  Programmable radio environments parametrized by reconfigurable intelligent
surfaces (RISs) are emerging as a new wireless communications paradigm, but
currently used channel models for the design and analysis of signal-processing
algorithms cannot include fading in a manner that is faithful to the underlying
wave physics. To overcome this roadblock, we introduce a physics-based
end-to-end model of RIS-parametrized wireless channels with adjustable fading
(coined PhysFad) which is based on a first-principles coupled-dipole formalism.
PhysFad naturally incorporates the notions of space and causality, dispersion
(i.e., frequency selectivity) and the intertwinement of each RIS element's
phase and amplitude response, as well as any arising mutual coupling effects
including long-range mesoscopic correlations. PhysFad offers the to-date
missing tuning knob for adjustable fading. We thoroughly characterize PhysFad
and demonstrate its capabilities for a prototypical problem of RIS-enabled
over-the-air channel equalization in rich-scattering wireless communications.
We also share a user-friendly version of our code to help the community
transition towards physics-based models with adjustable fading.
