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Pervasive wireless channel modeling theory and applications to 6G GBSMs for all frequency bands and all scenarios
Cheng-Xiang Wang, Zhen Lv, Xiqi Gao, Xiaohu You, Yang Hao, Harald Haas
TL;DR
6G channel modeling must combine diverse channel characteristics across mixed technologies, frequency bands, and scenarios within a realistic unified framework. This paper proposes pervasive channel modeling theory and applies it to a 3D STF non-stationary GBSM, whose 6GPCM models broad 6G conditions and agrees with simulations and measurements.
Problem
6G channel modeling needs a unified framework that combines diverse characteristics, including STF non-stationarity and spatial consistency, across mixed applications and scenarios.
Method
The paper proposes pervasive wireless channel modeling theory and applies it to a 3D GBSM, forming the 6GPCM with unified CIR modeling across spectra and scenarios.
Results
The 6GPCM’s derived and simulated statistical properties show good agreement with channel measurements across selected frequency bands and scenarios, including UAV, maritime, and massive MIMO channels.
Takeaways & Limitations
By adjusting model parameters, the 6GPCM can represent specific frequency-band or scenario models and includes standard 5G channel models as special cases.
Abstract
from arXiv · showhide
In this paper, a pervasive wireless channel modeling theory is first proposed, which uses a unified channel modeling method and a unified equation of channel impulse response (CIR), and can integrate important channel characteristics at different frequency bands and scenarios. Then, we apply the proposed theory to a three dimensional (3D) space-time-frequency (STF) non-stationary geometry-based stochastic model (GBSM) for the sixth generation (6G) wireless communication systems. The proposed 6G pervasive channel model (6GPCM) can characterize statistical properties of channels at all frequency bands from sub-6 GHz to visible light communication (VLC) bands and all scenarios such as unmanned aerial vehicle (UAV), maritime, (ultra-)massive multiple-input multiple-output (MIMO), reconfigurable intelligent surface (RIS), and industry Internet of things (IIoT) scenarios. By adjusting channel model parameters, the 6GPCM can be reduced to various simplified channel models for specific frequency bands and scenarios. Also, it includes standard fifth generation (5G) channel models as special cases. In addition, key statistical properties of the proposed 6GPCM are derived, simulated, and verified by various channel measurement results, which clearly demonstrates its accuracy, pervasiveness, and applicability.
I. INTRODUCTION
The paper addresses the challenge of modeling diverse 6G channel characteristics within one framework. It proposes pervasive channel modeling theory and a 6GPCM that spans frequency bands, scenarios, and model specializations.
- Research gap: 6G channel modeling must combine mixed frequency-, space-, and scenario-dependent characteristics while balancing accuracy, complexity, and pervasiveness.Examples include STF non-stationarity, spatial consistency, blockage, absorption, spherical wavefronts, RIS cascades, and multi-mobility.
- Research gap: Existing B5G and standard 5G models do not jointly capture all-spectra and all-scenario channel properties.Reported omissions include VLC, frequency non-stationarity, gas absorption, and blockage effects.
- Proposed approach: The paper proposes a unified channel modeling framework and CIR equation for important channel characteristics across all frequency bands and scenarios.The framework is intended to remain adaptable through channel model parameters.
- Proposed approach: The 6GPCM applies this theory within a GBSM framework and covers spectra from sub-6 GHz to VLC, global-coverage scenarios, and full-application scenarios.Covered examples include LEO satellite, UAV, maritime, UHST, massive MIMO, RIS, and IIoT channels.
- Model flexibility: Adjusting channel model parameters reduces the 6GPCM to specific frequency-band or scenario models and includes standard 5G models as special cases.The model is designed to support multiple links, frequencies, antenna arrays, and spatial consistency.
- Model construction: The model constructs spatially correlated LSPs, generates ellipsoid Gaussian scattering clusters, and derives ray delays and angles from moving geometries at each snapshot.This geometry-based procedure supports changing transmitter, receiver, and cluster locations.
A. CIR
The CIR formulation combines large-scale fading and small-scale fading within a unified channel matrix, while adapting propagation components to different scenarios and frequency bands.
- Unified CIR: The complete channel matrix combines path loss, shadowing, blockage, weather effects, atmospheric absorption, and small-scale fading.Large-scale fading factors are calculated at the power level.
- Unified CIR: Small-scale fading is represented by a MIMO CIR matrix formed from superposed line-of-sight and non-line-of-sight components.The formulation includes K-factor, antenna patterns, polarization terms, cross-polarization power ratio, and random initial phases.
- Scenario adaptations: Faraday rotation is included for ionospheric propagation in LEO satellite scenarios and set to zero when ionospheric influence is not considered.The rotation angle depends on carrier frequency according to the stated model expression.
- Scenario adaptations: Maritime channels model line-of-sight propagation plus multipath from the rough ocean surface and evaporation duct, with power-control factors governing component appearance and disappearance.The factors vary with the distance between ships and satisfy S1+S2 = 1.
- Scenario adaptations: IIoT channels include line-of-sight, specular multipath, and dense multipath components, with dense multipath representing smaller scatterers near specular components.The paper states that considering dense multipath can significantly improve channel-model accuracy.
- VLC specialization: In VLC bands, the model sets Hs = 1 and focuses on path loss and shadowing because incoherent optical signals have no phase and no small-scale fading.The VLC channel is therefore treated as a large-scale model with real-valued optical power signals.
B. Generation of Spatially Correlated LSPs
The model generates spatially correlated large-scale parameters by combining frequency- and position-dependent statistics with Gaussian-process variation. It also adapts reference parameters to user-terminal height, scenario, and link elevation.
- Large-scale parameters include delay spread, K-factor, shadowing, elevation and azimuth spreads, and cross-polarization ratio.
- Delay spread is generated from a Gaussian process using frequency-specific mean DSµ,fc and standard deviation DSσ,fc.
- Spatially correlated variation XDS(P)~N(0,1) preserves parameter continuity within the correlation distance dcorr DS.
- Reference delay-spread parameters vary with user-terminal height, using distinct terrestrial, UAV, and LEO satellite scenario configurations.
- The model considers spatial consistency, carrier frequency, user-terminal altitude, and link elevation when generating LSPs.
C. STF Cluster Evolution
STF non-stationarity arises from continuously varying channel parameters and cluster birth-death processes across spatial, temporal, and frequency axes. The model defines survival, generation, recombination, and sampling mechanisms for cluster evolution.
- STF non-stationarity results from varying parameters and cluster birth-death processes across three axes.
- The cluster count satisfies N(t)=Nsurv(t)+Nnew(t), combining surviving and newly generated clusters.
- Birth-death evolution uses channel sampling intervals for continuous updates and larger birth-death intervals for cluster appearance and disappearance.
- Clusters contribute received power only when visible to at least one transmit and one receive antenna element in the same frequency bin.
- Newly generated cluster counts follow a Poisson distribution, while vacuum-tube UHST scenarios additionally account for waveguide effects.
D. Generation of New Clusters
When a cluster is newly generated, the model assigns its position, delay, angle, and power parameters.
- New clusters receive assigned position, delay, angle, and power parameters at their generation time t0.
1) Position of the Ray:
The model represents rays through distributed scatterer geometry, multi-bounce delays, frequency-dependent power, and spatially varying massive-MIMO power processes. These mechanisms support 3D, multi-frequency, and non-stationary channel construction.
- 1) Position of the Ray:: Scatterers within each cluster follow an ellipsoid Gaussian distribution around a cluster center, with axis-specific standard deviations.
- 1) Position of the Ray:: Ray geometry is converted to spherical coordinates, yielding distances, azimuth angles, and elevation angles at the transmitter or receiver.
- 1) Position of the Ray:: In multi-bounce paths, ray delay combines the transmitter-to-cluster distance with a virtual-link delay based on inter-cluster distance and an exponentially distributed non-negative link delay.
- 1) Position of the Ray:: Massive-MIMO ray power varies over time and antenna-array axes through temporal and two-dimensional spatial lognormal processes.
- 1) Position of the Ray:: For large bandwidths, a frequency-dependent factor modifies power before normalization makes the cluster powers sum to one.
- 1) Position of the Ray:: Across carrier frequencies, ray delays and angles are generated from an anchor frequency, while multi-frequency correlation is mainly represented through power.
E. Evolution of Survived Clusters
The model evolves surviving scattering clusters over successive time instants using updated transmitter, receiver, and scatterer geometry. Spherical-wave relations then provide antenna-pair-specific propagation parameters with improved spatial resolution.
- E. Evolution of Survived Clusters: Surviving clusters require updated scatterer parameters at each successive time instant.The model uses trajectory-segment geometry and previous-time positions to update delays and powers.
- E. Evolution of Survived Clusters: At each time instant, delays and powers are obtained from the geographical positions of transmitters, receivers, and scatterers.The procedure recursively uses positions from the preceding corresponding time instant.
- E. Evolution of Survived Clusters: Spherical-wave propagation derives antenna-pair-specific SSPs from geometric relations among transmitters, receivers, and scatterers.This mechanism accounts for ray-angle drift across the antenna array.
- E. Evolution of Survived Clusters: The geometry-based SSP calculation is closer to reality and increases the 6GPCM's spatial resolution.
F. Simplified Channel Models
The 6GPCM can represent simplified channel models by adjusting its parameters, while RIS modeling separates the channel into three sub-channels and combines them into a whole channel matrix.
- F. Simplified Channel Models: The 6GPCM is reduced to specific frequency-band or scenario models by adjusting channel model parameters.Table III lists simplified models derived from the 6GPCM under particular parameter settings.
- F. Simplified Channel Models: RIS scenarios divide propagation into Tx–RIS, RIS–Rx, and direct Tx–Rx sub-channels.The channel matrices for the three sub-channels are calculated using the same process as the general channel formulation.
- F. Simplified Channel Models: The RIS channel formulation uses a reflecting-coefficients matrix and a Tx steering vector to form the whole channel matrix.The three component matrices are denoted HIR, HTI, and HTR.
- F. Simplified Channel Models: The framework includes single-link, single-frequency and scenario-specific reductions through constraints on model parameters and channel characteristics.The supplied reductions cover global-coverage and full-application scenarios.
RIS [47]
The RIS formulation treats the channel as three sub-channels and evaluates space-time-frequency correlation through reductions of the STFCF. These reductions yield spatial, temporal, and frequency correlation functions.
- RIS [47]: The STFCF characterizes correlation between channel transfer functions separated in space, time, and frequency.The formulation uses statistical averaging and complex conjugation in the correlation calculation.
- RIS [47]: Setting time and frequency intervals to zero reduces the STFCF to a spatial cross-correlation function.The spatial reduction retains antenna-index variation across the channel transfer functions.
- RIS [47]: Setting the appropriate intervals and antenna indices to zero reduces the STFCF to temporal ACF or frequency correlation function.Temporal ACF uses identical antenna indices, while FCF uses zero time and spatial separations.
B. Delay Power Spectrum Density (PSD)
The delay PSD is obtained by inverse Fourier transforming the frequency correlation function and describes time-frequency-dependent ray delays and powers. Related channel variation is also characterized through Doppler PSD and stationary intervals.
- B. Delay Power Spectrum Density (PSD): The delay PSD is the inverse Fourier transform of the frequency correlation function with respect to frequency interval.It is also called the power delay profile or multipath intensity profile.
- B. Delay Power Spectrum Density (PSD): The delay PSD reflects time-frequency-dependent delay and power characteristics for rays between transmitting and receiving antenna elements.
- B. Delay Power Spectrum Density (PSD): Ray power evolves with clusters over time and frequency, thereby affecting the delay PSD.Pqp,mn,fc(t, f) denotes the power of the corresponding ray.
- B. Delay Power Spectrum Density (PSD): The Doppler PSD is the Fourier transform of the temporal autocorrelation function with respect to the time interval.The transform variable is Doppler frequency υ.
- B. Delay Power Spectrum Density (PSD): The stationary interval is the largest duration over which the correlation coefficient of two delay PSDs exceeds a threshold, usually 0.8.It evaluates channel time variation using the local region of stationarity method.
E. Singular Value Spread (SVS)
The 6GPCM’s statistical properties are evaluated across frequency bands and scenarios, with simulations generally matching measurement data and illustrating scenario-dependent channel behavior.
- THz and VLC channels: The model also fits measurements for THz relative azimuth angles and VLC channel 3-dB bandwidths under varied conditions.The THz comparison uses a 300 GHz indoor setting, while the VLC comparison varies receiver field of view.
- UAV channels: In UAV-to-ground channels, faster UAV motion and smaller UAV–Rx distance produce shorter stationary intervals.The model attributes stronger channel fluctuation near the receiver to more dramatic angular-parameter changes.
- Maritime channels: The 6GPCM’s maritime ship-to-ship normalized Doppler PSD agrees well with measurements during ship-passing events.The simulation uses a ship speed of 7 m/s, within the 2–7 m/s measurement range.
- Ultra-massive MIMO: Increasing the receiver antenna count lowers SVS and makes channel vectors among users more orthogonal in ultra-massive MIMO.Simulation results with MR increased to 128 correspond well with measurements and indicate increasingly evident channel hardening.
- IIoT channels: RMS delay spread simulations match IIoT measurements, with larger spreads in NLoS than LoS and in heavy clutter than light clutter.The comparison covers light-clutter Scenario A and heavy-clutter Scenario B.
VI. CONCLUSIONS
The paper proposes a pervasive wireless channel modeling theory and applies it to construct the 6GPCM. The model covers diverse spectra and scenarios, reduces to standard 5G models through parameter adjustment, and shows good agreement with channel measurements.
- The paper proposes a pervasive wireless channel modeling theory and applies it within a GBSM to construct the 6GPCM.
- The 6GPCM represents important channel characteristics across all spectra, global-coverage scenarios, and full-application scenarios.
- Adjusting channel model parameters simplifies the 6GPCM to standard 5G channel models.
- Derived and simulated statistical properties show good fits with measurements at specific frequency bands and scenarios.