arXiv subjects

Takumi Takahashi

Publications and source records attributed to Takumi Takahashi.

At least 19 recordsLinked to original sources

arXiv2026

Electromagnetic Singularity-Aware MIMO Channels: Scattering-Based Channel Modeling and Physics-Aware Power Allocation

Electromagnetic information theory (EIT) brings electromagnetic physics into wireless channel analysis and offers a physical view of channel structures hidden by conventional models. This paper studies channel instability near electromag- netic singular states, where small environmental perturbations can cause large variations in the end-to-end channel. Using resolvent-based spectral analysis, we develop an electromag- netic multiple-input multiple-output (MIMO) channel model that decomposes the end-to-end channel into a smooth regular component and singularity-associated components. The analysis shows that the singularity-associated components become more sensitive to environmental perturbations near singular states. The proposed model also reveals a limitation of conventional water filling (WF): power allocation based only on instan- taneous channel gains does not account for such instability. We therefore estimate singularity information from broadband MIMO channel state information (CSI) and develop a singularity- aware transmit covariance optimization method. Simulations demonstrate numerical stability of the estimated pole frequencies and illustrate the environmental sensitivity of pole-associated channel components. The proposed allocation reduces weighted singular-channel exposure by 90.32% while retaining 95% of the nominal WF rate.

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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.

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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.

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arXiv2026

State-Evolution-based Score Matching for Generalized Approximate Message Passing

Generalized approximate message passing (GAMP) equipped with minimum mean-square error (MMSE) denoisers, commonly referred to as Bayes-GAMP, is a powerful framework for solving inverse problems described by generalized linear models (GLMs) with arbitrary component-wise nonlinearities in the observation process. However, despite its theoretical tractability and rigorously established asymptotic optimality, the range of practical observation models for which Bayes-GAMP admits a closed-form implementation remains severely limited, particularly in complex-valued settings. This limitation largely stems from the restrictive requirement that the corresponding output denoiser, given by a conditional expectation, admit a closed-form expression. To overcome this limitation, we propose a principled approach that enables the implementation of Bayes-GAMP for complex-valued models with \emph{virtually arbitrary} nonlinear observation mappings. Specifically, within a score-matching framework, we train a neural network to emulate the output denoiser using training data generated from a characterization of the message dynamics based on state evolution (SE). Notably, the proposed approach requires neither explicit evaluation of the denoiser nor knowledge of an explicit functional form of the nonlinear mapping; it requires only access to forward evaluations of the mapping during offline training. We show that, under ideal training conditions, GAMP with the trained network replacing the analytically intractable denoiser asymptotically matches the performance of Bayes-GAMP with the exact denoiser.

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arXiv2026

Ill-Posedness Analysis of CSI-Based Electromagnetic Inverse Scattering for Material Reconstruction in ISAC Systems

Channel state information (CSI)-based electromagnetic inverse scattering for material reconstruction in ISAC systems enables physics-grounded, material-aware DT. Yet the resulting CSI-induced scattering operator is often severely ill-conditioned. To understand the origin of the ill-posedness, this paper analyzes the mathematical properties of the electromagnetic inverse problem and investigates the operator structure of the ISAC scattering matrix jointly shaped by in-domain scattering responses and Tx/Rx propagation channels. We show that background-related matrix columns are highly coherent and dominate the near rank deficiency, whereas scatterer-related columns are comparatively weakly correlated; their coherence decreases with the number of probing frequencies and thus contributes to the effective rank. Motivated by this analysis, we prove that restricting the ROI around the true scatterer yields a provable condition-number reduction and a tightened CRLB, and we quantify the impact of ROI mismatch numerically. To operationalize these insights, an ROI-constrained QP framework is adopted, where a linear sampling method delineates a coarse ROI and the QP update is performed in the reduced subspace. Full-wave FDTD simulations over multiple geometries and SNR validate pronounced conditioning improvement, substantial complexity savings, and improved robustness, consistent with the proposed analysis, compared with the full-domain formulation.

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arXiv2026

Electromagnetic Digital Twin-Enabled Closed-Loop Beam Management in ISAC Systems

Digital twin (DT) is envisioned as a key enabler of sixth-generation (6G) communication systems, evolving from offline descriptive replicas for monitoring and analysis to inthe-loop agents within digital twin networks (DTNs) that couple physical and digital worlds. Recent advances in integrated sensing and communication (ISAC)-driven electromagnetic (EM) scattering methods enable environment twinning by linking channel behaviors to EM properties of the scatterers, supporting interpretable DT states and EM-grounded optimization. However, existing studies primarily focus on DT construction and lack mechanisms for closed-loop control in wireless systems. Moreover, array-geometry mismatch can bias DT reconstruction and degrade control performance, while prior works assume known arrays. To address these gaps, we propose an EM-ISACbased closed-loop DTN framework with a hierarchical design integrating environment twinning, prior injection, and control decision into an end-to-end loop. Leveraging ISAC measurements, the proposed framework jointly reconstructs scatterer information and array-dependent forward operator and employs a low-complexity Bayesian message-passing algorithm to perform contrast inference and array calibration. The reconstructed DT guides codebook preselection to reduce training overhead and narrow candidate beams. Subsequently, downlink beamforming (BF) is performed based on DT-predicted channels, enabling latency-bounded closed-loop control. Simulation results demonstrate improved robustness and control performance under array mismatch.

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arXiv2026

Quaternion-Domain Super MDS for Robust 3D Localization

This paper proposes a novel low-complexity three-dimensional (3D) localization algorithm for wireless sensor networks, termed quanternion-domain super multi-dimensional scaling (QD-SMDS). The algorithm is based on a reformulation of the SMDS, originally developed in the real domain, using quaternion algebra. By representing 3D coordinates as quaternions, the method constructs a rank-1 Gram edge kernel (GEK) matrix that integrates both relative distance and angular information between nodes, which enhances the noise reduction effect achieved through low-rank truncation employing singular value decomposition (SVD), thereby improving robustness against information loss. To further reduce computational complexity, we also propose a variant of QD-SMDS that eliminates the need for the computationally expensive SVD by leveraging the inherent structure of the quaternion-domain GEK matrix. This alternative directly estimates node coordinates using only matrix multiplications within the quaternion domain. Simulation results demonstrate that the proposed method significantly improves localization accuracy compared to the original SMDS algorithm, especially in scenarios with substantial measurement errors. The proposed method also achieves comparable localization accuracy without requiring SVD.

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arXiv2026

Three-Module SC-VAMP for LDPC-Coded Nonlinear Channels

We propose a three-module extension of score-based VAMP (SC-VAMP) for signal recovery in nonlinear channels, where the received signal is obtained by applying a nonlinearity to a linear mixture of the transmitted signal, followed by additive Gaussian noise. The key idea is to introduce a latent variable representing the output of the linear mixing stage, which decomposes the inference problem into three modules: a likelihood module that handles the nonlinear observation via Gauss--Hermite quadrature, a coupling module that enforces the linear constraint between the transmitted signal and the latent variable via LMMSE estimation, and a denoiser module that incorporates the code constraint using belief propagation (BP) decoding. Each module exchanges extrinsic scalar-Gaussian messages with Onsager corrections derived from posterior variances that are computed in closed form or to quadrature accuracy. Numerical experiments with BPSK-modulated LDPC codewords transmitted through a hyperbolic tangent channel demonstrate that the proposed method achieves a clear waterfall in bit error rate (BER), with the gap to the capacity estimate narrowing as the block length increases from 128 to 2304. The framework provides a modular receiver architecture applicable to a broad class of nonlinear channels. Since only the likelihood module depends on the channel nonlinearity, the architecture readily adapts to other channel models by replacing a single module while leaving the coupling and decoder modules unchanged.

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arXiv2026

Vector Similarity Search-Based MCS Selection in Massive Multi-User MIMO-OFDM

This paper proposes a novel modulation and coding scheme (MCS) selection framework that integrates mutual information (MI) prediction based on vector similarity search (VSS) for massive multi-user multiple-input multiple-output orthogonal frequency-division multiplexing (MU-MIMO-OFDM) systems with advanced uplink multi-user detection (MUD). The framework performs MCS selection at the transport block (TB)-level MI and establishes the mapping from post-MUD MI to post-decoding block error rate (BLER) using a prediction function generated from extrinsic information transfer (EXIT) curves. A key innovation is the VSS-based MI prediction scheme, which addresses the challenge of analytically predicting MI in iterative detectors such as expectation propagation (EP). In this scheme, an offline vector database (VDB) stores feature vectors derived from channel state information (CSI) and average received signal-to-noise ratio (SNR), together with corresponding MI values achieved with advanced MUD. During online operation, an approximate nearest neighbor (ANN) search on graphics processing units (GPUs) enables ultra-fast and accurate MI prediction, effectively capturing iterative detection gains. Simulation results under fifth-generation new radio (5G NR)-compliant settings demonstrate that the proposed framework significantly improves both system and user throughput, ensuring that the detection gains of advanced MUD are faithfully translated into tangible system-level performance improvements.

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arXiv2026

Secure Cell-Free Massive MIMO ISAC Systems: Joint AP Selection and Power Allocation Against Eavesdropping

This paper investigates a cell-free massive multiple-input-multiple-output (CF-mMIMO) integrated sensing and communication (ISAC) system that addresses the critical challenge of information leakage to potential eavesdroppers located within sensing zones. A novel access point (AP) selection strategy is proposed, which partitions the distributed APs into two functional groups: communication APs (C-APs), dedicated exclusively to data transmission, and sensing APs (S-APs), responsible for target detection and eavesdropper suppression. Closed-form expressions for the achievable communication rate, eavesdropping rate, and mainlobe-to-average-sidelobe ratio (MASR) are derived to evaluate system performance. Two complementary optimization problems are formulated using the successive convex approximation (SCA): (i) maximizing user rates under security constraints and (ii) minimizing eavesdropping rates while satisfying quality of service (QoS) requirements. The proposed joint optimization framework determines the optimal AP operational modes and power allocation across communication and sensing links. Extensive numerical results validate the theoretical analysis and demonstrate significant performance gains, revealing inherent trade-offs among communication efficiency, sensing accuracy, and security. These insights offer practical guidelines for designing secure CF-mMIMO ISAC systems.

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arXiv2026

Reciprocity Calibration of Dual-Antenna Repeaters via MMSE Estimation

This paper proposes a novel Bayesian reciprocity calibration method that consistently ensures uplink and downlink channel reciprocity in repeater-assisted multiple-input multiple-output (MIMO) systems. The proposed algorithm is formulated under the minimum mean-square error (MMSE) criterion. Its Bayesian framework incorporates complete statistical knowledge of the signal model, noise, and prior distributions, enabling a coherent design that achieves both low computational complexity and high calibration accuracy. To further enhance phase alignment accuracy, which is critical for calibration tasks, we develop a von Mises denoiser that exploits the fact that the target parameters lie on the circle in the complex plane. Simulation results demonstrate that the proposed MMSE algorithm achieves substantially improved estimation accuracy compared with conventional deterministic non-linear least-squares (NLS) methods, while maintaining comparable computational complexity. Furthermore, the proposed method exhibits remarkably fast convergence, making it well suited for practical implementation.

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arXiv2026

Score-Based VAMP with Fisher-Information-Based Onsager Correction

We propose score-based VAMP (SC-VAMP), a variant of vector approximate message passing (VAMP) in which the Onsager correction is expressed and computed via conditional Fisher information, thereby enabling a Jacobian-free implementation. Using learned score functions, SC-VAMP constructs nonlinear MMSE estimators through Tweedie's formula and derives the corresponding Onsager terms from the score-norm statistics, avoiding the need for analytical derivatives of the prior or likelihood. When combined with random orthogonal/unitary mixing to mitigate non-ideal, structured or correlated sensing settings, the proposed framework extends VAMP to complex black-box inference problems where explicit modeling is intractable. Finally, by leveraging the entropic CLT, we provide an information-theoretic perspective on the Gaussian approximation underlying SE, offering insight into the decoupling principle beyond idealized i.i.d. settings, including nonlinear regimes.

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arXiv2025

Physics-Aware Sparse Signal Recovery Through PDE-Governed Measurement Systems

This paper introduces a novel framework for physics-aware sparse signal recovery in measurement systems governed by partial differential equations (PDEs). Unlike conventional compressed sensing approaches that treat measurement systems as simple linear systems, our method explicitly incorporates the underlying physics through numerical PDE solvers and automatic differentiation (AD). We present physics-aware iterative shrinkage-thresholding algorithm (PA-ISTA), which combines the computational efficiency of ISTA with accurate physical modeling to achieve improved signal reconstruction. Using optical fiber channels as a concrete example, we demonstrate how the nonlinear Schrödinger equation (NLSE) can be integrated into the recovery process. Our approach leverages deep unfolding techniques for parameter optimization. Numerical experiments show that PA-ISTA significantly outperforms conventional recovery methods. While demonstrated on optical fiber systems, the proposed framework provides a general methodology for physics-aware signal recovery applicable to a wide range of various PDE-governed measurement systems.

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arXiv2025

Expectation Propagation-Based Signal Detection for Highly Correlated MIMO Systems

Large-scale multiple-input-multiple-output (MIMO) systems typically operate in dense array deployments with limited scattering environments, leading to highly correlated and ill-conditioned channel matrices that severely degrade the performance of message-passing-based detectors. To tackle this issue, this paper proposes an expectation propagation (EP)-based detector, termed overlapping block partitioning EP (OvEP). In OvEP, the large-scale measurement vector is partitioned into partially overlapping blocks. For each block and its overlapping part, a low-complexity linear minimum mean square error (LMMSE)-based filter is designed according to the partitioned structure. The resulting LMMSE outputs are then combined to generate the input to the denoiser. In this combining process, subtracting the overlapping-part outputs from the block outputs effectively mitigates the adverse effects of inter-block correlation induced by high spatial correlation. The proposed algorithm is consistently derived within the EP framework, and its fixed point is theoretically proven to coincide with the stationary point of a relaxed Kullback- Leibler (KL) minimization problem. The mechanisms underlying the theoretically predicted performance improvement are further clarified through numerical simulations. The proposed algorithm achieves performance close to conventional LMMSE-EP with lower computational complexity.

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arXiv2025

Integrated Communication and Computing in Time-Varying mmWave Channels

We propose a novel framework for integrated communication and computing (ICC) transceiver design in time-varying millimeter-wave (mmWave) channels. In particular, in order to cope with the dynamics of time-varying mmWave channels, the detection of communication symbols and the execution of an over-the-air computing (AirComp) operation are performed in parallel with channel tracking, as opposed to existing state-of-the-art (SotA) on ICC where perfect knowledge of the channel at all time instances is typically assumed. For clarity of exposition, we consider a single-input multiple-output (SIMO) uplink scenario where multiple single-antenna user equipment (UE) transmit to a base station (BS) equipped with multiple antennas, such that each UE, or edge device (ED), precodes its own transmit signal, while the BS, or access points (APs), also performs receive beamforming. The proposed transceiver framework then estimates channel state information (CSI) and data symbols in parallel, using a bilinear Gaussian belief propagation (BiGaBP) algorithm for joint channel and data detection (JCDE), aided by a channel prediction (CP) algorithm executed before each estimation window at the BS. The AirComp operation is then executed by means of an optimal combination of the residual signal. Simulation results demonstrate the effectiveness of the proposed scheme in performing ICC in challenging time-varying mmWave channels, with minimal degradation to both communication and computing performance.

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arXiv2025

A Flexible Design Framework for Integrated Communication and Computing Receivers

We propose a framework to design integrated communication and computing (ICC) receivers capable of simultaneously detecting data symbols and performing over-the-air computing (AirComp) in a manner that: a) is systematically generalizable to any nomographic function, b) scales to a massive number of user equipments (UEs) and edge devices (EDs), c) supports the computation of multiple independent functions (streams), and d) operates in a multi-access fashion whereby each transmitter can choose to transmit either data symbols, computing signals or both. For the sake of illustration, we design the proposed multi-stream and multi-access method under an uplink setting, where multiple single-antenna UEs/EDs simultaneously transmit data and computing signals to a single multiple-antenna base station (BS)/access point (AP). Under the communication functionality, the receiver aims to detect all independent communication symbols while treating the computing streams as aggregate interference which it seeks to mitigate; and conversely, under the computing functionality, to minimize the distortion over the computing streams while minimizing their mutual interference as well as the interference due to data symbols. To that end, the design leverages the Gaussian belief propagation (GaBP) framework relying only on element-wise scalar operations coupled with closed-form combiners purpose-built for the AirComp operation, which allows for its use in massive settings, as demonstrated by simulation results incorporating up to 200 antennas and 300 UEs/EDs. The efficacy of the proposed method under different loading conditions is also evaluated, with the performance of the scheme shown to approach fundamental limiting bounds in the under/fully loaded cases.

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arXiv2025

Quaternion Domain Super MDS for 3D Localization

We propose a novel low-complexity three-dimensional (3D) localization algorithm for wireless sensor networks, termed quaternion-domain super multidimensional scaling (QD-SMDS). This algorithm reformulates the conventional SMDS, which was originally developed in the real domain, into the quaternion domain. By representing 3D coordinates as quaternions, the method enables the construction of a rank-1 Gram edge kernel (GEK) matrix that integrates both relative distance and angular (phase) information between nodes, maximizing the noise reduction effect achieved through low-rank truncation via singular value decomposition (SVD). The simulation results indicate that the proposed method demonstrates a notable enhancement in localization accuracy relative to the conventional SMDS algorithm, particularly in scenarios characterized by substantial measurement errors.

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arXiv2025

Joint Channel, Data, and Radar Parameter Estimation for AFDM Systems in Doubly-Dispersive Channels

We propose new schemes for joint channel and data estimation (JCDE) and radar parameter estimation (RPE) in doubly-dispersive channels, such that integrated sensing and communications (ISAC) is enabled by user equipment (UE) independently performing JCDE, and base stations (BSs) performing RPE. The contributed JCDE and RPE schemes are designed for waveforms known to perform well in doubly-dispersive channels, under a unified model that captures the features of either legacy orthogonal frequency division multiplexing (OFDM), state-of-the-art (SotA) orthogonal time frequency space (OTFS), and next-generation affine frequency division multiplexing (AFDM) systems. The proposed JCDE algorithm is based on a Bayesian parametric bilinear Gaussian belief propagation (PBiGaBP) framework first proposed for OTFS and here shown to apply to all aforementioned waveforms, while the RPE scheme is based on a new probabilistic data association (PDA) approach incorporating a Bernoulli-Gaussian denoising, optimized via expectation maximization (EM). Simulation results demonstrate that JCDE in AFDM systems utilizing a single pilot per block significantly outperforms the SotA alternative even if the latter is granted a substantial power advantage. Similarly, the AFDM-based RPE scheme is found to outperform the OTFS-based approach, as well as the sparse Bayesian learning (SBL) technique, regardless of the waveform used.

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