An Improved Performance Radar Sensor for K-Band Automotive Radars

Keywords: automotive radar, MIMO, PGAA, SRR, superstrate, UWB

Table 1.

3.1. Design of SRR Element

The basic principles of the proposed design are clarified through a detailed analysis of a single SRR and the grid structures. The SRR consists of two conductive rings that are printed on a Rogers substrate and positioned with a small gap between them. The two rings in the SRR have slits, and they are arranged so that the slits are positioned on opposite sides of the line of symmetry. The dimensions of the SRR are considerably smaller than the wavelength. Taking this into account, the SRR can be conceptualised as two small loop antennas coupled to each other.

The excited voltages are treated as two discrete voltage sources at points $A$ and $B$, denoted as source $Vo$ and source $Vi$, respectively. Figure 4a depicts the analogous circuit in its entirety. The symbol $C_{slit}$ represents the capacitance of the slots, where $R\prime$ and $L\prime$ represent the distributed resistance and inductance, respectively. C′ refers to the distributed capacitance of the gap between the rings. Two primary loops—the inner and the outer rings of the circuit shown in Figure 4a are connected across the gap by the distributed capacitance $C\prime$.

The ratio of the areas created by the outer and inner rings, respectively, shows that voltage $Vo$ is always higher than voltage $Vi$. As a result, the current virtually crosses the gap from the outer ring to the inner ring via several branches created by the dispersed capacitance C′. This branching causes the current in the outer ring to vary according to its location. It reaches its maximum value at point $A$ and then starts to decrease along the ring before becoming negligible at the gab. Of course, any current that flows from the outer ring into the inner ring contributes to the total inner-ring current. As a result, the current in the inner ring is greatest at the position of the voltage source $Vi$ (point $B$), and then it gradually decreases along the ring until it reaches its lowest value at the slit. Since the net-ring current is barely affected by the current flowing through the slit ($C_{slit}$), $C_{slit}$ can actually be considered to be zero. Since the current flows primarily through the slit, the entire circuit can be approximated using the much simpler circuit shown in Figure 4b. This consists of a single voltage source and a serial tank circuit. In fact, a single, electrically tiny loop antenna loaded with a capacitor should perform very similarly to the SRR.

The radiator arrangement is the only factor that controls the structure’s radiation characteristics of the structure. The SRR resonance frequency is considered at 24 GHz. The parameters of the basic structure are extracted from the simplified equivalent circuit shown in Figure 4b. The values of the inductance $L$ and $C$ are extracted according to Equation (1).

The value of $L$ is supposed to be 0.875 nH, so the value of $C$ is calculated as 0.05 PF. To obtain a low-quality factor, the value of $R$ is 10 ohms. Accordingly, a single element of a planner SRR antenna was simulated using ADS software, as shown in Figure 4. Figure 5 compares the reflection coefficients of the CST design and the RLC circuit model, which were extracted using ADS software, and the results show good agreement. The reason for neglecting the effect of the upper termination line shown in Figure 2 in the single-element equivalent circuit is due to the presence of an opposing current in the corresponding lower section. This opposing current leads to a cancellation effect, as shown in the electric field distribution in Figure 3, resulting in the negligible contribution of the upper termination section to the overall circuit behaviour. Figure 3a presents the electric field distribution of a single element, emphasising that even when simulating a single element, the influence of the horizontal termination section is minimal and can be ignored.

3.2. Grid Antenna Array Results

Two simulators were used to verify the simulated prototype results: CST Microwave Studio Version 2021 and HFSS Version 2021. The voltage standing wave ratio (VSWR) of the proposed GAA is demonstrated in Figure 6, which shows a wide bandwidth ranging from 20 GHz to 26 GHz with a magnitude of <2 dB. A very good agreement between CST and HFSS results is observed.

Furthermore, the realised gain radiation patterns are depicted in both the E plane and the H plane in Figure 7. The proposed GAA antenna shows a half-power beamwidth (HPWB) of 18 ° in the E plane and 69 ° in the H plane at 24 GHz. The gain over the frequency shows an average value of 12 dBi, as shown in Figure 8. It is seen that the gain at 24 GHz is almost 13.8 dBi.

3.3. Bandwidth and Gain Enhancement Using a Superstrate Dielectric Layer

In general, automotive radars have to operate in temperatures ranging from 40 °C to 85 °C or even higher. They must tolerate shock and vibration and sometimes operate in wet, icy, or other adverse weather conditions. Therefore, the choice of materials, manufacturing techniques, packaging, and sensor installation is important. Materials used as substrates must be suitable for sub-millimetre-wave frequencies and have physical and electrical properties that remain mostly unchanged over a wide temperature range, and they should not absorb moisture. On the other hand, standard microwave substrates can be somewhat expensive, so a trade-off must be considered. Standard printed circuit board (PCB) processes should be used to etch the planar structures as far as possible. However, the 24 GHz frequency range may require accuracies down to 200 μm, which also presents a significant problem for optimum antenna design. In addition, the right coating must be used to prevent corrosion on metal surfaces. A Rogers RO3003 material with a relative permittivity of 3 and a thickness of 1.527 mm was therefore chosen for both packaging and gain enhancement. The dielectric layer is located at a distance of approximately $\left(\lambda \right)⁄2$, corresponding to 6 mm from the top of the antenna array substrate, as shown in Figure 9. Numerous reflections between the radiating element and the dielectric slab result in gain enhancement and simultaneous projections of the radiators. In other words, the radiation intensity of the antenna's primary beam is focused using supertasters as a lens, resulting in an apparent increase in antenna gain. The presence of superstrates does not affect the area of the automotive radar as there is sufficient space in the z-direction. The effect of the dielectric superstrate on the antenna bandwidth is shown in Figure 9. The impedance matching is improved and covers the frequency range from 20 GHz to 29.3 GHz with a VSWR level of <2. Figure 10 illustrates the normalised realised gain radiation patterns, with an HPBW of 15 deg in the E plane and 60 deg in the H plane, and an SLL of −15 dB in the E plane. The superstrate technique provides again enhancement of 2.7 dB, reaching 16.5 at 24 GHz, as shown in Figure 11.

Table 2.

5.1. MIMO Antenna Configuration

In the proposed radar system, nine elements (six transmitters and three receivers) were arranged to form a virtual array of eighteen closely spaced elements, as shown in Figure 14a. The radar sensor should be carefully designed to avoid reflections from traffic signs or bridges above the road at a height of at least 5 m. Accordingly, the number of antenna elements was chosen to satisfy this condition in the elevation direction. A relatively wide beamwidth of about 60° in the azimuth direction is required to detect adjacent paths. To design the antenna coverage area, we assume a perspective antenna operating at a central wavelength λ; $x_m$ is the position of the Tx antennas, where m varies from 1 to 6; and Rx antennas are placed in position $y_n$, where $n$ varies from 7 to 9. Suppose an object is positioned at a distance $r$ from the automotive radar. The corresponding virtual MIMO array factor FMIMO is obtained by multiplying the $Tx$ array factor $\left({AF}_{Tx}\right)$ by the $Rx$ array factor $\left({AF}_{Rx}\right)$, as given in Equation (2) [5].

According to Equation (2), the $Tx$ array factor is advised to be null at every grating lobe of $Rx$, and vice versa, to achieve a low SLL for a specific MIMO arrangement. Therefore, the spacing between the $Tx$ elements is chosen to be ${\lambda }_0$ for $Tx$ and 1.5${\lambda }_0$ for $Rx$, as shown in Figure 14a. Figure 14b illustrates the MIMO configuration, including the packaging (superstrate). The array factor and 3D radiation pattern of the proposed configuration are depicted in Figure 14c,d. According to the proposed MIMO configuration, the SLL of the virtual array is less than −20 dB along the effective monitoring angle from 60° to 120°, where the AFTX nulls cancel the AFRX grating lobe. The coupling between the closest Tx–Rx antennas is examined and shown in Figure 15, illustrating excellent isolation of more than 20 dB.

5.2. Radar Image Reconstruction

With M transmitters and N receivers in the linear array radar system, we assume that they are all located on the x-axis with ($x_m$, 0) and ($x_n$, 0), where m = 1, 2, ..., M and n = 1, 2, ..., N, [5]. The complex representation of the transmitted stepped frequency continuous wave (SFCW) signal is given by

where Δf is the frequency step, Q is the number of frequencies, and T is the dwell time of each frequency. Assuming a target located at ($x_0$, $y_0$), for the mth transmitter, nth receiver, and qth frequency, $f_q=f_0+(q-1)∆f$, the echo signal mixed with the transmitted signal can be written as follows:

where ${\tau }_{mn}=\left(\sqrt{{\left(x_0-x_m\right)}^2+{y_0}^2}+\sqrt{{\left(x_0-x_n\right)}^2+{y_0}^2}/c\right)$ is the time delay of the received signal, α is the reflection coefficient of the target, and c is the velocity of light. For distributed target, the received signal can be expressed as follows:

We utilised the time-domain back-projection (TDBP) algorithm. Moreover, the point spread function (PSF), which is always used to demonstrate the resolution and SLL of the radar system, is defined as follows:

Furthermore, the design procedure of a linear uniform array can be summarised as follows: First, with the range resolution requirement ${\delta }_r$, the bandwidth of the SFCW $B$ is determined using ${\delta }_r=c/2B$. Secondly, with the azimuth resolution requirement ${\delta }_a$ at the given range $R_0$, the array length is determined using $L=\lambda R_0{\delta }_a$, where $\lambda =c/f_H$ is the wavelength, and $f_H$ is the highest frequency. The proposed radar consists of six TX and three RX antennas. The SFCW radars transmit 2048 frequencies within a bandwidth of 500 MHz with a centre at 24 GHz (K-band). The radar has a maximum range ambiguity of 613 m and an azimuth angular resolution of 0.2 degrees.

Figure 16 shows the simulated radar image acquired with the parameters of the MIMO automotive radar system where six targets are located at (x, y) locations of (1, 2), (1.5, 2.5), (−2, 3), (−3, 4), (0, 5), and (1, 6) from the radar system, while the position location is in metre. The proposed system shows a very good resolution in both range and azimuth directions, verifying the applicability of the proposed configuration for MIMO radar systems. In order to guarantee the precision and credibility of our results in terms of azimuth resolution, we carried out an investigation using two targets positioned in close proximity at a distance of 10 m range, with a separation of 0.2 degrees. As depicted in Figure 17, we were able to accomplish this distinction by detecting a significant 3 dB difference in the signals returned from each target. This notable difference serves as a clear indication of the system’s ability to discriminate between closely positioned objects and validates the azimuth resolution achieved.

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Data Availability Statement

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