The Role of Losses in the Definition of the Overmoded Condition for Reverberation Chambers and Their Statistics

Multiple-Source Time-Reversal Transmissions in Random Media

“…6, where an estimate of the variability of the TRT is shown. This quantity spans values going from 1.1 to 1.7; the lower value is close to what is expected for an ideal diffuse-field configuration, related to Rayleigh fading in wireless communications [17], [41], while the higher value is a measure that field propagation is less complex than expected, with a reduced number of degrees of freedom [39]. Moreover, ς 2 W = 1 implies that the underlying field cannot be described as a Gaussian process, and therefore neither as a Rayleigh propagation.…”

“…In this respect, they provide a natural setting for testing our theory; 2) reverberation chambers often come with mechanical field stirrers, intended to modify the boundary conditions for waves propagating through them. A stirrer comes in handy here, as a simple way of generating a large number of random configurations, i.e., an ensemble of media sharing the same statistical properties; 3) it was found in [39] that the variability of the field within a reverberation chamber is far from being a constant value, and can be expected to take rapidly changing values in the lower-frequency range. This property is here interesting as it allows testing our predictions against different values of ς 2 W , i.e., varying random-field statistics, depending on the central frequency of operation; by the same token, spatial coherence is also expected to be a function of frequency [40], so that our predictions can be tested against a whole range of values ofμ r .…”

A statistics-based definition of the overmoded condition for reverberation chambers

“…The sum in (1) is taken over the set M of modes that are effectively excited at the working frequency. A proper justification for this model has been provided in [4]. Rather than attempting to apply (1) in a deterministic way, we will regard all of these modal quantities as random ones, with statistical properties dictated (or suggested) by their physical properties.…”

“…As opposed to this hypothesis, by computing the first two moments of W (r, f ) and employing the previously introduced assumptions on the statistics of the modal quantities should allow to check under what conditions the ideal behavior is actually met. The procedure for this calculation has been presented in details in [4], and leads to the following standardized variance…”

“…Acoustics, too, tends to consider the idea of a threshold frequency [3], often referred to as Lowest Usable Frequency (LUF) in EMC. In a recent paper [4], we have proposed such a model, establishing a direct link between the physics of an RC and the statistical properties of the field it supports. In this paper we recall the most important steps and assumptions that have led to this result, and show how it can explain another phenomenon with an unsatisfying description, that of local statistical non-compliancy of field-related quantities.…”