Statistics of a coherent lidar signal in a turbulent atmosphere

Absolute and conditional statistical properties of a pulse coherent Doppler lidar signal in a turbulent atmosphere are studied. Upon coherent receiving of optical fields scattered by a large number of particles, the lidar signal is shown to be a nonstationary non-Gaussian random process with Gaussian conditional statistical characteristics. The appearance of non-Gaussian properties of the signal is caused by correlation of turbulent fluctuations of the wind velocity field within the scattering volume. For the considered signal model, which corresponds to the single scattering approximation and is a sum of a large number of random variables, the central limit theorem is found to be untrue due to the statistical dependence of particles’ positions in a turbulent atmosphere. The results of numerical calculations show that, for a homogeneous and isotropic turbulence, the behavior of the signal statistics significantly depends on the size of the scattering volume and on the state of atmospheric turbulence. A Gaussian statistics is observed at small heights; with an increase in height, the non-Gaussian component becomes considerable in fluctuations of the lidar signal.     

Estimation of acoustic attentuation in liver using one megabyte of data and the zero-crossings technique

Statistical fluctuations due to scatter-induced frequency variations in reflected acoustic pulses are a major problem when estimating acoustic attenuation. Disagreement exists in the ultrasound community as to how much data is sufficient to overcome these statistical fluctuations. The range of attenuation values for normal livers and a tissue equivalent phantom, using 1 megabyte of data per liver and the zero-crossings technique, was investigated. The significance of statistical fluctuations and their effects on attenuation are discussed.     

临界堆中子增殖系数测量统计涨落数值模拟

建立了临界堆中子增殖系数(参数)计算模型,采用闪烁体加光电倍增管组成的电流型探测器对参数进行测量。采用构造理想函数加统计涨落偏差的方式,利用数值模拟方法,研究了统计涨落对参数测量结果的影响。结果表明:测量信号统计涨落会影响参数测量精度;考虑统计涨落影响,为使参数满足要求,需要使探测器入射粒子数达到一定数量;针对不同测量时间,入射粒子起始强度需要满足不同要求;当起始强度不能满足要求时,可以采用增加测量时间;指数信号带随机涨落时,较大的求值区间能有效减弱统计涨落的影响。     

Phase Fluctuations of Radio Waves in the Saturated-Scintillation Regime

We consider the problem of phase fluctuations of radio waves behind a strong phase screen and in an optically thick layer. It is shown that the phase-fluctuation distribution of the received radiation at an observation point located in the saturated-scintillation area behind a turbulent phase screen is almost identical to the normal distribution of phase fluctuations of the wave on the screen. Amplitude and phase fluctuations of the received radiation are uncorrelated both for single-point and space-diversity reception if, in the latter case, the distance between the observation points exceeds the spatial scale of the diffraction component of the complex field of the received signal. Expressions for the mean square and the structural function of phase fluctuations of radio waves behind a turbulent phase screen in the saturated-scintillation regime are obtained. It is shown that the structural function of phase fluctuations in the diffraction component of the scattered field, which is exactly the function that forms saturated scintillations of the received radiation, almost coincides with the structural function of phase fluctuations on the screen. It is also shown that the diffraction effects can be neglected and the geometric-optical approximation should be used when calculating statistical characteristics of phase fluctuations of a plane wave in the saturated-scintillation area in an optically thick layer with large-scale refractive-index irregularities. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 4, pp. 275–282, April 2005     

Correlation characteristics of optical coherence tomography images of turbid media with statistically inhomogeneous optical parameters

Noisy structure of optical coherence tomography (OCT) images of turbid medium contains information about spatial variations of its optical parameters. We propose analytical model of statistical characteristics of OCT signal fluctuations from turbid medium with spatially inhomogeneous coefficients of absorption and backscattering. Analytically predicted correlation characteristics of OCT signal from spatially inhomogeneous medium are in good agreement with the results of correlation analysis of OCT images of different biological tissues. The proposed model can be efficiently applied for quantitative evaluation of statistical properties of absorption and backscattering fluctuations basing on correlation characteristics of OCT images.     

Weight vector fluctuations in adaptive antenna arrays with nonlinear function in a feedback loop

We present the results of statistical analysis of adaptive antenna arrays with nonlinear function in the feedback loop, which are adjusted by an algorithm for recurrent inversion of a sample estimate of the input-signal correlation matrix with allowance for the weight-coefficient fluctuations. Using the perturbation-theory methods in the first (Born) approximation, we obtain expressions for the correlation function and power of the output signal of an adaptive antenna array and a formula for the covariance matrix of the weight-coefficient vector. The weight-coefficient fluctuations are shown to result in signal distortions at the antenna-array output and appearance of additional terms in the statistical characteristics of the antenna array. These terms are second-order infinitesimals with respect to adaptation coefficient. Fluctuations are first-order infinitesimals and, thus, are much greater in an antenna array without nonlinear function in the feedback loop. It is also shown that the weight-vector fluctuations are anisotropic, i.e., they are absent in the constraint direction, minimal in the interference direction, and maximal in all other directions. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 2, pp. 164–172, February 2006.     

Deterministic patterns of noise and the control of chaos

Real systems in physics, chemistry and biology are always subject to fluctuations that change qualitatively the systems' dynamics. In particular, rare large fluctuations are responsible for the nucleation at phase transitions, mutations in DNA sequences, protein transport in cells and failure of electronic devices. In many cases of practical interest systems are away from thermal equilibrium, and understanding the fluctuations in such systems is one of the fundamental problems of statistical physics that has challenged researchers for decades. Recent progress in the solution of this problem is closely related to the emerging understanding of patterns of deterministic trajectories underlying non-equilibrium fluctuations. These trajectories correspond to the Hamilton equations of motion written for the asymptotic solution of the Fokker - Planck equation and were often thought of as a mere mathematical abstraction. The possibility of quantitative experiments could not be entertained until the appropriate statistical quantity (prehistory probability distribution) had been introduced. In this paper it is shown how such trajectories can be measured experimentally in a number of systems and how the knowledge of these trajectories can be used to solve long standing problems in the theory of fluctuations and in the control theory.     

Exact results of statistical analysis of multichannel adaptive systems with continuous gradient algorithms

We obtained some exact expressions for the power of the output signal of adaptive systems with continuous gradient adjustment algorithms. It is shown that fluctuations of weight coefficients result in a decrease in the signal power at the adaptive-system output as compared with the output-signal power in the absence of fluctuations of the weight coefficients. The “overcompensation” phenomenon is explained by the presence of a non-Gaussian statistical relation between the weight- coefficient and input-signal vectors. N. I. Lobachevskii State University, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 9, pp. 914–921, September, 1999.     

Sound fluctuations caused by internal waves in a shallow sea

Estimates are presented for the fluctuations of the parameters of low-frequency sound fields in shallow-water regions of the Barents Sea, in the presence of seasonal internal gravity waves. The objective of the experiments is to reveal the main mechanisms that govern the sound fluctuations and their statistical parameters on paths of moderate lengths (50–60 to 100–120 km). Another objective is to determine the features of the sound interaction with internal waves for the sound speed profile of the summer—autumn type for which the water stratification is most pronounced. As the probing signals, continuous tonal ones produced by bottommoored sources at the frequencies about 100 and 300 Hz are used along with the 1/3-octave noise signals with the central frequency 1000 Hz, which are generated by a source deployed from a vessel. For the signal reception, both fixed bottom-moored hydrophones and a vertical chain of hydrophones are used, the chain also being deployed from the vessel. The water temperature, the salinity, and the thermocline displacements are monitored with standard hydrographic sensors. The following main results are presented: the estimate of the degree of correlation between the sound fluctuations and the parameters of the water layer, the comparison of the fluctuations in the signal amplitude envelope with the data obtained in other regions, and the estimate of the statistical parameters of the signal amplitude fluctuations, including their dependence on the path length. One more result consists in the proof of the wave nature of the interaction of sound and internal waves, which manifests itself in a strong dependence of the sound interaction with internal waves of discrete frequencies on the frequency of the probing signal and on the angle at which these wave beams intersect. An attempt is made to explain the observed phenomena by the synchronism in the interacting sound and gravity waves. The data obtained can be used to analyze and compare the fluctuations of the sound fields in the ocean, especially in shallow-water regions.     

The statistical characteristics of adaptive antenna arrays when processing discrete signals with correlated readouts

The most important statistical characteristics of adaptive antenna arrays are determined. These are the mean value and covariance matrix of the vector of the weighting factors, and the powers of the fluctuations of the weighting factors and of the output signal of the array. It is found that under steady-state operating conditions the fluctuations of the vector of the weighting factors lead to a bias of its mean value for an adaptive antenna array without constraints, but the mean value of the weighting vector of an array with constraints and of an array operating using the criterion of the minimum root mean square error is not biased. It is shown that the effect of fluctuations of the weighting vector on the output signal of an adaptive antenna array may be different and is determined by the value of the correlation coefficient between the input-signal read-outs.Nizhegorod State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 12, pp. 1532–1545, December, 1994.     

Monitoring statistical magnetic fluctuations on the nanometer scale

Statistical fluctuations of the magnetization are measured on the nanometer scale. As the experimental monitor we use the characteristic photoluminescence signal of a single electron-hole pair confined in one magnetic semiconductor quantum dot, which sensitively depends on the alignment of the magnetic ion spins. Quantitative access to statistical magnetic fluctuations is obtained by analyzing the linewidth broadening of the single dot emission. Our all-optical technique allows us to address a magnetic moment of only approximately equal 100 micro(B) and to resolve statistical changes on the order of a few micro(B).     

Some effects of partial averaging of signal fluctuations in a random medium

The concept of partial averaging of signal fluctuations in a stretched turbulent medium is considered. Such uncontrollable averaging over time, frequency, or space arises from the mutual influence of signals scattered by irregularities of different scales (or different scattering layers) on fluctuations of the received signal intensity. The scintillation index of a partially averaged field is defined for the averaging action of a radiation source of finite angular dimensions. The proposed concept and obtained results may be useful in many applications as a development of the statistical theory of wave propagation in random media.Scientific-Research Institute of Radiophysics. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 6, pp. 754–762, June, 1994.     

Phase Fluctuations of Radio Waves Behind a Turbulent Phase Screen

We consider the problem of phase fluctuations of radio waves behind a turbulent optically thin irregular layer (phase screen). Expressions are derived for the main statistical characteristics of phase fluctuations in the case where modern direct methods based on measurements of the complex field of the received radiation are used to obtain these characteristics. Regimes of weak and saturated scintillations of signals are analyzed. It is shown that in the case of weak scintillations, such statistical characteristics of phase fluctuations of the received radiation as the structure function and the fluctuation spectra for single-point and interference reception almost coincide with those at the screen output. In the regime of saturated scintillations, we obtain an information on the structure function of phase fluctuations of the received radiation in the cases of relatively large and small spatial separations of the reception points. The results obtained allow one to correctly analyze the data of modern experiments on remote sensing of the near-Earth and space plasmas with the help of direct phase methods for environmental diagnostics. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 7, pp. 563–573, July 2005.     

Radar equations in the radio wave backscattering problem

We present a method for finding the relation between the singly scattered signal and the Fourier spectrum of dielectric permittivity fluctuations of a medium with regard to the scattering volume which is controlled by the antenna pattern and is not small. Using this method, we found a radar equation which relates the temporal Fourier spectrum of the scattered signal and the spatio-temporal spectrum of permittivity fluctuations. We also obtained a statistical radar equation to relate the statistically averaged spectral power of the scattered signal and the spectral density of permittivity fluctuations without the conventional assumption that the spatial correlation radius of irregularities is small compared with the Fresnel radius. Institute of Solar-Terrestrial Physics, Siberian Branch of the Russian Academy of Sciences, Irkutsk, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 43, No. 6, pp. 520–544, June, 2000.     

Spectral correlation characteristics of an adaptive Antenna array tuned by the Hebb algorithm with allowance for the weight-vector fluctuations

In this paper, we present the results of statistical analysis of the characteristics of an adaptive antenna array tuned by the Hebb algorithm with allowance for the weight-vector fluctuations in the case where signals with different levels of autocorrelatedness of the input-signal readouts arrive at the antenna array. Expressions for the correlation function of the output signal and the power spectral density at the antenna-array output are obtained. It is shown that fluctuations lead to distortions of the output signal of the adaptive antenna array and appearance of additional terms in the formulas for these characteristics.     

The Influence of Weight-Vector Fluctuations on Statistical Properties of an Adaptive Antenna Array with a Fast Recurrent Tuning Algorithm

We present the results of statistical analysis of an adaptive antenna array tuned in accordance with the fast recurrent algorithm of inversion of a sample estimate of the correlation matrix with allowance for weight-vector fluctuations. Using the perturbation-theory methods in the first (Born) approximation, we obtain the spectral-correlation characteristics of the output signal of an antenna array. Fluctuations are shown to result in signal distortions at the output of an adaptive antenna array. Comparing the obtained expressions with the corresponding formulas for the antenna array with a gradient tuning algorithm, we see that for equal convergence rates of the above algorithms, the output-signal distortions are more pronounced for the fast recurrent algorithm. It is also shown that the weight-vector fluctuations are anisotropic for the fast algorithm, i.e., they are absent in the restriction direction, minimal in the interference direction, and maximal in all other directions. The weight-vector fluctuations in an adaptive antenna array with a gradient tuning algorithm are isotropic in the restriction subspace, i.e., they are the same in all directions and are equal in magnitude to fluctuations in the interference direction for the fast algorithm. The weight-vector fluctuations are also absent in the restriction direction for the gradient tuning algorithm.     

Statistical properties of speckle recorded on film

The statistical properties of speckle recorded on photographic film are studied theoretically and experimentally. When saturation and threshold effects are negligible and the gamma is equal to one, the probability distribution function of spatially integrated film transmittance has the form of a double exponential. Experimental results confirm that under those conditions, the density fluctuations caused by the speckle are independent of the signal.     

诱惑态量子密钥分配系统中统计涨落的研究

针对实用的量子密钥分配(QKD)系统是基于强衰减的弱激光脉冲作为单光子源, 光子数分束攻击极大限制了通信双方在非理想条件下QKD的传输距离和密钥生成率,采用大数定律对诱惑态协议中单光子的计数率、单光子增益和误码率分别进行统计涨落分析, 利用双诱惑态比较了1310 nm和1550 nm条件下,编码脉冲的长度为(N = 10⁶-N = 10¹²)实际QKD协议中密钥的生成率与安全传输距离之间的关系、安全传输距离随编码长度的变化的关系, 得出脉冲编码长度增大到N = 10¹²时,密钥的最大安全传输距离为135 km.     

Statistical Properties of a Ring Laser with Injected Signal and Backscattering

The Statistical Properties of a homogeneously broadened ring laser with an injected signal are investigated and the normalized two-mode intensity auto-and cross-correlation functions are calculated by a full saturation laser theory with backscattering.The theoretical predictions are in good agreement with the experimental measurements.Further inverstigation reveals that the backscattering can reduce the fluctuations in the system while the full saturation effect plays a major role when the laser is operated above threshold.It is also quite important to notice that the injected signal can drive the weak mode from incoherent light to coherent light.     

非平衡涨落问题的微观唯象分析理论(Ⅰ)——一种新的广义不可逆热力学理论与热涨落中涨落—耗散表示式的非平衡修正

本文给出非平衡涨落问题的微观唯象分析理论——非平衡涨落的统计学描述理论。该理论的基础是广义非平衡熵与描述涨落几率的爱因斯坦表示式的推广。通过计算求得刚体热传导中比能与热通量的非平衡涨落的二阶矩。导出对热涨落的通用涨落-耗散表示式的非平衡修正,同时发现该修正相当于固体电介质中的光子热输运与金属中电子热输运的数值修正。