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Study on 3GPP Rural Macrocell Path Loss Models for Millimeter Wave Wireless Communications

George R. MacCartney Jr., Theodore S. Rappaport

arXiv:1703.10300v1cs.ITmath.IT

TL;DR

Rural macrocell path-loss models have limited published validation above 6 GHz and in mmWave bands. The paper examines existing 3GPP/ITU-R models and evaluates CI and height-dependent CIH alternatives using measurements and simulations. It reports that CI and CIH can model rural path loss across microwave and mmWave frequencies without a discontinuity at 6 GHz.

  • Problem

    The existing 3GPP RMa LOS model was not confirmed for rural settings or with extensive measurements above 6 GHz or at mmWave frequencies.

    Source: A. 3GPP RMa LOS Path Loss Model · p. 2

  • Method

    The paper analyzes existing RMa models and evaluates CI and height-dependent CIH path-loss models using simulated and measured data.

    Source: §I · p. 1, A. CI Path Loss Model · p. 3, B. CIH Path Loss Model · p. 4

  • Results

    For TX heights of 150 m versus 10 m, measured CIH results show an average 17 dB NLOS path-loss decrease across T-R distances, compared with 29 dB in simulated 3GPP results.

    Source: §VI · p. 7

  • Takeaways & Limitations

    The authors propose CI and CIH as alternatives for modeling RMa path loss across low microwave and mmWave frequencies, including above 100 GHz.

    Source: §VI · p. 7

Abstract

from arXiv · show

Little research has been done to reliably model millimeter wave (mmWave) path loss in rural macrocell settings, yet, models have been hastily adopted without substantial empirical evidence. This paper studies past rural macrocell (RMa) path loss models and exposes concerns with the current 3rd Generation Partnership Project (3GPP) TR 38.900 (Release 14) RMa path loss models adopted from the International Telecommunications Union - Radiocommunications (ITU-R) Sector. This paper shows how the 3GPP RMa large-scale path loss models were derived for frequencies below 6 GHz, yet they are being asserted for use up to 30 GHz, even though there has not been sufficient work or published data to support their validity at frequencies above 6 GHz or in the mmWave bands. We present the background of the 3GPP RMa path loss models and their use of odd correction factors not suitable for rural scenarios, and show that the multi-frequency close-in free space reference distance (CI) path loss model is more accurate and reliable than current 3GPP and ITU-R RMa models. Using field data and simulations, we introduce a new close-in free space reference distance with height dependent path loss exponent model (CIH), that predicts rural macrocell path loss using an effective path loss exponent that is a function of base station antenna height. This work shows the CI and CIH models can be used from 500 MHz to 100 GHz for rural mmWave coverage and interference analysis, without any discontinuity at 6 GHz as exists in today's 3GPP and ITU-R RMa models.

I. INTRODUCTION

The paper questions whether RMa path-loss models adopted for use above 6 GHz are supported by rural or mmWave evidence, and examines their derivation and limitations. It introduces CI and height-dependent CIH alternatives for rural macrocell modeling.

I. INTRODUCTION

  • The paper presents CI and height-dependent CIH models as physically based alternatives for rural mmWave coverage and interference analysis.The motivation is mmWave’s promise of multi-gigabit-per-second transfers and new applications; 3GPP TR 38.900 Release 14 introduced models for above-6-GHz frequencies.Source: §I · p. 1

II. 3GPP RMA PATH LOSS MODELS

  • RMa models generally address tall transmitter sites above 35 m and predict statistical received-signal strength in rural areas.The paper describes the 3GPP LOS model as two path-loss sections, with a steeper slope beyond its breakpoint.Source: §II · p. 1, A. 3GPP RMa LOS Path Loss Model · p. 1

I. INTRODUCTION

  • The RMa models in 3GPP TR 38.900 were adopted from ITU-R M.2135, whose LOS model source was based largely on 2.6 GHz measurements in metropolitan Tokyo.RMa was a new 3GPP TR 38.900 scenario, absent from the earlier below-6-GHz TR 36.873 study.Source: §I · p. 1, A. 3GPP RMa LOS Path Loss Model · p. 2

A. 3GPP RMa LOS Path Loss Model

  • The 3GPP/ITU-R RMa LOS model lacks published confirmation in rural settings or extensive measurements above 6 GHz, while its building-height correction terms are curve-fitting adjustments.The paper notes that the model’s breakpoint distance has a physical basis, unlike those correction terms.Source: A. 3GPP RMa LOS Path Loss Model · p. 2
  • With default heights, the LOS breakpoint exceeds the 10 km model limit at 9.1 GHz and is unusable above 32 GHz for any defined base-station height.The paper notes this may explain why 3GPP limits the model’s applicability to 30 GHz.Source: A. 3GPP RMa LOS Path Loss Model · p. 2

B. 3GPP RMa NLOS Path Loss Model

The 3GPP/ITU-R RMa NLOS model adapts the Sakagami model, developed from urban measurements, with extensions and correction factors. Its rural applicability and validation above 6 GHz remain limited.

B. 3GPP RMa NLOS Path Loss Model

  • The model originates in Sakagami’s 813 MHz and 1433 MHz measurements in metropolitan Tokyo, not rural settings.Its extensions include building-height substitutions, a frequency term, and a mobile-height correction.Source: B. 3GPP RMa NLOS Path Loss Model · p. 2
  • The model’s “max” operator patches close-in predictions that otherwise produce NLOS signal stronger than free-space loss or equivalent LOS predictions.The footnote specifies 0.8–30 GHz, although the authors report little supporting work above 6 GHz.Source: B. 3GPP RMa NLOS Path Loss Model · pp. 2–3
  • The rural applicability is questionable: Sakagami’s measurements were at 813 and 1433 MHz, and concludes the model applies only where average building height exceeds 5 m.An extension to 2200 MHz existed but was not included in 3GPP or ITU-R.Source: B. 3GPP RMa NLOS Path Loss Model · p. 3
  • The only validation effort the authors found was a limited 24 GHz campaign over 200–500 m; it combined LOS and NLOS data and reported no best-fit indicators.The authors subsequently conducted a 73 GHz measurement campaign.Source: B. 3GPP RMa NLOS Path Loss Model · p. 3

III. 73 GHZ RMA MEASUREMENTS

The authors measured rural path loss at 73 GHz in two southwest Virginia towns using a narrowband continuous-wave signal and high-gain horn antennas.

III. 73 GHZ RMA MEASUREMENTS

  • Measurements used a 73 GHz narrowband signal and high-gain narrowbeam horns, with maximum measurable path loss of 190 dB and 11.7 dBW EIRP.They were conducted in Riner and Christiansburg, Virginia, over two days in clear weather.Source: §III · p. 3
  • The receiver antenna was 1.6–2 m above ground, along country roads and streets near rural homes and businesses.The receiver was fixed on a tripod outside the measurement van.Source: §III · p. 3
  • Signal was detected at 14 LOS and 17 NLOS locations; LOS distances ranged from 33 m to 10.8 km, versus 3.4–10.6 km for NLOS.The average transmitter height was approximately 110 m.Source: §III · p. 3

IV. NOVEL RMA PATH LOSS MODELS AND SIMULATIONS

The paper proposes CI and CIH alternatives for rural macrocell path loss. The CI model uses a 1 m free-space reference, while CIH additionally incorporates base-station height through the path-loss exponent.

IV. NOVEL RMA PATH LOSS MODELS AND SIMULATIONS

  • The proposed CI and CIH models use a 1 m reference distance and are presented as physically grounded, accurate, reliable alternatives with few parameters for broad frequency ranges.The CIH model makes the path-loss exponent dependent on transmitter height.Source: §IV · p. 3

A. CI Path Loss Model

  • The CI model’s first term represents frequency-dependent free-space loss up to 1 m; beyond that, its path-loss exponent describes distance dependence.The model uses separation distance, frequency, and shadow fading; the distance can be 2D or 3D at multi-kilometer ranges.Source: A. CI Path Loss Model · p. 3
  • A 1 m free-space reference gives the CI model a single path-loss exponent parameter and a standardized basis for comparing path loss.The authors state that the first meter has no obstructions and that this reference models outdoor frequency dependence.Source: A. CI Path Loss Model · pp. 3–4
  • Fig. 2 relates transmitter height to NLOS path-loss decrease across 150 m–5 km separations and their average, for a 1.5 m mobile height.It depicts the existing 3GPP RMa NLOS model, not the proposed CI model.Source: Figure 2 · p. 4

B. CIH Path Loss Model

The CIH model retains the CI model’s close-in free-space basis while adjusting the path-loss exponent for base-station height. The authors select transmitter height as the key environmental parameter for rural modeling.

B. CIH Path Loss Model

  • The authors select transmitter height as the lone significant environmental parameter, given its 10–150 m range versus the receiver’s 1.5–10 m range over kilometer-scale distances.They set aside building height and street width as physically unsuitable for rural modeling.Source: B. CIH Path Loss Model · p. 4
  • In the existing 3GPP NLOS model, raising transmitter height from 10 m to 150 m reduces path loss by approximately 26 dB at 150 m separation and 32 dB at 5 km.The corrections are independent of frequency; the paper describes this difference as potentially yielding a thousand-fold received-power improvement.Source: B. CIH Path Loss Model · p. 4
  • CIH keeps the close-in free-space reference while making the path-loss exponent depend on base-station height, extending the CIF model’s approach to secondary frequency effects.The authors motivate this height dependence as an alternative to ad hoc correction factors.Source: B. CIH Path Loss Model · p. 4
  • The CIH weighting factor scales the path-loss exponent according to base-station height relative to the default or average height; setting it to zero reduces CIH to CI.CIH also reduces to CI when the base-station height equals the default height.Source: B. CIH Path Loss Model · p. 4

C. 3GPP RMa Monte Carlo Simulations

Monte Carlo simulations fit close-in (CI) models to 3GPP RMa LOS and NLOS path-loss samples. The fitted models use simple equations and have nearly identical RMSE performance to the more complex 3GPP/ITU-R models.

1) Case One – Simulation For 3GPP Default Parameters:

  • The simulations generated 50,000 samples at each of nine frequencies from 1 to 100 GHz for both LOS and NLOS.LOS distances ranged from 10 m to 10 km; NLOS distances ranged from 10 m to 5 km.Source: 1) Case One – Simulation For 3GPP… · p. 4
  • The fitted LOS and NLOS equations use distance coefficients of 23.1 and 30.4, respectively, alongside a 20 log10(fc) term.Both equations specify d ≥ 1 m.Source: 1) Case One – Simulation For 3GPP… · pp. 4–5
  • The CI models achieve nearly identical RMSE to the 3GPP/ITU-R models, with shadow-fading standard deviations of 5.9 dB for LOS and 8.2 dB for NLOS.The corresponding 3GPP values are 4–6 dB for LOS and 8.0 dB for NLOS.Source: 1) Case One – Simulation For 3GPP… · p. 5

2) Case Two – Simulation For 3GPP Default Parameters with Varying Base Station Heights:

Simulations varied base-station height from 10 m to 150 m to fit CIH models. Height dependence is much more pronounced for NLOS than LOS, while both models show RMSE comparable to the corresponding 3GPP models.

2) Case Two – Simulation For 3GPP Default Parameters with Varying Base Station Heights:

  • Simulations used base-station heights from 10 m to 150 m in 5 m increments across nine frequencies, generating 13,050,000 samples each for LOS and NLOS.The CIH fits minimized RMSE, with h_B0 set to 35 m to match the 3GPP default TX height.Source: 2) Case Two – Simulation For 3GPP… · p. 5
  • For LOS, the fitted CIH model shows only a minuscule decrease in effective PLE as base-station height increases, with 5.6 dB SF versus 4–6 dB for 3GPP.The paper attributes the small height dependence likely to the 3GPP model lacking an explicit TX-height correction factor.Source: 2) Case Two – Simulation For 3GPP… · p. 5
  • For NLOS, increasing base-station height from 10 m to 150 m reduces the effective PLE from 3.2 to 2.5; the CIH model RMSE is 8.7 dB, similar to 3GPP’s 8.0 dB shadow-fading standard deviation.The height effect is more noticeable than for LOS, where b_tx = −0.006.Source: 2) Case Two – Simulation For 3GPP… · p. 5
  • The fitted CI and CIH models have RMSE performance comparable to 3GPP while using simpler forms and fewer parameters.The passage identifies the model parameters and corresponding equation numbers in Table II.Source: 2) Case Two – Simulation For 3GPP… · p. 5

V. EMPIRICALLY-BASED RMA PATH LOSS MODELS

The empirical model parameters were fit using measured 73 GHz rural-macrocell path-loss data.

V. EMPIRICALLY-BASED RMA PATH LOSS MODELS

  • Measured 73 GHz path-loss values were used as sample data to derive best-fit CI and CIH parameters.The measurements are described in Section III.Source: §V · p. 5
  • The measured data were used to fit both the CI and CIH path-loss models.The passage points to closed-form best-fit optimization approaches in,.Source: §V · p. 5
  • Best-fit model parameters were derived from the measured path-loss sample data.The cited optimization approach is described in,.Source: §V · p. 5

A. Empirical CI Model Results

At 73 GHz, measured rural-macrocell data support CI models for LOS and NLOS, including LOS links beyond 10 km. The reported NLOS PLE is lower than those reported for UMi and UMa mmWave channels.

A. Empirical CI Model Results

  • The measurements distinguish LOS, NLOS, and LOS with partial diffraction; small-scale fluctuations were fractions of a dB in LOS and about 3–5 dB in NLOS.The data were locally time- and spatially averaged over a few seconds.Source: A. Empirical CI Model Results · p. 5
  • The measured LOS PLE is 2.16 at 73 GHz with a 110 m TX height, close to the free-space PLE of 2.LOS links extended beyond 10 km; diffraction edges added 15–20 dB over long-range distances and those data were excluded from the CI fit.Source: A. Empirical CI Model Results · p. 5
  • Clear-weather RMa NLOS measurements yielded a PLE of 2.75, below the reported 2.9–3.2 range for NLOS UMi and UMa mmWave channels.The paper attributes the difference to taller base-station heights and the lack of tall building obstructions in RMa.Source: A. Empirical CI Model Results · p. 5
  • The measured-data CI models are reported as simpler and comparably accurate to existing 3GPP/ITU-R RMa models.The presented LOS and NLOS equations use distance coefficients of 21.6 and 27.5, respectively.Source: A. Empirical CI Model Results · p. 6
  • The RMa CI LOS and NLOS models are reported valid up to and beyond 10 km, consistent with the existing 3GPP distance limits of 10 km and 5 km, respectively.Related UMa studies found the CI PLE independent of frequency beyond the first meter.Source: A. Empirical CI Model Results · p. 6

B. Empirical CIH Model Results

The empirical CIH models capture how increasing base-station height lowers the effective path loss exponent. At 150 m versus 10 m, the NLOS model predicts up to 22 dB lower path loss at 5 km.

B. Empirical CIH Model Results

  • The empirical CIH parameters were derived by equating the measured 73 GHz CI models at 110 m with simulated CIH models, then solving for the height dependence.Table II compares empirical and simulated CI/CIH parameters; its CIH reference base-station height is 35 m.Source: B. Empirical CIH Model Results · p. 6, Table II · p. 6
  • Figure 4 compares NLOS path-loss decreases across TX heights at T-R distances from 150 m to 5 km, with mobile height fixed at 1.5 m.It also reports the average over all T-R distances.Source: Figure 4 · p. 6, B. Empirical CIH Model Results · p. 6
  • For the CIH NLOS model, at a 5 km T-R separation, path loss can be reduced by up to 22 dB with a 150 m TX height compared with 10 m.Source: B. Empirical CIH Model Results · p. 6
  • The empirical CIH model’s effective PLE falls from 2.4 to 2.1 in LOS and from 3.2 to about 2.6 in NLOS as TX height rises from 10 m to 150 m.The fitted btx values are −0.03 for LOS and −0.049 for NLOS; at 110 m, the models revert to CI PLEs of 2.16 and 2.75, respectively.Source: B. Empirical CIH Model Results · p. 6

VI. CONCLUSIONS

The paper identifies weak empirical support for existing 3GPP/ITU-R RMa models above 6 GHz and develops CI and CIH alternatives using rural 73 GHz measurements and simulations. The measured height effect is smaller than the simulated 3GPP effect, and further measurements are needed.

VI. CONCLUSIONS

  • The existing 3GPP RMa models were derived from low-GHz metropolitan Tokyo measurements and were not verified above 6 GHz or in rural mmWave settings.The paper also identifies a mathematical inconsistency in the 3GPP LOS model above 9.1 GHz with default parameters and questions correction factors such as street width and average building height.Source: §VI · p. 6
  • The authors derive physically based CI and CIH models from 73 GHz rural Virginia measurements, simulations, and empirical data as alternatives to 3GPP/ITU-R RMa models.CIH incorporates base-station-height dependence without the extraneous correction factors criticized in the existing models.Source: §VI · pp. 6–7
  • At 150 m versus 10 m TX height, measured average NLOS path loss decreases by 17 dB, versus 29 dB in the simulated 3GPP model, potentially leading 3GPP to overestimate coverage and interference.The CIH models capture the decrease in effective PLE as TX height increases.Source: §VI · p. 7
  • The authors propose CI and CIH for RMa modeling above 6 GHz, with stated applicability through mmWave and beyond 100 GHz; additional measurements across frequencies and TX heights are needed for further validation.The models are validated with real-world mmWave measurements and have the same mathematical form as optional 3GPP path-loss models.Source: §VI · p. 7
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