Holographic MIMO: Continuous Aperture Systems

• Holographic MIMO is defined as a wireless paradigm using nearly continuous sub-wavelength radiating elements to form dense electromagnetic apertures.
• It enables fine-grained beamforming and distance-selective focusing by exploiting near-field propagation and spatial Fourier mode representations.
• The approach integrates electromagnetic modeling and wavenumber-domain processing to improve channel estimation, spectral efficiency, and ISAC performance.

Holographic multiple-input multiple-output (H-MIMO, also HMIMO) denotes a communication paradigm in which the transmit and/or receive array is implemented as an electromagnetically continuous or quasi-continuous surface formed by a nearly infinite density of sub-wavelength, reconfigurable radiating elements over a finite physical area or volume. Rather than treating the array primarily as a finite set of antenna ports, H-MIMO models wireless propagation through continuous fields, surface currents, or spatial Fourier modes over large apertures, which makes electromagnetic constraints, dense-array correlation, and near-field propagation central rather than secondary considerations (An et al., 2023). In the recent literature, H-MIMO is variously associated with metasurfaces, large intelligent surfaces, dynamic metasurface antennas, holographic MIMO surfaces, and waveguide-fed metamaterial apertures; across these formulations, the unifying idea is that the physically meaningful spatial degrees of freedom are governed chiefly by aperture size and wavelength, not simply by the raw number of discrete antenna samples (Zhang et al., 9 Feb 2026).

1. Defining characteristics and physical motivation

H-MIMO differs from conventional and massive MIMO first at the level of aperture realization. Conventional MIMO uses a small number of antennas, typically with spacing near $\lambda/2$, and massive MIMO scales this to tens or hundreds of discrete elements. H-MIMO instead assumes deep sub-wavelength spacing such as $\lambda/4$, $\lambda/16$, or smaller, so that the array approaches a spatially continuous aperture and can manipulate amplitude, phase, and polarization with very fine spatial resolution (An et al., 2023). The field over the array is therefore naturally represented as a continuous function $h(\mathbf{r})$ over spatial coordinates $\mathbf{r}=[x,y,z]^T$, and the discrete ports are interpreted as samples of that field rather than as the primary abstraction (An et al., 2023).

A second defining feature is the prominence of electrically large surfaces and radiative near-field operation. Because the aperture dimension can span many wavelengths, the Fraunhofer or Rayleigh distance grows, and users frequently lie in the radiative near field rather than the far field. In that regime, spherical wavefronts, distance-dependent phase curvature, and amplitude variation across the aperture become essential, which enables distance selectivity, near-field focusing, and user separability even for users sharing similar angular directions (An et al., 2023, Chen et al., 2024). This is why the literature repeatedly frames H-MIMO as moving from angle-only representations toward angle-and-distance or full EM-domain descriptions (Gong et al., 2024).

The practical motivation is correspondingly twofold. On the communication side, the dense and electrically large aperture can approach the ultimate spatial resolution allowed by the aperture, yielding fine beamforming, low sidelobe leakage, and additional multiplexing capability in line-of-sight or weakly scattering environments (An et al., 2023). On the hardware side, metasurface implementations, including RF-free or low-RF architectures, promise reduced RF-chain count, lower power consumption, and lower hardware complexity than a fully digital array with the same number of effective radiating elements (An et al., 2023). Large, conformal surfaces integrated into walls, ceilings, vehicles, or panels are therefore a recurrent architectural theme (An et al., 2023, Gong et al., 2024).

A recurring misconception in the literature is that H-MIMO gains derive directly from packing more and more elements into a fixed area. The more precise statement is that dense sampling does not by itself increase the intrinsic spatial degrees of freedom; those are primarily aperture-limited. Oversampling instead increases spatial correlation and redundancy, which is useful only when the associated signal processing explicitly exploits the induced structure (An et al., 2023, Guo et al., 2024).

2. Electromagnetic and wavenumber-domain foundations

The foundational stochastic formulation treats small-scale fading as a complex scalar random field $h(\mathbf{r})$ whose correlation is determined by a wavenumber-domain power spectral density supported on the Helmholtz sphere. Under spatial stationarity, the correlation function is written as a Fourier integral over the wavenumber vector $\mathbf{k}$, and imposing the scalar Helmholtz equation constrains the spectral support to $\|\mathbf{k}\|=\kappa$ with $\kappa=2\pi/\lambda$ (An et al., 2023). In this model, the field is a superposition of plane waves weighted by a directional spectral factor.

Two important limiting cases connect H-MIMO to classical fading theory. For isotropic scattering in three dimensions, the autocorrelation reduces to a sinc form, and samples spaced by $n\lambda/2$ are uncorrelated. For isotropic scattering in two dimensions, the correlation becomes $\lambda/4$0, exactly recovering the Clarke–Jakes spatial correlation model (An et al., 2023). This statistical consistency is central: the H-MIMO channel model is not a disconnected replacement for conventional MIMO models, but a generalization that reduces to them when apertures are compact and sampling is around $\lambda/4$1.

For planar transmit and receive surfaces, the EM-consistent H-MIMO channel admits a Fourier plane-wave series expansion over two lattice ellipses in the transmit and receive wavenumber planes. In compact form, the discrete sampled channel can be written as

$\lambda/4$2

where $\lambda/4$3 and $\lambda/4$4 are wavenumber-domain basis matrices determined by aperture geometry, and $\lambda/4$5 contains the random Fourier coefficients or modal couplings (Guo et al., 2024). The index sets are constrained by the radiating condition $\lambda/4$6, so the number of admissible modes is fixed by the aperture dimensions rather than by the element spacing (Guo et al., 2024). This is the wavenumber-domain expression of spatial band-limitation.

That same point underlies much of the recent signal-processing literature. For fixed aperture size, the number of wavenumber modes is independent of element spacing $\lambda/4$7, even when $\lambda/4$8; dense sampling adds antennas but not new propagating modes (Guo et al., 2024). This is why discrete Fourier transform representations tied to antenna count become increasingly ill-conditioned in sub-wavelength arrays, whereas wavenumber-domain bases remain physically meaningful. The 2026 survey on wavenumber-domain signal processing further frames this as a unified basis that remains valid from far field to near field, capturing both sub-wavelength correlation and spherical-wave propagation in one representation (Zhang et al., 9 Feb 2026).

The same literature also clarifies a second misconception: H-MIMO is often associated exclusively with near-field communication, but not every H-MIMO operating point is near-field dominant. In one representative wavenumber-domain channel-estimation study, the array geometry yields Rayleigh distances for which the authors explicitly state that “near-field effect is negligible and can be ignored,” even though the system still uses sub-half-wavelength H-MIMO apertures and an EM-compliant Fourier plane-wave model (Guo et al., 2024). The defining feature is therefore the aperture-centric EM representation, not a mandatory near-field regime.

3. Channel modeling regimes and EM-domain formulations

The channel-modeling literature distinguishes deterministic and stochastic approaches. Deterministic models include extended Friis formulations for large intelligent surface links, full EM-based narrowband models that account for waveguide propagation, mutual coupling, and insertion loss, and EM-compliant channel models that also include antenna pattern distortion (An et al., 2023). Their advantage is geometric accuracy; their drawback is that they require detailed Maxwell-equation solutions or ray tracing and are not convenient for general system analysis (An et al., 2023).

Stochastic models seek EM consistency without geometry-specific full-wave simulation. The Fourier plane-wave expansion described above is the dominant example, because it encodes correlation and modal coupling through a four-dimensional power spectral density while remaining statistically consistent with classical MIMO limits (An et al., 2023). In multi-user formulations, this wavenumber-domain structure leads to tractable models for downlink zero-forcing analysis and spectral-efficiency expressions that remain accurate even under strong correlation (Wei et al., 2022).

For line-of-sight near-field H-MIMO with arbitrary surface placements, a parallel thread of work formulates the channel directly in the EM domain through dyadic or tensor Green’s functions. The exact model is an integral operator mapping transmit surface currents to receive electric fields over continuous surfaces (Gong et al., 2023, Gong et al., 2023). Because brute-force evaluation is computationally expensive, several reduced-complexity approximations have been derived. The coordinate-dependent and coordinate-independent channel models simplify the integral form while preserving vector EM structure, and the partially separable and fully separable models further reduce measurement requirements by expressing geometry through aperture-center relationships and local array coordinates (Gong et al., 2024). The reported complexity reduction is from $\lambda/4$9 for the integral model to $\lambda/16$0 for the efficient approximations (Gong et al., 2024).

These EM-domain models are used not only for channel synthesis but also for capacity analysis. In point-to-point line-of-sight H-MIMO with arbitrary surface placements, the capacity upper bound is shown to grow logarithmically with the product of transmit element area, receive element area, and the combined effects of $\lambda/16$1, $\lambda/16$2, and $\lambda/16$3 over all transmit–receive element pairs, with the $\lambda/16$4 term dominant in the near field and $\lambda/16$5 dominant in the far field (Gong et al., 2023). This explicitly ties H-MIMO capacity to near-field EM behavior rather than to a purely far-field aperture law.

A further development addresses hybrid near-/far-field propagation without prespecifying how many paths belong to each regime. In that model, each path is assigned a binary latent variable indicating near-field spherical steering or far-field planar steering, and expectation–maximization is used to infer the path types and geometric parameters jointly (Chen et al., 2024). Simulation results in that work show better outage-probability fitting than near-field-only or far-field-only baselines when the propagation environment contains a mixture of both (Chen et al., 2024). This hybridization is a direct response to the fact that H-MIMO enlarges the near-field region but does not eliminate far-field components.

4. Channel estimation and structured inference

Channel estimation in H-MIMO is difficult for two reasons that recur across the literature: the number of sampled elements can be enormous, and the resulting channels are strongly correlated and often rank-deficient. In a canonical single-user uplink model with $\lambda/16$6 and correlated Rayleigh fading $\lambda/16$7, least-squares and MMSE estimators remain natural baselines, but they do not fully exploit H-MIMO structure (An et al., 2023).

One broad strategy is subspace-based estimation. Under isotropic scattering and spacing $\lambda/16$8, the rank of the H-MIMO correlation matrix is approximately $\lambda/16$9, and for $h(\mathbf{r})$0 approximately 80% of the eigenvalues are essentially zero (An et al., 2023). This supports reduced-subspace least squares (RS-LS), which projects the observation onto the dominant signal subspace. When the true subspace is known, RS-LS approaches MMSE at high SNR; when only a conservative geometry-based subspace is available, such as the isotropic subspace implied by the array geometry, substantial gains over plain LS remain possible without environment-specific correlation estimation (An et al., 2023).

A second strategy is sparse or compressed-sensing estimation. In far-field THz settings with limited scattering, angular or joint angular-delay sparsity supports OMP- or SOMP-type recovery, sometimes in two-stage procedures involving coarse line-of-sight angle estimation and grouped uplink recovery (An et al., 2023). In near-field H-MIMO, the literature replaces angle-only sparsity by polar-domain sparsity indexed jointly by angle and distance, with on-grid polar-domain simultaneous OMP used to recover dominant angle–distance pairs under spherical-wave steering (An et al., 2023).

More recently, sparsity has been reformulated directly in the wavenumber domain. The wavenumber-domain channel-estimation framework writes the pilot measurements as

$h(\mathbf{r})$1

with $h(\mathbf{r})$2 sparse or compressible in the wavenumber basis and proposes wavenumber-domain orthogonal matching pursuit (WD-OMP) that selects rank-1 atoms $h(\mathbf{r})$3 without forming the full Kronecker dictionary (Guo et al., 2024). The notable empirical finding is that the proposed wavenumber-domain sparsifying basis maintains its detection accuracy regardless of the number of antenna elements and antenna spacing, and remains highly accurate when the spacing is much less than half a wavelength (Guo et al., 2024). This directly addresses one of the distinctive H-MIMO estimation pathologies: oversampling degrades conventional angular dictionaries but does not enlarge the wavenumber dictionary.

A different form of structured inference appears in recent continuous-aperture multi-user uplink work, where the optimization variable is the continuous current density function itself. After expanding the current density in Fourier communication modes, the problem reduces to optimizing mode-space covariance matrices under colored noise, and an iterative water-filling algorithm is used to maximize spectral efficiency (Qian et al., 2024). This approach sits at the boundary between channel modeling, transceiver design, and estimation, because the communication object is no longer an antenna-domain vector but a finite-dimensional projection of a continuous current distribution.

5. Performance limits, spectral efficiency, and integrated sensing

Performance analysis in H-MIMO has emphasized the interplay between aperture-limited degrees of freedom and dense-array correlation. In multi-user downlink Holographic MIMO surfaces, a convenient wavenumber-domain channel model leads to a zero-forcing spectral-efficiency approximation in which the relevant gains are governed by the number of spatial harmonics and sampled channel variances rather than by i.i.d. matrix entries (Wei et al., 2022). The reported simulations show that performance improves when the number of patch antennas grows through a larger aperture, and also when spacing increases for a fixed number of patches, because a larger physical aperture reduces effective correlation (Wei et al., 2022). This reinforces the aperture-versus-density distinction already present in the EM models.

Energy-efficiency analysis yields a complementary conclusion. In a multi-user downlink H-MIMO system with fixed surface side lengths, the spatial Nyquist conditions require at least $h(\mathbf{r})$4 and $h(\mathbf{r})$5, where $h(\mathbf{r})$6 and $h(\mathbf{r})$7 are the transmit and receive spatial degrees of freedom inferred from aperture size (Bahanshal et al., 2023). Under MRT and a hardware-oriented power model, the resulting energy-efficiency maximization over the number of antennas on the fixed surfaces is strictly pseudo-concave and admits a globally optimal solution (Bahanshal et al., 2023). The main regime separation is that in noise-limited operation the energy-optimal design may use more antennas than the degree-of-freedom count, whereas in interference-limited high-SNR operation the optimum collapses to $h(\mathbf{r})$8 and $h(\mathbf{r})$9 (Bahanshal et al., 2023). In other words, oversampling can be energy-efficient only when the added array gain offsets the linear circuit-power increase.

The same aperture-centric viewpoint extends to integrated sensing and communications. In H-MIMO-based ISAC, the communication channel is modeled as correlated Rayleigh fading with a Fourier plane-wave/Karhunen–Loève structure, while the sensing link uses a spherical-wave target model (Zhao et al., 2024). Closed-form expressions are derived for sensing rates, communication rates, outage probabilities, high-SNR slopes, and diversity orders under sensing-centric, communications-centric, and Pareto-optimal designs (Zhao et al., 2024). The reported numerical results show that the H-MIMO-based ISAC framework outperforms both conventional MIMO-based ISAC and H-MIMO-based frequency-division sensing and communications systems (Zhao et al., 2024). The diversity orders are explicitly linked to the rank of the spatial correlation matrix, again tying performance to the physically available modal structure rather than to nominal antenna count.

Multi-user continuous-aperture uplink analysis reaches a similar endpoint from a different route. There, spectral efficiency is maximized over current-density expansion coefficients in a finite communication-mode space, with colored electromagnetic interference and hardware noise incorporated through a non-white noise covariance (Qian et al., 2024). The numerical results show that optimized mode-domain power allocation substantially outperforms equal-power allocation and discrete-array baselines, and that higher frequency, shorter distance, and larger transmit or receive apertures increase spectral efficiency by enlarging the effective set of useful modes (Qian et al., 2024).

6. Architectures, constraints, and open problems

The implementation literature makes clear that H-MIMO is not a single hardware platform. One prominent realization is the waveguide-fed metamaterial array, in which each RF chain excites a microstrip carrying a reference wave, and sub-wavelength metamaterial elements along the waveguide reradiate that wave through tunable complex responses (Zhi et al., 23 Feb 2025). In a multi-cell downlink formulation, the analog feed propagation is represented by a block-diagonal matrix $\mathbf{r}=[x,y,z]^T$0, the metamaterial tuning by a diagonal matrix $\mathbf{r}=[x,y,z]^T$1, and the digital precoder by per-cell baseband matrices, all under practical per-RF-chain power constraints (Zhi et al., 23 Feb 2025).

Two tuning models receive particular emphasis. Binary tuning restricts each element to $\mathbf{r}=[x,y,z]^T$2, while grayscale tuning follows a Lorentzian-constrained phase model

$\mathbf{r}=[x,y,z]^T$3

which couples amplitude and phase through the element physics (Zhi et al., 23 Feb 2025). Weighted-sum-rate maximization in this setting is handled through block coordinate descent and WMMSE, with a closed-form per-RF precoder update, a hidden-convexity-based algorithm plus accelerated sphere decoding for binary tuning, and an MM algorithm for the Lorentzian constraint (Zhi et al., 23 Feb 2025). In a simplified MISO setting, the paper derives SNR scaling laws showing linear scaling with the number of elements for both HMIMO and conventional arrays, but with different coefficients under binary and Lorentzian tuning constraints (Zhi et al., 23 Feb 2025). This suggests that H-MIMO’s practical advantage is not raw asymptotic scaling superiority under idealized equal-area comparisons, but the feasibility of realizing extremely large apertures with simplified hardware.

Across surveys and tutorials, the major unresolved issues are consistent. Unified EM-consistent stochastic models remain incomplete for wideband, frequency-selective, polarized, and mutual-coupling-aware channels; realistic H-MIMO also requires spatial non-stationarity models for extremely large apertures and distributed or multi-surface deployments (An et al., 2023, Gong et al., 2024). Channel estimation still needs reduced-overhead schemes robust to imperfect sparsity or imperfect low-rank structure, especially in hybrid near-/far-field conditions (An et al., 2023, Chen et al., 2024). Hardware-aware signal processing must accommodate finite control resolution, phase-only or Lorentzian constraints, and limited-RF architectures (Zhi et al., 23 Feb 2025). The 2026 wavenumber-domain survey further emphasizes tri-hybrid architectures, mutual-coupling exploitation, network-level feedback formats, and electromagnetic information theory as central future directions (Zhang et al., 9 Feb 2026).

Taken together, the contemporary literature presents H-MIMO as a shift from antenna-indexed communication toward aperture-indexed electromagnetic communication. The field’s core insight is not merely that more elements can be packed into a surface, but that a dense and programmable aperture supports a continuous or mode-domain description in which near-field propagation, spatial correlation, polarization, and physical aperture constraints become first-class objects. The resulting theory spans channel modeling, estimation, spectral-efficiency analysis, energy-efficiency design, and ISAC, while practical implementations increasingly force these abstractions to confront waveguide feeding, metamaterial constraints, and colored electromagnetic noise.