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Modeling and Design of Millimeter-Wave Networks for Highway Vehicular Communication
Andrea Tassi, Malcolm Egan, Robert J. Piechocki, Andrew Nix
TL;DR
Future ITS applications need high-rate, low-latency communication, motivating analysis of roadside mmWave highway networks where large vehicles can block LOS links. The paper develops a stochastic-geometry model for SINR outage and rate coverage, finding that narrower beams need not sharply reduce outage and sparse deployments can still attain low outage.
Problem
Future ITS services require high-rate, low-latency links, while DSRC and LTE-A cannot always meet their delay and bandwidth constraints.
Source: §I · p. 1Method
The paper models roadside mmWave downlink coverage with large vehicles as LOS blockages and derives approximations for SINR outage and rate coverage probabilities.
Source: §VI · p. 12Results
Reducing antenna beamwidth from 90° to 30° does not necessarily have a disruptive impact on SINR outage, and reduced outage can be achieved in moderately sparse deployments.
Source: §VI · p. 12Takeaways & Limitations
The analysis provides design insights for mmWave highway networks, including that performance is not largely impacted across moderately sparse to dense base-station deployments.
Source: §I · p. 2, §VI · p. 12
Abstract
from arXiv · showhide
Connected and autonomous vehicles will play a pivotal role in future Intelligent Transportation Systems (ITSs) and smart cities, in general. High-speed and low-latency wireless communication links will allow municipalities to warn vehicles against safety hazards, as well as support cloud-driving solutions to drastically reduce traffic jams and air pollution. To achieve these goals, vehicles need to be equipped with a wide range of sensors generating and exchanging high rate data streams. Recently, millimeter wave (mmWave) techniques have been introduced as a means of fulfilling such high data rate requirements. In this paper, we model a highway communication network and characterize its fundamental link budget metrics. In particular, we specifically consider a network where vehicles are served by mmWave Base Stations (BSs) deployed alongside the road. To evaluate our highway network, we develop a new theoretical model that accounts for a typical scenario where heavy vehicles (such as buses and lorries) in slow lanes obstruct Line-of-Sight (LOS) paths of vehicles in fast lanes and, hence, act as blockages. Using tools from stochastic geometry, we derive approximations for the Signal-to-Interference-plus-Noise Ratio (SINR) outage probability, as well as the probability that a user achieves a target communication rate (rate coverage probability). Our analysis provides new design insights for mmWave highway communication networks. In considered highway scenarios, we show that reducing the horizontal beamwidth from $90^\circ$ to $30^\circ$ determines a minimal reduction in the SINR outage probability (namely, $4 \cdot 10^{-2}$ at maximum). Also, unlike bi-dimensional mmWave cellular networks, for small BS densities (namely, one BS every $500$ m) it is still possible to achieve an SINR outage probability smaller than $0.2$.
I. INTRODUCTION
Future ITS services need high-rate, low-latency links, while existing vehicular technologies may not meet their communication constraints. The paper models roadside mmWave service with vehicle blockages and develops an analytical framework for evaluating highway-network performance.
Motivation
- DSRC and LTE-A cannot always meet the delay and bandwidth constraints of future ITS services.The introduction notes that DSRC rates hardly exceed 6 Mbps, while LTE-A supports up to 100 Mbps and has end-to-end latencies no lower than 100 ms.Source: §I · pp. 1–2
Highway setting
- Large vehicles in slow lanes can block LOS paths between roadside mmWave base stations and vehicles in faster lanes.The paper focuses on roadside infrastructure-to-vehicle communications and does not consider scenarios without roadside base stations.Source: §I · p. 2
Contribution
- The proposed tractable model uses multiple time-independent one-dimensional PPPs for base-station and blockage positions, accommodating irregular deployments and varying network conditions.It is designed to predict performance across different base-station densities, traffic intensities, antenna gains, and directivities without requiring positions to be known in advance.Source: §I · p. 2
Findings
- The model is reported to approximate network performance well, and narrower antenna beams do not necessarily reduce SINR outage probability.The paper also reports that reduced SINR outage can be achieved with low-density base-station deployments for a fixed probability threshold.Source: §I · p. 2
II. RELATED WORK
Prior work covers mmWave cellular and vehicular communications, but existing blockage models and highway models do not jointly capture the paper’s roadside mmWave setting. The paper distinguishes its focus on infrastructure-to-vehicle coverage and beamforming from earlier vehicular approaches.
MmWave modeling
- Prior mmWave work includes dense cellular networks and vehicular ITS applications, but the paper positions its analysis around roadside highway deployments with vehicle blockages.The related-work overview mentions mmWave cellular proposals and earlier applications to ITS communications.Source: §II · pp. 2–3
- Prior mmWave blockage models for urban and suburban cellular networks use two-dimensional base-station processes and blockage assumptions that do not fit highway layouts.The related work states that no roadside mmWave base-station model accounting for vehicular blockages had been proposed to the authors’ knowledge.Source: §II · p. 3
Highway models
- Earlier highway studies – address DSRC systems, whose propagation conditions and antenna capabilities differ from mmWave systems.The paper notes that IEEE 802.11p/DSRC systems lack beamforming-capable antenna arrays.Source: §II · p. 3
- The highway stochastic-geometry model in studies multi-hop LOS inter-vehicle communication and routing, unlike this paper’s one-hop infrastructure-to-vehicle coverage focus.The cited model also uses devices without beamforming, whereas beamforming is central to the proposed mmWave system.Source: §II · p. 3
III. SYSTEM MODEL AND PROPOSED BS-STANDARD USER ASSOCIATION SCHEME
The system models roadside mmWave downlink coverage for highway users whose LOS links may be blocked by vehicles in other lanes. Base stations and blockages are represented by one-dimensional spatial processes, with lane-specific traffic densities.
Road layout
- Each traffic direction has one user lane and No obstacle lanes, with vehicles moving along parallel lanes and larger vehicles assumed mainly in obstacle lanes.The road is represented by two infinitely long parallel sides with equal-width lanes.Source: §III · p. 4
Spatial processes
- Base stations are modeled by a one-dimensional PPP along the road sides, with their side assignment split equally between upper and bottom sides.The projected base-station processes on the two sides are independent PPPs with density 0.5 · λBS.Source: §III · p. 4
- Blockages are modeled as lane-specific one-dimensional PPPs whose points carry footprint segments of length τ; densities can differ across obstacle lanes.The model samples blockage positions at each time step and is reported to approximate performance when blockages follow a Krauss car-following mobility model.Source: §III · p. 4
System objective
- The model targets SINR outage and rate coverage for users in high-speed lanes, where vehicles in other lanes can act as communication blockages.The standard user is placed at the origin for tractability.Source: §III · pp. 4–5
A. BS-Standard User Association and Antenna Model
The association and antenna model separates LOS and NLOS base stations, determines serving-base-station choice by path loss, and represents directional beamforming with sectored antenna patterns. It approximates blockage probabilities to enable tractable LOS/NLOS analysis.
LOS/NLOS modeling
- A base station is LOS only when no blockage footprint intersects the segment to the user; otherwise it is NLOS, and the model approximates the LOS probability independently of base-station distance.The NLOS probability is approximated as one minus the LOS probability, and thinning yields separate LOS and NLOS base-station PPPs.Source: A. BS-Standard User Association and… · p. 5
Association
- The user associates with the base station having the minimum path-loss component, choosing between the closest LOS and NLOS candidates.The analysis derives distance PDFs for the closest LOS and NLOS base stations and association probabilities for each type.Source: A. BS-Standard User Association and… · pp. 5–6
- The LOS-to-NLOS path-loss crossover distances define exclusion thresholds used to characterize which base-station type can serve the user.The model prevents these distances from falling below the distance from the user to a road side.Source: A. BS-Standard User Association and… · p. 5
Antenna model
- The model uses a sectored antenna pattern with main-lobe and side-lobe gains, and assumes the serving base station and user steer their beams toward each other.The user’s beam-steering assumption makes opposite-side interfering base stations arrive through a sidelobe.Source: A. BS-Standard User Association and… · p. 6
IV. SINR OUTAGE AND RATE COVERAGE CHARACTERIZATION
The section defines the standard user's SINR and specifies channel assumptions used to characterize it.
IV. SINR OUTAGE AND RATE COVERAGE CHARACTERIZATION
- The standard user's SINR compares the serving BS's faded, antenna-gained path-loss signal with thermal noise plus interference from other BSs.The serving BS is indexed 1; BSs 2 through b contribute interference.Source: §IV · p. 6
- The model assumes Doppler effects are mitigated, based on directional antennas that reduce incoming-signal angular spread.The paper notes that a receiver automatic frequency-control loop can compensate for non-zero Doppler bias.Source: §IV · p. 6
- The serving link uses Nakagami fading, while interfering links use independent Rayleigh fading to capture clustered interfering transmissions.The serving-channel power follows a gamma distribution; interfering-channel powers are independent exponentials with mean 1.Source: §IV · p. 6
A. Analytical Characterization of I
The section approximates interference by separating LOS and NLOS BS contributions on both sides of the road, then deriving Laplace transforms for the components and their sum.
A. Analytical Characterization of I
- Interference is split into LOS and NLOS contributions from BSs on each side of the road, yielding four components.These are IU,L, IU,N, IB,L, and IB,N.Source: A. Analytical Characterization of I · p. 7
- Theorem 4.1 approximates the conditional Laplace transform of interference for each serving-side and serving-link state combination.The cases distinguish an upper- or bottom-side serving BS and LOS or NLOS service.Source: A. Analytical Characterization of I · p. 7
- Example 4.1 evaluates the upper-side LOS interference case when the serving BS is LOS and J > 0.The example uses parameter sequences from Table IV.Source: A. Analytical Characterization of I · p. 7
- Corollary 4.1 approximates the Laplace transform of total interference by combining statistically independent interference components.The corollary follows from Theorem 4.1 and the independence of the components.Source: A. Analytical Characterization of I · p. 7
B. SINR Outage and Rate Coverage Probability Framework
The framework defines SINR outage and rate coverage from serving-link state probabilities and conditional success probabilities, with approximations for specific cases.
B. SINR Outage and Rate Coverage Probability Framework
- SINR outage is the probability that the standard user's SINR falls below threshold θ.The framework accounts for whether service is LOS or NLOS.Source: B. SINR Outage and Rate Coverage… · p. 8
- Conditional success probabilities for LOS and NLOS service are combined with the NLOS serving probability to obtain the outage expression.The derivation uses the serving-distance distributions and the interference transform.Source: B. SINR Outage and Rate Coverage… · p. 8
- As the NLOS path-loss exponent αN increases, NLOS service becomes less likely and the LOS-serving probability can be approximated accordingly.The approximation follows when AN approaches w(No + 1).Source: B. SINR Outage and Rate Coverage… · p. 8
- If NLOS signals are entirely attenuated by blockages, the NLOS serving probability is zero and the outage expression simplifies.The paper also gives a modified expression for BSs deployed only along the center line between driving directions.Source: B. SINR Outage and Rate Coverage… · p. 8
- Rate coverage is the probability that the standard user achieves a rate at least κ.The expression uses system bandwidth W.Source: B. SINR Outage and Rate Coverage… · p. 8
A. Simulation Framework
The simulation framework uses Monte Carlo estimates to validate the analytical model under finite-road, moving-vehicle scenarios with specified blockage and channel assumptions.
A. Simulation Framework
- A MATLAB Monte Carlo simulator estimates SINR outage and rate coverage to validate the theoretical model.The simulator and theoretical-framework implementation are available online.Source: A. Simulation Framework · p. 8
- Simulations use finite road sections to approximate the infinitely long highway, with radius selected in relation to simulation accuracy error.The paper relates the simulated radius to error ε for a one-dimensional PPP.Source: A. Simulation Framework · p. 8
- Vehicles and blockages move under the Krauss car-following model, with wrap-around maintaining blockage density over time.Maximum speeds are 70 mph for user-lane vehicles and 60 mph for obstacle-lane blockages.Source: A. Simulation Framework · p. 9
- Simulation classifies a BS as NLOS only when the ideal user-to-BS segment intersects a vehicle, whereas the theoretical derivation uses an approximation based on blockage footprints.Thus the simulated and analytical LOS/NLOS classifications are not identical.Source: A. Simulation Framework · p. 9
- The model treats large vehicles in obstacle lanes as blockages and assumes a 5 m BS antenna height, so those vehicles always obstruct links.The paper states that a blockage-free setup in its four-lane example would require a BS height above 12.5 m.Source: A. Simulation Framework · p. 9
B. Theoretical Model Assessment
The section assesses the theoretical approximation against simulations across SINR thresholds, BS densities, blockage-lane counts, rate coverage, and altered path-loss and road-length settings. It reports close agreement in the evaluated scenarios alongside several design sensitivities.
B. Theoretical Model Assessment
- 4·10^-2 is the maximum change in SINR outage probability when beamwidth changes from 30° to 90°.Outage probability increases with beamwidth; the paper attributes the limited change to the serving BS's position and the antenna model's directivity.Source: Figure 3 · p. 10, B. Theoretical Model Assessment · p. 11
- At λBS = 4·10^-3, simulated LOS connection probability is 0.94 with one obstacle lane and 0.92 with two; the LOS approximation overestimates it by less than 0.03 for λBS ∈[2·10^-4, 10^-2].The paper also reports a non-trivial minimum in LOS probability, especially with two obstacle lanes, and blockage events occurring with probability above 0.22 and lasting up to 2.68 s.Source: B. Theoretical Model Assessment · p. 10
- With two obstacle lanes, simulated outage rises by more than 9·10^-2 for x-ISD = 100 m, GTX = 20 dB, and θ ≥25 dB, while the increase is negligible at GTX = 10 dB.The broader comparison reports that increasing obstacle lanes from one to two raises PT by no more than 1·10^-2; the cited high-gain case is a specific exception noted for the x-ISD = 100 m comparison.Source: Figure 4 · p. 10, B. Theoretical Model Assessment · p. 11
- For Fig. 3, the theoretical model follows simulated outage trends and has maximum MSE below 3.2·10^-3; in Fig. 5, theory-simulation MSE never exceeds 5·10^-3 in Figs. 4a and 4b.For Fig. 3, the approximation is a tight upper bound for most threshold values; in Figs. 3 and 4, deviations are negligible for important θ values such as θ ≤20 dB.Source: B. Theoretical Model Assessment · pp. 10–11
- For large θ, increasing maximum transmit antenna gain from 10 dB to 20 dB reduces SINR outage probability by more than 0.25.The paper attributes this to the antenna model's directivity and BS disposition, for which interfering-power growth is no greater than signal-power growth.Source: Figure 3 · p. 10, B. Theoretical Model Assessment · p. 11
- For θ = 5 dB and 15 dB, BS density has a more evident effect on PT in sparse scenarios, and PT below 0.2 is achievable at λBS ≈ 2.2·10^-3.The reported sparse-density ranges are λBS ≤3·10^-3 for θ = 5 dB and λBS ≤5·10^-3 for θ = 15 dB.Source: Figure 5 · p. 11, B. Theoretical Model Assessment · p. 11
- For ψ = 30°, λBS = 4·10^-3, and No = 2, greater GTX yields higher rate coverage, with simulation-theory MSE below 5.8·10^-3.The rate-coverage expression directly follows from the SINR outage probability.Source: Figure 6 · p. 11, B. Theoretical Model Assessment · pp. 11–12
- With αN = 5.76 and a 20 km highway section, the model remains valid, although PT is more than 1.1·10^-2 higher than in the corresponding Fig. 5 cases.This validation uses the same transmission parameters and road layout as Fig. 5.Source: Figure 7 · p. 12, B. Theoretical Model Assessment · p. 12
VI. CONCLUSIONS AND FUTURE DEVELOPMENTS
The proposed model describes highway mmWave downlink performance with moving vehicles treated as blockages, and simulations support its accuracy. The results show limited beamwidth impact and that reduced outage is possible with moderately sparse deployments.
VI. CONCLUSIONS AND FUTURE DEVELOPMENTS
- The theoretical framework efficiently describes SINR outage and rate coverage across the evaluated scenarios.The authors compared its predictions with simulation results.Source: §VI · p. 12
- Reducing antenna beamwidth from 90° to 30° does not necessarily have a disruptive impact on SINR outage or rate coverage.Source: §VI · p. 12
- Unlike in bi-dimensional mmWave cellular networks, highway network performance is not largely impacted by BS densities from moderately sparse to dense deployments.Source: §VI · p. 12
- For a fixed SINR threshold, reduced SINR outage probability is achievable with moderately sparse network deployments.Source: §VI · p. 12
APPENDIX A PROOF OF THEOREM 4.1
The proof derives the interference Laplace transform using expectations over base-station locations, antenna gains, and fading. It approximates antenna-gain calculations by conditioning on link geometry and enumerating LOS/NLOS and road-side configurations.
APPENDIX A PROOF OF THEOREM 4.1
- The proof expresses the interference Laplace transform as an expectation over base-station distances, antenna gains, and fading, then uses the PPP probability generating functional and mapping theorem to obtain an exponential form.Source: Appendix A · p. 12
- The exact transmit antenna gain of each interfering BS would make the model intractable, so the proof approximates it as gTX.For the fading expectation, it assumes a Rayleigh channel model.Source: Appendix A · p. 13
- Receiver gain depends on serving and interfering BS road sides, LOS/NLOS status, and geometry; the proof enumerates configurations with LOS or NLOS distance constraints.The configurations are summarized in Table IV.Source: Appendix A · pp. 13–14
- The proof approximates gain-and-fading expectations by dividing possible interference distances into gain-specific intervals; one intermediate step assumes w(No + 1) = 0.The paper points to Section V-B for validation of that approximation.Source: Appendix A · pp. 13–14