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.
Highlights
I N the characterization of dynamic complex electromagnetic (EM) environments based on stochastic methods, first-order probabilistic [1], [2] and second-order spectral [3], [4] density functions are essential tools
Accurate models for the probability density functions (PDFs) are needed for estimating the probability of failure, uncertainty quantification based on propagation of probability, confidence intervals, extreme-value distributions, etc
Statistical field anisotropy of Cartesian components and finite-sample effects have served as useful departures for realistic random fields, the effect of noncircularity on the distribution of field magnitude, power, and phase remains to be investigated generally and systematically, which is the subject of this paper
Summary
I N the characterization of dynamic complex electromagnetic (EM) environments based on stochastic methods, first-order probabilistic [1], [2] and second-order spectral [3], [4] density functions are essential tools. In overmoded conditions, modeled by an angular spectrum of random plane waves, circularity arises are a result of the local incoherent superposition of multiple reflected waves whose range of phase differences is well in excess of 2π. Even an initially linearly polarized CW excitation field (I-component) rapidly tends toward circularity (I/Q balance) at the receiving antenna because of 1) a large number of reflections and 2) path length differences in excess of the wavelength. While a large number of reflections is essential in order to make statistical modeling feasible, differences in path lengths can be limited, resulting in an imperfect mixing (randomization) of the reflected field and a smaller spread among Q- compared to I-fields. In wireless communications, noncircularity arises in certain digital modulation schemes (BPSK, PAM, etc.) Precise knowledge of their statistics is important to optimize the transmission
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