Excess Power, Energy and Intensity of Stochastic Fields in Quasi-Static and Dynamic Environments

TL;DR

This paper analyzes the statistical behavior of excess power, energy, and intensity in stochastic electromagnetic fields under quasi-static and dynamic conditions, providing theoretical models and validated results for high-threshold excursions.

Contribution

It introduces new probabilistic models for excess field characteristics in both quasi-static and dynamic environments, including distributional forms and dependence on modulation parameters.

Findings

Excess intensity distribution transitions from chi-squared to chi-squared with fewer degrees of freedom as threshold increases.

Excursion area for excess energy follows a chi-cubed distribution at high thresholds.

Closed-form expressions for mean and standard deviation of dynamic excess power are validated by simulations.

Abstract

The excess power, energy and intensity of a random electromagnetic field above a high threshold level are characterized based on a Slepian--Kac model for upcrossings. For quasi-static fields, the probability distribution of the excess intensity in its regression approximation evolves from $\chi^2_3$ to $\chi^2_2$ when the threshold level increases. The excursion area associated with excess energy exhibits a chi-cubed ($\chi^3_2$) distribution above asymptotically high thresholds, where excursions are parabolic. For dynamic fields, the dependence of the electrical and environmental modulations of the excess power on the hybrid modulation index and threshold level are established. The normalized effective power relative to the quasi-static power increases non-monotonically when this index increases. The mean and standard deviation of the dynamic excess power are obtained in closed form and validated by Monte Carlo simulation.