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Millimeter-Wave Distance-Dependent Large-Scale Propagation Measurements and Path Loss Models for Outdoor and Indoor 5G Systems

Shu Sun, George R. MacCartney, Theodore S. Rappaport

arXiv:1511.07345v4cs.IT

TL;DR

MmWave systems need path loss models that remain accurate across distance, frequency, and propagation environments while retaining physical meaning and practical simplicity. The paper measures outdoor and indoor channels at 28 GHz and 73 GHz, then compares five FI, CI, ABG, and CIF formulations. CI is preferred for multi-frequency outdoor modeling, whereas CIF better captures indoor frequency dependence, with comparable accuracy and fewer parameters than less physically grounded alternatives.

  • Problem

    Accurate large-scale path loss models must represent distance and frequency across outdoor and indoor environments while remaining physically grounded, stable, simple, and repeatable.

  • Method

    The paper conducts extensive 28 GHz and 73 GHz measurements in urban micro-cellular and indoor office scenarios and compares FI, CI, ABG, multi-frequency CI, and CIF models.

  • Results

    CI and CIF provide physically grounded, stable path loss estimates with accuracy comparable to more complex models; CI suits outdoor multi-frequency modeling, while CIF captures indoor frequency dependence.

  • Takeaways & Limitations

    The CI model is appropriate for outdoor environments, while the two-parameter CIF model is better suited to indoor environments with frequency-dependent path loss.

Abstract

from arXiv · show

This paper presents millimeter-wave propagation measurements for urban micro-cellular and indoor office scenarios at 28 GHz and 73 GHz, and investigates the corresponding path loss using five types of path loss models, the singlefrequency floating-intercept (FI) model, single-frequency closein (CI) free space reference distance model, multi-frequency alpha-beta-gamma (ABG) model, multi-frequency CI model, and multi-frequency CI model with a frequency-weighted path loss exponent (CIF), in both line-of-sight and non-line-of-sight environments. Results show that the CI and CIF models provide good estimation and exhibit stable behavior over frequencies and distances, with a solid physical basis and less computational complexity when compared with the FI and ABG models. Furthermore, path loss in outdoor scenarios shows little dependence on frequency beyond the first meter of free space propagation, whereas path loss tends to increase with frequency in addition to the increased free space path loss in indoor environments. Therefore, the CI model is suitable for outdoor environments over multiple frequencies, while the CIF model is more appropriate for indoor modeling. This work shows that both the CI and CIF models use fewer parameters and offer more convenient closedform expressions suitable for analysis, without compromising model accuracy when compared to current 3GPP and WINNER path loss models.

I. INTRODUCTION

The paper motivates mmWave 5G through abundant bandwidth and emphasizes path loss models that are physically grounded, simple, stable, repeatable, and convenient for system analysis.

  • MmWave bands offer abundant bandwidth for multi-Gbps data rates and can relieve congestion below 6 GHz.
  • Accurate large-scale path loss modeling is critical for estimating communications-system behavior over distance and frequency.
  • Preferred models use fewer parameters, intuitive physics-based rationales, closed-form expressions, and stable parameters across data sets.
  • Path loss models commonly use either a physical anchor, as in CI, or data-fitting without a physical anchor, as in FI.
  • The study compares FI, CI, ABG, multi-frequency CI, and CIF models using outdoor urban micro-cellular and indoor office measurements at 28 GHz and 73 GHz.

A. Outdoor Measurements

The outdoor campaigns measured mmWave propagation in downtown Manhattan at 28 GHz and 73 GHz using directional channel sounders and steerable horn antennas across urban micro-cellular links.

  • More than 10,000 directional power delay profiles were recorded during two Manhattan campaigns at 28 GHz and 73 GHz.
  • Both campaigns used similar 400 Mcps spread-spectrum sliding-correlator channel sounders and directional steerable horn antennas at the transmitter and receiver.
  • The 28 GHz campaign used three transmitter locations and 27 receiver locations in downtown Manhattan.
  • The 73 GHz campaign used five transmitter locations and 27 receiver locations across mobile and backhaul scenarios.

B. Indoor Measurements

The indoor campaign measured 28 GHz and 73 GHz propagation on the ninth floor of a Brooklyn office building using broadband sounders, widebeam antennas, and many transmitter–receiver combinations.

  • Indoor measurements at 28 GHz and 73 GHz were conducted on the ninth floor of 2 MetroTech Center in downtown Brooklyn.
  • The campaign used the same 400 Mcps broadband sliding-correlator channel sounders as the outdoor measurements, with system differences indoors.
  • Indoor measurements used widebeam transmitter and receiver antennas with different gains and azimuth beamwidths at the two frequencies.
  • The cubicle-farm environment included long corridors, hallways, closed offices, and laboratories.
  • Five transmitter and 33 receiver locations produced 48 transmitter–receiver combinations at each frequency.

III. LARGE-SCALE PATH LOSS MODELS

The paper compares five large-scale path loss models, contrasting physically anchored CI formulations with floating-intercept and frequency-fitting alternatives.

  • The study compares single-frequency FI and CI models with multi-frequency ABG, CI, and CIF models using outdoor and indoor data.
  • The FI model represents path loss with a distance coefficient, floating intercept, and shadow-fading term.
  • FI requires two model parameters and lacks a physically based anchor to transmitted power.
  • The CI model anchors path loss to 1 m free-space path loss and uses one optimized path loss exponent.
  • The CI model embeds frequency dependence in the 1 m free-space term and applies to both single- and multi-frequency cases.
  • The 1 m reference separates first-meter free-space loss from the path loss exponent governing distances beyond 1 m.

1 GHz

The ABG and CIF models represent path loss across frequency and distance, while the CIF model adds frequency dependence around a measurement-derived reference frequency. The CI and CIF models retain physical grounding through a close-in free-space reference, whereas ABG introduces fitted terms with weaker physical basis.

  • ABG model: The ABG model represents path loss as a function of both carrier frequency and distance using distance, frequency, and offset coefficients.Its coefficients are optimized through closed-form solutions that minimize shadow-fading standard deviation.
  • CIF model: The CIF model adds a linear frequency-dependence term to the distance exponent around a reference frequency computed from the measurement set.The reference frequency is calculated from the number of path-loss data points at each unique frequency.
  • CIF model: The CIF model reduces to the CI model for a single frequency or when its frequency-dependence parameter b equals 0.This makes the CIF formulation compatible with single-frequency modeling.
  • Physical basis: The CI and CIF models tie distance dependence to transmitted power through a close-in free-space path-loss reference rather than a floating intercept.Their physical basis derives from fundamental wireless-propagation principles, including Friis and two-ray models.
  • Model comparison: The ABG model departs from propagation physics through its optimized offset and frequency-weighting terms, despite retaining some physical basis in its distance term.The passage notes that recent indoor measurements nevertheless show increasing path loss with frequency across the mmWave band.

IV. OUTDOOR PROPAGATION PATH LOSS RESULTS

Outdoor UMi street-canyon measurements at 28 GHz and 73 GHz show that CI and CIF models preserve physically intuitive distance behavior with nearly identical shadow-fading accuracy to ABG. The CIF frequency term is negligible beyond the first meter, supporting the single-parameter CI model for outdoor channels.

  • Single-frequency models: At 73 GHz UMi LOS, the CI model gives a PLE of 2.0, while the FI model gives α = -0.8, implying decreasing path loss with distance.The CI value matches the theoretical free-space PLE, whereas the FI parameter contradicts passive-channel behavior.
  • Measurement and comparison: Outdoor path-loss parameters are compared across single-frequency FI and CI models and multi-frequency ABG, CI, and CIF models using 28 GHz and 73 GHz measurements.The reported UMi data are summarized in the paper’s single-frequency and multi-frequency parameter tables.
  • Multi-frequency models: For outdoor LOS, CI and CIF both give a distance exponent of 2.0, matching the theoretical free-space PLE.The multi-frequency ABG model instead gives α = 1.0.
  • Multi-frequency models: ABG, CI, and CIF have virtually identical outdoor shadow-fading standard deviations, differing by at most 0.2 dB.This comparison shows similar fitting accuracy despite differences in physical interpretability.
  • Outdoor frequency dependence: The CIF frequency term b is -0.06 in LOS and -0.00 in NLOS, indicating negligible path-loss frequency dependence beyond the first meter outdoors.The CIF distance exponent also matches the CI PLE for the UMi street-canyon scenario.

V. INDOOR PROPAGATION PATH LOSS RESULTS

Indoor measurements show frequency-dependent path loss beyond 1 m, while CI and CIF retain physical grounding with accuracy comparable to the more flexible ABG model.

  • Single-frequency models: At 73 GHz, indoor path loss exceeds 28 GHz beyond the first meter, with LOS PLEs of 1.3 versus 1.1 and NLOS PLEs of 3.2 versus 2.7.The NLOS difference corresponds to 5 dB more attenuation per decade of distance at 73 GHz.
  • Multi-frequency models: The multi-frequency CIF model reduces standard deviation from 2.3 to 2.1 dB in LOS and from 10.9 to 10.4 dB in NLOS relative to CI.Its frequency-dependent balancing term improves fit while retaining a 1 m free-space reference.
  • Multi-frequency models: The ABG, CIF, and CI models compare distance and frequency dependence across 28 GHz and 73 GHz in indoor LOS and NLOS environments.Figures 1–3 show omnidirectional data alongside corresponding multi-frequency model fits.
  • Model comparison: ABG achieves slightly lower standard deviations, but its LOS slope attenuation term of 0.9 lacks agreement with propagation physics.In NLOS, the differences are small: 10.3 dB for ABG, 10.4 dB for CIF, and 10.9 dB for CI.

VI. COMPARISON OF OUTDOOR AND INDOOR PATH LOSS RESULTS

Outdoor and indoor environments exhibit different multi-frequency path-loss behavior: outdoor parameters show little frequency dependence, while indoor propagation reflects stronger environmental effects.

  • CIF comparison: The CIF frequency-weighting parameter b is smaller outdoors, at -0.06 in LOS and -0.00 in NLOS, than indoors, at 0.18 and 0.21.This comparison indicates weaker modeled frequency dependence in the outdoor measurements.
  • CI comparison: Outdoor LOS PLE is 2.0, matching free-space theory, whereas indoor LOS PLE is 1.2 because waveguiding enhances received signal strength.Indoor NLOS PLE is also lower than outdoor: 2.9 versus 3.4, associated with waveguiding and stronger reflected paths.
  • CI comparison: The multi-frequency CI model fits outdoor propagation consistently with the theoretical free-space exponent, while indoor CI behavior departs from that reference.The indoor departure is linked in the measurements to waveguiding and reflected paths.

VII. CONCLUSION

The paper compares five path-loss models using 28 GHz and 73 GHz measurements in outdoor and indoor environments. It concludes that CI is preferable outdoors, whereas CIF is better suited indoors because it captures indoor frequency dependence.

  • Conclusion: Measurements cover urban micro-cellular and indoor office scenarios at 28 GHz and 73 GHz, with single- and multi-frequency FI, CI, ABG, and CIF models compared.The analysis uses extensive measurement campaigns across LOS and NLOS environments.
  • Conclusion: The CI model is suitable for outdoor multi-frequency modeling because path loss shows little frequency dependence beyond the first meter of free-space propagation.Its physical basis, stability, and simplicity are highlighted in the comparison.
  • Conclusion: The CIF model is well suited to indoor environments because it preserves a physics-based structure while incorporating observed frequency dependence with two parameters.It extends CI with a frequency-dependent term for indoor path loss.
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