Correlation Of Phase Fluctuations Research Articles

Development of a method for estimating the effect of transformation of the normalized frequency mismatch function of a coherent bundle of radio pulses on the quality of radar frequency resolution

The necessity of studying the influence of the transformation of the frequency mismatch function of a coherent bundle of radio pulses on the quality of solving the radar frequency resolution problem is substantiated. This solution determines the effectiveness of radar observation of high-speed and maneuvering individual and group aerodynamic objects. The method is based on explicit expressions for calculating the normalized frequency mismatch function of a coherent bundle of radio pulses, taking into account its transformation due to the radial motion of high-speed and maneuvering individual and group aerodynamic objects. The estimation of the potential frequency resolution of bundles with different numbers of radio pulses with typical parameters for a coherent pulse radar is carried out. Possible values of frequency resolution under the additive effect of uncorrelated internal noise of the radar receiver and the multiplicative effect of correlated phase fluctuations of the radar signal are estimated. With an insignificant multiplicative effect of correlated phase fluctuations, a twofold increase in the number of radio pulses in a bundle provides an improvement in the frequency resolution (reduction of the width of the normalized frequency mismatch function) by 100 %. With the predominant multiplicative effect of these fluctuations, a twofold increase in the number of radio pulses results in an improvement in the frequency resolution by about 40 %. The developed method is of great theoretical and practical importance for the further development of the radar theory of high-speed and maneuvering individual and group aerodynamic objects.

Development of an optimization method for measuring the Doppler frequency of a packet taking into account the fluctuations of the initial phases of its radio pulses

The necessity of estimating the decrease in the accuracy of measuring the informative parameters of a radar signal in real conditions of its propagation and reflection has been substantiated. The results of the estimation determine the requirements for optimizing this measurement to achieve the required efficiency. A numerical analysis of the decrease in the accuracy of measuring the Doppler frequency of a coherent packet is presented, depending on the statistical characteristics of fluctuations of the initial phases of its radio pulses. Expressions are given for calculating the fluctuation component of the measurement error of radio pulse packet frequency for various coefficients of interpulse correlation of phase fluctuations. An assessment is made of the possibility of increasing the accuracy of Doppler frequency measurement, which can be ensured by statistical optimization of the algorithm for time-frequency processing of a given radar signal by taking into account its phase fluctuations. The conditions for the multiplicative influence of phase fluctuations of radio pulses of the received packet are substantiated, which determine the efficiency of optimization of Doppler frequency measurement. Based on the results of the study, an optimization method for measuring the Doppler frequency of the packet taking into account fluctuations in the initial phases of its radio pulses is proposed. The accuracy of Doppler frequency measurement under the influence of both the internal noise of the radar receiver and the correlated phase fluctuations of its radio pulses is estimated. The efficiency of optimization of measuring the Doppler frequency of the packet is estimated taking into account fluctuations of the initial phases of its radio pulses by means of computer simulation. It is proved that, under the influence of phase fluctuations, the accuracy of Doppler frequency measurement can be increased due to the performed optimization from 1.86 to 6.29 times. This opens the way to improving the existing algorithms for measuring the higher time range derivatives to improve the quality of tracking complex maneuvering aerodynamic objects. This explains the importance and usefulness of the work for the radar theory.

Influence of flicker noise and nonlinearity on the frequency spectrum of spin torque nano-oscillators

The correlation of phase fluctuations in any type of oscillator fundamentally defines its spectral shape. However, in nonlinear oscillators, such as spin torque nano-oscillators, the frequency spectrum can become particularly complex. This is specifically true when not only considering thermal but also colored 1/f flicker noise processes, which are crucial in the context of the oscillator’s long term stability. In this study, we address the frequency spectrum of spin torque oscillators in the regime of large-amplitude steady oscillations experimentally and as well theoretically. We particularly take both thermal and flicker noise into account. We perform a series of measurements of the phase noise and the spectrum on spin torque vortex oscillators, notably varying the measurement time duration. Furthermore, we develop the modelling of thermal and flicker noise in Thiele equation based simulations. We also derive the complete phase variance in the framework of the nonlinear auto-oscillator theory and deduce the actual frequency spectrum. We investigate its dependence on the measurement time duration and compare with the experimental results. Long term stability is important in several of the recent applicative developments of spin torque oscillators. This study brings some insights on how to better address this issue.

THE INFLUENCE OF STATISTICAL CHARACTERISTICS OF THE FLUCTUATIONS OF THE RADIATION SIGNAL INITIAL PHASES ON THE ACCURACY OF THE MEASUREMENT AERODYNAMIC OBJECT RADIAL VELOCITY

The article deals with the estimation of radial velocity when using a coherent packet of radio pulses regarding the case of the presence of correlated fluctuations of the initial phases in the reflected from the aerodynamic object pulses. The subject of the research is the accuracy of measuring the frequency of the received packet for the case of concerted processing without taking into account the phase fluctuations of its radio pulses. The purpose is a numerical analysis of the influence of the statistical characteristics of the fluctuations of the received pack’s initial phases on the decrease in the accuracy of measuring the radial velocity of the aerodynamic object. The task : to estimate the possible values of fluctuation constituent middling quadratic error of measuring of radial speed of aerodynamic object. Consideration is given to the assumption that an additive mixture of deflected signal and uncorrelated Gaussian noise is input to the radar receiver. It is considered that the phase fluctuations of the received packet are distributed according to the normal law with zero mean, and the correlation of phase fluctuations with the increase of the interval between the packet radio pulses decreases according to the alternating law. Methods used: methods of probability theory and mathematical statistics. The following results are obtained: the accuracy of frequency measurement of the pack had been estimated in the presence of correlated phase fluctuations of its radio pulses. Conclusions . The results indicate that for modern radars in the conditions of regular measurement the accuracy of estimating the frequency of the packet of radio pulses is much more influenced by the statistical characteristics of the phase fluctuation than the signal-to-noise ratio. Due to the phase fluctuations of the radio pulses of the received packet, the mean-square error (MSE) of radial velocity measurement of the aerodynamic object is able to exceed the values determined by the requirements for coherent pulse radar.

ANALYSIS OF POSSIBILITIES OF PROVIDING OF NECESSARY EXACTNESS OF MEASURING OF SPATIAL COORDINATES OF AIR OBJECTS IN THE RADIO-LOCATION STATION OF ACCOMPANIMENT WITH PHASE AERIAL BY A GRATE

Modern Phased-Array Antenna (PAA) radars are an effective mean of aerial reconnaissance and provide radar information on aerial objects in a complex environment. The subject of the article is the influence of the inhomogeneities of the troposphere and the earth’s surface on the decrease in the accuracy of measurement of angular coordinates and altitude of air objects in radars with PAA. The purpose of the article is to numerically estimate the possible values of the root mean square error of measuring the angular coordinates and the height of air objects due to the influence of fluctuations of the phase edge of the radar wave. Task : analysis of possible mechanisms of origin and statistical characteristics of correlated phase fluctuations of a radio signal for a model of a signal with random amplitude and initial phase. Methods used : methods of probability theory and mathematical statistics. The following results were obtained . The estimation technique is developed and possible values of the mean-square errors of measurement of angular coordinates and altitude of air objects are obtained, which are caused by the influence of radar signal phase wave front fluctuations for the three-coordinate PAA radar of centimeter range. The above calculation method allows to carry out the numerical estimation of errors of measurement of angular coordinates and object height. Conclusions . This technique can be practically used in assessing the effect of real conditions of propagation and reflection of radar signal on the reduction of the capabilities of modern radars with PAA to perform tasks on purpose.

ПОСТАНОВКА ЗАДАЧІ ОПТИМАЛЬНОГО ВИМІРЮВАННЯ ДАЛЬНОСТІ ДО ЦІЛІ В КОГЕРЕНТНО-ІМПУЛЬСНІЙ РЛС ПРИ ВРАХУВАННІ ФАЗОВИХ СПОТВОРЕНЬ РАДІОЛОКАЦІЙНОГО СИГНАЛУ

У статті розглянуто питання аналізу можливостей забезпечення заданої дальності дії РЛС, здатної здійснювати радіолокаційне спостереження малопомітних, малорозмірних та маневруючих цілей. Обгрунтована доцільність використання когерентної пачки радіоімпульсів для забезпечення необхідної дальності виявлення із заданими показниками якості. Надано порівняльний аналіз можливостей використання поодинокого і пачкового радіосигналів. Доведена необхідність врахування корельованих фазових флуктуацій радіоімпульсів прийнятої пачки при вимірюванні дальності до цілі. Вважається, що фазові флуктуації розподілені за нормальним законом с нульовим середнім, а їх кореляція убуває зі збільшенням інтервалу між радіоімпульсами пачки за експоненціальним або знакозмінним законами. На вхід приймального пристрою РЛС надходять відбиті від цілей сигнали на фоні некорельованого гаусівського шуму. Розгляд проводиться для моделі сигналу з випадковою амплітудою та початковою фазою. Оцінювання часу запізнення радіолокаційного сигналу здійснюється за критерієм максимуму натурального логарифма відношення правдоподібності, усередненого по усім можливим значенням випадкових неінформативних параметрів. В явному вигляді отримано вираз нормованої функції розузгодження когерентної пачки за наявністю фазових флуктуацій її радіоімпульсів. Врахування фазових флуктуацій радіоімпульсів прийнятої пачки при вимірюванні дальності до цілі дозволить покращити ефективність вирішення когерентно-імпульсними РЛС завдань за призначенням.

Hydrodynamic synchronization of colloidal oscillators.

Two colloidal spheres are maintained in oscillation by switching the position of an optical trap when a sphere reaches a limit position, leading to oscillations that are bounded in amplitude but free in phase and period. The interaction between the oscillators is only through the hydrodynamic flow induced by their motion. We prove that in the absence of stochastic noise the antiphase dynamical state is stable, and we show how the period depends on coupling strength. Both features are observed experimentally. As the natural frequencies of the oscillators are made progressively different, the coordination is quickly lost. These results help one to understand the origin of hydrodynamic synchronization and how the dynamics can be tuned. Cilia and flagella are biological systems coupled hydrodynamically, exhibiting dramatic collective motions. We propose that weakly correlated phase fluctuations, with one of the oscillators typically processing the other, are characteristic of hydrodynamically coupled systems in the presence of thermal noise.

Coherent Population Trapping Induced by Phase Modulated andFluctuating Fields

We examine the effects of cross correlated phase fluctuations on thecoherent population trapping (CPT) induced by a pair of phase-modulatedfields with equal modulation frequencies in a three-level Λ system.The maximal coherence of -0.5, which appears when CPT occurs for equalmodulation indices, is preserved in the presence of the criticallycross-correlated fluctuations. Unexpectedly, the non-maximal coherence,which is established when CPT is obtained for different modulation indices, issignificantly enhanced due to the critically cross-correlated fluctuations.

Two-component Bose gas in an optical lattice at single-particle filling

The Bose-Hubbard model of a two-fold degenerate Bose gas is studied in an optical lattice with one particle per site and virtual tunneling to empty and doubly-occupied sites. An effective Hamiltonian for this system is derived within a continued-fraction approach. The ground state of the effective model is studied in mean-field approximation for a modulated optical lattice. A dimerized mean-field state gives a Mott insulator whereas the lattice without modulations develops long-range correlated phase fluctuations due to a Goldstone mode. This result is discussed in comparison with the superfluid and the Mott-insulating state of a single-component hard-core Bose.

On propagation of decametric-decimentric radiowaves under conditions of middle-latitude F-spread

In this paper we analyze the influence of the large-scale inhomogeneous structure of a middlelatitude ionosphere with F-spread on the propagation of decametric-decimetric radiowaves. The phase fluctuations of short waves in the presence of middle-latitude F-spread are considered. A general integral formula for the frequency dispersion of phase fluctuations of short radiowaves during their propagation in a three-dimensional randomly-inhomogeneous ionosphere with an arbitrary electron-density distribution is obtained. For some of the simplest types of ray trajectories we find analytical solutions which allow us to obtain simple estimates of the frequency correlation of phase fluctuations of short radiowaves under conditions of middle-latitude F-spread. The amplitude fluctuations of short radiowaves under conditions of ionospheric F-spread are considered by the example of wave propagation with strong backscattering in a layered randomly inhomogeneous medium. It is shown that the presence of a strongly developed large-scale structure of electron density in a middle-latitude ionosphere with F-spread can cause reflected short-wave signals with relatively large delays and abnormally high fluctuation levels. The fluctuational and quasiregular effects accompanying the transionospheric propagation of metric-decimetric radiowaves are discussed. In particular, it is shown that under conditions of middle-latitude F-spread the inhomogeneous structure of the ionospheric plasma does not have a significant influence on the fluctuational or quasi-regular propagation characteristics of decametric-decimetric radiowaves.

Pulse matching and correlation of phase fluctuations in Lambda systems.

The interaction of a bichromatic quantized field with three-level \ensuremath{\Lambda}-type atoms is analyzed on the basis of c-number Langevin equations. In the presence of ground-state coherence one particular combination of field modes is selectively absorbed leading to a correlation of the output fields. This correlation manifests itself in a matching of Fourier components of the field modes and in a strong reduction of the diffusion of the difference phase. This correlation phenomenon is studied for the case of externally generated coherence as well as for coherence produced by population trapping in conjunction with a nonadiabatic atomic response.

On correlated phase fluctuations in a frequency doubled Nd:YAG laser

We report here observations of correlated frequency fluctuations between the fundamental and the second harmonic of a flash lamp pumped Nd:YAG laser. Also we show that the frequency of the second harmonic can be stabilised using an error signal derived from frequency fluctuations in the second harmonic to control the length of the Nd:YAG cavity, and hence the frequency of the fundamental.

Non-Markovian stochastic jump processes. II. The case of resonance fluorescence.

Strong laser fields, when tuned on resonance to an atomic (molecular) transition, give rise to the well-known triplet of resonance fluorescence. The laser field is normally assumed to be strong and monochromatic, even though the spectrum of real lasers is never a \ensuremath{\delta} function. A standard way to treat laser fluctuations has been to assume a well-defined nominal frequency and a randomly fluctuating phase. Recently we introduced the generalized jump model (GJM) for correlated phase fluctuations, where correlated phase jumps are considered, leading to Markovian as well as non-Markovian stochastic behavior. In the GJM, each phase jump may be correlated to the previous jump, and the degree of correlation, the typical jump size, and the mean time between jumps are the three parameters defining the stochastic character of the laser field. In this paper we apply the GJM model to the case of resonance fluorescence from an atom excited by a stochastic field. The ``standard'' Mollow triplet is obtained in the monochromatic limit of small jumps, and several new predictions are made in the different limits of the stochastic parameters. In the small-jump limit, a new ``field effect'' is predicted. The spectral line shape and the triplet separation deviate from the Mollow predictions for a monochromatic field in a substantial way, giving rise to observable differences.In the highly correlated small-jump limit, which is approximated by the Kubo oscillator model, the previous results are corrected to include nonzero line shifts and extended to the case of non-Lorentzian line shapes. In all regions, even input fields of the same line shape (which would be considered identical in the one-parameter linewidth description) give rise to very different output spectra, justifying the more complete stochastic description. Effective relaxation constants ${\mathrm{\ensuremath{\Gamma}}}_{1}^{\mathrm{*}}$ and ${\mathrm{\ensuremath{\Gamma}}}_{2}^{\mathrm{*}}$ that simplify the description of the spectrum are calculated in all appropriate cases, and ${\mathrm{\ensuremath{\Gamma}}}_{1}^{\mathrm{*}}$ is found to equal the input laser linewidth. In addition to predicting the resonance fluorescence spectra, the present analysis provides a way to extract the stochastic parameters from the nonlinear measurement in those cases where the linear characterization of the input field cannot do it. The analytic work is fully supported by extensive numerical simulations.

Speckle Contrast Variation in the Confocal Scanning Microscope

The speckle contrast variation in the confocal scanning optical microscope (CSOM) as a function of defocus, and the statistical properties of random diffusing objects is studied. It is assumed that the number of scattered contributions is very large, so that the central limit theorem can be applied. The diffuser is modelled as a thin phase screen which introduces Gaussian distributed and Gaussian correlated phase fluctuations. The main results are plotted, discussed and compared with some experimental data.

Investigation of the Correlation of Phase Fluctuations of an Optical Field by a Photoelectric Predetection Interferometer

A two-element photoelectric predetection interferometer has been examined. It was found that for small amplitude fluctuations, the correlation coefficient of the phase fluctuations of an optical field may be determined, in principle, from photoelectron counts. A simplification occurs in the particular case of small phase fluctuations.

Approximation to the Array Signal-Gain Fluctuation Spectrum

It is known that the signal gain of an array of hydrophones fluctuates randomly in time. Several authors have investigated these fluctuations from different viewpoints; most of them determine mean-square array responses assuming correlated phase fluctuations. Since the signal gain varies with time, it should be regarded as a stochastic process. All attempts to find the multidimensional distribution functions of this process assuming Gaussian inputs have failed. It is not difficult, however, to develop an approximation for the power spectrum of the gain fluctuations of the array output in terms of the spectra at the individual hydrophones and the cross spectra between the array elements. Data were taken on the individual elements of an array of five hydrophones and the spectrum of the array gain variations was computed in accordance with the procedure given. This spectrum is compared with the spectrum obtained directly from the fluctuations of the array output. It is hoped that measuring array fluctuations in terms of spectra at individual hydrophones and cross spectra between hydrophones will give some insight into the mechanism causing the fluctuations.

Power Spectrum of Array Signal-Gain Fluctuations

It is known that the signal gain of an array of hydrophones fluctuates randomly in time. Several authors have investigated these fluctuations from different viewpoints; most of them determine meansquare array responses assuming correlated phase fluctuations. Since the signal gain varies with time, it should be regarded as a stochastic process. All attempts to find the multidimensional distribution functions of this process assuming Gaussian inputs have failed. It is not difficult, however, to develop an expression for the power spectrum of the gain fluctuations of the array output in terms of the spectra at the individual hydrophones and the cross spectra between the array elements. Data were taken on the individual elements of an array of five hydrophones and the spectrum of the array-gain variations was computed in accordance with the procedure to be presented. This spectrum is compared with the spectrum obtained directly from the fluctuations of the array output. It is hoped that measuring array fluctuations in terms of cross spectra between the individual hydrophones will give some insight into the mechanism causing the fluctuations. [Work supported by the U. S. Office of Naval Research.]