Detection of weak signals against the background of artificial noise fields scattered by an inhomogeneous medium. I. Gaussian approximation

We consider an optimal procedure for weak signal detection against the background of scattered artificial noise fields within the framework of a Gaussian approximation. We focus on the specific problems of detection and adaptive recovery of the primary wave field at the inputs of a multichannel detector. Antiaircraft Command High School, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 9, pp. 1177–1194, September, 1998.     

Detection of weak useful signals on the background of noise in atomic absorption spectroscopy

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 56, No. 3, pp. 467–473, March, 1992.     

Detection of an ultra-wideband quasi radio signal against background random noise

We perform synthesis and analysis of the maximum-likelihood detector of an ultra-wideband quasi radio signal whose duration may amount to several periods or even a fraction of a period of harmonic oscillation with unknown amplitude and phase. Characteristics of the classical quadrature detector on receipt of the ultra-wideband quasi radio signal are found. Applicability conditions of the model of a narrow-band radio signal for solving the detection problem to specified accuracy are formulated.     

混沌噪声背景下微弱脉冲信号的检测及恢复

构建了一种在混沌噪声背景下检测并恢复微弱脉冲信号的模型.首先,基于混沌信号的短期可预测性及其对微小扰动的敏感性,对观测信号进行相空间重构、建立局域线性自回归模型进行单步预测,得到预测误差,并利用假设检验方法从预测误差中检测观测信号中是否含有微弱脉冲信号.然后,对微弱脉冲信号建立单点跳跃模型,并融合局域线性自回归模型,构成双局域线性(DLL)模型,以极小化DLL模型的均方预测误差为目标进行优化,采用向后拟合算法估计模型的参数,并最终恢复出混沌噪声背景下的微弱脉冲信号.仿真实验结果表明本文所建的模型能够有效地检测并恢复出混沌噪声背景中的微弱脉冲信号.     

Propagation of the two-frequency coherence function in an inhomogeneous background random medium

The spatial and temporal structures of time-dependent signals can be appreciably affected by random changes of the parameters of the medium characteristic of almost all geophysical environments. The dispersive properties of random media cause distortions in the propagating signal, particularly in pulse broadening and time delay. When there is also spatial variation of the background refractive index, the observer can be accessed by a number of background rays. In order to compute the pulse characteristics along each separate ray, there is a need to know the behaviour of the two-frequency mutual coherence function. In this work, we formulate the equation of the two-frequency mutual coherence function along a curved background ray trajectory. To solve this equation, a recently developed reference-wave method is applied. This method is based on embedding the problem into a higher dimensional space and is accompanied by the introduction of additional coordinates. Choosing a proper transform of the extended coordinate system allows us to emphasize 'fast' and 'slow' varying coordinates which are consequently normalized to the scales specific to a given type of problem. Such scaling usually reveals the important expansion parameters defined as ratios of the characteristic scales and allows us to present the proper ordering of terms in the desired equation. The performance of the main order solution is demonstrated for the homogeneous background case when the transverse structure function of the medium can be approximated by a quadratic term.     

Noisy one-dimensional maps near a crisis. II. General uncorrelated weak noise

The escape rate for one-dimensional noisy maps near a crisis is investigated. A previously introduced perturbation theory is extended to very general kinds of weak uncorrelated noise, including multiplicative white noise as a special case. For single-humped maps near the boundary crisis at fully developed chaos an asymptotically exact scaling law for the rate is derived. It predicts that transient chaos is stabilized by basically any noise of appropriate strength provided the maximum of the map is of sufficiently large order. A simple heuristic explanation of this effect is given. The escape rate is discussed in detail for noise distributions of Lévy, dichotomous, and exponential type. In the latter case, the rate is dominated by an exponentially leading Arrhenius factor in the deep precritical regime. However, the preexponential factor may still depend more strongly than any power law on the noise strength.     

Energy detection of partially polarized radio signals against the background of Gaussian noise

We propose a structural diagram of the energy receiver of partially polarized radio signals. Analytical expressions for characteristics of the energy detection of partially polarized radio signals against the background of Gaussian noise are obtained. The behavior of these characteristics in various cases is analyzed.     

Detecting and filtering a flow of different pulsed signals against the noise background

We consider the problem of separate detection and filtration of a flow of pulsed signals. We assume that statistically independent pulsed signals of different shape and random amplitude appear randomly against the background of noise. An algorithm for estimation of the detection probability of each signal is obtained. Recurrent expressions for thea posteriori probability density of each signal are found. The results of numerical simulation of the proposed algorithms of signal processing are presented. Lobachevsky State University of Nizhny Novgorod Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 1, pp. 92–100, January, 1999.     

Detection of an ultra-wideband quasi-radio signal with unknown arrival time against the background of white noise

We synthesize and analyze the maximum-likely detector of an ultra-wideband quasi-radio signal whose duration can be several periods or even a part of the period of harmonic oscillation with unknown amplitude, phase, and arrival time. Characteristics of the classical quadrature detector during reception of an ultra-wideband quasi-radio signal are found. The results of statistical simulation of detection algorithms are presented.     

Energy detection of radio signals against the background of Nongaussian noise with unknown intensity

We find a distribution of the decision statistic of an adaptive energy detector with training. Expressions for the probabilities of false alarm and correct detection are obtained.     

Characteristics of the energy detection of unknown radio signals against the background of Likhter noise

We analyze operation of the energy detector in the case of a non-Gaussian noise background. Analytical expressions for the probabilities of correct detection and false alarm of the energy detector receiving unknown signals against the background of Likhter noise are obtained. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 10, pp. 889–898, October 2008.     

The evolution of polarization in an inhomogeneous birefringert,optically active medium

This note presents a method giving the change of polarization of an e.m. wave propagating in an inhomogeneous medium which is birefringent and optically active. The method has proved useful in a problem where the medium is a plasma with a magnetic field: it can be applied to other cases of interest, e.g. liquid crystals, as is here briefly discussed.     

Crossing resonance of wave fields in a medium with an inhomogeneous coupling parameter

The dynamic susceptibilities (Green’s functions) of the system of two coupled wave fields of different physical natures in a medium with an arbitrary relation between the mean value ? and rms fluctuation Δ? of the coupling parameter have been examined. The self-consistent approximation involving all diagrams with noncrossing correlation lines has been developed for the case where the initial Green’s function of the homogeneous medium describes the system of coupled wave fields. The analysis has been performed for spin and elastic waves. Expressions have been obtained for the diagonal elements G _mm and G _uu of the matrix Green’s function, which describe spin and elastic waves in the case of magnetic and elastic excitations, and for the off-diagonal elements G _mu and G _um , which describe these waves in the case of cross excitation. Change in the forms of these elements has been numerically studied for the case of one-dimensional inhomogeneities with an increase in Δ? and with a decrease in ? under the condition that the sum of the squares of these quantities is conserved: two peaks in the frequency dependences of imaginary parts of G _mm and G _uu are broadened and then joined into one broad peak; a fine structure appears in the form of narrow resonance at the vertex of the Green’s function of one wave field and narrow antiresonance at the vertex of the Green’s function of the other field; peaks of the fine structure are broadened and then disappear with an increase in the correlation wavenumber of the inhomogeneities of the coupling parameter; and the amplitudes of the off-diagonal elements vanish in the limit ? → 0.     

Image formation in CARS and SRS: effect of an inhomogeneous nonresonant background medium

We investigate the role of a spatially inhomogenous nonresonant background medium on several Raman-based imaging modalities. In particular, we consider a small resonant bead submerged in a spatially heterogeneous nonresonant χ(3) background. Using detailed 3D electrodynamic simulations, we compare coherent anti-Stokes Raman scattering (CARS), frequency-modulated CARS, amplitude-modulated stimulated Raman scattering (SRS), and frequency-modulated SRS. We find that only FM-SRS is background-free.     

Recovering the acoustic Green's function from ambient noise cross correlation in an inhomogeneous moving medium

We study long-range correlation of diffuse acoustic noise fields in an arbitrary inhomogeneous, moving fluid. The flow reversal theorem is used to show that the cross-correlation function of ambient noise provides an estimate of a combination of the Green's functions corresponding to sound propagation in opposite directions between the two receivers. Measurements of the noise cross correlation allow one to quantify flow-induced acoustic nonreciprocity and evaluate both spatially averaged flow velocity and sound speed between the two points.