Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2604.08531

Wideband Compressed-Domain Cram\'{e}r-Rao Bounds for Near-Field XL-MIMO: Data and Geometric Diversity Decomposition

Rıfat Volkan Şenyuva
View original source ↗Read source document ↗Export metadata ↓

Abstract

Wideband orthogonal frequency-division multiplexing (OFDM) over near-field extremely large-scale MIMO (XL-MIMO) arrays couples beam squint and wavefront curvature, and existing single-frequency compressed covariance models are severely biased as a result. To the best of our knowledge, no compressed-domain Cram\'{e}r-Rao bound (CRB) has been reported for this regime under hybrid analog-digital architectures; existing wideband near-field bounds assume full-array observation. We derive the wideband compressed-domain CRB and decompose its Fisher information gain into two terms: a dominant data-diversity term, exactly 10 log10(K_s) dB, where K_s denotes the number of independent subcarrier observations, and we prove that for a centred array the full-array range bound is invariant to beam squint, so the full-array wideband gain equals the data-diversity term to within 3x10^-4 dB. Under hybrid compression, however, this invariance breaks: the residual is a combiner-dependent fluctuation of either sign rather than a propagation-geometry effect, with mean +0.157 dB and standard deviation 0.767 dB over 385 realizations at N_RF = 16, B = 400 MHz, and its spread shrinks toward zero as the number of RF chains grows. At 28 GHz with B = 400 MHz, data diversity contributes +27.1 dB and hybrid compression contributes an additional 12.6 dB gap relative to the full-array bound at N_RF = 16 RF chains. Frequency-aware covariance modeling is therefore the dominant requirement, and the residual is a property of the analog front end rather than of the propagation geometry.

Explore related subjects

eess.SPcs.ITmath.IT

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Rıfat Volkan Şenyuva. 2026-04-09. Wideband Compressed-Domain Cram\'{e}r-Rao Bounds for Near-Field XL-MIMO: Data and Geometric Diversity Decomposition. https://arxiv.org/abs/2604.08531

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Load Balancing in Multi-Shell LEO Satellite Networks with Successive Interference Cancellation

Multi-shell low Earth orbit (LEO) networks can increase service opportunities, but altitude-dependent propagation can concentrate traffic on lower shells and create strong inter-shell interference under full frequency reuse. This paper develops a mathematical framework for load balancing in multi-shell LEO satellite networks. Satellites on each shell form an independent spherical Poisson point process (SPPP), and the typical user associates with one of the per-shell serving satellites through a shell-dependent biased received-power rule, with receiver-side successive interference cancellation (SIC) under full frequency reuse. Shell-wise association probabilities, conditioned serving-distance distributions, and the rate coverage probability under shell-dependent traffic loads are derived and validated by simulation. The results show that shell-dependent biasing alleviates lower-shell traffic concentration and improves rate coverage, while receiver-side SIC mitigates the dominant lower-shell interference experienced by users associated with upper shells. Load balancing provides its largest rate-coverage gain in traffic hotspots, while SIC becomes more valuable as receive-side isolation weakens. With a fixed satellite budget, distributing satellites across multiple shells can further improve hotspot rate coverage by adding shell-wise serving opportunities.

eess.SP↗
arXiv2026

Tensor Decomposition Based Mixed-Field Sensing for XL-MIMO AFDM Systems

Integrated sensing and communications enabled by extremely large-scale MIMO (XL-MIMO) and affine frequency division multiplexing (AFDM) is a highly promising paradigm for vehicular networks. However, the near-field spherical wavefront distortions induce severe non-linear parameter coupling, while the highly dynamic scattering environments exacerbate mismatch errors. To address these critical challenges, this paper proposes a novel tensor-based sensing scheme for XL-MIMO AFDM systems. First, the received signals are reformulated into a tensor, followed by an efficient decomposition approach that exploits the inherent Vandermonde structure of the factor matrices. This allows parameters to be directly estimated from the decomposed matrices, effectively avoiding inter-parameter coupling. Subsequently, a symmetric decoupling and real-domain manifold optimization algorithm is proposed for angle of arrival estimation, circumventing the high-dimensional searches typically induced by near-field effects. Furthermore, a baseband reconstruction and analytical gradient-based algorithm is developed to perform delay-Doppler estimation in the continuous parameter domain, fundamentally eradicating the grid-mismatch errors inherent in high-mobility scenarios. With these decoupled factors, the remaining unknown angle of departure can be readily extracted. Extensive simulation results demonstrate that the proposed scheme achieves orders-of-magnitude improvements in delay-Doppler accuracy and eliminates the error floors in angular estimation that severely bottleneck state-of-the-art baselines.

eess.SP↗
arXiv2026

Radio Map Construction with Post-Hoc Location Calibration under Quasi-Static Positioning Errors: Joint Estimation, Performance Bounds, and GNSS-Based Evaluation

Radio maps enable environment-aware wireless and Internet-of-Things applications and can be constructed from location-tagged received signal strength (RSS) measurements collected by mobile devices. In urban environments, temporally correlated GNSS errors can shift an entire sensing trajectory, causing systematic spatial misregistration that is not mitigated by collecting more measurements. This paper presents a radio-map construction framework that uses the radio measurements themselves to calibrate erroneous location tags after data collection. The dominant positioning error is modeled as a sensor-specific quasi-static offset, which is jointly estimated with radio-propagation parameters in a Gaussian process regression (GPR) framework by exploiting complementary spatial information from distance-dependent path loss and spatially correlated shadowing. We establish lower and upper bounds on the conditional Bayes risk and show that, under a translation-invariant trajectory model, trajectory information alone cannot identify the quasi-static offset, thereby motivating the use of RSS-derived spatial information for calibration. Numerical evaluations across propagation conditions show that the proposed method reduces the mean squared error (MSE) gap from ideal GPR to approximately $3.26\mathrm{dB}^2$, compared with about $10\mathrm{dB}^2$ for position-error-agnostic and noisy-input GPR baselines. Evaluation using positioning-error models derived from smartphone GNSS measurements shows that the proposed method outperforms a KF--RTS trajectory-smoothing baseline despite unmodeled time-varying positioning errors, remaining within approximately $5\mathrm{dB}^2$ of ideal GPR at the median MSE. These results demonstrate that RSS measurements can serve not only as observations for radio-map reconstruction but also as spatial cues for post-hoc calibration of imperfectly geotagged sensing data.

eess.SP↗