Giuseppe Thadeu Freitas de Abreu

Hyeon Seok Rou, Giuseppe Thadeu Freitas de Abreu, Emil Björnson et al.

Orthogonal frequency-division multiplexing (OFDM) and its static sinusoidal subcarriers have underpinned the 4G and 5G eras, delivering high spectral efficiency and resilience to multipath fading through an efficient multicarrier architecture. However, as future systems move toward doubly dispersive environments driven by high-mobility applications and migration to mmWave/sub-THz bands, the time-invariance assumption underlying OFDM becomes increasingly difficult to maintain, and Doppler-induced degradation becomes prominent. While enhancements such as MIMO, advanced coding, and scheduling provide incremental remedies, they introduce additional overhead, because the sinusoidal subcarrier itself offers no inherent waveform-level robustness to Doppler impairments. Accordingly, two time-frequency spreading philosophies have emerged to improve Doppler resilience by distributing each symbol's energy across both dimensions of the time-frequency plane: (i) 2D isotropic spreading via the delay-Doppler (DD) domain, exemplified by the orthogonal time frequency space (OTFS) family, and (ii) sheared spreading via parameterizable chirps, exemplified by the affine frequency-division multiplexing (AFDM) family. In this article, we examine key considerations for future waveform design across these paradigms and argue that transitioning from the sinusoidal subcarriers of OFDM to the chirp-based subcarriers offers a viable design direction for improving Doppler robustness while retaining much of the mature OFDM infrastructure. This perspective also highlights the suitability of chirp-based waveforms for integrated sensing and communications (ISAC) and their extensibility to emerging physical-layer techniques. Overall, we argue that the transition from sinusoids to chirps is a technically motivated, compelling evolutionary direction for future wireless physical layer design.

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, Getuar Rexhepi, Giuseppe Thadeu Freitas de Abreu

We consider a novel algorithm, for the completion of partially observed low-rank tensors, as a generalization of matrix completion. The proposed low-rank tensor completion (TC) method builds on the conventional nuclear norm (NN) minimization-based low-rank TC paradigm, by leveraging the alternating direction method of multipliers (ADMM) optimization framework. To that extend the original NN minimization problem is reformulated into multiple subproblems, which are then solved iteratively via closed-form proximal operators, making use of over-relaxation and an adaptive penalty parameter update scheme, to further speed up convergence and improve the overall performance of the method. Simulation results demonstrate the superior performance of the new method in terms of normalized mean square error (NMSE), compared to the conventional state-of-the-art (SotA) techniques, including NN minimization approaches, as well as a mixture of the latter with a matrix factorization approach, while its convergence can be significantly improved by initializing the algorithm with the solution of the SotA.

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.