Fundamental Theorems on Controllability in Wave-domain Processing for Holographic MIMO

TL;DR

This paper establishes fundamental controllability theorems for reconfigurable electromagnetic devices in wave-domain processing, crucial for advancing holographic MIMO systems by analyzing geometry, coupling, and degrees of freedom.

Contribution

It introduces necessary and sufficient controllability conditions for passive scatterers in wave processing, a novel theoretical framework for electromagnetic device configuration.

Findings

Derived controllability conditions based on geometry and mutual coupling.

Numerical analysis of element number, size, and directivity effects.

Characterized the interplay between physical parameters and degrees of freedom.

Abstract

Wave-domain processing is an emerging paradigm where signal processing operations are partially shifted from the digital to the electromagnetic (EM) domain. Leveraging reconfigurable EM devices, this approach aims to reduce complexity, energy consumption, and latency in next-generation wireless systems employing holographic MIMO. This paper establishes fundamental theorems on the controllability of generic reconfigurable EM devices, where wave processing is achieved through the dynamic configuration of passive scatterers. Specifically, we derive necessary and sufficient conditions for controllability as a function of geometry and mutual coupling between elements. Finally, we provide a detailed discussion and numerical results characterizing the interplay between the number of elements, physical size, degrees of freedom, and directivity.