⚡ electrical engineering

Radar Operating Metrics and Network Throughput for Integrated Sensing and Communications in Millimeter-wave Urban Environments

This paper utilizes a stochastic geometry-based framework to analyze how radar operating parameters, such as duty cycle and beamwidth, impact radar detection performance and subsequent communication throughput in millimeter-wave ISAC systems within urban environments.

Original authors: Akanksha Sneh, Shobha Sundar Ram

Published 2026-02-10

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CC0 1.0

Original authors: Akanksha Sneh, Shobha Sundar Ram

Original paper dedicated to the public domain under CC0 1.0 (http://creativecommons.org/publicdomain/zero/1.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are a high-tech security guard at a massive, busy music festival. To do your job, you have two main tasks:

The Search (Radar): You need to scan the crowd with a flashlight to find specific people (targets) and make sure no one is sneaking in through the bushes (clutter).
The Chat (Communication): Once you find someone, you need to walk up to them and have a long, clear conversation to give them instructions.

This paper is about a new way to do both at once using a single "super-tool" (Integrated Sensing and Communications, or ISAC). However, there is a catch: you only have one flashlight and one mouth.

Here is the breakdown of the paper’s "drama" in simple terms:

1. The Great Balancing Act (The Duty Cycle)

The researchers are looking at a fundamental conflict called the Duty Cycle.

Imagine you have 10 minutes to work.

Option A (The Perfectionist): You spend 9 minutes slowly scanning the crowd with a very narrow, powerful beam of light. You will definitely find every single person, but you only have 1 minute left to actually talk to them. Your "throughput" (the amount of information shared) might be low because you ran out of time.
Option B (The Speedster): You spend only 1 minute scanning, but you have to use a wide, dim flashlight to cover the whole area quickly. You’ll have 9 minutes to talk, but because your light was dim, you might miss half the people in the crowd.

The paper uses complex math (Stochastic Geometry) to figure out the "sweet spot"—the perfect amount of time to spend searching so that you find enough people to make the talking time worth it.

2. The "Noise" and the "Bushes" (Clutter and Noise)

In a real city, it’s not just you and the target.

The Noise: This is like the static on a radio or the background hum of the crowd. It makes it hard to hear.
The Clutter: Imagine the festival is surrounded by thick bushes and moving trees. When you shine your light, the light hits the leaves and bounces back. Your brain might think a moving leaf is a person. This is a False Alarm.

The researchers created a mathematical model to predict how often these "fake people" (clutter) will trick the radar and how much power you need to see through the "static" (noise).

3. What affects the "Score"?

The paper tests different "knobs" to see how they change the results:

Turning up the Power: If you use a brighter flashlight, you find more people (higher throughput), but you also create more "glare" from the bushes, leading to more false alarms.
Changing the Bandwidth: This is like changing the "clarity" of your vision. If it's too wide, you might see too much "fog" (noise), which actually makes it harder to work.
The Target's Size (RCS): A person wearing a giant, reflective neon vest (High RCS) is much easier to find than someone in a dark hoodie. The bigger the "vest," the better the system performs.

The Bottom Line

The researchers aren't just guessing; they've built a mathematical map. This map helps engineers design future self-driving cars and smart cities. It tells them: "If you want to communicate a lot of data, don't spend too much time scanning; but if you want to be safe and see everything, you'll have to sacrifice some talking time."

They are essentially trying to find the perfect rhythm for a machine that has to see and speak at the exact same time.

Technical Summary: Radar Operating Metrics and Network Throughput for ISAC in mmWave Urban Environments

1. Problem Statement

As intelligent transportation systems (ITS) evolve toward autonomous driving, there is a critical need for reliable sensing (to detect obstacles) and high-speed communication (for V2X connectivity). Traditional systems use separate hardware and spectrum for radar and communication, leading to spectral congestion and increased costs.

Integrated Sensing and Communication (ISAC) aims to merge these functions onto a single platform. However, a fundamental resource allocation trade-off exists: in a time-multiplexed system, the radar duty cycle ( $\xi$ ) determines the balance between sensing and communication. A long radar duration allows for narrower, high-gain beams (better detection of weak targets) but leaves less time for data transmission. Conversely, a short radar duration requires broader beams (lower gain/higher missed detections) but provides more time for communication. The paper seeks to mathematically model this trade-off and analyze how radar operating metrics (Probability of False Alarm $P_{fa}$ and Probability of Detection $P_d$ ) impact the overall network throughput ( $\gamma$ ) in complex, clutter-heavy millimeter-wave (mmWave) urban environments.

2. Methodology

The authors employ a Stochastic Geometry (SG) framework to model the spatial distribution of targets and clutter, avoiding the computational intensity of traditional Monte Carlo simulations for the entire system design.

Signal Modeling: The system is modeled as a monostatic dual-functional unit. The radar signal follows the inverse $\alpha$ -law for mmWave propagation. Target returns are modeled using the Swerling-1 (exponential) RCS model, while clutter is modeled as a homogeneous Poisson Point Process (PPP).
Radar Metrics Estimation:
- To find the Probability of False Alarm ( $P_{fa}$ ), the authors derive the Characteristic Function (CF) of the clutter returns using the Probability-Generating Functional (PGFL) of the PPP.
- Since the resulting Cumulative Distribution Function (CDF) cannot be solved analytically, they apply Gil-Pelaez’s inversion theorem to obtain an integral form, which is then solved via numerical integration.
- The Probability of Detection ( $P_d$ ) is similarly derived by considering the signal power plus clutter and noise against a predefined threshold $\eta$ .
Throughput Modeling: The network throughput ( $\gamma$ ) is modeled as a function of the duty cycle $\xi$ , the number of detected targets $\beta(\xi)$ , and the communication duration $(1-\xi)$ . The beamwidth $\Delta\psi$ is treated as a function of $\xi$ , creating a direct link between the radar's temporal allocation and its spatial sensing capability.

3. Key Contributions

Mathematical Framework for ISAC: Developed a rigorous stochastic geometry-based model that links radar sensing performance (specifically $P_d$ and $P_{fa}$ ) directly to communication throughput in mmWave bands.
Clutter-Noise Analysis: Unlike prior works that focused on Line-of-Sight (LoS) conditions, this work explicitly accounts for discrete clutter scatterers and Rayleigh fading in urban environments.
Duty Cycle Optimization Insight: Established the analytical relationship between the radar duty cycle, antenna beamwidth, and the resulting impact on the number of successfully serviced mobile users.

4. Key Results

The authors validated their mathematical models through Monte Carlo simulations, revealing several critical behaviors:

Duty Cycle ( $\xi$ ) Trade-off: The network throughput $\gamma$ follows a concave pattern. It initially increases with $\xi$ because better sensing (higher $P_d$ ) brings more targets into the communication network. However, beyond an optimal point, $\gamma$ decreases because the time remaining for communication becomes too short.
Transmitted Power ( $P_{tx}$ ): Increasing power improves throughput by increasing $P_d$ , but it also increases $P_{fa}$ because clutter returns become stronger.
Bandwidth ($BW$): Increasing bandwidth reduces the clutter area ( $A_r$ ), which can lower $P_{fa}$ . However, in this specific model, higher bandwidth increased noise power, which eventually degraded the number of detected targets and reduced throughput.
Clutter and RCS: Higher surface clutter coefficients ( $\sigma_o$ ) and higher target RCS ( $\sigma_t$ ) both lead to higher $P_{fa}$ and higher throughput, respectively (as higher $\sigma_t$ makes targets easier to detect).

5. Significance

This research is significant for the design of 60 GHz (IEEE 802.11ad) based ISAC systems used in automotive applications. By providing a mathematical way to predict how radar parameters (like beamwidth and duty cycle) affect the "bottom line" of communication performance, it allows engineers to optimize the balance between safety (sensing) and connectivity (communication) in dense, cluttered urban environments.