A Recent Survey on Radio Map Estimation Methods for Wireless Networks

Abstract

As a visualization of radio frequency environment state, radio maps are of significant importance in enhancing the efficiency of spectrum resources and the quality of service of general-purpose wireless networks. For a comprehensive review on radio map estimation (RME) methods, representative achievements in recent years on RME are categorized. Firstly, according to the extent of dependency on model knowledge, existing RME methods are categorized into three major classifications for the first time: model-driven methods, data-driven methods, and hybrid model data-driven methods. Subsequently, typical works in each classification of RME methods, as well as their pros and cons, are illustrated in detail. Moreover, this survey compiles public datasets for radio maps and points out that hybrid simulation measurement datasets are crucial for RME. Finally, future directions on the RME problem are discussed. Unlike existing surveys, this survey not only ensures academic accuracy in its literature review, but also preserves the evolutionary trajectory of RME methods, enabling readers to quickly grasp the history and development trends of RME.

1. Introduction

With the advancement of wireless communication technologies, modern wireless communication environments are typically characterized by the dense deployment of various heterogeneous wireless communication devices, leading to increasingly severe radio frequency (RF) interference. Therefore, the design of future wireless networks (e.g., B5G and 6G) urgently requires accurate RF environment states to enhance the spectrum efficiency and quality of service of wireless networks. The RF environment state is a function of time, space, and frequency, determined by the superposition of RF signals. As a visualization of the RF environment state, the radio map plays a crucial role in enabling efficient environmental perception for the design and optimization of wireless networks. As a result, radio map estimation (RME) has emerged as a significant research focus in the field of wireless networks in recent years.

A radio map encapsulates rich knowledge of spectral activity and propagation channels, providing detailed spatial information on various RF parameter distributions [1,2]. It can be broadly categorized into two types: signal strength maps and propagation maps [3]. The former aim to characterize the combined effects of transmission signals and channels, while the latter focus on the channel itself. Signal strength maps include coverage maps, outage probability maps, power maps, path loss maps, and power spectral density (PSD) maps. Propagation maps are typically represented by channel gain maps. When the power and location of a transmitter are known, different types of signal strength maps can be conveniently derived from channel propagation maps. Given the prior statistical channel knowledge embedded in radio maps, traditional wireless applications can utilize spectrum resources more efficiently, thereby improving the quality of wireless service. Currently, radio maps have been widely applied in various wireless scenarios, including wireless localization [4,5,6,7,8], physical layer security [9], resource allocation [10,11,12,13], network planning [14,15,16,17], activity detection [18], fault diagnosis [19], and so on.

However, due to the labor-intensive collection process and physical constraints, practical RME is unable to gather extensive measurement data. Therefore, the key challenge in RME is how to accurately estimate the global RF parameter distribution based on sparse measurement data. Many research efforts have been dedicated to RME methods. As illustrated in Figure 1, existing RME methods in the literature can be categorized into model-driven methods, data-driven methods, and hybrid model data-driven methods.

• Model-driven methods are based on specific signal propagation models, which model the radio map as a function of location and frequency. However, model-driven methods strongly rely on sophisticated domain knowledge in wireless communications.
• Data-driven methods leverage measurement data to predict signal strengths at unknown locations or frequencies, thereby constructing complete radio maps. The performance of data-driven methods is heavily determined by the quantity and quality of measurements or simulation data.
• Hybrid model data-driven methods integrate signal propagation models with data-driven methods, achieving high-accuracy radio maps even with a limited number of samples.

The contributions of this survey over existing surveys [2,3] are as follows: Pesko et al. [2] reviews interpolation-based RME methods up to 2014 in the context of cognitive radio networks, while this survey focuses on different categories of RME methods for general-purpose wireless networks. Although Romero and Kim [3] provides a comprehensive survey of various data-driven methods for RME up to 2022, it lacks discussion of model-driven and hybrid model data-driven methods. With the rapid improvements in deep learning, numerous representative studies on RME have emerged since 2022. This survey, for the first time, summarizes the literature in the field of RME based on the degree of reliance on model knowledge. In addition to ensuring academic accuracy in its literature review, more importantly, this survey preserves the evolutionary trajectory of RME methods, enabling researchers in related fields to quickly grasp the development history and future trends of RME. Last but not least, this survey compiles publicly available datasets for RME which have not been mentioned before.

The structure of this survey is as follows: Section 2 introduces model-driven methods, including both parametric and non-parametric methods. Section 3 presents data-driven methods, encompassing interpolation methods and deep learning methods. Section 4 summarizes hybrid model data-driven methods. Section 5 compiles publicly available datasets for RME. Section 6 discusses future research directions. Finally, Section 7 concludes the survey.

2. Model-Driven Methods

Model-driven methods are based on specific signal propagation models, where the radio map $\Phi (\mathit{x},f)$ is formulated as a function of unknown location $\mathit{x}$ and frequency f [1]. As illustrated in Figure 2, given the number of transmitters $N_t$ and the transmit PSD of the k-th transmitter, denoted as ${\psi }_k\left(f\right)$, $\Phi (\mathit{x},f)$ can be expressed as

$$\Phi (\mathit{x},f)=\sum _{k=1}^{N_t}{g}_k(\mathit{x},f){\psi }_k\left(f\right),$$

(1)

where $g_k(\mathit{x},f)$ represents the channel gain function at the frequency f from the k-th transmitter to the location $\mathit{x}$. The core challenge of model-driven methods lies in estimating $g_k(\mathit{x},f)$ (hereafter denoted as $g_k$ for short). Depending on whether the functional form of $g_k$ is known, model-driven methods can be classified into parametric methods and non-parametric methods. Parametric methods have a fixed number of parameters, whereas the number of parameters in non-parametric methods depends on the quantification of available samples.

2.1. Parametric Methods

Parametric methods typically describe $g_k$ as an explicit function with a fixed number of parameters. The main parametric methods include electromagnetic simulation methods [20,21,22], path loss prediction methods [23,24,25,26,27,28], and dominant path prediction methods [29,30].

2.1.1. Electromagnetic Simulation Methods

• Ray Tracing Method [20]: Based on the principles of geometric optics and the uniform theory of diffraction, the ray tracing method calculates the electromagnetic field strength in a simulated scenario to derive the signal strength distribution (i.e., a radio map). Firstly, the ray tracing method establishes a simulation scenario, by completing the following steps, including defining the electromagnetic properties of the propagation medium, determining the scenario boundaries, modeling the geometric shapes and dielectric properties of objects, and setting the locations of transmitters and receivers. Subsequently, considering the orientation and emission waveform of the transmitter, a set of rays is initialized from the transmitter. Figure 3 illustrates the ray paths from a single transmitter to a single receiver in a three-dimensional (3D) scenario. Specifically, the emitted rays follow the principles of geometric optics and, upon interacting with objects in the scenario, may generate multiple reflection, scattering, diffraction, and transmission phenomena of electromagnetic waves (Figure 4), before reaching the receiver. At each point of interaction with an object, parameters such as reflection coefficients of the rays are calculated based on the object’s dielectric properties, which determine the energy attenuation of the rays. Finally, by tracing the paths of all rays, the signal strength distribution in the propagation space is obtained. When the simulation scenario is modeled with sufficient precision and accuracy, the ray tracing method can generate radio maps that closely match real-world measurements.
• Geometry Based Stochastic Model (GBSM) [21]: GBSM describes the propagation environment by defining the distribution function of obstacles (also termed as scatterers). Based on the statistical distribution of channel parameters and geometric stochastic scattering theory, GBSM calculates the attenuation of rays between scatterers to obtain the path loss between any two points. Specifically, the construction of the GBSM includes the following steps: Firstly, channel measurements are conducted in typical scenarios to analyze the spatial distributions of scatterers and extract the statistical distributions of channel parameters, including delay spread, delay values, angular spread, shadow fading, and cross-polarization ratio, among others. Subsequently, for a specific target scenario, the propagation environment is described by setting the shape of the scattering area or the distribution function of scatterers. Finally, based on the geometric stochastic scattering theory and the statistical distribution of channel parameters, the spatio-temporal correlation functions of channels between transmitters and receivers (such as path loss and received signal strength (RSS)) are calculated. Similar to the ray tracing method, GBSM obtains channel characteristics by calculating the propagation rays between transmitters and receivers, and is thus often referred to as “statistical ray tracing”. However, unlike the ray tracing method, GBSM only requires calculating rays between scatterers, making it more versatile and of moderate complexity. The model parameters can be easily adjusted to simulate various radio frequency environments.
  The quasi-deterministic radio channel generator (QuaDRiGa) [22], based on GBSM, is a professional radio frequency simulation platform recommended by 3GPP as the preferred 5G simulation platform. QuaDRiGa is suitable for channel simulation in the frequency range of 2 GHz to 26 GHz and includes six classic models (such as 3GPP 3D, 3GPP 38.901, and WINNER) which can simulate 25 representative scenarios. However, since GBSM does not account for propagation mechanisms such as reflection, scattering, and diffraction, the simulation accuracy of QuaDRiGa is lower than that of the ray tracing method.

2.1.2. Path Loss Prediction Methods

As shown in Figure 5, a scenario with $N_t$ transmitters is considered. The location and transmission power of the k-th transmitter are denoted as ${\mathit{x}}_k$ and $P_k$, respectively. The signal strength $\Phi (\mathit{x},f)$ (in dB) at an arbitrary location $\mathit{x}$ and frequency f can be expressed as

$$\Phi (\mathit{x},f)=\sum _{k=1}^{N_t}\left(P_k-L_k(\mathit{x},f)\right),$$

(2)

where $L_k(\mathit{x},f)$ represents the path loss (in dB) between location ${\mathit{x}}_k$ and $\mathit{x}$. For simplicity, $L_k(\mathit{x},f)$ is noted as $L_k$ in the following text. The key challenge of path loss prediction methods lies in modeling $L_k$. Path loss prediction methods rely on empirical channel models for specific environments to compute the path loss between any two locations. The expression of $L_k$ is highly scenario-dependent and is typically developed by radio engineers based on extensive real-world measurement data collected. Representative path loss models include the log-distance path loss (LDPL) model [24], the Okumura-Hata model [25], and the 3GPP model [27], etc.

The LDPL model [24] characterizes the path loss by using a logarithmic distance function with base 10, expressed as

$$L_k=10{\theta }_k{log}_{10}{∥\mathit{x}-{\mathit{x}}_k∥}_2,$$

(3)

where ${\theta }_k$ is the path loss exponent. Thus, the signal strength $\Phi (\mathit{x},f)$ can be represented as

$$\Phi (\mathit{x},f)=\sum _{k=1}^{N_t}\left(P_k-10{\theta }_k{log}_{10}{∥\mathit{x}-{\mathit{x}}_k∥}_2\right).$$

(4)

The Okumura–Hata model [25] is a classical path loss model designed for urban communication scenarios, given by

$$L_k=69.55+26.16logf-13.82log{H}_m-\alpha \left(h_m\right)+(44.9-6.55log{H}_m)log{R}_{km},$$

(5)

where f ranges from 150 MHz to 1500 MHz and $R_{km}$ representing communication distance ranges from 1 $\mathrm{km}$ to 20 $\mathrm{km}$. The transmitter antenna height $H_m$ and receiver antenna height $h_m$ are in the ranges of 30–200 $\mathrm{m}$ and 1–10 $\mathrm{m}$, respectively. The term $\alpha \left(h_m\right)$ is a function of $h_m$, representing the correction factor of the model [25]. The Okumura–Hata model also has extended models for higher communication frequencies, the most representative one among which is the COST-231-Hata model [26], applicable to the frequency range of 1500–2000 MHz. At present, the Okumura–Hata model and the COST-231-Hata model are mainly used to characterize path loss in frequency bands below 2 GHz.

The 5G communication system mainly adopts the Sub-6 GHz band and the millimeter-wave (mmWave) band above 24 GHz, and existing path loss models are not applicable for the coverage prediction of 5G base stations (BS). For different scenarios, the technical report 3GPP TR 38.901 [27] defines path loss models applicable to 5G NR in the frequency range from 0.5 GHz to 100 GHz, including urban macro (UMa), urban micro (UMi), rural macro (RMa), and indoor hotspot (InH). The path loss calculation formula for the UMa scenario [27] is given by

$$L_k=\left\{\begin{array}{cc}28+22{log}_{10}\left(d_{3\mathrm{D}}\right)+20{log}_{10}\left(f\right),\hfill & 10\mathrm{m}\le d<d_{\mathrm{BP}},\hfill \\ 28+40{log}_{10}\left(d_{3\mathrm{D}}\right)+20{log}_{10}\left(f\right)\hfill \\ -9{log}_{10}\left({d_{\mathrm{BP}}}^2+{\left(h_{\mathrm{BS}}-h_u\right)}^2\right),\hfill & d_{\mathrm{BP}}\le d\le 5000\mathrm{m},\hfill \end{array}\right.$$

(6)

where d and $d_{3D}$ represent the ground distance and the 3D distance between the BS and the user, respectively. $h_{\mathrm{BS}}$ and $h_u$ denote the effective antenna heights of the BS and the user, respectively. $d_{\mathrm{BP}}=4(h_{\mathrm{BS}}-1)(h_u-1)f/c$ is a break point distance [28], where c is the speed of light.

2.1.3. Dominant Path Prediction Methods

Dominant path prediction methods are designed based on the dominant path model (DPM) [29,30]. Compared to electromagnetic simulation methods, DPM is based on a simplified environmental description, searching for all possible paths between any two points and selecting the one with the lowest path loss as the dominant path, whose path loss is then used as the path loss between a pair of transceivers. Dominant path prediction methods do not require precise scenario modeling, and their computational complexity and accuracy lie between electromagnetic simulation methods and path loss prediction methods.

Figure 6 presents a comparison of the three model-driven methods. Path loss prediction methods do not account for the impact of obstacles on signal attenuation, as a result of which path loss prediction methods suffer large estimation errors when obstacles exist. Electromagnetic simulation methods calculate multiple ray paths from the transmitter (T) to the receiver (R) and determine the signal attenuation for each path. The RSS is then obtained by superimposing all rays. Dominant path prediction methods, aiming to avoid the high complexity of electromagnetic simulation methods, focus on the dominant path only and neglect other paths with large path losses.

Distinct DPMs have been developed for urban, rural, and indoor scenarios. In the following, the DPM for urban scenarios is used as an example to illustrate the workflow of dominant path prediction methods.

• Step 1: Search for Candidate Dominant Paths

Figure 7 presents candidate dominant paths of (T,R) in a street scenario where two types of corners, i.e., convex corners (➁ ➂ ➃) and concave corners (➀ ➄ ➅), are considered. The dominant path from T to R must lead via convex corners to the receiver. To this end, a tree with all convex corners is computed for the search of all candidate dominant paths.

• Step 2: Path Loss Prediction for Different Candidate Dominant Paths

After obtaining all candidate dominant paths, DPM next calculates their path losses in dB as follows:

$$L=20{log}_{10}\left({\displaystyle \frac{4\pi }{\lambda }}\right)+20plogd+\sum _{i=1}^n\alpha \left({\phi }_i\right)-{\displaystyle \frac{1}{c}}\sum _{k=1}^c{w}_k,$$

(7)

where $\lambda$ is the wavelength, p is the path loss exponent depending on the visibility state between T and R, d is the path length in space, $\alpha \left({\phi }_i\right)$ is the loss introduced by the i-th interaction with obstacles, ${\phi }_i$ is the change in signal propagation angle, and $w_k$ is the empirical waveguiding factor.

• Step 3: Determination of the Dominant Path

Based on the path losses obtained in Step 2, the path with the minimum path loss is selected as the dominant path.

• Summary

Although electromagnetic simulation methods can provide accurate signal strength estimation, they require detailed information about wireless environments, including locations, heights, and the number of obstacles in terrain maps. Moreover, as wireless networks scale and the complexity of terrain maps increases, the computational complexity of electromagnetic simulation methods grows rapidly, making them unsuitable for time-sensitive applications that require fast responses. In contrast, path loss prediction methods employing empirical path loss models (such as the LDPL model, the Okumura–Hata model, and the 3GPP model) yield much lower computation complexity and implement signal strength estimation over large areas. However, path loss prediction methods only distinguish wireless environments at a macroscopic level. In complex RF environments such as industrial sites, the accuracy of path loss prediction methods degrades significantly. Dominant path prediction methods balance the trade-off between computation complexity and estimation accuracy, but still require high-resolution environmental databases to determine the dominant path.

2.2. Non-Parametric Methods

When $g_k$ cannot be described by an explicit function, non-parametric methods (i.e., kernel methods [31]) approximate $g_k$ based on measurements by introducing a kernel function in the reproducing kernel Hilbert space (RKHS).

For simplicity of presentation, the following discussion considers the kernel method in a single-frequency case. Let $N_s$ denote the number of measurements and $q_i$ denote the measurement value at the location ${\mathit{x}}_i$ ($i=1,2,\cdots ,N_s$). Based on measurement data ${\left\{{\mathit{x}}_i,q_i\right\}}_{i=1}^{N_s}$, kernel methods postulate the existence of an estimation function ${\widehat{g}}_k$ within a function space $\mathcal{G}$, such that ${\widehat{g}}_k\left(\mathit{x}\right)\approx g_k\left(\mathit{x}\right)$ holds for any input $\mathit{x}$. Here, $\mathcal{G}$ denotes a specific class of functions known as RKHS [3]

$$\mathcal{G}:=\left\{g:g\left(\mathit{x}\right)=\sum _{i=1}^{+\infty }{\alpha }_i\kappa \left(\mathit{x},{\mathit{x}}_i\right),{\mathit{x}}_i\in \mathcal{X},{\alpha }_i\in \mathbb{R},\forall i\right\},$$

(8)

where $\kappa :\mathcal{X}\times \mathcal{X}\to \mathbb{R}$ is the reproducing kernel function, which satisfies two properties: (1) symmetry, i.e., $\kappa \left(\mathit{x},{\mathit{x}}^{\prime }\right)=\kappa \left({\mathit{x}}^{\prime },\mathit{x}\right)$; (2) positive definiteness, i.e., $K={\left\{\kappa \left({\mathit{x}}_i,{\mathit{x}}_j\right)\right\}}_{1\le i,j\le N_s}$ is positive definite.

Kernel methods strive to obtain an optimal estimation function ${\widehat{g}}_k^{*}$ by solving the following problem:

$${\widehat{g}}_k^{*}\in \underset{g_k\in \mathcal{G}}{argmin}{\displaystyle \frac{1}{N}}\sum _{i=1}^{N_s}\mathcal{L}\left(q_i,g_k\left({\mathit{x}}_i\right)\right)+\lambda {\parallel g\parallel }_{\mathcal{G}}^2,$$

(9)

where $\mathcal{L}(·)$ is the loss function measuring the estimation error ${\left\{g_k\left({\mathit{x}}_i\right)\right\}}_{i=1}^{N_s}$, and $\lambda (\lambda >0)$ is the regularization coefficient. The Representer Theorem [32] states that any high-dimensional regularized function can be represented as a finite linear combination of measurement data. As a result, ${\widehat{g}}_k^{*}$ must have the following form:

$${\widehat{g}}_k^{*}\left(\mathit{x}\right)=\sum _{i=1}^{N_s}{\alpha }_i\kappa \left(\mathit{x},{\mathit{x}}_i\right),$$

(10)

where ${\alpha }_i$ is referred to as the “representation coefficient”. The Representer Theorem reduces the dimensionality of problem (9) from $+\infty$ to $N_s$. For a given kernel function $\kappa (·)$, problem (9) reduces to a regression problem of representation coefficients ${\alpha }_i$ ($i=1,2,\dots ,N_s$). Similarly, for any frequency f, repeating the above process yields ${\widehat{g}}_k^{*}(\mathit{x},f)$. Finally, the radio map $\Phi (\mathit{x},f)$ is obtained by replacing $g_k(\mathit{x},f)$ in (1) with ${\widehat{g}}_k^{*}(\mathit{x},f)$.

The key challenge in kernel methods lies in selecting an appropriate kernel function. To cope with the challenge, multi-kernel methods [33] construct a new kernel function by combining multiple typical kernels, effectively mitigating performance degradation caused by inappropriate kernel selection. In addition, kernel-based online methods have been proposed to reconstruct radio maps between arbitrary locations. Gutierrez-Estevez et al. [34] utilize a framework of stochastic learning to process the sequential arrival of samples and introduce a nonlinear kernel method based on forward-backward splitting, yielding lower computational complexity compared to existing online batch-processing algorithms. Kasparick et al. [35] presents two kernel-based online coverage map reconstruction methods (i.e., adaptive projected subgradient method and adaptive multi-kernel method), leveraging moving trajectories of users as side information to improve convergence speed and estimation accuracy.

• Summary

Kernel methods remove the assumption on $g_k$ regarding explicit functions and the performance of kernel methods can be improved, provided sufficient measurement data and the proper use of multiple kernels (e.g., polynomial kernel, Gaussian kernel, exponential kernel, etc.). However, there is no universal and effective methodology to guide the selection of appropriate kernel functions. Consequently, it is not guaranteed that the chosen kernel will always provide an accurate estimate of $g_k$.

3. Data-Driven Methods

Data-driven methods rely on measurement data to estimate signal strength at unmeasured locations or frequencies, thereby obtaining a radio map for the entire region. Data-driven methods can be mainly categorized into two types: interpolation methods and deep learning methods.

3.1. Interpolation Methods

Interpolation methods estimate the signal strength $\Phi (\mathit{x},f)$ at an unmeasured location $\mathit{x}$ over frequency f by using the signal strength ${\phi }_i({\mathit{x}}_i,f)$ at measured locations ${\mathit{x}}_i$ over frequency f. Existing interpolation methods can be categorized into linear and nonlinear interpolation methods.

3.1.1. Linear Interpolation Methods

Given $N_s$ and ${\phi }_i({\mathit{x}}_i,f)$, the signal strength $\Phi (\mathit{x},f)$ at $\mathit{x}$ over frequency f is given by (see Figure 8)

$$\Phi (\mathit{x},f)=\sum _{i=1}^{N_s}{w}_i(\mathit{x},f){\phi }_i({\mathit{x}}_i,f),$$

(11)

where $w_i(\mathit{x},f)$ is the weight corresponding to ${\phi }_i({\mathit{x}}_i,f)$. It is evident from (11) that the performance of linear interpolation methods critically depends on the definition of $w_i(\mathit{x},f)$. Typical linear interpolation methods include inverse distance weighted (IDW) interpolation and Kriging interpolation.

The IDW interpolation method [36] defines the weight as $w_i(\mathit{x},f)={|\mathit{x}-{\mathit{x}}_i|}^{-\sigma }$, where $\sigma$ is a given non-negative attenuation parameter. However, IDW interpolation cannot prioritize ${\phi }_i({\mathit{x}}_i,f)$ when multiple ${\mathit{x}}_i$ are equidistant from $\mathit{x}$. To address this issue, Denkovski et al. [37] propose an improved IDW interpolation method that incorporates both distance and angular factors in the definition of $w_i(\mathit{x},f)$.

With the inclusion of side information, a series of Kriging interpolation methods have emerged. It is well known that, under the assumption of spatial stationarity (i.e., the covariance of PSD between any two locations is known and constant), ordinary Kriging interpolation is an optimal unbiased linear interpolation method. When spatial stationarity does not hold, universal Kriging interpolation introduces spatial drift structures to capture the spatial variation pattern of target signal strengths [38] which are then interpolated based on ordinary Kriging interpolation. In [39], ordinary Kriging interpolation is employed, where $w_i(\mathit{x},f)$ are determined by minimizing the variance of the estimation error. Sato et al. [40] propose an RME method leveraging the strong correlation of shadow fading in the frequency domain, utilizing ordinary Kriging interpolation in both space and frequency domains to predict RSS. For non-stationary spatial scenarios, El-Frikh et al. [41] introduce an RME method based on universal Kriging interpolation. Furthermore, Wang et al. [42] propose an RME method based on deep Gaussian processes, which effectively captures spatially non-stationary components in sparse measurements and accurately characterizes the correlation between RSS and locations.

3.1.2. Nonlinear Interpolation Methods

Nonlinear interpolation methods model complex relationships in measurement data using nonlinear functions (e.g., polynomials, splines, radial basis functions (RBF)) of signal strengths [43,44]. RBF-based interpolation methods [45] represent a class of classical nonlinear interpolation methods. The signal strength at an unmeasured location $\mathit{x}$ over frequency f is expressed as a combination of RBFs of measured locations ${\mathit{x}}_i$, i.e.,

$$\Phi (\mathit{x},f)=\sum _{i=1}^{N_s}{w}_{i}h(\parallel \mathit{x}-{\mathit{x}}_i{\parallel }_2),$$

(12)

where $h(·)$ denotes an RBF (e.g., Gaussian basis function, multiquadric basis function, spline basis function [46]), and $w_i$ represents the RBF weight. The core challenge of RBF-based interpolation methods lies in the selection of an appropriate RBF. Given measurements ${\{{\mathit{x}}_i,{\phi }_i\}}_{i=1}^{N_s}$, $w_i$ are obtained via least squares regression, and the estimated signal strength $\Phi (\mathit{x},f)$ is computed according to (12).

• Summary

Although linear interpolation methods are simple and easy to implement, their weight definitions may not adequately capture complex spatial relationships. Nonlinear interpolation methods offer greater flexibility in modeling, but their performance heavily depends on the choice of RBFs. An inappropriate selection of RBFs may significantly degrade interpolation accuracy.

3.2. Deep Learning Methods

With the rapid development of deep learning technology [47], numerous RME studies based on deep neural networks (DNNs) have emerged in the last ten years. The universal approximation theorem proves the powerful representational capability of DNNs, stating that a DNN can approximate any continuous function on a compact domain with arbitrary precision. Consequently, deep learning-based RME methods can learn the underlying physical phenomena of radio propagation, exhibiting high estimation accuracy and strong generalization performance. So far, deep learning methods have been commonly considered as the mainstream research direction in RME.

According to the network architecture of DNNs, deep learning-based RME methods can be broadly categorized into three types: feedforward neural network (FNN)-based RME methods, convolutional neural network (CNN)-based RME methods, and vision transformer (ViT)-based RME methods.

3.2.1. FNN-Based RME Methods

An FNN is a fully connected DNN architecture in which each neuron in one layer is connected to all neurons in the preceding and succeeding layers. FNNs can learn empirical knowledge of radio propagation from measurement data. FNN-based RME methods use an FNN model learned from measurement data to predict path losses at unmeasured locations (Figure 9).

Saito et al. [48] propose a two-step path loss prediction method based on FNN. Firstly, the estimation region is partitioned into multiple subregions according to the path loss range of measurements. Then, one FNN is trained for each subregion to predict the path loss. Finally, the effectiveness of the proposed method is evaluated via ray tracing simulation data. Parera et al. [49] address the RME problem with angle variations in antenna tilt of the BS. Firstly, an FNN-based RME method is employed to construct the radio map under the initial antenna tilt. Subsequently, by transferring the initial FNN structure, the radio map is rapidly reconstructed based on only sparse measurement data in the target antenna tilt configuration. Sato et al. [50] design a neural network residual kriging method, where an FNN is utilized to model the anisotropy in path loss caused by terrain and obstacles, and then ordinary Kriging interpolation is applied to estimate the shadowing values.

Table 1. The literature on FNN-based RME methods.

Reference	Architecture	Scenario	Results	Input Data	Frequency	Number of Tx	Tx Parameters *	Terrain Map
[48]	FNN	Indoor cellular	Path loss map	Transmitter and receiver locations	Single	Single	Yes	No
[49]	FNN	Outdoor cellular	Received power map	Physical distance and relative elevation and relative azimuth	Single	Single	Yes	No
[50]	FNN	MANET	Path loss map	Measurements and locations	Single	Multiple	Yes	No

* Tx Parameters include power, height, location, etc.

lists the representative literature on FNN-based RME methods.

3.2.2. CNN-Based RME Methods

In the RME problem, auxiliary information such as terrain maps and measurement maps is often available. CNNs are typical deep learning models which are naturally suited for learning the mapping from image data to radio maps [51]. Based on the architecture of CNNs, existing works on CNN-based RME methods can be roughly categorized into three types: traditional CNN-based RME methods, fully convolutional network (FCN)-based RME methods, and conditional generative adversarial network (CGAN)-based RME methods.

• Traditional CNN-based RME Methods

Traditional CNNs are architecturally composed of convolutional layers, pooling layers, and fully connected layers (see Figure 10). Different from FNNs, traditional CNNs are characterized by two fundamental properties: local connectivity and weight sharing, and thus preserve invariance properties with respect to geometric transformations including translation, scaling, and rotation, rendering them particularly effective for image processing tasks.

Imai et al. [51] propose a CNN-based path loss prediction method that constructs two local coordinate maps (i.e., a BS distance map and a mobile station (MS) distance map) and a building height map. With constructed maps and ray tracing simulation data, a CNN model is trained to predict path loss distributions in urban macro-cell scenarios. Iwasaki et al. [52] first pre-train a CNN model based on ray tracing simulation data, and then augment sparse measurements through data augmentation techniques. Finally, the pre-trained model is fine-tuned with the augmented data to cope with unseen outdoor WiFi scenarios. Li et al. [53] propose Supreme, a high-resolution RME method based on CNNs. Supreme consists of a spatio-temporal reconstruction network and an external data fusion network. Firstly, the spatio-temporal reconstruction network extracts spatio-temporal features from the measured RSS maps at different historical times. Then, the external data fusion network extracts the external factor features. Finally, spatio-temporal features and external factor features are fused to reconstruct a fine-grained RSS map. Li et al. [54] further propose Supreme-UDA, an adversarial learning-based transfer learning method, which improves the generalization performance of Supreme in unknown target domains. Gupta et al. [55] present a CNN-based path loss prediction method in mmWave bands for urban canyon scenarios. A CNN is employed to extract building features and expert knowledge is used to design key features of street clutters. Based on the building and clutter features, classical regression algorithms (e.g., lasso regression, support vector regression, random forest, etc.) are proposed to predict path loss. Seretis et al. [56] propose a CNN-based RME method for indoor office scenarios. Firstly, ray tracing simulations are performed to generate target RSS maps. Then, four geometry-based features are computed based on two ray tracing-based features. All six features and target RSS maps constitute training samples to train a CNN model. Finally, the trained CNN can predict RSS in unseen scenarios. Wang et al. [57] propose a CNN-based path loss prediction method for general outdoor scenarios. The CNN, which incorporates residual structures, attention mechanisms, and spatial pyramid pooling, is specifically engineered to extract latent features from satellite images. Concurrently, a FNN is utilized to extract state features. Finally, a second FNN is employed to merge the two sets of features and predict per-link path loss.

Table 2. The literature on traditional CNN-based RME methods.

Reference	Architecture	Scenario	Results	Input Data	Frequency	Number of Tx	Tx Parameters *	Terrain Map
[51]	Traditional CNN	Urban macro-cell	Per-link path loss	BS and MS distance map and building height map	Single	Single	Yes	3D
[52]	Traditional CNN	Outdoor WiFi	Per-link received power	BS and MS distance map and building map	Single	Single	Yes	3D
[53]	Traditional CNN	Outdoor WiFi	RSS map	Historical data and external factors	Multiple	Multiple	No	No
[55]	Traditional CNN	Urban canyon	Per-link path loss	Path loss measurements and building and clutter features	Single	Multiple	Yes	2D
[56]	Traditional CNN	Indoor office	RSS map	Ray tracing-based features and geometry-based features	Multiple	Single	Yes	2D
[57]	Traditional CNN	Outdoor communications	Per-link path loss	Satellite map and distance map	Single	Single	Yes	2D

* Tx Parameters include power, height, location, etc.

lists the representative literature on traditional CNN-based RME methods.

• FCN-based RME Methods

FCNs are a type of CNN composed solely of convolutional layers and pooling layers, without fully connected layers. FCNs typically adopt an encoder-decoder architecture, rendering them suitable for image-to-image learning. The encoder-decoder architecture enables FCNs to process input images of different sizes, without any modification to the network architecture. Additionally, FCNs can preserve spatial information during feature extraction, allowing for a better understanding of contextual information within images.

The convolutional autoencoder (CAE) is a typical FCN consisting of an encoder and a decoder (see Figure 11). The encoder extracts low-dimensional features from high-dimensional input images (termed as feature encoding), while the decoder reconstructs the original input image based on the low-dimensional features (termed as feature decoding). In [58], a CAE is employed to learn the spatial variation patterns of radio propagation phenomena such as shadowing, reflection, and diffraction from measurement datasets. Subsequently, PSD maps with high accuracy are obtained by fine-tuning the CAE model with a minimal amount of measurements. Zhang et al. [59] propose a CAE-based RSS prediction method for distributed RME. Firstly, a large area is partitioned into small regions. Then, CAEs are implemented across distributed fusion centers to reconstruct their respective regions of the target radio map. After CAEs are trained via a federated learning scheme, the entire RSS map can be obtained.

UNet [60] is another type of widely used FCN, originally designed for medical image segmentation but later adopted in applications such as image translation and image in-painting. Unlike the symmetric encoder-decoder structure of CAEs, UNet introduces skip connections between encoder layers and decoder layers (see Figure 12). Skip connections assist in the feature decoding process by passing feature maps from encoder layers to corresponding decoder layers. Krijestorac et al. [61] propose a UNet-based spatial signal strength prediction method that constructs input tensors by concatenating 3D terrain maps and sparse measurement maps. The proposed method employs a loss function based on Kullback0-Leibler divergence and learns the probability distribution of spatial signal strength. Levie et al. [62] propose a UNet-based RME method called RadioUNet. Firstly, ray tracing simulations are used to generate a path loss dataset (referred to as RadioMapSeer) for different city maps and transmitter locations. Subsequently, city maps, transmitter location maps, and measurement maps are concatenated to form input tensors for training a UNet model. Finally, by fine-tuning the trained UNet model with a small amount of real-world measurement data, high-accuracy radio maps can be obtained for unknown urban environments. Sallouha et al. [63,64] propose a UNet-based RME method called REM-U-Net. Line-of-sight (LoS) maps are calculated for each receiver location in 3D city maps, according to the number of blocking buildings. Three-dimensional city maps, transmitter location maps, and LoS maps are stacked as input feature maps. REM-U-Net proposes to model signal strength as a Gaussian variable and trains two UNets to predict the mean and the variance of signal strength, respectively.

Several studies have modified the classic UNet to improve the prediction accuracy of the RME method. Ratnam et al. [65] introduce a large-scale channel fading prediction method based on a modified UNet called FadeNet. FadeNet adds three convolutional layers before the input layer and after the output layer of the classic UNet architecture, respectively, to fuse input features such as terrain, buildings, and vegetation height. Zhou et al. [66] propose a novel UNet-based RSS prediction method by replacing the convolutional layers in classic UNet with 3D convolutional layers to fully exploit the correlation of RSS across different frequencies. Lee et al. [67,68,69] propose a UNet-based path loss map prediction method (PMNet) by introducing extra dilated convolutions to address scale variations and capture broader contextual information in map data.

Similar to the architecture of UNet, SegNet [70] passes crucial pooling index information from encoder layers to corresponding decoder layers. Qiu et al. [71,72] propose a SegNet-based outdoor path loss prediction method in mmWave bands called PPNet. PPNet is trained with ray tracing simulation data and takes as input features a three-channel tensor consisting of a city map, a transmitter location map, and a distance heatmap. PcNet [73] is a UNet-alike network that replaces the convolutional layers of UNet with partial convolutional layers. Considering the issue of inaccessible areas, Li et al. [74] propose a PcNet-based RME method for urban environments to distinguish unmeasured and measured areas during the convolution process. SDU-Net [75] is a UNet variant using stacked dilated convolutions, aiming to learn features at multiple spatial scales. Bakirtzis et al. [76] propose an RME method based on SDU-Net called EM DeepRay. EM DeepRay takes indoor layout maps with color-coded material information, transmitter location maps, and frequency annotation maps as input tensors, and outputs RSS maps at different heights. sEM DeepRay [77], an extended version of EM DeepRay, further incorporates antenna radiation patterns in input tensors to learn path loss distributions in 3D space.

Table 3. The literature on FCN-based RME methods.

Reference	Architecture	Scenario	Results	Input Data	Frequency	Number of Tx	Tx Parameters *	Terrain Map
[58]	CAE	Outdoor cellular	PSD map	PSD measurements and locations	Multiple	Multiple	No	No
[59]	CAE	Urban canyon	RSS map	Incomplete radio map and sensor locations and landscape map	Single	Single	No	2D
[61]	UNet	Urban cellular	Spatial signal strength distribution	3D terrain map and sparse measurements	Single	Single	No	3D
[62]	UNet	Urban cellular	Path loss map	City map and transmitter location map and measurements map	Single	Single	Yes	2D
[64]	UNet	Urban cellular	Path loss map	3D city map and transmitter location map and LoS map	Single	Single	Yes	3D
[65]	UNet	Urban 5G cellular	Path loss map	Terrain and building and vegetation height	Single	Single	No	2D
[66]	UNet	Cellular network	Received power map	Sparse measurements map	Multiple	Multiple	No	No
[69]	UNet	Cellular network	Path loss map	Building map and transmitter location	Single	Single	Yes	2D
[71]	SegNet	Urban 5G cellular	Path loss map	City map and transmitter location map and distance heatmap	Single	Single	Yes	2D
[74]	PcNet	Urban cellular	RSS map	Non-uniformly distributed measurements	Single	Single	No	No
[76]	UNet	Indoor LoRa	Received power map	Indoor layout map and transmitter location map and Frequency annotation map	Multiple	Single	Yes	2D

* Tx Parameters include power, height, location, etc.

lists the representative literature on FCN-based RME methods.

• CGAN-based RME Methods

Generative adversarial networks (GANs) [78] are game-theoretic generative models that have been widely applied in image generation and related fields. A GAN consists of a generator and a discriminator. The generator takes a random input and synthesizes a piece of artificial data (e.g., an image), while the discriminator is a binary classifier that judges whether the output of the generator is real. During the adversarial training process, the generator and the discriminator iteratively update their network parameters, eventually reaching a Nash equilibrium. As a result, the learned generator can synthesize data that are indistinguishable from real data. CGAN [79] is a notable extension of GANs. CGAN incorporates reliable labeled data as conditional inputs for both the generator and the discriminator (see Figure 13). CGAN-based RME methods typically use terrain maps, historical radio maps, or other prior information as conditional inputs to aid model training. Due to the adversarial training mechanism, CGANs sometimes achieve superior performance in RME tasks than CNN-based methods.

Chaves-Villota et al. [80] propose a CGAN-based RME method called DeepREM. DeepREM uses sparsely sampled radio maps as conditional inputs for the CGAN. Conditional inputs are combined with the generated radio maps and the real radio maps to form two sets of training tensors to train the discriminator. The generator learns and improves every time the discriminator misclassifies fake data as real. Liu et al. [81] propose DA-CGAN, a spatial dimension-aware indoor received power map estimation method. DA-CGAN leverages a UNet-based generator to fuse three inputs (i.e., indoor floorplans annotated with wall types, spatial dimension-aware feature vectors, and outdoor macro-cell received power measurement maps) and PatchGAN [82] as the discriminator. A two-stage training strategy with different combinations of loss functions is designed to enhance its generalizability. Cissé et al. [83] propose two CGAN-based RME methods: IRGAN and E-IRGAN, both of which adopt PatchGAN as the discriminator. IRGAN adopts a novel generator model that integrates multiple residual modules with UNet, while E-IRGAN further replaces standard convolutions in residual modules of IRGAN with dilated convolutions, and incorporates attention mechanisms in skip connections to facilitate the decoding process. Zheng et al. [84] propose a CGAN-based method for reference signal receiving power (RSRP) estimation. Firstly, environment maps as conditional inputs are constructed to include building heights, altitudes, and BS parameters. Then, environment maps and measured RSRP maps are combined as labeled samples to train a Pix2Pix [82]-based CGAN model.

Table 4. The literature on CGAN-based RME methods.

Reference	Architecture	Scenario	Results	Input Data	Frequency	Number of Tx	Tx Parameters *	Terrain Map
[80]	CGAN	Urban cellular	Received power and coverage map	Received power measurements and locations	Single	Multiple	No	No
[81]	CGAN	Indoor WiFi	Received power map	Indoor floorplan and dimension-aware feature vectors and macro-cell power map	Multiple	Multiple	No	No
[83]	CGAN	Indoor WiFi	Path loss map	Site floorplan and transmitter location map	Single	Single	Yes	2D
[84]	CGAN	Urban cellular	RSRP map	Environment map and RSRP measurement map	Multiple	Single	Yes	3D

* Tx Parameters include power, height, location, etc.

lists the representative literature on CGAN-based RME methods.

3.2.3. ViT-Based RME Methods

Transformer [85] leverages attention mechanisms to automatically capture key features in training samples and excels in modeling correlations between sequential samples, achieving significant success in natural language processing tasks such as machine translation. Dosovitskiy et al. [86] design a transformer architecture tailored for vision tasks (termed as ViT). As illustrated in Figure 14, ViT partitions each input image into equally sized patches and includes a linear projection layer to transform the flattened patches into a sequence of tokens which are subsequently processed by the Transformer encoder. Superior generalization performance over CNNs has been demonstrated in vision tasks, such as image classification, object detection, and semantic segmentation [87].

Tian et al. [88] propose a ViT-based received power map prediction method called RadioTrans. A grid anchor technique is adopted to accurately describe the spatial correlations between transceivers and obstacles. Spread layers are designed in each decoder layer of ViT to extract related features to RME, based on the grid anchor technique. Hehn et al. [89] propose a ViT-based path loss prediction method that takes a map containing building and foliage information as well as the distance between transceivers as inputs to ViT and outputs the per-link path loss. Benefiting from the attention mechanism, the proposed ViT-based method can automatically focus on the most critical regions for generating accurate path loss predictions. Zheng et al. [90] propose to use a ResNet34 [91] network to extract features from building maps, and feed the extracted features into the ViT encoder. The output of the ViT encoder and the BS location (in the form of point embedding) are fed to a ViT decoder, which subsequently outputs the radio feature and the BS score. Finally, the information fusion pyramid module (IFPM) [92] is introduced to reconstruct high-accuracy path loss maps based on the radio feature and the BS score.

Table 5. The literature on ViT-based RME methods.

Reference	Architecture	Scenario	Results	Input Data	Frequency	Number of Tx	Tx Parameters *	Terrain Map
[88]	ViT	Dense urban	Received power map	Transmitter location and tree and building map	Single	Single	Yes	3D
[89]	ViT	Urban cellular (mmWave)	Per-link path loss	Building map and distance	Single	Single	Yes	2D
[90]	ViT	Urban cellular	Path loss map	Building map and BS locations	Single	Single	Yes	2D

* Tx Parameters include power, height, location, etc.

lists the representative literature on ViT-based RME methods.

4. Hybrid Model Data-Driven Methods

Although empirical signal propagation models cannot finely characterize radio environments, the domain knowledge embedded in propagation models remains highly valuable for RME and should be appropriately utilized. Hybrid model data-driven methods integrate propagation models with data-driven methods, significantly reducing the required training samples without compromising the RME accuracy [93,94]. Because of this, hybrid model data-driven methods have emerged as one promising paradigm of RME methods, effectively bridging the gap between physical modeling precision and data-driven adaptability.

DeepViT [95] adopts a novel re-attention mechanism to increase the diversity of attention maps, allowing for the training of deeper ViT architectures. Yu et al. [96] propose a hybrid RSS prediction method for outdoor cellular scenarios. Specifically, a 3GPP UMa model-assisted prediction block is used to predict large-scale path loss; a DeepViT block is used to extract key features of buildings and vegetation from satellite images; a long short-term memory (LSTM) block is designed to exploit historical RSS measurements. Finally, the outputs of all the blocks mentioned above are fused to predict the RSS for each link. Thrane et al. [97] propose a hybrid path loss prediction method that integrates 3GPP UMa model with DNN. Firstly, the UMa model is utilized to estimate the path loss at each target location. Subsequently, path loss estimations are combined with location coordinates and satellite images as inputs to a DNN consisting of a CNN and two FNNs, with the CNN extracting features from satellite imagery, and the FNNs learning features from both location and image data.

Suto et al. [98] propose a hybrid received power map prediction method that integrates the LDPL model with UNet. The problem of image-to-image spatial interpolation is first reformulated as a shadowing adjustment problem. Then, the LDPL model is applied to regress the large-scale RSS and a UNet is trained to capture small-scale signal variations. By combining large-scale signal strength and small-scale fluctuations, the proposed method finally achieves high-accuracy received power maps. Zhang et al. [99] propose a hybrid path loss map prediction method that integrates the LDPL model and CGAN called RME-GAN. The LDPL model is first applied to predict path losses at unmeasured locations based on sparse measurements, and the global radio propagation patterns (i.e., pixel gradients) of the coverage area are thereby obtained. The obtained pixel gradients of the coverage area are then used to boost the training of a CGAN, which finally outputs path loss maps capturing multi-scale signal propagation characteristics.

Shrestha et al. [100] propose a PSD map prediction method that integrates a radio map aggregation model with a CAE. Firstly, the PSD map in a multi-transmitter scenario is modeled as an aggregation of multiple spatial loss fields (SLF) in a single-transmitter scenario. Next, non-negative matrix factorization is applied to decompose the measurement data tensor into SLF data for each transmitter, and the CAE is trained to estimate missing SLF data in the single-transmitter scenario. Finally, the SLF data from all transmitters are aggregated to obtain the PSD map for the multi-transmitter scenario. Li et al. [101] propose a hybrid RSS map prediction method (RadioGAT) for the multi-band radio map reconstruction via graph attention networks (GAT). Sparse measurements over different frequencies are first represented as sparse graphs via a signal propagation model [40] to capture the spatial-spectral correlation inherent in measurement data. These sparse graphs are subsequently integrated as prior structural knowledge into a GAT, significantly enhancing the capability of GAT to reconstruct high-accuracy cross-band radio maps.

Table 6. The literature on hybrid model data-driven methods.

Reference	Architecture	Scenario	Results	Input Data	Frequency	Number of Tx	Tx Parameters *	Terrain Map
[96]	3GPP UMa and DeepViT and LSTM	Urban cellular	Per-link received power	Trajectory information and satellite map and historical RSS	Single	Single	Yes	2D
[97]	3GPP UMa and DNN	Urban cellular	Per-link received power	Satellite map and location information	Single	Single	Yes	2D
[98]	LDPL and UNet	Urban and suburban cellular	Received power map	Sparse measurement map	Single	Single	No	2D
[99]	LDPL and CGAN	Outdoor cellular	Path loss map	Measurements and locations and building map and transmitter location	Single	Single	Yes	2D
[100]	Radio map aggregation model and CAE	Outdoor communication	PSD map	Measurements and locations	Multiple	Multiple	No	No
[101]	Signal propagation model and GAT	Outdoor cellular	RSS map	Measurements over different frequencies	Multiple	Multiple	No	2D

* Tx Parameters include power, height, location, etc.

lists the representative literature on hybrid model data-driven methods.

5. Public Datasets for Radio Maps

The learning of radio maps and the performance evaluation of RME methods rely heavily on a large volume of RF data, which are obtained either via real-world measurements or simulations. Table 7 summarizes representative public datasets for radio maps. Next, we introduce a few public datasets from Table 7 in detail.

Levie et al. [62] released the RadioMapSeer dataset, which was originally created to train RadioUNet. The RadioMapSeer dataset consists of 56,080 path loss maps for 701 different city maps and 80 different transmitter locations. Each path loss map describes the path loss distribution within an area of $256\mathrm{m}\times 256\mathrm{m}$ with a resolution of $1\mathrm{m}\times 1\mathrm{m}$. The RadioMapSeer dataset allows for developing and testing the accuracies of path loss RME methods for realistic urban scenarios. Further, Yapar et al. [102] extended the simulations to the 3D setting and released the RadioMap3DSeer dataset [103], where different building heights and transmitter deployment on rooftops are considered. Based on the RadioMap3DSeer dataset, Yapar et al. [104,105] organized the First Pathloss Radio Map Prediction Challenge (https://RadioMapChallenge.GitHub.io/ (accessed on 9 April 2025)) at ICASSP 2023.

Chaves-Villota et al. [80] published the Urban REMs dataset [106], which was originally created to train DeepREM. The DeepREM dataset comprises two sets of radio maps for various cities and regions in the United States and Colombia. The first set contains 1800 RSS radio maps for single-transmitter scenarios, while the second one includes 3600 radio maps for four-transmitter scenarios. Each radio map represents an RF environment that ranges from $2290\mathrm{m}\times 3670\mathrm{m}$ to $3810\mathrm{m}\times 5160\mathrm{m}$, with a resolution of $10\mathrm{m}\times 10\mathrm{m}$. The DeepREM dataset facilitates the learning of radio propagation characteristics in hilly, plain, suburban, and urban scenarios.

Zheng et al. [84] published the RSRPSet dataset [107], which was originally created to train a cell-level RSRP estimation method. The RSRPSet dataset is extracted based on the raw data measured and provided by Huawei Technologies Co., Ltd. (Shenzhen, China). The RSRPSet dataset includes RSRP measurements of 415,244 signal-receiving locations in 181 dense urban communication cells, i.e., 181 measured RSRP radio maps. Each RSRP map measures an area of $320\mathrm{m}\times 320\mathrm{m}$ with a resolution of $5\mathrm{m}\times 5\mathrm{m}$.

The Indoor Radio Map Dataset [108] includes 32,750 path loss radio maps generated with an intelligent ray tracing algorithm at 25 different indoor geometries, three different frequency bands, and five antenna radiation patterns. The spatial resolution for all the simulations is $0.25\mathrm{m}\times 0.25\mathrm{m}$. The Indoor Radio Map Dataset was exclusively created for the First Indoor Path Loss Prediction Challenge (https://IndoorRadioMapChallenge.GitHub.io/ (accessed on 9 April 2025)) at ICASSP 2025 [109], which is a continuation of the previous radio map prediction challenge [104,105] in the less explored case of directional radio signal emissions in indoor scenarios.

The High-Resolution Radio Environment Map Dataset [110] includes two real-world measured radio maps of an office corridor, with a resolution of $0.8\mathrm{mm}\times 0.8\mathrm{mm}$. To this end, an automated guided vehicle (AGV) equipped with a transmitter moves along a predefined trajectory at a constant speed of 0.8 $\mathrm{m}/\mathrm{s}$ within the office corridor, while periodically transmitting test signals in the frequency band of 3.75 GHz. The fixed receiver collects 5000 measurements, based on which two measured radio maps are created. The High-Resolution Radio Environment Map Dataset is not only suited for channel characterization but works also as ground truth for RME tasks.

The AI4MOBILE Industrial Wireless Dataset [111,112] collects real-world measurements in industrial environments and consists of an industrial vehicle-to-vehicle (iV2V) dataset and an industrial vehicle-to-infrastructure plus sensor (iV2I+) dataset. The iV2V dataset records 5G sidelink communication data among three AGVs operating in the frequency band of 3.7 GHz. The iV2I+ dataset records 4G downlink communication data from a BS to an autonomous cleaning robot, where the BS transmits in the frequency band of 3.7 GHz to 3.8 GHz. Both the iV2V and the iV2I+ datasets are valuable data resources for training and testing RME methods.

Table 7. Representative public datasets for radio maps.

Datasets	Scenario	Data Source	Data Format	Data Volume	Frequency	Number of Tx	Antenna Form	Map Type
RadioMapSeer [62,102]  https://dx.doi.org/10.21227/0gtx-6v30	Urban	Ray tracing	Path loss/ToA map	56,080	Multiple	Single	Isotropic	2D/3D
Urban REMs [80]  https://zenodo.org/records/7839447	Urban	Ray tracing	RSS/coverage map	5400	Multiple	Multiple	Isotropic	3D
RSRPSet_urban [84]  https://dx.doi.org/10.21227/vmw5-c226	Urban	Measurements	RSRP map	181	Multiple	Single	Isotropic	3D
Indoor Radio Map Dataset [108]  https://dx.doi.org/10.21227/c0ec-cw74	Indoor	Ray tracing	Path loss map	32,750	Multiple	Single	Directional	2D
High-Resolution REM [110]  https://dx.doi.org/10.21227/waxd-9525	Office corridor	Measurements	Measurement values	5000	Single	Single	Isotropic	2D
AI4MOBILE [111]  https://dx.doi.org/10.21227/04ta-v128	Industrial scenario	Measurements	Measurement values	50 GB	Single	Single	Isotropic	2D
Rosslyn dataset [58]  https://github.com/fachu000/deep-autoencoders-cartography	Urban	Ray tracing	Path loss map	125,000	Single	Single	Isotropic	2D
PMNet dataset [69]  https://github.com/abman23/PMNet	Urban	Ray tracing	Path loss map	20,913	Multiple	Single	Isotropic	2D
BART-Lab [101]  https://github.com/BRATLab-UCD/Radiomap-Data	Urban	Ray tracing	RSS map	21,000	Multiple	Multiple	Isotropic	2D
RMDirectional Berlin [113] https://zenodo.org/records/10210089	Urban	Ray tracing	Path loss map	74,515	Single	Single	Directional	3D
CKMImageNet [114]  https://github.com/Darwen9/CKMImagenet	Various scenarios	Ray tracing	Path loss/ AoA/AoD map	40,000	Single	Multiple	Isotropic	2D
SpectrumNet [115]  https://github.com/ShuhangZhang/FDRadiomap	Various scenarios	Ray tracing	3D Path loss map	300,000	Multiple	Multiple	Isotropic	3D
3DiRM3200 [116]  https://github.com/lighttime2023/3DiRM3200	Indoor	Ray tracing	3D Path loss map	3200	Single	Single	Isotropic	3D

All links are accessed on 9 April 2025.

Table 7. Representative public datasets for radio maps.

Datasets	Scenario	Data Source	Data Format	Data Volume	Frequency	Number of Tx	Antenna Form	Map Type
RadioMapSeer [62,102]  https://dx.doi.org/10.21227/0gtx-6v30	Urban	Ray tracing	Path loss/ToA map	56,080	Multiple	Single	Isotropic	2D/3D
Urban REMs [80]  https://zenodo.org/records/7839447	Urban	Ray tracing	RSS/coverage map	5400	Multiple	Multiple	Isotropic	3D
RSRPSet_urban [84]  https://dx.doi.org/10.21227/vmw5-c226	Urban	Measurements	RSRP map	181	Multiple	Single	Isotropic	3D
Indoor Radio Map Dataset [108]  https://dx.doi.org/10.21227/c0ec-cw74	Indoor	Ray tracing	Path loss map	32,750	Multiple	Single	Directional	2D
High-Resolution REM [110]  https://dx.doi.org/10.21227/waxd-9525	Office corridor	Measurements	Measurement values	5000	Single	Single	Isotropic	2D
AI4MOBILE [111]  https://dx.doi.org/10.21227/04ta-v128	Industrial scenario	Measurements	Measurement values	50 GB	Single	Single	Isotropic	2D
Rosslyn dataset [58]  https://github.com/fachu000/deep-autoencoders-cartography	Urban	Ray tracing	Path loss map	125,000	Single	Single	Isotropic	2D
PMNet dataset [69]  https://github.com/abman23/PMNet	Urban	Ray tracing	Path loss map	20,913	Multiple	Single	Isotropic	2D
BART-Lab [101]  https://github.com/BRATLab-UCD/Radiomap-Data	Urban	Ray tracing	RSS map	21,000	Multiple	Multiple	Isotropic	2D
RMDirectional Berlin [113] https://zenodo.org/records/10210089	Urban	Ray tracing	Path loss map	74,515	Single	Single	Directional	3D
CKMImageNet [114]  https://github.com/Darwen9/CKMImagenet	Various scenarios	Ray tracing	Path loss/ AoA/AoD map	40,000	Single	Multiple	Isotropic	2D
SpectrumNet [115]  https://github.com/ShuhangZhang/FDRadiomap	Various scenarios	Ray tracing	3D Path loss map	300,000	Multiple	Multiple	Isotropic	3D
3DiRM3200 [116]  https://github.com/lighttime2023/3DiRM3200	Indoor	Ray tracing	3D Path loss map	3200	Single	Single	Isotropic	3D

All links are accessed on 9 April 2025.

To summarize, existing radio map datasets are primarily generated using ray tracing simulations. Although ray tracing enables the efficient production of large-scale datasets without real-world measurements, the difference between ray tracing simulation data and real-world measurements may degrade the generalization performance of RME methods. Therefore, it is crucial to develop hybrid simulation measurement datasets, as they help improve the applicability of RME methods in practical scenarios.

6. Future Research Directions

So far, this survey has provided a detailed introduction to three major types of RME methods: model-driven methods, data-driven methods, and hybrid model data-driven methods. Existing RME methods still suffer severe limitations in coping with varying scenarios, characterizing industrial RF environments, and dynamically updating radio maps. In the following, this section will point out future directions for RME methods.

6.1. Cross-Scenario RME Methods

Existing RME methods are primarily designed for single-application scenarios such as urban cellular networks and indoor hotspots. When the application scenario varies, the estimation accuracy of RME methods may degrade dramatically. Consequently, the training of a new DNN is needed. However, the collection of a large volume of measurement data in the new scenario is, in general, costly or even infeasible.

From the perspective of electromagnetic wave propagation, different application scenarios share common physical principles such as reflection, diffraction, and scattering. Transfer learning [117] can leverage the shared propagation knowledge to adapt DNN models across diverse application scenarios. By fine-tuning model parameters of source scenarios based on a small amount of measurements in target scenarios, transfer learning enables the rapid development of high-accuracy DNN models suited to target scenarios. Therefore, exploring transfer learning methods tailored for RME presents a promising direction for future research.

6.2. RME Methods for Industrial RF Environments

Existing RME methods are good at modeling spatial propagation characteristics (which are either static or quasi-static), such as path loss, RSS, shadowing effects, etc. With the rapid development of smart factories, wireless applications such as network planning, resource allocation, wireless localization, and physical-layer security in industrial environments are gaining increasing attention [118]. Nevertheless, industrial RF environments exhibit unique propagation characteristics due to the presence of dense metallic structures, heavy machinery, and moving objects such as AGVs and robotic arms. These factors lead to severe multipath effects, frequency-selective fading, and Doppler shifts, making conventional RME methods unsuitable to industrial RF environments. Consequently, there exists a critical imperative to develop sophisticated RME methods that can effectively characterize complicated propagation phenomena in industrial RF environments.

6.3. Dynamic RME Methods

The majority of existing RME methods employ offline learning approaches, which have proved inadequate for tracking dynamic variations in RF scenarios when environmental changes necessitate the reconstruction of new radio maps. Katagiri et al. [119] propose a hypothesis testing-based method for dynamically updating radio maps by replacing each piece of outdated information with time-series mean values independently. While being straightforward, this method overlooks spatio-temporal and frequency-domain correlations across different locations. Therefore, dynamic RME methods that effectively capture spatio-temporal variations in radio maps enable real-time or anticipative radio map estimation, holding theoretical importance and practical application value.

6.4. Emerging Deep Learning Methods for RME

Recent advances in deep learning methods present promising avenues for RME. For exmaple, by leveraging graph structures, graph neural networks (GNNs) excel at capturing spatial-spectral correlations in sparse and non-uniform training data, making them particularly effective for RME tasks in complex large areas [120]. Moreover, physics-informed neural networks (PINNs) integrate fundamental physical principles, such as Maxwell’s equations, into the training process, ensuring the estimation consistency of radio maps with physical laws [121]. These methods hold great potential for RME in reducing dependency on large datasets and enhancing generalization performance. Therefore, it is beneficial to develop RME methods based on emerging deep learning methods such as GNNs and PINNs in future.

7. Conclusions

Radio maps play a crucial role in improving the spectral efficiency and quality of service of wireless networks, making RME methods a research hotspot in the field of wireless communications and networking. This survey has categorized recent RME methods into three main classifications: model-driven methods, data-driven methods, and hybrid model data-driven methods. The fundamental principles and representative works of each classification have been introduced in detail. Model-driven methods utilize specific classic signal propagation models to estimate radio maps, eliminating training data dependency but relying on sophisticated domain knowledge. Data-driven methods predict radio maps through machine learning techniques, effectively capturing complex spatial-spectral patterns but requiring large quantity and high quality measurements or simulation data. Hybrid model data-driven methods take advantage of both model-driven and data-driven methods by integrating propagation models with DNN models, achieving high accuracy even with limited samples. Finally, four research directions–cross-scenario RME methods, RME methods for industrial RF environments, dynamic RME methods, and emerging deep learning methods for RME–are listed as some of the most promising topics in the realm of RME that will require substantial future research development.