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

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 χ 2 3 to χ 2 2 when the threshold level increases. The excursion area associated with excess energy exhibits a chi-cubed (χ 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 nonmonotonically 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.

Excess and Deficiency of Extreme Multidimensional Random Fields

“…As in [1], all intensities will be normalized by the Cartesian mean value U α = 2σ 2 Xα with α = x, y or z, where σ Xα is the standard deviation of the in-phase or quadrature component of the Cartesian circular complex electric or magnetic field X α = X α + jX α . For notational simplicity, such normalized quantities are denoted with a prime, i.e.,…”

“…II and III for definitions of other symbols). Unlike in [1], sample values are here considered regardless of their mutual correlation. Consequently, the height h ± is that for any sample point, not just the maximum height of an excursion.…”

Excursions and Excess of Power in Stochastic Fields

“…Furthermore, an analytic expression for the mean and standard deviation of the time between failures (TBF) is obtained as with a demonstrated agreement with experimental values obtained in a mode-stirred reverberation chamber (Figure 1(a)). The theory is further extended to obtain the probability distribution of the effective power for narrow-and wideband random fields in a dynamic environment that fluctuates at a relative rate (modulation index)  (Figure 1(b)) [1].The results form the basis for an analysis of the excess power and energy [2].…”