A Review on Electromagnetic Spectrum Map Construction: Methods, Challenges, and System Integration for 6G

Abstract

As wireless networks evolve from 5G toward 6G, the complexity of the electromagnetic environment increases sharply. Spectrum usage expands significantly into millimetre-wave (mmWave) and terahertz (THz) high-frequency bands. Network node density and mobility increase markedly. Moreover, communication-sensing-computation functions are deeply integrated. Accurate, real-time, full-band Electromagnetic Spectrum Maps (ESMs) have become a core infrastructure for 6G spectrum situational awareness, Dynamic Spectrum Access (DSA), interference coordination, and Integrated Sensing and Communication (ISAC). However, while a growing body of recent work extends radio mapping to multi-band and temporal domains, the predominant focus of existing Radio Map research remains the two-dimensional spatial power distribution at a single fixed frequency—essentially a degenerate special case of ESM after the frequency and time dimensions are collapsed—and no existing survey unifies 3D spatial construction, time-varying prediction, and full 6G system integration under a shared 4D formalism. This paper focuses on the three core research dimensions of ESMs, i.e., 3D spatial ESM construction, dynamic time-varying ESM modelling and prediction, and ESM integration with 6G systems. Under a unified four-dimensional ESM framework (space × frequency × time × power), we clarify the hierarchical relationships among ESM/SEM/REM/Radio Map/Channel Knowledge Maps (CKMs). Then, we systematically review 3D ESM construction, dynamic ESM modelling and prediction, and the integration of ESM with CKM/Digital Twin Networks (DTNs)/ISAC. Finally, we identify five, core open problems that constrain the development of the field to provide a systematic reference for 6G intelligent spectrum management research.

1. Introduction

Wireless communication technology is evolving toward 6G along three trends: spectra expanding into mmWave/THz bands [1,2,3,4]; sharply increasing density and mobility of base stations, UAVs, and LEO satellites [5,6,7,8]; and deep fusion of communication, sensing, and computation into ISAC [1,2,9]. ESMs—four-dimensional joint distributions of electromagnetic signals over space, frequency, time, and power—serve as shared knowledge infrastructure for spectrum situational awareness, DSA, interference coordination, ISAC, radio vortex communications, and DTN [10,11,12,13,14,15,16]. Freshness-sensitive DSA scenarios, including AoI minimization in ambient-backscatter-assisted energy-harvesting cognitive radio networks [17], exemplify settings where ESM timeliness directly determines system performance. Furthermore, in high-mobility 6G deployment scenarios, such as high-speed-train corridors and UAV communication links, the electromagnetic environment exhibits non-Gaussian heavy-tailed channel fading characterized by $\alpha$-stable Lévy processes [18], imposing additional robustness requirements on ESM reconstruction methods that conventionally assume Gaussian measurement noise. The body of existing survey literature on radio environment mapping spans from early taxonomy work to recent deep learning-oriented reviews, as summarized in

Table 1. Comparison of existing surveys and this paper.

Survey	Year	Spatial	Frequency	Temporal	6G Integration
Pesko et al. [19]	2014	2D	△	×	×
Reddy et al. [21]	2022	2D	✓	△	△
Romero & Kim [20]	2022	2D	×	×	×
Feng et al. [22]	2025	2D	×	×	△
Chen et al. [23]	2025	2D	✓	✓	△
This paper	2026	3D	✓	✓	✓

✓: covered; ×: not covered; △: partially covered.

. Pesko et al. [19] provided a foundational survey of radio environment map (REM) construction methods, categorizing interpolation, model-driven, and measurement-based approaches at a 2D single-band resolution. Romero and Kim [20] established rigorous statistical theory for radio map estimation, introducing kernel-based and Gaussian process frameworks that remain widely referenced but focus exclusively on 2D spatial inference without frequency or temporal dimensions. Reddy et al. [21] surveyed multi-band spectrum cartography techniques, cataloguing challenges and opportunities across frequency bands while remaining within the 2D spatial domain. Feng et al. [22] reviewed recent machine learning-based radio map estimation techniques, classifying methods into model-driven, data-driven, and hybrid categories and compiling available public datasets, yet without addressing 3D spatial structure or 6G system integration. Most recently, Chen et al. [23] advanced closest to a multi-dimensional scope by jointly reconstructing spatial–spectral–temporal radio frequency maps via tensor completion, yet their work remains confined to the 2D horizontal plane. Considered jointly, these surveys reveal three residual structural gaps with respect to 6G requirements: (1) the absence of a unified 3D spatial construction framework addressing simultaneous multi-band coverage; (2) the lack of a systematic account of time-varying ESM in the 3D spatial context; (3) no existing survey connecting ESM, CKM, DTN, and ISAC under a common 4D formalism. No existing survey simultaneously addresses all three dimensions; this paper’s contribution lies therefore in their unification under a 4D ESM framework. Therefore, this paper takes three core research dimensions into consideration: (1) 3D spatial ESM construction, (2) dynamic time-varying ESM modelling and prediction, (3) integrating ESM with 6G systems. We review recent work under a unified four-dimensional ESM framework and clearly identify five core open problems that constrain the development of the field. Table 1 compares existing surveys with this paper.

The defining novelty of this survey lies in unification: no existing work simultaneously addresses all three dimensions—3D spatial construction, temporal dynamics, and full 6G system integration—under a shared 4D ESM formalism, as shown in Table 1. The main contributions of this paper are summarized as follows: (1) a unified four-dimensional ESM problem framework clarifying hierarchical relationships among ESM/SEM/REM/Radio Map/CKM; (2) a systematic survey of 3D spatial ESM construction covering model-driven and data-driven approaches with dataset status; (3) a systematic survey of time-varying ESM modelling and prediction, providing a dedicated 3D treatment absent from existing surveys; (4) a review of ESM integration frameworks with CKM, DTN, and ISAC; and (5) five explicit open problems providing a concrete agenda for future research. The overall structure is illustrated in Figure 1.

Review Methodology and Scope

The literature reviewed in this paper was assembled through systematic searches of IEEE Xplore, Google Scholar, arXiv, and Web of Science using the following primary search terms: radio map, radio environment map (REM), spectrum cartography, electromagnetic spectrum map (ESM), channel knowledge map (CKM), and spectrum situational awareness, combined in turn with modifiers 3D, time-varying, prediction, 6G, ISAC, and digital twin. The search window spanned January 2015 to March 2026, with selective inclusion of earlier foundational works. Inclusion criteria: (i) the work directly addresses the construction, estimation, or prediction of a spatially resolved radio or spectrum power field; (ii) it contributes to at least one of the three survey dimensions (3D spatial construction, temporal dynamics, or 6G system integration). Exclusion criteria: (i) pure physical-layer channel estimation without a spatial mapping dimension; (ii) spectrum sensing or occupancy monitoring without spatial field reconstruction; (iii) hardware contributions with no mapping or inference component. Retained papers were classified under the unified 4D ESM framework (Section 2) and further organized by method type (model-driven, data-driven, generative, hybrid). Approximately 120 references were reviewed in total.

2. Definition, Framework, and Classification of ESM

Conceptual Hierarchy and Unified Mathematical Framework

Figure 2 illustrates the relationships among key concepts. ESM is the core object of this paper: the joint distribution of electromagnetic signals over space, frequency, time, and power [11,16]. SEM is the primary instance emphasizing complete environmental description [23,24,25]. REM describes spatial power distribution at a fixed frequency ($\left|\mathcal{F}\right|=1$) [19,21,26,27]. Radio Map is a simplified REM focusing on 2D static path loss or RSS [20,28,29]. CKM is a wideband channel prior database indexed by location, complementary to ESM [6,10,30,31]. The scope relationship is formally: $\mathrm{ESM}\supseteq \mathrm{SEM}\supseteq \mathrm{REM}\supseteq \mathrm{Radio}\mathrm{Map}.$ Radio Map is a degenerate special case of ESM when $\left|\mathcal{F}\right|=1$ and $\left|\mathcal{T}\right|=1$. Equating this degenerate case with the general problem results in research gaps [16].

Let $\mathcal{R}\subset {\mathbb{R}}^3$ be the target geographic region, $\mathbf{x}\in \mathcal{R}$ the spatial coordinate, $f\in \mathcal{F}$ the frequency, and $t\in \mathcal{T}$ the time. Each sparse measurement is modelled as:

$$y_s=\mathsf{\Gamma }({\mathbf{x}}_s,f_s,t_s)+n_s,s=1,\dots ,S,$$

(1)

where $n_s\sim \mathcal{N}(0,{\sigma }_n^2)$ is additive noise, and $S\ll \left|\mathcal{R}\right|·\left|\mathcal{F}\right|·\left|\mathcal{T}\right|$ reflects the sparse sampling condition. Let ${\mathbf{y}}_S={[y_1,\dots ,y_S]}^{\top }$ collect all measurements, and ${\mathbf{I}}_{\mathrm{prior}}$ denote available prior information. Here, $\mathsf{\Gamma }(\mathbf{x},f,t)\in \mathbb{R}$ denotes the received power spectral density (e.g., in dBm/MHz); the spatial, frequency, and temporal resolutions are $\Delta x$, $\Delta f$, and $\Delta t$, respectively, (discretization detailed in (4)). Writing $\mathbf{n}={[n_1,\dots ,n_S]}^{\top }\sim \mathcal{N}(\mathbf{0},{\sigma }_n^2\mathbf{I})$, the measurements take the matrix form ${\mathbf{y}}_S=\mathbf{A}\mathrm{vec}\left(\mathsf{\Gamma }\right)+\mathbf{n}$, where $\mathbf{A}\in {\{0,1\}}^{S\times N}$ is the binary sampling-selection matrix, with $N=N_x{N}_y{N}_z{N}_f{N}_t$ (see (4)) making the ill-posed nature of the inverse problem explicit. The posterior uncertainty ${\sigma }^2(\mathbf{x},f,t)=\mathrm{Var}\left[\mathsf{\Gamma }(\mathbf{x},f,t)\right|{\mathbf{y}}_S]$ quantifies reconstruction confidence and motivates active sensing strategies (Section 4); reconstruction quality is evaluated via the normalized mean squared error (NMSE, (7)). The unified ESM construction problem is:

$$\widehat{\mathsf{\Gamma }}(\mathbf{x},f,t)=\mathcal{F}\left({\mathbf{y}}_S,{\mathbf{I}}_{\mathrm{prior}}\right),\forall (\mathbf{x},f,t)\in \mathcal{R}\times \mathcal{F}\times \mathcal{T},$$

(2)

where $\mathcal{F}(·)$ may be a traditional interpolator, a machine learning model, or a generative model [20,32,33].

The ESM construction problem in (2) is fundamentally an ill-posed inverse problem: the power field over a continuous 4D domain must be recovered from a finite set of noisy sparse measurements. Romero et al. [32] provided a rigorous theoretical analysis of this problem, establishing upper and lower bounds on the spatial variability of power maps via the proximity coefficient:

$$\rho \left(\mathcal{R}\right)={\displaystyle \sum _{k=1}^K}{\displaystyle \frac{P_k}{d_k^3\left(\mathcal{R}\right)}},d_k\left(\mathcal{R}\right)=\underset{\mathbf{x}\in \mathcal{R}}{\min }{\parallel \mathbf{x}-{\mathbf{x}}_k\parallel }_2,$$

(3)

where $P_k$ is the transmit power of the k-th source and $d_k\left(\mathcal{R}\right)$ its minimum distance to the mapped region. Their analysis reveals that power maps exhibit relatively slow spatial variation with energy concentrated at low spatial frequencies, implying that a higher measurement density (larger $\rho$) is required when sources are closer to the mapped region. This result theoretically motivates compressed-sensing-based recovery, exploiting the restricted isometry property (RIP) [34], and partially explains why data-driven CNN approaches can achieve good reconstruction from sparse measurements in practice. Nevertheless, the fundamental limits of 4D ESM reconstruction—including observability conditions for multi-source, multi-band scenarios and the precise interplay among sampling density, source sparsity, and reconstruction error—remain open.

The discretized 4D ESM is represented as a tensor:

$$\mathsf{\Gamma }\in {\mathbb{R}}^{N_x\times N_y\times N_z\times N_f\times N_t},{\left[\mathsf{\Gamma }\right]}_{i,j,k,l,m}=\mathsf{\Gamma }({\mathbf{x}}_{ijk},f_l,t_m),$$

(4)

where $N_x,N_y,N_z,N_f,N_t$ are the discretization sizes along the spatial ($x,y,z$), frequency, and time dimensions, respectively. The four-dimensional ESM tensor structure is further depicted in Figure 3, and the unique physical constraints of the three extension dimensions are summarized in

Table 2. Physical characteristics of the three core extension dimensions of the 4D ESM.

Dimension	Core Physical Characteristics	Limitation of Radio Maps
Frequency	Heterogeneous propagation mechanisms across frequency bands (sub-6G/mmWave/THz); physical correlations exist between frequency points [3,35,36]	Independent construction per frequency point ignores cross-band coupling; computational cost grows linearly with the number of frequency points
Time	Mobile radiation sources continuously change; spectral occupancy has temporal dependencies [23,24,37,38]	Multiple static maps with misaligned timestamps cannot describe situational evolution or radiation source trajectories
Altitude	UAVs and LEO satellites invalidate the 2D planar assumption; vertical propagation characteristics differ significantly from horizontal ones [5,39,40,41]	Two-dimensional planar maps cannot describe the signal distribution and shadowing relationships in three-dimensional space

.

3. Construction Methods for 3D Spatial ESM

3.1. Overview and Method Taxonomy

The 2D planar assumption fails systematically with low-altitude UAV networks, vertical cell coverage, THz directional communication, and LEO satellite interference management [6,40,41,42]. Extending from 2D to 3D scales unknown variables from $N^2$ to $N^3$, imposing higher demands under sparse sampling [32,43,44]. We review the literature from the following categories.

Model-driven methods. 3D ray tracing accurately models reflection, diffraction, and scattering but its high cost (minutes to hours per scene) limits it to generating synthetic training data [45,46,47]. Sparse Bayesian Learning (SBL) exploits spectral sparsity for low-sampling-rate recovery with strong physical interpretability [34,48]. The underlying sparse recovery is typically formulated as:

$$\widehat{\mathsf{\alpha }}=\arg \underset{\mathsf{\alpha }}{\min }{\displaystyle \frac{1}{2}}\parallel {\mathbf{y}}_S{-\mathsf{\Phi }\mathsf{\alpha }\parallel }_2^2+\lambda {\parallel \mathsf{\alpha }\parallel }_1,$$

(5)

where $\mathsf{\Phi }\in {\mathbb{R}}^{S\times M}$ is a dictionary (e.g., spatial Fourier basis) and $\lambda$ is the regularization parameter. Krijestorac et al. [44] extended Kriging to 3D using UAV-mounted sensors and found that matrix completion outperforms Kriging at low measurement density. The Kriging predictor takes the form:

$$\widehat{\mathsf{\Gamma }}\left(\mathbf{x}\right)={\mathbf{k}}_{\mathbf{x}}^{\top }{\left(\mathbf{K}+{\sigma }_n^2\mathbf{I}\right)}^{-1}{\mathbf{y}}_S,$$

(6)

where ${\left[{\mathbf{k}}_{\mathbf{x}}\right]}_i=\kappa (\mathbf{x},{\mathbf{x}}_i)$ and ${\left[\mathbf{K}\right]}_{ij}=\kappa ({\mathbf{x}}_i,{\mathbf{x}}_j)$ are evaluations of a kernel (covariance) function; the $\mathcal{O}\left(S^3\right)$ matrix inversion exposes its scalability bottleneck. Cao et al. [49] proposed a novel electromagnetic-compliant model with mutual coupling for active RIS-assisted wireless systems.

Data-driven deep learning methods. RadioUNet [28] pioneered end-to-end path loss prediction from building maps; 3D UNet extensions exploit inter-layer altitude correlations [43,46]. PMNet [50,51] achieved NMSE $\approx -31.8$ dB at ∼8 ms with 4.5× training data reduction. Wang et al. [46] proposed UrbanRadio3D—ray-traced with path loss, DoA, and ToA, 7× more altitude layers than prior datasets—and RadioDiff-3D, which supports transmitter-known and sparse-observation modes, significantly outperforming deterministic baselines. RadioDiff-k2 [52] injects the Helmholtz equation as a hard physical constraint, achieving NMSE $\approx -32$ dB as the state of the art for physics-integrated generative ESM.

NeRF and 3D Gaussian Splatting methods. NeRF2 [53] achieves ∼50% accuracy improvement via physics–neural turbo learning. NeRF-REM [54] injects path loss and shadow fading priors for effective extrapolation to unobserved altitudes. WRF-GS+ [55] integrates electromagnetic constraints into deformable 3D Gaussian primitives, outperforming ray tracing at ∼25 ms inference. F4-CKM [56] and RadSplatter [57] further extend the NeRF/GS paradigm to CKM construction and RF map extrapolation.

Environment semantics-driven reconstruction. The Virtual Obstacle Model (VOM) was proposed in [58] to jointly reconstruct radio maps and virtual obstacles from RSS, achieving 10–18% accuracy improvement. Liu and Chen [42] constructed a full-dimensional (6D) radio map via joint virtual obstacle and propagation parameter estimation. Wang et al. [59] demonstrated the value of 3D point cloud geometric priors for low-altitude mmWave CKM construction.

To highlight the critical technical differences among these approaches,

Table 3. Comparison of ESM construction methods: Physical assumptions, scalability, and computational complexity.

Category	Core Physical Assumptions	Scalability	Infer. Cost	Representative Works
Ray Tracing	Full 3D geometry; explicit EM propagation (reflection/diffraction/scattering); no statistical assumptions	Poor; exponential w.r.t. scene complexity	>600 ms	[45,47]
SBL/Kriging	Spectral sparsity prior (SBL); Gaussian random field with stationary isotropic covariance (Kriging)	Poor; $\mathcal{O}\left(N^3\right)$	Seconds	[34,44,48]
Deterministic CNN	Building map input; translational equivariance; fully data-driven	Good; $\mathcal{O}(N^2\times L)$	8–30 ms	[28,50]
Physics-Constrained Diffusion	Helmholtz equation as hard constraint; deep generative prior	Moderate; $T_{\mathrm{step}}\times \mathcal{O}\left(N^2\right)$	1500–2200 ms	[46,52]
NeRF/3DGS	Continuous implicit radiance field; differentiable rendering analogy	Scene-specific training	∼25 ms	[53,55]
Environment Semantics	Virtual obstacle/point cloud priors; joint propagation parameter estimation	Moderate; depends on scene geometry granularity	Medium	[58,59]

N: spatial grid resolution per dimension; L: network depth; $T_{\mathrm{step}}$: diffusion step count.

systematically compares them across physical assumptions, scalability, and computational complexity [60]. Model-driven methods rely on explicit physical assumptions and offer high interpretability but suffer from poor scalability. Data-driven CNN methods make minimal physical assumptions but achieve the best engineering balance of accuracy and inference speed. Physics-constrained generative models inject hard physical constraints into the generative prior, breaking the accuracy ceiling of deterministic CNNs at the cost of higher inference latency. NeRF/GS methods employ a continuous implicit representation amenable to differentiable rendering analogies, enabling fine-grained 3D reconstruction with fast inference but requiring scene-specific training.

3.2. Accuracy–Complexity Tradeoff and Dataset Status

Throughout this paper, reconstruction quality is quantified by the normalized mean squared error (NMSE):

$$\mathrm{NMSE}=10{\log }_{10}\left({\displaystyle \frac{\parallel \widehat{\mathsf{\Gamma }}{-\mathsf{\Gamma }\parallel }_F^2}{{\parallel \mathsf{\Gamma }\parallel }_F^2}}\right)\left[\mathrm{dB}\right],$$

(7)

where $\widehat{\mathsf{\Gamma }}$ and $\mathsf{\Gamma }$ are the estimated and ground-truth ESM tensors, respectively.

Each data point in Figure 4 is extracted from the best-reported result in the original publication under its respective experimental conditions: RadioUNet [28] and RadioDiff-k2 [52] were evaluated on the RadioMapSeer benchmark (56,000 ray-traced maps, 256 × 256 m² urban area, 5.9 GHz; Quadro GV100 and RTX Pro 6000, respectively); PMNet [50] on real-world ray-traced datasets of three US cities (sub-6 GHz; RTX 3080 Ti, ∼8 ms, NMSE $\approx -31.8$ dB); RadioDiff-3D [46] on the UrbanRadio3D three-dimensional dataset (5.9 GHz; DDIM 20-step inference at ≈2.4 s on NVIDIA 4090); WRF-GS+ [55] on an indoor NeRF2 laboratory dataset (RTX 3090, ∼25 ms); and model-driven baselines (ray tracing, SBL, Kriging) on simulated urban and measurement-derived campus environments [44,45,48]. Because heterogeneous datasets, frequency bands, spatial resolutions, and hardware platforms are involved, absolute NMSE values are not directly comparable across methods; the figure is intended to illustrate broad accuracy–latency trends across method categories rather than serve as a controlled pairwise benchmark.

This cross-category analysis reveals a systematic stratification. Model-driven methods (ray tracing, SBL, Kriging) are confined to the offline regime (>600 ms) by physics-intensive iterative computation—full electromagnetic ray casting, $\mathcal{O}\left(N^3\right)$ matrix inversion in Kriging, and outer-loop optimization in SBL. Deterministic CNN methods (RadioUNet, PMNet) achieve the best engineering tradeoff at ∼8–30 ms and NMSE $\approx -26$ to $-32$ dB, because a single feedforward pass replaces iterative solvers; their accuracy, however, is bounded by the purely discriminative training objective. Physics-constrained diffusion models (RadioDiff-3D/k2) achieve the highest reported accuracy (NMSE $\approx -30$ to $-32$ dB) at 1500–2200 ms: $T_{\mathrm{step}}$ iterative denoising passes incorporate Helmholtz-derived physical constraints into the generative prior, breaking the CNN accuracy ceiling without raising computation by an additional order of magnitude relative to classical model-driven approaches. WRF-GS+ bridges generative quality and real-time speed at ∼25 ms via a differentiable 3D Gaussian scene representation trained once offline. Critically, the region below 50 ms and NMSE $<-20$ dB remains unoccupied—no existing method simultaneously satisfies 6G real-time reconstruction constraints (Open Problem 1, Section 6).

Table 4. Publicly available ESM/Radio Map spatial construction research datasets (competition benchmarks: Table 7).

Dataset	Dim.	Freq. Band	Time	Generation	Access
RadioMapSeer	2D	5.9 GHz (single)	×	Ray tracing	GitHub
RadioMap3DSeer [51]	3D	Single	×	Ray tracing	GitHub
UrbanRadio3D [46]	3D	Single (DoA/ToA)	×	Ray tracing	arXiv
CKMImageNet [61]	2D/3D	Multi-band	×	Sim.+Image	arXiv
DeepSense 6G [62]	2D	Multi-modal	×	Real meas.	Public
Indoor dataset [63]	2D (indoor)	Single	×	Real meas.	IEEE Dataport
ESM multi-dim. benchmark	3D + freq. + time	Multi-band	✓ (needed)	—	Does not yet exist

summarizes current 3D ESM datasets. A critical gap is that all existing 3D datasets are single-band and lack the time dimension. A benchmark combining multi-band and time-varying 3D coverage does not yet exist [11,16].

Beyond algorithm-level tradeoffs, translating ESM methods from simulation to real-world deployment introduces hardware-level challenges that the existing literature inadequately addresses. First, hardware synchronization: Distributed heterogeneous sensors (terrestrial base stations, UAVs, and LEO satellites) require sub-microsecond timestamp alignment; IEEE 1588 Precision Time Protocol (PTP) is standard in wireline infrastructure, but GPS-disciplined oscillator drift and frequency offset in mobile platforms introduce timing errors that propagate into the ESM as apparent spatial discontinuities. Second, sensing calibration: Receiver noise floors, antenna gain patterns, and frequency responses vary across sensor types, age, and temperature, causing systematic power biases that violate the homogeneous noise assumption in (1); calibration against known reference transmitters is rarely described in the surveyed datasets. Third, measurement inconsistency: Heterogeneous front-ends, scan resolutions, and co-channel interference produce non-identically distributed measurements whose naive aggregation degrades reconstruction quality in ways not captured by the NMSE metric alone. Establishing standardized hardware-in-the-loop testbeds and calibration procedures is a prerequisite for reliable real-world ESM deployment.

4. Dynamic Time-Varying ESM Modelling and Prediction

Dynamic time-varying ESM has received only limited systematic treatment in existing Radio Map surveys: while Chen et al. [23] address temporal spectrum prediction in a 2D setting, a dedicated account of 3D time-varying ESM construction and prediction has yet to be provided. Static-transmitter assumptions were acceptable before 5G, but the large-scale deployment of fast-moving radiation sources (vehicles, UAVs, LEO satellites) has made this a fundamental practical bottleneck.

4.1. Time Variability Sources and Online Update Methods

Time-variability sources span vastly different rates requiring different strategies (

Table 5. Classification, sources, and countermeasures for dynamic ESM time variability.

Type	Typical Source	Rate	Key Works	Strategy
Slow	Building construction, seasonal vegetation changes	Weeks/months	[19,64,65]	Periodic offline reconstruction
Medium	Base station on/off, new interference sources	Min/hours	[38,66,67]	Triggered online update
Fast	Mobile sources (vehicles, UAVs, LEO satellites)	Seconds/sub-second	[23,24,37,68]	Real-time prediction

): slow variations (building construction, seasonal changes, weeks/months) handled by periodic offline reconstruction, medium variations (base station on/off, minutes/hours) by triggered online update, and fast variations (mobile sources; seconds/sub-second) requiring real-time prediction [23,24,37].

The updating of time-varying ESM faces two major challenges: efficiency in handling large-scale spectrum maps and the timeliness of updates. Recently, generative AI (GenAI) techniques have demonstrated significant potential in facilitating various information maintenance tasks, and thus can be leveraged for spectrum map reconstruction. Meanwhile, emerging evaluation metrics, such as the age of generative information [69], can be employed to quantify the freshness of the spectrum map updating strategy. Formally, the $\tau$-step-ahead temporal prediction task is defined as:

$${\widehat{\mathsf{\Gamma }}}_{t+\tau }=\mathcal{P}\left({\mathsf{\Gamma }}_t,{\mathsf{\Gamma }}_{t-1},\dots ,{\mathsf{\Gamma }}_{t-K+1};{\mathbf{I}}_{\mathrm{prior}}\right),$$

(8)

where $\tau \ge 1$ is the prediction horizon, K is the historical context window length, and $\mathcal{P}(·)$ is the prediction operator. Different strategies are applied for the three variability regimes in Table 5. For online updates, Kalman filter frameworks naturally support recursive Kriging map updates [70]:

$${\widehat{\mathsf{\gamma }}}_{t|t}={\widehat{\mathsf{\gamma }}}_{t|t-1}+{\mathbf{G}}_t\left({\mathbf{y}}_t-\mathbf{H}{\widehat{\mathsf{\gamma }}}_{t|t-1}\right),$$

(9)

where ${\widehat{\mathsf{\gamma }}}_{t|t-1}$ is the prior map estimate, ${\mathbf{G}}_t$ is the Kalman gain, and $\mathbf{H}$ is the linear measurement matrix. Li et al. [64] proposed Supreme using crowdsourced spatiotemporal modelling for cross-region transfer. Wang et al. [38] proposed a spatiotemporal graph attention network with dual graph structure for dynamic spectrum cartography. The iterative denoising nature of diffusion models causes second-level inference latency. Wang et al. [71] proposed RadioDiff-Flux, which precomputes and reuses static intermediate latent points shared across semantically similar scenes, reducing inference to real-time acceptable ranges—among the earliest works achieving real-time dynamic ESM inference. Diffusion- and Transformer-based spatiotemporal prediction frameworks [37,68] and multimodal SEM prediction combining historical sequences, environment images, and radiation source locations [25] further advance multi-step forecasting accuracy. For joint spatial–temporal–spectral modelling, Wang et al. [72] represented the spectrum map as a fourth-order tensor and proposed a two-stage framework combining a Transformer with forget-sparse interpolation attention and an ADMM-RLS online algorithm, achieving robust prediction under incomplete and corrupted measurements. Pan et al. [73] proposed ViTransLSTM, which integrates shifted-window visual self-attention into the LSTM gate structure to simultaneously capture local and global spatiotemporal dependencies, validated on real-world spectrum datasets. Uncertainty quantification is increasingly recognized as essential for reliable dynamic ESM. Gu et al. [74] formulated spectrum cartography as a conditional generation problem driven by a diffusion prior, deriving tractable closed-form posterior transition kernels to jointly address reconstruction and uncertainty-aware active sensing. Zeng et al. [75] introduced GeoUQ-GFNet, which jointly produces dense gain maps and spatial uncertainty estimates from sparse measurements with geometry-aware priors, demonstrating that uncertainty-guided measurement selection outperforms non-adaptive sampling under equal measurement budgets.

4.2. Mobile Radiation Source-Driven Prediction and Wide-Area Sensing

Zhao et al. [24] proposed a systematic optical flow-based SEM temporal prediction framework, using globally constrained optical flow to capture radiation source motion from historical sequences. Multi-band joint temporal prediction remains the most challenging open direction [23,36], with core challenges including unknown/dynamic radiation source counts [76], power discontinuities from building shadowing [42,58], and absence of systematic multi-band joint temporal modelling [16,36].

For wide-area sensing, Huang et al. [5] proposed LEO satellite-based global ESM using GANs for spatial correlation modelling and reinforcement learning for narrow-beam uplink monitoring. UAV-based active surveying [40,77,78,79] maintains uncertainty maps and plans trajectories to maximize information gain:

$${\mathbf{x}}_{t+1}^{*}=\arg \underset{\mathbf{x}\in {\mathcal{X}}_{\mathrm{cand}}}{\max }{\sigma }_t^2\left(\mathbf{x},f,t+1\right),$$

(10)

where ${\sigma }_t^2(\mathbf{x},f,t+1)$ is the posterior predictive variance of $\mathsf{\Gamma }(\mathbf{x},f,t+1)$, conditioned on all measurements up to time t, with multi-UAV cooperative approaches [76,80] enabling large-scale distributed sensing. Jiang et al. [81] proposed a three-tier (edge–aggregation–cloud) co-design framework for efficient distributed ESM updates, as illustrated in Figure 5. The heterogeneous sensing system faces serious bottlenecks in data fusion: inconsistency across platforms in spatial resolution (km level for satellites to m level for ground sensors), latency, frequency bands, and coverage range; optimal fusion weight design and distributed inference mechanisms remain theoretically underexplored [44,81]. Dynamic ESM also requires a dedicated evaluation framework beyond static RMSE, incorporating prediction-step/accuracy tradeoff curves, trajectory tracking accuracy, and end-to-end map update latency [82,83].

5. ESM–6G System Integration Framework

5.1. ESM-Driven Dynamic Spectrum Management and ISAC

Time-varying ESM enables “predictive spectrum management”: advance situational estimates from historical sequences support proactive interference avoidance, upgrading cognitive radio from reactive to anticipatory [13,14,66]. Representative works include REM-guided RIS-assisted cognitive ISAC [84], joint beamforming and spectrum sensing with REM prior [85], and RIS–movable-antenna ESM-driven resource optimization for low-altitude ISAC [86]. In low-altitude airspace management, where ground base stations must simultaneously serve authorized UAVs and localize non-cooperative intruders for collision avoidance, Zheng et al. [87] proposed an optimal-transport-based joint cell-association and power-allocation framework (J2OT) that directly handles discrete variables without relaxation, achieving a 1.5 bits/s/Hz improvement in system objective and a 7.5% reduction in localization Cramér–Rao bound over baselines; ESM-provided spatial interference priors are an enabling prerequisite for such dual-function resource allocation over distributed ground-station networks. In mmWave/THz bands, ESM-based beam management reduces training overhead [35]: probabilistic radio map representations support robust beam prediction under positioning uncertainty [88], while CKM-based position priors enable environment-aware hybrid beamforming [89]. ESM can also enhance the radio frequency identification accuracy by providing statistical knowledge and the time-varying nature of spectrum usage [90]. More broadly, electromagnetic signal waveform recognition (ESWR) is a key downstream beneficiary of ESM: Zhao et al. [91] proposed FUTUREs, a meta-transfer learning framework that transfers feature-extraction utility from seen to unseen signal modulations, achieving accurate recognition of 6G candidate waveforms, including OTFS and OFDM with limited labelled samples. A systematic AI-component survey of the ESWR field [92] further reveals that the deep-learning paradigms central to ESM construction—convolutional encoders, physics-informed networks, and diffusion models—also underpin state-of-the-art automatic modulation recognition, motivating a unified signal intelligence platform for 6G. Hardware-oriented assessments confirm that sharing a single phased-array platform across sensing and communication functions imposes tight and often divergent antenna-performance requirements, including control over beam shape, scanning resolution, and sidelobe tolerance [93,94]. As a concrete system-level illustration of the ESM-ISAC closed loop, the RIS-assisted cognitive ISAC framework [84] shows that a precomputed ESM suppresses candidate beams in predicted interference-null regions, reducing beam-sweeping overhead. The operational cycle proceeds as follows: (1) ESM predicts the interference field at horizon $t+\tau$ via (8); (2) the ISAC beamformer maximizes worst-case SINR using the predicted map as a soft constraint; (3) sensing echoes update the ESM through the Kalman correction in (9). Completing this closed loop within 50 ms remains the central engineering challenge (Open Problem 1, Section 6). In distributed cell-free ISAC architectures, where multiple geographically separated access points (APs) must be jointly coordinated, Guo et al. [95] proposed a cooperative beamforming framework that maximizes sensing signal-to-clutter-plus-noise ratio (SCNR) under communication SINR constraints via semidefinite relaxation, demonstrating superior performance over single-objective methods. The geographic diversity of APs amplifies the value of a shared ESM, since each AP observes a complementary spatial segment of the interference landscape and global ESM integration reduces the coordination overhead that otherwise limits distributed ISAC performance. Symbiotic radio (SR) [96] represents another emerging paradigm for 6G intelligent spectrum management: a backscatter device (BD) parasitically modulates onto the primary transmitter’s (PTx) radio-frequency signals, while the PTx is jointly designed to assist both primary and BD transmissions, realizing a mutualism spectrum-sharing relationship. Accurate ESMs play a dual enabling role in SR systems: they provide the BD with spatially resolved spectral opportunity maps to identify favourable PTx transmission periods, and supply the PTx with interference-geography priors for joint precoding that simultaneously serves primary communication and backscatter relay objectives. As SR is increasingly considered for 6G networks where ambient energy harvesting and ultra-low-power IoT connectivity are design priorities, the tight coupling between ESM update latency and SR coordination constitutes an open co-design challenge.

5.2. ESM and CKM Cooperative Construction

ESM and CKM form the core dual pillar of 6G environment-awareness infrastructure [6,10]: ESM provides regional-level multi-dimensional spectrum situational descriptions while CKM provides location-indexed wideband channel priors. Romero and Kim [97] derived the minimum sampling density theorem when using CKM priors for ESM construction, theoretically quantifying the value of CKM side information.

Table 6. Comparison and complementarity of ESM and CKM in methodological technical routes.

Method Type	Representative ESM Work	Representative CKM Work
Image super-resolution	RadioUNet series [28]	CKM super-resolution [98]
Generative diffusion	RadioDiff series [71,99]	CKMDiff [100], BeamCKMDiff [101]
Cross-region inference	Domain adaptive GNN [102]	Cross-AP CKM inference [89]
3D environment awareness	3D point cloud ESM [46]	3D point cloud CKM [59]
Neural radiance field	NeRF-REM [54]	WRF-GS [55], F4-CKM [56]
Physical constraint	RadioDiff-k2 [52]	Physical CKM [103,104]

compares methodological parallels across the two domains.

At the generative AI level, CKMDiff [100] applies conditional diffusion to CKM construction. BeamCKMDiff [101] injects beamforming vectors into a Diffusion Transformer, enabling fine lobe reconstruction beyond discrete codebooks. A CKM-enabled NLoS ISAC scheme [105] converts channel angle-delay maps into sensing channel priors, simultaneously serving communication and target localization. The key unresolved framework is unified ESM-CKM construction theory, i.e., shared sparse sampling strategies and joint update mechanisms serving both communication and sensing needs [97]. Quantitatively, Romero and Kim [97] showed that incorporating CKM side information reduces the minimum required ESM measurement density by 30–50% in dense urban deployments where location-indexed path-loss priors from prior drive-test campaigns are available, directly motivating joint ESM-CKM sensing platform design.

5.3. ESM Integration with Digital Twin Networks and Dataset Status

DTN is the core enabling architecture for 6G network intelligence, and ESM is the core data source for the spatial spectrum layer of the Digital Twin Channel (DTC) [106,107,108]. Wang et al. [109] proposed the Radio Environment Knowledge (REK) framework, encoding propagation mechanism contributions as physical priors and enabling a lightweight CNN to achieve NMSE $\approx -28$ dB at 3 ms inference latency—within the update budget for a 5 Hz DTN refresh cycle. The key ESM-DTN design tension is between update granularity (finer updates improve accuracy but increase uplink overhead) and model coherence time (coarser updates reduce overhead but allow larger state drift under rapid topology changes). ESM-DTN closed-loop updating faces three core challenges: the tradeoff between update frequency and computational overhead, simulation-to-measurement domain gap [47,110], and unified access for heterogeneous sensor data [111,112].

Table 7 summarizes ESM competition benchmarks and open evaluation environments; for construction research datasets, refer to Table 4 (Section 3). Beyond the structural dimension gaps, three additional quality dimensions limit ESM benchmark utility. (i) Dataset quality and simulation-to-reality gap: The overwhelming majority of datasets are ray-traced under idealized propagation conditions—smooth terrain, simplified building geometry, and no vehicular blockage dynamics—creating a domain shift that degrades trained models when transferred to real field measurements; DeepSense 6G remains among the most comprehensive publicly available multi-modal real-measurement datasets but is confined to 2D spatial coverage. (ii) Benchmark standardization: The ICASSP 2023 and 2025 competitions [82,83] adopt different sampling densities, path-loss models, and evaluation splits, making cross-paper NMSE comparisons unreliable; cross-band and time-varying scenarios remain largely absent from existing competition benchmarks. (iii) Reproducibility: A majority of reviewed works release neither code nor complete hyperparameter details, a critical gap for physics-constrained generative models where the diffusion schedule and constraint-weighting dominantly determine accuracy. A community-coordinated open dataset covering multi-band (sub-6G/mmWave/THz), time-varying, 3D, and large-scale urban scenarios, paired with a standardized evaluation harness, is the most urgent infrastructure investment for the ESM field. The evolution of key methods from 2011 to 2026 is summarized in Figure 6.

Table 7. ESM competition benchmarks and evaluation environments (for spatial construction research datasets, see Table 4).

Competition/Dataset	Year	Dim.	Freq. Band	Task/Focus	Access
AI4MOBILE (iV2I+)	2023	2D	3.7 GHz	Vehicle-to-infrastructure received power map	Public
ICASSP 2023 Challenge [82]	2023	2D	Single	Path-loss map prediction, 1–10% sampling density	Competition
ICASSP 2025 Indoor [83]	2025	2D (indoor)	Single	Indoor RSS map prediction	Competition
ESM multi-dim. benchmark	—	3D + freq. + time	Multi-band	Multi-dimensional ESM evaluation (needed)	Does not yet exist

Table 7. ESM competition benchmarks and evaluation environments (for spatial construction research datasets, see Table 4).

Competition/Dataset	Year	Dim.	Freq. Band	Task/Focus	Access
AI4MOBILE (iV2I+)	2023	2D	3.7 GHz	Vehicle-to-infrastructure received power map	Public
ICASSP 2023 Challenge [82]	2023	2D	Single	Path-loss map prediction, 1–10% sampling density	Competition
ICASSP 2025 Indoor [83]	2025	2D (indoor)	Single	Indoor RSS map prediction	Competition
ESM multi-dim. benchmark	—	3D + freq. + time	Multi-band	Multi-dimensional ESM evaluation (needed)	Does not yet exist

6. Challenges and Open Problems

6.1. Core Conclusions

Along the three dimensions: Spatially, 3D ESM methods (deep learning, diffusion, NeRF/GS) have taken initial shape and UrbanRadio3D fills the dataset gap, but methods remain single-band. Indoor 3D ESM has received very limited attention, and theoretical reconstruction bounds are unestablished. Temporally, this remains the most underexplored dimension—optical flow-driven SEM prediction [24] and real-time diffusion inference [71] are among the earliest dedicated works for dynamic ESM. Multi-band joint temporal prediction and dedicated evaluation systems remain insufficiently addressed. In system integration, ESM-CKM [97], ESM-DTN, and ESM-ISAC [85] are all in early stages with no system-level joint optimization framework. Radio Map is a degenerate special case of ESM; yet, 6G requires complete four-dimensional ESM, while current technological accumulation is far from ready.

6.2. Five Core Open Problems

The following five open problems were selected because each represents a bottleneck where the literature consistently acknowledges an unresolved gap: together they span all three axes of this survey—spatial construction, temporal dynamics, and 6G system integration—and their interdependencies are evidenced by the comparative analysis in Table 1.

Open Problem 1: Reliable Extremely Sparse 4D Reconstruction. Diffusion models achieve high-quality 2D reconstruction below 1% sampling [99,113], but “hallucination”—visually plausible but physically unrealistic maps—has unacceptable consequences in spectrum management. Bayesian uncertainty quantification [114], hard physical constraint injection [52], and active sampling [77,115] are candidate paths, yet no unified theoretical framework exists [97]. The key technical question is: At what minimum sampling density can reconstruction reliability be guaranteed across all four ESM dimensions? A suitable evaluation metric is worst-case NMSE over randomized (rather than fixed) sampling masks, paired with the calibration error of uncertainty estimates. Conformal prediction, deep-unfolding architectures with hard physical-constraint layers, and information-theoretic active sensing are the most applicable methodological tools.

Open Problem 2: Joint Modelling of Multi-Band Heterogeneous Propagation. Sub-6G, mmWave, and THz exhibit highly heterogeneous propagation within the same ESM framework [3,35,116]. Whether a unified cross-band physical constraint suffices, or whether per-band modelling followed by merging is unavoidable, remains theoretically unresolved [11,23]. The concrete technical question is: Does a shared latent propagation basis exist across sub-6G/mmWave/THz that permits unified tensor completion, or is per-band modelling with learned cross-band coupling the more tractable formulation? Progress should be measured by cross-band transfer gain when a new frequency band is added with zero additional measurements. Multi-task neural operators and physics-informed frequency-domain factorization are the primary candidate methodologies.

Open Problem 3: Establishing ESM-Dedicated Benchmark Datasets. Existing datasets predominantly operate in single-band, static, 2D settings—the principal infrastructure bottleneck [16,46]. A community-defined benchmark covering multi-band (sub-6G/mmWave/THz), time-varying dynamics, 3D space, mixed real/simulated data, diverse scenarios (urban/suburban/indoor/low-altitude), and standardized evaluation metrics remains absent [82,117]. The operational question is: What is the minimum scenario diversity and sampling protocol that enables statistically reliable cross-method comparison? Evaluation should specify fixed stratified sampling masks per scenario class, a held-out test split inaccessible during training, and NMSE leaderboards stratified by sampling density and frequency band. Community coordination modelled on the ImageNet challenge or 3GPP channel-measurement campaigns is the appropriate organizational framework.

Open Problem 4: Cooperative Fusion Theory for Space–Air–Ground Heterogeneous Sensing. Satellite, UAV, and ground sensors differ substantially in resolution, latency, frequency, and coverage, making unified fusion theoretically non-trivial [5,44,81]. Deriving optimal fusion weights, designing cooperative sampling strategies, and adapting federated learning [118,119] to ESM’s statistical structure are the key challenges for global-scale ESM. The core theoretical question is: What is the Cramér–Rao lower bound for heterogeneous-sensor ESM estimation as a function of sensor placement, resolution heterogeneity, and inter-sensor correlation? Fusion gain over the best single-modality baseline under equal measurement cost is the natural evaluation metric. Distributed Bayesian estimation with heterogeneous likelihood models and graph neural network-based cooperative sensor scheduling are the most mature methodological tools.

Open Problem 5: System-Level Optimization of the ESM-DTN-ISAC End-to-End Closed Loop. Each module in the pipeline—spectrum sensing, beamforming, interference coordination, and DTN updating—is independently optimized, producing local optima that fail to aggregate globally [79,81]. A unified multi-objective framework balancing ESM accuracy, ISAC performance, spectrum management quality, and update overhead is needed. Semantic communication [120] offers a promising direction, with task-oriented coding potentially reducing ESM sharing overhead by 95% while preserving downstream management quality. The fundamental question is: What is the Pareto frontier between ESM reconstruction accuracy and ISAC beamforming SINR under a joint update–latency constraint, and how does it scale with network density? A tandem metric combining NMSE, beamforming SINR, and spectrum efficiency under a fixed uplink-overhead budget would operationalize progress. Multi-objective Lyapunov network optimization and task-oriented semantic communication are the most applicable methodological frameworks.

7. Conclusions

This paper surveyed ESM across three core dimensions under a unified 4D ESM framework (space × frequency × time × power), revealing the fundamental limitations of existing Radio Map surveys. The key findings of this paper are as follows. Deep learning and generative methods have surpassed ray tracing for online 3D ESM, with UrbanRadio3D as a key dataset milestone. Temporal prediction driven by mobile radiation sources remains largely underexplored, with RadioDiff-Flux achieving a real-time diffusion inference breakthrough. ESM integration with CKM, DTN, and ISAC is converging but lacks a unified framework. The five open problems provide a concrete research agenda for advancing ESM from theoretical concept to 6G-enabled core technologies.