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Analysis of Human-Body Blockage in Urban Millimeter-Wave Cellular Communications
Margarita Gapeyenko, Andrey Samuylov, Mikhail Gerasimenko, Dmitri Moltchanov, Sarabjot Singh, Ehsan Aryafar, Shu-ping Yeh, Nageen Himayat, Sergey Andreev, Yevgeni Koucheryavy
TL;DR
mmWave communications are highly sensitive to human blockage, yet analytical models for this effect have been limited. The paper develops a tractable stochastic-geometry model for randomly located, randomly dimensioned human blockers and validates it with ray-launching simulations. The analysis shows that blockage depends on system geometry and human density, and that an optimal transmitter height exists.
Problem
Analytical models for human-caused mmWave blockage and its dependence on system and human parameters are limited, despite the importance of line-of-sight propagation in crowded environments.
Method
The paper models humans as randomly located cylinders with random dimensions, derives blockage probability for finite and infinitesimal receivers, and validates the analysis using ray-launching simulations.
Results
The analysis shows that blockage probability increases with human density and transmitter-receiver separation, decreases with transmitter height, and has an optimal transmitter height for each separation distance.
Takeaways & Limitations
The framework provides system designers with a tractable way to assess human-body blockage and select transmitter height in urban mmWave deployments.
Abstract
from arXiv · showhide
The use of extremely high frequency (EHF) or millimeter-wave (mmWave) band has attracted significant attention for the next generation wireless access networks. As demonstrated by recent measurements, mmWave frequencies render themselves quite sensitive to "blocking" caused by obstacles like foliage, humans, vehicles, etc. However, there is a dearth of analytical models for characterizing such blocking and the consequent effect on the signal reliability. In this paper, we propose a novel, general, and tractable model for characterizing the blocking caused by humans (assuming them to be randomly located in the environment) to mmWave propagation as a function of system parameters like transmitter-receiver locations and dimensions, as well as density and dimensions of humans. Moreover, the proposed model is validated using a ray-launcher tool. Utilizing the proposed model, the blockage probability is shown to increase with human density and separation between the transmitter-receiver pair. Furthermore, the developed analysis is shown to demonstrate the existence of a transmitter antenna height that maximizes the received signal strength, which in turn is a function of the transmitter-receiver distance and their dimensions.
I. INTRODUCTION AND MOTIVATION
mmWave links are especially vulnerable to blockage in crowded urban environments, while existing blockage models provide limited detail. The paper addresses this gap with a tractable human-body blockage model validated against ray-launching simulations.
- Motivation: mmWave propagation suffers losses from obstacles that were comparatively insignificant for UHF signals.The issue is particularly relevant in densely populated areas where mmWave networks are likely to be deployed.
- Research gap: Existing mmWave channel research has devoted limited attention to analytical blockage modeling.Prior models primarily considered building blockage with simplifying assumptions about receiver size and blocker placement.
- Modeling challenge: Human blockers require modeling their random heights alongside transmitter and receiver heights, separation, and object dimensions.Shorter mmWave links and lower transmitter heights make people near the receiver relevant blockers.
- Contribution: The paper proposes a tractable human-body blockage model using randomly located cylindrical humans with arbitrarily distributed heights and radii.The model derives line-of-sight blockage probability as a function of receiver dimension and transmitter-receiver separation.
- Contribution: The model is validated against detailed mmWave ray-launching simulations and yields an optimal transmitter height proportional to transmitter-receiver separation.The validation supports the paper’s design insights for crowded outdoor environments.
A. Spatial model
The spatial model represents a transmitter and receiver at specified heights and separation, with human blockers modeled as randomly dimensioned cylinders distributed across the landscape.
- Spatial model: The scenario places a transmitter at height hT and a receiver at height hR, with receiver-base separation r from the transmitter base.The considered scenario is illustrated in Fig. 1.
- Blocker model: Human blockers are modeled as cylinders with random height H and base diameter D.Human height follows a Normal approximation, while diameter is uniformly distributed between dmin and dmax.
- Spatial distribution: Blocker centers follow a Matern hard-core point process with intensity λI, preventing overlap between blocker locations.The receiver has length lm, and blockage probability is evaluated for both finite and infinitesimal receivers.
B. Blockage probability
The blockage analysis transforms the spatial blocker process into a distance-dependent effective process and models each blocker’s projected shadow on the receiver circumference. It then computes shadow distributions numerically when closed forms are unavailable.
- Effective blocker process: Blocker intensity along the transmitter-receiver path is λ(x) = λI g(x), where g(x) is the probability that a blocker exceeds the required height at distance x.The effective process is obtained by thinning the original process according to the height-dependent probability g(x).
- Effective blocker process: The effective blocker intensity increases nonlinearly with distance from the transmitter because more blockers can intersect the line of sight.The intensity is minimal at x = 0 and increases as x approaches the receiver.
- Circumference projection: The projected blocker centers form a process on the circumference, whose intensity is obtained by analyzing the expected number of blocker centers in an angular sector.The projection widths are then used to characterize coverage of the receiver-side arc.
- Numerical evaluation: The shadow distribution and related integrals are evaluated numerically because the error-function terms prevent elementary closed-form solutions.This numerical evaluation supplies the distributions needed for blockage-probability calculations.
- Shadow geometry: For r >> D, the receiver-side arc can be replaced by a chord, allowing each blocker’s shadow length W to be derived from blocker width D and distance L.The shadow is treated as a random variable whose distribution is obtained from the ratio of the transformed blocker-width and distance variables.
C. Non-infinitesimal receiver
For a receiver with nonzero length, the model treats projected human shadows as random blocked intervals in a renewal process and derives the probability that the entire receiver is blocked.
- The receiver interval is modeled as an arc of length l covered by random-length projected shadows whose centers form a Poisson process.
- Projected shadows generate alternating blocked and unblocked intervals, forming a renewal process on the receiver path.
- Unblocked intervals are exponentially distributed with parameter µ and mean E[ω] = 1/µ.
- The probability that a random point is blocked is E[η]/E[ξ], while the probability that it is unblocked is E[ω]/E[ξ].
- The total blockage probability is obtained by conditioning on whether the receiver's left endpoint is blocked and evaluating whether the blocked interval extends across its length.
- When the receiver length is smaller than the minimum blocker diameter, a specialized expression gives the total blockage probability.
D. Infinitesimal receiver
For an infinitesimal receiver, the paper calculates line-of-sight probability over a rectangular blocking area by combining Poisson blocker counts with independent geometric and height-based blockage events.
- The point-receiver model uses a rectangular area of length r and width bounded by the maximum blocker width dmax.
- Blocker counts in the area are represented by Poisson events Ai, including the zero-blocker event A0.
- Event B0 denotes a blocker whose base radius cannot cross the line of sight, while complementary event B1 denotes sufficient lateral extent.
- Event C0 denotes a blocker that is not tall enough to block the line of sight, while complementary event C1 denotes sufficient height.
- Because blocker height and width are independent, the joint event probability factors as Pr{B1|C0} = Pr{B1}Pr{C0}.
A. Calibration with simulations
The analytical blockage model is calibrated and compared against ray-launching and system-level simulations. The comparison shows close agreement, with deviations attributed to replacing the hard-core blocker process by an equivalent Poisson process.
- Calibration with simulations: The ray-launching tool compares simulated LoS, non-LoS, and average path loss with the analytical model.The analytical average path loss uses LoS probability together with LoS and non-LoS path-loss components.
- Calibration with simulations: The analytical and average ray-launching path losses differ only marginally over the simulated shorter distances.The simulations are restricted to shorter distances because of excessive computational complexity.
- Calibration with simulations: LoS path loss exceeds the corresponding non-LoS path loss by at least 20 dB.The paper associates absence of the LoS component with a high probability of a poor mmWave link due to very low SNR.
- Calibration with simulations: The analytical blockage probabilities are compared with simulations for point and 10 cm interval receivers.The system-level simulator evaluates full, at-least-half, and at-least-part receiver blockage events using subdivided receiver lines.
- Calibration with simulations: The maximum absolute simulation-model difference is below 0.1 for a 10 cm receiver.The largest deviation occurs around average distances of 40–100 meters, while deviations are marginal at short and long distances.
B. Understanding analytical results
The analytical results show how transmitter height, separation distance, and receiver size shape mmWave blockage and path loss. They reveal an optimal transmitter height and systematic blockage trends with distance and receiver dimensions.
- Understanding analytical results: For every transmitter-receiver separation distance, an optimal transmitter height minimizes average path loss.The average path loss is evaluated as a function of transmitter height.
- Understanding analytical results: Point receivers have slightly higher blockage probability than interval receivers for every separation distance and receiver-size-to-blocker-diameter ratio.The comparison varies r and l/dmean.
- Understanding analytical results: Increasing l/dmean decreases the blockage probability for interval receivers.Here l is the receiver size and dmean is the mean blocker diameter.
- Understanding analytical results: Blockage probability decreases exponentially with transmitter height and increases with transmitter-receiver separation distance.For large transmitter heights, the distance effect is linear; for smaller heights, it is exponential.
- Understanding analytical results: At sufficiently large separation distances, blockage probability becomes nearly constant for human density λI = 0.3.The paper explains this saturation by the high probability of encountering a blocker along the LoS path.
IV. CONCLUSION
The analysis shows that line-of-sight blockage is consequential in crowded urban mmWave environments and develops a framework for studying blockage across key system parameters. Ray-launching validation confirms that the analysis accurately models human-body blockage and identifies an optimal transmitter height.
- At least 20 dB separates LoS and non-LoS path loss, underscoring the importance of LoS blockage analysis for mmWave communications.
- The framework captures blockage probability for infinitesimal and fixed-length receivers across transmitter height, receiver height, separation, blocker density, and blocker dimensions.
- The analysis demonstrates an optimal transmitter height, providing a system-design parameter for maximizing received signal strength.
- Advanced ray-launching simulations confirm that the analytical model accurately represents human-body blockage in urban mmWave deployments.