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Path Loss, Shadow Fading, and Line-Of-Sight Probability Models for 5G Urban Macro-Cellular Scenarios

Shu Sun, Timothy A. Thomas, Theodore S. Rappaport, Huan Nguyen, Istvan Z. Kovacs, Ignacio Rodrigue

arXiv:1511.07374v2cs.ITmath.IT

TL;DR

Emerging technologies, potential new spectra such as millimeter-wave (mmWave) frequencies, and novel architectural concepts, make reliable channel models vital for 5G design. The paper analyzes UMa propagation measurements from Aalborg at 2, 10, 18, and 28 GHz and Austin at 38 GHz, modeling LOS probability, path loss, and distance-dependent shadow fading. Dual-slope path loss reduces RMS error by no more than 0.3 dB in most cases, while Aalborg shadow-fading magnitude slightly increases with distance in LOS and decreases in NLOS.

  • Problem

    Emerging technologies, potential new spectra such as millimeter-wave (mmWave) frequencies, and novel architectural concepts, make reliable channel models vital for 5G design.

    Source: §I · p. 1

  • Method

    The paper analyzes UMa propagation measurements from Aalborg at 2, 10, 18, and 28 GHz and Austin at 38 GHz, modeling LOS probability, path loss, and distance-dependent shadow fading.

    Source: §I · p. 2, §VII · p. 6

  • Results

    Dual-slope path loss reduces RMS error by no more than 0.3 dB in most cases, while Aalborg shadow-fading magnitude slightly increases with distance in LOS and decreases in NLOS.

    Source: §VI · p. 6, §VII · p. 7

  • Takeaways & Limitations

    The dual-slope model is likely not worth its added computational complexity for the studied UMa distance range, and ABG and CI remain potential omnidirectional path loss models.

    Source: §VII · pp. 6–7

    Shadow-fading trends may reflect limited measurement range, with fewer detectable measurements at larger distances.

    Source: §VI · p. 6

Abstract

from arXiv · show

This paper presents key parameters including the line-of-sight (LOS) probability, large-scale path loss, and shadow fading models for the design of future fifth generation (5G) wireless communication systems in urban macro-cellular (UMa) scenarios, using the data obtained from propagation measurements at 38 GHz in Austin, US, and at 2, 10, 18, and 28 GHz in Aalborg, Denmark. A comparison of different LOS probability models is performed for the Aalborg environment. Alpha-betagamma and close-in reference distance path loss models are studied in depth to show their value in channel modeling. Additionally, both single-slope and dual-slope omnidirectional path loss models are investigated to analyze and contrast their root-mean-square (RMS) errors on measured path loss values. While the results show that the dual-slope large-scale path loss model can slightly reduce RMS errors compared to its singleslope counterpart in non-line-of-sight (NLOS) conditions, the improvement is not significant enough to warrant adopting the dual-slope path loss model. Furthermore, the shadow fading magnitude versus distance is explored, showing a slight increasing trend in LOS and a decreasing trend in NLOS based on the Aalborg data, but more measurements are necessary to gain a better knowledge of the UMa channels at centimeter- and millimeter-wave frequency bands.

I. INTRODUCTION

5G’s emerging spectra and architectures make reliable channel models important for system design, while existing models require reconsideration above 6 GHz. This paper examines UMa propagation measurements across centimeter- and millimeter-wave bands to study LOS probability, path loss, and shadow fading.

I. INTRODUCTION

  • Reliable channel models are needed to assist 5G system design amid emerging technologies, new spectra such as mmWave, and novel network architectures.Source: §I · p. 1
  • Existing 3GPP and WINNER channel models are applicable only below 6 GHz, so modeling needs to be revisited for higher bands.Source: §I · p. 1
  • Single-slope models are simple, but their RMS error can be large across wide transmitter-receiver distances, especially in NLOS environments.Dual-slope models use different slopes across distance regions to target lower RMS error.Source: §I · pp. 1–2
  • The study analyzes UMa measurements at 2, 10, 18, 28, and 38 GHz to examine LOS probability, path loss, and distance-dependent shadow fading.The measurements were conducted in Aalborg, Denmark, and Austin, US.Source: §I · p. 2
  • The paper studies ABG and CI path loss models, single- and dual-slope path loss, and distance-dependent shadow fading for 5G UMa channel modeling.Angular channel statistics are identified as future work beyond this paper’s scope.Source: §I · p. 2

II. PROPAGATION MEASUREMENTS IN UMA SCENARIOS

The paper draws on two outdoor UMa propagation measurement campaigns, one at UT Austin and one at Aalborg University.

II. PROPAGATION MEASUREMENTS IN UMA SCENARIOS

  • The study uses outdoor UMa propagation measurements from campaigns at UT Austin in the US and Aalborg University in Denmark.Source: §II · p. 2

A. UMa Measurements at UT Austin

The UT Austin campaign measured 38 GHz propagation from campus building transmitters to surrounding receiver locations, using directional horn antennas and a sliding-correlator sounder. The analysis uses narrowbeam receiver data.

A. UMa Measurements at UT Austin

  • The 38 GHz UT Austin campaign used a spread-spectrum sliding-correlator sounder, steerable high-gain horn antennas, and up to 21.2 dBm transmit power over 800 MHz bandwidth.The maximum measurable dynamic range was 160 dB.Source: A. UMa Measurements at UT Austin · p. 2
  • Three of four transmitter sites had heights of 23 m or 36 m, and the campaign measured 33 narrowbeam and 15 widebeam transmitter-receiver combinations.The reported 3D separation ranges were 61–930 m for narrowbeam and 70–728 m for widebeam receiver measurements.Source: A. UMa Measurements at UT Austin · p. 2
  • The analysis uses narrowbeam receiver measurements, comprising 21 LOS and 12 NLOS omnidirectional data points, while widebeam studies are deferred.For each location combination, PDPs were recorded across multiple transmitter and receiver azimuth and elevation pointing combinations.Source: A. UMa Measurements at UT Austin · p. 2

B. UMa Measurements at Aalborg University

The Aalborg campaign collected UMa measurements in Vestby across four frequency bands, with a mobile receiver recording received signal strength and GPS position along selected routes.

B. UMa Measurements at Aalborg University

  • Vestby was characterized as a medium-sized European city with approximately 17 m buildings and 20 m streets, and six transmitter sites at 15, 20, or 25 m height.Source: B. UMa Measurements at Aalborg… · p. 2
  • The campaign measured 2, 10, 18, and 28 GHz using continuous-wave signals, with the 2 GHz signal transmitted in parallel as a reference.Source: B. UMa Measurements at Aalborg… · p. 2
  • A van-mounted receiver drove at 20 km/h on routes within transmitter antenna beamwidths, recording received signal strength and GPS at 20 samples/s.Data points were visually classified as LOS or NLOS using Google Maps.Source: B. UMa Measurements at Aalborg… · p. 2

III. LINE-OF-SIGHT PROBABILITY IN UMA SCENARIOS

The section compares four LOS-probability models against Aalborg measurements. The inverse exponential model has the lowest MSE, while the NYU model visually fits best except near 150 m.

III. LINE-OF-SIGHT PROBABILITY IN UMA SCENARIOS

  • LOS modeling uses only AAU data because the UT-Austin dataset is too sparse, with measured locations classified as LOS or NLOS using Google Maps.The analysis compares four models for the Aalborg measurements.Source: §III · p. 2
  • The compared models include 3GPP d1/d2, NYU’s squared-probability variant, and an inverse exponential; d1 and d2 were optimized to fit the data.The 3GPP UMa model specifies d1=18 m and d2=63 m for a 25 m base height, while the measured transmitter heights were 20 or 25 m.Source: §III · pp. 2–3
  • The inverse exponential model had the lowest MSE; visually, NYU fit best except near 150 m, while 3GPP dropped steepest within 200 m and d1/d2 extended beyond 1 km.The measured data appear most likely to be LOS within 200 m; the authors note that more data are needed to assess the original 3GPP model.Source: §III · p. 3, Figure 1 · p. 3
  • The measured LOS probability was smoothed using points within +/-5 m of each distance, then each model was fitted by MMSE across the curve locations.The fitted model parameters are summarized in Table I.Source: §III · p. 3, Table I · p. 3

IV. SINGLE-SLOPE ALPHA-BETA-GAMMA AND CLOSE-IN REFERENCE DISTANCE PATH LOSS MODELS

The section compares two multi-frequency path-loss models: the three-parameter ABG model and the physics-based, 1 m reference-distance CI model. Their measured shadow-fading difference is small, supporting CI as suitable for UMa mmWave channels.

IV. SINGLE-SLOPE ALPHA-BETA-GAMMA AND CLOSE-IN REFERENCE DISTANCE PATH LOSS MODELS

  • ABG models mean path loss over frequency and distance using distance and frequency coefficients plus an optimized offset, fitted by MMSE to minimize shadow-fading standard deviation.The three parameters are α, β, and γ.Source: §IV · p. 3
  • CI combines 1 m free-space path loss with a path-loss exponent, embedding frequency dependence in the reference loss and using one parameter rather than ABG’s three.The 1 m reference distance is presented as a standard that simplifies comparison and supports intuition and rapid path-loss computation.Source: §IV · pp. 3–4
  • The authors describe CI as grounded in propagation principles, while ABG’s floating offset lacks a physical basis and its frequency-weighting term has no proven physical basis for outdoor channels.The paper notes that outdoor mmWave path-loss exponent has little frequency dependence, whereas indoor path loss shows noticeable frequency dependence beyond the first meter.Source: §IV · pp. 3–4
  • The CI model’s shadow-fading standard deviation is up to 0.4 dB higher than ABG’s, a nonsignificant difference an order of magnitude below either model’s actual shadow fading.The authors conclude that the single-parameter, physics-based CI model is suitable for UMa mmWave channels.Source: §IV · p. 4

V. SINGLE-SLOPE AND DUAL-SLOPE PATH LOSS MODELS

The section compares single- and dual-slope CI and FI path-loss models for UMa scenarios. Dual-slope models reduce shadow-fading error slightly, but the improvement does not justify their added complexity over the studied distance range.

V. SINGLE-SLOPE AND DUAL-SLOPE PATH LOSS MODELS

  • The study evaluates single-slope CI and FI and dual-slope CI and FI models; the dual-slope breakpoint is selected by minimizing global shadow-fading standard deviation.The fitting procedure iteratively tests measured distances as breakpoints in 1 m increments.Source: §V · p. 4
  • Negative fitted slopes are unusable where the sample count is low.The limitation applies to negative slopes marked with an asterisk.Source: §V · p. 5
  • The 38 GHz and 28 GHz path-loss scatter plots show no obvious dual-slope breakpoint, where the rate of path-loss change differs before and after the breakpoint.The figures compare single- and dual-slope models; σ denotes shadow-fading standard deviation.Source: §V · p. 5, Figure 4 · p. 5, Figure 5 · p. 5
  • For UMa scenarios, the single-slope CI model’s NLOS PLE is 2.6–3.2 from 2 to 38 GHz; CI also exhibits consistent PLEs across frequencies and environments, making it preferable to FI.Source: §V · pp. 5–6
  • For fixed frequencies, dual-slope models reduce shadow-fading standard deviation in every investigated case, but the FI–CI differences stay within 1 dB.At 28 GHz, dual-slope CI reduces the standard deviation from 6.7 dB to 6.6 dB; typical shadow fading is 6–10 dB.Source: §V · p. 6
  • Dual-slope models reduce RMS error by no more than 0.3 dB in most cases, making them unnecessary over the studied range despite possible need at larger distances.The 28 GHz figure compares single- and dual-slope CI and FI models.Source: Figure 5 · p. 5, §V · p. 6

VI. DISTANCE-DEPENDENT SHADOW FADING MODELS

The section models shadow-fading magnitude against 3D transmitter–receiver distance and reports opposite distance trends in LOS and NLOS for Aalborg measurements, while noting that further study is needed.

VI. DISTANCE-DEPENDENT SHADOW FADING MODELS

  • The study models shadow-fading magnitude as a function of 3D T-R distance using the CI and FI single-slope path-loss models.The fitted relationship is SF [dB] = A*d + B; A is the distance-change rate and B the MMSE-fit intercept.Source: §VI · p. 6
  • Fig. 6 plots shadow-fading magnitude against 3D T-R distance for 28 GHz, with magnitudes averaged in 1 m distance bins.The figure includes scatter plots and fitted linear models.Source: Figure 6 · p. 6, §VI · p. 6
  • Aalborg measurements show shadow-fading magnitude slightly increasing with distance in LOS and decreasing in NLOS; limited measurement range may explain the NLOS trend.Similar trends were observed at 2, 10, and 18 GHz; the 38 GHz set had relatively few data points.Source: §VI · p. 6

VII. CONCLUSION

The paper presents UMa LOS-probability, path-loss, and distance-dependent shadow-fading models from measurements across Aalborg and Austin. It concludes that dual-slope models offer only small error reductions in most cases, while further measurements are needed to clarify distance-related shadow fading.

VII. CONCLUSION

  • The study presents LOS-probability, multi-frequency ABG and CI path-loss, single- and dual-slope CI and FI path-loss, and distance-dependent shadow-fading models.The measurements cover 2, 10, 18, and 28 GHz in Aalborg and 38 GHz in Austin.Source: §VII · p. 6
  • Dual-slope path loss reduces RMS error by no more than 0.3 dB in most cases, making the gain unlikely to justify its added computational complexity.The paper notes a 1.9 dB improvement for the 38 GHz dual-slope CI model, but it produced a negative second slope.Source: §VII · p. 7
  • Measured AAU data suggest shadow-fading magnitude increases with distance in LOS and decreases in NLOS, but limited measurement range may explain the NLOS trend.The authors encourage further measurements, especially at larger distances, to improve understanding at centimeter- and millimeter-wave frequencies.Source: §VII · p. 7
  • The CI model ties path loss to transmitted power and has a frequency-dependent first-meter factor; its PLEs are more similar across frequencies, with virtually identical shadowing standard deviation to ABG or FI.Source: §VII · p. 7
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