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Small-Scale, Local Area, and Transitional Millimeter Wave Propagation for 5G Communications

Theodore S. Rappaport, George R. MacCartney, Shu Sun, Hangsong Yan, Sijia Deng

arXiv:1707.07816v2cs.IT

TL;DR

The paper addresses how mmWave propagation changes during mobility, a gap relevant to handoffs, beam steering, and MIMO. It combines propagation measurements with diffraction, blockage, fading, autocorrelation, and local-area channel models, finding substantial blockage and diffraction losses alongside short spatial decorrelation distances and measurable channel transitions.

  • Problem

    Small-scale wideband mmWave behavior as mobile users move through local areas is insufficiently known, although it matters for handoff and beam-steering design.

  • Method

    The paper measures propagation from 10 to 73 GHz and evaluates KED, creeping-wave, DKED, fading-distribution, autocorrelation, and local-area channel models.

  • Results

    The measurements show diffraction and blockage losses up to 30 dB indoors, 40 dB or more outdoors, and more than 40 dB for human blockage, while spatial decorrelation spans 0.27 cm to 13.6 cm.

  • Takeaways & Limitations

    The findings support modeling small-scale fading, spatial consistency, handoff behavior, and beam steering using environment- and antenna-dependent propagation characteristics.

Abstract

from arXiv · show

This paper studies radio propagation mechanisms that impact handoffs, air interface design, beam steering, and MIMO for 5G mobile communication systems. Knife edge diffraction (KED) and a creeping wave linear model are shown to predict diffraction loss around typical building objects from 10 to 26 GHz, and human blockage measurements at 73 GHz are shown to fit a double knife-edge diffraction (DKED) model which incorporates antenna gains. Small-scale spatial fading of millimeter wave received signal voltage amplitude is generally Ricean-distributed for both omnidirectional and directional receive antenna patterns under both line-of-sight (LOS) and non-line-of-sight (NLOS) conditions in most cases, although the log-normal distribution fits measured data better for the omnidirectional receive antenna pattern in the NLOS environment. Small-scale spatial autocorrelations of received voltage amplitudes are shown to fit sinusoidal exponential and exponential functions for LOS and NLOS environments, respectively, with small decorrelation distances of 0.27 cm to 13.6 cm (smaller than the size of a handset) that are favorable for spatial multiplexing. Local area measurements using cluster and route scenarios show how the received signal changes as the mobile moves and transitions from LOS to NLOS locations, with reasonably stationary signal levels within clusters. Wideband mmWave power levels are shown to fade from 0.4 dB/ms to 40 dB/s, depending on travel speed and surroundings.

I. INTRODUCTION

The paper addresses limited knowledge of small-scale wideband mmWave behavior during local-area mobility, using measurements and models spanning diffraction, blockage, fading, and channel transitions for 5G design.

  • I. INTRODUCTION: Broadband mmWave channel models already capture signal-strength and multipath statistics, but small-scale mobility behavior remains insufficiently characterized.The paper positions its measurements as complementary to existing broadband statistical spatial channel models and 5G air-interface work.
  • I. INTRODUCTION: The study targets propagation knowledge needed for handoff and beam-steering design as mobile users move through local areas.It investigates diffraction, human blocking, small-scale fading and autocorrelation, local-area transitions, and signal-power stationarity from 10 to 73 GHz.
  • I. INTRODUCTION: 10, 20, and 26 GHz diffraction measurements use indoor and outdoor test objects to evaluate KED and creeping-wave models.The measurements cover realistic indoor and outdoor scenarios and seek simple, accurate models for wireless planning.
  • I. INTRODUCTION: The measurement campaign uses horn antennas, spectrum analysis, motorized linear tracking, and free-space calibration to quantify diffraction loss.Indoor tests include drywall, wood, and plastic corners, while outdoor tests include stone and marble corners.

D. Theoretical Diffraction Models

The theoretical diffraction treatment relates received-field loss to the Fresnel diffraction parameter and uses KED for sharp obstacles under stated geometric conditions.

  • 1) KED Model:: The KED model is suited to sharp knife edges and estimates diffraction loss relative to free space through the Fresnel parameter.The received diffracted field is compared with the free-space field, and the resulting power gain is expressed in decibels.
  • 1) KED Model:: The Fresnel diffraction parameter depends on wavelength, diffraction angle, effective obstacle height, and transmitter-receiver distances.The model assumes d1 and d2 are much larger than both the obstacle height and wavelength.
  • 1) KED Model:: The corner geometry specifies transmitter and receiver positions relative to the knife edge and the diffraction angle used in model evaluation.The geometry is represented in a top-view corner-diffraction configuration.

2) Convex Surfaces based Diffraction Model:

For rounded obstacles, the paper replaces sharp-edge KED with a creeping-wave model and evaluates a linear MMSE approximation against indoor diffraction measurements.

  • 2) Convex Surfaces based Diffraction Model:: KED does not account for obstacle curvature, so a creeping-wave model is used for rounded corners such as stone pillars.The convex-surface model describes a creeping ray field launched around a circular obstacle.
  • 2) Convex Surfaces based Diffraction Model:: The creeping-wave formulation uses incident field, cylinder radius, wave number, diffraction angle, launch-to-receiver distance, excitation coefficient, and attenuation constant.A single p = 1 term provides a lower-complexity approximation for the field on a flat surface.
  • 2) Convex Surfaces based Diffraction Model:: The linear model estimates curved-surface diffraction loss with an MMSE-derived frequency- and radius-specific slope plus a fixed 6.03 dB anchor point.The slope n is fitted for each frequency and object radius, while c is set from the KED loss at zero diffraction angles.
  • E. Indoor Diffraction Results and Analysis: Approximately 30 dB of loss occurs as the receiver moves 20° into the shadow region behind drywall and wooden corners.KED fits drywall well in early and deep shadow but overestimates wooden-corner loss by 5–10 dB across 10, 20, and 26 GHz.
  • E. Indoor Diffraction Results and Analysis: For plastic board, KED overestimates loss near the lit-shadow boundary and underestimates portions of deep shadow, especially at 20 and 26 GHz.Measured oscillations indicate contributions from corner diffraction, material penetration, and partial environmental scattering.
  • E. Indoor Diffraction Results and Analysis: At 73 GHz, copolarized penetration loss ranges from 0.8 dB/cm for drywall to 9.9 dB/cm for a steel door.The reported standard deviation about average loss ranges from 0.3 dB/cm for drywall to 2.3 dB/cm for clear glass.

F. Outdoor Diffraction Results and Analysis

Outdoor diffraction measurements at 10, 20, and 26 GHz show that creeping wave linear models fit measured shadow-region loss and outperform KED for the tested stone pillar at 10 GHz. Surface geometry affects attenuation, with rougher stone producing greater slopes than smoother marble.

  • Outdoor diffraction model fit: The creeping wave linear model predicts linearly increasing diffraction loss in the deeply shadowed region, unlike the leveling-off behavior of the alternative model.The model matches measured data for the outdoor stone pillar and marble corner at 10, 20, and 26 GHz.
  • Outdoor diffraction model fit: At 10 GHz, the creeping wave linear model fits the measured stone-pillar shadow-region loss better than the KED model.The comparison uses measured stone-pillar results against both KED and creeping wave linear models.
  • Frequency and material dependence: The creeping wave linear model slopes are 0.75, 0.88, and 0.96 for stone and 0.62, 0.77, and 0.96 for marble at the tested frequencies.The figure compares measured diffraction loss as a function of diffraction angle at 10, 20, and 26 GHz.
  • Frequency and material dependence: The rougher stone surface with a slightly rounded edge has greater attenuation slopes than the smoother marble surface with a straight edge at identical frequencies.The authors describe the slope values as useful parameters for reducing diffraction-model computational complexity and supporting mobile handoff design.
  • Relevance to mobile links: Human blockage can greatly attenuate mmWave links, requiring phased-array antennas to seek alternative propagation paths when the LOS path is blocked.This blockage behavior contrasts with the use of omnidirectional antennas at sub-6 GHz frequencies and motivates beam-steering design.

B. Human Blockage Measurement System

The human-blockage system measures perpendicular walks across a 5 m LOS path at 73.5 GHz and models the blocker as a rectangular screen using double knife-edge diffraction. The model computes two-edge diffraction and can incorporate directional TX and RX antenna gains.

  • Measurement system: The sounder uses a 73.5 GHz center frequency with 1 GHz null-to-null RF bandwidth for wideband human-blockage measurements.A pseudorandom-noise sequence is generated at baseband, modulated to 5.625 GHz IF, and upconverted to 73.5 GHz.
  • Measurement environment: Measurements use 5 m TX-RX separation, boresight-aligned high-gain narrowbeam horns at 1.4 m height, and a blocker walking perpendicularly at approximately 1 m/s.Nine paths place the blocker at 0.5 m increments from 0.5 m to 4.5 m from the transmitter.
  • Measurement environment: The nine measurement locations are spaced by 0.5 m along the LOS path between the TX and RX antennas.The blocker walks through each location with a perpendicular orientation.
  • DKED screen model: The blocker is modeled as a thin rectangular screen whose two side edges produce the double knife-edge diffraction loss.The screen is treated as infinitely high, so diffraction is calculated only at the two side edges; its top and bottom dimensions are specified by the measurement geometry.
  • DKED screen model: The screen remains perpendicular to the TX-RX line as it moves, simplifying the geometry and computation of the two diffraction edges.The side-edge separation equals the blocker depth or screen width for perpendicular walking.
  • Diffraction calculation: The diffraction parameter uses TX-to-screen distance, screen-to-RX distance, diffraction angle, and carrier wavelength, with sign choices differing between LOS and NLOS conditions.The model evaluates Fresnel-integral approximations for each edge before combining the resulting complex signals.
  • Diffraction calculation: The total diffraction loss is obtained from the magnitude squared of the sum of the complex signals from the two screen edges.The extended model includes TX and RX antenna gains for the projected edge angles, while unobstructed conditions use normalized gain G(θ) = 1.
  • Antenna-gain extension: The original DKED model assumes omnidirectional antennas and can underestimate the deepest fades when directional antennas are used.The antenna-gain extension addresses off-boresight gains that remain when the blocker obstructs the LOS path.

E. Human Blockage Results and Analysis

At 73 GHz, measured human-blockage received power agrees with the DKED-AG model, including severe fades that exceed 40 dB. The measurements also show rapid power changes as a blocker approaches an antenna.

  • Model validation: The DKED-AG model accurately predicts measured 73 GHz human-blockage received power, including the deepest attenuation caused by a blocker.The comparison includes measured power, the antenna-gain model, and constructive and destructive edge-signal sums.
  • Model validation: Deepest human-blockage attenuation exceeds 40 dB when the blocker obstructs the LOS path.The reported model comparison evaluates loss relative to a free-space reference without blockage.
  • Rapid fading and mitigation: At a blocker speed of 1 m/s, signal strength drops at 0.4 dB/ms as the blocker begins to shadow the transmitter or receiver.The rate is observed in measurements 1 and 9, where the blocker starts near the TX or RX.
  • Rapid fading and mitigation: The results motivate sub-millisecond beam steering or handoffs to another access point to rescue links from severe blockage fades.The paper also notes that the model can be extended to multiple blockers, top and bottom screen edges, phase corrections, and nonperpendicular orientations.

A. Introduction of Small-Scale Spatial Statistics

The study measures 73 GHz small-scale fading and spatial behavior in urban microcell LOS and NLOS environments using linear tracks, directional antennas, and synthesized omnidirectional statistics. The measurements show modest local-track power variation despite changing multipath conditions.

  • Measurement scope: Small-scale mmWave fading and autocorrelation measurements support MIMO channel modeling at 73 GHz.The campaign investigates received voltage-amplitude behavior in urban microcell environments.
  • Measurement setup: A 35.31-cm track was sampled at 2.04-mm half-wavelength increments over 175 positions.Six measurement sets were performed at each receiver with fixed elevation and varying azimuth angles.
  • Measurement scope: The study compares its 73 GHz measurements with prior 28 GHz work by using a wider 60° RX beamwidth and total received voltage amplitude.The measured quantity integrates the entire PDP before taking the square root of total power.
  • LOS results: The LOS track showed 11 dB power variation across positions, reduced to 3.7 dB when oriented along the T-R line.The reported LOS measurements used a 60° HPBW horn antenna pointed on boresight toward the transmitter.
  • NLOS results: The NLOS track showed 4.1 dB power variation despite rich and varying multipath components.The receiver pointed toward the transmitter but was obstructed by a building corner while moving along the street.

E. Small-Scale Spatial Statistics Results and Analysis

The analysis synthesizes omnidirectional small-scale statistics from directional measurements and fits distributions and spatial-correlation models to 73 GHz LOS and NLOS data. LOS correlation exhibits damped oscillation, while NLOS correlation is closer to an undamped exponential trend.

  • Omnidirectional statistics: Omnidirectional received power was synthesized at each track interval from directional measurements to support channel-modeling statistics.The approach enables arbitrary antenna patterns when accurate temporal and spatial statistics are available.
  • Fading distributions: The LOS received-voltage amplitude was approximated by a Ricean distribution with a 10 dB K-factor over the 35.31-cm track.The dominant LOS path contributes most of the received power, and the voltage amplitude varies little across the track.
  • Fading distributions: Broadband frequency-selective fading causes total received power to change little over a small-scale local area.Different frequency components fade independently, making simultaneous deep fades across the full bandwidth unlikely.
  • Spatial autocorrelation: LOS spatial autocorrelation first becomes uncorrelated near 3.5λ, then oscillates before decaying toward zero after 18λ.The measured curve is modeled by a damped oscillation, represented by f(∆X) = cos(a∆X)e−b∆X.
  • Spatial autocorrelation: The model uses ∆X as antenna separation, a as oscillation distance, and b as the decay constant, with parameters fitted by MMSE.The spatial oscillation period is T = 2π/a and the spatial decay constant is d = 1/b.
  • Spatial autocorrelation: NLOS spatial autocorrelation follows a trend closer to an undamped exponential and is fitted using the same model with a set to 0.The difference from LOS is attributed to shadowing effects that alter multipath phase relationships.

2) Directional Small-Scale Spatial Statistics:

Directional 73 GHz measurements characterize small-scale fading and spatial autocorrelation across LOS and NLOS environments for directional receive antennas. The autocorrelation follows sinusoidal-exponential behavior in LOS and generally exponential behavior in NLOS, with pointing direction affecting oscillation and decay.

  • Directional fading distributions: Figures 14 and 15 compare measured directional voltage-amplitude fading distributions with Ricean fits across LOS and NLOS pointing angles.The figure legends encode receiver azimuth angle; “b” denotes boresight to the transmitter, while “s, to TX” denotes street direction toward the transmitter.
  • Directional measurement setup: Directional receive antennas were evaluated for 73 GHz small-scale fading and spatial autocorrelation in LOS and NLOS environments.Measurements used a 7° azimuth/elevation HPBW transmitter and 60° azimuth/elevation HPBW receiver along a linear track.
  • LOS spatial autocorrelation: LOS autocorrelation curves exhibit sinusoidally exponential decay, with oscillation patterns and decay rates varying by antenna pointing angle.Boresight-to-boresight pointing has the smallest oscillation because the power-delay profile contains a single LOS component; other directions include multiple multipath components.
  • NLOS spatial autocorrelation: NLOS directional autocorrelation generally follows the exponential model used for omnidirectional reception.At 30° pointing, decorrelation decreases to 1/e at 25.0λ, or 10.2 cm, likely because diffraction provides a dominant path with relatively constant signal level.
  • Measurement scope: Correlation distances vary among mmWave measurements because propagation is site-specific.The paper identifies the southeast corner of Rogers Hall as the relevant measurement setting for the directional statistics.

V. LOCAL AREA CHANNEL TRANSITION

The local-area transition campaign measures how a 73 GHz channel changes across LOS and NLOS routes and clusters around an urban building corner. It uses directional antennas, repeated azimuth sweeps, and receiver locations spaced at 5 m.

  • Measurement system: Local-area transition measurements use a 27 dBi, 7° beamwidth transmitter antenna and a 20.0 dBi, 15° beamwidth receiver antenna.The measurement system otherwise matched the earlier small-scale fading and autocorrelation setup.
  • Measurement environment: Measurements were conducted at 73 GHz in the MetroTech Commons courtyard with transmitter and receiver heights of 4.0 m and 1.5 m.The transmitter remained fixed while repeated receiver azimuth sweeps were performed for each cluster or route location.
  • Measurement procedure: Each receiver location used five azimuth sweeps at 15° increments, producing at most 120 power-delay profiles per transmitter–receiver combination.Some azimuth angles had no detectable signal above the noise floor.
  • Route scenario: Route measurements used 16 receiver locations spaced by 5 m along an L-shaped path from LOS to NLOS around a building corner.LOS separations ranged from 29.6 m to 49.1 m, while NLOS separations ranged from 50.8 m to 81.5 m.
  • Cluster scenario: Cluster measurements used ten receiver locations in separate LOS and NLOS semicircular clusters, with adjacent locations separated by 5 m.The clusters were measured for a fixed transmitter location to study local-area stationarity.

C. Local Area Channel Transition Results and Stationarity

Route measurements show a sharp power reduction as a receiver moves from LOS to deeply shadowed NLOS around an urban corner, while cluster measurements indicate comparatively stationary average power over local areas. The transition also changes the angular distribution of arriving energy.

  • Route transition: The LOS-to-NLOS transition causes an initial 8 dB loss and an overall 25 dB signal-power drop around the building corner.The overall drop occurs over approximately 25 m along the perpendicular urban canyon, with about 10 m additional Euclidean transmitter–receiver separation.
  • Route transition: Path loss increases in several abrupt increments after the initial transition, reaching deep shadow along the NLOS route.The successive increases are 9 dB, 1 dB, 6 dB, and 1 dB between the measured receiver locations.
  • Fading rate: The signal fading rate is 35 dB/s at 35 m/s vehicle speed and 1 dB/s at 1 m/s walking speed.These rates motivate beam scanning and phased-array technologies to search for stronger signal paths.
  • Azimuth spectra: NLOS-to-LOS movement changes the received angular energy from reflected and scattered components to a strong central lobe from the transmitter.At RX92, the central lobe arrives from 285°, with a secondary 100° lobe from building reflections and nearby objects.
  • Route stationarity: LOS route power is relatively stable with 1.2 dB standard deviation, whereas NLOS route power varies by 7.9 dB.The larger NLOS variation is attributed to substantial scattering and nonlinear path-loss growth along the urban canyon.
  • Cluster stationarity: A LOS cluster shows a relatively small 4.3 dB omnidirectional received-power standard deviation over a 5 m × 10 m local area.The cluster measurements were designed to assess stationarity over distances of many hundreds to thousands of wavelengths.

VI. CONCLUSION AND DISCUSSION

The paper combines measurements of diffraction, blockage, small-scale fading, autocorrelation, and local-area transitions to characterize mmWave propagation for mobile 5G. The results identify severe blockage losses, short spatial correlation scales, and abrupt LOS-to-NLOS changes relevant to link maintenance.

  • Diffraction and blockage: KED models indoor diffraction, while a creeping-wave linear model applies outdoors; mmWave diffraction is not dominant in the measured scenarios.Deep-shadow attenuation reached 30 dB indoors and 40 dB or more outdoors.
  • Design implications: Large diffraction and blockage fades require transmitter and receiver antenna systems to search cooperatively for secondary spatial paths.The paper connects these fades to physical-layer protocol and frame-structure design for maintaining links.
  • Diffraction and blockage: Human blockage can exceed 40 dB of loss at 0.5 m from the transmitter or receiver, with a 0.4 dB/ms decay rate while walking.The DKED-AG model includes directional antenna patterns and better matches measured blockage envelopes than the 3GPP/METIS model.
  • Small-scale statistics: Measured 73 GHz, 1 GHz-bandwidth fading shows Ricean LOS behavior for omnidirectional reception and log-normal NLOS behavior with 0.65 dB standard deviation.The measurements covered a 35.31 cm linear track, approximately 87 wavelengths.
  • Local-area propagation: LOS-to-NLOS movement around a building corner produces 8 dB initial and 25 dB overall power losses, while fading rates range from 0.4 dB/ms to 40 dB/s.The results support mmWave channel modeling for handoff algorithms, beam scanning, and spatial consistency.
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