Sampling of stochastic electromagnetic fields

Abstract

Stochastic electromagnetic fields can be described by the auto-and cross correlation spectra of the electric and magnetic field values at pairs of points in space. In this work the characterization of noisy electromagnetic fields by sampling the field values in pairs of sampling points is discussed. Sampling of the electric or magnetic field values in all pairs of a set of sampling points yields the correlation matrix of the field samples. If the near-field in a surface of reference enclosing the stochastic field sources is sampled and characterized by its correlation matrix the field radiated in the space outside the surface of reference can be calculated and described by the field correlation spectra. Depending on the number of statistically independent field sources the eigenvalue decomposition of the correlation matrix yields a compact description of the measured EM noise field. I. INTRODUCTIONNumerical values of noise amplitudes cannot be specified for stochastic signals. For numerical modeling of noisy circuits one has to deal with energy and power spectra. Correlation matrix based methods have been developed for the numerical simulation of noisy linear circuits [1]- [4]. Stochastic electromagnetic fields can be described by the auto-and cross correlation spectra of the electric and magnetic field values at pairs of points in space. In this work the characterization of noisy electromagnetic fields by sampling the field values in pairs of sampling points is discussed. Sampling of the electric or magnetic field values in all pairs of a set of sampling points yields the correlation matrix of the field samples. If the nearfield in a surface of reference enclosing the stochastic field sources is sampled and characterized by its correlation matrix the field radiated in the space outside the surface of reference can be calculated and described by the field correlation spectra. Depending on the number of statistically independent field sources the eigenvalue decomposition of the correlation matrix yields a compact description of the measured EM noise field.According to the uniqueness theorem the field in a sourcefree region outside a volume V enclosing electromagnetic radiation sources is determined in a unique way, if the tangential component of either the electric field intensity or the magnetic field intensity is known on the boundary surface ∂V of the volume V [5]. Therefore based on either the tangential electric field or the tangential magnetic field sampled on the boundary ∂V of the volume V enclosing the field sources allows to compute the electromagnetic field in the region outside V .

Neural Model for Far-Field 1D Localization of Mobile Stochastic EM Sources with Partially Correlated Radiation

“…The movement scenario that is used in this paper may be described by the azimuth plane and sources disposition in one linear direction (1D movement scenario), while the dipole directions are perpendicular to the azimuth plane. If the total number of sources is S, and if fed current of dipoles can be described by the vector I = [I1, I2, …, IS]), the mutual correlation of stochastic sources radiation is described by the correlation matrix [12,13]:…”

“…Today, a high attention is paid for interference sources that have stochastic radiation nature [12,13], so spatial location estimation of this kind of sources is of crucial interest. In [9][10][11] the neural models for 1D DoA [9,10] and 2D DoA estimation [11] and spatial position estimation of stochastic radiation sources are presented, developed for sources whose radiation is mutually uncorrelated.…”

An Artificial Neural Network Model for Eficient Estimation of the Number of Mobile Stochastic EM Sources in a Space Sector

“…The model of stochastic radiation sources in the distant zone represents radiation of a uniform linear antenna array of N elements located at the distance d (Figure 1). The degree of correlation between the current supply element antenna array that is described by the vector I=[I 1 , I 2 , …, I N ]), is defined by the correlation matrix c I (ω) [3,4]:…”

“…In this sense, the procedures based on spatial filtering, signal antenna arrays and design characteristics of radiation using adaptive antenna arrays now receive special attention [1,2]. The above-mentioned processes show some of the key techniques that implement such procedures based on DoA estimation techniques [1.2], and the spatial localization of various sources of interference as deterministic and stochastic nature of radiation [3,4]. MUSIC (Multiple Signal User Classification) algorithm [2], and its modifications are so far the best known and most commonly used superresolution algorithms for DOA estimation.…”

Modeling of Noisy EM Field Propagation Using Correlation Information

“…Stochastic electromagnetic fields with Gaussian probability distribution can be described completely by the autocorrelation spectrum of each field variable and the cross-correlation spectra of field variables at distinct points of observation [13]- [19]. Characterization of a stochastic electromagnetic field requires the sampling of the EM field in pairs of observation points and the determination of the cross-correlation functions for all pairs of field samples.…”