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Probabilistic Omnidirectional Path Loss Models for Millimeter-Wave Outdoor Communications
Mathew K. Samimi, Theodore S. Rappaport, George R. MacCartney
TL;DR
Dense urban mmWave path loss modeling must account for whether propagation is LOS or NLOS, using information that varies with the site. This letter builds a probabilistic omnidirectional model from New York City measurements and ray-traced LOS probabilities, finding virtually no difference between two NLOS model choices.
Problem
Predicting omnidirectional path loss in dense urban mmWave channels requires models based on LOS and NLOS propagation conditions for estimating network coverage and capacity.
Method
The paper combines LOS free-space path loss with NLOS close-in or floating-intercept path loss and weights them using a site-specific LOS probability versus transmitter-receiver separation.
Results
The probabilistic model gives virtually no difference when NLOS path loss uses either the 1 m close-in free-space-reference model or the floating-intercept model.
Takeaways & Limitations
The models can estimate signal coverage, interference, and outage as functions of distance for future mmWave systems.
Abstract
from arXiv · showhide
This letter presents a probabilistic omnidirectional millimeter-wave path loss model based on real-world 28 GHz and 73 GHz measurements collected in New York City. The probabilistic path loss approach uses a free space line-of-sight propagation model, and for non-line-of-sight conditions uses either a close-in free space reference distance path loss model or a floating-intercept path loss model. The probabilistic model employs a weighting function that specifies the line-of-sight probability for a given transmitter-receiver separation distance. Results show that the probabilistic path loss model offers virtually identical results whether one uses a non-line-of-sight close-in free space reference distance path loss model, with a reference distance of 1 meter, or a floating-intercept path loss model. This letter also shows that site-specific environmental information may be used to yield the probabilistic weighting function for choosing between line-of-sight and non-line-of-sight conditions.
I. INTRODUCTION
The paper develops omnidirectional mmWave path loss models from New York City measurements, incorporating the site-specific probability of LOS at each transmitter-receiver separation. The resulting hybrid model makes the mean path loss probabilistic across LOS and NLOS conditions.
- The study models omnidirectional path loss using unique-pointing-angle 28 GHz and 73 GHz measurements collected in New York City.
- The approach extends conventional close-in free-space-reference and floating-intercept modeling by making the estimated mean path loss probabilistic.
- The proposed hybrid model uses LOS and NLOS data while weighting their mean path losses by a site-specific LOS probability function of transmitter-receiver separation.
II. PROBABILITY OF LINE-OF-SIGHT
LOS probability is defined by whether buildings or other obstructions block a straight path between transmitter and receiver. The study derives this probability from a 3-D site-specific urban environment model and ray-tracing tests.
- LOS denotes an unobstructed straight propagation path with zero reflections, whereas NLOS denotes obstruction involving scattering or one or more reflections.
- LOS and NLOS probabilities depend strongly on the physical site-specific environment containing the transmitter and receiver.
- The method represents nearby buildings as simple 3-D geometric shapes, exports the model to XML, and discretizes it numerically in MATLAB.
- For each transmitter, the method samples 100 evenly spaced receiver positions around a circle at the target separation distance.
R Separation (m)
Ray-tracing estimates LOS probability across four New York City transmitter sites and transmitter-receiver distances, then fits a common probability curve and site-specific parameters.
- Fig. 2 reports ray-traced LOS probability versus transmitter-receiver separation for COL1, COL2, KAU, and KIM2, plus their mean curve.
- The LOS probability is computed over all possible receiver locations in the modeled environments rather than only the measured receiver locations.
- KIM1 was excluded because its location near Washington Square Park produced unusually large LOS probabilities out to 150 m.
- Table I summarizes dBP and α values obtained by MMSE for the four transmitter locations considered.
- The MMSE fit to the mean LOS curve yielded dBP = 27 m and α = 71 m for the shared probability model.
III. PROBABILISTIC PATH LOSS MODEL
The model combines LOS and NLOS path-loss formulations by weighting them according to the probability of LOS at each transmitter-receiver distance. It supports either a 1 m close-in NLOS model or a floating-intercept NLOS model, which produce virtually identical probabilistic curves.
- The floating-intercept model can produce nonrealistic path-loss results when extrapolated outside the measured transmitter-receiver separation range.
- The hybrid model weighs LOS and NLOS path losses using a distance-dependent LOS probability for omnidirectional mmWave propagation.It combines a close-in free-space reference model for LOS with either a close-in or floating-intercept model for NLOS.
- A fixed reference distance of d0 = 1 m provides a viable alternative for modeling both LOS and NLOS conditions with little loss of accuracy.
- The LOS and NLOS formulations use path-loss exponents, floating-intercept parameters, and a lognormal random variable to represent large-scale shadowing.The shadowing variable has standard deviation σ in dB; α and β denote the floating-intercept model's intercept and slope.
- 28 GHz and 73 GHz measurements used 74 transmitter-receiver location combinations at each frequency, while the plotted models compare close-in and floating-intercept NLOS formulations.
- Virtually no difference appears between probabilistic curves using the 1 m close-in NLOS model and the floating-intercept NLOS model.The probabilistic mean remains between the LOS and NLOS models and follows the LOS data where LOS probability is 100%.
IV. CONCLUSION
The probabilistic model combines LOS and NLOS omnidirectional path-loss data using a site-specific LOS probability distribution. It produces virtually identical results with either NLOS model and can estimate coverage, interference, and outage as functions of distance.
- Virtually identical results arise when the probabilistic model uses either the NLOS 1 m close-in reference-distance or floating-intercept model.The comparison is reported for the 73 GHz New York City models in Fig. 4.
- The model uses a probability distribution for LOS derived from a 3-D site-specific database in New York City.
- The models may estimate signal coverage, interference, and outage as functions of distance for future millimeter-wave systems.The paper highlights sensitivity to LOS conditions for highly directional antennas and shorter wavelengths.