The concept of spectral relative entropy rate is introduced for jointly stationary Gaussian processes. Using classical information-theoretic results, we establish a remarkable connection between time and spectral domain relative entropy rates. This naturally leads to a new spectral estimation technique where a multivariate version of the Itakura-Saito distance is employed. It may be viewed as an extension of the approach, called THREE, introduced by Byrnes, Georgiou, and Lindquist in 2000 which, in turn, followed in the footsteps of the Burg-Jaynes Maximum Entropy Method. Spectral estimation is here recast in the form of a constrained spectrum approximation problem where the distance is equal to the processes relative entropy rate. The corresponding solution entails a complexity upper bound which improves on the one so far available in the multichannel framework. Indeed, it is equal to the one featured by THREE in the scalar case. The solution is computed via a globally convergent matricial Newton-type algorithm. Simulations suggest the effectiveness of the new technique in tackling multivariate spectral estimation tasks, especially in the case of short data records.

The rise of Industry 4.0 and data-intensive manufacturing makes Advanced Process Control (APC) applications more relevant than ever for process/production optimization, related costs reduction, and increased efficiency. One of the most important APC technologies is Virtual Metrology (VM). VM aims at exploiting information already available in the process/system under exam, to estimate quantities that are costly or impossible to measure. Machine Learning approaches are the foremost choice to design VM solutions. A serious drawback of traditional Machine Learning methodologies is that they require a features extraction phase that generally limits the scalability and performance of VM solutions. Particularly, in presence of multi-dimensional data, the feature extraction process is based on heuristic approaches that may capture features with poor predictive power. In this work, we exploit modern Deep Learning-based technologies that are able to automatically extract highly informative features from the data, providing more accurate and scalable VM solutions. In particular, we exploit Deep Learning architectures developed in the realm of Computer Vision to model data that have both spatial and time evolution. The proposed methodology is tested on a real industrial dataset related to Etching, one of the most important Semiconductor Manufacturing processes. The dataset at hand contains Optical Emission Spectroscopy data and it is paradigmatic of the feature extraction problem in VM under examination.

For a physical layer message authentication procedure based on the comparison of channel estimates obtained from the received messages, we focus on an outer bound on the type I/II error probability region. Channel estimates are modeled as multivariate Gaussian vectors, and we assume that the attacker has only some side information on the channel estimate, which he does not know directly. We derive the attacking strategy that provides the tightest bound on the error region, given the statistics of the side information. This turns out to be a zero mean, circularly symmetric Gaussian density whose covariance matrices can be obtained by solving a constrained optimization problem. We propose an iterative algorithm for its solution: starting from the closed-form solution of a relaxed problem, we obtain, by projection, an initial feasible solution; then, by an iterative procedure, we look for the fixed-point solution of the problem. Numerical results show that for cases of interest the iterative approach converges, and perturbation analysis shows that the found solution is a local minimum.