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Modeling and Statistical Characterization of Large-Scale Automotive Radar Networks

Mohammad Taha Shah, Gourab Ghatak, Ankit Kumar, Shobha Sundar Ram

TL;DR

The work develops street-aware stochastic-geometry models for automotive radar networks by employing a homogeneous Poisson line process (PLCP) and an inhomogeneous Binomial line Cox process (BLCP) to capture urban street layouts and their transitions to suburbs. It defines the interfering set via mutual visibility within radar sectors, derives maximum/minimum interfering distances, and provides analytic expressions for detection probability under LOS/NLOS propagation with Nakagami fading, incorporating bounded ranges and realistic beam patterns. Validation is performed with real-world street data from multiple cities and time-of-day traffic variations, showing significant spatial performance gradients and establishing design guidelines that prioritize interference management through density-aware strategies. The BLCP model, in particular, captures city-scale heterogeneity and edge effects that the PLCP misses, enabling more accurate city-wide radar-network planning and optimization for ADAS and ISAC contexts.

Abstract

The impact of discrete clutter and co-channel interference on the performance of automotive radar networks has been studied using stochastic geometry, in particular, by leveraging two-dimensional Poisson point processes (PPPs). However, such characterization does not take into account the impact of street geometry and the fact that the location of the automotive radars are restricted to the streets as their domain rather than the entire Euclidean plane. In addition, the structure of the streets may change drastically as a vehicle moves out of a city center towards the outskirts. Consequently, not only the radar performance change but also the radar parameters and protocols must be adapted for optimum performance. In this paper, we propose and characterize line and Cox process-based street and point models to analyze large-scale automotive radar networks. We consider the classical Poisson line process (PLP) and the newly introduced Binomial line process (BLP) model to emulate the streets and the corresponding PPP-based Cox process to emulate the vehicular nodes. In particular, the BLP model effectively considers the spatial variation of street geometry across different parts of the city. We derive the effective interference set experienced by an automotive radar, the statistics of distance to interferers, and characterize the detection probability of the ego radar as a function of street and vehicle density. Finally, leveraging the real-world data on urban streets and vehicle density across different cities of the world, we present how the radar performance varies in different parts of the city as well as across different times of the day. Thus, our study equips network operators and automotive manufacturers with essential system design insights to plan and optimize automotive radar networks.

Modeling and Statistical Characterization of Large-Scale Automotive Radar Networks

TL;DR

The work develops street-aware stochastic-geometry models for automotive radar networks by employing a homogeneous Poisson line process (PLCP) and an inhomogeneous Binomial line Cox process (BLCP) to capture urban street layouts and their transitions to suburbs. It defines the interfering set via mutual visibility within radar sectors, derives maximum/minimum interfering distances, and provides analytic expressions for detection probability under LOS/NLOS propagation with Nakagami fading, incorporating bounded ranges and realistic beam patterns. Validation is performed with real-world street data from multiple cities and time-of-day traffic variations, showing significant spatial performance gradients and establishing design guidelines that prioritize interference management through density-aware strategies. The BLCP model, in particular, captures city-scale heterogeneity and edge effects that the PLCP misses, enabling more accurate city-wide radar-network planning and optimization for ADAS and ISAC contexts.

Abstract

The impact of discrete clutter and co-channel interference on the performance of automotive radar networks has been studied using stochastic geometry, in particular, by leveraging two-dimensional Poisson point processes (PPPs). However, such characterization does not take into account the impact of street geometry and the fact that the location of the automotive radars are restricted to the streets as their domain rather than the entire Euclidean plane. In addition, the structure of the streets may change drastically as a vehicle moves out of a city center towards the outskirts. Consequently, not only the radar performance change but also the radar parameters and protocols must be adapted for optimum performance. In this paper, we propose and characterize line and Cox process-based street and point models to analyze large-scale automotive radar networks. We consider the classical Poisson line process (PLP) and the newly introduced Binomial line process (BLP) model to emulate the streets and the corresponding PPP-based Cox process to emulate the vehicular nodes. In particular, the BLP model effectively considers the spatial variation of street geometry across different parts of the city. We derive the effective interference set experienced by an automotive radar, the statistics of distance to interferers, and characterize the detection probability of the ego radar as a function of street and vehicle density. Finally, leveraging the real-world data on urban streets and vehicle density across different cities of the world, we present how the radar performance varies in different parts of the city as well as across different times of the day. Thus, our study equips network operators and automotive manufacturers with essential system design insights to plan and optimize automotive radar networks.
Paper Structure (32 sections, 5 theorems, 37 equations, 12 figures, 4 tables)

This paper contains 32 sections, 5 theorems, 37 equations, 12 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Motivation
  4. Organization and Contributions
  5. Notations
  6. System Model
  7. Network Geometries
  8. PLCP
  9. BLCP
  10. SIR and Channel Model
  11. Importance of SIR
  12. Characterization of the Interference Process
  13. Interfering Set
  14. Interfering Distance
  15. Detection Success Probability
  16. ...and 17 more sections

Key Result

Theorem 1

For $L_i$ line with parameters $(\theta_i,r_i)$ intersecting $L_0$ at a distance $d_i$ from the ego radar, the maximum ($a_{{\rm B},i}$) and the minimum ($b_{{\rm B},i}$) distances of the interfering radars from the point of intersection on $L_i$, for BLCP are given as: where,

Figures (12)

  • Figure 1: (a) Road map of New Delhi city. (b) and (c) Single realization of the PLCP and BLCP model where the ego radar represented as a blue astrix is located at the origin in case of PLCP and at location $r_0 = 60$ from the origin in case of BLCP. Interfering vehicles are illustrated in blue and non-interfering vehicles in red dots. For (c), to emphasize local interference behavior, a magnified inset shows the immediate neighborhood of the ego radar, including the target location, nearby vehicles, and sector boundaries.
  • Figure 2: PDF of signal + interference power and only interference power received at ego radar, if the target is at a distance uniformly distributed between $5$ to $15\, {\rm m}$, $\Omega = 30^\circ$, $\lambda_{\rm L} = 0.01\, {\rm m}^{-1}$, $\lambda = 0.05\, {\rm m}^{-1}$, and transmit power is $1$ dB.
  • Figure 3: Illustration of a scenario showing interfering and non-interfering radar sectors w.r.t. ego radar.
  • Figure 4: Illustration of a scenario where two radars are present at the edge point of the line $L_i$ inducing interference.
  • Figure 5: (a) Comparison of Monte Carlo simulations and analytical results for both PLCP and BLCP models w.r.t $\beta$, Probability of successful detection with respect to (b) $\beta$ for varying $\zeta$ in PLCP model, (c) $r_0$ for varying $\alpha_{\rm N}$
  • ...and 7 more figures

Theorems & Definitions (16)

  • Remark 1
  • Remark 2
  • Remark 3
  • Definition 1
  • Definition 2: Set of Interfering Radars
  • Theorem 1
  • proof
  • lemma 1
  • Theorem 2
  • proof
  • ...and 6 more