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A General 3D Non-Stationary Wireless Channel Model for 5G and Beyond

Ji Bian, Cheng-Xiang Wang, Xiqi Gao, Xiaohu You, Minggao Zhang

arXiv:2101.06610v1eess.SP

TL;DR

Existing 5G channel models do not jointly cover the diverse non-stationary, geometric, mobility, and scenario requirements of 5G and B5G systems. This paper proposes a general 3D STF non-stationary GBSM that combines these properties across frequency bands and scenarios, with key statistics compared against standard models and measurements. The resulting B5GCM is presented as generalizable and useful for massive MIMO, HST, V2V, and mmWave-THz communications.

  • Problem

    Standard 5G channel models do not meet all requirements involving multiple bands, large bandwidths, massive MIMO, mobility, 3D propagation, and STF non-stationarity.

  • Method

    The paper develops a general 3D STF non-stationary GBSM combining spherical wavefronts, evolving clusters, spatial consistency, and multi-mobility in a configurable framework.

  • Results

    Key statistics of the B5GCM are derived and compared with standard 5G models and measurement data, showing the model’s generalization and usefulness.

  • Takeaways & Limitations

    The B5GCM can support multiple frequency bands and scenarios, including massive MIMO, HST, V2V, and mmWave-THz communications.

Abstract

from arXiv · show

In this paper, a novel three-dimensional (3D) non-stationary geometry-based stochastic model (GBSM) for the fifth generation (5G) and beyond 5G (B5G) systems is proposed. The proposed B5G channel model (B5GCM) is designed to capture various channel characteristics in (B)5G systems such as space-time-frequency (STF) non-stationarity, spherical wavefront (SWF), high delay resolution, time-variant velocities and directions of motion of the transmitter, receiver, and scatterers, spatial consistency, etc. By combining different channel properties into a general channel model framework, the proposed B5GCM is able to be applied to multiple frequency bands and multiple scenarios, including massive multiple-input multiple-output (MIMO), vehicle-to-vehicle (V2V), high-speed train (HST), and millimeter wave-terahertz (mmWave-THz) communication scenarios. Key statistics of the proposed B5GCM are obtained and compared with those of standard 5G channel models and corresponding measurement data, showing the generalization and usefulness of the proposed model.

I. INTRODUCTION

5G and B5G channel models must represent increasingly diverse frequency bands, large bandwidths, massive arrays, mobility, and three-dimensional non-stationarity. The paper therefore proposes a general 3D STF non-stationary model combining these requirements across multiple scenarios.

  • Channel-modeling requirements: Massive MIMO channels are spatially non-stationary: parameters, statistical properties, angles, delays, and cluster powers can vary along large arrays.Clusters may be visible across the whole array or only over part of it, requiring efficient modeling of spatial non-stationarity.
  • Channel-modeling requirements: V2V and HST channels exhibit temporal non-stationarity, while V2V additionally involves time-varying motion of the transmitter, receiver, and scatterers.V2V clusters can appear, persist, and disappear, and standard models may rely on restrictive scatterer geometries or temporal WSS assumptions.
  • Channel-modeling requirements: mmWave-THz channels require high delay resolution and per-ray spatial, temporal, and frequency characterization because of large bandwidths and frequency non-stationarity.Rays within a cluster may have different arrival times and unequal powers, while simplified time-invariant models cannot capture time evolution.
  • Proposed framework: The proposed B5GCM is a general 3D STF non-stationary channel model configurable for multiple frequency bands and communication scenarios.Its contributions include STF correlation and spectrum functions, spherical-wavefront modeling, cluster evolution, spatial power variation, ellipsoid Gaussian scattering, spatial consistency, and multi-mobility.
  • System characterization: The model describes wireless channels through a space- and time-varying channel impulse response and derives related transfer, correlation, and spectrum functions.The spatial-Doppler variable and corresponding spectrum characterize dispersion across spatial-Doppler frequency, Doppler frequency, and delay domains.
  • System characterization: STF-wide-sense stationarity is obtained only under restricted spatial, temporal, and frequency conditions.Examples include distances below the Rayleigh distance, observation times shorter than the stationary interval, and relative bandwidth typically below 20% of the carrier frequency.

III. THE 3D NON-STATIONARY ULTRA-WIDEBAND MASSIVE MIMO GBSM

The proposed 3D non-stationary ultra-wideband massive-MIMO GBSM represents propagation using large Tx and Rx arrays, paired clusters, and time-varying geometry. It tracks three-dimensional angles, distances, trajectories, and multi-bounce propagation for evolving links.

  • Array geometry: The model deploys large uniform linear arrays at the transmitter and receiver, with antenna spacings δT and δR.The geometry is formulated for a 3D non-stationary ultra-wideband massive-MIMO channel.
  • Propagation structure: Each path is represented by paired transmit-side and receive-side clusters connected through a virtual link.The link may contain additional clusters between the paired clusters, allowing multi-bounce propagation; zero virtual-link delay reduces multi-bounce rays to single-bounce rays.
  • Time evolution: The total number of paths can vary with time for each Tx–Rx antenna pair, while geometric parameters are initialized at time t0.The path count is indexed by the antenna pair and time instant, and the model then describes subsequent temporal variation.
  • Mobility: The model allows the transmitter, receiver, and clusters to change velocities and trajectories over time.Their movements are described using time-dependent speeds and travel azimuth angles.
  • 3D geometry: For each ray, the geometry tracks azimuth and elevation departure and arrival angles for the Tx and Rx clusters.The formulation also defines line-of-sight angles and initial propagation distances for the relevant links.

A. Channel Impulse Response

The channel impulse response combines propagation effects with a 3D, time-varying spherical-wavefront formulation. Its travel-distance model separates plane-wavefront, spherical-wavefront, and non-wide-sense-stationary contributions.

  • Channel formulation: The complete channel matrix combines small-scale fading with path loss, shadowing, blockage, and oxygen absorption.PL, SH, BL, and OL are represented as multiplicative power-level factors.
  • Channel formulation: The small-scale fading matrix represents the channel impulse response between transmit and receive antenna elements.The model includes line-of-sight and non-line-of-sight components with antenna patterns, polarization terms, ray powers, delays, and phases.
  • Non-stationary modeling: The number of clusters, ray powers, and propagation delays vary with both antenna position and time.This explicitly models space- and time-dependent channel evolution for large arrays and high-mobility scenarios.
  • Propagation geometry: The formulation accounts for time-varying transmitter motion and propagation geometry between antenna elements and scatterers.The geometry uses relative motion quantities and travel distances for the transmitter-side and receiver-side links.
  • Non-stationary modeling: The travel-distance expression models 3D spherical wavefront propagation under time-non-stationary conditions using plane-wavefront, spherical-wavefront, and non-WSS terms.The authors describe this formulation as efficient and scalable; the second and third terms represent spatial and temporal non-stationarity.

2) Case II: WSS & SWF:

Under the WSS and SWF case, slow motion or short observation periods suppress the temporal non-WSS contribution, leaving a stationary-in-time model with spherical-wavefront effects.

  • 2) Case II: WSS & SWF:: When v_T t ≪ d_Tmn, the non-WSS term tends to zero and the channel becomes stationary over time.The travel-distance expression consequently reduces to a simpler form.

3) Case III: WSS & PWF:

Under the WSS and PWF case, propagation uses conventional plane-wavefront distances while retaining the model’s line-of-sight and non-line-of-sight transfer-function components.

  • 3) Case III: WSS & PWF:: When the spherical-wavefront and temporal non-stationary terms are simplified, the travel-distance expression becomes the fundamental form used in many existing channel models.This case corresponds to WSS and PWF assumptions.
  • 3) Case III: WSS & PWF:: The Doppler shift is obtained from the time derivative of phase and is time-varying when travel distance changes with motion.The phase contributions include transmitter motion relative to clusters and receiver motion relative to clusters.
  • 3) Case III: WSS & PWF:: The transfer function is obtained by Fourier transforming the channel impulse response with respect to delay.Its line-of-sight and non-line-of-sight components are then written for the considered propagation case.
  • 3) Case III: WSS & PWF:: For B/f_c > 20%, frequency dependence cannot be neglected and the uncorrelated-scattering assumption may not hold.The non-line-of-sight transfer-function model therefore uses frequency-dependent path gain, including an environment-dependent random variable.

B. Space and Time-Varying Ray Power

The model makes ray powers vary across both antenna arrays and time, using a spatial lognormal process to represent smooth large-array power variation.

  • Space and time-varying ray power: Standard 5G models often keep cluster powers constant across antenna elements, whereas this model allows ray powers to vary spatially.The motivation is consistency with measurement results reporting nonconstant powers across arrays.
  • Space and time-varying ray power: A 2D spatial lognormal process models smooth power variation over the transmit and receive arrays.Its local mean accounts for path loss, while a 2D Gaussian process represents shadowing along the large arrays.
  • Space and time-varying ray power: Under conventional receive arrays, the 2D spatial process reduces to a 1D process; setting ξ_n(q,p) = 1 represents the farfield condition at both ends.If cluster delays are unresolvable, ray powers can instead be generated from a cluster delay and equally assigned within the cluster.

C. Unified Space-Time Evolution of Clusters

The model represents cluster evolution jointly across time and antenna-array axes using a unified birth-death process. This formulation accounts for shared cluster visibility across transmitter and receiver arrays and scenario-dependent correlation behavior.

  • Unified evolution: Cluster evolution is modeled uniformly across time and array axes using probabilities of cluster survival and generation.The formulation includes transmitter- and receiver-side persistence over time intervals and antenna-element spacings.
  • Birth-death process: The cluster-generation and recombination rates are linked to scenario characteristics and antenna patterns.These rates determine the mean number of newly generated clusters and cluster disappearance behavior.
  • Correlation parameters: For the transmitter side, εT_2 represents position differences across the array and time, while D_A and D_c characterize scenario-dependent correlation factors.Typical correlation-distance values such as 10 m and 30 m are provided.
  • Joint visibility: A cluster contributes to received power only when it is visible to at least one transmitter antenna and one receiver antenna.The joint existence probability combines transmitter- and receiver-side cluster visibility over time and antenna spacing.

D. Ellipsoid Gaussian Scattering Distribution

The ellipsoid Gaussian scattering distribution models unequal angular, elevation, and delay dispersions while preserving cluster orientation and spread parameters after coordinate transformation. Theoretical and Monte Carlo results show good consistency for the modeled distribution.

  • Distribution model: The Gaussian scattering model represents unequal cluster angular, elevation, and delay dispersions using CAS, CES, and CDS.Measurements motivate unequal spatial dispersions within a cluster rather than a single isotropic shape.
  • Coordinate transformation: The scatterer distribution is shifted from the origin to a cluster center defined by distance d and mean elevation and azimuth angles φE and φA.The transformation places scatterers around spherical coordinates (d, φE, φA).
  • Coordinate transformation: The transformation preserves cluster orientation toward the transmitter or receiver, keeping CDS, CAS, and CES unchanged.The resulting angle-distance joint distribution follows from substituting the spherical-coordinate expressions into the scatterer model.
  • Single-bounce propagation: For single-bounce rays, the delay-angle joint distribution is obtained by transforming the cluster-center distance parameter d into delay τ.The single-bounce case follows by setting the multi-bounce delay contribution to zero.
  • Spatial consistency: Physically persistent cluster locations provide spatial consistency and support CSI prediction from nearby users or previous time snapshots.This differs from models that randomly generate clusters independently for every link.
  • Validation: Theoretical and simulated distributions agree well for σDS = 8, σAS = 10, σES = 6, d ∼ N(100, 10) m, and 500 Monte Carlo rays.The comparison uses an urban micro-cell NLoS setting for the mean angles.

A. Local STF-CF

The local STF correlation function characterizes channel similarity across space, time, and frequency, including line-of-sight and non-line-of-sight components. Specializing the coordinate differences recovers stationary cases in selected domains.

  • Correlation definition: The local STF-CF is defined between channel responses separated by spatial, temporal, and frequency offsets.Its formulation is further expanded by substituting the channel expression into the correlation definition.
  • Correlation components: The STF-CF separates line-of-sight and non-line-of-sight contributions and incorporates cluster survival, spatial displacement, and frequency-dependent terms.The component expressions include the joint cluster-survival probability and a coefficient associated with wave propagation.
  • Stationary reduction: Under stationary assumptions, setting cluster survival to one, γmn to zero, and amn to 1/Mn removes the corresponding non-stationary and spherical-wavefront terms.The resulting expression assumes irresolvable delays within a cluster.
  • Stationary reductions: Setting Δf = 0 removes frequency selectivity and yields a correlation function that is wide-sense stationary in space and time.Setting Δt = 0 and Δr = 0 instead yields wide-sense stationarity in frequency.
  • Spatial-Doppler PSD: The local spatial-Doppler power spectral density is obtained by Fourier transforming the spatial correlation function with respect to spatial displacement Δr.It describes average-power distribution over the spatial-Doppler frequency axis at a specified antenna, time, and frequency.

C. Local Doppler Spread

The B5GCM models Doppler behavior as time-varying when the transmitter, receiver, and scatterers move, and its predicted Doppler spread agrees with analytical results and measurements. The model also captures associated space-frequency non-stationarity and array-dependent effects.

  • Local Doppler Spread: The local Doppler spread is calculated from the model’s instantaneous Doppler-frequency expression.The instantaneous frequency is obtained from the channel phase change and then used to derive Doppler spread.
  • Local Doppler Spread: Time-varying transmitter, receiver, and scatterer motion makes the instantaneous Doppler frequency non-stationary.The model separates conventional stationary Doppler terms from additional terms caused by time variation.
  • Model Validation: The model’s broader validation compares spatial, temporal, and frequency statistics with measurements, including spatial-Doppler spectra and cluster evolution.These comparisons include spatial correlation functions, VR length, cluster-power variation, and array-dependent spatial-Doppler behavior.
  • Local Doppler Spread: Good consistency is observed among the simulated, analytical, and measured Doppler spreads across effective speeds.The measurements were conducted at 5.9 GHz in highway, rural, and suburban environments, with effective speed defined from transmitter and receiver velocities.
  • Local Doppler Spread: Nonzero Doppler spread at zero effective speed arises from scatterer motion and is absent from models assuming static clusters.This distinguishes the proposed treatment from channel models that do not include moving scatterers.

VI. CONCLUSIONS

The paper proposes a general 3D STF non-stationary GBSM applicable across multiple (B)5G scenarios and incorporating key channel characteristics. Its framework supports scenario-specific simplification, while derived statistics and measurement validation indicate generalization and usefulness.

  • The proposed model integrates SWF, cluster power variation, scatterer-induced Doppler shifts, time-variant motion, and spatial consistency.
  • The model applies to massive MIMO, HST, V2V, and mmWave-THz communication scenarios.
  • The general framework can reduce to simplified models for specific scenarios or extend to new scenarios through appropriate parameter settings.
  • Key statistics are derived, with some validated against measurement data, illustrating the model’s generalization and usefulness.
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