Giuseppe Thadeu Freitas de Abreu

Zhaolin Wang, Kuranage Roche Rayan Ranasinghe, Giuseppe Thadeu Freitas de Abreu et al.

The phenomenon of mutual coupling in continuous aperture arrays (CAPAs) is studied. First, a general physical model for the phenomenon that accounts for both polarization and surface dissipation losses is developed. Then, the unipolarized coupling kernel is characterized, revealing that polarization induces anisotropic coupling and invalidates the conventional half-wavelength spacing rule for coupling elimination. Next, the beamforming design problem for CAPAs with coupling is formulated as a functional optimization problem, leading to the derivation of optimal beamforming structures via the calculus of variations. To address the challenge of inverting the coupling kernel in the optimal structure, two methods are proposed: 1) the kernel approximation method, which yields a closed-form solution via wavenumber-domain transformation and GaussLegendre quadrature, and 2) the conjugate gradient method, which addresses an equivalent quadratic functional optimization problem iteratively. Furthermore, the optimal array gain and beampattern are analyzed at the large-aperture limit. Finally, the proposed continuous mutual coupling model is extended to spatially discrete arrays (SPDAs), and comprehensive numerical results are provided, demonstrating that: 1) coupled SPDA performance correctly converges to the CAPA limit, while uncoupled models are shown to violate physics, 2) polarization results in anisotropic array gain behavior, and 3) the coupled beampattern exhibits higher directivity than the uncoupled beampattern.

Zhaolin Wang, Chongjun Ouyang, Kuranage Roche Rayan Ranasinghe et al.

Emerging wireless systems are evolving toward larger, denser, higher-frequency, and more reconfigurable apertures, which motivates the study of continuous-aperture arrays (CAPAs). Unlike conventional spatially discrete arrays (SPDAs), CAPAs are more naturally modeled as spatially continuous electromagnetic apertures and therefore call for a fundamental shift in both signal processing and information-theoretic analysis. In particular, the underlying channels, signals, and beamformers are no longer finite-dimensional vectors and matrices, but continuous fields and operators governed by Maxwell's equations. This paper provides a tutorial overview of CAPA systems from the perspective of electromagnetic signal and information theory (ESIT), with an emphasis on the transition from discrete array models to physics-consistent continuous-aperture formulations. We review the electromagnetic foundations of CAPAs, practical hardware implementations, line-of-sight and multipath channel modeling, continuous-space beamforming and channel estimation, and the fundamental degrees of freedom and capacity limits of CAPA systems. We also highlight how tools such as wavenumber-domain methods, functional analysis, and compressive sensing can transform challenging infinite-dimensional problems into tractable finite-dimensional ones while preserving the essential physical structure of the channel. Overall, this tutorial aims to clarify the key principles, analytical tools, and open challenges that shape CAPA-enabled wireless communications.

Niclas Führling, Giuseppe Thadeu Freitas de Abreu, David González G. et al.

We consider a robust and self-reliant (or "egoistic") variation of the rigid body localization (RBL) problem, in which a primary rigid body seeks to estimate the pose (i.e., location and orientation) of another rigid body (or "target"), relative to its own, without the assistance of external infrastructure, without prior knowledge of the shape of the target, and taking into account the possibility that the available observations are incomplete. Three complementary contributions are then offered for such a scenario. The first is a method to estimate the translation vector between the center point of both rigid bodies, which unlike existing techniques does not require that both objects have the same shape or even the same number of landmark points. This technique is shown to significantly outperform the state-of-the-art (SotA) under complete information, but to be sensitive to data erasures, even when enhanced by matrix completion methods. The second contribution, designed to offer improved performance in the presence of incomplete information, offers a robust alternative to the latter, at the expense of a slight relative loss under complete information. Finally, the third contribution is a scheme for the estimation of the rotation matrix describing the relative orientation of the target rigid body with respect to the primary. Comparisons of the proposed schemes and SotA techniques demonstrate the advantage of the contributed methods in terms of root mean square error (RMSE) performance under fully complete information and incomplete conditions.

Niclas Führling, Kengo Ando, Giuseppe Thadeu Freitas de Abreu et al.

We consider a novel algorithm, for the completion of partially observed low-rank matrices in a structured setting where each entry can be chosen from a finite discrete alphabet set, such as in common recommender systems. The proposed low-rank matrix completion (MC) method is an improved variation of state-of-the-art (SotA) discrete aware matrix completion method which we previously proposed, in which discreteness is enforced by an $\ell_0$-norm regularizer, not by replaced with the $\ell_1$-norm, but instead approximated by a continuous and differentiable function normalized via fractional programming (FP) under a proximal gradient (PG) framework. Simulation results demonstrate the superior performance of the new method compared to the SotA techniques as well as the earlier $\ell_1$-norm-based discrete-aware matrix completion approach.

Tyler Maunu, Gabriel Abreu

We consider the phase retrieval problem, which involves recovering a rank-one positive semidefinite matrix from rank-one measurements. A recently proposed algorithm based on Bures-Wasserstein gradient descent (BWGD) exhibits superlinear convergence, but it is unstable, and existing theory can only prove local linear convergence for higher rank matrix recovery. We resolve this gap by revealing that BWGD implements Newton's method with a nonsmooth and nonconvex objective. We develop a smoothing framework that regularizes the objective, enabling a stable method with rigorous superlinear convergence guarantees. Experiments on synthetic data demonstrate this superior stability while maintaining fast convergence.

Mika Ylianttila, Raimo Kantola, Andrei Gurtov et al.

The roles of trust, security and privacy are somewhat interconnected, but different facets of next generation networks. The challenges in creating a trustworthy 6G are multidisciplinary spanning technology, regulation, techno-economics, politics and ethics. This white paper addresses their fundamental research challenges in three key areas. Trust: Under the current "open internet" regulation, the telco cloud can be used for trust services only equally for all users. 6G network must support embedded trust for increased level of information security in 6G. Trust modeling, trust policies and trust mechanisms need to be defined. 6G interlinks physical and digital worlds making safety dependent on information security. Therefore, we need trustworthy 6G. Security: In 6G era, the dependence of the economy and societies on IT and the networks will deepen. The role of IT and the networks in national security keeps rising - a continuation of what we see in 5G. The development towards cloud and edge native infrastructures is expected to continue in 6G networks, and we need holistic 6G network security architecture planning. Security automation opens new questions: machine learning can be used to make safer systems, but also more dangerous attacks. Physical layer security techniques can also represent efficient solutions for securing less investigated network segments as first line of defense. Privacy: There is currently no way to unambiguously determine when linked, deidentified datasets cross the threshold to become personally identifiable. Courts in different parts of the world are making decisions about whether privacy is being infringed, while companies are seeking new ways to exploit private data to create new business revenues. As solution alternatives, we may consider blockchain, distributed ledger technologies and differential privacy approaches.