Rayleigh-Jeans-Clarke Model for Wireless Noise in a Resonant Cavity: Scalar Case.

A resonant electromagnetic cavity - effectively the interior of a copper box - constitutes a highly favorable propagation environment for MIMO communications. A fundamental limitation on wireless communication within the box is thermal noise. Under conditions of thermal equilibrium the Equipartition Theorem of classical statistical mechanics states that every orthogonal normal mode has an independent random amplitude such that the expected energies of the modes are equal and proportional to absolute temperature. Collectively the randomly excited modes constitute a space-time stochastic process, stationary in time but non-stationary in space because of boundary conditions. As the linear dimensions of the box grow relative to a wavelength the process is asymptotically stationary. At each temporal frequency the wavenumber spectral density is identical to that of the Clarke model - a superposition of random plane waves having no preferred direction of propagation. At a single point in space the spectral density is proportional to the square of temporal frequency - the Rayleigh-Jeans spectrum. We call our space-time noise model Rayleigh-Jeans-Clarke (RJC).