Channel Knowledge Map (CKM) Overview

Updated 14 November 2025

CKM is a mapping of spatially indexed wireless propagation parameters—including path loss, delay spread, and multipath structure—used for environment-aware optimization.
Construction methods range from interpolation and generative AI models to wireless radiance field frameworks, balancing accuracy with computational demands.
Practical applications include training-free beam alignment, UAV trajectory optimization, and integrated sensing-communication, vital for next-generation networks.

A Channel Knowledge Map (CKM) is a site-specific, location-indexed database that encodes rich wireless channel information—such as path loss, multipath structure, angle of arrival (AoA), delay spread, and additional parameters—across spatial coordinates or transmitter–receiver (TX–RX) geometry. CKMs serve as priors for environment-aware optimization in wireless communications and for integrated sensing and communication (ISAC) systems, providing a means to infer channel conditions, guide resource allocation, and obviate exhaustive in situ channel state information (CSI) measurement.

1. Formal Definition and Taxonomy

A general CKM is a mapping

$\mathcal{M} : \mathcal{X} \to \mathcal{Y}$

where:

For the Base Station to Any (B2X) case:

$\mathcal{M} : \mathbb{R}^2 \to \mathbb{R}^d, \quad \mathcal{M}(x, y) = [PL, \tau, \Omega_{\text{AoA}}, \Omega_{\text{AoD}}, \ldots]^T$

with $PL$ = path loss, $\tau$ = delay spread, $\Omega_{\text{AoA}},\Omega_{\text{AoD}}$ = AoA/AoD vectors, and possible extensions to Doppler, shadowing, or spatial covariance.

For the Any-to-Any (X2X) case:

$\mathcal{M} : \mathbb{R}^3 \times \mathbb{R}^3 \to \mathbb{C}^M, \quad \mathcal{M}(r_{\mathrm{TX}}, r_{\mathrm{RX}}) = [h_1, \ldots, h_M]^T$

where $h_m$ are the complex path gains.

CKMs subsume several specific representations:

Channel Gain Map (CGM): Large-scale path loss or power gain at points or TX–RX pairs.
Channel Path Map (CPM): Parameters of dominant multipath components, including amplitude, phase, delay, and angles.
Beam Index Map (BIM): For each location (or grid), the indices of near-optimal beam pairs in the codebook.

CKM dimensionality scales with the environment and application: 2D for horizontal plane, 3D for altitude/elevation, 4D/6D for TX–RX pairs in general space.

2. Paradigms for CKM Construction

CKM construction methods can be classified according to modeling paradigm and input requirements, ranging from classical interpolation to advanced AI and physics-informed generative methods (Ren et al., 7 Nov 2025):

2.1 Interpolation-Based Methods

Inverse-Distance Weighting (IDW): Weighted averages of observed values, $w_i = \|x_0 - x_i\|^{-p}$ , fast but prone to over-smoothing or numerical instability depending on the power $p$ .
Kriging (Gaussian Process Regression): Models spatial correlation via a covariance kernel; provides the best linear unbiased estimator but faces $O(N^3)$ scaling for $N$ samples and poor performance near blockages/discontinuities.
Radial Basis Function (RBF) Interpolation: Generalizes spatial smoothing but is sensitive to kernel and regularization, facing ill-conditioning and poor extrapolation across abrupt environmental features.

Limitations: All such methods rely on spatial stationarity and sufficient measurement density; they are inaccurate near sharp edges or rapidly varying environments and scale poorly to high-dimensional (3D/6D) domains.

2.2 Image-Based and Generative AI Techniques

By representing CKMs as 2D images, advanced computer vision models can be leveraged:

CNN/U-Net/Transformer Architectures: Take environment masks and BS location as inputs; networks (RadioUNet, RMTransformer) achieve 20–30 dB lower MSE than interpolation, but are limited to 2D, ignore elevation, and require large labeled/simulated datasets (e.g., RadioMapSeer, CKMImageNet (Wu et al., 14 Apr 2025, Wu et al., 29 Sep 2024)).
Diffusion Models (CKMDiff): Learn generative priors for CKM restoration under missing/noisy data, enabling denoising, inpainting, and super-resolution with up to 30% RMSE reduction over CNNs, but inference requires hundreds of denoising steps with significant latency (Fu et al., 24 Apr 2025).

Limitations: Most effective for 2D coverage; insufficient for full multipath 3D structure and computationally expensive for real-time operation.

2.3 Wireless Radiance Field (WRF) and Gaussian Splatting Frameworks

Emerging methods adapt neural scene representations:

Neural Radiance Fields (NeRF $^2$ ): Models spatial–angular channel propagation as a continuous function $(x, \omega) \mapsto (\sigma, \alpha)$ with full complex gain, via volume rendering integrals; provides highest fidelity at amplitude and phase but is slow per query ( $\sim$ 0.1–1 s) due to ray marching.
3D Gaussian Splatting (WRF-GS): Represents the environment as $N$ anisotropic Gaussians, each parameterized by means, covariances, and complex scattering weights; enables orders-of-magnitude faster inference ( $\sim$ 10 ms), though originally uni-directional (Ren et al., 7 Nov 2025).
Bidirectional WGS (BiWGS): Extends 3DGS for arbitrary TX–RX pairs (6D mapping) via bidirectional spherical harmonic expansions; outperforms black-box MLP models for X2X mapping by up to 54% mean absolute gain improvement, efficiently capturing bidirectional multipath scattering (Zhou et al., 30 Oct 2025).

Advantages: WRF frameworks are scene-adaptive, scalable to sparse measurements, and tractable for high-dimensional channels, with explicit physics-inspired structure.

3. Hybrid and Structure-Enhanced Learning Approaches

To address the limitations of both classical and pure data-driven approaches, recent works integrate geometric priors, semantic scene understanding, and sparse real-world measurements:

Point Cloud-Driven CKM: A jointly model- and data-driven pipeline leverages high-resolution 3D point clouds (from LiDAR or photogrammetry) spatially segmented into confocal ellipsoidal shells (determined by TX, RX, and ToA bins), with neural estimators (PointNet++ variants) trained to predict channel profiles (RSS, PDP) for each shell (Wang et al., 9 Oct 2025, Wang et al., 26 Jun 2025). This outperforms both conventional ray-tracing (by $\sim$ 4 dB RMSE in PDP) and 2D-only learning.
Semantic Feature Fusion: Fusing RGB images, 3D semantic segmentation, and environmental metadata enriches channel prediction, especially for mmWave/THz bands where material properties and object shape critically affect multipath.

Implementation: In practice, the model-driven point selector extracts physically relevant geometry for each candidate path (e.g., via ToA ellipsoid intersection), and a neural network maps these structured clusters to predicted channel statistics.

4. Practical Applications and Use-Cases

CKM deployment provides critical environment-awareness for a variety of tasks:

Beamforming and Training-Free Alignment: BIMs and CKM-assisted beam selection enable near-optimal beam alignment in mmWave systems without exhaustive search, reducing alignment time by up to 60 $\times$ and maintaining robust coverage in NLoS/dynamic scenarios (Zhang et al., 12 Aug 2024, Dai et al., 13 Mar 2024).
UAV Trajectory Optimization: For UAV and multi-UAV networks, CKM-based placement and trajectory design leveraging Kriging or hybrid model-learning achieves near-optimal data rates with sub-second planning and robust performance under noisy or incomplete channel knowledge (Li et al., 2022, Zhang et al., 24 Sep 2024).
Integrated Sensing and Communication (ISAC): CKM enables simultaneous communications and NLoS sensing; e.g., Channel Angle-Delay Maps (CADM) transform communication priors into sensed multipath likelihoods for accurate localization under blockage (Wu et al., 4 Jul 2025). Cramér–Rao analysis shows that CKM-driven inference achieves tighter error bounds as multipath richness increases.

Real-world Prototypes: ISAC-based CKM implementation with OFDM mmWave hardware demonstrates training-free beam alignment, real-time CKM updates, and substantial speedup/robustness over conventional approaches (Zhang et al., 12 Aug 2024).

5. Critical Comparisons and Performance Considerations

Paradigm	Accuracy	Complexity	Data Requirement	Real-World Use
Interpolation	Low (sharp edges missed)	$O(N^3)$ precompute; $O(N)$ query	Dense samples ( $>$ 10%)	Inexpensive but inaccurate in complex scenes
CNNs/Transformers	SSIM $\sim$ 0.7; good 2D	$O(HW)$ ( $<$ 10 ms/map)	$10^4$ – $10^5$ labeled maps	Needs up-to-date environment imagery, retraining
Diffusion AI	RMSE $\downarrow$ 30% vs. CNN	$>$ 0.5 s query (100s steps)	Large simulation datasets	Not real-time; 2D only
WRF/3DGS/BiWGS	Highest (3D/6D, phase/amp)	$O(N_{\text{gauss}})$ ( $\sim$ 10ms)	Sparse, adaptive measurements	Real-time query; scene-specific adaptation

Key takeaways:

Interpolation is fast and lightweight but fails in nonstationary or occluded regions.
Image-based AI models are effective for 2D path loss but are not extensible to 3D propagation or direction-sensitive tasks without extensive 3D data.
Diffusion/generative models offer best-in-class 2D restoration but at the cost of sampling latency; they are not yet scalable to ultra-high-dimensional CKMs.
WRF methods, especially with bidirectional and scene-adaptive modeling (BiWGS), enable scalable, high-fidelity 3D/6D CKM synthesis with tractable sample complexity and inference latency.

6. Open Challenges and Future Research Directions

6.1 Real-Time and Incremental CKM Updating

Lightweight, quantized neural architectures and adaptive updates (e.g., splitting/merging Gaussians or online network retraining) are required for sub-millisecond CKM refresh in dynamic environments.

6.2 Cross-Domain and Cross-Frequency Generalization

Embedding hard constraints from Maxwell or Friis laws into neural architectures to improve transferability, and developing meta-learning frameworks to adapt CKMs to new cities/bands with minimal labeled data (Ren et al., 7 Nov 2025).

Integrating LiDAR, RGB–IR, and radar modalities supports richer geometry and material inference and addresses the multi-faceted impact of environment on wireless propagation.

6.4 Scalability and Dataset Infrastructure

Distributed/federated CKMs partitioned across edge/cloud, hardware-aware (NPU-friendly) layers for real-time inference, and standardized, open-source benchmarks (e.g., CKMImageNet, RadioMapSeer) for transparent evaluation.

6.5 Physical-Model Integration and Explainability

Hybrid models that fuse ray-tracing, parametric loss models, and learned representations, as well as uncertainty quantification via Bayesian neural networks and posterior estimation for risk-sensitive applications.

7. Conclusion

CKMs unify environment- and location-aware channel knowledge representation across dimensions and modalities, spanning path loss prediction, full multipath angular-delay structure, and ISAC tasks. Construction methodologies now range from classical spatial interpolation to point cloud–semantics–fusion, image-based AI, generative diffusion, and fully differentiable wireless radiance field representations. The field's trajectory is toward fully 6D, multi-modal, cross-domain, adaptive, and explainable CKMs as critical digital twins for 6G wireless systems—enabling predictive transmission, efficient beam management, robust sensing, and resource-efficient network management (Ren et al., 7 Nov 2025, Zhou et al., 30 Oct 2025, Wang et al., 9 Oct 2025).