Mean time to lose lock for the "Langevin"-type delay-locked loop

The classical result of Kramers (1940), originally related to chemical reaction rates, is applied in this letter to a second-order all-pole, coherent code tracking delay-locked loop (DLL). A very simple, explicit expression for the leading order term of the mean time to lose lock (MTLL) is presented. The dependence of the MTLL on the loop tension (offset) due to Doppler shift and code clock mismatch is given, and optimal loop parameters which minimize the MTLL are proposed. >

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

[2]  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.

[3]  Harold J. Kushner,et al.  Stochastic systems with small noise, analysis and simulation; a phase locked loop example , 1985 .

[4]  J. Holmes.  First Slip Times Versus Static Phase Error Offset for the First- and Passive Second-Order Phase-Locked Loop , 1971 .

[5]  Arnold L. Welti,et al.  Mean Time to Lose Lock for a Coherent Second-Order PN-Code Tracking Loop - The Singular Perturbation Approach , 1990, IEEE J. Sel. Areas Commun..

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

[7]  M. K. Simon,et al.  The performance of suppressed carrier tracking loops in the presence of frequency detuning , 1970 .

[8]  S. Arrhenius.  Über die Reaktionsgeschwindigkeit bei der Inversion von Rohrzucker durch Säuren , 1889 .

[9]  Zeev Schuss,et al.  Theory and Applications of Stochastic Differential Equations , 1980 .

[10]  B. Bobrovsky,et al.  Mean Time To Lose Lock Of A Coherent Second Order Delay Lock Loop With Passive Filter , 1990, IEEE International Symposium on Spread Spectrum Techniques and Applications.

[11]  S. Orszag,et al.  Advanced Mathematical Methods For Scientists And Engineers , 1979 .

[12]  U. P. Bernhard,et al.  Optimal design of a noncoherent second-order delay-locked loop using the exit-time criterion , 1993, Proceedings of ICC '93 - IEEE International Conference on Communications.

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

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

[15]  Gerd Ascheid,et al.  Phase-, frequency-locked loops, and amplitude control , 1990 .

[16]  Richard L. Brunson,et al.  Linear Control System Analysis and Design , 1988, IEEE Transactions on Systems, Man, and Cybernetics.

[17]  Bernard J. Matkowsky,et al.  Uniform expansion of the transition rate in Kramers' problem , 1984 .

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

[19]  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.