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3-D Statistical Channel Model for Millimeter-Wave Outdoor Mobile Broadband Communications
Mathew K. Samimi, Theodore S. Rappaport
TL;DR
The paper addresses the need for measured 3-D spatial and temporal channel models for millimeter-wave urban NLOS communications. It develops a 28 GHz New York City statistical model using directional measurements, synthesized absolute timing, and measured angular spectra, reproducing realistic channel statistics for simulation and design.
Problem
Existing statistical models lacked measured elevation data or relied on ray tracing and quasi-omnidirectional measurements, motivating a measured 3-D model for urban NLOS channels.
Method
The paper combines 28 GHz ultrawideband directional measurements, ray-tracing-based absolute timing synthesis, measured AOD/AOA power spectra, and lobe-cluster statistics into a 3-D statistical channel model.
Results
The model recreates measured omnidirectional channel statistics over large ensembles of simulated 3-D channels, including time-cluster and intra-cluster power decay behavior.
Takeaways & Limitations
The resulting model supports millimeter-wave physical-layer simulations, including system-wide studies, air-interface design, and 3-D beamforming and beamcombining simulations.
Abstract
from arXiv · showhide
This paper presents an omnidirectional spatial and temporal 3-dimensional statistical channel model for 28 GHz dense urban non-line of sight environments. The channel model is developed from 28 GHz ultrawideband propagation measurements obtained with a 400 megachips per second broadband sliding correlator channel sounder and highly directional, steerable horn antennas in New York City. A 3GPP-like statistical channel model that is easy to implement in software or hardware is developed from measured power delay profiles and a synthesized method for providing absolute propagation delays recovered from 3-D ray-tracing, as well as measured angle of departure and angle of arrival power spectra. The extracted statistics are used to implement a MATLAB-based statistical simulator that generates 3-D millimeter-wave temporal and spatial channel coefficients that reproduce realistic impulse responses of measured urban channels. The methods and model presented here can be used for millimeter-wave system-wide simulations, and air interface design and capacity analyses.
I. INTRODUCTION
The paper addresses the need for measured 3-D statistical spatial channel models at millimeter-wave frequencies by extending prior 2-D modeling with elevation-aware temporal and angular statistics. It develops the model from extensive 28 GHz New York City measurements using directional antennas and wideband channel sounding.
- Motivation: MmWave statistical spatial channel models are needed to estimate temporal delays, multipath powers, and AOA/AOD information for link- and system-level simulations.The stated need covers both directional and omnidirectional models based on real-world measurements.
- Contribution: The paper presents the first 3-D statistical spatial channel model based on wideband 28 GHz New York City measurements.
- Contribution: The model extends prior 2-D work into a true 3-D formulation containing AOA, AOD, and multipath time statistics derived from measured angular spectra.
- Measurements: The measurement campaign collected over 4,000 directional PDPs across unique azimuth and elevation pointing angles using a 400 Mcps sounder and steerable horn antennas.Measurements covered an 800 MHz RF null-to-null bandwidth at 75 TX-RX locations.
- Measurements: Ray-tracing supplied absolute propagation timing so PDPs measured at different angles could be aligned independently of their AOAs.
III. SYNTHESIZING 3-D ABSOLUTE TIMING OMNIDIRECTIONAL POWER DELAY PROFILES
The paper resolves the lack of absolute timing in independently triggered directional PDPs by combining measured angular PDPs with ray-traced propagation delays. The shifted PDPs are summed into omnidirectional absolute-timing profiles for each TX-RX location.
- Timing problem: Directional PDPs used the strongest arriving component as a relative t = 0 ns trigger, preventing direct recovery of absolute arrival times across angular sweeps.
- Ray-tracing method: A MATLAB-based 3-D ray-tracer predicts first-arrival propagation delays at the strongest measured AOAs for each measured TX-RX location.The predicted and measured strongest directions agreed within ± two antenna beamwidths.
- Synthesis procedure: Measured PDPs are shifted to the ray-traced absolute times and summed across strongest azimuth and elevation AOAs.
- Output: The procedure produces one omnidirectional 3-D absolute-timing PDP for each TX-RX location combination.Orthogonal beam patterns in adjacent pointing angles allow directional PDPs to be combined in time and space.
IV. 3-D STATISTICAL CHANNEL PARAMETERS
The channel impulse response is generalized over absolute time and both transmitter and receiver azimuth/elevation angles. Its multipath components are organized by time clusters and joint AOD-AOA spatial-lobe combinations.
- 3-D impulse response: The model represents the omnidirectional impulse response as a function of absolute propagation time, AOD azimuth/elevation, and AOA azimuth/elevation.
- Model structure: The impulse response is composed of subpaths grouped into time clusters and assigned to transmitter and receiver spatial lobes.
- Multipath parameters: Each subpath is characterized by amplitude, phase, propagation time, and a joint AOD-AOA lobe combination.
- Spatial power spectra: The model generates joint AOD-AOA power spectra by taking the squared magnitude of the impulse response and integrating over time.The resulting lobe powers are total received powers assigned to the AOD and AOA lobes.
A. 28 GHz Omnidirectional NLOS Path Loss Model
The omnidirectional 28 GHz NLOS path-loss model is recovered by summing received powers over all unique TX-RX azimuth/elevation pointing combinations and removing antenna-related counting effects.
- Power recovery: Omnidirectional received power is recovered by summing measurements over every unique azimuth and elevation pointing-angle combination.Antenna gains are removed and double counting from azimuth sweeps is corrected.
- Path-loss model: PL_NLOS(d)[dB] = 61.4 + 34 log10(d) + χσ for d > 1 m.
- Parameters: The shadow factor is σ = 9.7 dB, while 61.4 dB represents 28 GHz free-space path loss at 1 m.
B. Cluster and Lobe Statistics
The model represents temporal multipath with time clusters and spatial energy with spatial lobes, using primary statistics as inputs and secondary statistics to validate simulated channels.
- Time clusters group multipath components close in time across directions, while spatial lobes capture contiguous transmit or receive angular energy spans.
- Multiple time clusters can arrive within one spatial lobe, linking temporal and spatial channel structure.
- Primary statistics include the number of time clusters and cluster power levels used as model inputs.
- Secondary statistics, including RMS delay and angular spreads, evaluate simulator accuracy across many generated channel realizations.
C. Time Cluster Partitioning
Omnidirectional PDPs are partitioned into time clusters using a 25 ns minimum void interval, producing a scalable representation whose temporal details depend on that threshold while RMS delay spread remains unchanged.
- 25 ns separates neighboring multipath groups into time clusters, approximating propagation delays across typical 8 m urban walkways or streets.
- Increasing the inter-cluster void interval reduces time clusters and increases intra-cluster subpaths, redistributing received power between these levels.
- RMS delay spread remains unchanged as the inter-cluster void interval varies, making it suitable for comparing simulated and measured PDP ensembles.
- Cluster powers are obtained from each cluster’s integrated PDP area normalized by total omnidirectional PDP power, then fitted with an exponential model.
- P 0 = 0.883 and Γ = 49.4 ns parameterize the temporal cluster-power decay, while a cluster near τ = 80 ns contains close to 80% of total power.
- P 0 = 0.342 and γ = 16.9 ns indicate that intra-cluster subpaths decay faster than time clusters.
D. 3-D Lobe Thresholding
The model extracts 3-D spatial lobes by thresholding measured angular power spectra relative to their strongest peak and grouping contiguous above-threshold energy.
- A -10 dB threshold below the maximum 3-D power-spectrum peak defines candidate spatial-lobe energy.
- Contiguous segments above threshold in azimuth and elevation form one 3-D spatial lobe.
- Thresholding uses 3-D AOA spectra and 2-D AOD azimuth spectra after linear interpolation of measured directional powers.
V. GENERATING 3-D MMWAVE CHANNEL COEFFICIENTS
The channel-generation procedure combines temporal clusters, spatial lobes, and statistical power assignments to produce joint spatio-temporal millimeter-wave channel coefficients.
- Temporal cluster powers are normalized to total omnidirectional received power and modeled with an exponential decay curve using Γ = 49.4 ns.
- Intra-cluster subpath powers are normalized to time-cluster powers and modeled with an exponential decay curve using γ = 16.9 ns.
- The model bridges temporal and spatial components by randomly assigning temporal subpath powers to spatial-lobe AODs and AOAs.
- The generation steps use discrete uniform and discrete lognormal distributions, with common notation for rounded integer quantities.
A. Step Procedure for Generating Channel Coefficients
The simulator generates temporal and spatial channel coefficients by sampling measured distance, power, cluster, subpath, phase, and 3-D lobe statistics. It then discretizes spatial lobes and assigns angular powers to form the channel representation.
- Initialization: The procedure begins by generating NLOS transmitter–receiver distances from 60–200 m and total received omnidirectional power using a close-in path-loss model.The NLOS path-loss model uses a 1 m reference distance and the omnidirectional path-loss parameters given in the procedure.
- Cluster and lobe counts: Time clusters and spatial lobes are sampled from standard distributions, with at most six time clusters and five AOD or AOA lobes.The mean lobe counts are 1.6 for AOD and 1.7 for AOA, and spatial-lobe counts cannot exceed the number of time clusters.
- Temporal structure: Each time cluster receives a bounded number of subpaths, intra-cluster delays, excess cluster delays, powers, and uniformly random phases.The model uses 30 subpaths for both frequency bands, enforces a 25 ns minimum inter-cluster void, and normalizes subpath powers to cluster powers.
- Power generation: Cluster and subpath powers are generated hierarchically so subpath powers sum to cluster power and cluster powers sum to total omnidirectional received power.The first cluster and first intra-cluster subpath use normalized average powers P0 = 0.883 and Π0 = 0.342, respectively.
- 3-D spatial structure: The model recovers absolute subpath delays from transmitter–receiver separation and assigns subpaths to 3-D spatial lobes using generated AOD and AOA azimuth and elevation angles.Lobe centers, spreads, segment angles, and angular powers are generated separately for departure and arrival directions.
B. Measured vs. Simulated Statistics using a MATLAB-Based Statistical Simulator
A MATLAB-based simulator generated 10,000 millimeter-wave power delay profiles and angular power spectra for comparison with synthesized measurements. Simulated temporal and spatial statistics closely matched the measured distributions.
- Simulation comparison: 10,000 simulated power delay profiles and AOD and AOA power spectra were compared with synthesized and measured channel statistics.The comparison used a MATLAB-based simulator implementing the 3-D statistical spatial channel model.
- Temporal statistics: 31 ns and 32 ns were the median synthesized and simulated omnidirectional RMS delay spreads, respectively.The delay-spread CDF was skewed by one 222.4 ns value, so the median represented the empirical trend.
- Spatial statistics: Simulated RMS lobe azimuth and elevation spreads showed good agreement with measured spreads using a −10 dB lobe threshold.This agreement supports the spatial component of the NLOS statistical channel model.
VI. CONCLUSION
The paper presents a comprehensive 3-D statistical spatial channel model for millimeter-wave NLOS channels. It reproduces measured channel statistics across large simulated ensembles and supports physical-layer and MIMO simulation applications.
- Conclusion: The 3-D statistical channel model recreates measured millimeter-wave NLOS channel statistics over large ensembles of simulated channels.The model is based on thousands of measured power delay profiles and represents both temporal and spatial channel behavior.
- Conclusion: The model can be extended to arbitrary bandwidths and antenna patterns for physical-layer design and 3-D beamforming or beamcombining simulations.The stated applications include MIMO systems operating in NLOS environments.