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A Tutorial on Environment-Aware Communications via Channel Knowledge Map for 6G

Yong Zeng, Junting Chen, Jie Xu, Di Wu, Xiaoli Xu, Shi Jin, Xiqi Gao, David Gesbert, Shuguang Cui, Rui Zhang

arXiv:2309.07460v2cs.ITeess.SP

TL;DR

Because 6G’s larger channel dimensions make real-time CSI acquisition challenging, this article surveys channel knowledge maps built from location-tagged channel data to represent local wireless environments. In reported mmWave scenarios, CKM-based training-free beam alignment performed comparably to exhaustive sweeping and achieved higher received power than location-based alignment.

Abstract

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Sixth-generation (6G) mobile communication networks are expected to have dense infrastructures, large antenna size, wide bandwidth, cost-effective hardware, diversified positioning methods, and enhanced intelligence. Such trends bring both new challenges and opportunities for the practical design of 6G. On one hand, acquiring channel state information (CSI) in real time for all wireless links becomes quite challenging in 6G. On the other hand, there would be numerous data sources in 6G containing high-quality location-tagged channel data, e.g., the estimated channels or beams between base station (BS) and user equipment (UE), making it possible to better learn the local wireless environment. By exploiting this new opportunity and for tackling the CSI acquisition challenge, there is a promising paradigm shift from the conventional environment-unaware communications to the new environment-aware communications based on the novel approach of channel knowledge map (CKM). This article aims to provide a comprehensive overview on environment-aware communications enabled by CKM to fully harness its benefits for 6G. First, the basic concept of CKM is presented, followed by the comparison of CKM with various existing channel inference techniques. Next, the main techniques for CKM construction are discussed, including both environment model-free and environment model-assisted approaches. Furthermore, a general framework is presented for the utilization of CKM to achieve environment-aware communications, followed by some typical CKM-aided communication scenarios. Finally, important open problems in CKM research are highlighted and potential solutions are discussed to inspire future work.

I. INTRODUCTION … 4) More diversified high-quality positioning methods:

6G’s ambitious performance goals are driving new network, radio, communication, and computing technologies. These developments point toward denser infrastructure, larger channel dimensions, more cost-effective hardware, and more accessible, higher-quality location information.

I. INTRODUCTION

  • 6G targets include 10 million devices per km2, Tbps peak rates, sub-1-ms latency, tenfold 5G energy efficiency, and 1–10 cm positioning accuracy.These KPIs are associated with applications such as autonomous vehicles, connected robots, and mixed reality, and with six ITU usage scenarios for 2030 and beyond.Source: A. 6G KPIs and Potential Technologies · p. 1

A. 6G KPIs and Potential Technologies

  • 6G network and radio research spans cell-free MIMO, non-terrestrial networks, wider spectrum, larger arrays, intelligent surfaces, and new modulation schemes.The passage gives OTFS for high-mobility ICI and DDAM for addressing ISI or manipulating delay spread using path-based beamforming and delay/Doppler alignment.Source: A. 6G KPIs and Potential Technologies · pp. 1–2
  • 6G also combines active and passive communication, localization, sensing, and communication, as well as edge computing and AI.Passive devices may reuse spectrum and energy while adding multipath components; ILSAC outputs can aid communication, and edge nodes can cooperatively train models and perform AI tasks.Source: A. 6G KPIs and Potential Technologies · p. 2

B. Important Trends Towards 6G

  • 6G’s developing trends include denser wireless nodes, larger antennas, wider spectrum, lower-cost hardware, more diverse high-quality positioning, and greater intelligence.The paper presents these trends as arising from the aforementioned technologies.Source: A. 6G KPIs and Potential Technologies · p. 2

1) Higher node density:

  • 6G densification is driven by more users, 3D aerial access, smaller cells at higher frequencies, dense cell-free access points, and passive infrastructure.Passive reflectors and radar sensing can require dense deployment because of double-hop attenuation.Source: 1) Higher node density · pp. 2–3

2) Larger dimensional channel:

  • 6G channel dimensions may grow by two or three orders of magnitude as antenna arrays and bandwidth expand, making complete channel estimation costly or impossible.BS antennas may rise from 64 to hundreds or thousands, bandwidth from hundreds of MHz to GHz, and subcarriers by an order of magnitude; mobility and complex environments further increase channel fluctuations.Source: 2) Larger dimensional channel · p. 3

3) More cost-effective hardware:

  • Reducing hardware and energy costs while expanding frequency, antenna size, and bandwidth makes cost-effective hardware important; fewer RF chains and cheaper RF components are two approaches.Analog and hybrid beamforming, lens arrays, passive reflectors, backscatter, and low-resolution ADCs are among the approaches discussed; low-resolution ADCs require more advanced processing to recover performance loss.Source: 3) More cost-effective hardware · p. 3

4) More diversified high-quality positioning methods:

  • 6G location information for UEs, reflectors, and obstacles is expected to be more accessible and higher quality through cellular and non-cellular positioning and sensing.Cellular methods target submeter or centimeter accuracy and millisecond updates; GPS or Beidou, cameras or lasers, and IMUs provide complementary location estimates.Source: 4) More diversified high-quality… · p. 4

5) More intelligence: … D. Toward Environment-Aware Communications via CKM

6G’s growing channel dimensions and dense networks make real-time CSI acquisition harder, while richer location-tagged channel data and stronger data-mining capabilities enable environment-aware communications. CKM provides a site-specific store of local channel knowledge for using that environment information in communication design.

5) More intelligence:

  • 6G’s AI, machine learning, edge computing, blockchain, and over-the-air computing are expected to support real-time data analysis and intrinsic network intelligence.Edge processing can reduce data-processing latency.Source: 5) More intelligence · p. 4

1) More difficult for CSI acquisition:

  • Dense nodes, larger channels, simpler hardware, and interference make CSI acquisition harder, with training or beam-sweeping overhead growing with channel dimensions.Hybrid beamforming can require MBS/MRF times as many training durations as fully digital systems; exhaustive beam sweeping scales on the order of MrMt, and sweeping 64 BS antennas with 16 UE antennas may take seconds.Source: 1) More difficult for CSI acquisition · pp. 4–5, C. New Challenges and Opportunities · p. 4

2) Abundant location-specific channel data:

  • Dense BSs and UEs can generate fine-grained, location-specific channel samples, including received signal strength, channel gains, and angle measurements, that reflect actual propagation.At 10 devices per m2, uniformly scattered devices would average about 30 cm apart, potentially finer than the coherence distance of channel shadowing.Source: 2) Abundant location-specific channel… · p. 5

3) Powerful data mining capability:

  • Mining location-specific channel data can help 6G adapt communication strategies to local propagation, improving spectral efficiency, energy efficiency, and reliability.Data mining can also automate feature selection and dimensionality reduction to improve storage and processing efficiency.Source: 3) Powerful data mining capability · p. 5

D. Toward Environment-Aware Communications via CKM

  • Environment-aware communication uses a priori knowledge of the actual local environment, beyond device location, to address real-time CSI challenges and is enabled by location information, channel data, and data mining.The paper frames it as an advancement of location-aware communication.Source: D. Toward Environment-Aware… · p. 5
  • Environment awareness can improve channel prediction before sophisticated real-time training: it can distinguish channel quality for equally distant UEs, direct beams via reflectors, and identify LoS links more accurately than probabilistic models.The examples are channel-gain prediction, training-free beamforming, and LoS prediction.Source: D. Toward Environment-Aware… · p. 6, Figure 2 · p. 6
  • CKM is a site-specific, location-tagged database of intrinsic channel properties that can facilitate or obviate sophisticated real-time CSI acquisition, unlike physical maps that need channel parameters and ray tracing for channel inference.CKM is mainly maintained offline, and location-specific knowledge from it need not consume communication resources; ray tracing may support offline CKM construction, with online measurements used to update the map.Source: D. Toward Environment-Aware… · pp. 6–7
  • The tutorial covers CKM concepts and classifications, construction methods, and a framework and use cases for CKM-enabled training-free or light-training communication, prediction, localization, and sensing.It also compares CKM with channel-inference techniques and identifies future research directions.Source: D. Toward Environment-Aware… · p. 8

II. CHANNEL KNOWLEDGE MAP: BASIC CONCEPT · A. Channel Knowledge Map · B. Basic Principles of CKM

A channel knowledge map (CKM) maps locations to channel knowledge and uses historical location-tagged data to infer channel knowledge at new locations, without explicitly modeling the propagation function or environment.

A. Channel Knowledge Map

  • A channel matrix map (CMM) stores all subcarrier MIMO matrices, whereas a channel path map (CPM) stores parameters for L dominant multipath components.Their dimensions are JCMM = MBSMUE NSC and JCPM = 7L, respectively; under multipath sparsity and large arrays, JCPM ≪ JCMM.Source: A. Channel Knowledge Map · p. 9
  • CKM maps a transmitter/receiver location vector q ∈ R^D to channel knowledge z ∈ C^J, with dimensions determined by the application and desired output.For BS-centric CKM, q may contain only the UE location: D = 2 for typical ground UEs and D = 3 for high-rise or aerial UEs.Source: A. Channel Knowledge Map · pp. 8–9
  • With known UE trajectories, a BS can use its CKM to infer location-specific channel knowledge across users and time before applying sophisticated real-time CSI acquisition.The passage describes K UE trajectories qk[n] over N time epochs and corresponding inferred knowledge zk[n].Source: A. Channel Knowledge Map · p. 9

B. Basic Principles of CKM

  • Because devices revisiting a location are likely to encounter similar wireless conditions, CKM can reduce channel uncertainty and improve inference accuracy over environment-unaware counterparts.UE mobility is a major source of channel variation and can be characterized by its trajectory.Source: B. Basic Principles of CKM · pp. 9–10
  • Channel knowledge depends on the radio wave, UE location, and propagation environment, but direct inference is hindered by difficult function modeling and environment representation.The environment includes static terrain and buildings as well as dynamic vehicles and pedestrians; ray tracing is computationally intensive and suited to offline rather than real-time inference.Source: B. Basic Principles of CKM · p. 10
  • CKM uses historical location–channel pairs to infer new channel knowledge without explicitly characterizing the propagation function or environment.For a quasi-static environment, the historical pairs serve as samples of the location-to-channel relationship, and the resulting mapping can reflect the local wireless environment.Source: B. Basic Principles of CKM · p. 10
  • Historical location-channel data may come from different devices, and sufficient visited locations can in principle support environment reconstruction and online inference at a new location.The data need not come only from dedicated site surveys: it may also be collected during online communication or generated by offline numerical computation.Source: B. Basic Principles of CKM · p. 10

C. CKM Classifications … D. CKM Typical Usage Scenarios

CKM is classified by communication mode and by the type of channel knowledge it provides, with each design carrying different input, accuracy, and storage demands. Its typical use is to predict channels where conventional acquisition is infeasible or too costly.

C. CKM Classifications

1) Classification based on communication modes:

  • B2X CKM maps BS-to-UE channels using UE locations, while X2X CKM maps mobile transmitter–receiver pairs and requires higher-dimensional inputs.B2X inputs have D = 2 for typical ground UEs and D = 3 for high-rise or aerial UEs; X2X inputs range from D = 4 for ground-ground to D = 6 for air-air links, increasing acquisition, storage, and mining demands.Source: 1) Classification based on… · pp. 10–11

2) Classification based on channel knowledge types:

  • Region-specific parameter CKMs provide local model parameters, including path-loss, shadowing, angular, and delay/Doppler statistics, for inference using established channel expertise.They are more stable and less demanding of localization accuracy and storage than location-specific CKMs, but inference can be biased by pre-assumed mathematical models.Source: 2) Classification based on channel… · p. 11
  • Location-specific large-scale CKMs store knowledge such as LoS presence, channel gain, deterministic path angles, and strongest-power beam indices without relying on expert models or region partitioning.Because this knowledge varies over correlation distances much larger than a wavelength, the map can use grid spacing on the order of those distances.Source: 2) Classification based on channel… · pp. 11–12
  • Small-scale CKMs offer fine-grained, location-specific channel information, but require wavelength-scale localization and surveys and must account for channel dynamics in map updates and queries.Their content can include instantaneous channel gains, path angles, delays and gains, or the full channel impulse response; practical use of centimeter- or millimeter-level localization for accurate construction remains to be studied.Source: 2) Classification based on channel… · p. 12
  • CKM storage demands can be alleviated by hierarchical maps across BSs or by extracting key features from raw data instead of storing it directly.Source: 2) Classification based on channel… · p. 12

D. CKM Typical Usage Scenarios

  • CKM supports four typical scenarios: predicting channels at yet-to-reach or never-to-reach locations, for non-cooperative nodes, in high-dimensional settings, and under stringent hardware or signal-processing limits.Source: D. CKM Typical Usage Scenarios · p. 12

1) Channels for yet-to-reach or never-to-reach locations: … 4) Radar/Lidar/Vision-aided communication:

CKM supports location-specific channel inference where real-time training is unavailable, costly, or impractical, and the section compares it with other channel-inference approaches.

1) Channels for yet-to-reach or never-to-reach locations:

  • CKM provides channel knowledge for yet-to-reach locations, enabling proactive motion planning, resource allocation, handover, and node sleep/wake decisions without waiting for channel training.For network-connected ground or aerial robots, it can guide trajectories away from blind coverage zones.Source: 1) Channels for yet-to-reach or… · p. 12

2) Channels for non-cooperative nodes:; 3) Channels with large dimensions:

  • Location-based CKM can infer channels for non-cooperative nodes and reduce costly CSI acquisition for high-dimensional channels, especially under short coherence times or low-latency requirements.Such inferred channels can support zero-forcing beamforming for physical-layer security or interference-temperature control; sensing can provide non-cooperative nodes’ locations.Source: 2) Channels for non-cooperative nodes · p. 12, 3) Channels with large dimensions · p. 12

4) Channels under stringent hardware/signal processing limitations:

  • CKM is attractive when semi-passive devices or energy-efficient analog or hybrid beamforming and low-resolution ADC architectures make training-based channel acquisition difficult.The limitation applies to devices such as backscatter radios and IRSs, and to systems with antenna arrays growing toward XL-MIMO.Source: 4) Channels under stringent… · p. 12

E. CKM Versus Other Relevant Technologies; 1) Time-domain channel prediction:

  • Time-domain prediction forecasts future CSI from past observations but still needs frequent training and infers only one device’s future channel, whereas CKM uses historical data across devices, time, frequency, and space.The comparison section also situates CKM among channel inference or extrapolation technologies and discusses its relation to fingerprinting-based localization.Source: E. CKM Versus Other Relevant… · p. 12, 1) Time-domain channel prediction · p. 13

2) Channel inference using out-of-band measurements:

  • Out-of-band inference exploits spatially correlated paths for cross-frequency channel or beam extrapolation, but its accuracy depends on inter-band correlation and may require extensive measurements and signal processing.CKM instead uses location information to infer channel knowledge at different frequencies directly.Source: 2) Channel inference using out-of-band… · pp. 13–14

3) Channel-to-channel mapping:

  • Channel-to-channel mapping can infer CSI across antenna sets and frequencies when location-to-channel mapping is bijective, but unlike CKM it requires real-time CSI and deep-learning approximation.CKM does not require bijectivity or real-time CSI, and uses location information directly; mapping can preserve privacy by not explicitly using location.Source: 3) Channel-to-channel mapping · p. 14

4) Radar/Lidar/Vision-aided communication:

  • Radar, lidar, or vision measurements can estimate UE location or angles before beam inference, or infer the best beam pair directly, but add hardware and processing costs.CKM avoids separate sensing requirements and can also use sensor measurements to improve prediction; sensor-aided approaches may depend on LoS, large labeled datasets, or vision conditions.Source: 4) Radar/Lidar/Vision-aided… · pp. 14–15

5) Fingerprinting-based localization and channel charting: … 1) Simulation-generated Data:

CKM uses device-location information to infer local channel knowledge, avoiding fingerprinting’s requirement for distinct location fingerprints and supporting both communication and localization. The section summarizes CKM’s construction from location-specific data and its potential to reduce channel-acquisition overhead and improve environment-aware communications.

5) Fingerprinting-based localization and channel charting:

  • CKM reverses fingerprinting-based localization by inferring channel knowledge from device locations without requiring distinct fingerprints for unambiguous localization.Both approaches exploit the dependence of wireless channels on device location, but CKM’s relaxed mapping requirement supports indoor and outdoor use.Source: 5) Fingerprinting-based localization… · p. 15
  • One CKM can support communication through forward channel inference and localization through reverse fingerprinting, serving both types of UEs.CKM-based communication may reduce real-time channel-acquisition overhead and improve channel-estimation quality by providing a priori local-environment knowledge.Source: 5) Fingerprinting-based localization… · p. 15, F. Summary · p. 16
  • Channel charting learns a low-dimensional CSI representation that preserves local spatial geometry, but yields relative UE positions rather than absolute locations.Unlike fingerprinting-based localization, it is unsupervised and does not require extensive offline measurement or location information for training or inference.Source: 5) Fingerprinting-based localization… · p. 15
  • ISAC can provide location-tagged data and sensing for CKM construction and use, while CKM can reduce repeated sensing and improve ISAC sensing performance.CKM and ISAC address different challenges, and sensing for CKM can also use alternatives such as separate sensing and communication, ray tracing, or GPS.Source: 5) Fingerprinting-based localization… · pp. 15–16

III. CONSTRUCTING CHANNEL KNOWLEDGE MAPS

  • CKM construction interpolates channel knowledge at interested locations from data collected at a few locations, and is most effective in static or semistatic environments.It aims to capture channel information over the environment’s static background, where only a small portion of scatterers vary over time.Source: §III · p. 16

A. Data Acquisition

  • CKM data acquisition has two main streams: simulation-based and measurement-based collection of location-specific data for the actual radio environment.The section distinguishes environment model-free and environment model-assisted construction approaches after introducing data acquisition.Source: A. Data Acquisition · p. 16, §III · p. 16

1) Simulation-generated Data:

  • Stochastic channel models use city or physical maps to configure propagation scenarios and model path loss, shadowing, and small-scale fading.They suit large-area simulations such as city-level radio maps for coverage analysis and base-station planning.Source: 1) Simulation-generated Data · pp. 16–17
  • Ray tracing can generate more detailed, accurate channels than stochastic models, but requires fine-grained environment information and substantially greater computation.Hybrid models combine stochastic and ray-tracing methods to balance complexity and accuracy; real-world measurements can further refine model parameters.Source: 1) Simulation-generated Data · pp. 17–18

2) Measurement data: … 2) Kriging Interpolation:

CKM construction can use dedicated offline campaigns or measurements retained from routine network operation, then fill spatial gaps through environment model-free interpolation methods such as IDW, KNN, local polynomial regression, and Kriging.

2) Measurement data:

  • Offline campaigns collect carefully planned, cleaned measurements with controlled mobility, while online measurement retains data gathered during conventional channel measurement, estimation, and communication.Offline campaigns require intensive labor but provide high-quality datasets for performance evaluation and network optimization.Source: 2) Measurement data · p. 18
  • MDT, introduced in 3GPP Release 9, helps operators collect UE radio measurements, but commercial restrictions and UE battery or privacy concerns can leave CKMs only partially measured.The resulting challenge is to build a full CKM from partial measurements.Source: 2) Measurement data · p. 18

B. Environment Model-free CKM Construction

  • Where geographic propagation models are unavailable, model-free CKM construction treats map completion as spatial interpolation or extrapolation, using methods including Kriging, kernel regression, and matrix completion,.Matrix completion exploits a low-rank assumption; canonical alternatives include KNN, IDW, and polynomial regression.Source: B. Environment Model-free CKM… · p. 18

1) Canonical Interpolation Methods:

  • IDW estimates a location by averaging measurements with weights proportional to inverse distance, but selecting its distance-decay parameter is difficult without propagation-environment information.A suitable parameter can yield a good estimate, though the propagation field may be complex.Source: 1) Canonical Interpolation Methods · p. 18
  • KNN estimates a location from its K nearest measurements, weighting them by IDW or a kernel such as Gaussian or Laplacian.Kernel weights decrease with distance from the target location.Source: 1) Canonical Interpolation Methods · p. 18
  • Local polynomial regression fits a separate polynomial at each target location using weighted least squares, emphasizing nearby measurements and reducing the limited representability of a global model.Cross-validation can select the weighting bandwidth to minimize expected interpolation MSE.Source: 1) Canonical Interpolation Methods · pp. 18–19

2) Kriging Interpolation:

  • Kriging models measurements through spatial statistics and designs a predictor with enforced statistical properties; its variants assume a mean that is known and constant, unknown and constant, or varying and unknown.Its second-order model uses the mean and covariance, and its weights minimize MSE subject to unbiasedness.Source: 2) Kriging Interpolation · p. 19
  • Kriging construction estimates a semivariogram from collected data, solves the resulting Kriging system with weights summing to one, and uses the solution for best unbiased prediction under a constant, known-mean stationary assumption.The Kriging variance has a closed-form expression.Source: 2) Kriging Interpolation · p. 19

3) Kriging for static CKM construction: · 4) Kriged Kalman filtering for time-varying CKM:

Kriging constructs static CKMs for interference, SINR, and shadowing, while Kriged Kalman filtering uses spatio-temporal channel correlations to construct and track time-varying CKMs. These approaches combine measured channel data with spatial interpolation and, for time-varying maps, state-space filtering.

3) Kriging for static CKM construction:

  • Kriging supports construction of static interference, SINR, and shadowing maps as CKM types requiring systematic design.The construction process requires consideration of data acquisition, message passing, information processing, and resource allocation and control.Source: 3) Kriging for static CKM construction · p. 19
  • An Interference Cartography Manager collects terminal measurements, builds a Kriging-interpolated interference map, and stores it in a database.Source: 3) Kriging for static CKM construction · p. 19
  • For heterogeneous networks, two-tier Kriging models separate macro- and small-cell SINR processes, whose cross-tier correlation supports range expansion and coverage optimization.The processes are denoted SM(q) and Sm(q), respectively.Source: 3) Kriging for static CKM construction · p. 19
  • In licensed shared access, a shadowing map can help estimate potential interference to primary users and guide secondary-user power control.The passage identifies this interference-estimation challenge in cognitive radio networks and notes that LSA is supported in LTE.Source: 3) Kriging for static CKM construction · p. 19
  • Shadowing-map construction estimates large-scale shadowing from sensor-measured primary-user RSS, infers partial map entries, then applies Kriging to interpolate the full map.The propagation model is pr = (G◦S)pt+n; with S known, the RSS map can be dynamically computed from the power-allocation vector pt.Source: 3) Kriging for static CKM construction · pp. 19–20

4) Kriged Kalman filtering for time-varying CKM:

  • Because radio propagation environments and CKMs vary over time, a Kriged Kalman filter exploits spatio-temporal channel correlation to construct and track shadowing maps.The setup uses noisy measurements at N locations across T time slots.Source: 4) Kriged Kalman filtering for… · p. 20
  • The filter models a spatially correlated trend evolving between time slots with spatially correlated, temporally white Gaussian processes, then applies ordinary Kalman filtering to estimate the trend with Kriging interpolation.Source: 4) Kriged Kalman filtering for… · p. 20
  • Orthonormal-basis expansion gives finite representations of the continuous trend and spatial transition functions, reducing state-space dimensionality for the finite measurement set.The expansion expresses the state evolution and measurement model in finite-dimensional form.Source: 4) Kriged Kalman filtering for… · p. 20

5) Kernel Regression: · 6) Kernel Approach for CKM Construction:

Kernel regression provides an RKHS framework for estimating channel maps and connects to Kriging under specified covariance conditions. CKM construction must also address dimensionality, quantized measurements, multi-scale channel variation, and spatial discretization.

5) Kernel Regression:

  • Kernel-based function estimation is nonparametric; RKHS connects to Gaussian processes through covariance kernels and to Kriging when the covariance matrix equals the kernel Gram matrix [152]–[155].A symmetric positive-definite kernel defines the space of interpolating functions, while kernel choice can impose structure such as low curvature from a spline kernel.Source: 5) Kernel Regression · p. 20
  • The RKHS representation theorem reduces regularized least-squares interpolation from N samples to a finite-dimensional solution with coefficients a = (W + μI)^−1z [154].W is the kernel-dependent Gram matrix with entries Wij = w(qi, qj).Source: 5) Kernel Regression · p. 20
  • Under zero-mean stationary simple Kriging with noisy measurements, the estimator matches the RKHS form when the kernel is chosen as the field covariance.Noise variance adds σ²I to the signal covariance matrix; the resulting estimator is a kernel expansion with coefficients determined by the noisy covariance system.Source: 5) Kernel Regression · pp. 20–21

6) Kernel Approach for CKM Construction:

  • Because CKMs can be high-dimensional, construction should seek lower-dimensional representations to manage complexity.The spectrum-map example is (D + 1)-dimensional before narrowband reduction.Source: 6) Kernel Approach for CKM Construction · p. 21
  • For PSD maps, estimating or knowing transmitters’ location-independent spectra reduces construction to a 2D power map suitable for kernel regression.The narrowband model represents the spectrum map as a sum of location-dependent path-loss terms multiplied by transmitter PSDs, plus noise.Source: 6) Kernel Approach for CKM Construction · pp. 21–22
  • Quantization-aware construction can replace squared loss with ε-insensitive L1 or L2 losses that ignore errors within the quantization interval [156].For uniform quantization error in (−ε, ε), the proposed losses penalize only deviations beyond ε.Source: 6) Kernel Approach for CKM Construction · p. 22
  • A dual-kernel CKM approach tracks slowly varying path loss and fast-varying shadowing, improving accuracy over single- and multi-kernel approaches.It combines a slowly changing DC-component kernel with a fast-varying-component kernel, using θDC ≫ θvar.Source: 6) Kernel Approach for CKM Construction · p. 22
  • Discretized CKMs can be represented as matrices or tensors for completion, and optimized non-uniform grids may improve identifiability when measurements are unevenly distributed –.On a 2D uniform grid, measurements form a sparse observation matrix whose entries record samples located within each grid cell.Source: 7) Matrix and Tensor Completion · p. 22

7) Matrix and Tensor Completion: · 8) Issues and Remedies for Matrix-based CKM Construction:

Low-rank matrix and tensor models enable CKM completion from sparse observations, but matrix resolution and observation noise constrain reliable recovery. Interpolation-assisted completion combines local estimates with global matrix structure to address these issues.

7) Matrix and Tensor Completion:

  • A channel matrix is often low rank; Gaussian propagation yields a provably rank-1 matrix, with further numerical and experimental examples across propagation models,.This low-rank property motivates completing the matrix from sparse observations using nuclear-norm minimization.Source: 7) Matrix and Tensor Completion · p. 22
  • With sufficient uniformly random observations O(M log^2 M) or deterministic patterns satisfying identifiability conditions, nuclear-norm completion recovers the full matrix with high probability.The matrix resolution M^2 cannot be too large for these identifiability guarantees to hold.Source: 7) Matrix and Tensor Completion · p. 22
  • Tensor models extend CKM construction to higher dimensions, frequency spectra, and multimodal measurement domains.For spectrum cartography, aggregation from R emitters yields an LL1 tensor model; its propagation maps capture path loss and shadowing, and may capture narrowband small-scale fading.Source: 7) Matrix and Tensor Completion · p. 22
  • A classical alternating least-squares method can construct the LL1 spectrum tensor from sparse measurements.Source: 7) Matrix and Tensor Completion · p. 22

8) Issues and Remedies for Matrix-based CKM Construction:

  • CKM observations contain measurement and grid-discretization noise, addressed with weighted least squares plus a nuclear-norm penalty or error-aware observation constraints.The weighted formulation uses an observation indicator matrix and trade-off parameter; confidence intervals for the alternative can come from local Kriging or polynomial regression.Source: 8) Issues and Remedies for… · pp. 22–23
  • With N measurements, matrix dimension M must remain limited because observed entries cannot exceed N; although N should scale as O(M log^2 M), no exact maximum M is known.A safe practical choice is a small M with an empirically sufficient margin.Source: 8) Issues and Remedies for… · p. 23
  • Interpolation-assisted completion first estimates entries with sufficient nearby measurements, then applies nuclear-norm minimization; window size b controls the observation pattern and local estimation.Uniform sampling selects CM log^2 M grid points and tunes entry-specific windows, while measurement-aware sampling selects points with enough nearby measurements and tunes b to reduce average error.Source: 8) Issues and Remedies for… · p. 23
  • A moderate, adaptive window b performs best because local interpolation exploits nearby correlation while matrix completion fills sparse regions using global structure.Small b approaches conventional completion, whereas large b approaches interpolation of all entries; interpolation alone may perform poorly where measurements are very sparse.Source: 8) Issues and Remedies for… · p. 23

9) Deep Learning with Neural Network: … 2) Virtual Obstacle Model:

CKM construction can use neural networks to complete or infer radio maps, or reconstruct propagation environments and channel models from measurements. Environment-assisted methods use spatial loss fields or virtual obstacles to represent propagation and extend CKMs to arbitrary transmitter and receiver locations.

9) Deep Learning with Neural Network:

  • Neural networks replace difficult propagation models, extrapolate multipath angle and delay with CNNs, or use autoencoders to complete sparsely observed radio maps.The autoencoder compresses spatial structure into feature vectors and decodes them into a full map, trained by comparing input and output.Source: 9) Deep Learning with Neural Network · p. 23
  • Neural networks fuse satellite-image features with transceiver parameters or use city-map and transmitter/receiver images as U-net inputs to learn shadowing.Satellite imagery can distinguish propagation scenarios, while binary maps encode building occupancy and transceiver locations.Source: 9) Deep Learning with Neural Network · pp. 23–24

C. Environment Model-assisted CKM Construction

  • Environment-assisted construction reconstructs propagation geometry to exploit shared-environment correlations and build CKMs for arbitrary transmitter and receiver locations; simplified models address ray tracing’s complexity –.Examples include the 2D spatial loss field – and joint 3D environment and radio-map construction using virtual obstacles –.Source: C. Environment Model-assisted CKM… · p. 24

1) Spatial Loss Field Model:

  • The spatial loss field models incremental shadowing along propagation paths, with direct-path or ellipse-based weighting and a discretized measurement model for estimating the field [175].The inverse-area ellipse gives greater weight near the direct path and decreasing weight toward the ellipse edge.Source: 1) Spatial Loss Field Model · p. 24

2) Virtual Obstacle Model:

  • Virtual obstacles encode electromagnetic attenuation rather than visual structures, representing deep shadow, slight attenuation, or LoS with solid, light, or absent obstacles –.The model approximates scattered propagation with an equivalent direct path through effective obstacles, as illustrated in Fig. 8.Source: 2) Virtual Obstacle Model · p. 24, Figure 8 · p. 24
  • A segmented channel model assigns location pairs to disjoint LoS or obstacle-class regions and uses region-specific path loss and residual shadowing to reconstruct the CKM from fitted parameters [172]–[174].The model parameters and environment representation are estimated from measurement data.Source: 2) Virtual Obstacle Model · p. 25
  • Virtual-obstacle regions can be inferred with Kriging or subspace clustering, or derived from simplified ray tracing; grid-cell obstacle heights determine whether direct paths are blocked.Estimating obstacle heights can be non-convex and ill-posed, motivating likelihood-based methods and CNN/DNN approaches.Source: 2) Virtual Obstacle Model · p. 25

D. Performance Evaluation · 1) Environment model-free approaches for CKM construction:

The evaluation compares CKM construction methods using pixelwise error metrics and finds NNM-t strongest among seven environment model-free methods in an indoor RSS reconstruction task. The study also describes public radio-map datasets as useful resources for evaluating radio-map construction and use.

D. Performance Evaluation

  • Radio-map construction and utilization evaluation relies on data collected or simulated in real geographic environments, and Table V summarizes public radio-map datasets reported in the literature.The datasets are presented as useful for radio and channel knowledge maps.Source: D. Performance Evaluation · p. 25, Table V · p. 26

1) Environment model-free approaches for CKM construction:

  • The indoor RSS reconstruction uses 166 measurements per emitter across a 14×34 m2 area, with 20–140 measurements randomly selected for reconstruction.The area is divided into 1 × 1 m2 grid cells, with measurements at grid centers; the selected-measurement fraction is the sampling rate.Source: 1) Environment model-free approaches… · p. 25
  • The evaluation measures reconstruction error using pixelwise MSE on the 14 × 34 grid representation of the RSS CKM.The broader evaluation discussion identifies pixel-by-pixel MSE or MAE as prevailing CKM performance metrics.Source: 1) Environment model-free approaches… · p. 25, D. Performance Evaluation · p. 25
  • The passages describe k-LP, Ordinary Kriging, TPS, NNM-t, GPR, and KNN, with KNN using K = 5.They include local polynomial regression, thin plate spline, Gaussian process regression, and nearest-neighbor methods; NNM-t is used for matrix completion.Source: 1) Environment model-free approaches… · pp. 25–26
  • KNN performs poorly with non-uniform measurements, while Ordinary Kriging is limited by its constant-mean assumption and ALS encounters recoverability issues below a 0.2 sampling rate.ALS results below that sampling rate are omitted; TPS and GPR perform well but may be difficult to tune because selecting a suitable kernel can be challenging.Source: 1) Environment model-free approaches… · p. 26
  • NNM-t addresses matrix-completion recoverability through local polynomial regression, outperforming pure matrix-based and pure interpolation-based approaches.The compared pure matrix-based approach is ALS; the interpolation-based approaches are k-LP, Kriging, TPS, GPR, and KNN.Source: 1) Environment model-free approaches… · p. 26
  • NNM-t performs best among the seven tested methods and outperforms both pure matrix-completion and pure interpolation schemes.The comparison is shown across sampling rates in Fig. 9; the reported alternatives include ALS and k-LP, Kriging, TPS, GPR, and KNN.Source: Figure 9 · p. 26, 1) Environment model-free approaches… · p. 26

2) Environment model-assisted approaches for environment and radio map construction: … A. Optimization Framework for CKM Utilization

The section evaluates environment-model-assisted radio-map construction and outlines how CKMs support system-utility optimization when current, future, or non-cooperative-node CSI is difficult to obtain.

2) Environment model-assisted approaches for environment and radio map construction:

  • The evaluation constructs joint 3D environment and radio maps from simulated RSS in central Shanghai using ray-traced narrowband signals at 2.5 GHz.The urban scene includes concrete buildings and obstacles, with randomly placed street receivers and transmitters distributed in the sky.Source: 2) Environment model-assisted… · pp. 26–27
  • The DL-based segmented model achieves the highest radio-map construction accuracy among the compared methods.U-Net and RadioUNet use geographic city maps to predict path loss across a target area, whereas the segmented approaches use transmitter–receiver position pairs. Fig. 10 reports prediction MAE.Source: 2) Environment model-assisted… · p. 27, Figure 10 · p. 27
  • Virtual obstacle maps inferred from RSS measurements reveal hidden geographic structure, although the segmented model is geometrically closer to the true city map than the DL-based model.The virtual map is an interpretation of radio propagation and is not necessarily expected to match the true city map exactly.Source: 2) Environment model-assisted… · p. 27, Figure 11 · p. 28

E. Summary

  • Environment-model-assisted methods require more data and heavier training, but scale more easily to geographically large CKMs than classical approaches.Kriging and kernel regression are computationally efficient with sparse data but scale poorly for massive, high-dimensional maps; tensor methods face identifiability constraints, with finer grids requiring more data.Source: E. Summary · p. 27

IV. UTILIZING CHANNEL KNOWLEDGE MAPS

  • The utilization section builds on constructed CKMs to enable environment-aware communications efficiently.Source: §IV · p. 27

A. Optimization Framework for CKM Utilization

  • The optimization framework considers transmitters, receivers, cooperative helpers, and non-cooperative nodes, and seeks to maximize system utility over T channel blocks.It assumes block fading: node locations and channels remain fixed within each block but may change between blocks.Source: A. Optimization Framework for CKM… · p. 27
  • CKMs can reduce training for cooperative-node current CSI, predict their future CSI, and help obtain non-cooperative-node CSI when conventional training is impractical.Utility optimization depends on current and future CSI, but acquiring current CSI can consume substantial resources as network size grows, future predictions can degrade with mobility and fast-changing channels, and non-cooperative-node CSI is difficult to acquire.Source: A. Optimization Framework for CKM… · p. 28

1) Conventional channel training based design: · 2) Location-aware design without CKM: · 3) Environment-aware design with CKM:

Conventional channel training incurs overhead that grows with channel dimensions and network scale, while location-only approximations are limited in obstructed, richly scattered environments. CKM enables current and future channel inference from node locations to support training-free or light-training design and additional predictive and network applications.

1) Conventional channel training based design:

  • Training estimates each link’s CSI from pilots and feedback, with signaling overhead generally proportional to MBSNSC.Exploiting channel correlation and sparsity across subcarriers and antennas may reduce the required training signals.Source: 1) Conventional channel training based… · pp. 28–29
  • With multiple transmitters or receivers, orthogonal-pilot overhead scales by K1K2, while nonorthogonal pilots risk contamination.Training can also be difficult for passive IRS links and uncoordinated nodes; proposed alternatives require higher overhead and complexity.Source: 1) Conventional channel training based… · p. 29

2) Location-aware design without CKM:

  • Location-aware designs use GPS or sensing with simplified channel models to reduce training in strong-LoS scenarios, but do not suit rich scattering or obstructions.Examples of the approximations include LoS, location-dependent probabilistic-LoS, and Rician channel models.Source: 2) Location-aware design without CKM · p. 29

3) Environment-aware design with CKM:

  • Given CKM and localized nodes, the controller can infer current channel knowledge and estimate future channels from predicted trajectories.With CMM, the map provides estimated channel matrices; with CPM, delays, Dopplers, and path angles can be used to construct channel estimates.Source: 3) Environment-aware design with CKM · p. 29
  • CKM-based channel estimates let the controller evaluate and optimize network utility without channel training, enabling training-free communications.The framework approximates current and future utility using CKM-derived channel estimates and trajectory-based future channel predictions.Source: 3) Environment-aware design with CKM · p. 29
  • CKM and localization errors can degrade training-free performance, while online training can refine channel estimates with reduced pilot overhead.Coarse CKM estimates guide the online training process, enabling light-training communications.Source: 3) Environment-aware design with CKM · p. 29
  • CKM also supports predictive communication, interference management for non-cooperative nodes, network planning, link scheduling, localization, and sensing.Predictive communication plans designs over blocks for yet-to-reach locations, while CKM provides channel knowledge for non-cooperative nodes without sophisticated channel learning.Source: 3) Environment-aware design with CKM · p. 29

B. Training-Free and Light-Training Communications · 1) Hybrid beamforming for mmWave massive MIMO:

The section uses hybrid beamforming for mmWave massive MIMO to illustrate how CKM can reduce or eliminate training overhead by using location and environment information. It outlines the conventional training challenges and introduces CKM types for training-free and light-training designs.

1) Hybrid beamforming for mmWave massive MIMO:

2) CMM and CPM enabled training-free hybrid beamforming: … C. Predictive Communication for Yet-to-Reach Locations

CKM supports training-free or light-training beamforming by supplying channel or beam information, and enables prediction of channels along future trajectories for resource and mobility planning.

2) CMM and CPM enabled training-free hybrid beamforming:

  • CMM returns location-specific channel matrices with low implementation complexity but high storage cost; CPM provides significant-path information for channel reconstruction, enabling training-free beamforming.Training-free performance depends on CKM and location accuracy; environmental changes and localization errors can degrade channel estimates, so limited additional training may help.Source: 2) CMM and CPM enabled training-free… · p. 30

3) CAM and BIM enabled light-training hybrid beamforming:

  • CAM supplies path angles, leaving path gains to estimate with about one pilot symbol per significant path, reducing overhead versus conventional training.The known angles determine the array-response vectors, while the BS and UE design hybrid beamformers to send the pilots.Source: 3) CAM and BIM enabled light-training… · p. 31
  • As BS antennas increase, CAM/BIM rates rise monotonically and outperform location-based alignment, while LS channel-estimation rates fall as training overhead outweighs beamforming gain.Fig. 14 compares these approaches.Source: Figure 14 · p. 31, 3) CAM and BIM enabled light-training… · p. 31
  • BIM maps locations to candidate transmit and receive beams, allowing beam sweeping over a reduced set with expected performance comparable to exhaustive sweeping and lower overhead.Unlike CAM-based design, BIM directly obtains beamformers through the candidate-beam mapping and sweeping.Source: 3) CAM and BIM enabled light-training… · p. 31

4) Extensions:

  • For IRS-assisted communications, CKM supports training-free reflective beamforming via CMM/CPM and light-training designs via CAM/BIM.The IRS’s lack of signal-processing components prevents conventional channel training.Source: 4) Extensions · pp. 31–32
  • For WPT, CKM is expected to enable training-free or light-training energy beamforming, avoiding receiver energy costs from pilot-based CSI acquisition.Conventional CSI acquisition requires reverse-link pilots or power feedback after the transmitter sends different pilots.Source: 4) Extensions · p. 32

C. Predictive Communication for Yet-to-Reach Locations

  • CKM predicts channels along controllable or predictable trajectories before nodes arrive, enabling resource allocation and path planning for long-term utility rather than one-shot optimization.This is especially relevant to B5G/6G machines such as factory AGVs and UAVs.Source: C. Predictive Communication for… · p. 32
  • For UAV communication, CKM provides environment-specific channel predictions that capture air-to-ground line-of-sight availability, unlike free-space or stochastic models, supporting trajectory optimization and multi-UAV placement.The section identifies single-UAV trajectory optimization and multi-UAV placement as two CKM-assisted scenarios.Source: C. Predictive Communication for… · p. 32

1) CKM-assisted single-UAV trajectory design: … F. Summary

Across UAV, ground-mobility, resource-management, localization, and sensing scenarios, CKM supplies spatial channel knowledge for environment-aware decisions, including predictive communication and mobility planning. Using CKM with location information can enable training-free or light-training channel acquisition, but outdated or inaccurate maps remain challenging and may require real-time sensing updates.

1) CKM-assisted single-UAV trajectory design:

  • CKM-guided single-UAV trajectories support cellular links meeting minimum SINR and mission-latency objectives, or UAV-BS paths maximizing throughput over strong LoS links to multiple users.Conventional deterministic or stochastic designs can miss blockage; reinforcement learning has also been used for communications and joint mapping and communication.Source: 1) CKM-assisted single-UAV trajectory… · pp. 32–33

2) CKM-assisted multi-UAV placement design:

  • Derivative-free optimization places multiple UAVs at locations with strong desired links and weak interference links, mitigating co-channel interference and enhancing sum-rate.The method addresses placement optimization without an analytic objective function; the two-UAV example is shown in Fig. 15 [202].Source: 2) CKM-assisted multi-UAV placement… · p. 33, Figure 15 · p. 33

3) Extensions:

  • For ground vehicles and robots, CKM can support predictive communication on predetermined routes or network-controlled mobility optimization, but rich scattering and constrained paths complicate channel prediction and planning.Additional light training may be needed in complex ground-channel environments.Source: 3) Extensions · p. 33

D. Resource Management for Non-cooperative Nodes and Dense Networks

  • CKM can infer channels for non-cooperative primary users or eavesdroppers from their locations, which sensing methods such as radar and cameras can provide.This can support cognitive-radio and secrecy-communication design when direct channel acquisition is difficult.Source: D. Resource Management for… · p. 33
  • For dense D2D networks, CKM-guided link scheduling can reduce co-channel interference, while deep learning can address integer decisions and channel maps lacking analytic forms.Estimating channels across massive links may be costly or infeasible.Source: D. Resource Management for… · pp. 33–34

E. CKM-Assisted Localization and Sensing

  • A LoS map can simplify anchor selection using prior target-location information, and CKM-informed selection can improve localization accuracy measured by the Bayesian Cramér-Rao lower bound.NLoS anchors may fail to improve accuracy or may interfere when their paths are unknown.Source: E. CKM-Assisted Localization and Sensing · p. 34
  • CKM expands fingerprint-based localization with heterogeneous channel data and can improve robustness to environmental dynamics and device variety; its channel information also supports passive obstacle and scatterer localization and sensing.CKM fingerprints can offer higher spatial resolution and more stable, device-independent features than measured RSS; temporal changes can reveal dynamic scatterers and their trajectories.Source: E. CKM-Assisted Localization and Sensing · p. 34

F. Summary

  • Combining CKM’s spatial channel knowledge with node locations can enable low-cost resource allocation with training-free or light-training channel acquisition and predictive resource allocation through path prediction or planning.Outdated or inaccurate CKM remains a challenge; real-time sensing may update maps for robust operation.Source: F. Summary · p. 34

V. OPEN PROBLEMS … VI. CONCLUSION

The article surveys CKM construction and use for environment-aware 6G communications, identifies open research problems, and highlights CKM’s potential role in digital twins and semantic communication.

A. How Much Data Is Sufficient?; C. CKM Based on Heterogeneous Data Sources

  • CKM research needs theories for sufficient location-specific data and methods that account for heterogeneous data sources’ format, granularity, quality, and redundancy.Spatial statistics can model channel-data dependencies; required sample density depends on spatial correlation and sample locations, while location uncertainty can be modeled as a probability distribution.Source: A. How Much Data Is Sufficient? · p. 35, C. CKM Based on Heterogeneous Data… · p. 35

B. CKM in Highly Dynamic Environment

  • For highly dynamic environments, CKM should adapt using sensory information or physical maps to infer prior channel knowledge and distinguish major from minor environmental changes.Radar, lidar, or cameras can reveal people’s and objects’ locations and movement; physical maps can guide CKM updates.Source: B. CKM in Highly Dynamic Environment · p. 35

D. CKM Update with Sequential/Continuous Data Arrival

  • For continuous data arrivals, incremental learning can update CKM without recomputing the map, and Recursive Least Squares provides a computationally efficient, scalable recursive update [209], [210].RLS incorporates new data into the existing CKM without retraining the entire model.Source: D. CKM Update with… · p. 35

E. Privacy and Security Issues

  • Because location data can expose users’ routines and whereabouts, CKM needs privacy protection, such as crowdsourcing or virtual locations with uniqueness, irreversibility, and adjacency invariance.Hashing algorithms can generate virtual locations; crowdsourcing aggregates data from multiple users to make individual locations and activities harder to identify [211].Source: E. Privacy and Security Issues · p. 35

F. CKM with Device Orientation Information

  • Adding device orientation as a CKM dimension can improve channel inference when UE orientation varies, but requires measurements across locations and orientations.The map can be represented as a tensor of Cartesian coordinates and orientation.Source: F. CKM with Device Orientation… · p. 35

G. Prototyping and Experiment Validation

  • In quasi-static and dynamic scenarios, CKM-based training-free mmWave beam alignment matched exhaustive sweeping over 4096 beam pairs and achieved much higher received power than location-only alignment.The prototype uses BIM and UE location to infer transmit–receive beam pairs without channel estimation or beam sweeping.Source: G. Prototyping and Experiment Validation · pp. 35–36

H. CKM for 6G Digital Twin; I. CKM with Semantic Communication

  • CKM can support 6G digital twins as a wireless-environment representation and aid semantic communication through channel semantics and efficient exchange of CKM information, [216].Digital-twin operation requires timely, accurate CKM construction and updates. CKM can inform adaptive JSCC design, while semantic communication can extract essential CKM information to improve transmission efficiency.Source: H. CKM for 6G Digital Twin · p. 36, §I · p. 36

VI. CONCLUSION

  • The article concludes that CKM-enabled environment-aware communication is a promising 6G paradigm shift and calls for further research to realize its potential.The tutorial reviews CKM’s concept, construction and utilization, and discusses open problems for future investigation.Source: §VI · p. 36

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