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

被引:0
|
作者
Groh, Ingmar [1 ]
Gentner, Christian [1 ]
Selva, Jesus [2 ]
机构
[1] German Aerosp Ctr DLR, Inst Commun & Nav KN, D-82234 Wessling, Germany
[2] Univ Alicante, Dept Phys Syst Engn & Signal Theory DFISTS, E-03080 Alicante, Spain
关键词
Spread-spectrum system; code synchronization; loss of lock phenomenon; Ornstein-Uhlenbeck random process; SPREAD-SPECTRUM SYSTEMS; CODE TRACKING LOOP;
D O I
10.1109/TCOMM.2012.082812.100629
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
0808 ; 0809 ;
摘要
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.
引用
收藏
页码:3491 / 3498
页数:8
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