Extremely Large Aperture Arrays (ELAAs)

• Extremely Large Aperture Arrays (ELAAs) are antenna arrays with electrically large apertures that transition channel modeling from far-field plane waves to near-field spherical-wave propagation.
• They enable finite-depth beamforming and depth-domain multiplexing, allowing simultaneous service of users at different ranges and enhanced spectral efficiency.
• ELAAs present new research challenges in estimation, non-stationary fading, hardware impairments, and integrated sensing and communications, driving advancements in both theory and practice.

Searching arXiv for recent and foundational ELAA papers to ground the article. Search query: "Extremely Large Aperture Arrays near-field ELAA survey channel estimation" Extremely Large Aperture Arrays (ELAAs) are antenna arrays whose physical aperture is large compared with the wavelength, so the key issue is not merely “many antennas,” but that the electrical size of the array becomes so large that users are no longer well-described by the far-field plane-wave model (Ramezani et al., 2023). In the ELAA regime, the radiative near-field becomes communication-relevant over very large distances, the wavefront across the array is spherical rather than planar, and the channel response depends on angle and distance rather than angle alone (Ramezani et al., 2022). This shift changes channel modeling, beamforming, multiplexing, estimation, and sensing; it also makes ELAA a central construct in current 6G discussions on near-field communication, integrated sensing and communication (ISAC), and extra-large MIMO (Long et al., 31 Jul 2025).

1. Aperture scaling and the radiative near-field

For a single aperture of maximum length $D$, the classical Fraunhofer distance is

$d_{\mathrm{F}}=\frac{2D^2}{\lambda},$

while for an array the relevant scale is the array aperture $W$, giving the Fraunhofer array distance

$d_{\mathrm{FA}}=\frac{2W^2}{\lambda}.$

For a planar ELAA, one formulation further gives

$$d_{\mathrm{FA}}=\left(\frac{W}{D}\right)^2 d_{\mathrm{F}}=\frac{M^2+N^2}{2}\,d_{\mathrm{F}},$$

and for a planar array with diagonal $W=D\sqrt{N}$, another equivalent scaling law is

$$d_{\mathrm{FA}}=\frac{2W^2}{\lambda}=N d_{\mathrm{F}}.$$

These relations formalize the defining ELAA effect: as aperture grows and/or $\lambda$ shrinks, the near-field boundary expands rapidly (Ramezani et al., 2023, Ramezani et al., 2022).

The field regions are conventionally divided into the reactive near-field, the radiative near-field, and the far-field. For electrically large antennas, the reactive near-field boundary is approximately

$$d_{\mathrm{N}}\approx 0.62\sqrt{\frac{D^3}{\lambda}},$$

and for ELAAs the practically important regime is the region where each antenna element can still be treated as far-field with respect to the source, but the array as a whole is in the radiative near-field. One formulation describes this as $d_{\mathrm{F}}<d<d_{\mathrm{FA}}$, while another highlights the operational range

$d_{\mathrm{F}}=\frac{2D^2}{\lambda},$0

where the Björnson distance is

$d_{\mathrm{F}}=\frac{2D^2}{\lambda},$1

About $d_{\mathrm{F}}=\frac{2D^2}{\lambda},$2 of the maximum array gain is already achieved for $d_{\mathrm{F}}=\frac{2D^2}{\lambda},$3, so maximum array gain is typically attainable well before the Fraunhofer array distance (Ramezani et al., 2023, Ramezani et al., 2022).

The numerical consequences can be large. A concrete example gives, for $d_{\mathrm{F}}=\frac{2D^2}{\lambda},$4 m, $d_{\mathrm{F}}=\frac{2D^2}{\lambda},$5 m and $d_{\mathrm{F}}=\frac{2D^2}{\lambda},$6 m corresponding to $d_{\mathrm{F}}=\frac{2D^2}{\lambda},$7 m and $d_{\mathrm{F}}=\frac{2D^2}{\lambda},$8 km, while for $d_{\mathrm{F}}=\frac{2D^2}{\lambda},$9 m the corresponding values become $W$0 m and $W$1 km (Ramezani et al., 2022). A separate survey notes that for a base-station array at $W$2 THz with physical aperture $W$3 m $W$4 $W$5 m, the Rayleigh distance becomes about $W$6 m, which can span an entire cell (Long et al., 31 Jul 2025). This suggests that near-field operation is not an edge case once aperture and carrier frequency are jointly scaled.

2. Propagation laws and channel models

In ELAA channels, spherical-wave propagation replaces the far-field plane-wave approximation. For a uniform planar array (UPA) with $W$7 antennas and antenna positions indexed row-by-row as

$W$8

the near-field array response can be written as

$W$9

Using a Fresnel approximation,

$d_{\mathrm{FA}}=\frac{2W^2}{\lambda}.$0

which yields an approximate steering term containing both the familiar angular phase and a range-dependent curvature term. The last term vanishes in the far field, recovering the usual far-field array response (Demir et al., 2024).

A survey formulation expresses the near-field response for a generic array as

$d_{\mathrm{FA}}=\frac{2W^2}{\lambda}.$1

with path-length increment

$d_{\mathrm{FA}}=\frac{2W^2}{\lambda}.$2

This is the canonical mathematical statement of angle–range coupling in the near field (Long et al., 31 Jul 2025).

For non-line-of-sight modeling, one correlated Rayleigh construction writes

$d_{\mathrm{FA}}=\frac{2W^2}{\lambda}.$3

with a zero-mean circularly symmetric complex Gaussian spreading function satisfying

$d_{\mathrm{FA}}=\frac{2W^2}{\lambda}.$4

The resulting channel satisfies

$d_{\mathrm{FA}}=\frac{2W^2}{\lambda}.$5

and each diagonal entry of $d_{\mathrm{FA}}=\frac{2W^2}{\lambda}.$6 equals $d_{\mathrm{FA}}=\frac{2W^2}{\lambda}.$7, so the near-field does not itself create per-antenna power variation (Demir et al., 2024).

Near-field fading models also depart from conventional stationarity assumptions. A 3D fading framework for ELAA uniform rectangular arrays (URAs) allows mixed line-of-sight and non-line-of-sight links, spherical-wave propagation, and spatially non-stationary shadow fading, with the array partitioned into stochastic “windows” of identical propagation state (Liu et al., 2024). A plausible implication is that ELAA modeling requires not only spherical phase laws but also array-dependent non-stationarity mechanisms.

3. Finite-depth beamforming and new multiplexing modes

In the far field, beamforming depends mainly on direction; in the ELAA radiative near-field, the array focuses on a specific point, so beamforming depends on both angle and distance. This is the finite-depth beamforming regime (Ramezani et al., 2022). For a focal point $d_{\mathrm{FA}}=\frac{2W^2}{\lambda}.$8, the beam has finite width and finite depth, rather than the effectively infinite depth of a plane-wave beam (Ramezani et al., 2023).

Along the lateral dimensions, one approximation gives

$d_{\mathrm{FA}}=\frac{2W^2}{\lambda}.$9

leading to

$$d_{\mathrm{FA}}=\left(\frac{W}{D}\right)^2 d_{\mathrm{F}}=\frac{M^2+N^2}{2}\,d_{\mathrm{F}},$$0

Along the depth axis, the beam has a finite 3 dB beam depth when the focal distance is below a threshold related to the Fraunhofer array distance (Ramezani et al., 2023). An equivalent formulation gives, for focal distance $$d_{\mathrm{FA}}=\left(\frac{W}{D}\right)^2 d_{\mathrm{F}}=\frac{M^2+N^2}{2}\,d_{\mathrm{F}},$$1,

$$d_{\mathrm{FA}}=\left(\frac{W}{D}\right)^2 d_{\mathrm{F}}=\frac{M^2+N^2}{2}\,d_{\mathrm{F}},$$2

This identifies $$d_{\mathrm{FA}}=\left(\frac{W}{D}\right)^2 d_{\mathrm{F}}=\frac{M^2+N^2}{2}\,d_{\mathrm{F}},$$3 as a natural border between near-field and far-field beamforming (Ramezani et al., 2022).

The most distinctive multiplexing consequence is depth-domain multiplexing. Because near-field beams have finite depth intervals, users aligned in angle but separated in range can have substantially different channel vectors and can be served simultaneously. Illustrative focal points such as

$$d_{\mathrm{FA}}=\left(\frac{W}{D}\right)^2 d_{\mathrm{F}}=\frac{M^2+N^2}{2}\,d_{\mathrm{F}},$$4

can have non-overlapping 3 dB depth intervals (Ramezani et al., 2023). In a five-user example with users in the same angular direction but different distances, zero-forcing beamforming plus waterfilling yields roughly $$d_{\mathrm{FA}}=\left(\frac{W}{D}\right)^2 d_{\mathrm{F}}=\frac{M^2+N^2}{2}\,d_{\mathrm{F}},$$5 higher sum spectral efficiency than a scheduling baseline where each user takes turns (Ramezani et al., 2022).

Near-field operation also alters line-of-sight MIMO rank. For two arrays with spacing chosen as

$$d_{\mathrm{FA}}=\left(\frac{W}{D}\right)^2 d_{\mathrm{F}}=\frac{M^2+N^2}{2}\,d_{\mathrm{F}},$$6

the Fresnel approximation yields

$$d_{\mathrm{FA}}=\left(\frac{W}{D}\right)^2 d_{\mathrm{F}}=\frac{M^2+N^2}{2}\,d_{\mathrm{F}},$$7

so all singular values are equal and the capacity becomes

$$d_{\mathrm{FA}}=\left(\frac{W}{D}\right)^2 d_{\mathrm{F}}=\frac{M^2+N^2}{2}\,d_{\mathrm{F}},$$8

The key point is that spherical curvature can create orthogonality between signals from different antennas, enabling several parallel spatial layers even in line-of-sight (Ramezani et al., 2023).

The spatial degrees of freedom remain aperture-limited. Multiple sources cite

$$d_{\mathrm{FA}}=\left(\frac{W}{D}\right)^2 d_{\mathrm{F}}=\frac{M^2+N^2}{2}\,d_{\mathrm{F}},$$9

or equivalently $W=D\sqrt{N}$0, underscoring that ELAA gains are fundamentally aperture-driven rather than antenna-count-driven (Ramezani et al., 2023, Ramezani et al., 2022).

4. Estimation, codebooks, and beam training

The near-field channel-estimation problem is high-dimensional because each path is parameterized by angle and distance. One line of work therefore uses reduced-dimensional geometry-aware subspaces. For a UPA ELAA, a representative correlation matrix $W=D\sqrt{N}$1 can be constructed from array geometry and the 3D coverage region where scatterers may lie. If the true scattering function is supported in

$W=D\sqrt{N}$2

then the column space of the true correlation matrix $W=D\sqrt{N}$3 is contained in the column space of $W=D\sqrt{N}$4, so any channel in that region can be expressed as

$W=D\sqrt{N}$5

for some reduced-dimensional vector $W=D\sqrt{N}$6, where $W=D\sqrt{N}$7. The resulting reduced-subspace least squares estimator is

$W=D\sqrt{N}$8

which exploits array geometry and coverage-region knowledge without requiring the full user-specific covariance matrix (Demir et al., 2024).

A related pilot-design study derives an achievable spectral-efficiency expression and a Jensen-based lower bound for RS-LS, then proves that the pilot-length optimization problem is strictly concave and admits a unique global maximizer $W=D\sqrt{N}$9. Under low SNR, an approximate optimizer is

$$d_{\mathrm{FA}}=\frac{2W^2}{\lambda}=N d_{\mathrm{F}}.$$0

The same work reports that denser arrays can reduce the optimal pilot length because higher spatial correlation and the geometry-induced low-dimensional subspace improve the noise-rejection capability of RS-LS (Alıcıoğlu et al., 2024).

Another estimation route is explicitly parametric. For a UPA BS serving $$d_{\mathrm{FA}}=\frac{2W^2}{\lambda}=N d_{\mathrm{F}}.$$1 single-antenna users, a two-step MUSIC method first estimates azimuth and elevation from a 2D spectrum,

$$d_{\mathrm{FA}}=\frac{2W^2}{\lambda}=N d_{\mathrm{F}}.$$2

then estimates range from a 1D distance spectrum. Spatial smoothing is used when the pilot length is shorter than the number of users, and an LS-based complex scalar corrector compensates residual amplitude and phase errors (Kosasih et al., 2024). The reported conclusion is that the proposed parametric MUSIC plus LS-corrector approach outperforms LS and regularized LS in normalized beamforming gain and NMSE.

Near-field sparsity is not identical to far-field angular sparsity, so dictionary design also changes. For UPA ELAAs, a polar-domain dictionary with the distance-ring coupling rule

$$d_{\mathrm{FA}}=\frac{2W^2}{\lambda}=N d_{\mathrm{F}}.$$3

and the closed-form non-uniform distance grid

$$d_{\mathrm{FA}}=\frac{2W^2}{\lambda}=N d_{\mathrm{F}}.$$4

was proposed to reduce column coherence and avoid fully correlated columns that arise in earlier designs (Demir et al., 2023). For mmWave/THz ULA ELAAs, another approach constructs a matched unitary dictionary and proves that the hybrid near/far-field channel admits a block-sparse representation whose nonzero fraction decreases as $$d_{\mathrm{FA}}=\frac{2W^2}{\lambda}=N d_{\mathrm{F}}.$$5, converting channel estimation into a block-sparse recovery problem (Wang et al., 2024).

Beam training likewise becomes nontrivial because narrower ELAA beams increase alignment overhead. In a THz MISO setting with $$d_{\mathrm{FA}}=\frac{2W^2}{\lambda}=N d_{\mathrm{F}}.$$6 DFT beams and $$d_{\mathrm{FA}}=\frac{2W^2}{\lambda}=N d_{\mathrm{F}}.$$7 training beams, hash beam training forms each training beam as a superposition of $$d_{\mathrm{FA}}=\frac{2W^2}{\lambda}=N d_{\mathrm{F}}.$$8 DFT beams and uses voting statistics

$$d_{\mathrm{FA}}=\frac{2W^2}{\lambda}=N d_{\mathrm{F}}.$$9

The reported findings are that the beam alignment success probability depends strongly on $\lambda$0, the proposed fixed hash codebook improves beam alignment accuracy by about $\lambda$1 over the proposed random one in the simulated practical THz channel, and at high SNR the proposed hash codebook approaches the performance of beam sweeping while using only half the training overhead (Si et al., 2024).

5. Architectures, wideband effects, and hardware nonidealities

ELAA implementation raises architectural questions because monolithic centralized processing is expensive. A modular ELAA architecture with $\lambda$2 subarrays, each connected to its own baseband unit and coordinated by a CPU, addresses hardware scaling, fronthaul overhead, and scalability (Demir et al., 20 Sep 2025). Under near-field line-of-sight assumptions and LNA-induced hardware impairments, a hierarchy of estimators exploits constant-modulus steering structure, reduced subspaces, and a 2D-DFT masking technique that keeps an

$\lambda$3

portion of the total 2D-DFT energy. The reported coefficient fractions decrease as subarray size grows, indicating that only a small fraction of coefficients must be forwarded to the CPU (Demir et al., 20 Sep 2025).

Wideband ELAAs introduce a distinct phenomenon beyond ordinary beam squint. In THz-wideband near-field operation, beams at different frequencies focus on different physical locations, not merely different directions; this is the near-field beam split effect (Cui et al., 2021). A piecewise-far-field model partitions the full array into sub-arrays, models phase across sub-arrays as near-field spherical, and approximates phase within each sub-array as far-field planar. On that basis, phase-delay focusing combines phase shifters and time delayers to compensate intra-array far-field phase discrepancy and inter-array near-field phase discrepancy. The same work defines an effective Rayleigh distance through beamforming gain loss: $\lambda$4 arguing that it is more accurate than the classical Rayleigh distance for practical communications (Cui et al., 2021).

Nonlinear hardware distortion is also geometrically structured in ELAAs. With a third-order memoryless power amplifier model

$\lambda$5

Bussgang decomposition yields

$\lambda$6

In the near field, the distortion is beamformed not only in azimuth and elevation but also in depth. For a $\lambda$7-th order nonlinear term, the focused distortion point is characterized approximately by

$\lambda$8

with accompanying angle expressions depending on user angles (Kolomvakis et al., 2024). Numerical results show that larger arrays make nonlinear distortion more spatially concentrated and therefore more dangerous if not managed, motivating distortion-aware scheduling (Kolomvakis et al., 2024).

A more hardware-oriented implementation strategy is metasurface-enabled extremely large-scale antenna systems, where a reconfigurable transmissive metasurface replaces bulky switch matrices and costly phase-shifter networks. In this formulation, MELA is an ELAA implementation strategy rather than a competing concept, and the paper derives physically grounded field-propagation models, decoupled-distance approximations with explicit thresholds, and a two-stage hybrid near-/far-field channel-estimation framework (Wang et al., 5 Aug 2025). This suggests that ELAA research increasingly couples propagation theory to scalable transceiver architecture.

6. Localization, sensing, and ISAC

ELAA near-field physics is also a sensing resource. In a monostatic SIMO radar with a linear ELAA, the projection of target velocity onto the line of sight differs across antennas, making both radial and transverse velocity components observable. The geometric factors

$\lambda$9

enter the Fisher information matrix for $$d_{\mathrm{N}}\approx 0.62\sqrt{\frac{D^3}{\lambda}},$$0 (Giovannetti et al., 2024). For half-wavelength spacing, the transverse-velocity bound becomes independent of carrier frequency, which differs sharply from conventional Doppler sensing (Giovannetti et al., 2024).

A broader motion-state localization study models a mobile receiver equipped with a linear ELAA and estimates 3D position, 3D velocity, and 2D orientation from delay and Doppler measurements. The near-field delay and Doppler are element dependent: $$d_{\mathrm{N}}\approx 0.62\sqrt{\frac{D^3}{\lambda}},$$1 Using equivalent Fisher information and a constrained Cramér–Rao framework, that work concludes that delay measurements carry richer information than Doppler measurements, while standalone Doppler measurements cannot overcome information losses due to unknown channel gains and frequency offsets and enable only coarse estimation capabilities (Hussain et al., 26 Mar 2026). The same study states that at least 3 anchors are required for single-snapshot full-motion localization, while 2 snapshots can reduce the requirement to 2 anchors (Hussain et al., 26 Mar 2026).

For communication-oriented multiuser localization, ELAA aperture sharpens angular and range resolution but also makes the objective highly non-convex, especially with limited RF chains. An uplink near-field MIMO formulation with a UPA ELAA and analog beamforming partitions the array into subarrays and exploits geometric constraints among subarray reference coefficients through message passing. The proposed APLE-LM algorithm is reported to achieve superior localization accuracy compared to baseline algorithms and to approach the Bayesian Cramér–Rao Bound at high SNR (Teng et al., 1 Jun 2025).

ISAC and non-stationarity problems extend this sensing role. A 3D ELAA fading framework introduces mixed LoS/NLoS links, window-based spatial non-stationarity, and sensing-object-induced partial blockage in URAs (Liu et al., 2024). Under partial blockage, a joint sensing and visibility-region detection method models the blockage pattern with an Ising prior,

$$d_{\mathrm{N}}\approx 0.62\sqrt{\frac{D^3}{\lambda}},$$2

and alternates among channel, visibility, and geometry estimates (Huang et al., 28 Feb 2025). The reported result is that the proposed AO-based method outperforms LS–MLE baselines that ignore spatial non-stationarity or assume random spatial non-stationarity (Huang et al., 28 Feb 2025).

7. Conceptual clarifications and research directions

A recurring clarification in the ELAA literature is that an ELAA is not simply a larger version of massive MIMO. The central change is the transition from linear phase to non-linear phase across the array, from angle-only parameterization to angle–distance parameterization, and from angular beam steering to point focusing (Long et al., 31 Jul 2025). Several papers explicitly note that conventional far-field codebooks such as DFT beams are not appropriate in the near field, and that far-field subspace models can underestimate channel rank and worsen NMSE (Kosasih et al., 2024, Demir et al., 2024).

Another clarification concerns power scaling. Near-field modeling does not imply unbounded array gain. For a centered transmitter facing a planar array, one upper bound on the total matched-filtered channel gain is

$$d_{\mathrm{N}}\approx 0.62\sqrt{\frac{D^3}{\lambda}},$$3

with $$d_{\mathrm{N}}\approx 0.62\sqrt{\frac{D^3}{\lambda}},$$4, and as $$d_{\mathrm{N}}\approx 0.62\sqrt{\frac{D^3}{\lambda}},$$5,

$$d_{\mathrm{N}}\approx 0.62\sqrt{\frac{D^3}{\lambda}},$$6

If polarization effects are ignored, the limit becomes $$d_{\mathrm{N}}\approx 0.62\sqrt{\frac{D^3}{\lambda}},$$7; if effective-area variation is also ignored, the gain can diverge, which is unphysical (Ramezani et al., 2022). This demonstrates that accurate ELAA modeling must retain amplitude, effective-aperture, and polarization effects where relevant.

The major open problems identified across the literature are consistent. They include channel estimation and beamforming methods that explicitly include the depth dimension, mutual coupling for densely packed arrays, phase synchronization errors, manufacturing imperfections, non-linear phase characteristics, statistical near-field estimation, dynamic near-field estimation, CAP-array estimation, non-stationarity-aware modeling and estimation, scalable RIS-assisted estimation, and hybrid algorithmic design combining physics-based structure with learning-based refinement (Ramezani et al., 2023, Long et al., 31 Jul 2025). A plausible implication is that ELAA research is moving from isolated near-field formulas toward a systems view in which aperture, hardware, estimation, and sensing are inseparable.

In sum, ELAAs define a communication and sensing regime in which aperture is large enough that spherical wavefront curvature, range dependence, and spatial non-stationarity become first-order effects. Their technical significance lies not only in higher array gain, but in the emergence of finite-depth focusing, depth-domain multiplexing, geometry-aware low-dimensional structure, and near-field sensing modalities that have no direct far-field analogue (Ramezani et al., 2023, Ramezani et al., 2022).