Dynamic CKM Construction

Updated 30 December 2025

Dynamic CKM Construction Method is a framework that enables real-time and incremental channel map updates using spatio-temporal models.
It examines various algorithms including interpolation, deep learning, generative AI, and radiance field approaches with emphasis on adaptive updating mechanisms.
The method leverages rapid measurement assimilation and localized updates to achieve low-latency performance for applications in mobile MIMO-OFDM, UAV, and urban wireless networks.

Dynamic CKM Construction Method refers to a class of frameworks, algorithms, and representations enabling real-time, incremental, or time-varying construction and update of channel knowledge maps (CKMs) under dynamic propagation environments. CKMs provide spatially resolved a priori channel knowledge to facilitate network optimization, resource allocation, sensing, and environment-aware wireless system design. Dynamic methods aim to cope with time-varying channels at millisecond-to-second timescales, leveraging real-time measurements, adaptive computational architectures, and update rules that extend static formulations toward spatio-temporal settings. These advances are critical for scenarios such as mobile MIMO-OFDM, UAV networks, and rapidly changing urban wireless environments.

1. Dynamic CKM Problem Formulation and Spatio-temporal Representation

Dynamic CKMs generalize static CKM representations $K(\mathbf{r})$ or $K(x,y)$ to spatio-temporal mappings $K(\mathbf{r},t)$ or $K(x,y,t)$ , where both spatial location and observation time are parameters. The objective is to track or predict the channel state in each spatial cell as the environment, transceiver configuration, or system load changes. Canonical models augment classical interpolation/estimation frameworks to allow for streaming or batched updates, and introduce time-indexed parameters in model-based, neural, or radiance-field-based systems (Ren et al., 7 Nov 2025).

Dynamic extensions require:

On-line measurement assimilation at high temporal rates (1–10 kHz for fast-fading channels).
Model structures that allow incremental incorporation of new data, local refinement, and selective re-optimization (e.g., split/merge/prune of primitives).
Temporal filtering or forecasting to maintain CKM fidelity as channel statistics evolve.

A typical parameterization for a dynamic CKM based on a Gaussian splat model is:

$K(\mathbf{r}, t) = \sum_{i=1}^M \alpha_i(t) \exp\Big(-\frac{1}{2}(\mathbf{r} - \mu_i)^\top \Sigma_i^{-1} (\mathbf{r} - \mu_i)\Big) \exp(j\varphi_i(t))$

with $\{\alpha_i(t), \varphi_i(t)\}$ evolving over time (Ren et al., 7 Nov 2025).

2. Families of Dynamic CKM Construction Algorithms

The principal algorithmic approaches for dynamic CKM construction and update, their typical complexity regimes, and their limitations are summarized in the table below:

Method Family	Update Style	Dynamic Mechanism/Extension
Interpolation	Batch/Incremental	Kalman-filter update, recursive Kriging, GP regression
Image/Deep Learning	Re-inference	New measurements as extra channels, fine-tuning, retrain
Generative AI	Conditional Sampling	New input conditions, distilled low-latency diffusion
Wireless Radiance Field	Local Adaptive Updates	Primitives split/merge, least-squares coefficient update

Interpolation-based methods. Classic approaches (Kriging, kernel regression, matrix completion) support incremental updates by re-solving for new observations using Kalman-filter or recursive Gaussian-process rules, such as:

$\mu_{n+1}(\mathbf{r}) = \mu_n(\mathbf{r}) + K_n(\mathbf{r}, \mathbf{r}_{n+1}) [y_{n+1} - \mu_n(\mathbf{r}_{n+1})]$

where the Kalman gain $K_n$ depends on the spatial kernel and measurement noise (Ren et al., 7 Nov 2025). These methods, however, present high computational complexity ( $O(N^3)$ ) and are generally unsuitable for millisecond-scale adaptation at large $N$ .

Image-processing and neural architectures. Models such as RadioUNet and RMTransformer learn static mappings from environmental features to CKM images. Incremental adaptation is possible by re-invoking the forward pass with new measurements as additional input channels, retraining on a window of recent data, or deploying lightweight fine-tuning approaches. In the absence of explicit temporal filtering, the time-dynamics are handled implicitly, and low-latency inference (10–100 ms per tile) is feasible for real-time applications at the edge (Ren et al., 7 Nov 2025).

Generative AI approaches. Methods based on diffusion models (e.g., CKMDiff) or generative adversarial networks provide inpainting, denoising, or super-resolution from sparse or noisy input (Fu et al., 24 Apr 2025). Dynamic adaptation is achieved by re-conditioning the sampler on the latest measurement set $y_t$ , and, after distillation, enables inference latencies in the tens of milliseconds. Such approaches can be further accelerated by one-shot diffusion and distilled UNet architectures.

Wireless radiance-field (WRF) frameworks. NeRF $^2$ uses implicit neural representations (MLPs) to encode spatial fields and is extendable to dynamic settings via continual fine-tuning or explicit time embedding. WRF-GS and BiWGS (bidirectional Gaussian splatting) maintain a set of locally adaptive primitives (Gaussians/ellipsoids) whose amplitudes and phases can be re-optimized in a small neighborhood of the measurement location for each update. "Split/merge/prune" procedures are proposed to achieve structural refinement without full retraining, promoting high sample efficiency and local adaption (Ren et al., 7 Nov 2025, Zhou et al., 30 Oct 2025).

3. Incremental and Online Update Strategies

Incremental update rules in dynamic CKM frameworks enable efficient assimilation of new measurements while minimizing computation and storage requirements. The principal paradigms include:

Kalman/Gaussian-process recursion for Kriging-based CKMs, allowing explicit state-space filtering with temporal smoothing.
Pseudo-residual-driven local optimization in WRF-GS/BiWGS: on detecting significant local prediction error, only Gaussians whose projections intersect the error region are adaptively split, merged, or have their parameters updated by local least squares.
Neural architecture re-inference or fine-tuning, where new environment data is fed as input to the existing model and only the final prediction layer, or a small subset of weights, is updated.
Dynamic sampler re-conditioning in generative models, where the latest partial measurement replaces older side information as the conditioning variable.

A generic incremental WRF-GS update pseudocode is as follows (Ren et al., 7 Nov 2025):

Inputs: {Gi} (current Gaussians), (rm, ym) (new measurement)
1: Project {Gi} onto rm ⇒ predicted ym'
2: Compute e = ym - ym'
3: If |e| > threshold:
      a) Find primitives P near rm
      b) For i ∈ P, split/clone as necessary
      c) Update αi, ϕi via small least-squares fit
4: Return updated {Gi}

This approach scales as

O(|P|^2)

per update, where

|P|

is the number of affected primitives, typically much smaller than

M

(total).

4. Performance, Latency, and Empirical Benchmarks

Dynamic CKM frameworks are evaluated by spatial accuracy metrics (e.g., MSE, SSIM, LPIPS), temporal refresh rate, computational latency per update, and adaptability to new measurements. Reported empirical benchmarks (Ren et al., 7 Nov 2025) include:

Interpolation (Kriging, matrix completion): perceptible artifacts and blurred diffraction edges at low sampling rates (5–10%), with slow update rates due to cubic complexity.
Neural models (RadioUNet/RMTransformer): MSE reduction by 20–30%, CPU inference latency of 10–100 ms per $256\times256$ tile.
Diffusion models (CKMDiff): 31.7% lower RMSE than UNet in super-resolution, but inference latency of 200–500 ms; potential for sub-50 ms updates with distilled variants.
WRF-GS and BiWGS: millisecond latency per inference, sample-efficient incremental update; BiWGS achieves SSIM ≈ 0.679, LPIPS 0.457, 54% non-LOS MAE reduction versus baselines; inference costs for a single 6D spatial query are $\sim$ 0.01 s or less.

These results demonstrate that local-adaptation mechanisms (WRF-GS/BiWGS) are the most suitable for low-latency real-time operation under stringent sampling and mobility conditions.

5. Sensing, Data Fusion, and Measurement Protocols

Dynamic CKM construction relies on rapid, spatially distributed measurement acquisition. Strategies discussed include:

Sparse sampling, exploiting spatial consistency at rates of 5–10% over 1 m grids on large areas (100×100 m).
Sensor fusion, where multiple modalities—radio (RSS, CSI, AoA/AoD), LiDAR, radar, building footprints—are combined at the feature or decision level using hybrid neural models.
Adaptive measurement scheduling, particularly relevant for mobile agents (e.g., UAVs), wherein navigation and CKM completion are co-optimized (e.g., via shortest-path or TSP-based path planning under Kriging interpolation) (Song et al., 6 Dec 2025).

Periodic upload and (re-)distribution of completed or partially updated CKMs between edge devices and central servers facilitates scalable deployment.

6. Scalability, Hardware Efficiency, and Practical Deployment

Scaling dynamic CKM algorithms to large-scale wireless networks and hardware-constrained nodes demands:

Model compression (MLP/Transformer quantization, pruning).
Hierarchical grids or distributed CKM shard partitioning with seamless boundary stitching.
GPU-accelerated inference and primitive updates, particularly for Gaussian splat rendering and BiWGS frameworks.
Restriction of active update regions to sliding windows near the trajectory or regions of new measurement, substantially reducing memory and compute overhead.

Standardized benchmarks for time-series CKMs, cross-band and cross-scenario transferability, and 5G/6G integration principles will be needed to enable robust real-world deployments (Ren et al., 7 Nov 2025).

7. Future Research Directions and Open Challenges

Key open issues in dynamic CKM construction include:

Achieving sub-10 ms update latency for ultrafast channel variation; exploratory solutions include deployment of ultra-shallow neural architectures, low-step diffusion, and split-only local retraining.
Cross-domain generalization, requiring inductive architectures that blend physical constraints (e.g., embedded Maxwell/Friis models) with domain-adaptive meta-learning.
Real-time multi-modal fusion for robust, multi-environment adaptation.
Establishing widely accepted, high-fidelity open-source datasets with temporal granularity for benchmark comparison.
Systematic extension to multi-agent/federated scenarios, downlink reciprocity, and joint communication-sensing tasks.

Significant progress is expected by equipping existing CKM construction pipelines with lightweight, incremental update protocols and temporal modeling, as well as by integrating physics-informed learning paradigms for greater robustness in dynamic, complex wireless settings (Ren et al., 7 Nov 2025).