PaperlayerView exact revision on arXiv

Source-linked AI summary

Directional Radio Propagation Path Loss Models for Millimeter-Wave Wireless Networks in the 28-, 60-, and 73-GHz Bands

Ahmed Iyanda Sulyman, Abdulmalik Alwarafy, George R. MacCartney, Theodore S. Rappaport, Abdulhameed Alsanie

arXiv:2012.00636v1eess.SP

TL;DR

At mmWave frequencies, path-loss models need to reflect measured propagation and directional beam combining for 5G planning. The paper modifies FS and SUI models for 60 and 73 GHz and develops BC-CI models for 28 and 73 GHz. These models match CI behavior while extending path-loss estimation across beam counts and directional scenarios.

  • Problem

    Measured mmWave propagation requires suitable path-loss models for 5G planning, while existing corrected FS and SUI factors did not cover 60 and 73 GHz and beam-combining models needed broader parameterization.

  • Method

    The paper applies slope correction factors to FS and SUI models and develops BC-CI models using the strongest-beam PLE, weighting factor A, and number of combined beams.

  • Results

    The modified models fit CI path-loss models at 60 and 73 GHz, while BC-CI models achieve virtually identical RMSE standard deviation to original CI models and support arbitrary beam counts.

  • Takeaways & Limitations

    The models provide physically anchored tools for estimating mmWave path loss in 5G planning and directional systems across measured and extended beam-combining configurations.

Abstract

from arXiv · show

Fifth-generation (5G) cellular systems are likely to operate in the centimeter-wave (3-30 GHz) and millimeter-wave (30-300 GHz) frequency bands, where a vast amount of underutilized bandwidth exists world-wide. To assist in the research and development of these emerging wireless systems, a myriad of measurement studies have been conducted to characterize path loss in urban environments at these frequencies. The standard theoretical free space (FS) and Stanford University Interim (SUI) empirical path loss models were recently modified to fit path loss models obtained from measurements performed at 28 GHz and 38 GHz, using simple correction factors. In this paper, we provide similar correction factors for models at 60 GHz and 73 GHz. By imparting slope correction factors on the FS and SUI path loss models to closely match the close-in (CI) free space reference distance path loss models, millimeter-wave path loss can be accurately estimated (with popular models) for 5G cellular planning at 60 GHz and 73 GHz. Additionally, new millimeter-wave beam combining path loss models are provided at 28 GHz and 73 GHz by considering the simultaneous combination of signals from multiple antenna pointing directions between the transmitter and receiver that result in the strongest received power. Such directional channel models are important for future adaptive array systems at millimeter-wave frequencies.

I. INTRODUCTION

5G systems are expected to use cmWave and mmWave bands, where path loss challenges motivate measurement-based modeling and beamforming. The paper extends corrected path-loss models to 60 and 73 GHz and introduces beam-combining models for directional links.

  • 5G systems are expected to exploit 3–300 GHz spectrum, which offers abundant bandwidth for multigigabit mobile and backhaul applications.
  • Higher mmWave free-space path loss motivates high-gain antennas, beamforming, and beam combining to improve link quality.
  • Path-loss models support modulation and coding design, power-budget calculations, and cellular coverage and interference prediction.
  • Earlier work modified FS and SUI models for 28 and 38 GHz using slope correction factors matched to empirical CI models.
  • This paper provides corresponding FS and SUI correction factors for 60 and 73 GHz, accounting for atmospheric and rain attenuation considerations.
  • The paper also introduces beam-combining path-loss models that explicitly account for the number of combined receiver beams.

A. Modified FS and SUI Path Loss Models

The paper uses theoretical FS and empirical SUI models as starting points, then modifies their slopes to match 1 m CI reference-distance models. The resulting formulations distinguish LOS and NLOS propagation and retain environmental and antenna-height parameters.

  • SUI parameters: The SUI formulation includes carrier frequency, antenna heights, terrain parameters, and log-normal shadowing with standard deviation σ ranging from 8.2 dB to 10.6 dB.
  • LOS modeling: Friis’ FS model estimates LOS path loss versus distance using theoretical free-space loss at 1 m as a physical anchor.
  • CI reference: The CI model combines the 1 m free-space reference loss with a path-loss exponent describing attenuation beyond the reference distance.
  • LOS modeling: For LOS, a slope correction factor modifies the FS model to match the measured-data-based CI model.
  • NLOS modeling: For NLOS, a slope correction factor modifies the SUI model to match the 1 m CI NLOS model.

B. Directional Beam Combining Path Loss Models at mmWave Bands

The paper develops a beam-combining close-in path loss model that incorporates the number of simultaneously combined directional beams. The model uses measured beam-combining data and scales the strongest-beam path loss exponent logarithmically with beam count.

  • Model formulation: The proposed BC-CI model incorporates the number of combined beams directly into directional millimeter-wave path loss equations.It extends the close-in model for NLOS urban environments.
  • Model parameters: The model uses three parameters: the strongest-beam PLE, weighting factor A, and number of combined beams Nr.The strongest-beam PLE and A remain fixed while Nr represents the available beam combinations.
  • Beam-combining behavior: Beam combining can reduce the aggregate path loss exponent, with reductions increasing logarithmically as more unique angles are combined under both CC and NCC schemes.The model considers simultaneously combined signals from distinct antenna pointing directions.
  • Parameter estimation: The weighting factor A is fitted by MMSE to minimize the squared error between measured path loss and BC-CI predictions.The fitting procedure solves the derivative of the squared-error objective with respect to A.
  • Model behavior: When Nr = 1, the BC-CI model reduces to the single strongest-beam close-in model and can generalize beyond four combined beams.Measurements indicate that antenna beamwidths greater than 7° seldom produce more than five distinct arrival directions.

III. RESULTS AND PARAMETERS FOR MODIFIED PATH LOSS MODELS AT 60 GHZ AND 73 GHZ

The study evaluates directional path loss measurements at 28, 60, and 73 GHz across New York City and Austin environments. These measurements use broadband sliding-correlator sounders and directional antennas across LOS and NLOS links.

  • Measurement campaigns: Measurements at 28 and 73 GHz were conducted in New York City, while 60 GHz measurements used courtyard and in-vehicle environments in Austin.The campaigns used broadband sliding-correlator channel sounders with different chip rates across frequency bands.
  • Antenna configurations: The New York City campaigns used 24.5 dBi antennas at 28 GHz and 27 dBi antennas at 73 GHz.Their azimuth half-power beamwidths were 10.9° and 7°, respectively.
  • Measurement ranges: New York City links ranged from 31 m to 102 m in LOS scenarios and from 53 m to 187 m in NLOS scenarios.TX and RX antenna sweeps covered directional links in dense urban environments.
  • Scenario definitions: At 60 GHz, LOS links used aligned antennas with a clear optical path, whereas NLOS links included obstructions or off-boresight alignment.The 60 GHz measurements covered peer-to-peer courtyard and street-to-vehicle settings.

A. 60 GHz Peer-to-Peer Courtyard and In-Vehicle

At 60 GHz, standard FS and SUI models do not adequately match measured or empirical CI path loss in courtyard and in-vehicle environments. MMSE-derived slope corrections improve the model trends, although NLOS fitting remains limited.

  • 60 GHz environments: The 60 GHz environments are modeled as flat, dense vegetation corresponding closely to SUI terrain type A.Terrain A uses a = 4.6, b = 0.0075, and c = 12.6.
  • Unmodified models: Standard FS and SUI models fail to match the respective 1 m CI models or accurately estimate measured path loss without correction factors.This mismatch applies to LOS FS modeling and NLOS SUI modeling in the evaluated environments.
  • LOS correction factors: At 60 GHz LOS, the modified FS model uses α = 1.1 for courtyard and α = 1.25 for in-vehicle environments.These values are shown alongside the 1 m CI path loss models.
  • Fit quality and scope: MMSE-derived slope corrections better match empirical CI trends, but NLOS fit remains weaker and may require a model accounting for car body loss.Correction factors are also provided for SUI terrain types B and C in NLOS.
  • NLOS correction factors: At 60 GHz NLOS, the modified SUI model uses α = 0.277 for courtyard and α = 0.416 for in-vehicle environments.The comparison uses the terrain A SUI model and 1 m CI path loss models.

B. 73 GHz Mobile and Backhaul

At 73 GHz, unmodified FS and SUI models do not match measured directional path loss or empirical CI models, while slope-corrected versions match the 1 m CI models for LOS and NLOS scenarios.

  • 73 GHz Mobile and Backhaul: Modified FS and SUI models are provided for 73 GHz directional LOS and NLOS measurements across mobile and backhaul antenna-height scenarios.The models cover TX heights of 7 m and 17 m and RX heights of 2 m and 4.06 m.
  • 73 GHz Mobile and Backhaul: The original FS model for LOS and SUI model for NLOS do not accurately estimate measured 73 GHz path loss or match empirical CI models.This mismatch is reported for the directional scenarios shown in Figs. 3–6.
  • 73 GHz Mobile and Backhaul: Slope correction factors make the modified FS and SUI models match the estimated CI path loss models relative to a 1 m free-space reference distance.The corrected models are described as accurately predicting path loss and matching the physically motivated CI models.
  • 73 GHz Mobile and Backhaul: For 73 GHz NLOS mobile conditions with RX height 2 m, the modified SUI model uses α = 0.772 for htx = 7 m and α = 0.844 for htx = 17 m.These parameters correspond to the terrain A scenario shown in Fig. 4.
  • 73 GHz Mobile and Backhaul: For 73 GHz LOS backhaul conditions with RX height 4.06 m, the modified FS model uses α = 1.2 for htx = 7 m and α = 1.15 for htx = 17 m.The corresponding NLOS backhaul figure reports modified SUI parameters α = 0.756 and α = 0.863 for the two TX heights.

IV. RESULTS AND PARAMETERS FOR BEAM COMBINING MODEL AT 28 GHZ AND 73 GHZ

The proposed BC-CI model estimates path loss after combining directional beams at 28 and 73 GHz. Its fixed weighting factors generalize beyond four beams, while coherent combining reduces path loss exponent more than non-coherent combining.

  • Model construction: The BC-CI model is optimized using coherent and non-coherent measurements combining up to the four best beams at 28 GHz and 73 GHz.Optimization uses MMSE-derived A weighting factors for both combining types.
  • Model validation: The BC-CI and original CI models have nearly identical PLEs and practically zero RMSE between comparative entries.Both models use a frequency-dependent 1 m close-in free-space reference distance.
  • Model generalization: A weighting factors remain constant across beam counts for a particular measurement setup, enabling path-loss estimation when Nr exceeds four.The setup includes TX/RX heights, carrier frequency, and combining type; the example uses A = 0.0671 for multiple beam counts.
  • Model validation: At 73 GHz, mobile and backhaul BC-CI estimates differ from original CI models by only approximately 0.1 dB per distance decade.Their effective PLEs are within two decimal places, making the difference not discernible in practical field measurements.
  • Beam-combining results: Coherent combining reduces PLE more than non-coherent combining, although both methods considerably increase received power.At 28 GHz, adding four beams reduces PLE by approximately 0.5 coherently and 0.3 non-coherently, corresponding to 5 dB and 3 dB per decade.
  • Beam-combining results: At 73 GHz, coherently combining four beams reduces PLE from 3.728 to 3.226 for mobile and from 3.823 to 3.348 for backhaul scenarios.For the mobile scenario, the 100 m single-best-beam path loss is achieved at approximately 205 m with four-beam combining.

V. CONCLUSION

The paper introduces physically anchored correction factors for FS and SUI models at 60 and 73 GHz and a generalized BC-CI model for 28 and 73 GHz directional measurements. These models support path-loss estimation and comparison for millimeter-wave planning and channel-model standardization.

  • Conclusion: Correction factors modify FS and SUI models to fit empirical 1 m CI path-loss models at 60 GHz and 73 GHz in LOS and NLOS scenarios.The resulting models estimate path loss as a function of distance and environmental or system-specific parameters.
  • Conclusion: The modified propagation models are suitable for 5G cellular planning and millimeter-wave path-loss estimation at 60 GHz and 73 GHz.Their use is tied to the empirical CI models and the 1 m free-space reference distance.
  • Conclusion: The BC-CI model uses the single-best-beam PLE, weighting factor A, and beam count Nr to estimate distance-dependent path loss.It is based on directional measurements at 28 GHz and 73 GHz.
  • Conclusion: BC-CI models have virtually identical RMSE standard deviation to original CI models and can extend beyond the four beams used in the paper.This provides a generalized beam-combining model for millimeter-wave path-loss prediction.
  • Conclusion: A standardized 1 m close-in reference distance supports model stability, simplicity, and direct comparison toward standardization of 5G millimeter-wave channel models.The reference is physically tied to unobstructed propagation in the first meter from the transmitter.
Loading 2012.00636v1…