arXiv subjects

Giuseppe Thadeu Freitas de Abreu

Publications and source records attributed to Giuseppe Thadeu Freitas de Abreu.

At least 19 recordsLinked to original sources

arXiv2026

Effects of Residual Chirp Rate on DAFT-s-AFDM Uplink Performance

Affine frequency division multiplexing (AFDM) is robust to doubly dispersive channels in high-mobility 6G systems but, like orthogonal frequency division multiplexing (OFDM), suffers from a high peak-to-average power ratio (PAPR). Spreading with a discrete affine Fourier transform (DAFT) yields DAFT-s-AFDM, whose precoder and modulator chirps can be chosen independently. For a single user with zero-offset localized allocation, we show that these two chirps merge into a single residual chirp whose rate, with the other two chirp rates fixed, alone determines their effect. At the transmitter, this rate defines a circulant spreading kernel whose fourth moment quantifies the envelope fluctuation; symmetries reduce its characterization to rates in [0, 1/4]. At a linear minimum mean-square error (MMSE) receiver, the residual chirp redistributes the mean- square error across symbols without changing its total; under a Gaussian approximation, a more uniform per-symbol error lowers the uncoded bit error rate (BER). In uncoded QPSK simulations, a zero rate yields the lowest PAPR, whereas a generic rate reduces the signal-to-noise ratio required for a BER of $10^{-3}$ by 4.4 dB at a 3.33 dB PAPR cost (exceedance probability $10^{-3}$);a rate of 1/3 captures 2.8 dB of this gain for only 0.88 dB of that cost.

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arXiv2026

Rigid Body Localization via Gaussian Belief Propagation with Quadratic Angle Approximation

Gaussian belief propagation (GaBP) is a technique that relies on linearized error and input output models to yield low-complexity solutions to complex estimation problems, which has been recently shown to be effective in the design of range-based GaBP schemes for stationary and moving rigid body localization (RBL) in three-dimensional (3D) space, as long as the relative rotation between the prior position and the target rigid body is sufficiently small. In this article we present a novel range-based RBL scheme via GaBP that relaxes the latter limitation significantly. To this end, the proposed method incorporates a quadratic angle approximation to linearize the relative orientation between the prior and the target rigid body, enabling high precision estimates of corresponding rotation angles even for large deviations. Leveraging the resulting linearized model, we derive the corresponding message-passing (MP) rules to obtain estimates of the translation vector and rotation matrix of the target rigid body, relative to a prior reference frame. Numerical results corroborate the good performance of the proposed angle approximation itself, as well as the consequent RBL performance in terms of root mean square errors (RMSEs) in comparison to the state-of-the-art (SotA), while maintaining a low computational complexity.

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arXiv2026

On the State Evolution of Approximate Message Passing with Discontinuous Denoisers

We consider approximate message passing (AMP) with discontinuous denoisers, such as hard slicers, quantizers and hard thresholding, for which the classical state evolution (SE) analysis does not apply. It is first shown that the standard Onsager coefficient; i.e., the average pointwise derivative of the denoiser, misses a boundary term, namely, the sum over the jumps of the jump size times the density of the denoiser input at the jump. Then, for real independent and identically distributed (i.i.d.) Gaussian matrices, a positive noise variance, a fixed number of iterations and a prior with finite second moment, we transfer the Lipschitz SE theorem directly to denoisers, fixed in advance, that are continuously differentiable with bounded derivative except at finitely many jumps, by bounding the distance between the iterates of AMP and of AMP on Lipschitz ramps of the denoisers through the fraction of inputs that cross a jump. It is thereby proven that AMP follows SE, also for test functions such as symbol errors, if its Onsager coefficient contains the boundary term, evaluated either along SE or, as we propose, at the noise level estimated from the residual, with the density computed from the known prior. Simulation results with 4- and 8-level pulse amplitude modulation (PAM) demonstrate that AMP with a hard slicer, whose standard coefficient is identically zero, fails with this coefficient, while with the proposed one, it follows SE and comes close to Bayes-optimal AMP.

cs.IT↗

arXiv2026

Comparative Analysis of Filter Bank Waveforms for ISAC Systems: 2D-FFT FB and AFBM

We present a comparative analysis of two promising filter bank multicarrier waveforms for integrated sensing and communications (ISAC) systems operating in high-mobility environments. In particular, we consider two-dimensional FFT-precoded filter bank (2D-FFT FB) modulation and the recently-proposed affine filter bank modulation (AFBM) waveforms, which exploit different signal representations across the time-frequency, delay-Doppler and affine domains to improve robustness against Doppler effects, each resulting in distinct features. On the one hand, 2D-FFT FB improves spectral localization under high Doppler conditions, while AFBM combines chirp-based modulation with filter bank processing to achieve low peak-to-average power ratio (PAPR) and reduced out-of-band emission (OOBE). These schemes are compared in terms of OOBE, PAPR and bit-error-rate (BER), as well as the delay and Doppler cuts of the ambiguity function (AF) under deterministic and random sensing symbols. Results for orthogonal time frequency space (OTFS) and affine frequency division multiplexing (AFDM) are also included to provide additional basis of comparison. The results show the performance trade-offs between the two filter bank (FB)-based schemes, providing insights into waveform candidates for high-mobility ISAC scenarios such as vehicular communications and future sixth generation (6G) networks.

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arXiv2026

Integrated Communication and Computing with Index Modulation

We propose an integrated communication and computing (ICC) architecture that repurposes the inactive antennas of a spatial index modulation (IM) transmitter to perform over-the-air computation (AirComp). While IM delivers excellent spectral efficiency by selectively activating a subset of transmit antennas, the unused antennas are conventionally completely deactivated, forgoing spatial degrees of freedom (DoF) that can be exploited without additional bandwidth. By instead transmitting a pre-equalized, low-power computing stream over these idle antennas, the proposed architecture achieves simultaneous data transmission and computation without requiring orthogonal frequency or time resources. Alignment is performed entirely at the transmitters, such that the pre-equalization occurs leveraging local channel state information (CSI), while at the receiver, a vector Gaussian belief propagation (VGaBP) detector recovers the data payload under the discrete IM codebook constraint before the target function is estimated from the residual. Numerical results against exact maximum likelihood (ML) baselines confirm near-optimal detection under the adopted statistical model, and reveal that the number of antennas assigned to data transmission governs a direct trade-off between modulation robustness and AirComp accuracy.

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arXiv2026

AFDM as a Software Upgrade of OFDM: One Firmware Patch, a New Frontier

In this white paper, we summarize for the benefit of the wider research community on wireless communications, the two key results that we shared with the attendees of the 2026 IEEE Communication Theory Workshop in Azores, Portugal, about affine frequency division multiplexing (AFDM). Firstly, we show that in contrast to the wide perception by most researchers, AFDM can be implemented at marginal costs by means of a simple software upgrade (firmware patch) of conventional orthogonal frequency division multiplexing (OFDM), indicating that its adoption can potentially be achieved across a wide range of OFDM-based wireless infrastructure and systems. The most crucial relevance of this finding is that such an upgrade would enable, under the specific conditions of the corresponding systems and their applications, exploiting various advantageous features of AFDM, including robustness to doubly dispersive channels (i.e., to support high-mobility use-cases in 6G), inherent integrated sensing and communications (ISAC) compatibility (i.e., to support sensing use-cases in 802.11bf), and the straightforward introduction of low-complexity physical-layer security at the waveform level (as needed in next-generation IoT systems). Secondly, we also show that the same mathematical principles underpinning the aforementioned finding, also imply an inherent capability of AFDM to reap the full uncoded diversity of static linear time-invariant (LTI) channels, demonstrating that this simple upgrade taps into previously undiscovered strengths of multicarrier waveforms.

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arXiv2026

AFDM: Evolving OFDM Towards 6G+

As sixth generation (6G) standardization accelerates, there is growing consensus in favor of evolutionary waveforms that add new capabilities while preserving compatibility with the orthogonal frequency division multiplexing (OFDM) core of 4G and 5G. This article positions affine frequency division multiplexing (AFDM) as such a candidate, providing structural robustness for high-mobility communications and integrated sensing and communication (ISAC) over doubly dispersive channels while remaining backward-compatible with the legacy OFDM air interface. We first develop a generalized fractional-delay-fractional-Doppler (FDFD) channel model that accounts for practical pulse-shaping filters and the resulting inter-sample coupling. Building on this model, we show that the AFDM transceiver reuses nearly the entire OFDM chain, adding only lightweight digital pre- and post-processing. We then analyze the impact of hardware impairments such as phase noise and carrier frequency offset, and examine the advanced functionalities enabled by the chirp-parameter domain, including index modulation and physical-layer security. Assessing reusability across the radio-frequency, physical, and higher layers, we conclude that AFDM offers an efficient path toward high-fidelity later versions of 6G and beyond (6G+) communications.

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arXiv2026

Orbital Detection: On Maximum-Entropy Priors

Soft-input detection over a discrete constellation $\mathcal{M}$ of cardinality $M$ requires computing a posterior whose mean and mode are respectively given by the minimum mean square error (MMSE) and maximum a posteriori (MAP) estimates, both of which incur a computational cost of order $\mathcal{O}(M)$ per symbol. We show that this cost is reduced to $\mathcal{O}(L)$, where $L \le M$ is the number of distinct amplitudes (rings), once the discrete prior is replaced by its maximum-entropy counterpart subject to the same radial marginal. This orbital prior, which is a mixture of uniform circular shells, is obtained by maximizing a mixed discrete-continuous entropy. We prove in this paper that such a distribution is the only distribution on $\mathbb{C}$ that preserves the amplitude statistics of $\mathcal{M}$ exactly while remaining maximally noncommittal in phase. Under the additive white Gaussian noise (AWGN) channel, the orbital prior induces a closed-form posterior that factors into a softmax over the $L$ rings and a von Mises phase distribution whose concentration is supplied entirely by the observation, yielding closed-form orbital MMSE and MAP detectors of the discrete symbol at $\mathcal{O}(L)$ cost. The resulting hierarchical rule selects the ring by posterior mass and the phase by conditional mode. We compare the pairwise ring boundary with that of the joint posterior-density and quantify the leading-order outward shift at high signal-to-noise ratio (SNR). Numerical results using standard constellations confirm that the orbital detectors maintain similar symbol error rate (SER) performance to optimal detectors, at a fraction of the complexity.

cs.IT↗

arXiv2026

The Resurrection of Spectrum Spreading for 6G and Beyond: From Sinusoids to Chirps

Orthogonal frequency-division multiplexing (OFDM) and its 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.

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arXiv2026

Joint PAPR and OOBE Reduction for AFDM via Chirp Parameter Tuning

This paper addresses the joint reduction of the peak-to-average power ratio (PAPR) and out-of-band emissions (OOBE) in affine frequency division multiplexing (AFDM) systems by selecting the pre-chirp parameter c2. While existing approaches typically optimize either PAPR or OOBE independently, the proposed method jointly considers both metrics. To this end, a weighted cost function combining PAPR and OOBE is introduced to evaluate the trade-off between the two objectives. A pre-chirp selection scheme, inspired by the selected mapping (SLM) technique, is then employed to identify the optimal c2 value from a finite set of candidates, yielding a Pareto-optimal operating point within a discrete set. Simulation results demonstrate that the proposed approach simultaneously reduces both PAPR and OOBE compared with conventional AFDM. Moreover, its performance remains close to that of methods specifically optimized for a single objective, with only about a 1 dB degradation in PAPR reduction and a 2-3 dB degradation in OOBE suppression.

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arXiv2026

Distortion-Aware Integrated Sensing and Communication with Affine Filter Bank Modulation

The stringent energy-efficiency requirements of future Integrated Sensing and Communications (ISAC) systems are fundamentally challenged. Unlike conventional communication systems, ISAC transmitters must radiate significantly higher power to ensure reliable target detection, forcing the High-Power Amplifier (HPA) to operate closer to saturation, where nonlinear distortions become unavoidable. Consequently, the robustness of every candidate ISAC waveform to HPA nonlinearities must be carefully assessed. In this context, this paper investigates the robustness of Affine Filter Bank Modulation (AFBM), a recently proposed waveform that combines the delay-Doppler resilience of affine modulation with reduced Peak-to-Average Power Ratio (PAPR) and improved spectral containment. We develop a statistical characterization of the Ambiguity Function (AF) of the amplified AFBM waveform, deriving approximate expressions for its mean, variance, and Rician-distributed magnitude. Furthermore, a low-complexity Gaussian belief propagation receiver accounting for HPA nonlinearities is proposed for communication detection. Simulation results validate the analytical framework and demonstrate that AFBM preserves favorable sensing characteristics and robust Bit Error Rate (BER) performance even under severe nonlinear amplification.

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arXiv2026

Orbital Detection

We introduce orbital detection (OD), a framework for designing asymptotically optimal, low-complexity message passing (MP) receivers for digitally modulated multiple-input multiple-output (MIMO) systems, based on relaxing the discrete symbol prior into a mixed discrete-continuous density. The resulting orbital prior factors each symbol's distribution into a discrete radial component, supported on only the $L << M$ amplitude rings of an arbitrary constellation $\mathcal{M}$ of cardinality $M = |\mathcal{M}|$, and a continuous, maximum-entropy phase density on each ring. This compresses the propagated posterior mean and variance losslessly into $3L$ real scalars, and collapses the optimal $\mathcal{O}(M)$-complexity denoiser into a closed-form hierarchy whose per-symbol cost falls to $\mathcal{O}(L)$ and ultimately $\mathcal{O}(1)$: the orbital Bessel denoiser (OBD), its Bessel-free variant the orbital Gaussian denoiser (OGD), and the orbital phase denoiser (OPD), proved irreducible on the ring manifold. A Jacobi-Anger ladder recovers the exact detector with geometrically vanishing error. Five information-theoretic results follow. First, the OBD, OGD, and OPD share an identical leading-order state evolution (SE) fixed point. Second, the sole price is a change in the high-SNR error-decay law, from exponential to linear, which never hardens into an error floor. Third, for any underloaded system the induced rate loss vanishes exponentially in SNR, so every level is asymptotically capacity-achieving in the constellation-constrained sense, attaining $\log_2 M$. Fourth, OD attains a minimum mean square error (MMSE) dimension $d=1/2$, halfway between the $d=0$ Bayes-optimal denoiser (BOD) and the $d=1$ linear receiver. Fifth, a non-asymptotic optimal-transport bound in Wasserstein distance links constellation ring geometry directly to the achievable rate.

cs.IT↗

arXiv2026

Bistatic Integrated Sensing and Communications with Flexible Intelligent Metasurfaces

We propose a novel doubly-dispersive (DD) multiple-input multiple-output (MIMO) channel model incorporating flexible intelligent metasurfaces (FIMs), suitable for integrated sensing and communications (ISAC) in high-mobility scenarios. We show how the proposed FIM-parameterized DD (FPDD) channel model extends to multicarrier waveforms known to perform well in DD environments, namely, orthogonal frequency division multiplexing (OFDM), orthogonal time frequency space (OTFS), and affine frequency division multiplexing (AFDM). Leveraging this model, we formulate an achievable rate maxi-mization problem with a sensing constraint for all waveforms and solve it via gradient ascent with closed-form gradients. Numerical results indicate that FIM technology significantly impacts the achievable rate, with careful parametrization essential for strong ISAC performance across all waveforms.

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arXiv2026

Multi-Chirp AFDM for Rydberg Atomic Quantum Receivers: Waveform and Algorithm Design

We propose a multi-chirp affine frequency division multiplexing (MC-AFDM) scheme for joint delay-Doppler estimation with Rydberg atomic quantum receivers (RAQRs). The work is motivated by the fact that RAQRs, while offering superior sensitivity and advantageous sensing capabilities, suffer from an optical ambiguity due to Doppler shifts in doubly-dispersive (DD) channel caused by target mobility, which precludes the reliable estimation of delay-Doppler parameters. To resolve this optical ambiguity and unleash the potential of RAQRs in DD channel, the proposed MC-AFDM employs multiple distinct AFDM post-chirp signals to overcome the rank-deficiency problem of the classical single-chirp AFDM (SC-AFDM), thereby enabling accurate delay-Doppler estimation of multiple targets. Our analysis reveals that the edge distribution of the multiple post-chirp parameters can further improve estimation accuracy by minimizing the condition number. Building on the proposed MC-AFDM waveform, we design a sequential signal processing algorithm based on orthogonal matching pursuit (OMP) and least squares (LS), and we derive the theoretical lower bounds for delay and Doppler estimation. Numerical results show that the proposed MC-AFDM improves range and velocity estimation accuracy by up to two orders of magnitude compared to the classical SC-AFDM, and approaches its theoretical bounds through post-chirp optimization, validating the quantum-induced advantage of RAQRs for high-resolution quantum wireless sensing.

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arXiv2026

Characterization of Continuous Electromagnetic Manifolds via Calculus of Variations

We present a novel calculus of variations (CoV)-based framework for the characterizing of, and beamforming over, continuous electromagnetic manifolds of arbitrary multiple-input multiple-output (MIMO) array geometries. Building upon the discrete moment-matrix formulation of the state-of-the-art (SotA), the proposed framework simultaneously overcomes three of its fundamental limitations: (i) the point-source approximation error incurred by the near-field radiation operator; (ii) the confinement of the beamforming space to the N-dimensional subspace dictated by the hardware port count; and (iii) the generalization to arbitrary array geometries. To this end, each mesh element is modeled as a two-dimensional planar patch whose spatially averaged Green's function is evaluated via Gauss-Legendre (GL) quadrature, yielding a strictly more accurate near-field representation at negligible additional cost, while a continuous feeding function w(p) in L^2(S_T), introduced as the infinite-dimensional limit of the N-port network, lifts the optimization onto a hardware-decoupled current subspace of dimension K >> N. As an application example, we employ the proposed CoV-based framework to derive closed-form optimal beamformers for both unconstrained field-strength maximization, and a near-field pattern synthesis under a power density (PD) and region constraints, establishing their exact analogy to the discrete and generalized matched filters. Full-wave MATLAB Antenna Toolbox validation confirms consistent near-field accuracy gains over the SotA baseline for both linear and planar geometries at comparable computational cost.

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arXiv2026

Group-Connected Riemannian Manifold Optimization for Reciprocal BD-RIS

Reconfigurable intelligent surfaces (RISs) provide a flexible means of engineering wireless propagation channels through configurable multiport scattering networks. Among their architectures, group-connected beyond-diagonal RISs (BD-RISs) offer a practical tradeoff between scattering flexibility and hardware complexity by partitioning the surface into inter-connected groups. In reciprocal and lossless implementations, each group scattering block must be symmetric and unitary. In this paper, we investigate sum-rate maximization for reciprocal group-connected BD-RIS-assisted multiple-input multiple-output (MIMO) systems under such structural constraints. In particular, we build on a recent result where the feasible space determined by the symmetry and unitary constraints was characterized as a Riemannian manifold, extending it into a product manifold of symmetric-unitary block manifolds, thus expanding the approach to manifold phase optimization in the group-connected setting. As a consequence, the proposed group-extended framework performs tangent-space projections and Takagi retractions block-wise, while preserving the coupling among all groups through the common MIMO equivalent channel. The formulation naturally includes single-connected and fully connected reciprocal BD-RIS architectures as special cases and enables a flexible performance-complexity tradeoff through the group size.

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arXiv2026

Mutual Coupling in Continuous Aperture Arrays: Physical Modeling and Beamforming Design

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.

cs.IT↗

arXiv2026

Multibit Quantized Precoding for MU-mMIMO

We propose a novel multibit quantized precoding method for the downlink of multi-user massive MIMO systems with low-resolution digital-to-analog converters. The new method, termed multibit quantized precoding (MQP), enforces the finite-alphabet constraint through an l0-norm penalty, approximated by a smooth surrogate so as to yield a reformulated problem, which is then convexized via fractional programming, ultimately extending quantized precoding beyond 1-bit alphabets. The regularization parameter of the proposed method is selected via a discrepancy principle integrated with graduated non-convexity continuation, resulting in a principled and reproducible hyperparameter tuning method and an efficient iterative algorithm with a closed-form, least-squares-type update per iteration. In order to further reduce the computational complexity of the method, we include a Gaussian belief propagation (GaBP) step for turning the least-squares update in linear-time. Simulations performed for systems with different sizes demonstrate that both methods, namely the MQP with and without GaBP, achieve competitive or superior error-rate performance compared to state-of-the-art quantized precoding algorithms under various channel conditions.

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