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A General 3D Non-Stationary 5G Wireless Channel Model
Shangbin Wu, Cheng-Xiang Wang, el-Hadi M. Aggoune, Mohammed M. Alwakeel, Xiao-Hu You
TL;DR
The paper addresses the need for channel models that capture small-scale fading across major 5G scenarios and their evolving spatial-temporal characteristics. It proposes a unified 3D non-stationary GBSM combining WINNER II and Saleh-Valenzuela modeling, and reports good agreement between simulated statistical properties and corresponding measurements.
Problem
Existing channel models do not uniformly capture the small-scale fading characteristics of massive MIMO, V2V, HST, and mmWave scenarios, including continuous cluster evolution.
Method
The paper combines WINNER II and Saleh-Valenzuela models in a 3D non-stationary GBSM with array-time cluster evolution and time-varying channel parameters.
Results
Simulated statistical properties fit corresponding measurements well across the modeled scenarios, including massive MIMO, HST, and V2V channel characteristics.
Takeaways & Limitations
The general GBSM can represent multiple 5G channel scenarios and can be reduced to simplified models by adjusting model parameters.
Abstract
from arXiv · showhide
A novel unified framework of geometry-based stochastic models (GBSMs) for the fifth generation (5G) wireless communication systems is proposed in this paper. The proposed general 5G channel model aims at capturing small-scale fading channel characteristics of key 5G communication scenarios, such as massive multiple-input multiple-output (MIMO), high-speed train (HST), vehicle-to-vehicle (V2V), and millimeter wave (mmWave) communication scenarios. It is a three-dimensional (3D) non-stationary channel model based on the WINNER II and Saleh-Valenzuela (SV) channel models considering array-time cluster evolution. Moreover, it can easily be reduced to various simplified channel models by properly adjusting model parameters. Statistical properties of the proposed general 5G small-scale fading channel model are investigated to demonstrate its capability of capturing channel characteristics of various scenarios, with excellent fitting to some corresponding channel measurements.
I. INTRODUCTION
The paper proposes a unified 3D non-stationary 5G GBSM to represent massive MIMO, V2V, HST, and mmWave small-scale fading while addressing time and array evolution.
- Research gap: Existing models often omit cluster evolution over time, making continuous channel tracking difficult.This limitation is identified for several METIS, 3GPP NR, IMT-2020, and V2V models.
- Motivation and scope: The model targets 5G scenarios including massive MIMO, V2V, HST, and mmWave communications.These scenarios involve large arrays, mobility, high carrier frequencies, and broad bandwidths.
- Model design: The proposed GBSM combines WINNER II and Saleh-Valenzuela models to support time-varying parameters and high delay resolution.It includes spherical wavefronts, array-time cluster birth-death processes, geometric updates, and ray-power updates.
- Model flexibility: The general model can be reduced to simplified channel models by setting appropriate channel parameters.The paper demonstrates this reduction by fitting statistical properties to corresponding channel measurements.
- Model design: The model supports arbitrary antenna array layouts and allows each antenna to observe its own cluster set.This design represents spherical wavefronts and cluster appearance or disappearance across massive MIMO arrays.
A. Channel Impulse Response
The channel impulse response is represented as a time- and delay-dependent MIMO matrix whose entries combine LOS and NLOS components with evolving clusters and resolvable rays.
- Channel representation: The channel at time t and delay τ is an MR × MT matrix H(t, τ) with LOS and NLOS components.Each matrix entry is the channel impulse response between one receive and one transmit antenna.
- NLOS component: The NLOS component sums contributions from a time-varying number of clusters and rays with cluster and relative-ray delays.Each resolvable ray has its own complex gain and delay, supporting mmWave high time resolution.
- LOS component: The model computes LOS delay from the time-dependent LOS distance divided by the speed of light.The delay is τ_LOS(t) = ∥D(t)∥/c.
- NLOS component: A cluster contributes to an antenna pair only when it is observable; otherwise its complex channel gain is zero.Cluster observability is represented through antenna-specific cluster sets.
- Parameter generation: Virtual cluster delays are exponentially distributed, while cluster parameters and ray parameters are generated according to specified model distributions.The virtual delay represents the link between the first and last cluster bounces.
B. Array-Time Cluster Evolution for the General 3D 5G GBSM
The model evolves clusters across antenna arrays and time using a birth-death process, updating surviving clusters and generating new ones at each time step.
- The unified framework uses a birth-death process for array-time cluster evolution, with generation and recombination rates λG and λR.The algorithm is based on an earlier procedure but adds mean power evolution and ray updates.
- At time t, the algorithm generates an initial cluster set before entering iterative time evolution.
- At t + ∆t, clusters evolve using survival probabilities calculated from mean relative velocities rather than cluster-specific velocities.This simplification applies the mean relative velocities of clusters to compute survival probabilities.
- Surviving clusters are updated geometrically, while new clusters are generated according to a Poisson distribution and assigned rays and geometrical parameters.
- The procedure returns to the next time instant after array-time evolution is completed.
C. Generation of New Clusters
New clusters receive stochastic delay, power, angular, and ray parameters, then are assigned to antennas according to spatial visibility conditions.
- New clusters are assigned ray counts, virtual delays, mean powers, angular parameters, and relative ray delays from distributions listed in Table II.Virtual cluster delays follow an exponential distribution associated with the WINNER II model.
- The virtual-delay generation uses scenario-dependent delay scalars and randomly generated delay spreads for NLOS urban outdoor and indoor office scenarios.
- Angular parameters use wrapped Gaussian distributions for cluster angles, while ray angular offsets follow zero-mean Laplace distributions.The stated angular-offset standard deviation is 1 degree (0.017 radian), subject to modification using measurements.
- Ray mean powers are generated separately from cluster powers and then scaled by the corresponding cluster power.
- The new cluster generation procedure is documented with pseudocode in Fig. 3.
- A newly generated cluster is propagated across receive antennas by selecting an initial antenna, constructing a 3D ball, and testing antenna distances against a normalized spacing coefficient.
D. Evolution of Survived Clusters
Surviving clusters are updated from t to t+∆t through changes in antenna positions, geometry, delays, and mean powers, with smoothing applied when clusters appear or disappear.
- The model updates geometrical relationships, virtual delays, and mean powers of survived clusters between consecutive time instants.
- Antenna position vectors and cluster distance vectors are adjusted as part of the time-evolution procedure.
- Virtual delays retain information from the previous time instant through a coherence-controlled update involving an identically distributed random variable.The coherence parameter has typical values of 5 s, 7 s, and 30 s under the stated assumptions.
- Cluster mean powers evolve under an inverse square law rather than remaining constant.The resulting mean power terms are normalized before being used in the channel model.
- Cluster powers are linearly scaled over 1 ms when clusters disappear or appear, transitioning respectively to zero or from zero.The transition duration is aligned with one LTE subframe for system-level simulations.
E. Simplified Channel Models
The general channel model can produce simplified channel models by adjusting antenna, velocity, delay, and elevation parameters.
- The general 3D non-stationary 5G GBSM reduces to simplified channel models through suitable parameter adjustments.
- Using relatively few transmit and receive antennas makes spherical-wavefront and array-axis cluster-evolution effects insignificant, yielding conventional MIMO.
- Setting transmitter velocity vT = 0 reduces the V2V model to a fixed-to-mobile channel model.
- Setting relative ray delays τmn = 0 makes within-cluster rays irresolvable in delay and produces an SCM-like wideband mmWave model.
- Setting all elevation angles to zero removes elevation effects and reduces the 3D model to 2D.
A. Time-Variant Power Delay Profile (PDP)
The model represents the channel through a time-variant power delay profile and derives correlation functions that account for evolving scattering geometry and clusters. Its space-time-frequency correlation function reduces to time, spatial, or frequency correlations under specific parameter settings.
- Time-Variant PDP: The time-variant PDP Λ(t, τ) captures all observable clusters across transmit and receive arrays.Its time variation arises from time-dependent ray powers and delays caused by updates to the scattering geometry.
- Stationary Interval: The proposed stationary interval measures the maximum duration over which the PDP autocorrelation remains above an 80% threshold.An improved definition addresses nonmonotonic autocorrelation functions and multiple threshold crossings.
- Transfer Function: The time-variant transfer function Hqp(ξ, t) is obtained by Fourier transforming the channel impulse response with respect to delay.Here, ξ denotes frequency.
- Correlation Modeling: The STFCF combines LOS and NLOS correlation contributions while assuming the two components are uncorrelated.The LOS term depends on transmitter-receiver relative position, whereas NLOS correlation accounts for surviving clusters.
- Cluster Evolution: Newly generated clusters are independent of survived clusters and therefore do not contribute to the correlation coefficient.Cluster survival probability determines the mean number of clusters shared across channel states.
- Correlation Reductions: The STFCF specializes to the time-variant ACF, receive or transmit space CCF, and time-variant FCF by fixing selected antenna, time, and frequency offsets.These reductions provide lower-dimensional correlation functions from the general formulation.
IV. RESULTS AND ANALYSIS
The simulations validate the proposed model against analytical results, measurements, and WINNER II across conventional MIMO, massive MIMO, HST, V2V, and mmWave scenarios. The model generally fits measured channel statistics while capturing effects that WINNER II omits.
- Conventional MIMO: The simulated ACFs align well with the analytical ACFs for both clusters in the wideband conventional MIMO model.The comparison uses normalized ACFs for Cluster1 and Cluster2.
- Massive MIMO: The proposed massive MIMO space CCF aligns with measurements for antenna index differences below 3, whereas WINNER II overestimates antenna correlations.The proposed model’s cluster evolution on the array axis accounts for this difference.
- HST: The HST model has a median stationary interval of approximately 40 ms and fits the measurement result well.WINNER II predicts a much higher stationary interval because it lacks cluster power evolution in time.
- V2V: The V2V model’s 90% coherence-bandwidth distribution is validated against suburban measurements, while WINNER II exhibits a smaller spread.The smaller WINNER II spread is attributed to its time-invariant PDP.
- mmWave: The mmWave angular power spectrum shows few clusters and cluster appearance or disappearance along the massive-MIMO array axis.The spectrum is estimated with the smooth MUSIC algorithm using a sliding window of three consecutive antennas.
- mmWave: The mmWave model fits measured RMS delay-spread distributions, whereas WINNER II overestimates RMS delay spread and shows smaller variations.The modeled mmWave RMS delay spread ranges from 20 ns to 50 ns.
V. CONCLUSIONS
The paper proposes a unified general 3D non-stationary 5G channel model covering several key scenarios and incorporating channel evolution over time. Its statistical properties fit corresponding measurements, and parameter settings allow reduction to simplified models.
- The unified 3D non-stationary model covers massive MIMO, V2V, HST, and mmWave communication scenarios.It is based on the WINNER II and Saleh-Valenzuela channel models.
- Channel time evolution models cluster evolution, geometrical relationship updates, and the evolution of ray delays and powers.
- The simulated statistical properties fit the corresponding channel measurements well.
- Proper parameter settings reduce the general 5G GBSM to various simplified channel models.
- Future work includes applying the model to 5G system simulators and estimating its parameters from more channel measurements.
APPENDIX A CALCULATION OF ANTENNA PATTERNS IN (9)
The appendix computes antenna patterns in three-dimensional geometry by rotating between global and local coordinate systems, transforming directions, and applying antenna-specific gains. It also describes time-varying ray-power evolution under an inverse power-law assumption.
- Antenna-pattern calculation: Antenna orientation is represented by sequential rotations from the GCS to the LCS about the global and rotated coordinate axes.The rotations use αT, βT, and γT.
- Antenna-pattern calculation: Direction vectors are transformed into LCS coordinates, from which four-quadrant inverse tangent functions obtain the local angular variables.The local angles are then used to evaluate antenna patterns.
- Antenna-pattern calculation: The horizontal and vertical antenna patterns combine the antenna gain G(˜θ, ˜φ) with cos ˜θ and sin ˜θ, respectively.Dipole antennas are assumed at the transmitter, while omnidirectional antennas are assumed at the receiver.
- Antenna-pattern calculation: The transmitter and receiver antenna gains may be replaced by those of the actual antennas used.The rotation angles are set to 15 for simplicity but can be modified for realistic settings.
- Ray-power evolution: Ray mean-power evolution is derived between nearby time instants from the inverse power-law dependence on travel distance.The model uses η = 2, following the inverse square law.
- Antenna-pattern calculation: The coordinate-rotation matrix includes the standard γT rotation in the xG-yG plane.
APPENDIX C PARAMETER ESTIMATION PROCEDURE OF THE PROPOSED
The parameter-estimation procedure fits the proposed channel model directly to measured statistical properties through iterative channel generation, error computation, and parameter updates. Parameters are estimated by minimizing the discrepancy between measured and model statistics.
- Parameter estimation: Parameters are estimated by minimizing differences between statistical properties from the model and measurements.The procedure directly estimates parameters to fit channel statistics.
- Parameter estimation: The estimated parameter vector can be obtained with optimization methods such as exhaustive search.The objective minimizes the squared discrepancy between measured and model statistical properties.
- Iterative procedure: The procedure initializes parameters, generates channel coefficients, and calculates the resulting statistical property.
- Iterative procedure: The model computes the squared error between generated and measured statistical properties.
- Iterative procedure: Parameters are output when the error is at most the target threshold; otherwise, a new parameter set is generated and the process repeats.