Interferences in Phase-Locked Loops

An analysis of the behavior of a second-order phase-locked loop is presented when an unwanted signal is added to the useful signal. Both signals are sinusoidal and unmodulated, and the analysis is made in the absence of additive noise. When the loop remains locked on the useful signal, a parasitic signal exists at the phase detector output. This signal produces a parasitic phase modulation of the VCO and a static phase error in the loop. The parasitic signal amplitude, the parasitic phase modulation index, and the static phase error are calculated. A necessary condition for the loop to remain in lock is derived. When the loop is initially unlocked, locking can occur either on the useful signal or on the unwanted signal, depending on the amplitude ratio and the frequency difference of the two signals. A formula allowing one to compute the pull-in time is obtained. When the loop locks on the useful signal, acquisition can be slower or faster than in the absence of an unwanted signal. The same phenomenon is observed when the loop locks on the unwanted signal.     

Performance analysis of GPS carrier phase observable

The accuracy analysis of Global Positioning System (GPS) carrier phase observable measured by a digital GPS receiver is presented. A digital phase-locked loop (DPLL) is modeled to extract the carrier phase of the received signal after a pseudorandom noise (PRN) code synchronization system despreads the received PRN coded signal. Based on phase noise characteristics of the input signal, the following performance of the first, second, and third-order DPLLs is analyzed mathematically: (1) loop stability and transient process; (2) steady-state probability density function (pdf), mean and variance of phase tracking error; (3) carrier phase acquisition performance; and (4) mean time to the first cycle-slipping. The theoretical analysis is verified by Monte Carlo computer simulations. The analysis of the dependency of the phase input noise and receiver design parameters provides with an important reference in designing the carrier phase synchronization system for high accuracy GPS positioning     

Modeling and analysis for the GPS pseudo-range observable

In this paper, a digital system for the Global Positioning System (GPS) pseudo-range observable is modeled and analyzed theoretically. The observable is measured in a GPS receiver by accurately tracking the pseudorandom noise (PRN) code phase of the input GPS signal using a digital energy detector and a digital delay lock loop (DDLL). The following issues are presented: (1) mathematical modeling of the digital PRN code acquisition and tracking system, (2) the closed-form expression derivation for the detection and false-alarm probabilities of the acquisition process and for the variance of code phase tracking error, and (3) the linear and nonlinear performance analysis of the DDLL for optimizing the receiver structures and parameters with tradeoff between the tracking errors due to receiver dynamics and due to input noise     

Imperfect Carrier Recovery Effect on Filtered PSK Signals

Coherent demodulation of a PSK signal requires the generation of a local carrier phase reference. Methods are given to determine the detection loss caused by noisy phase recovery and its use in the coherent detection of filtered BPSK and QPSK signals. It is assumed that the phase noise can have a static part and a random component with a Tikhonov-type distribution. The static part is mostly due to offset frequency tracking of the PLL used to recover the carrier, while the random component is due to thermal noise present in the carrier recovery loop and is also due to the random nature of the phase modulation. It is shown that the probability of error of BPSK and QPSK can be expressed as a finite sum of a set of strictly alternating converging series when the number of ISI terms is finite. Upper and lower bounds on the probability of error have been derived when this number becomes infinite and we show how this error rate can be computed with any desired accuracy. Numerical results are presented for various values of static error and phase noise variance when the transmit and receive filters are 4-pole Butterworth filters. For filtered PSK signals and for a bit error rate of 10-6, our results show that the additional degradation in presentday receiver systems due to imperfect carrier recovery can be less than 0.1 dB for BPSK and less than 1 dB for QPSK.     

A Delay-Lock Loop for Tracking Pulsed-Envelope Signals

A sampled-data delay-lock loop (SDDLL) which tracks the arrival time of a biphase modulated, pulsed-envelope RF signal is described. A pseudo-noise (PN) code generator is used as the modulation source as in conventional delay-lock loop tracking devices. Time base shifting of the loop's local clock is performed by digital means. The technique permits the use of a stable-frequency clock to maintain accurate timing between timing correction instants. An expression is derived for the standard deviation of the timing error due to additive Gaussian noise at the SDDLL input. Experimental results are then given which include the effects of control-system quantization error on timing jitter. Assuming that the errors due to input noise and quantized timing corrections are independent and additive, the theoretical and experimental results agree to within approximately one decibel.     

On the Acquisition Time for an Apollo Ranging Code

An Apollo ranging system is considered whose phase reference is obtained by a phase-locked loop for bit synchronization. The bit phase reference is noisy, and the error probability for the ranging code is shown to depend on the input signal energy per bit to noise density ratio. The procedure of computing the acquisition time for the ranging code is then presented and the acquisition time for a lunar ranging code is plotted versus the input signal-to-noise density ratio.     

GPS小波去噪的误差方差建模技术与试验

如何消除GPS观测数据的噪声以提高定位精度并估算消噪信号的误差方差对工程测量具有重要意义。在介绍小波多尺度分析的基础上,推导了在小波多尺度分析巾平滑信号误差的理论方差模型。并通过实际的GPS单点静态定位试验给予验证。试验结果表明,该方法在有效消除噪声的同时,计算得到的各尺度平滑信号的误差方差与理论方差模型基本一致。     

带通限幅器对锁相环噪声性能的影响

锁相环路中,在鉴相器前加上AGC（自动增益控制）,可以使环路性能在输入信噪比发生变化时保持稳定,带通限幅器也可以起到类似作用。尽管有一些文章对限幅器的性能作了研究,但是在PLL（锁相环）闭环条件下,鲜有文章分析其对环路噪声性能的影响。因此,文章以基本PLL环路的数学模型为基础,推导出PLL中分别加入相干AGC和带通限幅器后新的环路数学模型,以一阶PLL为例,计算和比较不同控制方式下环路相位误差均方值的变化,最后说明应当根据飞行任务的不同选择对环路更有利的控制方式。     

基于反馈的振荡器注频锁相研究

注频锁相技术是非线性有源阵列天线的关键技术之一,论文提出了一种带反馈的振荡器注频锁相闭环结构。与开环结构相比,该电路能够提高锁频带宽,可用来构成非线性有源天线阵。仿真结果表明该电路相噪低,具有更宽的锁相带宽。     

Third-Order Loop Filter Design for Acceleration-Rate Tracking

A perfect third-order loop filter design that can be implemented as a digital filter is obtained which minimizes the noiseless steady-state acceleration rate (jerk) error for a fixed loop noise bandwidth. Simulations were performed to obtain transient responses of the third-order loop plus a sample fourth-order loop under a jerk input. The results enable one to obtain a loop design that minimizes the loop noise bandwidth required for a given steady-state jerk error and thus obtain better noise jitter performance.     

Phase-Lock Loop Jump Phenomenon in the Presence of Two Signals

Jump phenomena are known to exist in many non-linear systems [I], [2], [3]. The non-linear analysis presented in this paper explains and predicts the conditions for the jump phenomenon that is observed in a phase-locked loop (PLL) preceded by an automatic gain control (AGC). The jump phenomenon occurs when the frequency separation AM of two sinusoids at the input to the AGC is greater than the bandwidth B of the linearized PLL. If the loop is initially locked to the stronger signal, the weaker signal will frequency-modulate the PLL voltage-controlled oscillator (VCO) with a modulation frequency AI. The amplitude S2 of the weaker signal al can be increased until it becomes greater than the amplitude Si of the signal being tracked, without causing the loop to lose lock; i. e., the VCO continues to track the original signal. However, if the ratio of the amplitudes S2 S1 = R is increased above some critical value RC > 1, the loop will lose lock on the original signal, and jump to track the interfering signal. If the frequency separation is at least twice the PLL bandwidth, a good approximation for this critical ratio is Rc ? ?w/B.     

基于提前停止判决的编码软信息辅助载波同步

 针对目前编码辅助载波同步算法中复杂度较高、延时大的问题,提出了引入辅助停止判决机制的编码辅助载波同步算法。在现有的编码辅助载波同步结构基础上,该算法能对环路信噪比(SNR)进行实时判定,在环路SNR满足限定条件后提前停止编码辅助载波同步迭代,而不影响译码性能。采用新的相位估计方式估计含相位噪声的载波相位,提升了该条件下的环路信噪比。仿真采用码率为1/2的低密度奇偶校验(LDPC)码作为编码方式,结果表明:在误码率为10^-5时,该算法减少了约50%的编码辅助载波同步迭代次数;在含相位噪声的信号条件下,与理想解调译码相比,性能损失不超过0.15 dB。     

Linear Minimum Variance Estimation with Complex Phase Errors

The linear minimum variance estimator of a random signal, received multiplied by a complex Gaussian phase error and added to random noise, is investigated. The results apply to the propagation of images through the turbulent atmosphere, fading channels, and synthetic-aperture radar. Among others, a result is that the multiplicative error can be replaced by an additive error, usually white. The best signal modulation is found in two important special cases.     

Uniform Sampling Analysis of a Hybrid Phase-Locked Loop with a Sample-and-Hold Phase Detector

Phase-locked-loop (PLL) bit synchronizers often employ integrate-and-dump type phase detectors that provide phase error information only at discrete points in time. Usually these phase detectors are followed by sample-and-hold circuits to produce a stairstep error voltage as the input to a standard analog circuit loop filter. When the loop is configured in this manner, it is referred to as a hybrid PLL. Sampled-data analysis methods (Z transforms) are used to determine the stability and transient response of this loop.     

Noise Dynamics of the Phase-Locked Loop with Signal Clipping

Employing techniques similar to the averaging methods of Krylov and Bogoliubov, an approximate noise analysis of the phase-locked loop with signal clipping is presented. The validity of the method is demonstrated by comparing the stationary probability density function for the phase error, generated by a system simulation, with the derived theoretical results. The latter portion of the paper discusses the relation of the phase-locked loop to Kalman-Bucy filter theory and presents a demodulator design that illustrates the self-adaptive properties attainable in phase-locked loops with signal clipping.     

Carrier-Tracking Loop Performance for Quaternary and Binary PSK Signals

By expressing the open-loop response voltage as a Fourier series in terms of the phase-tracking error and then utilizing a very useful mean-value expression, we assess the performance of loops suited to recovering the carrier of four-phase (quaternary) and two-phase (binary) phase-shift-keyed (QPSK and BPSK) signals. At high signal to noise ratios (SNRs) they perform comparably, but at low SNRs the former's performance deteriorates much more rapidly. The loop's ability to maintain the carrier frequency despite the noise accompanying the PSK signal is measured by the mean and the variance of the oscillator's control voltage. In particular, Spilker's loop for QPSK and the Costas loop for BPSK signals are discussed.     

Now You See It, Now You Don't

The signal enhancement properties of a single-loop delayline integrator (DLI) are derived for operation in the presence of correlated noise. The signal is assumed periodic with a period equal to the delay of the DLI and present only for a finite time interval. The noise is assumed additive, zero mean, statistically independent from the signal, and present for an infinite time. The noise also is assumed covariance stationary with a specified auto correlation function. Enhancement is defined as the ratio of the increase in average signal power to the increase in average noise power due to integration. The results are general in that the enhancement is derived in terms of the autocorrelation coefficients of the input noise. Plots of enhancement versus number of signal observations and feedback gain are shown for uncorrelated and exponentially correlated noise. The plots show graphically the optimum choices of feedback gain and number of signal observations for a specified auto correlation function and signal observation time. When strongly correlated noise, characteristic of 10-GHz backscatter from salt flats at low incidence angles, rather than uncorrelated noise is assumed present at the input of the DLI, an example, using DLI parameters typical of modern airborne radars, shows a degradation in the maximum achievable enhancement of 9 dB.     

Synthesis and Analysis of Tracking Systems with Optimal Acquisition

The behavior of a tracking system during its acquisition phase is studied in the case where the input signal is a frequency step. The tracking system considered is a generalization of a type-II phase-lock loop where the phase detector characteristic is a general function. In order to improve the acquisition characteristics, the natural evolution of the local oscillator is modified by a command signal chosen in order to minimize the acquisition time, on the one hand, and, on the other hand, to maximize the lock-in range and the capture range of the tracking system. The influence of the different parameters (input, damping, natural frequency, pha e characteristic,command signal) on the acquisition of the resulting systems has been précised by means of a theoretical study of the trajectories in the phase plane and by an analog simulation. A simple criterion adopted in order to characterize the acquisition of a system disturbed by noise permits the study of the influence of S/N ratio on acquisition time.     

Effects of CW Interference on Narrow-Band Second-Order Phase-Lock Loops

This paper describes an experimental study of the effect of continuous wave (CW) interference and white noise on a second-order phase-lock loop. The reciprocal of the loop mean-square phase error is used as an index of performance, and the effect of interference levels that do not cause cycle skipping or loss of lock is described in terms of this index. Loop thresholds are determined by measurement of cycle-skipping rates. Stationary or slowly-sweeping CW interference caused a degradation in loop threshold of roughly 3 dB for every 6 dB of interference power above the noise power level. The effective loop signal-to-noise ratio was decreased approximately 1 dB at interference-to-noise power ratios of -3 dB. Interference levels equal to the signal level consistently caused loss of lock, regardless of the loop signal-to-noise ratio.     

Dynamics of the Phase-Locked Loop without a Limiter

The general (nth order) phase-locked loop is analyzed, of which the amplitude is not constant. The input carrier signal is amplitude-modulated by wide-band stationary Gaussian noise, and the signal, superposed with the additive white stationary Gaussian noise, enters the nonlimited phase-locked loop. Under the above assumptions the loop can be shown to constitute an n-dimensional vector Markov process, so that the process satisfies the n-dimensional Fokker-Plank equation. The probability density function depends on the effective loop signal-to-noise ratio and the effective modulation power.