On the Detection of Vulnerable Road Users—Simulating Limits of an FMCW Radar

Abstract

The complexity of urban traffic environments poses unique challenges for automotive radar sensors. Limited range and Doppler resolution hinder the ability to distinguish closely spaced objects and detect vulnerable road users, particularly pedestrians. Therefore, it is important to know the limits of FMCW radars. To assess these limitations, the WinProp channel simulator is used to model and simulate traffic scenarios regarding the detection of the range, velocity, and SNR of targets. To validate WinProp as a simulation tool for traffic scenarios, a real traffic scenario is configured and the simulation results compared to the measurement results in order to demonstrate the suitability of WinProp for simulating traffic scenarios and evaluating radar detection performance. The close agreement between the simulation and measurement results provides validation for WinProp’s accuracy in modeling detections and signal processing within traffic scenarios. To showcase the limitations of FMCW radars, two scenarios with challenging detection conditions are simulated: an occluded pedestrian between parked vehicles and a densely populated road. A monostatic setup with a single patch antenna and a 16 × 16 patch antenna array is evaluated, using chirp bandwidths of 1 GHz and 4 GHz. The simulations have shown that although it is feasible to detect an occluded pedestrian by multipath propagation, there is still a need in improving the detection performance when there is no multipath from an occluded pedestrian. Furthermore, the results indicate that higher bandwidth improves target separation but is insufficient for occluded pedestrian detection without multipath. However, with some targets, even the range resolution at 4 GHz was not sufficient, which required a separation in the Doppler dimension, emphasizing the need for overall resolution improvement of FMCW radars. Future work should focus on developing more complex road user models and simulating a broader range of scenarios to comprehensively evaluate radar performance in road traffic environments.

1. Introduction

In 1999, the German car manufacturer Mercedes-Benz, headquartered in Stuttgart, Germany, introduced radar-based Adaptive Cruise Control (ACC) in their S-class models, enabling the car to detect the distance and speed of the vehicle ahead and maintain a set distance. Since then, extensive research has led to improvements in automotive radar systems, enhancing their performance, cost, and size. Today, radar is an essential sensor in cars due to its unique capabilities compared to LiDAR, cameras, and ultrasound [1]. Radar sensors are crucial for autonomous driving due to their robustness in harsh weather conditions and their ability to measure range and velocity simultaneously [2]. Currently, radar sensors are employed in many driver assistance systems, such as ACC, Automated Emergency Braking (AEB), and Cross Traffic Alert (CTA), enhancing the safety of the driver and traffic participants. The importance of enhanced safety is highlighted by the National Highway Traffic Safety Administration (NHTSA), which estimates that 42,915 deaths occurred in 2021, representing a 10 percent increase from 2020 and the highest number since 2005 [3]. Early obstacle and danger recognition is key to avoiding fatal car accidents. For instance, accident statistics show that AEB prevents 83 percent of rear-end crashes [4]. The safety functions mentioned are based on radar sensors operating in the 76–81 GHz automotive radar band, which offers advantages such as smaller antenna sizes, higher range, and improved Doppler and angle resolution [5].

While radar technology promises increased traffic safety for the future, it is crucial to understand its inherent limitations before fully relying on this sensor technology in traffic environments. Radar sensors, for instance, have limited range resolution, making it difficult to distinguish targets that are very close to each other. Additionally, their Doppler resolution is constrained, requiring a minimum velocity difference between two moving targets to detect them separately. Furthermore, radar’s angular resolution is influenced by wavelength and the number of transmit/receive antennas, necessitating a minimum angular difference between targets to resolve them spatially. Moreover, targets can be occluded by other objects in urban traffic, such as a pedestrian hidden behind a car. Understanding these limitations of Frequency Modulated Continuous Wave (FMCW) radar is crucial for developing innovative solutions to overcome these challenges. To optimize radar technology and improve autonomous vehicle safety, it is essential to thoroughly investigate these limitations and innovate accordingly. The key contributions of this work include the following:

• Validating WinProp as a reliable tool for analyzing FMCW radar performance in traffic environments, particularly assessing the accuracy of channel simulation and FMCW radar signal processing through a comparative analysis between a simulated and real scenario.

• Demonstrating FMCW radar sensor limitations by simulating two common scenarios encountered in urban traffic, and proposing mitigation techniques for these challenges. Emphasizing occluded pedestrians, the simulations provide important relevance for contemporary urban traffic conditions.

• Evaluating and comparing different radar and antenna configurations in the scenarios to analyze their impact on detection performance regarding range, velocity, and Signal-to-Noise Ratio (SNR) as well as resulting trade-offs.

Unlike previous studies that have broadly addressed radar limitations, this work uniquely delves into specific scenarios to pinpoint the performance boundaries of FMCW radar. In particular, this work aims to answer the following research questions: Is WinProp a reliable tool for simulating and analyzing traffic scenarios, providing results comparable to real radar measurements? How does the high range resolution in the 77–81 GHz band perform in a target-dense environment? Under what conditions can an occluded pedestrian be detected? The latter question is particularly significant due to radars being non-optical sensors, with potential for detecting hidden objects out of line of sight. This property is often touted as an advantage of radar sensors, and this study investigates the reliability of detecting such hidden targets through simulations that assess radar performance and limitations under realistic conditions. Real experiments and measurements of 77 GHz FMCW radars are infrequently found in the literature due to their time-consuming and costly nature. Therefore, this study also aims to demonstrate WinProp as a dependable tool for obtaining realistic simulation results, providing a credible alternative to real-world measurements.

In the following, the simulation methodology in this work and fundamentals of FMCW radars are introduced in Section 2, including the ray-tracing simulation approach, an overview of FMCW signal processing, range resolution, and Doppler resolution, which determine the detectability of individual targets in a target-dense scenario. Further, the validation of WinProp as a ray-tracing simulation tool for traffic scenarios is presented in Section 3. Following, the actual scenarios that are simulated in this work with respect to the limits of an FMCW radar are shown in Section 4 and the simulation setup is described. After presenting the traffic scenarios, the simulation results for each scenario are shown in Section 5. Based on the results, Section 6 provides a thorough discussion of the results, outlining the limitations of FMCW radar across various scenarios. The work is finished by a conclusion and outlook suggesting methods to bypass or minimize the effects of the FMCW radar’s limits.

2. Fundamentals and Simulation Methodology

2.1. Fundamentals

The fundamentals chapter provides the basics required to understand the results in this work. The ray-tracing simulation approach, which is the method all simulations in this work are based on, is first explained. In order to understand the limits of an FMCW radar, its working principle and natural limitations, such as the range resolution and Doppler resolution, are provided in this chapter.

2.1.1. Ray Tracing for RF Wave Propagation Simulations

Simulations can accelerate the development of modern radar sensors for automotive applications and provide a safe, practical way to meet high testing demands [6]. Ensuring a sufficiently accurate channel model is crucial for simulating traffic scenarios at the radar system level [7]. Full electromagnetic simulation software tools provide highly accurate results for Radio Frequency (RF) wave propagation as well as system and target characteristics, but they are unsuitable for dynamic scenarios due to their complexity. Numerical methods are impractical for simulating complex traffic scenarios due to their electrically large size. At 77 GHz, with a wavelength of approximately 3.9 mm, objects in real traffic scenarios are comparatively large and require high computational power for numerical simulation.

Ray-tracing simulations offer an effective alternative for simulating dynamic and time-variant urban scenarios, providing sufficiently accurate results [7]. Combining Fresnel equations with the geometrical and uniform theories of diffraction (GTD and UTD) allows ray-tracing simulations to accurately approximate mmWave propagation effects, such as transmission, reflection, scattering, and diffraction. The computational cost is lowered by configuring the target’s material properties at 77 GHz and importing RCS and antenna patterns from full electromagnetic simulations, enabling the analysis of wave propagation in dynamic scenarios with moving targets [8]. The ray-tracing approach is a valid method for simulating wave propagation at 77 GHz, given the wavelength’s significantly smaller size compared to traffic elements like cars, trucks, and pedestrians. WinProp has been evaluated as a reliable tool for simulating traffic scenarios using ray tracing, as demonstrated in [9,10].

2.1.2. FMCW Radar

Automotive radars utilize the FMCW waveform to sense the environment, providing simultaneous range, velocity, and relative angle information of objects. This work focuses on Single Input–Single Output (SISO) simulations, emphasizing range and Doppler detection while excluding Direction of Arrival (DoA) estimation, which typically requires multiple Rx antennas for angle extraction. Figure 1 shows the frequency modulated signal over time used in FMCW radars. The black line denotes the transmitted signal sweeping from an initial to an end frequency, defining a sweep bandwidth, ${\mathit{B}}_{\mathrm{S}}$. In the 76–77 GHz automotive band, the bandwidth, ${\mathit{B}}_{\mathrm{S}}$, is equal to 1 GHz, whereas the 77–81 GHz band employs a bandwidth of 4 GHz. The frequency sweep happens within a certain sweep time, ${\mathit{T}}_{\mathrm{S}}$. The received signal is a time-delayed version of the transmitted signal in monostatic radar systems, indicated by the blue line in Figure 1. This is valid for targets with a relative velocity of 0 m/s compared to the radar’s movement. The time delay $\tau =2R$ corresponds to the signal propagation time, with R being the distance between the radar and the target in m and c the speed of light in m/s. The radar’s range and velocity resolution depend on the chirp parameters, ${\mathit{B}}_{\mathrm{S}}$ and ${\mathit{T}}_{\mathrm{S}}$, allowing adjustment of these key radar properties [11].

2.1.3. Range Resolution

The range resolution is crucial for distinguishing targets located close together radially. In a scenario with two closely spaced targets, the range resolution of an FMCW radar is defined as

(1)${\delta }_{\mathrm{range}}=\frac{\mathrm{c}}{2·B_{\mathrm{S}}},$

where c is the speed of light in m/s and ${\mathit{B}}_{\mathrm{S}}$ is the sweep bandwidth in Hz [12]. According to Equation (1), the range resolution of an FMCW radar improves with a higher sweep bandwidth, $B_{\mathrm{S}}$. For example, an FMCW radar operating in the 77–81 GHz frequency band with a sweep bandwidth of 4 GHz theoretically achieves a range resolution of 3.75 cm according to Equation (1). However, practical considerations such as signal processing windowing reduce this theoretical resolution. The explanation of the windowing in signal processing is out of the scope of this work, and further information can be obtained in [13].

2.1.4. Velocity Resolution

Alongside range resolution, velocity resolution is crucial for FMCW radars to distinguish targets moving at similar velocities within a scene. The velocity resolution of an FMCW radar is given by

(2)$v_{\mathrm{res}}=\frac{\lambda }{2T_{\mathrm{f}}},$

where $\lambda$ is the wavelength in m, ${\mathit{T}}_{\mathrm{f}}$ is the frame time in seconds, defined as the sweep time, ${\mathit{T}}_{\mathrm{S}}$, in seconds multiplied by the number of chirps, M, in one frame [14].

2.1.5. FMCW Radar Signal Processing

In this section, the FMCW radar signal processing steps are briefly explained, along with how a range-Doppler map from a radar data cube can be obtained. Figure 2 illustrates the signal processing, showing how the radial range and velocity of targets are visualized in a range-Doppler map [15]. When the M chirps are received and sampled by the Analog-to-Digital Converter (ADC), a column-wise Fast Fourier Transform (FFT) resolves the range of the targets. Subsequently, a second FFT, known as the Doppler-FFT, is applied across N sequences of chirps to determine target velocities [15]. The process of applying a range-FFT and Doppler-FFT is called 2D-FFT in the literature covering the FMCW radar signal processing [16]. Since the detailed analysis of the processing steps included in the 2D-FFT process is out of the scope of this thesis, publications that cover the radar signal analysis and processing in more detail are referenced [13,17,18].

2.2. Simulation Methodology

To assess the limits of an FMCW radar regarding resolution and target detectability in scenarios involving occlusion and clutter, realistic traffic scenarios are configured and simulated using the WinProp™ ©2000–2024 channel simulator by Altair (City of Troy, MI, USA). Road objects such as cars, trucks, and guardrails, modeled in 3D and provided in a database by Altair, include specific material properties such as relative permittivity, relative permeability, electrical conductivity, and material thickness. Properties vary among model parts; for instance, car tires exhibit lower conductivity than the body due to higher metallic content. The database also includes a pedestrian’s RCS profile at 77 GHz, facilitating accurate pedestrian simulation using a modeled rectangular box with human dimensions assigned with the pedestrian’s RCS. Scenario and target configuration is managed in WallMan (version 2021.0.3), part of the WinProp suite, facilitating the setup of monostatic simulations with two different antennas: a less directive patch antenna and a highly directive 16 × 16 patch antenna array. The directive 16 × 16 antenna array illuminates the scenarios with a focused beam and also receives rays in a narrow Field of View (FoV). The patch antenna has a less directive radiation pattern and illuminates the scenario with a wider beam as well as receiving in a broad FoV. These antennas evaluate detection performance based on their radiation pattern contrasts. Additionally, radar signal bandwidth variation assesses radar performance at different resolutions. Simulations are executed in ProMan (version 2021.0.3 for simulations and 2022.0.2 for I/Q data) within the WinProp suite. The results are imported into MATLAB (R2022a) for range-Doppler map generation using custom wave properties and target detection via the Constant False Alarm Rate (CFAR) algorithm. CFAR compares the signal intensities of the cell under test with neighboring cells [19], setting a minimum SNR threshold of 20 dB for target detection. Detected targets’ range, velocity, and SNR values are compared against configured scenario values for validation. Before analyzing radar limitations, in the next chapter WinProp’s channel simulation is validated against real urban traffic scenario measurements, comparing simulation and real-world results for discrepancies. Figure 3 illustrates the methodology’s block diagram for scenario configuration, simulation setup, and result analysis.

3. Validation of WinProp for Ray-Tracing Simulations

In this work, to validate WinProp for simulating traffic scenarios, its simulation results are compared with with real traffic measurements. The validation is based on the 77 GHz radar channel, a scenario configured from real measurements, and the FMCW radar signal processing algorithm. WinProp is considered validated if the simulation accurately detects targets at the same range and speed, with similar power intensity as the real measurements, accounting for parameters like bandwidth, chirp time, and number of chirps. It is important to note that the goal in this section is not to evaluate FMCW radar limitations but to demonstrate WinProp’s comparability to actual measurement data. Upon successful validation, it is confirmed that simulations involving FMCW radar limits and vulnerable road users will yield reliable results.

3.1. Urban Traffic Scenario

In [7], traffic measurements were conducted along a driving route including a crossroad near Beijing Jiaotong University in China. The traffic situation shown in Figure 4 (left) is analyzed and measurement results are presented. The same scenario is recreated as seen in Figure 4 (right) and simulated in this work to compare the simulation with the measurement results in [7]. The monostatic radar car is driving at a speed of 7 m/s. An SUV, 12.6 m ahead of the radar car, travels at 6.6 m/s. A red car, 15.8 m away and slightly to the left, travels at 9 m/s. A van, 25 m ahead of the radar car and in front of the red car, travels at 6.6 m/s. The vehicles’ bodies and chassis, primarily steel with high electrical conductivity (2 MS/m), are set as entirely reflective surfaces, similar to the traffic lamp positioned 30 m ahead of the radar car. It needs to be noted that Figure 4 (left) shows the 100th frae; however, the scenario during frame 60 is measured and simulated.

3.2. Simulation Parameters

A 2 × 2 antenna array with a gain of 10.355 dBi is used for the simulation, closely matching the 10.35 dBi antenna gain in [7]. The array also has a Sidelobe Level (SLL) of −11.99 dB and a wide azimuthal Half Power Beam Width (HPBW) of 36.25° [10]. The antenna characteristics used in the WinProp simulation are detailed in Table 1 [20]. Figure 5 shows the radiation pattern of the 2 × 2 antenna array used in the simulation (left) and the antenna pattern from [7] (right).

The radar setup in [7] utilizes the FMCW radar AWR1843 by Texas Instrument (Dallas, TX, USA), with a power amplifier output of 12 dBm, as specified in the datasheet [21]. The 2 × 2 patch antenna provides a gain of 10.36 dBi, resulting in an Effective Isotropic Radiated Power (EIRP) of 22.36 dBm. Assuming a receiver sensitivity of −120 dBm, as recommended by the International Telecommunications Union (ITU) [22], the maximum path loss of the rays is set to 142.36 dB, and the simulation is limited to 1024 rays. Furthermore, the carrier frequency, ${\mathit{f}}_{\mathrm{c}}$, is set to 77 GHz, with a sweep bandwidth, ${\mathit{B}}_{\mathrm{S}}$, of 568.62 MHz. Additionally, the chirp duration, ${\mathit{T}}_{\mathrm{c}}$, is 61.02 µs, with 128 chirps in one frame. According to Equations (1) and (2), the range resolution results in 0.263 m and the velocity resolution in 0.25 m/s. Table 2 shows the simulation parameters for the urban scenario in Figure 4 (right).

3.3. Simulation and Results

Figure 6 displays simulated rays in the scenario configuration. For clarity, only representative rays from each object are shown instead of all simulated rays. Reflections from the radar car and ground are present but are not problematic due to the objects’ distance from the radar. As anticipated, all objects reflect rays back to the radar, ensuring visibility in the power delay profile (PDP). The SUV, being closest, reflects the strongest signals, while the van also exhibits strong reflections due to its larger size compared to other objects.

Figure 7 shows the Power Delay Profile (PDP) for the current scenario, revealing reflections from the radar car and ground up to a range of 1.2 m. All objects in the scene, including the red car, SUV, van, and lamp, are reflecting rays corresponding accurately to their ranges. Comparing this PDP with the measured range power profile in [7], both figures align sufficiently in range accuracy and power levels. Variations in the power levels of road objects are attributed to their approximate models in this simulation, which differ from the precise configurations in Figure 4 (left). Notably, the van exhibits the strongest signal in Figure 7 (top), whereas it appears weakest in the range power profile of Figure 7 (bottom). This discrepancy may stem from the larger size of the simulated van compared to the one observed in [7], due to limitations in accurately modeling the real van using available 3D models. Figure 8 (left) in [7] displays the range-Doppler map from the measurement. It is important to note a labeling error where the SUV and red car positions are swapped in Figure 8 (left). According to the scenario depicted in Figure 6 (top), the labels should be corrected, as the SUV is closer to the radar car. Figure 8 (right) shows the range-Doppler map for the scenario simulated in Figure 6 (bottom). In summary, all targets are detected accurately with respect to range and speed in the WinProp simulation, which is displayed in Table 3 where their values closely match those from the real measurement in [7]. Comparing the simulated range-Doppler map in Figure 8 (right) with the measured range-Doppler map in Figure 8 (left), the simulated range and relative velocity of objects closely match the measurement results. The simulations demonstrate that WinProp accurately simulates real traffic scenarios regarding range and the relative velocity of objects. Minor differences in return signal strength are attributed to 3D models not fully resembling actual targets, yet these do not significantly affect the simulation’s ability to extract reliable range and Doppler values. Focusing on the limits of FMCW radar in the range, velocity resolution, and detectability of vulnerable road users, WinProp proves suitable for simulating dynamic traffic scenarios with sufficient accuracy, validated by its consistency with real measurements. Previous studies have also affirmed the fidelity of mmWave simulations in WinProp [9,23,24].

4. Configured Scenarios and Simulation Setup

This chapter describes configured scenarios aimed at testing the limits of an FMCW radar in terms of range resolution, velocity resolution, and detection of occluded road users, particularly pedestrians. It includes details of the scenarios configured for radar testing and their simulation setups.

4.1. Configured Scenarios

4.1.1. Scenario 1: Pedestrian between Two Parked Vehicles

Scenario 1 involves a pedestrian hidden between two parked vehicles on the roadside, Figure 9. This urban scenario tests the FMCW radar’s ability to detect hidden pedestrians, crucial for preventing accidents, especially in situations where pedestrians may unexpectedly step onto the road. Unlike cameras and LiDAR, radar can detect hidden targets using multipath propagation without requiring a direct line of sight. At 77 GHz, radar operates in a quasi-optical manner due to negligible wave diffraction, posing specific challenges in detecting occluded objects. The targets’ positions relative to the radar are detailed in Table 4. The cars and trucks in the scenario have a high metallic content, with an electrical conductivity of 2 MS/m chosen to represent their reflective properties. The pedestrian’s Radar Cross-Section (RCS) values are also specified, varying from 0.85 dBsm facing the torso to 0.35 dBsm facing the side.

4.1.2. Scenario 2: Dense Traffic-Reduced Street

Scenario 2 simulates an automotive radar scenario in a living street environment, characterized by numerous clutter sources and vulnerable road users. Living streets typically feature parked cars, benches, trash bins, and pedestrians, posing risks such as unexpected movements by children playing or pedestrians crossing. Figure 10 illustrates this scenario setup. Targets include two benches, a trash bin, and a bike rack to the left of the radar car. There are also 11 pedestrians, some stationary (pedestrians #1–#3, #10, #11), some moving (pedestrians #4–#7), and two occluded behind parked cars (pedestrians #8 and #9). Target distances, speeds, and movement directions relative to the radar are detailed in Table 5, with material parameters specified in Table 6.

4.2. Simulation Setup

This section defines the simulation setup for analyzing the described scenarios, focusing on antenna types and simulation parameters. First, the antenna models used in the simulations are outlined.

Two antenna models, a single patch antenna and a 16 × 16 array, were selected for their contrasting radiation characteristics to evaluate their target detection performance in traffic simulations. The patch antenna’s wide FoV detects objects over a larger area but with lower gain, reducing signal strength from distant targets. Conversely, the 16 × 16 array’s high gain improves detection range but its narrow FoV might miss objects outside the main beam. This selection enables a comparative evaluation of how antenna radiation patterns influence target acquisition in traffic scenarios. Figure 11 shows the 3D radiation patterns of both antennas, and Table 7 lists their characteristics.

The simulation setup and parameters are defined as follows: The antenna is mounted on the front of the radar car at a height of 0.5 m above the ground, which is a typical placement for radar sensors in modern vehicles. All simulations are based on a monostatic radar configuration, with the Tx and Rx antennas co-located. For the single patch antenna, which has a gain of 7.06 dBi and a power amplifier output of 10 dBm (as recommended by ITU [25]), the EIRP is 17.06 dBm. The 16 × 16 array antenna increases the EIRP to 38.75 dBm. The simulations limit transmissions/reflections to three and the number of simulated rays to 1024 to balance data sufficiency and computation time. The maximum path loss is set at 137.06 dB for the patch antenna and 158.75 dB for the 16 × 16 array, ensuring that only rays with a signal intensity above the receiver sensitivity of −120 dBm (based on ITU recommendations [22]) are considered. Table 8 summarizes the simulation parameters for each antenna type.

Besides the antenna variation, the bandwidth of the transmitted wave is also varied to analyze its effect on radar detection performance, specifically range resolution. Simulations use two bandwidths: 1 GHz and 4 GHz. Scenario 1 is simulated only with a 1 GHz bandwidth, as range resolution is less critical for detecting an occluded target, which relies more on antenna characteristics and signal penetration. Scenario 2, involving a dense target environment, uses both bandwidths to examine the impact on range resolution and the ability to separate closely spaced targets. The chirp duration is set to 40 µs, and the number of chirps is 128, yielding a velocity resolution of 0.38 m/s, a balance between realism and simulation efficiency [26,27,28,29]. A minimum SNR of 20 dB is required to detect a target [19]. Table 9 summarizes the wave parameters used in the simulations.

5. Results

With the scenarios and simulation setups defined, this section focuses on the simulation results. Scenario 1 aims to detect an occluded pedestrian between two parked cars, a common urban scenario, without varying the bandwidth, focusing on general target detectability. Scenario 2 presents a more challenging environment, requiring the radar to separate and detect multiple targets individually. Here, bandwidth and range resolution are varied to assess detection performance. These scenarios cover two key aspects of FMCW radar limits: the detectability of occluded pedestrians and the separability of targets based on range resolution.

5.1. Simulation Results of Scenario 1

5.1.1. Simulation Results of Scenario 1 with a Single Patch Antenna

The simulation setup uses the patch antenna parameters from Table 8 and the 4 GHz wave properties from Table 9. The range-Doppler map for Scenario 1 with this configuration is shown in Figure 12. Table 10 compares the actual range and speed values of the targets with those detected by CFAR.

Although the pedestrian is placed 13.5 m from the radar between the car and truck, they are not visible at that range and speed due to the lack of a line of sight. Instead, the pedestrian is detected through multipath propagation via the truck tail, creating a ghost target at 22.5 m in the range-Doppler map. The detected distances of the scatter centers of the car and truck are very accurate, with deviations within the radar’s range resolution. The detected speeds are also sufficiently accurate; for instance, the car’s tail and rear door are detected at 0.28 m/s and 0.37 m/s, respectively. This discrepancy is due to the car’s greater angle relative to the radar, affecting the radial velocity measurement. Table 11 shows the deviation of detected values from the configured values.

5.1.2. Simulation Results of Scenario 1 with a 16 × 16 Patch Antenna Array

Scenario 1 is then simulated with a 16 × 16 patch antenna array to compare with the single patch antenna simulation. Figure 13 shows the range-Doppler map for this setup with a 4 GHz bandwidth.

The range-Doppler map in Figure 13 indicates that the 16 × 16 patch antenna array reduces clutter from the car’s own reflection due to its more focused beam compared to the wider beam of the single patch antenna. The car and truck tails are clearly visible, but the truck tail has a lower SNR than with the single patch antenna. The focused 16 × 16 array does not improve detection of the occluded pedestrian, who still appears only as a ghost target in the range-Doppler map. Deviations in simulated and real range and speed values remain consistent with those in Table 11. The simulations confirm that without a direct line of sight, the pedestrian remains occluded. Multipath propagation from the pedestrian to the truck tail to the radar sensor is observed. Table 12 presents the CFAR algorithm detections.

5.2. Simulation Results of Scenario 2

5.2.1. Simulation Results of Scenario 2 with a Single Patch Antenna

In this section, the simulation results of Scenario 2 with a single patch antenna are presented. Figure 14 shows the range-Doppler map of Scenario 2 for a simulation with a single patch antenna.

Detecting all pedestrians in this cluttered environment proves challenging due to overlapping ranges with other objects. Bench #1 and the trash bin are more distinguishable as they are spaced farther apart. Pedestrians #1–#7 are discernible primarily by their Doppler shifts; if stationary, detecting them based on range alone would be difficult due to overlapping range bins. For example, pedestrians #5 and #7 almost occupy the same range bin and would merge into a single target without their differing speeds. Pedestrian #7’s higher velocity creates a distinct radial velocity, enabling separation from pedestrian #5. Pedestrians #2 and #3, with identical relative velocities, appear almost as a single target visually. Pedestrian #11 is entirely obscured by car #1 and remains undetected by both visual observation and CFAR. At 32 m, CFAR detects a reflection that could be interpreted as either pedestrian #11 or an additional reflection from car #3, which completely obscures the pedestrian in the range-Doppler map. Pedestrians #8 and #9 are obstructed by cars #1 and #2, respectively, and are neither visually distinguishable nor detected in the range-Doppler map. Table 13 shows the detection of each target in this scenario by the CFAR algorithm.

To see the effect of a higher range resolution in a dense urban scenario, the bandwidth is increased to 4 GHz and displayed in Figure 15. Table 14 shows the comparison of the detected SNRs between the simulation with a bandwidth of 1 GHz and 4 GHz.

The employment of the higher bandwidth of 4 GHz shows the range bins narrowing and separating some targets from other objects. For instance, pedestrian #11 is not blurred by the reflection of car #1 and instead is seen as a separate radar return signal at a slightly closer range than the car #1 from the radar’s perspective. Pedestrian #11 was placed at a range of 19 m and has a speed of 0 m/s, and is detected at a range of 19.02 m and 0 m/s. This shows a very accurate detection of the pedestrian when a bandwidth of 4 GHz is employed. Furthermore, pedestrian #10 is also detected as an individual target, despite the close range to car #3, which obscured the pedestrian in the simulation with a bandwidth of 1 GHz. Although pedestrians #1–#7 are separable by the Doppler dimension, the higher bandwidth shows that even in the range dimension it becomes easier to detect the pedestrians as individual targets due to narrower range bins. The detected range and speed values are close to identical with the values in Table 13. Additionally, the deviations of the detected and configured range and speed values of the pedestrians are shown in Table 15.

5.2.2. Simulation of Scenario 2 with a 16 × 16 Patch Antenna Array

Figure 16 shows the range-Doppler map of Scenario 2 using a 16 × 16 patch antenna array at a bandwidth of 4 GHz. The 1 GHz bandwidth simulation is excluded due to redundant insights already discussed. The range-Doppler map reveals that a more focused beam enhances the return signals from targets directly in front of the radar, such as pedestrians #4–#7, and car #3, which is within the main beam of the antenna array. Targets positioned to the sides of the radar appear weaker due to the focused beam. Thus, while the antenna array yields higher SNR detections for targets directly ahead, the single patch antenna is more effective for detecting targets at wider horizontal angles. However, the array setup is also not able to detect the occluded pedestrians #8 and #9. Table 16 compares the detected SNR values of targets for both the single patch antenna and the 16 × 16 array at 4 GHz bandwidth.

6. Discussion

A discussion of the simulation results in Section 5 follows. The results are evaluated considering the limits of an FMCW radar, including the influence of different bandwidths and antenna patterns on radar performance in the presented scenarios. This analysis aims to identify the limitations of an FMCW radar.

6.1. Discussion of Simulation Results of Scenario 1

The scenario discussed in this chapter reflects a common urban traffic situation where pedestrian detection is critical. Between 2010 and 2013, 94 percent of injured pedestrians were hit while crossing the road [30].

In this scenario, a pedestrian positioned 13.5 m from the radar is undetected by both the single patch antenna and the 16 × 16 antenna array due to occlusion by a parked car. However, a ghost target appears in the range-Doppler map due to multipath reflection from the pedestrian to the truck tail and then to the radar. Without the truck tail’s reflective surface, no detection would occur, making CFAR detection of the pedestrian impossible. Similar findings were reported in [31], where a scenario without a second parked vehicle resulted in low positive alarm rates for pedestrian detection.

The 16 × 16 array simulation shows stronger reflections from the truck due to higher gain, but the multipath reflection remains at the same range with slightly higher intensity. This highlights the challenge of detecting occluded pedestrians, with detection relying heavily on multipath propagation. In [32], a 79 GHz radar detected a pedestrian only after emerging from behind a car, supporting the conclusion that direct line of sight is crucial for detection without multipath reflections.

An occlusion-aware sensor fusion approach combining a stereo camera and radar is proposed in [30] to detect road-crossing pedestrians early. The authors highlight the importance of multipath reflections from other parked cars or underneath occluding vehicles for valuable information. This emphasizes the limitation of radar sensors in detecting occluded vulnerable road users, as it relies primarily on multipath reflections.

A correct detection method using Doppler information from multipath reflections is proposed in [33]. However, [30] suggests that radar alone is insufficient for detecting occluded targets, advocating for sensor fusion. Another approach in [34] implements tracking using a camera and a 77 GHz radar to maintain pedestrian detection. While velocity information helped perceive the pedestrian despite occlusion, position accuracy was still an issue, indicating a need for method improvement.

Various literature methods distinguish ghost targets from real targets using sensor fusion, demonstrating the limitations of FMCW radar in these scenarios. Lastly, Figure 17 illustrates the detection area in the scenario where reliable detections are hindered by high RCS targets.

The significance of early radar detection is highlighted in [35], which simulated driver behavior in emergencies involving pedestrians emerging from occluded areas. The study found that in 20.57 percent of instances, drivers failed to avoid collisions due to insufficient decision-making time [35]. Early radar detection would allow driver assistance systems to initiate emergency braking sooner, emphasizing the importance of detecting occluded pedestrians for advanced safety systems.

6.2. Discussion of Simulation Results of Scenario 2

Scenario 2 is modeled after traffic-reduced areas in German neighborhoods, which feature numerous targets like benches, trash bins, parked cars, trees, buildings, and playing children. Drivers in these areas are restricted to walking speed to ensure safety. Early detection of children, who may unpredictably appear from occluded areas, is crucial to avoid collisions. The following section discusses the impact of different bandwidths and antenna patterns on the detection performance of the FMCW radar.

6.2.1. Impact of the Bandwidth

First, the scenario was simulated with a chirp bandwidth of 1 GHz. Pedestrians #1–#7 are detected by the CFAR algorithm; however, they are only distinguishable by the Doppler dimension. Separating them in the range dimension is difficult due to the insufficient range resolution of 0.3 m. The spatial separation between some of the pedestrians, #1–#7, is lower than 0.3 m, which requires the Doppler dimension in order to detect the pedestrians as individual targets. Notably, pedestrian #5’s movement and therefore different Doppler profile makes a separation from the stationary bench #2 possible, despite their initial overlap in the range dimension. Furthermore, pedestrian #11 is not detected and also not visible in the range-Doppler map due to their occlusion by car #1. Here, the range resolution of the radar is also insufficient to distinguish the pedestrian from car #1. Additionally, car #1 has a higher RCS because of its material properties and size, which makes it even more difficult to detect pedestrian #11 as an individual target. Moreover, pedestrian #10 is detected as a target in a range of 32 m; however, it is visually difficult to separate pedestrian #10 from car #3. Additionally, pedestrians #8 and #9 are entirely invisible to the radar due to a lack of line-of-sight and absence of detectable multipath reflections. Pedestrian #11 might further block potential wave propagation paths to and from pedestrian #8. As observed previously, the detection of occluded pedestrians presents a significant challenge, likely requiring advanced algorithms and sensor fusion (e.g., camera and LiDAR integration) to facilitate reliable and timely detection.

In the next step, the range resolution was increased to a 4 GHz bandwidth. While this higher range resolution cannot detect occluded pedestrians #8 and #9 without line-of-sight, it aids in distinguishing closely positioned pedestrians. However, pedestrians #1–#7 remain indistinguishable in the range axis due to their dense positioning. Thus, higher range resolution does not always improve detection accuracy for closely spaced targets; additional dimensions like Doppler and angle should be used. Further increasing the range resolution would require a higher bandwidth and operating frequency, presenting a trade-off between detection range and resolution. This scenario demonstrates the radar’s limitation in range resolution within dense urban environments with clutter and many targets in the same range bins. Optical sensors like cameras and LiDAR may perform better in these conditions due to their superior resolution.

6.2.2. Impact of the Antenna Pattern

Additionally, the scenario was simulated using a 16 × 16 patch antenna array, yielding the range-Doppler map in Figure 16 with a 4 GHz bandwidth. This array, with a significantly higher gain (28.75 dBi compared to 7.06 dBi for the single patch), provides more focused illumination and narrower FoV reflections. The main lobe’s driving direction reduces clutter from bench #1, bench #2, and the trash bin, while pedestrians #4–#7 are detected with higher SNR due to their positioning in the focused main lobe. However, occluded pedestrians #8 and #9 remain undetected due to the absence of reflected rays and lack of multipath propagation. The 16 × 16 array demonstrated that a focused beam in a dense urban scenario enhances the detection of targets within the main lobe. For instance, pedestrian #3 was detected with an SNR increase of 2 dB, and pedestrian #7 by 15 dB. Despite this, the array’s directionality reduces the SNR of targets at greater azimuthal angles, highlighting a trade-off in the reliable detection of potentially vulnerable targets. A potential solution is using a forward-looking radar with a focused beam for front detection, complemented by corner radars with wider beams for detecting targets at the car’s sides. However, even with the array antenna, occluded pedestrians #8 and #9 were not detected, underscoring the challenge of identifying targets obscured by objects with larger RCS, such as cars in this scenario.

In summary, the two antennas used in the simulation offer distinct advantages: the array antenna provides higher SNR, while the single patch antenna offers a wider FoV. These benefits come with trade-offs, such as the array’s narrower FoV and the single antenna’s lower gain. Both antennas were unable to detect occluded pedestrians without a line of sight, highlighting this as a limitation of FMCW radars. Although radar sensors can detect partially and fully occluded pedestrians through multipath propagation, as documented in [31,33,34,36], Scenario 2 shows that this method is not always reliable. Occluded pedestrians may not always reflect waves back via multipaths, rendering them entirely invisible to the radar.

6.2.3. Potential Pedestrian Detection Strategies

To further augment pedestrian detection capabilities, the concept of joint communication and radar sensing is a current study field. This approach envisions a vehicle detecting an occluded pedestrian via radar, navigating accordingly, and communicating this critical information to following vehicles. The evolution of this concept leads to the exploration of radar networks and cooperative radar systems. Radar networks, leveraging the interconnectedness of multiple radar sensors across different vehicles and infrastructure, can provide a more comprehensive and dynamic understanding of the environment. This collective sensing framework enables the detection of occluded pedestrians by collecting data from various viewpoints, thereby overcoming the limitations of single-vehicle radar systems.

Moreover, the integration of 6G communication technology with radar opens new possibilities for real-time, high-bandwidth, low-latency data sharing between vehicles and infrastructure. 6G networks, with their advancements in wireless communication, are expected to support the vast data requirements of cooperative radar systems and enable more sophisticated and predictive pedestrian detection algorithms. The synergy between 6G communications, cooperative radar, and radar networks could lead to a decisive shift in how occluded pedestrian detection is approached, providing a foundation for highly reliable and effective detection systems. Nonetheless, the realization of these advanced pedestrian detection systems necessitates rigorous research and development efforts.

Lastly, the study’s primary limitation is the small number of analyzed cases in simulating traffic scenarios with FMCW radars. This was necessary to focus on detailed scenarios and evaluate radar performance under varied conditions, including different antenna configurations and radar parameters, like range resolution. Despite the limited scenarios, consistent results highlighted the specific detection limits of FMCW radars across various traffic conditions, suggesting underlying principles rather than random outcomes. Comparisons with existing literature support the reliability of these findings. Future research should expand to include a larger dataset to enhance reliability, validate findings, and explore additional variables impacting FMCW radar performance in traffic scenarios.

7. Conclusions and Outlook

In this study, WinProp was validated as a tool for simulating the 77 GHz radar channel, demonstrating high accuracy through comparative analysis with real-world measurements. Various traffic scenarios were simulated to assess the limits of FMCW radar in terms of range, Doppler resolution, and the detection of occluded vulnerable road users. The 77–81 GHz band with 4 GHz bandwidth showed superior range resolution and target detection compared to the 1 GHz bandwidth, albeit with limitations when targets occupy the same range cell. The study emphasizes the importance of multiple target parameters, particularly range, Doppler, azimuth, and elevation, for effective resolution. Simulation results confirmed challenges in detecting occluded pedestrians, especially in scenarios without multipath propagation, highlighting limitations despite proposed solutions like early detection systems and sensor fusion. Additionally, the study underscored the necessity of a wide FoV in urban environments for detecting targets around the radar’s car. Despite advantages such as higher gain and SNR for targets ahead, the 16 × 16 antenna array showed weaknesses in detecting off-axis targets.

The simulations explicitly demonstrate the impact of range and Doppler resolution constraints on target detection and separation. This highlights the need for advanced waveform design (e.g., wider bandwidth chirps or higher frequency bands) to improve resolution without sacrificing overall performance. Additionally, research into higher frequencies, like 120 GHz, shows promise for better range resolution and target separability. Enhancing Doppler resolution for distinguishing similar velocities can be achieved by using multiple FMCW chirps operating at different frequencies. Overcoming occlusion challenges requires strategic placement of FMCW radars for multiple viewing angles and sensor fusion with cameras or LiDAR systems to provide a comprehensive understanding of the environment and predict occluded objects.

Author Contributions

Conceptualization, F.Y. and M.L.; methodology, F.Y.; formal analysis, N.F. and M.L.; literature research, F.Y. and M.L.; discussion, F.Y. and M.L.; writing—original draft, F.Y.; writing—review and editing, all authors; supervision, N.F. and M.L. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

The data supporting the reported results of this study are available upon request from the corresponding author.

Conflicts of Interest

The authors declare no conflicts of interest.

Abbreviations

The following abbreviations are used in this manuscript:

ACC	Adaptive Cruise Control
ADC	Analog-to-Digital Converter
CFAR	Constant False Alarm Rate
DoA	Direction of Arrival
EIRP	Effective Isotropic Radiated Power
FFT	Fast Fourier Transform
FMCW	Frequency Modulated Continuous Wave
FoV	Field of View
HPBW	Half Power Beamwidth
NHTSA	National Highway Traffic Safety Administration
PDP	Power Delay Profile
RCS	Radar Cross Section
RF	Radio Frequency
SLL	Side Lobe Level
SNR	Signal-to-Noise Ratio

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Tables

Figure 1. Frequency sweep over time for FMCW radar chirps.

Figure 2. Implementation of a 2D-FFT radar processing for an FMCW radar, adapted from [15]. The different colors indicate different targets at various ranges and velocities.

Figure 3. Block diagram of the methodology used in this work to simulate scenarios, obtain results, and derive limitations of FMCW radars.

Figure 4. (Left) Traffic scenario measured in [7]. The image does not show the measured frame but rather a later frame in the scenario. However, it still provides an overview of how the scenario is measured. (Right) Configured scene in WinProp. The configured scene is reconstructed based on the traffic setup in [7]. Reprinted with permission from Ref. [7] © 2020 IEEE.

Figure 5. Radiation pattern of the 2 × 2 antenna array used in the simulation of the scenario shown in Figure 4 (Left); 3D antenna pattern of the antenna used in [7] (Right). Reprinted with permission from Ref. [7] © 2020 IEEE.

Figure 6. Simulated rays in the measurement frame [7] (top); Rays resulting from the simulation of the configured scene in WallMan shown in Figure 4 (bottom). Reprinted with permission from Ref. [7] © 2020 IEEE.

Figure 7. (Top) Simulated PDP of the scenario shown in Figure 4 (right) in WinProp; (Bottom) Range power profile, which is simulated with Ray Tracing (RT) and measured in [7]. Reprinted with permission from Ref. [7] © 2020 IEEE.

Figure 8. (Left) Range-Doppler map of the measured frame in [7]. Note: The authors labeled the red car and SUV wrong, so the labels of the red car and SUV need to be switched; (Right) Range-Doppler map of the simulation of the scenario shown in Figure 6 (bottom). Reprinted with permission from Ref. [7] © 2020 IEEE.

Figure 9. Configuration of Scenario 1: Pedestrian standing between a car and a truck parked on the roadside.

Figure 10. Configuration of Scenario 2: Traffic-reduced street with many clutter return signals and targets.

Figure 11. Radiation patterns of the antennas used in the simulations: Single patch antenna (Left) and 16 × 16 patch antenna array (Right).

Figure 12. Range-Doppler map of Scenario 1 simulated with a single patch antenna and a bandwidth of 4 GHz. The radar car is driving with a speed of 3 m/s (Left); Radar view of the scenario (Right).

Figure 13. Range-Doppler map of Scenario 1 simulated with a 16 × 16 patch antenna array at a bandwidth of 4 GHz.

Figure 14. Range-Doppler map of Scenario 2 with a single patch antenna and a bandwidth of 1 GHz (Top); Radar view of the scenario (Bottom).

Figure 15. Range-Doppler map of Scenario 2 with a single patch antenna and a bandwidth of 4 GHz.

Figure 16. Range-Doppler map of Scenario 2 with a 16 × 16 patch antenna array and a bandwidth of 4 GHz.

Figure 17. The red box shows the area in which detection by an FMCW radar is difficult due to occlusion.

Table 1

Antenna properties of the 2 × 2 patch antenna according to [20].

Antenna Gain (dB)	SLL (Horizontal) (dB)	SLL (Vertical) (dB)	HPBW (Horizontal) (°)	HPBW (Vertical) (°)
10.36	−0.35	−16.03	27.63	54.7

Table 2

Simulation parameters of the urban traffic scenario in Figure 4 (right).

Antenna Gain (dBi)	10.36
Transmit Power (dBm)	12
EIRP (dBm)	22.36
Maximum Path Loss (dB)	142.36 (receiver sensitivity of −120 dBm)
Simulated Number of Rays	1024
Number of Transmissions/Reflections simulated	3
Carrier frequency, ${\mathit{f}}_{\mathrm{c}}$ (GHz)	77
Sweep Bandwidth, ${\mathit{B}}_{\mathrm{S}}$ (MHz)	568.62
Chirp Duration, Tc (μs)	61.02
Number of Chirps	128
Range Resolution (m)	0.263
Velocity Resolution (m/s)	0.25

Table 3

Comparison of the detected targets between the WinProp simulation and the real measurement in [7].

Target	WinProp Simulation	Measurement
SUV	12.64 m; 0.4 m/s	12.6 m; −0.4 m/s
Red car	15.79 m; −1.95 m/s	15.8 m; 2 m/s
Van	24.98 m; 0.39 m/s	25 m; −0.4 m/s
Lamp	30.3 m; 7 m/s	30 m; −7 m/s

Table 4

Range and speed configuration of the targets in Scenario 1. The radar car is driving with a speed of 3 m/s.

Target	Distance from Radar (m)	Speed (m/s)
Car	6.1	0 (stationary)
Pedestrian	13.5	0 (stationary)
Truck	18.5	0 (stationary)

Table 5

Range and speed configuration of the targets in Scenario 2. The radar car is driving with a speed of 1.5 m/s.

Target	Distance from Radar (m)	Speed (m/s)
Bench #1	8.34	0 (stationary)
Bench #2	15.38	0 (stationary)
Trash bin	11.63	0 (stationary)
Bike rack	26.5	0 (stationary)
Car #1	19.24	0 (stationary)
Car #2	25.3	0 (stationary)
Car #3	31.3	0 (sationary)
Pedestrian #1	13.72	0 (stationary)
Pedestrian #2	14.95	0 (stationary)
Pedestrian #3	15.66	0 (stationary)
Pedestrian #4	14.96	−2 towards the radar
Pedestrian #5	16.67	2 away from the radar
Pedestrian #6	14.45	1.6 away from the radar
Pedestrian #7	16.5	2.86 away from the radar
Pedestrian #8	23.85	0 (stationary)
Pedestrian #9	29.6	0 (stationary)
Pedestrian #10	32	0 (stationary)
Pedestrian #11	19	0 (stationary)

Table 6

Material parameters of the targets in Scenario 2. All materials have a relative permeability of 1 due to non-magnetic properties. The relative permittivity for metals are neglected because the relative permittivity describes dielectric materials and their ability to store electrical energy. Metals do not have intrinsic electrical fields due to free moving electrons; therefore, they are described with their electrical conductivity.

Target (Material)	Rel. Permittivity	Electrical Conductivity (S/m)
Benches (Wood)	1.8	1.25
Trash bin (Plastic)	4.25	0.54
Bike rack (Metallic)	-	2,000,000
Cars (mostly Metallic)	-	2,000,000
Pedestrians	RCS

Table 7

Antennas characteristics used in the WinProp simulations: Gain, Side Lobe Level (SLL), and HPBW.

Antenna Type	Antenna Gain (dBi)	SLL (Horizontal) (dB)	SLL (Vertical) (dB)	HPBW (Horizontal) (°)	HPBW (Vertical) (°)
Single Patch	7.06	−0.06	−18.62	86.00	86.27
16 × 16 Patch Array	28.75	−0.63	−13.18	3.46	6.3

Table 8

Simulation parameters for both antenna types (Single patch antenna and 16 × 16 array).

Parameter	Value
	Patch Antenna	16 × 16 Array
Antenna height above ground (m)	0.5	0.5
Antenna gain (dBi)	7.06	28.75
EIRP (dBm)	17.06	38.75
Number of transmissions/reflections	3	3
Maximum path loss of rays (dB)	137.06	158.75
Number of simulated rays	1024	1024

Table 9

Wave and CFAR parameters for both bandwidths of 1 GHz and 4 GHz. Scenario 1 is simulated with a bandwidth of 4 GHz due to the focus on the detectability of an occluded pedestrian. In Scenario 2, both bandwidths are used to analyze the performance of both bandwidths regarding the individual target detection.

Parameter	Value
Bandwidth, $B_{\mathrm{S}}$ (GHz)	1	4
Carrier frequency, $f_{\mathrm{carrier}}$ (GHz)	77	77
Number of chirps, M	128	128
Chirp duration, $T_{\mathrm{c}}$ (µs)	40	40
Velocity resolution, $v_{\mathrm{res}}$ (m/s)	0.38	0.38
Range resolution, ${\delta }_{\mathrm{range}}$ (with Hanning window) (m)	0.3	0.075
Sampling Rate (MSamples/s)	25.6	25.6
Probability of False Alarm (PFA)	10−7	10−7
CFAR detection threshold (dB)	20	20

Table 10

Comparison of the targets’ range and speed between the configured and simulated Scenario 1 with a patch antenna and a bandwidth of 4 GHz. Additionally, the detected targets’ SNRs are given by the CFAR.

Target	Configured Scenario		CFAR
	Range (m)	Speed (m/s)	Range (m)	Speed (m/s)	SNR (dB)
Pedestrian	13.5	0	22.5 (multipath)	0.05	32.4
Car Tail	6.1	0	6.15	0.28	48.3
Rear Door (Car)	7.4	0	7.44	0.37	34.5
Front Mirror (Car)	9.15	0	9.16	0.01	36
Truck Tail	18.18	0	18.22	0.04	41
Front Left Tire (Truck)	23	0	22.97	0.06	33

Table 11

Deviations in range and speed of the targets between the configured and detected values of Scenario 1.

Target	$\mathbf{\Delta }\mathbf{Range}$ (m)	$\mathbf{\Delta }\mathbf{Velocity}$ (m/s)
Pedestrian	9 (ghost target)	0.05
Car Tail	0.05	0.28
Rear Door (Car)	0.04	0.37
Front Mirror (Car)	0.01	0.01
Truck Tail	0.04	0.04
Front Tire (Truck)	0.03	0.06

Table 12

Comparison of the targets’ range and speed between the configured and simulated Scenario 1 with a 16 × 16 array and a bandwidth of 4 GHz. Additionally, the detected targets’ SNRs are given by the CFAR.

Target	Configured Scenario		CFAR
	Range (m)	Speed (m/s)	Range (m)	Speed (m/s)	SNR (dB)
Pedestrian	13.5	0	22.5 (mulitpath)	0.05	29
Car Tail	6.1	0	6.15	0.29	45
Rear Door (Car)	7.4	0	7.44	0.37	29
Front Mirror (Car)	9.15	0	9.16	0.01	25
Truck Tail	18.18	0	18.22	0.04	38
Front Left Tire (Truck)	23	0	22.97	0.06	57

Table 13

Comparison of the targets’ range and speed between the configured and simulated Scenario 2 with a patch antenna and a bandwidth of 1 GHz. Additionally, the detected targets’ SNRs are given by the CFAR.

Target	Configured Scenario		CFAR
	Range (m)	Speed (m/s)	Range (m)	Speed (m/s)	SNR (dB)
Bench 1	8.34	0	8.30	0.83	35
Bench 2	15.38	0	15.38	0.29	34
Trash bin	11.63	0	11.64	0.34	35
Bike rack	26.5	0	26.51	0.02	34
Car 1	19.24	0	19.25	0	45
Car 2	25.3	0	25.4	0.01	35
Car 3	31.3	0	31.4	0	40
Pedestrian 1	13.72	0	13.74	0.03	34.6
Pedestrian 2	14.95	0	14.96	0.04	34.7
Pedestrian 3	15.66	0	15.67	0.02	36.8
Pedestrian 4	14.96	−2	14.98	−1.9	37
Pedestrian 5	16.67	2	16.67	1.97	34
Pedestrian 6	14.45	1.6	14.47	1.58	32
Pedestrian 7	16.5	2.86	16.51	2.87	35
Pedestrian 8	23.85	0	not detected
Pedestrian 9	29.6	0	not detected
Pedestrian 10	32	0	32	0.02	28
Pedestrian 11	19	0	not detected

Table 14

Comparison of the targets’ SNRs at a bandwidth of 1 GHz and 4 GHz. Both simulations were simulated with a single patch antenna. Additionally, the last column shows the difference between both SNR values with $\mathsf{\Delta }\mathrm{SNR}={\mathrm{SNR}}_{4\mathrm{GHz}}-{\mathrm{SNR}}_{1\mathrm{GHz}}$.

Target	SNR @ 1 GHz Bandwidth (dB)	SNR @ 4 GHz Bandwidth (dB)	ΔSNR (dB)
Bench 1	35	36	1
Bench 2	34	33	−1
Trash bin	35	30	−5
Bike rack	34	35	1
Car 1	45	45	0
Car 2	35	36	1
Car 3	40	42	2
Pedestrian 1	34.6	35	0.4
Pedestrian 2	34.7	34.9	0.2
Pedestrian 3	36.8	38	1.2
Pedestrian 4	37	37	0
Pedestrian 5	34	37	3
Pedestrian 6	32	33	1
Pedestrian 7	35	37	2
Pedestrian 8	not detected	not detected
Pedestrian 9	not detected	not detected
Pedestrian 10	28	30	2
Pedestrian 11	not detected	26

Table 15

Deviations in range and speed of the pedestrians between the configured and detected values of Scenario 2. The deviations are similar to identical between the simulation with a bandwidth of 1 GHz and 4 GHz.

Target	ΔRange (m)	ΔVelocity (m/s)
Pedestrian 1	0.02	0.03
Pedestrian 2	0.01	0.04
Pedestrian 3	0.01	0.02
Pedestrian 4	0.02	0.1
Pedestrian 5	0	0.03
Pedestrian 6	0.02	0.02
Pedestrian 7	0.01	0.01
Pedestrian 10	0	0.02
Pedestrian 11 (only detected at 4 GHz bandwidth)	0.02

Table 16

Comparison of the targets’ SNRs between the siulation with a patch antenna and 16 × 16 array at a bandwidth of 4 GHz. Additionally, the last column shows the difference between both SNR values with $\mathsf{\Delta }\mathrm{SNR}={\mathrm{SNR}}_{\mathrm{Array}}-{\mathrm{SNR}}_{\mathrm{Patch}}$.

Target	SNR (Patch Antenna) (dB)	SNR (16 × 16 Array) (dB)	ΔSNR (dB)
Bench 1	36	27	−9
Bench 2	33	29	−4
Trash bin	30	27	−3
Bike rack	35	39	4
Car 1	45	49	4
Car 2	36	47	11
Car 3	42	70	28
Pedestrian 1	35	45	10
Pedestrian 2	34.9	43	8.1
Pedestrian 3	38	40	2
Pedestrian 4	37	45	8
Pedestrian 5	37	44	7
Pedestrian 6	33	47	14
Pedestrian 7	37	52	15
Pedestrian 10	30	35	5
Pedestrian 11	26	32	6

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