Measurement Method for Evaluating the Probability Distribution of the Quality Factor of Mode-Stirred Reverberation Chambers

An original experimental method for determining the empirical probability distribution function (PDF) of the quality factor (Q) of a mode-stirred reverberation chamber is presented. Spectral averaging of S-parameters across a relatively narrow frequency interval at a single pair of locations for the transmitting and receiving antennas is applied to estimate the stored and dissipated energy in the cavity, avoiding the need for spatial scanning to obtain spatial volume or surface averages. The effective number of simultaneously excited cavity modes per stir state, M, can be estimated by fitting the empirical distribution to the parametrized theoretical distribution. The measured results support a previously developed theoretical model for the PDF of Q and show that spectral averaging over a bandwidth as small as a few hundred kHz is sufficient to obtain accurate results.Comment: submitted for publicatio

Probability distribution of the coherence bandwidth of a reverberation chamber

A theoretical probability distribution and associated statistics for the coherence bandwidth of an ideal mode-stirred reverberation chamber are derived. The stochastic model assumes and exploits the ergodicity of a dynamic wave chaotic cavity by expressing the coherence bandwidth in terms of the random effective excitation bandwidth and by replacing spatial averaging of transmitter-receiver locations with stir (ensemble) averaging. The theoretical model is validated through comparison with the empirical cumulative distribution function (cdf) extracted from measured S-parameter data from a real chamber, and through simulation using analytical calculations for a fictitious wall-stirred chamber. The results are particularly relevant to the improvement of transmission quality and uncertainty quantification of wireless multipath propagation

Sampling Distributions of Random Electromagnetic Fields in Mesoscopic or Dynamical Systems

We derive the sampling probability density function (pdf) of an ideal localized random electromagnetic field, its amplitude and intensity in an electromagnetic environment that is quasi-statically time-varying statistically homogeneous or static statistically inhomogeneous. The results allow for the estimation of field statistics and confidence intervals when a single spatial or temporal stochastic process produces randomization of the field. Results for both coherent and incoherent detection techniques are derived, for Cartesian, planar and full-vectorial fields. We show that the functional form of the sampling pdf depends on whether the random variable is dimensioned (e.g., the sampled electric field proper) or is expressed in dimensionless standardized or normalized form (e.g., the sampled electric field divided by its sampled standard deviation). For dimensioned quantities, the electric field, its amplitude and intensity exhibit different types of Bessel $K$ sampling pdfs, which differ significantly from the asymptotic Gauss normal and $\chi^{(2)}_{2p}$ ensemble pdfs when $\nu$ is relatively small. By contrast, for the corresponding standardized quantities, Student $t$, Fisher-Snedecor $F$ and root-$F$ sampling pdfs are obtained that exhibit heavier tails than comparable Bessel $K$ pdfs. Statistical uncertainties obtained from classical small-sample theory for dimensionless quantities are shown to be overestimated compared to dimensioned quantities. Differences in the sampling pdfs arising from de-normalization versus de-standardization are obtained.Comment: 12 pages, 15 figures, accepted for publication in Phys. Rev. E, minor typos correcte

Average Linear and Angular Momentum and Power of Random Fields Near a Perfectly Conducting Boundary

The effect of a perfectly conducting planar boundary on the average linear momentum (LM), angular momentum (AM), and their power of a time-harmonic statistically isotropic random field is analyzed. These averages are purely imaginary, and their magnitude decreases in a damped oscillatory manner with distance from the boundary. At discrete quasi-periodic distances and frequencies, the average LM and AM attain their free-space value. Implications for the optimal placement or tuning of power and field sensors are analyzed. Conservation of the flux of the mean LM and AM with respect to the difference of the average electric and magnetic energies and the radiation stresses via the Maxwell stress dyadic is demonstrated. The second-order spatial derivatives of differential radiation stress can be directly linked to the electromagnetic energy imbalance. Analytical results are supported by Monte Carlo simulation results. As an application, performance-based estimates for the working volume of a reverberation chamber are obtained. In the context of multiphysics compatibility, mechanical self-stirred reverberation is proposed as an exploitation of electromagnetic stress