Mean Time To Lose Lock Research Articles

Frequency-Locked Detector Threshold Setting Criteria Based on Mean-Time-To-Lose-Lock (MTLL) for GPS Receivers.

Frequency-locked detector (FLD) has been widely utilized in tracking loops of Global Positioning System (GPS) receivers to indicate their locking status. The relation between FLD and lock status has been seldom discussed. The traditional PLL experience is not suitable for FLL. In this paper, the threshold setting criteria for frequency-locked detector in the GPS receiver has been proposed by analyzing statistical characteristic of FLD output. The approximate probability distribution of frequency-locked detector is theoretically derived by using a statistical approach, which reveals the relationship between probabilities of frequency-locked detector and the carrier-to-noise ratio (C/N0) of the received GPS signal. The relationship among mean-time-to-lose-lock (MTLL), detection threshold and lock probability related to C/N0 can be further discovered by utilizing this probability. Therefore, a theoretical basis for threshold setting criteria in frequency locked loops for GPS receivers is provided based on mean-time-to-lose-lock analysis.

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

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.

A novel tracking jitter computation method for delay‐locked loops in spread‐spectrum systems

ABSTRACTIn spread‐spectrum navigation systems, the positioning error (or tracking accuracy) is determined from the jitter deviation of delay‐locked loops (DLLs). However, jitter simulations are computationally complex, and conventional analytical methods provide only unsatisfactory and incomplete jitter results. Thus, our contribution presents a novel method for the analytical jitter computation by mapping the stochastic differential equation (SDE) of the DLL onto an Ornstein–Uhlenbeck (OU) SDE. Its solution is the well‐known OU random process, which is a time‐variant Gaussian distribution. The expectation value and the variance of the OU random process yield the jitter deviation. Thus, we derive the analytical time‐variant jitter function with its transient response, which was to date unavailable. Contrary to previous jitter computations based on a loop transfer function, our method covers DLLs of any order. We obtain the loop parameters that minimise the jitter deviation analytically without computationally complex simulations. Above all, our method based on OU random processes enables for the first time an efficient joint analytical mean time to lose lock (MTLL) and jitter computation. Therefore, both computationally complex MTLL and jitter simulations become obsolete for many kinds of DLLs.Copyright © 2012 John Wiley & Sons, Ltd.

The Effect of Intermittent Signal on the Performance of Code Tracking Loop in GNSS Receivers

This paper analyzes the code tracking performance in the presence of signal blanking in Global Navigation Satellite System (GNSS). The blanking effect is usually caused by buildings that obscure the signal in either a periodic or random manner. In some cases, ideal blanking is used to remove random or periodic interference. Nevertheless, the effect of temporary discontinuity of signal often leads to the tracking and position error. To analyze this problem, three types of blanking model are considered: no blanking, periodic blanking, and random blanking of the signals input into the code tracking loop. The mean time to lose lock (MTLL) is to assess the performance of code tracking system under signal blanking. Finally, the effect of steady-state tracking errors on the performance of tracking loop resulting from blanking environment is also discussed.

Decision directed versus non-data aided plls: A comparative review

The performance of discrete-time Decision Directed (DD) and Non-Data Aided (NDA) first-order Phase Looked Loops (PLL) for a QPSK modulated signal is evaluated under the disturbance of thermal noise and 1/f2 phase noise. A well known continuous-time model is presented that closely approximates the loop?s behavior. Using the continuous time model, Fokker-Planck techniques are applied to compute the Mean Time to Lose Lock (MTLL) for both PLLs. We optimize the loop filter using the MTLL as the optimization criterion. On the basis of the optimal MTLL, we determine the regions where one PLL outperforms the other. Monte-Carlo simulation results are presented to validate the analytic analysis. For the setting under study, the NDA PLL outperforms the DD PLL for SNR below 4.5dB regardless of the phase noise level. Applicability of the results for a second-order PLL is discussed.

A constrained minimum mean square error code tracking loop for synchronous DS-CDMA systems

A constrained minimum mean square error code tracking loop (CMMSE-CTL) is proposed in this paper for synchronous direct sequence code division multiple access (DS-CDMA) systems in a multiuser environment. By introducing assistant weighted despreading signals into the local reference signals of the loop, we exploit the resultant extra degrees of freedom to improve the tracking performance under multiuser environment. The derived mean square tracking error is taken as the cost function and minimized with respect to the weight parameters, under the constraints which ensure an odd-symmetric bias-free S -curve with enhanced tracking range. Simulations based on Gold codes compare the S -curve, root-mean-square (rms) tracking error, mean-time-to-lose-lock (MTLL) performance of CMMSE-CTL and the traditional modified code tracking loop (T-MCTL). It is shown that CMMSE-CTL outperforms T-MCTL greatly in that it provides unbiased stable code tracking with reduced mean square tracking error, an enhanced tracking range, and near–far resistance.

Improved Delay-Locked Loop in a UWB Impulse Radio Time-Hopping Spread-Spectrum System

As ultra-wideband impulse radio (UWB-IR) uses short-duration impulse signals of nanoseconds, even a small number of timing errors can cause a detrimental effect on system performance. A delay-locked loop (DLL) is proposed to synchronize and reduce timing errors. The design of the DLL is vital for UWB systems. In this paper, an improved DLL is introduced to a UWB-IR time-hopping spread-spectrum system. Instead of using only two central correlator branches as in a conventional DLL, the proposed system uses two additional correlator branches with different delay parameters and different weight parameters. The performance of the proposed schemes with the optimal parameters is compared with that of traditional schemes through simulation: the proposed four-branch DLLs achieves less tracking jitter or a longer mean time to lose lock (MTLL) than the conventional two-branch DLLs if proper parameters are chosen.

Code Tracking Algorithms for Mitigating Multipath Effects in Fading Channels for Satellite-Based Positioning

The ever-increasing public interest in location and positioning services has originated a demand for higher performance global navigation satellite systems (GNSSs). In order to achieve this incremental performance, the estimation of line-of-sight (LOS) delay with high accuracy is a prerequisite for all GNSSs. The delay lock loops (DLLs) and their enhanced variants (i.e., feedback code tracking loops) are the structures of choice for the commercial GNSS receivers, but their performance in severe multipath scenarios is still rather limited. In addition, the new satellite positioning system proposals specify the use of a new modulation, the binary offset carrier (BOC) modulation, which triggers a new challenge in the code tracking stage. Therefore, in order to meet this emerging challenge and to improve the accuracy of the delay estimation in severe multipath scenarios, this paper analyzes feedback as well as feedforward code tracking algorithms and proposes the peak tracking (PT) methods, which are combinations of both feedback and feedforward structures and utilize the inherent advantages of both structures. We propose and analyze here two variants of PT algorithm: PT with second-order differentiation (Diff2), and PT with Teager Kaiser (TK) operator, which will be denoted herein as PT(Diff2) and PT(TK), respectively. In addition to the proposal of the PT methods, the authors propose also an improved early-late-slope (IELS) multipath elimination technique which is shown to provide very good mean-time-to-lose-lock (MTLL) performance. An implementation of a noncoherent multipath estimating delay locked loop (MEDLL) structure is also presented. We also incorporate here an extensive review of the existing feedback and feedforward delay estimation algorithms for direct sequence code division multiple access (DS-CDMA) signals in satellite fading channels, by taking into account the impact of binary phase shift keying (BPSK) as well as the newly proposed BOC modulation, more specifically, sine-BOC(1,1) (SinBOC(1,1)), selected for Galileo open service (OS) signal. The state-of-art algorithms are compared, via simulations, with the proposed algorithms. The main focus in the performance comparison of the algorithms is on the closely spaced multipath scenario, since this situation is the most challenging for estimating LOS component with high accuracy in positioning applications.

Mean time to loose lock of phase tracking by particle filtering

We consider the classical problem of phase lock on frequency modulation (FM) signals using the recent methods of particle filters (PF). This problem is nonlinear in nature, and building an optimal filter is impossible. State-of-the-art suboptimal phase estimators are based on phase lock loops (PLL) which are equivalent to an extended Kalman filter (EKF) realization. We show that applying PF methods, which preserve the nonlinearity of the phase measurements, result in improved performance of 0.94 dB carrier-to-noise (CNR) ratio considering the mean time to lose lock (MTLL). We show simulation results for the PLL-EKF and the PF estimators, compare their performance and demonstrate how an increase in the number of particles improves the performance of the particle filter estimator.

Mean time to loose lock of phase tracking by particle filtering

We consider the classical problem of phase lock on frequency modulation (FM) signals using the recent methods of particle filters (PF). This problem is nonlinear in nature, and building an optimal filter is impossible. State-of-the-art suboptimal phase estimators are based on phase lock loops (PLL) which are equivalent to an extended Kalman filter (EKF) realization. We show that applying PF methods, which preserve the nonlinearity of the phase measurements, result in improved performance of 0.94dB carrier-to-noise (CNR) ratio considering the mean time to lose lock (MTLL). We show simulation results for the PLL-EKF and the PF estimators, compare their performance and demonstrate how an increase in the number of particles improves the performance of the particle filter estimator.

The Exit Problem in a Nonlinear System Driven by 1/f Noise: The Delay Locked Loop

The frequency generated by high frequency oscillators contains a small but significant noise component known as phase noise, also known as oscillator noise or phase jitter. The phase noise belongs to the family of stochastic processes with spectra $1/f^\alpha$, which exhibits scaleinvariance (or self-similarity) and a long-term correlation structure that decays polynomially in time. Both the phase and thermal noises cause errors in receivers that contain the oscillators. In particular, they cause losses of lock in phase tracking systems such as the phase locked loop in coherent systems, which include cellular phones, global positioning systems (GPS), and radar (e.g., synthetic aperture radar (SAR)), and in the delay locked loop (DLL), which is an important component of code division multiple access receivers and interface to modern memory modules, such as double data rate synchronous dynamic random access memory. The mean time to lose lock (MTLL) is well known to be an important design objective for various tracking loops. The evaluation of the MTLL is known in the mathematical literature as the exit problem for a dynamical system driven by noise, which is the problem of calculating the mean time for the noisy trajectories to reach the boundary of the domain of attraction of a stable point of the noiseless dynamics. In this paper we develop an analytic approach to the evaluation of the leading order term for MTLL of a second order DLL, due to both the non-Markovian $1/f^\alpha$ noise and to thermal white noise. The method is applicable to more general systems driven by a wide class of phase noises. The keys to the solution of this exit problem are the construction of a series of higher order Markovian processes that converge to the non-Markovian $1/f^\alpha$ noise and the asymptotic solution to a multidimensional elliptic boundary value problem that the mean first passage time (MFPT) satisfies.

Numerical simulation of GNSS code tracking loops using Euler-Maruyama method

The Euler-Maruyama (EM) method for the numerical integration of stochastic differential equations is applied to simulate tracking loops for Global Navigation Satellite System (GNSS) signals. Use of a large step size and two-point pseudorandom numbers allow for computationally efficient simulation of statistics such as the mean time to lose lock (MTLL). To demonstrate this method, non-coherent delay-lock loops are simulated using the EM method. The MTLL computed from an ensemble of 50 sample paths is compared to a numerical integration of the Fokker-Plank equation. The dependence of computational time and error on step size is evaluated.

Optimal design of an all-digital chip timing recovery loop for direct-sequence spread-spectrum systems

Noncoherent digital delay lock loops (DDLL) are suited for chip timing synchronisation in band-limited direct-sequence spread-spectrum (DSSS) demodulators. The diffusion approximation and the singular perturbation method are used in this paper to calculate the mean time to lose lock (MTLL) of the DDLL. Loop bandwidth optimisation for first order loop with severe Doppler is presented. A simple design rule for the loop bandwidth and a systematic approach for the loop threshold calculation are presented. Copyright © 2005 AEIT.

Performance Analysis of Noncoherent Digital Delay Locked Loops for Direct Sequence Spread Spectrum Systems With Doppler Shift and Quantized Adaptation

The noncoherent second-order digital delay locked loop (DLL) with the presence of Doppler shift is investigated. The loop performance such as lock-in range, transient response, mean time-to-lose lock (MTLL), and mean square tracking error (MSE) are analyzed. The analysis is unique in two respects. First, MTLL and MSE are evaluated more accurately than by previous methods. Second, the impact of quantized adaptation on the loop performance is examined for digital DLL that was neglected previously. Numerical results show that: 1) the quantized adaptation may significantly alter the loop behaviors, including the lock-in range, transient responses, MTLL, and MSE; and 2) the traditional analysis based on Gaussian approximation may result in a large error in performance evaluation when quantized adaptation is taken into account.

Pseudonoise code tracking loop for a CDMA system with imperfect power control

AbstractIn this paper, performance of a pseudonoise (PN) code tracking loop is analysed and simulated for a direct‐sequence/code‐division‐multiple‐access (DS/CDMA) system with imperfect power control in a multipath fading channel. A non‐coherent first‐order delay‐locked loop (DLL) is considered as a PN code tracking loop. Power control error is modelled as a log‐normally distributed random variable. The multipath fading channel is modelled as a two‐ray Rayleigh fading model that is typically applied to land mobile communication environments. The tracking performance of DLL is evaluated in terms of tracking jitter and mean‐time‐to‐lose‐lock (MTLL). From the simulation results, it is shown that for smaller discriminator offset, tracking jitter performance is improved while MTLL performance is degraded. It is shown that large power control error and heavy shadowing substantially degrade the PN tracking performance. Therefore, an accurate power control scheme is very essential to compensate for fading and shadowing for a DS/CDMA system. The extension of analysis to higher‐order loop models is very straightforward. The analysis in this paper can be applied to design the PN code tracking loop for a DS/CDMA system. Copyright © 2001 John Wiley & Sons, Ltd.

A DS-CDMA tracking mode receiver with joint channel/delay estimation and MMSE detection

A tracking mode receiver for asynchronous direct-sequence CDMA is presented based on the extended Kalman filter (EKF). The EKF jointly estimates the delays and multipath coefficients of the received CDMA waveform, and provides a modified minimum mean-square error (MMSE) estimate of the user data (MMSE-EKF). In order to obtain a practical algorithm, each user signal is tracked individually, with the remaining users modeled as colored Gaussian noise. However, the EKFs are coupled through the multiple access interference (MAI) covariance estimates. In order to obtain meaningful performance measures, approximate worst-case undesired user delays that minimize the desired user SNR and delay estimation Cramer-Rao bound are obtained. It is shown that such worst-case delays can be efficiently computed using the alternating maximization (A-M) algorithm. The resulting bit error rate (BER) performance of the MMSE-EKF tracking receiver is evaluated through a combination of simulation and analysis. The mean-time to lose lock (MTTLL) for a genie-aided EKF delay estimator is also obtained using the A-M computed delays.

Half-sine and triangular despreading chip waveforms for coherent delay-locked tracking in DS/SS systems

The performance of a coherent delay-locked tracking scheme for direct-sequence/spread-spectrum systems using half-sine or triangular chip waveforms for early and late despreading sequences is analyzed. The effect of band-limiting on the received signals is considered. Mean time to lose lock (MTLL) and root mean square (rms) tracking error of the delay-locked loop (DLL) are compared with that of a conventional DLL which uses rectangular chip despreading waveforms. Linear and nonlinear (based on the renewal process approach) analyses are employed to evaluate the performance of the DLL. Results show that the use of either the half-sine or triangular chip waveform reduces the rms tracking error and increases the MTLL considerably when the early-late spacing is approximately between 0.7-1.3 chip times. The results apply in particular to the commonly used DLL using one chip early-late spacing. Computer simulation for band-limited signals confirms the analytical results. The use of these despreading chip waveforms also reduces tracking offset in multipath environments.

The Generalized Delay-Locked Loop

The delay-locked loop (DLL) is a synchronization device that is widely used for PN-code tracking in spread spectrum systems. The error detector characteristic (S-curve) of the DLL has a major impact on the performance. Using more than two correlators will extend the tracking range of the S-curve. The Generalized DLL (GenDLL) theory provides a concept to analyze a large class of DLL configurations including the classical DLL. The focus of the performance criteria is on tracking jitter and the mean time to lose lock (MTLL). It is shown that the MTLL can be considerably improved by using extended S-curves. However, the tracking jitter is increased by additional correlators. The tradeoff between the two criteria is explained. With the GenDLL theory loop configurations can be designed having both low tracking jitter and high loop robustness against loss of lock.

Performance of digital code tracking loops for direct-sequence spread-spectrum signals in mobile radio channels

The performance of first- and second-order non-coherent digital delay lock loops (DDLL) for direct-sequence spread-spectrum (DS-SS) signals is investigated in the mobile radio environment. The mobile radio channel is first characterized by Rayleigh fading and Doppler shift. A closed-form expression for the timing error transition probability density function of the Chapman-Kolmogorov (C-K) equation is proposed. The probability density function of the steady-state timing error for the first- and second-order DDLL is obtained by solving the C-K equation numerically, and the results are confirmed by computer simulations. Furthermore, the mean time to lose lock (MTLL) of the first-order loop is evaluated, and some numerical results and simulation results are reported. Finally, the steady-state timing error and MTLL of the first-order loop for DS-SS signals in the log-normal fading environment are also presented, and the results are compared with those of Rayleigh and AWGN channels.

A Novel EKF-Based Recovery in DS Scheme for DS/CDMA Systems Tracking Code Delay

Classical delay-lock loops (DLL) have beenwidely considered for code synchronization purposes inDS/CDMA systems, although they have not been devised foroperation when channel fading is present. This paper describes a new code synchronizationscheme based on a previously proposed extended Kalmanfilter (EKF) approach. The scheme proposed in this paperis able to operate under low signal-to-interference ratios (SIR), usual at the receiver input incellular CDMA mobile environments, and it outperformsthe behavior of previously proposed EKF-based schemes,which failed in such environments. Performance results under realistic mobile environment conditionsare shown in terms of the mean time to lose lock (MTLL)and the tracking error variancest2 for a wide range ofSIR values and under Rayleigh fading. Moreover, the Cramer-Rao lower boundonst2 is also computed inorder to validate the results obtained viasimulations