKT Tech. Rep., Mar. 1988.
2. —, “Singular perturbation in filtering theory,” SIAM J. Appl. Math., vol. 42, pp. 174–187, 1982.
3. B. Z. Bobrovsky and O. Zeitouni, “Some results on the problem of exit from a domain,” submitted to Stochastics.
4. C. R. Chester, Techniques in Partial Differential Equations. New York: McGraw-Hill, 1971.
5. M. V. Day, “Recent progress on the small parameter exit problem,” Stochastics, vol. 20, pp. 121–150, 1987.
6. M. I. Freidlin and A. D. Wentzell, Random Perturbations of Dynamical Systems. New York: Springer, 1984.
7. C. W. Gardiner, Handbook of Stochastic Methods. New York: Springer Ser. Synergetics, 1983.
8. J. K. Holmes, Coherent Spread Spectrum Systems. New York: Wiley, 1982.
9. K. Itô and H. P. McKean, Diffusion Process and Their Sample Paths. New York: Academic, 1964.
10. R. Karmy, B. Z. Bobrovsky, and Z. Schuss, “Loss of lock induced by Doppler or code rate mismatch in code tracking loops,” in Proc. MILCOM ’87, Washington, DC, Oct. 1987, pp. 294–298.
11. H. A. Kramers, “Brownian motion in field of force and the diffusion model of chemical reaction,” Physica, vol. 7, pp. 284–304, 1940.
12. W. C. Lindsey, Synchronous Systems in Communications and Control. Englewood Cliffs, NJ: Prentice-Hall, 1972.
13. B. J. Matkowsky and Z. Schuss, “The exit problem for randomly perturbed dynamical systems,” SIAM J. Appl. Math., vol. 33, no. 2. pp. 365–382, 1977.
14. H. Meyr, “Nonlinear analysis of correlative tracking systems using renewal process theory,” IEEE Trans. Commun., vol. COM-23, pp. 192–203, Feb. 1975.
15. F. W. J. Olver, Asymptotics and Special Functions. New York: Academic, 1974.
16. A. Polydoros and C. L. Weber, “Analysis and optimization of correlative code tracking loops in spread spectrum systems,” IEEE Trans. Commun., vol. COM-33, pp. 30–34, Jan. 1985.
17. A. Polydoros, private communication.
18. Z. Schuss, Theory and Applications of Stochastic Differential Equations. New York: Wiley, 1980.
19. Z. Schuss and B. J. Matkowsky, “The exit problem: A new approach to diffusion across potential barriers,” SIAM J. Appl. Math., no. 35, pp. 604–623, 1979.
20. M. K. Simon, J. Omura, R. A. Scholtz, and B. K. Levitt, Spread Spectrum Communications, Vols. I-III. Rockville, MD: Computer Science Press, 1985.
21. J. J. Spilker, Digital Communications by Satellite. Englewood Cliffs, NJ: Prentice-Hall, 1977.
22. —, “GPS signal structure and performance characteristics,” Navigation: J. Inst. Navigation, vol. 25, no. 2, pp. 121–146, 1978.
23. A. J. Viterbi, Principles of Coherent Communications. New York: McGraw-Hill, 1966.
24. A. L. Welti and B. Z. Bobrovsky, “Optimal design of a modified code tracking loop,” in Proc. 8th European Conf. Electrotechnics, EUROCON ’88, Stockholm, Sweden, June 1988, pp. 80–83.
25. —, “Optimization of a second-order PN-code tracking loop using the mean exit time criterion,” in Proc. IEEE Int. Conf. Syst. Eng., Dayton, OH, Aug. 1989, pp. 487–490.
26. —, “Doppler acceleration influence on code tracking in direct sequence spread spectrum systems: Threshold calculation and AGC algorithms,” presented at GLOBECOM ’89, Dallas, TX, Nov. 1989, pp. 1624–1628.
27. E. Wong and M. Zakai, “On the convergence of ordinary integrals to stochastic integrals,” Ann. Math. Statist., vol. 36, pp. 1560–1564, 1965.
28. R. E. Ziemer and R. L. Peterson, Digital Communications and Spread Spectrum Systems. New York: Macmillan, 1985.