The introduction of electromagnetic field processing directly at the lowest level of the OSI stack is a potentially disruptive advance in communications systems.The aim of this contribution is to discuss the role of electromagnetic theory in limiting the performance of a communication system using Electromagnetic Processing Devices (EPDs). To give a simple example, a 2-way ”electromagnetic network switch” that implements typical functions of the second layer of the OSI stack directly at the ”Deep Physical Layer” (DPL) level is analyzed in a 2D geometry.

A simple and effective two-step method to detect and localize scattering objects from the measurements of the total electric field, collected at a single frequency on a planar domain, is presented. The first step consists in solving a linear inverse source problem, looking for surface equivalent currents on a plane located between the measurement surface and the objects themselves. Thus, the equivalent currents associated with both the scatterer presence and the background contribution are obtained. In the second step, the support of the equivalent currents associated with the objects is separated from the background by exploiting the low-rank property of the background field. The proposed method does not require information on the source, except for its frequency, and it is easily implementable and entails a low computational burden. Experimental results validate the method.

The problem of determining the number of spatial degrees of freedom (d.o.f.) of the signals carrying information in a wireless network is reduced to the computation of the geometric variation of the environment with respect to the cut through which the information must flow. Physically, this has an appealing interpretation in terms of the diversity induced on the cut by the possible richness of the scattering environment. Mathematically, this variation is expressed as an integral along the cut, which we call cut-set integral, and whose scaling order is evaluated exactly in the case of planar networks embedded in arbitrary three-dimensional (3-D) environments. Presented results shed some new light on the problem of computing the capacity of wireless networks, showing a fundamental limitation imposed by the size of the cut through which the information must flow. In an attempt to remove what may appear as apparent inconsistencies with previous literature, we also discuss how our upper bounds relate to corresponding lower bounds obtained using the techniques of multihop, hierarchical cooperation, and interference alignment.

It is shown using first physical principles and without relying on stochastic fading channel models, that the number of spatial degrees of freedom available in planar wireless networks embedded in a three-dimensional propagation environment is limited by the spatial size of the cut that divides the environment into two parts. Specifically, in the case of propagation inside a cylinder of height h and base area n, containing n communicating source-destination node pairs, the number of available channels is at most proportional to h√n and hence, as the number of nodes increases, the per-user information capacity must follow an inverse square-root of n law.

It is shown that the capacity scaling of wireless networks is subject to a fundamental limitation which is independent of power attenuation and fading models. It is a degrees of freedom limitation which is due to the laws of physics. By distributing uniformly an order ofnusers wishing to establish pairwise independent communications at fixed wavelength inside a two-dimensional domain of size of the order ofn, there are an order ofncommunication requests originating from the central half of the domain to its outer half. Physics dictates that the number of independent information channels across these two regions is only of the order ofradicn, so the per-user information capacity must follow an inverse square-root ofnlaw. This result shows that information-theoretic limits of wireless communication problems can be rigorously obtained without relying on stochastic fading channel models, but studying their physical geometric structure.

It is shown that the capacity scaling of three- dimensional wireless networks is subject to a degrees of freedom limitation which is due to the propagation laws of electromagnetic waves. By distributing uniformly an order of n users wishing to establish pairwise independent communications at fixed wavelength lambda inside a domain of (normalized) volume of the order of n, there are an order of n communication requests originating from the central half of the domain to its outer half. Physics dictates that the number of independent information channels across these two regions is only of the order of n2/3, so the peruser information capacity must follow an inverse-cube root of n law.