Principal component analysis for efficient characterization of stochastic electromagnetic fields

Abstract

AbstractThe propagation of stochastic electromagnetic fields can be accurately modeled using the auto‐ and cross‐correlation spectra of the field components. In this work, we introduce the framework of principal component analysis for reducing the computational cost of handling stochastic electromagnetic fields described by correlation matrices. We consider noisy electromagnetic fields originating from stationary random processes with Gaussian probability distribution. The amount of data obtained by 2‐dimensional near‐field measurements and by determining the auto‐ and cross‐correlation information of electromagnetic interference can become burdensome for further processing even for problems of moderate size. For obtaining the correlation data, 2 measurement probes have to scan a defined grid of measurement points. For each pair of points, the spatial correlations need to be calculated, and hence, the data obtained scales quadratically with the number of sampling points. To reduce the amount of data, we project the given data obtained by measurement or simulation onto directions of maximum variation, the so called principal components, and keep only those principal components which contribute most to the total variance. In this way, the memory demand for storage and further computation of stochastic electromagnetic fields can be reduced significantly.