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Analytical Computation of Mean Time to Lose Lock for Langevin Delay-Locked Loops

Groh, Ingmar and Gentner, Christian and Selva, Jesus (2012) Analytical Computation of Mean Time to Lose Lock for Langevin Delay-Locked Loops. IEEE Transactions on Communications. IEEE - Institute of Electrical and Electronics Engineers. ISSN 0090-6778

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Abstract

This paper presents a novel method for the analytical mean time to lose lock (MTLL) computation of coherent second-order Langevin delay-locked loops (DLLs). Analytical MTLL computation is a key task for DLLs, since the computational complexity of numerical MTLL simulations is far too high in many operating ranges of the second-order Langevin DLLs. To obtain the crucial MTLL values analytically without simulations, we rewrite the Langevin stochastic differential equation (SDE) as a vector-valued Ornstein-Uhlenbeck (OU) SDE. It includes a Gaussian noise term, which yields as a solution of the vector-valued OU SDE a time-variant Gaussian distribution. Thus, the complementary error function yields the loss of lock probability and thereby the MTLL. If we replace the complementary error functions by suitable exponential approximations, we obtain a simple MTLL expression with an exponential function as dominant term. The simple exponential MTLL expression yields the optimum loop parameters corresponding to the maximum MTLL. Simulation results confirm that the optimum loop parameters corresponding to our analytical MTLL computation method and to the simplified exponential approximation coincide. Besides the crucial analytical MTLL results, the OU random processes yield additionally the likewise crucial analytical jitter results.

Item URL in elib:https://elib.dlr.de/79495/
Document Type:Article
Title:Analytical Computation of Mean Time to Lose Lock for Langevin Delay-Locked Loops
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Groh, Ingmaringmar.groh (at) intel.comUNSPECIFIED
Gentner, ChristianChristian.Gentner (at) dlr.deUNSPECIFIED
Selva, Jesusjesus.selva (at) ua.esUNSPECIFIED
Date:11 November 2012
Journal or Publication Title:IEEE Transactions on Communications
Refereed publication:Yes
Open Access:No
Gold Open Access:No
In SCOPUS:Yes
In ISI Web of Science:Yes
Publisher:IEEE - Institute of Electrical and Electronics Engineers
ISSN:0090-6778
Status:Published
Keywords:Computational modeling , Delay , Eigenvalues and eigenfunctions , Mathematical model , Noise , Random processes, Ornstein-Uhlenbeck random process , Spread-spectrum system , code synchronization , loss of lock phenomenon
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Communication and Navigation
DLR - Research area:Raumfahrt
DLR - Program:R KN - Kommunikation und Navigation
DLR - Research theme (Project):R - Vorhaben GNSS2/Neue Dienste und Produkte
Location: Oberpfaffenhofen
Institutes and Institutions:Institute of Communication and Navigation > Communications Systems
Deposited By: Gentner, Christian
Deposited On:06 Dec 2012 09:50
Last Modified:08 Mar 2018 18:33

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