Curve-fitting means the determination of the set of parameters that best fit the input data set as expressed by a given function that is usually non-linear. The paper addresses the curve fitting of Debye and Cole–Cole models to a dielectric permittivity spectrum. The success of a nonlinear curve fit heavily depends on the choice of the algorithm and how close the starting point is to the solution. For these reasons, two different algorithms, the Levenberg–Marquardt and the Variable Projection algorithms, were used for constrained optimization and compared, with particular reference to robustness with respect to the choice of the starting point of the reconstruction procedure. The dielectric spectrum of blood plasma with different glucose concentrations is taken as reference data and a Monte Carlo analysis was conducted to evaluate accuracy and precision in the two methods provided as the distance of the initial parameters from the true value’s changes. In general, both algorithms with constraints on the parameters provide good results for practical situations, although the Variable Projection Algorithm has a greater computational burden for large data sets.

The characterization of dielectric properties of blood–glucose (or similar) solutions is a tricky and critical element in the design, simulation, evaluation, and prototyping of microwave sensors for non-invasive glucose monitoring. Unfortunately, the extensive literature on dielectric properties of biological tissues—blood–glucose solutions in particular—is sometimes contradictory. The use of different materials, different frequency ranges, different glucose ranges, ad hoc assumptions, simplifications not always justified, different measurement techniques, different tissue models, different fitting algorithms often lead to divergent results and conclusions. This is confusing for those who do bibliographic research on the subject and are looking for experimental data to use in their projects and simulations. Therefore, we systematically reviewed, organized and presented the main knowledge available in the literature about blood–glucose models, to help researchers by providing them relevant information in one place. The systematic review of literature is conducted by applying the well-known and proven Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) protocol, a trustworthy method for establishing the published state of the art of any given topic. After screening, ten models are selected and their main characteristics are summarized. The proposed research questions about the common trends in the results, the current gaps and the future directions of research are addressed. The main outcomes are the absence of any reference model shared by the scientific community and the need to deepen the physical and mathematical modeling of dielectric properties of biological tissues.

This paper addresses the nonlinear inverse problem of estimating the parameters of the Cole–Cole model used to describe the behavior of the complex permittivity of blood samples. Such a model provides an efficient and accurate representation of biological tissues in the entire frequency band considered and reduces the complexity of the experimental data to a few parameters. In this way, it is possible to extract a “synthetic view” of the dielectric properties of tissues in such a way that more information on the glucose concentration can be derived, in addition to the resonance peak or phase shift. In order to perform the fitting of the Cole–Cole model, two different algorithms were used and compared: the Levenberg–Marquardt and the variable projection algorithms. Synthetic data present in the literature were used to evaluate the performances obtainable with these methods. In particular, Monte Carlo analysis was used in order to evaluate the accuracy and the precision that these two methods provide in the process of estimating the parameters involved, with respect to the starting points of the parameters. The results obtained showed that the variable projection algorithm always outperformed the Levenberg–Marquardt one, although the former has a greater computational burden than the latter.

One-dimensional (1D) inverse profiling aims to reconstruct the dielectric profile of 1D scatterers from the scattered field data. While the problem can be significantly simplified within a linearized framework (albeit at the cost of obvious performance limitations), the solution remains challenging due to the inherent ill-posedness of the problem, which is related to the “filtering” introduced by the linear scattering operator. To improve reconstruction accuracy, a host medium with known inhomogeneities can be exploited. Such a medium enriches the scattering environment by introducing additional reflections and scattering, which alters the properties of the scattering operator, resulting, in general, in less severe filtering. In this study, we investigate the effect of a perfect reflecting plane on the 1D linear inverse profiling problem using multi-frequency data. While this scenario has previously been explored through somewhat qualitative studies, we focus on the mathematical features of the involved scattering operator via its singular value decomposition (SVD). In particular, we derive an analytical estimation of the singular system, which in turn allows us to identify the influence of the configuration parameters on the achievable performance. In more detail, the point-spread function (PSF) can be analytically determined and linked to the configuration parameters. Results obtained by using a truncated-SVD regularized inversion scheme show that the reflecting plane doubles the band, with respect to the homogeneous host medium case, of the band-pass filtering that the unknown undergoes during the reconstruction process. Moreover, the presence of the reflecting plane facilitates the reconstruction of the continuous component (mean value) of the unknown dielectric profile as well. Overall, the inclusion of a reflecting plane enables the stable reconstruction of a broader class of dielectric profiles, improving both the resolution and the accuracy of the inverse profiling process.

This paper presents a novel technique for the diagnosis of faulty elements in phased array antennas. By exploiting the inherent steering diversity of phased arrays, the proposed approach overcomes the limitations imposed by truncation errors in the standard near-field Back-Transformation Method (BTM). Specifically, by reorganizing the spectra associated with each steering direction into a unified domain and leveraging data redundancy, the method effectively denoises the measurements and recovers a reliable bandwidth over the entire visible domain. Finally, an extensive Monte Carlo numerical analysis demonstrates the feasibility and enhanced accuracy of the proposed technique, highlighting its capability to achieve a high probability of detection with respect to the classical single-view approach.