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 of n users wishing to establish pairwise independent communications at fixed wavelength inside a two-dimensional domain of size 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 radicn, so the per-user information capacity must follow an inverse square-root of n law. 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.

A technique for array diagnosis using a small number of measured data acquired by a near-field system is proposed. The technique, inspired by some recent results in the field of compressed sensing, requires the preliminary measurement of a failure-free reference array. The linear system relating the difference between the field measured using the reference array and the field radiated by the array under test, and the difference between the coefficients of the reference and of the AUT array, is solved using a proper regularization procedure. Numerical examples confirm that the technique gives satisfactory results in terms of failure detection with a reduction in the number of data of two orders of magnitudes compared to standard back-propagation technique and of one order of magnitude compared to the number of elements of the array, provided that the number of fault elements is small. This result is relevant in practical applications, since the high cost of large array diagnosis in near-field facilities is mainly caused by the time required for the data acquisition. Accordingly, the technique is particularly suitable for routine testing of arrays.

The aim of this paper is to investigate the relationship between the effective number of degrees of freedom (ENDF) of a multiple input multiple output (MIMO) channel and the number of degrees of freedom (NDF) of the field. In particular, the NDF of the field represents an upperbound for the ENDF of a MIMO channel. Consequently, the evaluation of the maximum ENDF can be carried out by adopting the literature on the NDF based on the spatial bandlimitation properties of the field. This approach allows a simple and intuitive explanation of the maximum ENDF in a MIMO channel based on a geometrical interpretation of the spatial channel in terms of (spatial) Nyquist intervals.

Some connections are described between electromagnetic theory and information theory, identifying some unavoidable limitations imposed by the laws of electromagnetism to communication systems. Starting from this result, the role of the degrees of freedom of the field in radiating systems is investigated. Different classes of antennas use the available degrees of freedom in different ways. In particular, a multiple-input multiple-output antenna is a radiating system conveying statistically independent information on more than one degree of freedom of the field. Applications of the theory to antenna synthesis and antenna characterization in complex environments are shown.

The matrix method for array diagnosis is based on the reconstruction of the excitation from measured near-field data by solving the linear system relating the excitation coefficients to the field at the measurement points. In this paper the matrix method is applied to the diagnosis of element failures in high-performance conformal array radar. The results confirm the usefulness of this technique in the cases wherein the standard backward propagation technique cannot be applied.

The fast diagnosis of antenna arrays from a small number of far-field measurements is addressed. With the a priori knowledge of the failure-free array radiation pattern, it is possible to reformulate the diagnosis problem such as only the faulty elements or the localized field differences have to be retrieved. Efficient and readily available sparse recovery algorithms can then be applied to identify the failures from a small number of measurements compared to standard diagnosis techniques and hence speed up the diagnosis. More specifically, three regularization procedures namely the minimization of the ℓ ₁ , total variation (TV), and the mixed ℓ ₁ /ℓ ₂ norm are used to solve the ill-posed array diagnosis problems. These approaches are compared to two standard fault identification techniques: the back-propagation algorithm (BPA) and the matrix inversion method for the diagnosis from simulated and measured data. The simulation of a 10 × 10 waveguide array in realistic conditions of noise and taking into account the potential scaling factor between two measurements is first presented. Then, a reflectarray composed of 193 cells with metallic strips to emulate phase failures is considered. Both numerical and experimental results confirm the effectiveness of the sparse recovery algorithms and the importance of prior information on the source.