Groh, Ingmar und Gentner, Christian und 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. doi: 10.1109/tcomm.2012.082812.100629. ISSN 0090-6778.
![]() |
PDF
- Nur DLR-intern zugänglich
255kB |
Kurzfassung
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.
elib-URL des Eintrags: | https://elib.dlr.de/79495/ | ||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Dokumentart: | Zeitschriftenbeitrag | ||||||||||||||||
Titel: | Analytical Computation of Mean Time to Lose Lock for Langevin Delay-Locked Loops | ||||||||||||||||
Autoren: |
| ||||||||||||||||
Datum: | 11 November 2012 | ||||||||||||||||
Erschienen in: | IEEE Transactions on Communications | ||||||||||||||||
Referierte Publikation: | Ja | ||||||||||||||||
Open Access: | Nein | ||||||||||||||||
Gold Open Access: | Nein | ||||||||||||||||
In SCOPUS: | Ja | ||||||||||||||||
In ISI Web of Science: | Ja | ||||||||||||||||
DOI: | 10.1109/tcomm.2012.082812.100629 | ||||||||||||||||
Verlag: | IEEE - Institute of Electrical and Electronics Engineers | ||||||||||||||||
ISSN: | 0090-6778 | ||||||||||||||||
Status: | veröffentlicht | ||||||||||||||||
Stichwörter: | 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 - Forschungsbereich: | Luftfahrt, Raumfahrt und Verkehr | ||||||||||||||||
HGF - Programm: | Raumfahrt | ||||||||||||||||
HGF - Programmthema: | Kommunikation und Navigation | ||||||||||||||||
DLR - Schwerpunkt: | Raumfahrt | ||||||||||||||||
DLR - Forschungsgebiet: | R KN - Kommunikation und Navigation | ||||||||||||||||
DLR - Teilgebiet (Projekt, Vorhaben): | R - Vorhaben GNSS2/Neue Dienste und Produkte (alt) | ||||||||||||||||
Standort: | Oberpfaffenhofen | ||||||||||||||||
Institute & Einrichtungen: | Institut für Kommunikation und Navigation > Nachrichtensysteme | ||||||||||||||||
Hinterlegt von: | Gentner, Dr. Christian | ||||||||||||||||
Hinterlegt am: | 06 Dez 2012 09:50 | ||||||||||||||||
Letzte Änderung: | 14 Jun 2023 16:13 |
Nur für Mitarbeiter des Archivs: Kontrollseite des Eintrags