PaperlayerView exact revision on arXiv

Source-linked AI summary

A Tutorial on Near-Field XL-MIMO Communications Towards 6G

Haiquan Lu, Yong Zeng, Changsheng You, Yu Han, Jiayi Zhang, Zhe Wang, Zhenjun Dong, Shi Jin, Cheng-Xiang Wang, Tao Jiang, Xiaohu You, Rui Zhang

arXiv:2310.11044v3cs.ITeess.SP

TL;DR

XL-MIMO promises higher spectral efficiency and spatial resolution but requires models and designs beyond conventional far-field massive MIMO. This tutorial develops near-field models incorporating NUSW and spatial non-stationarity, analyzes performance, and reviews practical techniques. It reports nonlinear SNR scaling, beam focusing with distance resolution, and higher near-field LoS channel rank, while identifying unresolved design challenges.

  • Problem

    XL-MIMO introduces NUSW, spatial non-stationarity, large-dimensional CSI acquisition, and greater hardware and processing demands that conventional approaches do not fully address.

  • Method

    The paper provides a comprehensive tutorial covering near-field modelling, performance analysis, beamforming designs, channel estimation, DAM transmission, and implementation issues.

  • Results

    Near-field XL-MIMO exhibits nonlinear SNR scaling, distance-resolving beam focusing, and substantially greater LoS channel effective rank at short distances than far-field modelling.

  • Takeaways & Limitations

    Near-field modelling is required to characterize XL-MIMO performance and guide beam training, channel estimation, codebook, transmission, and implementation designs.

Abstract

from arXiv · show

Extremely large-scale multiple-input multiple-output (XL-MIMO) is a promising technology for the sixth-generation (6G) mobile communication networks. By significantly boosting the antenna number or size to at least an order of magnitude beyond current massive MIMO systems, XL-MIMO is expected to unprecedentedly enhance the spectral efficiency and spatial resolution for wireless communication. The evolution from massive MIMO to XL-MIMO is not simply an increase in the array size, but faces new design challenges, in terms of near-field channel modelling, performance analysis, channel estimation, and practical implementation. In this article, we give a comprehensive tutorial overview on near-field XL-MIMO communications, aiming to provide useful guidance for tackling the above challenges. First, the basic near-field modelling for XL-MIMO is established, by considering the new characteristics of non-uniform spherical wave (NUSW) and spatial non-stationarity. Next, based on the near-field modelling, the performance analysis of XL-MIMO is presented, including the near-field signal-to-noise ratio (SNR) scaling laws, beam focusing pattern, achievable rate, and degrees-of-freedom (DoF). Furthermore, various XL-MIMO design issues such as near-field beam codebook, beam training, channel estimation, and delay alignment modulation (DAM) transmission are elaborated. Finally, we point out promising directions to inspire future research on near-field XL-MIMO communications.

I. INTRODUCTION

XL-MIMO extends massive MIMO with much larger arrays, bringing higher spectral efficiency and spatial resolution while introducing near-field propagation and implementation challenges. This tutorial develops near-field models and analyses, then surveys practical designs and applications.

  • XL-MIMO uses several hundreds or even thousands of antennas, at least an order of magnitude beyond massive MIMO, to improve spectral efficiency and spatial resolution.
  • 1) NUSW: The transition to XL-MIMO changes propagation from far-field UPW to near-field NUSW and from spatial stationarity to spatial non-stationarity.
  • 1) NUSW: The Rayleigh distance is r_Rayl = 2D^2/λ = 2D^2f/c, and increases quadratically with array dimension, antenna number, and spacing for fixed frequency.
  • 1) NUSW: For fixed D, Rayleigh distance increases with frequency, whereas for fixed M it increases as frequency decreases; in XL-MIMO it can reach hundreds or thousands of meters.
  • 1) NUSW: Near-field NUSW requires nonlinear phase and potentially unequal element amplitudes, while spatial non-stationarity allows distinct propagation environments across array portions.
  • C. Different Categories of XL-MIMO: XL-MIMO may use discrete or continuous-aperture arrays and collocated, sparse, modular, or distributed architectures, but distributed systems require stringent synchronization and frequent information exchange.
  • E. Motivation and Organization: Key challenges include accurate near-field modelling, efficient CSI acquisition, higher RF-chain cost and power consumption, and increased signal-processing complexity.
  • E. Motivation and Organization: The tutorial covers near-field modelling, performance analysis, beam codebooks and training, channel estimation, DAM transmission, implementation, and future applications.

II. NEAR-FIELD MODELLING FOR XL-MIMO

Near-field XL-MIMO modelling replaces far-field simplifications with array responses based on exact source-element geometry, distance-dependent amplitudes, phases, and element directional gains. The section develops generic, ULA, and channel-response formulations before contrasting them with the conventional UPW model.

  • Generic near-field model: The generic wireless link models each channel coefficient using the exact source-to-element distance, with amplitude and phase determined by that distance.The source may be an active transmitter or passive environmental scatterer, and the array may have arbitrary architecture.
  • Generic near-field model: Each element’s gain coefficient can depend on its local elevation-azimuth signal direction, so large apertures may expose different directions across elements.The section discusses isotropic, cosine-pattern, and 3GPP directional-gain models.
  • Array response vectors: The general near-field array response vector depends on the exact source location, whereas the far-field UPW model approximates distance, gain, and phase across elements.The UPW approximation assumes uniform path loss and gain, then uses a first-order distance expansion for phase modelling.
  • ULA specialization: For a ULA, the far-field UPW response assumes identical amplitude and angle of arrival across elements, with phase varying linearly by antenna index.The ULA geometry is parameterized by spacing, direction, array dimension, and reference-point angle.
  • Near- versus far-field modelling: XL-MIMO users and scatterers are more likely to lie in the near field, where spherical-wave phase modelling is required because the far-field UPW approximation is no longer valid.The Rayleigh distance is introduced as a criterion based on maximum phase difference under normal incidence.

2) Near-Field Phase Modelling:

Near-field phase modelling accounts for nonlinear phase variation across large arrays. The section introduces a direction-dependent Rayleigh distance to determine when linear phase modelling is sufficiently accurate.

  • Direction-dependent Rayleigh distance: The direction-dependent Rayleigh distance is defined using the maximum phase error between exact and first-order Taylor link-distance models.It is the minimum distance satisfying a phase-error threshold of π/8 for a given signal direction.
  • Direction-dependent Rayleigh distance: At normal incidence, the direction-dependent Rayleigh distance equals the classic Rayleigh distance, rDDRayl(π/2) = 2D^2/λ.Its dependence on signal direction through sin^2θ means the classic Rayleigh distance can exaggerate the near-/far-field boundary.
  • Comparison: The direction-dependent criterion is compared with the classic Rayleigh distance for a 128-element ULA at 2.4 GHz using half-wavelength element spacing.The comparison illustrates how direction affects the separation boundary.
  • Relation to amplitude modelling: Uniform-amplitude assumptions can become inaccurate as aperture size increases or link distance decreases, because direction-gain and distance variations affect element amplitudes.This amplitude issue is distinct from the phase nonlinearity addressed by the Rayleigh-distance criteria.

3) Near-Field Amplitude Modelling:

Near-field amplitude modelling determines when array-element amplitudes can be treated as uniform. The UPD complements the direction-dependent Rayleigh distance, enabling direction-dependent and simplified three-region model separations.

  • Uniform-power distance: The uniform-power distance (UPD) is the distance threshold beyond which amplitude variation across array elements is negligible for a specified signal direction and power threshold.Below the UPD, significant power differences invalidate the uniform-wave assumption.
  • Direction-dependent separation: The direction-dependent separation partitions space into UPW, NUPW, USW, and NUSW regions according to phase and amplitude validity.NUSW is required when neither linear phase nor uniform amplitude is valid.
  • Direction-independent separation: A conservative direction-independent separation reduces the model regions to UPW, USW, and NUSW while preserving modelling accuracy.The simplification uses direction-independent UPD together with the Rayleigh distance; NUSW contains the more specialized models as cases.
  • Special directions: For sources along the ULA axis, the UPD is much larger than for normal incidence, so the commonly used 1.2D amplitude criterion is unsafe for inclined incidence.The UPD depends on physical array size, while the Rayleigh distance depends on electrical size.
  • Summary: The refined modelling procedure treats the direction-dependent Rayleigh distance as a phase criterion and the UPD as an amplitude criterion.Together they define the near-/far-field separation used to select array-response models.

B. Near-Field Free-Space LoS XL-MIMO

Near-field free-space LoS XL-MIMO can be modelled either from individual transmit-receive coefficients or from transmit and receive response-vector products. These choices differ in channel rank, with spherical-wave modelling enabling ranks above one at short distances.

  • Channel modelling methods: The direct LoS modelling method constructs the XL-MIMO channel matrix from the complex-valued coefficient of every transmit-receive antenna pair.It can incorporate distance and antenna-gain variations across antenna pairs.
  • Channel modelling methods: The response-vector method expresses the near-field LoS channel matrix as an outer product of near-field transmit and receive array response vectors.It is inspired by far-field UPW-based LoS MIMO modelling and treats each opposite array as a point when forming the response vectors.
  • Channel rank: The direct coefficient model can have rank greater than one, whereas the response-vector model is always rank one.This rank distinction is the major difference between the two near-field LoS modelling methods.
  • Far-field reference: The far-field UPW LoS XL-MIMO channel matrix is rank one under uniform path loss, uniform gain, and first-order phase approximations.These assumptions apply when the link distance is at least the MIMO Rayleigh distance.
  • Effective-rank behavior: In the illustrated 128-transmit-element and 32-receive-element setup, near-field LoS modelling yields effective rank much greater than one at short distances, decreasing toward one as distance increases.Effective rank counts singular values no smaller than 10% of the sum of all singular values; both the response-vector and far-field models remain rank one.
  • Implications: The higher near-field LoS rank enables the possibility of spatial multiplexing in free space, while distance-aware precoding can adjust RF-chain count to the distance-related rank.The latter connection is reported as related prior work exploiting the spherical-wave property.

C. Near-Field Multi-Path XL-MIMO

Near-field XL-MIMO multipath modelling superimposes LoS and NLoS components while accounting for spatial non-stationarity through visibility regions (VRs). VRs capture partial visibility of users and scatterers across the array, including blockage and evolving visibility.

  • The multipath XL-MIMO channel is formed by superimposing separately modelled LoS and NLoS components.
  • For isotropic scatterers, each NLoS path is represented by a complex gain multiplied by near-field transmit and receive response vectors.
  • The bistatic radar formulation characterizes scattered paths using scatterer RCS, additional phase, transmitter-scatterer distance, and scatterer-receiver distance.
  • Spatial non-stationarity arises because different array portions experience distinct propagation environments, including different cluster sets or obstacles.
  • Visibility regions: VRs include UE-side geographical regions and BS-side visible array portions, with UE-side visibility potentially switching as users move.
  • Visibility regions: Unequal pathloss and signal blockage create uneven channel-power distributions across XL-arrays, while UE-side VR evolution can be modelled as a birth-death process.

D. Spatial Correlation Based Near-Field Modelling

Spatial-correlation modelling extends conventional far-field formulations by incorporating near-field amplitude variation, NUSW propagation, and partial visibility through VRs. These effects make correlation depend on physical positions and local scattering conditions rather than relative antenna separation alone.

  • Conventional far-field spatial correlation uses a common large-scale factor and depends on the PAS and relative antenna locations, yielding spatial wide-sense stationarity.
  • Near-field elements experience different large-scale fading because each element has a distinct link distance, producing independent but non-identically distributed Rayleigh fading when correlation is identity.
  • Differences brought by NUSW: NUSW-based near-field spatial correlation is determined by scatterer distances and the scattering environment’s path-loss characteristics, so SWSS is no longer valid.
  • Differences brought by VR: VR-aware correlation models use diagonal visibility matrices to set channel contributions to zero for antenna elements unseen by the UE.
  • Differences brought by VR: Partial visibility and NUSW jointly invalidate SWSS, with BS-side VR evolution modelled using a two-stage homogeneous Markov process.
  • Extensions: Near-field modelling also extends to UPAs and modular XL-arrays, whose larger inter-module spacing produces stronger near-field effects than collocated arrays.
  • Extensions: Polarization mismatch and spatial-wideband effects require additional modelling in near-field XL-MIMO, particularly at short link distances and high bandwidths.

F. Near-Field Channel Measurements

Channel measurement campaigns across sub-6 GHz and mmWave bands validate the characteristic near-field effects of XL-MIMO. Measurements reveal NUSW, spatial non-stationarity, cluster birth-death behaviour, and channel hardening.

  • Near-field XL-MIMO measurements have been conducted across sub-6 GHz and mmWave frequency bands using several XL-array architectures.
  • Measured LoS paths exhibit angle offsets across the array, demonstrating that the far-field UPW model is invalid for XL-MIMO.
  • Channel gain, K-factor, delay spread, and angular spread vary across XL-arrays, evidencing spatial non-stationarity.
  • Measured power-delay and power-angle profiles show cluster birth-death behaviour, with some clusters visible across the whole array and others only partially visible.
  • Small channel-gain standard deviation in frequency and time domains supports the observation of channel hardening.

G. Lessons Learned

XL-MIMO requires near-field models because NUSW and spatial non-stationarity replace far-field assumptions as arrays become extremely large. Its SNR scaling, spatial correlation, and deployment behaviour therefore differ fundamentally from conventional MIMO.

  • Near-field XL-MIMO modelling must capture spherical-wave phase and amplitude variation through UPW, NUPW, USW, and NUSW array-response models.
  • Near-field spatial correlation is determined by path-loss characteristics rather than only PAS, and spatial wide-sense stationarity no longer holds.
  • SNR scaling laws: Near-field NUSW SNR scales nonlinearly with antenna number according to the angular span, rather than linearly as under UPW.
  • SNR scaling laws: As M → ∞, the NUSW angular span approaches π, while the corresponding SNR approaches a constant depending on projected distance.
  • SNR scaling laws: The UPW model predicts unbounded linear SNR growth with M, violating power conservation, whereas NUSW converges to UPW only in the far field.
  • SNR scaling laws: For the illustrated parameters, NUSW and UPW agree at small M but diverge as M increases, demonstrating the need for spherical-wavefront modelling.
  • SNR scaling laws: For continuous surfaces, received power approaches P/2 as M → ∞ for an isotropic source, reflecting the projected-aperture limit.
  • SNR scaling laws: Modular-array SNR depends on physical module dimensions and inter-module separation, with analogous scaling behaviour reported for modular XL-ULA and XL-UPA.

B. Near-Field Beam Focusing Pattern

Near-field beam focusing extends conventional directional beam patterns by making beam response depend on observation distance and enabling spatial discrimination beyond angle alone. The section compares far-field and near-field beamforming across collocated, modular, and sparse arrays.

  • Beam-focusing formulation: Near-field beam focusing must account for the observation region and the selected beamforming vector, which depends on CSI or a predefined codebook.The codebook includes both far-field and near-field beamforming designs.
  • Far-field observation with far-field beamforming: Far-field observation with far-field beamforming reduces the focusing formulation to the conventional far-field beam pattern.The paper notes an additional far-field-observation, near-field-beamforming case but does not discuss it further.
  • Far-field beam pattern: Far-field beam patterns depend on spatial-frequency difference rather than link distance, with angular resolution determined by array architecture.For collocated, modular, and sparse arrays, the null-to-null beam width of the Dirichlet-kernel term is 2/(M̃d̃).

NMI ,

Near-field XL-array focusing provides spatial resolution in both angle and distance, while array architecture trades sharper resolution against grating lobes. Near-field mismatch and energy spreading also affect interference and beamforming performance.

  • Angular resolution and grating lobes: Modular arrays provide higher angular resolution than collocated arrays, while sparse arrays can provide still higher resolution under the compared architecture parameters.For equal total element count, modular-array improvement over collocated arrays requires Γ > M and introduces grating lobes.
  • Angular resolution and grating lobes: Fig. 19 compares far-field beam patterns for collocated, modular, and sparse arrays, showing modular resolution between collocated and sparse architectures.The comparison uses NM = 16, N = 4, M = 4, Γ = 13, and I = 13; grating lobes appear in modular and sparse arrays.
  • Energy spread and interference: Far-field beamforming at a near-field observation point expands beam width and spreads energy toward neighboring directions.With 256 antennas, far-field observation concentrates energy on the desired direction, whereas near-field observation exhibits the expanded beam width.
  • Energy spread and interference: Energy spreading creates more complicated inter-user interference between near-field and far-field users, especially when they are neighbors.The beam focusing pattern reflects correlation between near- and far-field channels.
  • Distance resolution: Near-field beam focusing supports distance resolution in addition to angular resolution, with effective distance resolution improving quadratically with physical array dimension.Two same-direction locations can be separated when |1/r′ − 1/r| ≥ 1/rhp(θ′).
  • Distance resolution: For equal Γ and I in the compared setup, sparse XL-arrays achieve the highest distance resolution, modular arrays outperform collocated arrays, and all patterns decrease with distance separation.Fig. 21 uses NM = 512, N = 128, M = 4, Γ = 13, I = 13, and r′ = 200 m.

C. Achievable Rate of Near-Field Communication

Near-field XL-MIMO achievable-rate analysis relates user interference to channel correlation and evaluates receive beamforming under near-field channels. The results show that near-field designs become increasingly important as antenna number grows.

  • Inter-user interference and SINR: XL-MIMO can suppress inter-user interference through distance separation between users sharing the same direction, adding a spatial degree of freedom beyond angular separation.This mechanism is evaluated with MRC, ZF, and MMSE beamforming in multi-user near-field communications.
  • Inter-user interference and SINR: Increasing channel correlation deteriorates SINR for MRC, ZF, and MMSE, while MMSE provides the best SINR performance among the three schemes.The SINR is expressed as single-user SNR minus an interference penalty whose form depends on the beamforming scheme.
  • Achievable-rate comparison: For relatively small antenna numbers, far-field and near-field beamforming have similar sum-rate performance because users and scatterers remain effectively in the far field.The comparison uses near-field NUSW and far-field UPW receive designs with MRC, ZF, and MMSE.
  • Achievable-rate comparison: As antenna number increases, far-field beamforming performs much worse than near-field beamforming because UPW-based designs mismatch the actual near-field NUSW channels.For large M, near-field ZF performance is comparable to near-field MMSE performance.
  • Power control: Mixed near- and far-field communications require more complicated power control because energy spreading creates more complicated inter-user interference.When all users are in the far field, the near-field power-control scheme reduces to the far-field counterpart.
  • Practical considerations: Near-field and far-field polarization and mutual-coupling effects can further complicate near-field precoding and reduce radiation efficiency in densely packed arrays.The paper discusses polarized multi-user interference and coupling-induced radiation-pattern distortion as related implementation considerations.
  • Degrees of freedom: XL-MIMO DoF analyses include approximate ULA and UPA expressions based on physical dimensions, distance, and aperture areas.The paper identifies accurate DoF characterization as an open direction for practical XL-MIMO design.

E. Near-Field XL-MIMO Sensing

Near-field XL-MIMO supports sensing and related applications, while sparse and modular arrays introduce grating-lobe ambiguities that remain unresolved.

  • Near-field XL-MIMO sensing has been studied for radar, localization, and tracking applications.
  • Sparse arrays can improve spatial resolution and sensing capability for discriminating and characterizing electromagnetic environments.
  • Grating lobes in modular and sparse arrays can cause angular ambiguity and notable estimation errors when targets lie within them.
  • Spatial resolution in near-field XL-MIMO provides both angular and distance resolution, supporting sensing, localization, and tracking.

1) Cartesian Domain:

Near-field beam codebooks sample spatial angle and distance to match XL-MIMO’s two-dimensional focusing behavior, but their sampling choices create accuracy, size, and training-overhead trade-offs.

  • Cartesian Domain:: Cartesian-domain codebooks uniformly sample x-y coordinates to cover the entire two-dimensional plane.Each codeword steers toward a sampled location defined by x- and y-axis steps Δx and Δy.
  • Cartesian Domain:: Cartesian-domain codebooks can become prohibitively large because their size equals the product of sampled x- and y-axis points.The resulting codebook size imposes long beam-training overhead.
  • Cartesian Domain:: Polar-domain codebooks sample both spatial angle and distance, with codewords targeting paired angular and range samples.Uniform angular sampling can cover the angular domain, while distance sampling is chosen according to channel-representation accuracy.
  • Cartesian Domain:: Polar-domain distance sampling is denser at short range and sparser at longer range to limit correlation between near-field steering vectors.For correlation threshold Δ = 0.5, the passage gives Λ ≥ 1.6.
  • Cartesian Domain:: Slope-intercept-domain codebooks quantize the quadratic and linear phase terms as slope k and intercept b, potentially using fewer codewords than polar-domain codebooks.The associated beam-training design is more complicated.
  • Cartesian Domain:: Near-field beam-training methods are predominantly designed for non-uniform polar-domain codebooks and may not suit slope-intercept-domain codebooks.

1) Narrowband Near-Field Beam Training:

Near-field XL-MIMO beam training must search over both angle and distance, while wideband systems additionally face multipath and beam-split challenges; DAM offers a path-based transmission alternative for delay dispersion.

  • 1) Narrowband Near-Field Beam Training:: Two-dimensional exhaustive search evaluates all angular-distance codewords, requiring NS training symbols.For N = 512 and S = 6, the overhead is 3072 training symbols.
  • 1) Narrowband Near-Field Beam Training:: Two-phase search first estimates spatial angle with DFT beams and then resolves distance using a polar-domain codebook.Its training overhead is N + KS, using middle-K angle candidates to improve angle estimation.
  • 1) Narrowband Near-Field Beam Training:: Joint angle-distance estimation with DFT codebooks can reduce training overhead and improve distance-estimation accuracy.
  • 1) Narrowband Near-Field Beam Training:: Hierarchical near-field training progressively refines coarse angle and distance estimates with narrower beams.Design is difficult because each codeword spans both angular and distance domains, complicating coverage across layers.
  • 1) Narrowband Near-Field Beam Training:: Wideband near-field beam training must address multipath channels and beam split caused by large bandwidth and XL-array aperture.
  • D. Delay Alignment Modulation: DAM aligns multipath delays and uses path-based beamforming so signal components arrive concurrently and constructively.The approach can transform a time-dispersive channel into an ISI-free AWGN channel without equalization or multicarrier transmission.
  • D. Delay Alignment Modulation: Path-based DAM beamforming can achieve an ISI-free AWGN channel when M ≥ L.Here, the beamforming vector is designed in the orthogonal complement of the other path channels.
  • D. Delay Alignment Modulation: DDAM extends DAM to Doppler-ISI mitigation and can yield higher spectral efficiency than OTFS as M increases with lower receiver complexity and detection latency.

E. Cost-Efficient and Low-Complexity Implementation

XL-MIMO implementation must address both hardware cost and large-dimensional signal-processing complexity. Low-cost devices, antenna selection, and distributed or simplified processing are identified as routes toward more efficient designs.

  • XL-MIMO increases hardware cost through expensive RF chains and signal-processing complexity through large-dimensional channels.These issues motivate cost-efficient and low-complexity designs.
  • Distributed processing assigns tasks across local processing units instead of relying entirely on centralized CPU processing.
  • Low-cost and low-resolution devices can reduce XL-MIMO cost and energy expenditure, while spatial non-stationarity supports antenna selection.

1) Cost- and Energy-Efficient Implementation:

The paper surveys hardware-, energy-, and complexity-efficient XL-MIMO implementations, including reduced-resolution converters, antenna selection, iterative algorithms, distributed processing, and practical near-field design. It also identifies unresolved beam-training and hybrid active-passive communication challenges.

  • Cost- and Energy-Efficient Implementation: Low-resolution ADCs reduce XL-MIMO signal-processing complexity and support green communications, but can degrade performance; mixed-ADCs balance these trade-offs.
  • Cost- and Energy-Efficient Implementation: Antenna selection exploits spatial non-stationarity by serving users with only a suitable subset of antennas, reducing circuit cost and computational complexity.
  • Cost- and Energy-Efficient Implementation: FSS achieves comparable performance to FAS while reducing computational complexity and hardware implementation requirements.
  • Low Signal Processing Complexity Implementation: VMP receiver complexity scales linearly with the number of array elements and users because it avoids matrix inversion.
  • Low Signal Processing Complexity Implementation: Distributed processing partitions the XL-array into subarrays with LPUs, parallelizing signal processing and avoiding large-dimensional centralized processing.
  • Near-Field Beam Training and Beam Tracking: Near-field beam training requires angular-distance codebook searches, while multipath and high-mobility settings require new training and tracking methods.Multipath paths may have overlapping dominant angular regions, and tracking must follow both user angle and distance.
  • Near-Field Hybrid Active and Passive Communications With XL-MIMO: Near-field hybrid active-passive communications require efficient channel estimation and practical active and passive beamforming designs.Large IRS or reflector dimensions make near-field operation likely for users and scatterers.
Loading 2310.11044v3…