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Fine Grained Analysis and Optimization of Large Scale Automotive Radar Networks

Mohammad Taha Shah, Gourab Ghatak, Shobha Sundar Ram

TL;DR

This work tackles mutual interference among automotive radars in dense urban environments by developing two stochastic-geometry models, the Poisson line Cox process (PLCP) for dense urban cores and the Binomial line Cox process (BLCP) for mixed city–suburb regions. It introduces the meta-distribution (MD) framework to separate sources of randomness in radar detection and leverages the Chebyshev–Markov (CM) bound to reconstruct MDs from finite moments, enabling fine-grained per-link performance insights. The authors then optimize key radar parameters—beamwidth $\Omega$ and transmission probability $p$—to maximize the number of successful detections, and show that MD-based analysis yields actionable guidance for adaptive, environment-aware radar operation. The findings provide practical guidance for cognitive automotive radars to mitigate urban interference, improve detection reliability, and adapt to changing traffic and street geometries.

Abstract

Advanced driver assistance systems (ADAS) enabled by automotive radars have significantly enhanced vehicle safety and driver experience. However, the extensive use of radars in dense road conditions introduces mutual interference, which degrades detection accuracy and reliability. Traditional interference models are limited to simple highway scenarios and cannot characterize the performance of automotive radars in dense urban environments. In our prior work, we employed stochastic geometry (SG) to develop two automotive radar network models: the Poisson line Cox process (PLCP) for dense city centers and smaller urban zones and the binomial line Cox process (BLCP) to encompass both urban cores and suburban areas. In this work, we introduce the meta-distribution (MD) framework upon these two models to distinguish the sources of variability in radar detection metrics. Additionally, we optimize the radar beamwidth and transmission probability to maximize the number of successful detections of a radar node in the network. Further, we employ a computationally efficient Chebyshev-Markov (CM) bound method for reconstructing MDs, achieving higher accuracy than the conventional Gil-Pelaez theorem. Using the framework, we analyze the specific impacts of beamwidth, detection range, and interference on radar detection performance and offer practical insights for developing adaptive radar systems tailored to diverse traffic and environmental conditions.

Fine Grained Analysis and Optimization of Large Scale Automotive Radar Networks

TL;DR

This work tackles mutual interference among automotive radars in dense urban environments by developing two stochastic-geometry models, the Poisson line Cox process (PLCP) for dense urban cores and the Binomial line Cox process (BLCP) for mixed city–suburb regions. It introduces the meta-distribution (MD) framework to separate sources of randomness in radar detection and leverages the Chebyshev–Markov (CM) bound to reconstruct MDs from finite moments, enabling fine-grained per-link performance insights. The authors then optimize key radar parameters—beamwidth and transmission probability —to maximize the number of successful detections, and show that MD-based analysis yields actionable guidance for adaptive, environment-aware radar operation. The findings provide practical guidance for cognitive automotive radars to mitigate urban interference, improve detection reliability, and adapt to changing traffic and street geometries.

Abstract

Advanced driver assistance systems (ADAS) enabled by automotive radars have significantly enhanced vehicle safety and driver experience. However, the extensive use of radars in dense road conditions introduces mutual interference, which degrades detection accuracy and reliability. Traditional interference models are limited to simple highway scenarios and cannot characterize the performance of automotive radars in dense urban environments. In our prior work, we employed stochastic geometry (SG) to develop two automotive radar network models: the Poisson line Cox process (PLCP) for dense city centers and smaller urban zones and the binomial line Cox process (BLCP) to encompass both urban cores and suburban areas. In this work, we introduce the meta-distribution (MD) framework upon these two models to distinguish the sources of variability in radar detection metrics. Additionally, we optimize the radar beamwidth and transmission probability to maximize the number of successful detections of a radar node in the network. Further, we employ a computationally efficient Chebyshev-Markov (CM) bound method for reconstructing MDs, achieving higher accuracy than the conventional Gil-Pelaez theorem. Using the framework, we analyze the specific impacts of beamwidth, detection range, and interference on radar detection performance and offer practical insights for developing adaptive radar systems tailored to diverse traffic and environmental conditions.

Paper Structure

This paper contains 22 sections, 7 theorems, 25 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Contributions, Organization, and Notation
  3. System Model and Network Geometry
  4. PLCP
  5. BLCP
  6. Interfering Set
  7. Channel Access, SIR, and SF
  8. Interfering Distance
  9. Average number of potential targets
  10. Average number of PLCP points in $\mathcal{N}_{(0,0)}^{+} (R)$
  11. Average number of BLCP points in $\mathcal{N}_{\left(0,r_0\right)}^{+} (R)$
  12. Meta distribution Analysis
  13. Meta Distribution of SF
  14. Detection Success Probability
  15. Reconstruction of MD of $p_{{\rm SF},k}(\beta_{\rm SF})$ from $M_{b,k}(\beta_{\rm SF})$
  16. ...and 7 more sections

Key Result

lemma 1

The length of a line parameterized by $(\theta,r)$ present inside the radar sector $\mathcal{N}_{(0,0)}^{+}\!(R)$ of half beamwidth $\Omega$ and distance to target $R$ is, where $\alpha_{\rm n} = \arctan{\left(\frac{R\sin\Omega}{|R\cos\Omega - u|}\right)}$, and $\cos\alpha_{\rm m} = \frac{u}{R}\sin^2\theta + \sqrt{\frac{u^2}{R^2}(\sin^4\theta - \sin^2\theta) + \cos^2\theta}$.

Figures (9)

  • Figure 1: (a) A realization of PLCP having $\lambda_{\rm L} = 0.005 \,\rm{m}^{-2}$ and $\lambda = 0.005 \,\rm{m}^{-1}$, with ego radar present at origin, and (b) A realization of BLCP having $n_{\rm B} = 50$ and $\lambda = 0.005 \,\rm{m}^{-1}$, with ego radar present at $(0,r_0)$.
  • Figure 2: Illustration of a scenario where two radars are present at the edge point of the line $L_i$ inducing interference.
  • Figure 3: The figure illustrates different cases of a BLP line intersecting line $L_0$. Case $1$ to $5$ correspond to 5 different cases to find $l$, i.e., from $l = p_1$ to $l = p_5$.
  • Figure 4: (a) and (d) Number of successful detections versus $\Omega$ for PLCP and BLCP framework respectively, (b) and (c) Optimal beamwidth versus $\lambda$ and $R$ respectively for PLCP.
  • Figure 5: (a) and (b) Optimal beamwidth versus $r_0$ and $R$ respectively for BLCP.
  • ...and 4 more figures

Theorems & Definitions (17)

  • Definition 1
  • Definition 2
  • Definition 3
  • lemma 1
  • proof
  • Theorem 1
  • Remark 1
  • lemma 2
  • Theorem 2
  • proof
  • ...and 7 more