Elliptic Stochastic Fields in Reverberation Chambers

Abstract

A theoretical and experimental characterization of complex elliptic random fields inside a reverberation chamber is performed. The real and imaginary parts of the pseudovariance and noncircularity quotient are found to be simultaneously nonzero and to have comparable magnitudes, in general. The I/Q statistical anisotropy and correlation have a spectral envelope that is robust under varying experimental conditions and decays at −5 dB per decade, on average. Expansion coefficients for a circular random base field are extracted for a widely linear field representation. Joint, marginal and conditional probability density functions are derived for both the unconditional and the directional energy and for the phase. An iterative stochastic algorithm is developed for the systematic extraction of the sampling distributions. These distributions provide increased model accuracy and improved agreement with empirical distributions, provided the constellation of sample stir data conforms to a symmetric complex elliptic distribution.

Statistical Anisotropy in Imperfect Electromagnetic Reverberation

“…Per component, however, ideal circular Gaussianity of its inphase and quadrature contributions was assumed [21]. The methods and results can be extended to more general elliptic fields and their components, along the lines of [2], [17], and to include inter-Cartesian correlation or higher-order interdependence. Departures from circularity lead to increased kurtosis of the marginal pdfs, including a heavier tail of the pdf.…”

“…Near or below the LUF [1], this assumption may be unsustainable. In that case, a characterization based on sampling circular, elliptic [17], or even more general [18] joint pdfs for E i and E j may be appropriate. A complete generalization involves additional parameters of the distribution, each requiring individual estimation (e.g., using Bayesian inference), and the characterization of the dependence structure between E i and E j , e.g., using copulas [18].…”