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Propagation Path Loss Models for 5G Urban Micro- and Macro-Cellular Scenarios
Shu Sun, Theodore S. Rappaport, Sundeep Rangan, Timothy A. Thomas, Amitava Ghosh, Istvan Z. Kovacs, Ignacio Rodriguez, Ozge Koymen, Andrzej Partyka, Jan Jarvelainen
TL;DR
The paper examines which large-scale path loss model better supports 5G design across urban micro- and macro-cellular scenarios. It compares ABG and CI models using 20 measurement or ray-tracing data sets from 2 GHz to 73.5 GHz, finding comparable modeling performance while the CI model provides greater simplicity, physical grounding, and stability.
Problem
5G system design requires suitable large-scale propagation path loss models across urban micro- and macro-cellular scenarios and a broad frequency range.
Method
The paper compares ABG and CI path loss models using 20 measurement or ray-tracing data sets spanning 2 GHz to 73.5 GHz.
Results
The CI and ABG models offer very comparable modeling performance, while CI uses one parameter and ABG uses three parameters.
Takeaways & Limitations
The CI model provides a physically based, simpler, and more stable alternative for modeling across frequencies, distances, and scenarios.
Abstract
from arXiv · showhide
This paper presents and compares two candidate large-scale propagation path loss models, the alpha-beta-gamma (ABG) model and the close-in (CI) free space reference distance model, for the design of fifth generation (5G) wireless communication systems in urban micro- and macro-cellular scenarios. Comparisons are made using the data obtained from 20 propagation measurement campaigns or ray-tracing studies from 2 GHz to 73.5 GHz over distances ranging from 5 m to 1429 m. The results show that the one-parameter CI model has a very similar goodness of fit (i.e., the shadow fading standard deviation) in both line-of-sight and non-line-of-sight environments, while offering substantial simplicity and more stable behavior across frequencies and distances, as compared to the three-parameter ABG model. Additionally, the CI model needs only one very subtle and simple modification to the existing 3GPP floating-intercept path loss model (replacing a constant with a close-in free space reference value) in order to provide greater simulation accuracy, more simplicity, better repeatability across experiments, and higher stability across a vast range of frequencies.
I. INTRODUCTION
The paper addresses the need for channel models supporting 5G system design as higher data-rate demand drives exploration of new technologies and frequency bands. It compares ABG and CI path loss models using 20 measurement or ray-tracing data sets in urban micro- and macro-cellular scenarios.
- Higher data-rate demand is motivating carriers to pursue new technologies and frequency bands, including millimeter waves, for 5G communications.The paper links this development to the need for channel characterization and new standards to assist system design.
- New standards and channel models are needed to support engineering design for emerging 5G systems using potential new spectra and architectural concepts.
- Prior work includes mmWave channel measurements from multiple research groups and scenarios, including urban microcellular, urban macrocellular, indoor, and street-canyon environments.
- This paper compares the ABG and CI free-space-reference path loss models in UMi and UMa scenarios using 20 measurement or ray-tracing data sets.
II. CLOSE-IN REFERENCE DISTANCE AND ALPHA-BETA-GAMMA PATH LOSS MODELS
The ABG and CI models describe large-scale path loss across frequency and distance, but differ in parameterization and physical grounding. The CI model uses a 1 m free-space reference and one optimized PLE, while ABG uses three fitted parameters.
- Model formulations: The CI model is easily implemented in existing 3GPP models by replacing a floating non-physical constant with a frequency-dependent free-space reference value.The modification represents free-space path loss in the first meter of propagation.
- Model formulations: The ABG model uses distance and frequency coefficients plus an optimized path-loss offset, whereas the CI model uses one PLE with a 1 m free-space reference.ABG parameters are obtained by minimizing shadow-fading standard deviation; CI embeds frequency dependence in the 1 m FSPL term.
- Comparative behavior: CI PLEs were 2.0 and 1.9 in LOS environments, close to the free-space value of 2, while shadow-fading differences were small.The CI model’s shadow-fading standard deviation was up to 0.7 dB higher than ABG, within stated measurement error.
- Comparative behavior: ABG parameters varied substantially across frequency and distance, with reported maximum variations of 0.8–2.3 for α, 11.7–77.3 dB for β, and 0.7–1.6 for γ.The paper characterizes these variations as sensitivity to incomplete frequency, distance, and transmitter/receiver-location coverage.
- Comparative behavior: CI PLE variation remained marginal, with largest multiple-frequency variations of 0.2, 0.4, and 0.1 for UMi SC, UMi OS, and UMa, respectively.Single-frequency UMi PLEs tended to increase only slightly with frequency, while UMa showed no significant frequency sensitivity.
- Comparative behavior: CI and ABG shadow-fading standard deviations differed by less than an order of magnitude and typically by 0.2 dB or less.The largest reported difference was 0.9 dB, making the models virtually identical in fit in most cases.
- Comparative behavior: At 28 GHz in UMi street-canyon NLOS, ABG overestimated path loss at greater distances relative to CI, while near-transmitter differences were less important for practical design.The comparison used parameters derived from 2–73.5 GHz data.
III. CONCLUSION
Across 20 worldwide measurement and ray-tracing data sets, the CI model matches ABG modeling performance while using one physically based parameter instead of three. Replacing the 3GPP floating constant with a 1 m free-space reference improves simplicity, stability, and accuracy across frequencies, distances, and scenarios.
- The CI model provides virtually identical modeling accuracy to ABG while using only the path loss exponent as its single parameter.ABG uses three parameters and reduces standard deviation by only a fraction of a dB.
- ABG’s additional error improvement is usually well below an order of magnitude of the models’ actual shadow fading standard deviation.
- The CI model is physically tied to transmitter power through a 1 m free-space reference distance, supporting use across varying distances without a calculator.
- Replacing the 3GPP floating constant with frequency-dependent 1 m free-space path loss yields easier analysis, stability, and accuracy across microwave and mmWave conditions.The modification uses a simpler model with fewer parameters.
APPENDIX
The appendix derives closed-form parameter solutions for the ABG and CI models by minimizing shadow fading standard deviation.
- The appendix provides mathematical derivations for closed-form ABG and CI parameter solutions that minimize shadow fading standard deviation.
- The derivations define the fitting objective through the shadow fading standard deviation for each model.
- These closed-form solutions support the model-parameter calculations used in the paper’s comparisons.
A. ABG Path Loss Model
The ABG model expresses path loss as a function of distance and frequency with three fitted coefficients, obtained by minimizing shadow fading through closed-form least-squares solutions.
- The ABG model uses α, β, and γ coefficients to model path loss dependence on distance, frequency, and an optimized offset.The model uses 1 m and 1 GHz reference values.
- Defining B as measured path loss, D as 10log10(d), and F as 10log10(f) transforms the fitting problem into a quadratic error objective.
- Minimizing the ABG fitting error requires setting partial derivatives with respect to α, β, and γ to zero.
B. CI Path Loss Model
The CI model uses a 1 m free-space reference and fits a single path loss exponent by minimizing the shadow fading standard deviation.
- The CI model is formulated with a 1 m reference distance and a free-space path loss term.
- For CI fitting, A is measured path loss minus 1 m free-space path loss, while D is 10log10(d).
- The CI shadow fading standard deviation is minimized by minimizing the sum of squared residuals (A − nD)^2.N denotes the number of path loss data points.
- The optimal CI path loss exponent n is obtained by setting the derivative of the squared-residual objective with respect to n to zero.