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Investigation of Prediction Accuracy, Sensitivity, and Parameter Stability of Large-Scale Propagation Path Loss Models for 5G Wireless Communications
Shu Sun, Theodore S. Rappaport, Timothy A. Thomas, Amitava Ghosh, Huan C. Nguyen, Istvan Z. Kovacs, Ignacio Rodriguez, Ozge Koymen, Andrzej Partyka
TL;DR
The paper examines how three large-scale path loss models perform across microwave and mmWave frequencies and distances relevant to 5G design. Using measured datasets and sensitivity analyses, it finds that CI and CIF provide comparable accuracy with greater parameter stability than ABG, with CI suited to outdoor environments and CIF to indoor modeling.
Problem
Accurate propagation channel knowledge and models that remain reliable beyond their original measurement ranges are needed for 5G system design across microwave and mmWave frequencies.
Method
The paper compares ABG, CI, and CIF models using measured data, prediction-set evaluation, and sensitivity analyses across distances and frequencies.
Results
CI and CIF achieve comparable prediction accuracy to ABG while providing greater parameter stability and smaller sensitivity-test prediction errors with fewer parameters.
Takeaways & Limitations
The 1 m CI model is suitable for outdoor environments, whereas CIF is better suited to indoor modeling; both can be incorporated into existing 3GPP models by replacing the floating constant with a frequency-dependent free-space constant.
Abstract
from arXiv · showhide
This paper compares three candidate large-scale propagation path loss models for use over the entire microwave and millimeter-wave (mmWave) radio spectrum: the alpha-beta-gamma (ABG) model, the close-in (CI) free space reference distance model, and the CI model with a frequency-weighted path loss exponent (CIF). Each of these models have been recently studied for use in standards bodies such as 3GPP, and for use in the design of fifth generation (5G) wireless systems in urban macrocell, urban microcell, and indoor office and shopping mall scenarios. Here we compare the accuracy and sensitivity of these models using measured data from 30 propagation measurement datasets from 2 GHz to 73 GHz over distances ranging from 4 m to 1238 m. A series of sensitivity analyses of the three models show that the physically-based two-parameter CI model and three-parameter CIF model offer computational simplicity, have very similar goodness of fit (i.e., the shadow fading standard deviation), exhibit more stable model parameter behavior across frequencies and distances, and yield smaller prediction error in sensitivity testing across distances and frequencies, when compared to the four-parameter ABG model. Results show the CI model with a 1 m close-in reference distance is suitable for outdoor environments, while the CIF model is more appropriate for indoor modeling. The CI and CIF models are easily implemented in existing 3GPP models by making a very subtle modification -- by replacing a floating non-physically based constant with a frequency-dependent constant that represents free space path loss in the first meter of propagation.
I. INTRODUCTION
The paper addresses the need for path loss models applicable above 6 GHz by systematically comparing three candidate models across microwave and mmWave bands and deployment scenarios.
- 3GPP and WINNER channel models primarily apply below 6 GHz, requiring their modeling methodologies to be revisited for higher-frequency bands.
- The study compares the ABG, CI, and CIF large-scale path loss models across UMa, UMi street canyon, indoor office, and indoor shopping mall scenarios.
- The CI and CIF models use a physically based close-in reference that replaces ABG’s floating parameters, requiring fewer parameters while improving stability and accuracy.
A. UMa Measurements at Aalborg University
The Aalborg UMa campaign measured propagation in Vestby across four frequency bands using multiple transmitter locations and a mobile receiver.
- UMa measurements were collected in Vestby at 2, 10, 18, and 28 GHz during March 2015.
- Six transmitter locations used antenna heights of 20 or 25 m in a medium-sized European city with approximately 17 m buildings and 20 m streets.
- A 2 GHz continuous-wave signal was transmitted in parallel with the 10, 18, and 28 GHz signals as a reference.
- The receiver was mounted on a van at approximately 2.4 m height, driven at 20 km/h along routes confined within the experimental area.
B. UMa Measurements at UT Austin
The UT Austin campaign collected 38 GHz propagation measurements on campus using a sliding-correlator sounder and steerable horn antennas with different beamwidth configurations.
- Measurements were conducted at a 37.625 GHz center carrier frequency with 21.2 dBm maximum transmit power and 800 MHz RF bandwidth.
- The channel sounder provided a maximum measurable dynamic range of 160 dB.
- The campaign used narrowbeam transmit antennas and either narrowbeam or widebeam receive antennas.
C. UMi and InH Measurements at NYU
NYU conducted UMi street-canyon and indoor-office measurements at 28 and 73 GHz using directional steerable horn antennas at both link ends.
- NYU measured UMi street-canyon and indoor-office channels at 28 GHz and 73 GHz.
- The measurements used a 400 Mcps spread-spectrum sliding-correlator channel sounder.
- Directional steerable horn antennas were used at both the transmitter and receiver.
D. UMi and InH Measurements at Qualcomm
Qualcomm’s UMi and InH campaigns used multi-frequency channel sounding and directional or omnidirectional antenna measurements across outdoor campus, office, and shopping-mall environments.
- Measurement equipment and frequencies: The Qualcomm channel sounder operated at 2.9 GHz, 29 GHz, and 61 GHz for both UMi and InH measurements.Omnidirectional antennas were used at 2.9 GHz, while directional 10 dBi and 20 dBi antennas supported scans at 29 GHz and 61 GHz.
- Outdoor UMi measurements: The outdoor Qualcomm campaign covered an office campus with buildings, parking lots, streets, walkways, shopping malls, and dense rows of trees.Transmitter–receiver distances ranged from 35 m to 260 m.
- Indoor office measurements: The InH office campaign sampled two office floors with cubicles, closed offices, and corridors using four data sets and approximately 40 receiver locations per transmitter.Distances ranged from about 5 m to 67 m.
- Indoor shopping-mall measurements: The InH shopping-mall campaign used three transmitter locations and approximately 135 receiver locations across three floors.
III. LARGE-SCALE PROPAGATION PATH LOSS MODELS
The paper defines ABG, CI, and CIF as multi-frequency path loss models and evaluates their physical grounding, parameter stability, accuracy, and sensitivity across propagation conditions. CI and CIF retain comparable fitting accuracy while using physically anchored reference terms and generally providing more stable behavior than ABG.
- Model definitions: ABG, CI, and CIF are stochastic models describing large-scale propagation path loss over distance across relevant frequencies in a scenario.
- Physical anchoring and implementation: CI and CIF replace the floating intercept used by AB or ABG with a physically based, frequency-dependent free-space term.This requires only a subtle implementation change to existing 3GPP-style models.
- ABG model: The ABG model extends the 3GPP AB model by adding a frequency-dependent floating optimization parameter.Its parameters include distance and frequency coefficients, an optimized offset, and shadowing variation.
- CI model: The CI model uses free-space path loss at a close-in reference distance and a single path loss exponent to determine mean loss over distance and frequency.The model’s frequency dependence is embedded in the FSPL term, while its exponent is jointly calculated across measured frequencies.
- Reference-distance choice: 1 m provides a standardized close-in reference distance with excellent outdoor and indoor parameter stability and accuracy, despite possible near-field placement for large antenna arrays.The reported practical error from this near-field issue is negligible, and optimized-reference fits usually differ by no more than 0.3 dB in shadow-fading standard deviation.
- CIF behavior: CIF reduces to CI for a single frequency or when b = 0, and UMa CIF results show b very close to zero.This indicates that most frequency-dependent effects in those channels are incorporated through first-meter free-space propagation.
- Accuracy and stability: CI and CIF generally match ABG’s fitting accuracy within a fraction of a decibel while offering fewer parameters and more stable behavior across frequencies and distances.The CI path loss exponent varies by at most 0.5 across the single-frequency cases, whereas AB parameters can vary by 2.3 and 49.7 dB.
- Sensitivity to extrapolation: The ABG model can produce physically implausible extrapolations, including path loss much lower than free space near the transmitter and different far-distance predictions from CI.At 28 GHz in UMa NLOS, parameters derived from 2–38 GHz made ABG predict much less loss than CI out to approximately 30 m.
IV. PREDICTION AND SENSITIVITY PERFORMANCE
The study tests path loss prediction accuracy and parameter sensitivity by separating measured data into measurement and prediction sets. It compares performance under identical measurement-set conditions, using NLOS data because these environments have greater variability and shadow fading.
- The experiments evaluate ABG, CI, and CIF models outside the frequencies, locations, or distances used to construct them.Prediction performance and model sensitivity are tested by creating models from subsets of the measurements.
- Measurement sets determine optimized model parameters, while separate prediction sets evaluate shadow fading standard deviation as prediction error.As the measurement set changes with distance, frequency, or city, both optimized parameters and prediction error can change.
- The comparisons assess both prediction accuracy under identical measurement conditions and parameter stability across different measurement sets.
- Only NLOS data are used because these environments offer greater variability and higher shadow fading standard deviation.
A. Prediction in Distance
Distance-based tests vary the separation between fixed prediction data and measurement data across outdoor and indoor scenarios. The CI model remains especially stable when predicting closer-to-transmitter data from increasingly distant measurements, while ABG is more sensitive.
- A. Prediction in Distance: The distance investigation varies measurement sets farther from a fixed prediction set and recomputes optimum model parameters for each set.The prediction set is fixed while measurement distances progressively increase away from it.
- A. Prediction in Distance: The CI model’s prediction error remains constant as the measurement set moves farther away, whereas CIF generally increases and ABG varies substantially.
- A. Prediction in Distance: 10.5 dB is the ABG model’s prediction-set standard deviation at δd = 150 m, while its variation across the full range is 4.5 dB.
- A. Prediction in Distance: UMi and InH tests use shorter prediction distances than UMa, reflecting their generally shorter transmitter–receiver separations.UMi uses distances ≤50 m for prediction, while InH uses distances ≤15 m.
B. Prediction in Frequency
Frequency prediction excludes one frequency from the measurement set and uses the remaining frequencies to predict it. ABG exhibits the greatest error and parameter variation, while CI provides the most robust prediction across frequencies.
- B. Prediction in Frequency: Each frequency prediction uses one frequency as the prediction set and all other measured frequencies as the measurement set.For example, 2 GHz can be predicted from measurements at 10, 18, 28, and 38 GHz.
- B. Prediction in Frequency: The frequency-prediction experiment reports RMS error on both prediction and measurement sets for each excluded frequency.
- B. Prediction in Frequency: About 19 dB is the ABG prediction error at lower frequencies, where legacy 4G systems operate.The paper identifies this as evidence of ABG liability for simultaneous lower-frequency and mmWave use.
- B. Prediction in Frequency: The CI model provides the most robust and accurate prediction over all frequencies.
- B. Prediction in Frequency: ABG prediction-error variation across frequency is larger than the variation of the CI and CIF models.
C. Prediction Across Environments
Cross-environment results indicate stronger outdoor prediction ability for CI and an advantage for CIF in indoor settings. This distinction is relevant when selecting models for 5G mmWave standardization with incomplete measurement coverage.
- C. Prediction Across Environments: At 38 GHz, prediction combines Aalborg measurements at 2, 10, 18, and 28 GHz with Austin measurements at 38 GHz, testing cross-environment behavior.
- C. Prediction Across Environments: CI shows superior prediction ability and robust sensitivity for outdoor scenarios, while CIF has an advantage for indoor settings in most cases.
- C. Prediction Across Environments: The model distinction is useful for 5G mmWave standardization when complete measurements across frequencies and environments are unavailable.
V. CONCLUSION
Across 30 measurement datasets from 2–73 GHz, the CI and CIF models match ABG accuracy while offering simpler, more stable, and more robust behavior. The 1-m CI model is favored outdoors, whereas CIF is better suited indoors.
- 30 measurement datasets from 2 GHz to 73 GHz compare the four-parameter ABG, two-parameter CI, and three-parameter CIF models across UMa, UMi, and InH scenarios.
- Virtually identical accuracy is achieved by the 1-m CI model compared with CI-opt, while CI-opt can sometimes yield unrealistic PLEs.
- Comparable prediction accuracy is achieved by ABG, CI, and CIF, but CI and CIF use fewer parameters and provide greater parameter stability through a physical 1-m free-space reference.
- At 28 GHz, ABG NLOS can predict less than free-space loss near the transmitter and underestimate interference at several-hundred-meter distances, producing vastly different small-cell capacity simulations.
- CI and CIF outperform ABG in stability and prediction accuracy when predicting path loss at distances or frequencies different from those used for parameter fitting.
- The CI model is most suitable for outdoor environments, while CIF is well suited for indoor environments.
APPENDIX
The appendix derives closed-form parameter solutions for ABG, CI, and CIF by minimizing shadow-fading standard deviation. CIF requires a specified reference frequency to obtain a unique three-parameter solution.
- Closed-form ABG, CI, and CIF solutions are derived by minimizing the shadow-fading standard deviation.
- A. ABG Path Loss Model: ABG fitting minimizes the squared residual term P(B − αD − β − γF)^2 through zero partial derivatives with respect to α, β, and γ.
- B. CI Path Loss Model with Optimized Free Space Reference Distance: CI fitting with optimized d0 minimizes P(A − nD − b)^2 through the derivative with respect to n.
- C. CI Path Loss Model with 1-m Reference Distance: For the 1-m CI model, A is the path loss minus FSPL(f, 1 m), and D denotes 10log10(d).
- D. CIF Path Loss Model: CIF fitting minimizes P(A − D(a + gf))^2, solving for a and g before converting them to n and b.
- D. CIF Path Loss Model: A unique CIF solution is unavailable in general because two equations determine three unknowns; specifying f0 makes the solution unique.