Near-Field Radar Model

• Near-field radar model is a framework that employs spherical-wave propagation to accurately capture range and angle dependencies in imaging applications.
• It replaces far-field planar-wave approximations to enable precise sensing in short-range, large-aperture, and complex multistatic scenarios.
• Advanced reconstruction techniques and controlled model transformations improve computational efficiency while preserving key electromagnetic characteristics.

A near-field radar model is a sensing model in which electromagnetic propagation is treated with spherical, range-dependent geometry rather than with the planar-wave approximation used in far-field radar. Across synthetic aperture radar (SAR), multiple-input multiple-output (MIMO) radar, inverse SAR (ISAR), integrated sensing and communications (ISAC), and passive radar, the defining feature is that the signal collected by each transmit–receive channel depends on exact or approximated Euclidean path lengths to the scene, so the array response depends jointly on range and angle, often with antenna-dependent amplitude variation as well as nonlinear phase curvature (Smith et al., 2023). This modeling shift is essential when the target lies in the Fresnel region, when apertures are electrically large, when arrays are extremely large-scale, or when imaging is performed at short stand-off distances such as decimeters to tens of meters (Hamidi et al., 2020).

1. Geometric regime and defining assumptions

Near-field operation is usually characterized by Fresnel- or Fraunhofer-type criteria. For a uniform linear array with aperture $D=(N-1)d$, one criterion used in THz automotive radar is the Fraunhofer distance

$d_F=\frac{2D^2}{\lambda},$

with near-field behavior for targets satisfying $r_k<d_F$ (Elbir et al., 2023). In 6G ISAC with extremely large arrays, the corresponding Rayleigh-distance scaling

$\frac{2D^2 f_c}{c}$

can extend the near-field region to practical deployment distances, so communication scatterers and radar targets may both lie in the spherical-wave regime (Daei et al., 2024).

In short-range mmWave SAR, the near-field character can be explicit. A 79 GHz FMCW SAR experiment used a synthetic aperture of about $13.8\text{ cm} \times 29.8\text{ cm}$, computed a Fresnel distance of $5.41\text{ m}$, and imaged a target at $z_a=30\text{ cm}$, so the target lay well inside the Fresnel zone and far-field planar-wave assumptions were invalid (Hamidi et al., 2020). A similar concern appears in close-range multimodal depth sensing, where near-field imaging radar is treated as a 3D radio-frequency Time-of-Flight sensor and the approximation $\delta_z\approx\delta_r$, $\delta_{x,y}\approx\delta_{h,v}$ is stated to hold only at the sensor center and not generally in the near field (Wirth et al., 2024).

The near-field/far-field distinction is not merely a matter of adding a correction term to a conventional model. In the rotational MIMO-ISAR formulation, the exact square-root ranges are retained over a full $360^\circ$ rotational aperture, and the authors explicitly state that the near-field model is foundational to the reconstruction rather than a minor refinement (Smith et al., 2023). Likewise, exact spherical-wave models for extremely large-scale MIMO show that commonly used second-order Taylor approximations can be insufficient for Cramér–Rao bound analysis, because they fail to preserve the full Fisher-information structure of the spherical-wave manifold (Wang et al., 2023).

2. Canonical forward models

The most common near-field radar model expresses the measured signal as a superposition of responses from all scene points, with each response determined by exact transmit and receive path lengths. In near-field freehand MIMO-SAR, the multistatic signal is modeled as

$d_F=\frac{2D^2}{\lambda},$0

with

$d_F=\frac{2D^2}{\lambda},$1

so the model contains both spherical-wave phase and the amplitude factor $d_F=\frac{2D^2}{\lambda},$2 (Vasileiou et al., 2023).

A closely related formulation appears in near-field MIMO-ISAR. For a target point $d_F=\frac{2D^2}{\lambda},$3, transmitter position $d_F=\frac{2D^2}{\lambda},$4, receiver position $d_F=\frac{2D^2}{\lambda},$5, target rotation angle $d_F=\frac{2D^2}{\lambda},$6, and fixed radial distance $d_F=\frac{2D^2}{\lambda},$7, the exact ranges are

$d_F=\frac{2D^2}{\lambda},$8

$d_F=\frac{2D^2}{\lambda},$9

and the multistatic echo is

$r_k<d_F$0

Here the phase depends on the sum of two spherical ranges, not on a linearized angle-only term (Smith et al., 2023).

For monostatic or monostatic-equivalent FMCW SAR, the same structure reduces to a single square-root range. A point reflector at $r_k<d_F$1 contributes

$r_k<d_F$2

and a continuous scene gives

$r_k<d_F$3

This formulation can be written as a 2D convolution with a spherical-wave impulse response $r_k<d_F$4 (Hamidi et al., 2020).

In compressive 3D near-field MIMO imaging, the same physics is often expressed as a discrete linear inverse problem

$r_k<d_F$5

where the $r_k<d_F$6-th entry of the system matrix is

$r_k<d_F$7

This model makes the near-field dependence explicit through voxelwise transmit and receive distances $r_k<d_F$8 and $r_k<d_F$9 (Manisali et al., 2023).

A stronger version of the model retains exact antenna-varying amplitudes in addition to exact phases. In 3D near-field MIMO localization, the receive steering vector is written as

$\frac{2D^2 f_c}{c}$0

with

$\frac{2D^2 f_c}{c}$1

and an analogous transmit-side model (Hua et al., 2023). This formulation departs from constant-amplitude steering vectors and makes range-dependent path loss part of the signal manifold itself.

3. Equivalent monostatic reductions and model transformations

Because exact near-field multistatic models are computationally expensive, many practical methods introduce controlled transformations that preserve the relevant spherical-wave structure while enabling efficient inversion. In freehand mmWave mobile SAR, irregular multistatic measurements are mapped to a virtual planar monostatic array with the Efficient Multi-Planar Multistatic (EMPM) method: $\frac{2D^2 f_c}{c}$2 where

$\frac{2D^2 f_c}{c}$3

After this residual phase correction, the data are treated as if they were sampled on a planar monostatic aperture and reconstructed with an RMA-style method (Vasileiou et al., 2023).

Near-field rotational MIMO-ISAR uses the same principle in cylindrical geometry. The MIMO pair is phase-compensated so that it behaves approximately like a monostatic virtual element at the midpoint of the pair, after which the measurements are processed by efficient monostatic holographic imaging machinery (Smith et al., 2023). A related midpoint transformation is used in 3D virtual MIMO-SAR imaging at 77 GHz, where the original bistatic FMCW signal is shifted to the midpoint

$\frac{2D^2 f_c}{c}$4

and rewritten as a monostatic near-field convolution with an extra phase term accounting for the multistatic geometry (Hamidi, 2022).

Not all transformations are geometric. In near-field ELAA ISAC, the difficulty is that the exact steering vector

$\frac{2D^2 f_c}{c}$5

has a nonlinear phase law in antenna index because

$\frac{2D^2 f_c}{c}$6

A lifted super-resolution formulation shows that this nonlinearity can be represented in a higher-dimensional space as

$\frac{2D^2 f_c}{c}$7

where $\frac{2D^2 f_c}{c}$8 depends only on distance and $\frac{2D^2 f_c}{c}$9 is a Vandermonde-like angular vector (Daei et al., 2024). This suggests a different notion of model reduction: preserving near-field physics by changing the representation rather than by linearizing the geometry.

A recurring misconception is that any quadratic correction is sufficient. Exact near-field CRB analyses for XL-MIMO show that the commonly used second-order Taylor approximation can recover some curvature but can still predict incorrect asymptotic behavior for angle and range estimation (Wang et al., 2023). The literature therefore distinguishes between exact spherical-wave models, Fresnel approximations used for tractability, and virtual-array transformations used for acceleration.

4. Reconstruction and inverse methods

Near-field reconstruction methods generally fall into time-domain, wavenumber-domain, and learned or hybrid categories. In depth-slice FMCW SAR, the spatial Fourier transform of the measured field yields a depth-dependent phase factor, and reflectivity on each plane $13.8\text{ cm} \times 29.8\text{ cm}$0 is reconstructed by compensating that phase and applying a 2D inverse Fourier transform: $13.8\text{ cm} \times 29.8\text{ cm}$1 Repeating this operation over multiple $13.8\text{ cm} \times 29.8\text{ cm}$2 values produces a 3D volume (Hamidi et al., 2020).

In near-field MIMO-ISAR, the corresponding pipeline is explicitly spectral: gather raw 4-D MIMO data, apply multistatic-to-monostatic compensation, perform a 2-D FFT over $13.8\text{ cm} \times 29.8\text{ cm}$3 and $13.8\text{ cm} \times 29.8\text{ cm}$4, invert the rotational phase distortion with the conjugate filter, apply Stolt interpolation from polar to Cartesian wavenumber coordinates, and then perform a 3-D inverse FFT to recover $13.8\text{ cm} \times 29.8\text{ cm}$5 (Smith et al., 2023). Virtual MIMO-SAR at 77 GHz uses a similar range-migration style reconstruction after midpoint conversion, but with a hybrid aperture formed by a virtual MIMO dimension and a SAR scanning dimension (Hamidi, 2022).

For arbitrary handheld trajectories, exact backprojection remains the reference because it directly uses the true distance $13.8\text{ cm} \times 29.8\text{ cm}$6 for each voxel and aperture sample. The computational cost, however, is high. The HHFFBPA method preserves the spherical-wave Born model

$13.8\text{ cm} \times 29.8\text{ cm}$7

and accelerates reconstruction by factorized backprojection, analytical local spectrum support, spatial downconversion, and local linear transform; its asymptotic complexity is stated as $13.8\text{ cm} \times 29.8\text{ cm}$8, compared with BPA’s $13.8\text{ cm} \times 29.8\text{ cm}$9 (Wang et al., 30 Jun 2025).

Learned methods often retain a physics-based first stage. In real-time 3D near-field MIMO imaging, the Deep2S pipeline first computes the adjoint image

$5.41\text{ m}$0

takes its magnitude, normalizes it, and then refines it with a 4-level 3D U-Net to estimate a magnitude-only reflectivity image (Manisali et al., 2023). In mobile freehand SAR, Mobile-SRGAN uses EMPM and RMA to obtain a distorted low- or medium-fidelity image and then applies a compact conditional GAN with a depthwise/pointwise-convolution generator of 79,233 parameters and a PatchGAN-style discriminator. On a test set of 1027 never-seen-before images, the reported metrics are PSNR $5.41\text{ m}$1 dB, RMSE $5.41\text{ m}$2, and time per image $5.41\text{ m}$3 s, compared with BPA at PSNR $5.41\text{ m}$4 dB, RMSE $5.41\text{ m}$5, and $5.41\text{ m}$6 s per image (Vasileiou et al., 2023).

Backprojection also underlies near-field depth imaging and non-line-of-sight imaging. In MAROON, a Rohde & Schwarz QAR50 submodule operating from $5.41\text{ m}$7 GHz reconstructs a $5.41\text{ m}$8 voxel volume by FSCW backprojection and extracts a depth map by maximum projection over $5.41\text{ m}$9; an empirical threshold of $z_a=30\text{ cm}$0 dB relative to the maximum confidence value is used to suppress sidelobes and background (Wirth et al., 2024). In multi-view NLOS imaging with non-reconfigurable EM skins, the image is reconstructed by back-projection over the hypothesized hidden scene using the delay model imposed by the illuminated metasurface patch and vehicle position (Bellini et al., 2024).

Passive near-field imaging uses a different inverse problem. For each illuminating configuration and each frequency, a single-frequency inverse source solver reconstructs equivalent-source plane-wave spectra, and the resulting single-frequency images are then coherently summed across frequency and transmitter position with phase and magnitude corrections (Wang et al., 9 Mar 2026).

5. Estimation theory, waveform design, and information limits

Near-field radar models alter parameter identifiability because they couple range, angle, amplitude, and sometimes motion through spherical-wave geometry. In 3D near-field MIMO localization, the unknowns include target coordinates, complex reflection coefficients, and an unknown clutter/noise covariance matrix, and the Fisher information matrix is built from derivatives of exact steering vectors that contain both phase and amplitude terms. The resulting CRB depends explicitly on those derivatives, and the papers report that considering exact antenna-varying amplitudes yields more accurate CRBs than constant-amplitude approximations, especially when targets are close to the transceivers (Hua et al., 2023). A closely related formulation for cluttered environments reaches the same conclusion and further reports that transmit waveforms have a significant impact on CRB and localization performance (Hua et al., 2023).

In extremely large-scale MIMO sensing, the near-field uniform spherical-wave model changes the asymptotic behavior of the CRB itself. For monostatic XL-MIMO, the range CRB becomes finite, unlike the far-field uniform plane-wave model in which the range CRB is infinite, and the angle CRB decreases with diminishing return and approaches a limit as the number of antennas increases (Wang et al., 2023). In narrow-band ELAA sensing for moving targets, the same pattern reappears in a broader parameter set: closed-form CRBs are derived for position, velocity, and radar cross-section, with near-field correction terms such as

$z_a=30\text{ cm}$1

quantifying Fresnel curvature and element-dependent amplitude variation (Wei et al., 31 Dec 2025).

Near-field models also change subspace estimation. In THz automotive radar, the target-to-element distance

$z_a=30\text{ cm}$2

produces a steering vector that depends jointly on DoA and range, and beam-squint affects both quantities across subcarriers. A beam-squint-compensated MUSIC spectrum is therefore formed on the $z_a=30\text{ cm}$3 grid rather than on angle alone (Elbir et al., 2023).

Waveform design likewise changes because the beampattern becomes a range–angle function. In low-THz automotive radar, the near-field steering vector includes a quadratic phase term in array index through the Fresnel approximation

$z_a=30\text{ cm}$4

so the beampattern matching problem is posed over a two-dimensional spatial grid and combined with a low-WISL unimodular waveform design objective (Eamaz et al., 2023).

A further consequence is that phenomena traditionally treated as model mismatch can become informative. In tangential-velocity estimation for automotive radar, range migration, Doppler migration, and spatial migration are explicitly modeled and exploited. Under the near-field target kinematics,

$z_a=30\text{ cm}$5

the tangential component enters through quadratic and space–time coupling terms. The paper argues that what would smear the likelihood under a misspecified far-field model becomes the carrier of tangential-velocity information under the correct near-field model (Shifrin et al., 4 Sep 2025).

6. Extended targets, materials, and application-specific behavior

A near-field radar model need not imply a point target. Several recent formulations replace the point-scatterer abstraction with surface-based electromagnetic models. For a rectangular plate reflector in a multistatic automotive scenario, the received signal is derived from the scattered field integrated over the plate surface and then reduced by stationary phase to

$z_a=30\text{ cm}$6

where the dominant contribution comes from a pair-dependent specular point rather than from the target center (Moulin et al., 2024). The paper states that the signal therefore depends on specular-point geometry, pair-dependent range, and a Fresnel-based target coefficient, not just on a single delay and a constant scattering factor.

A more general extended-target framework models a smooth surface

$z_a=30\text{ cm}$7

and derives the received signal by integrating the physical-optics response over the surface. Closed-form or semi-closed-form stationary-phase reductions are then given for a flat rectangular plate, a sphere, and a cylinder (Sambon et al., 30 Apr 2025). The paper reports that point-target and extended-target models are similar when targets are small and curved, but that the point-target abstraction breaks down as targets become larger or flatter, introducing estimation errors due to model mismatch.

Close-range depth imaging exposes another layer of near-field behavior: the interaction between electromagnetic propagation and material properties. In MAROON, metal and metallic-coated objects yield the strongest radar signal magnitude, polymers, fibers, stone, and foam generally yield weaker returns, skin gives relatively strong returns, and transparent or partially transmissive objects often cause major deviations (Wirth et al., 2024). The same study reports that geometry is the strongest factor for radar reconstruction quality, with larger surface incidence angles reducing received energy, backprojection confidence, and depth completeness. The paper therefore argues that near-field radar should be treated as a 3D electromagnetic imaging problem, not as a simple range sensor (Wirth et al., 2024).

Complex scattering and multipath are likewise geometry dependent. In passive 3-D near-field imaging with multiple non-cooperative illumination sources, combining images from different transmitter positions reduces shadowing and suppresses configuration-dependent ghosts, especially for concave objects such as dihedral structures (Wang et al., 9 Mar 2026). In non-line-of-sight sensing with non-reconfigurable electromagnetic skins, a moving source progressively illuminates modules of a passive metasurface, synthesizing an effective aperture on the surface and enabling around-the-corner imaging with enhanced resolution relative to the standalone radar (Bellini et al., 2024).

These developments clarify a common misconception. Near-field radar modeling is not only a question of replacing a plane wave with a spherical wave. It also involves decisions about whether the scene is point-like or extended, whether amplitude variation across the aperture is negligible, whether specular points or distributed scattering dominate, whether materials are opaque or partially transmissive, and whether multipath should be treated as nuisance or as part of the imaging signal. A plausible implication is that the term “near-field radar model” designates a family of models linked by spherical-wave geometry rather than a single universal equation.