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Geometry-Based Vehicle-to-Vehicle Channel Modeling for Large-Scale Simulation

Mate Boban, Joao Barros, Ozan K. Tonguz

arXiv:1305.0124v3cs.NI

TL;DR

V2V simulators commonly use efficient statistical models that do not explicitly account for surrounding objects, while detailed geometry-based models are too computationally expensive for large networks. GEMV2 uses outlines of vehicles, buildings, and foliage to classify links and model their signal variations, and extensive measurements show that it captures propagation effects across multiple environments while scaling to large simulations.

  • Problem

    VANET simulators largely use statistical propagation models that ignore surrounding objects, whereas accurate geometry-based alternatives are too expensive for large-scale networks.

  • Method

    GEMV2 uses object outlines and R-trees to classify LOS, NLOSv, and NLOSb links and calculate deterministic large-scale and stochastic small-scale signal variations.

  • Results

    GEMV2 successfully captures small- and large-scale propagation effects across highway, urban, suburban, and open-space measurements and simulates hundreds of thousands of communicating vehicle pairs.

  • Takeaways & Limitations

    Location-specific modeling with limited geographic information supports efficient, fine-grained V2V channel simulation for large VANET networks.

Abstract

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Due to the dynamic nature of vehicular traffic and the road surroundings, vehicle-to-vehicle (V2V) propagation characteristics vary greatly on both small- and large-scale. Recent measurements have shown that both large static objects (e.g., buildings and foliage) as well as mobile objects (surrounding vehicles) have a profound impact on V2V communication. At the same time, system-level Vehicular Ad Hoc Network (VANET) simulators by and large employ simple statistical propagation models, which do not account for surrounding objects explicitly. We designed GEMV$^2$ (Geometry-based Efficient propagation Model for V2V communication), which uses outlines of vehicles, buildings, and foliage to distinguish the following three types of links: line of sight (LOS), non-LOS due to vehicles, and non- LOS due to static objects. For each link, GEMV$^2$ calculates the large-scale signal variations deterministically, whereas the small- scale signal variations are calculated stochastically based on the number and size of surrounding objects. We implement GEMV$^2$ in MATLAB and show that it scales well by using it to simulate radio propagation for city-wide networks with tens of thousands of vehicles on commodity hardware. We make the source code of GEMV$^2$ freely available. Finally, we validate GEMV$^2$ against extensive measurements performed in urban, suburban, highway, and open space environment.

I. INTRODUCTION

GEMV2 addresses the gap between indiscriminate statistical propagation models and computationally expensive geometry-based models by using object outlines for location-specific V2V modeling. It distinguishes LOS, NLOSv, and NLOSb links, models their signal variations, and validates scalable simulations against measurements.

  • Motivation: Simple statistical models ignore link-specific conditions, limiting accurate link-level VANET modeling in complex environments and safety applications.They remain useful for overall communication statistics, but previous measurements found them inaccurate for individual links.
  • Motivation: GEMV2 bridges statistical and ray-tracing approaches by using nearby buildings, foliage, and vehicles through their geographic outlines.The model limits calculations while retaining location-specific propagation effects.
  • Model: GEMV2 classifies links as LOS, NLOSv, or NLOSb and calculates large-scale signal variation deterministically for each type.NLOSv denotes vehicle obstruction, while NLOSb denotes building or foliage obstruction.
  • Model: The model calculates small-scale signal variation stochastically from the number and size of surrounding objects, using geographic data from mobility traces and object databases.R-trees support efficient processing of the object outlines.
  • Validation and scalability: GEMV2 successfully captures small- and large-scale effects across highway, urban, suburban, and open-space environments and scales to networks with tens of thousands of objects.The implementation is in MATLAB, with source code made freely available.

II. MEASUREMENT SETUP

The study collected V2V measurements across diverse routes and environments in Porto and Pittsburgh using passenger and commercial vehicles. Measurements included received power and packet delivery data, with links classified by LOS conditions using synchronized video and geographic information.

  • Vehicles and hardware: The experiments used regular passenger cars and commercial vehicles equipped with NEC LinkBird-MX V3 platforms implementing IEEE 802.11p.Vehicle dimensions were documented separately.
  • Link classification: Measured links were separated into LOS, NLOSv, and NLOSb categories using synchronized videos recorded during the experiments.Video synchronization used recognizable geographic locations and GPS coordinates, with periodic re-synchronization to reduce misalignment.
  • Data and objects: The study used received power and packet delivery rate to characterize the effects of vehicles, buildings, and foliage on V2V communication.The Porto dataset included building and vehicle information, supplemented by building and foliage outlines from OpenStreetMap.

III. USING R-TREES FOR EFFICIENT VANET OBJECT MANIPULATION

GEMV2 represents vehicles, buildings, and foliage with outlines organized in R-trees, enabling efficient spatial queries for large VANET simulations. Its geometric search region captures nearby objects affecting signal variations and link propagation.

  • Spatial data structures: R-trees organize geographically located vehicle, building, and foliage outlines for efficient object manipulation in large VANETs.The approach avoids checking every vehicle pair naively and uses hierarchical rectangular bounds.
  • Spatial data structures: The R-tree operation can become quadratic when all bounding rectangles overlap, although such extreme overlap does not occur in vehicular environments.
  • Geometric search region: The ellipse between Tx and Rx includes objects whose summed distances to the endpoints are below r, supporting large- and small-scale signal calculations.Its major diameter is r, while the area shrinks toward zero as Tx–Rx distance approaches r.
  • Modeled objects: GEMV2 focuses on vehicles, buildings, and foliage because these objects materially affect V2V propagation, while smaller static objects are difficult to obtain and model efficiently.
  • Validation and scalability: The model was validated against extensive measurements while limiting complexity to require orders of magnitude fewer computations than more complex geometry-based models.

A. Classification of link types

GEMV2 assigns each V2V link to LOS, NLOSv, or NLOSb and applies link-specific models to large- and small-scale signal variations. The design combines deterministic propagation calculations with a stochastic object-based variation model.

  • Link classification: GEMV2 distinguishes LOS, NLOSv caused by vehicles, and NLOSb caused by buildings or foliage.
  • NLOSb communication: NLOSb modeling uses single-interaction reflections and diffractions for around-the-corner communication, with log-distance path loss when such rays are absent or weak.GEMV2 can omit reflection and diffraction calculations for faster execution.
  • LOS communication: LOS large-scale variations use a two-ray ground-reflection model with exact antenna heights for the communicating vehicles.The exact heights affect interference between the direct and ground-reflected rays.
  • LOS communication: The road’s effective reflection-coefficient range is calibrated with relative permittivity ϵr, using a value selected to minimize error in the Porto Open Space dataset.

2) NLOSv communication:

For NLOSv links, GEMV2 models vehicle-induced obstruction through diffraction over and around vehicles, while reflections depend on vehicle height and the modeled ray interactions remain computationally bounded.

  • Vehicle diffraction: NLOSv attenuation uses exact obstructing-vehicle locations and dimensions with multiple knife-edge diffraction over vehicle rooftops.
  • Vehicle diffraction: The model also includes horizontal-plane diffraction from each vehicle side in addition to vertical-plane diffraction over roofs.
  • Vehicle reflection: Building and vehicle reflections are modeled, but a vehicle reflects only when it is taller than both communicating vehicles’ antennas.Consequently, reflecting vehicles are predominantly tall vehicles.
  • Static-object interactions: NLOSb diffraction over buildings is calculated in the horizontal plane because buildings are assumed too tall for rooftop diffraction.
  • Ray-interaction scope: The model limits reflected and diffracted rays to single interactions, except for multiple diffraction caused by vehicles, to keep computational load manageable.
  • Ray-interaction scope: For links away from the same or adjacent orthogonal streets, multiple interactions and scattering often dominate received power but require prohibitively high computation and detailed geographic data.

6) Transmission through foliage:

GEMV2 models foliage transmission using an empirically derived attenuation formulation, while combining LOS, reflected, and diffracted contributions to obtain received power. Diffraction is approximated with a knife-edge model, and foliage attenuation at 5.9 GHz is 2.3 dB per meter through trees.

  • Transmission through foliage:: Foliage attenuation is calculated per meter using an empirically derived formulation for deciduous trees.The model is based on measurements and can also represent coniferous trees and seasonal foliage changes.
  • Transmission through foliage:: At 5.9 GHz, transmission through trees produces 2.3 dB attenuation per meter.This value is reported as consistent with measurements in the 5.85 GHz band.
  • Transmission through foliage:: GEMV2 combines LOS, reflected, and diffracted ray contributions through their resultant E-field envelope before calculating received power.The received-power calculation assumes unit antenna gains and uses the resulting total E-field.
  • Transmission through foliage:: Diffracted-ray E-fields are approximated with the knife-edge model rather than calculating diffraction coefficients directly.The model includes diffraction coefficients for the received-power formulation, but obtains diffracted E-fields through this approximation.
  • Transmission through foliage:: For NLOSv and NLOSb links, received power can additionally include multipath from vehicle diffractions and static-object reflections or diffractions.These contributions supplement the large-scale LOS calculation.

D. Modeling small-scale signal variations

GEMV2 models small-scale V2V signal variation stochastically from measured per-bin behavior and the surrounding objects within each communication ellipse. It uses link-type-specific variation ranges and adds a normal random term to the modeled received power.

  • D. Modeling small-scale signal variations: Small-scale variation is characterized from measurements separated by LOS, NLOSv, and NLOSb conditions, environments, traffic levels, and two-meter distance bins.The bins are intended to limit distance-related path-loss changes within each bin while retaining enough data for characterization.
  • D. Modeling small-scale signal variations: The variation standard deviation σ_i depends on link type, vehicle density, and static-object area within the communication ellipse.Static-object area is used because object sizes vary substantially, and larger buildings or foliage are more likely to affect communication.
  • D. Modeling small-scale signal variations: The model uses one minimum and maximum σ pair for each of LOS, NLOSv, and NLOSb across multiple locations.These values are extracted from measurements and summarized in Table V rather than estimated separately for every experiment location.
  • D. Modeling small-scale signal variations: The simulation flow updates spatial indexes, identifies vehicles and static objects in the communication ellipse, computes link-type-specific received power, and adds object-based small-scale variation.The flow includes vehicle and building/foliage R-trees and separate handling for LOS and NLOSv links.
  • D. Modeling small-scale signal variations: Vehicle counts receive greater significance at lower densities because the first nearby vehicles produce a larger change than additional vehicles.The same reasoning is applied to buildings and foliage, with equal weights assigned to vehicle number and static-object area.
  • D. Modeling small-scale signal variations: GEMV2 adds N(0, σ_i) to the previously calculated received power to combine small- and large-scale variation.The random term is applied after σ_i has been determined for the communicating pair.

E. Implementation details and simulation structure of GEMV2

GEMV2 reduces computational complexity by exploiting VANET information and geometric properties to select which blockage and propagation calculations are needed. Its simulation flow integrates these rules with the large- and small-scale models for discrete-event VANET simulators.

  • E. Implementation details and simulation structure of GEMV2: GEMV2 uses VANET information and known environmental geometry to improve performance and support implementation in VANET simulators.The implementation rules are designed to reduce unnecessary propagation calculations.
  • E. Implementation details and simulation structure of GEMV2: The model checks building and foliage blockage before vehicle blockage because static objects reduce received power considerably more than obstructing vehicles.When static blockage is present, the vehicle R-tree is not checked for LOS blockage.
  • E. Implementation details and simulation structure of GEMV2: Reflections and diffractions are omitted for LOS and NLOSv links because they provide minimal accuracy benefits relative to their computational overhead.NLOSb links can benefit from single-interaction reflected and diffracted rays, although these can also be omitted when speed is critical.
  • E. Implementation details and simulation structure of GEMV2: The Fig. 8 flowchart synthesizes large- and small-scale propagation, complexity-reduction rules, and information needed for discrete-event VANET simulators.It provides the basic execution structure for implementing GEMV2 in such simulators.

F. Assumptions

GEMV2 assumes that rooftop diffraction is negligible and simplifies propagation calculations to keep computational complexity low. The model is validated against measurements using recorded vehicle positions and environmental geometry across multiple settings.

  • F. Assumptions: GEMV2 assumes buildings are too tall for meaningful received power over their rooftops.Knife-edge calculations give losses above 30 dB for the shortest buildings and above 40 dB for buildings at least 15 meters taller than vehicles.
  • F. Assumptions: A 30-minute downtown Porto experiment contained 16,500 data points and compared measured received power with GEMV2 predictions.The data were separated into LOS, NLOSv, and NLOSb links to evaluate each link type.
  • F. Assumptions: Validation uses measured vehicle GPS positions, actual vehicle dimensions, and corresponding buildings and foliage from geographical databases.The simulations reproduce the locations where the communication measurements occurred.
  • F. Assumptions: GEMV2 performance is upper-bounded by the empirically measured small-scale signal variation used to characterize its model.Results are therefore assessed alongside the mean received-power difference between measured and modeled signals.

A. LOS links

GEMV2 closely matches measured LOS and NLOSv received-power behavior, while vehicle height and obstruction type produce distinct link-level effects. NLOSb modeling is less precise because its scenarios are more varied and some foliage was absent from the geographic database.

  • LOS links: Within 0.6 dB, GEMV2’s LOS mean received power matched measurements across environments.Its standard error was also within 0.6 dB of the measured small-scale variation.
  • NLOSv links: Within 1.3 dB, GEMV2’s NLOSv mean received power matched measurements across environments.The NLOSv standard error was within 0.9 dB of measured small-scale variation; tall vehicles produced lower variation and standard error.
  • NLOSv links: At 100 m, obstructing cars, vans, and trucks attenuated received power relative to LOS by approximately 5, 13, and 20 dB, respectively.The attenuation also varied with the obstructing vehicle’s position.
  • NLOSb links: GEMV2 captured the steep LOS-to-NLOSb power drop at Porto Outlet, whereas log-distance path loss averaged across the two link types.The result supports identifying and modeling link types according to location-specific obstructions.
  • NLOSb links: GEMV2 matched measurements using reflections and diffractions without modeling through-building transmission.The paper therefore excludes through-building transmission as an important modeled effect.
  • NLOSb links: NLOSb modeling had a mean difference of -1.6 dB and standard deviation of 7.6 dB, reflecting diverse obstructions and unrecorded foliage.Measured NLOSb received-power variation was 6.8 dB, and measurements below -92 dBm were unavailable for comparison.

D. Small-scale signal variation

GEMV2 combines geometry-based propagation calculations with stochastic small-scale variation and supports city-scale processing through spatial indexing. Its scalability is linear across large networks, but reflection and diffraction calculations and communication-range selection affect processing cost.

  • D. Small-scale signal variation: GEMV2’s small-scale variation combines modeled propagation effects with a zero-mean normal variable whose standard deviation is determined by eq. 10.For NLOSv, the large-scale model includes three diffracted rays; for NLOSb, it includes reflections and diffractions.
  • Scalability: Linearly, processing time increased with network size for 10,000 links, even with more than 28,000 objects.R-tree construction and link-classification time also exhibited linear scaling with object count.
  • Scalability: Linearly, processing time increased with the number of links for a fixed network size, supporting per-link analysis for SINR calculations.The paper notes that many geometric operations can be parallelized.
  • Computational trade-offs: Between 45% and 95% of Porto Downtown NLOSb links relied on log-distance path loss because single-interaction reflections and diffractions contributed little.The affected-link proportion ranged from approximately 5% at r_NLOSb = 500 m to 55% at r_NLOSb = 50 m.
  • D. Small-scale signal variation: Within 2 dB, GEMV2’s mean and standard error matched the reflection-and-diffraction model for the evaluated links.The paper identifies separating link types by obstruction as a key factor in V2V propagation modeling.
  • Computational trade-offs: A communication range equal to the simulated area can make neighboring-object processing quadratic in the number of communicating pairs.The paper recommends minimizing each link type’s range while covering potentially communicating pairs.

VII. RELATED WORK

Prior VANET channel models use measurements, simplified path-loss formulations, or restricted urban geometries to balance realism and efficiency. The reviewed work highlights limited explicit incorporation of moving vehicles and assumptions that may not generalize across cities.

  • Measurement-based models: Several models target street-intersection NLOSb propagation by calibrating path-loss and fading parameters from measurements.These approaches focus on representative urban intersections where buildings create NLOSb conditions.
  • City-scale models: Grid-based city-scale models improve computational efficiency by assuming straight streets intersecting at right angles.The paper notes that these assumptions do not hold in all urban areas, including Porto.
  • Location-specific models: Aerial-photography methods infer local scatterer density to determine fading levels for road locations.This provides location-specific information without explicitly describing each surrounding object.
  • Measurement-based models: Fitted log-distance path-loss exponents varied from 1.83 to 3.59 across measured environments and locations.The variation illustrates the dependence of empirical propagation parameters on deployment setting.
  • Vehicular obstructions: Experimental studies quantified how obstructing vehicles affect packet reception, throughput, communication range, and V2I links involving tall vehicles.These studies establish the relevance of vehicular obstructions beyond V2V received power alone.
  • Vehicular obstructions: Research explicitly incorporating vehicles into propagation prediction remained scarce, with prior vehicle-loss modeling based on isolated parking-lot measurements and a three-ray knife-edge model.The cited method showed good agreement with those isolated measurements.

VIII. CONCLUSIONS

GEMV2 provides location-specific, time-dependent V2V propagation modeling while reducing the computational and geographic-data demands of more complex geometry-based models. It supports large-scale VANET simulation and can also assign fine-grained channel statistics by link type and environment.

  • Conclusions: GEMV2 models V2V channels using geographic descriptors and changing surrounding vehicles to capture location-specific and time-dependent link conditions.Its required geographic information is limited to outlines and types of buildings and foliage, plus vehicle locations and dimensions.
  • Conclusions: LOS, NLOSv, and NLOSb link categories limit calculations while incorporating object-dependent small-scale signal variation.LOS and NLOSv use principal propagation mechanisms with additional variation tied to surrounding objects; NLOSb can use simpler path loss for faster execution.
  • Conclusions: GEMV2 can serve as a basis for fine-grained channel modeling by assigning environment- and link-specific statistics such as delay and Doppler spreads.This use builds on its distinction between LOS, NLOSv, NLOSb, and different environments.
  • Conclusions: Hundreds of thousands of communicating vehicle pairs can be simulated in highway, suburban, and urban environments using the MATLAB implementation.The implementation demonstrates scalability for large VANET simulations.
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