Holographic Communication Systems

• Holographic communication systems are electromagnetic architectures that use programmable metasurfaces to control amplitude, phase, and polarization for direct synthesis and detection of wavefronts.
• They employ reconfigurable metamaterial elements to enable high spatial multiplexing and near-field sensing, departing from traditional plane-wave approximations.
• Advanced optimization algorithms and joint communication-sensing frameworks are used to balance channel capacity and radar-like performance in near-field regimes.

Holographic communication systems are electromagnetic architectures that leverage the full control of amplitude, phase, and polarization across nearly continuous surfaces to directly synthesize and detect arbitrary wavefronts. This paradigm differs from conventional antenna arrays by treating the transceiving surface as a programmable electromagnetic aperture—often realized with reconfigurable metamaterial elements—that enables both high-capacity spatial multiplexing and fine-resolution sensing. Especially when operating at millimeter-wave to terahertz frequencies and with electrically large surfaces, holographic systems depart from the classical far-field (plane wave) approximation by exploiting the true near-field (Fresnel) regime, allowing unprecedented control and flexibility in electromagnetic field manipulation, signal processing, and integration with radar-like functions.

1. Fundamental Architecture and Electromagnetic Modeling

Holographic communications are based on intelligent surfaces—either transmit, receive, or jointly—capable of programming arbitrary current density distributions, $J(\mathbf{s})$, on the surface and sampling the impinging field in a spatially continuous manner. These surfaces are physically realized using metamaterials or metasurfaces, which provide fine-grained local control over amplitude, phase, and sometimes polarization. The key formulation for field propagation is given by the electromagnetic Green's function:

$$E(\mathbf{r}) = \int_{\mathcal{S}_T} G(\mathbf{r}, \mathbf{s}) J(\mathbf{s})\, d\mathbf{s},$$

with

$$G(\mathbf{r}, \mathbf{s}) = \frac{e^{-jk|\mathbf{r}-\mathbf{s}|}}{4\pi|\mathbf{r}-\mathbf{s}|},$$

where $k = 2\pi/\lambda$ is the wavenumber, $\lambda$ is the wavelength, $\mathcal{S}_T$ is the transmit surface, and $\mathcal{S}_R$ is the receive surface.

This approach is essential when the surface size is comparable to the propagation distance (i.e., $D\sim d$), so that non-planar, spherical (Fresnel) wavefronts dominate field interactions and the basis for electromagnetic channel modeling must shift from discrete mode (element) representations to continuous orthogonal basis functions obtained via eigenfunction decomposition of the Green's kernel.

2. Degrees-of-Freedom, Channel Modeling, and Capacity

The degrees-of-freedom (DoF) in a holographic system are not directly tied to the number of discrete antennas but derive from the spatial bandwidth of the electromagnetic field across the surface. In the radiative near-field, the number of orthogonal spatial channels can be significantly increased:

$N \approx \frac{A_T A_R}{(\lambda d)^2}$

for traditional (small-area) surfaces, but for large surfaces or those with $D \sim d$, this approximation fails and a full eigenfunction-based analysis is necessary. The eigenfunctions $\{\phi_n(\mathbf{s})\}$ and $\{\psi_n(\mathbf{r})\}$ satisfy:

$$\int_{\mathcal{S}_T} G(\mathbf{r},\mathbf{s})\, \phi_n(\mathbf{s})\, d\mathbf{s} = \xi_n \psi_n(\mathbf{r}),$$

yielding parallel channels:

$y_n = \xi_n x_n + w_n, \quad n = 1,2,\dots,N,$

where $x_n$ and $y_n$ represent the symbol streams, and $w_n$ is noise. As demonstrated in the holographic MIMO channel modeling literature (Pizzo et al., 2020, Pizzo et al., 2021), this treatment generalizes to arbitrary planar and volumetric arrays and naturally incorporates spatial correlation, mutual coupling, and array orientation.

For electrically large apertures, classical i.i.d. fading channel models are not valid; instead, one must use physically derived, low-rank channel matrices informed by the system's spatial resolution and scattering environment, often employing a 4D plane-wave (Fourier) representation:

$$h(\mathbf{r}, \mathbf{s}) = \frac{1}{(2\pi)^2} \iint a_r(\mathbf{r})\, H_a(k_x, k_y, \kappa_x, \kappa_y)\, a_s(\mathbf{s}) \,dk_x\,dk_y\,d\kappa_x\,d\kappa_y$$

where $H_a$ encodes the channel's angular power spectrum.

3. Holographic Beamforming, Sensing, and ISAC Integration

A distinctive feature of holographic systems is their ability to "sculpt" electromagnetic fields directly on transmission and reception, enabling true wave-based signal processing before digital conversion. Holographic beamforming is realized by modulating amplitude (and sometimes phase) patterns, often using the interference between a reference and an object wave:

$$\Psi_{\mathrm{intf}} = \Psi_{\mathrm{obj}} \Psi_{\mathrm{ref}}^*.$$

Amplitude or intensity patterns, such as

$$M(\mathbf{r}_{m,n}^k, \theta_0, \phi_0) = \frac{ \Re\left[ \Psi_{\mathrm{intf}}(\mathbf{r}_{m,n}^k, \theta_0, \phi_0) \right] + 1 }{2}$$

directly set the radiation profile on the surface. This amplitude-only approach differs from the phase-driven beamforming of classical phased arrays, and is particularly significant at sub-wavelength element spacings where mutual coupling and near-field effects are pronounced.

These same surfaces can be used in integrated sensing and communication (ISAC) frameworks (Zhang et al., 2022), performing both data transmission and radar parameter estimation:

• Joint processing of transmitted signals’ echoes allows for high-resolution spatial sensing.
• Cramér–Rao Bounds (CRBs) for angle and range estimation quantify the theoretical limits of such aperture-based sensing:

$$\mathrm{CRB}(\theta) = \frac{\sigma_r^2}{2 |\gamma|^2} \left[ \mathrm{Tr}(v_d^\mathrm{H} W^\mathrm{H} A_\theta A_\theta^\mathrm{H} W v_d) \right]^{-1}.$$

A multi-objective design framework may be adopted to balance communication rate and sensing accuracy, though this typically results in non-convex optimization due to the inverse dependence of CRB on design variables (Sheemar et al., 21 Feb 2025). Alternating optimization and majorization-maximization (MM) techniques with tailored surrogate functions have been shown effective in such scenarios.

4. Mutual Coupling, Hardware Realization, and Algorithmic Design

High-density metamaterial arrays exhibit non-negligible mutual coupling, especially when elements are spaced well below $\lambda/2$. Coupling is captured in electromagnetic-compliant models using a mutual impedance or coupling matrix $G$:

$$B = k \left( [e^{j\tau} \Theta]^{-1} - G \right)^{-1} F_\text{ref}$$

where $\Theta$ parameterizes pattern control and $F_\text{ref}$ is the composite reference wave from multiple feeds. The mutual coupling must be included for accurate sidelobe control, especially for ISAC applications sensitive to clutter (Zeng et al., 9 Sep 2025).

Algorithms for optimizing holographic patterns under coupling start with Neumann series expansions to linearize the matrix inverse, facilitating the use of semidefinite relaxation (SDR) and quadratic programming. Iterative alternating optimization between digital and analog domains is commonly employed. Such frameworks enforce constraints on sidelobe suppression, main lobe gain, and communication rate simultaneously.

5. Recordable/Reconfigurable Surfaces and Interferometric Channel Estimation

Recent advances propose supplementing or replacing explicit channel state information (CSI) acquisition with physical recording of the interference pattern (“hologram”) on the surface (Wang et al., 24 Jun 2025, Yin et al., 14 Sep 2025). In this concept, an incoming object wave from the user and a known reference wave are superimposed on each element:

$W(m, n) = |E_o(m, n) + E_r(m, n)|^2$

The recording, via power detection, encodes both amplitude and phase information. Subsequent reconstruction employs matrix reindexing or phase shifting to produce the conjugate (matched filter) of the object wave, effectively generating a beam in the intended direction without explicit CSI estimation. Phase-shifting interferometry may be used to reconstruct the channel response from a small set of power measurements:

$$\hat{E}_o = \frac{1-j}{4 E_r^*} \{ I(0) - I(\pi/2) + j [I(\pi/2) - I(\pi)] \}$$

By combining such measurements in hardware-integrated fashion, channel estimation and beamforming are realized via simple power sensors, reducing RF complexity and hardware cost. Experiments confirm that such architectures can operate near the Cramér–Rao lower bound for wideband channel estimation and support ultra-large-scale arrays unattainable with conventional per-element RF chains (Yin et al., 14 Sep 2025).

6. Mathematical Formulations and Optimization Strategies

A core mathematical framework underpinning holographic communication includes:

• Green's function and eigenfunction channel diagonalization for the field-space representation.
• Fourier plane-wave expansions for mode decomposition and tractable simulation in both near- and far-field.
• Closed-form and bisection (or adaptive bisection) algorithms for high-dimensional joint transmit-receive beamforming (e.g., over continuous Fourier expansions (Liu et al., 7 Jun 2024)).
• Majorization-maximization (MM) optimization, exploiting surrogate inequalities of the form:

$$\frac{1}{v_d^\mathrm{H} B v_d} \leq \frac{2}{(v_d^{(t)})^\mathrm{H} B v_d^{(t)}} - \frac{v_d^\mathrm{H} B v_d}{[(v_d^{(t)})^\mathrm{H} B v_d^{(t)}]^2}$$

for proximal gradient or alternating updates in non-convex joint communications and sensing designs (Sheemar et al., 21 Feb 2025).

7. Challenges, Performance, and Outlook

Holographic communication systems offer significant performance gains:

• Capacity grows with surface area and operating in near-field, provided algorithms and hardware can exploit the increased spatial DoF (Dardari et al., 2020, Gong et al., 2023).
• Simulation evidence indicates communication-sensing trade-offs can be jointly optimized within MM or alternating optimization frameworks, achieving near-CRB limits in 3D angle estimation and maximal communication rates.
• Recordable/reconfigurable metasurfaces and interferometric surfaces avoid explicit large-scale CSI acquisition, further reducing system overhead while achieving comparable mutual information to conventional schemes (Wang et al., 24 Jun 2025, Yin et al., 14 Sep 2025).
• Accurately modeling mutual coupling and addressing the resulting non-convexity in beamforming is essential for integrating sensing without compromising communication, especially for large, continuous apertures.

Challenges remain in algorithmic scalability, practical synchronization across ultra-dense arrays, realization of robust hardware for recordable surfaces or envelope detection, and continuous adaptation under dynamic environmental conditions. Nevertheless, holographic architectures are positioned as a foundational technology for 6G and beyond, enabling seamless integration of communications and sensing at electromagnetic limits.