Introduction
In modern defense systems, precision-guided munition (PGM) is considered essential for enhancing the efficiency of military operations. However, advancements in stealth and jamming technologies have made accurate target detection by PGMs difficult to achieve. To improve their target detection performance, it is necessary to design PGMs by accounting for various factors, including radar cross-section (RCS) and clutter. PGMs employ radar to detect targets. According to the well-established radar equation, received power is considered a function of transmitted power, antenna gain, wavelength, RCS, and the distance between the radar and the target. However, this equation is only applicable when the radar and the target are located at a considerable distance from each other, with the electromagnetic scattering field typically occurring in the near-field when a PGM encounters a target [1, 2]. Antenna gain in the radar equation is defined as the product of directivity and antenna efficiency, where directivity is normalized with respect to distance assuming a far-field condition. This highlights the need to redefine antenna gain in the near-field [3]. Similarly, RCS is defined as the ratio of the scattered power density to the incident power density when a plane wave is incident on the target, assuming a far-field condition. Therefore, it is necessary to redefine RCS in the near-field as well.
Previous studies have attempted to calculate near-field RCS by using the near-field of electromagnetic fields [4], modifying the distance and antenna gain between the radar and the target [5], and employing physical optics, physical theory of diffraction, and shooting and bouncing ray (SBR) techniques [6]. However, these studies conducted calculations using commercial simulation tools, meaning that no actual measurements were performed. Additionally, to calculate the received power, a study employed the Fresnel diffraction equation to analyze the near-field gain and near-field RCS based on the near-field of the electromagnetic field [7]. Although the calculated received power could be validated against simulation data and actual measurement data, the application of the Fresnel diffraction equation required the use of Love’s equivalence principle, which allowed near-field analysis only on very simple target shapes.
Generally, measuring the RCS of a target or the received power between a target and an antenna requires significant time and cost. If it were possible to carry out these measurements in a simple laboratory environment rather than a large chamber by using a downscaled model, it could save a great deal of time and cost. Along these lines, a study was conducted to reduce the RCS calculation time using downscaled models of actual-sized targets [8]. However, this study did not calculate the near-field RCS, nor were actual measurements conducted.
Therefore, in this paper, the near-field gain of a PGM antenna and the near-field RCS of a target are analyzed in a simple laboratory measurement environment using the downscaled model of a scenario where the PGM encounters the target. The received power is calculated by substituting the analyzed near-field gain and near-field RCS into the radar equation. Furthermore, the validity of the calculated received power is confirmed by comparing it with the received power obtained using the far-field radar equation, a High Frequency Structure Simulator (HFSS) SBR+ simulation, and the actual measurement data using the time-gating technique.
In Section II, we introduce the methods adopted for analyzing near-field gain and near-field RCS. In Section III, the numerically calculated near-field gain and near-field RCS for different targets are presented as a function of distance. In Section IV, the process of measuring the received power in a simple laboratory environment using a downscaled model is explained, and the validity of the near-field gain and near-field RCS analyzed in the previous section is evaluated based on the measurement results. Finally, Section V concludes the paper.
Analysis Method
1. Radar Equation in Near-Field
where Pr is the received power, Pt refers to the transmitted power (which is set to 0 dBm in this paper), G denotes antenna gain, λ is the wavelength, σ signifies the RCS of the target, and R is the distance between the target and the radar. Notably, it is assumed that the radar’s transmitting and receiving antennas are the same. Electromagnetic waves radiating from the radar’s transmitting antenna reach the target, which then reflects the waves back toward the radar. The secondary radiation received by the radar’s receiving antenna allows it to detect the target. The radar equation mathematically expresses this process. However, as mentioned in the introduction, the antenna gain and the RCS of the target in the near-field need to be redefined. Therefore, in the next section, the numerically calculated near-field gain and near-field RCS are substituted into the radar equation to calculate the received power in the near-field.
2. Downscaled Model Setup
Considering a scenario in which the target and the PGM encounter each other, the PGM was replaced with a horn antenna (model SAV-0367312429-VF-21; Eravant Inc., Torrance, CA, USA) having a wide bandwidth of 6–67 GHz in the downscaled model. As for the targets, a perfect electric conductor (PEC) plate (140 mm × 140 mm, 14λ × 14λ) and PEC missile-shaped targets—large 220 mm (22λ) and small 110 mm (11λ)—were employed. To replicate a scenario where both the PGM and the target move together, the center of the target was fixed at the origin, as shown in Fig. 1, while the antenna was set to move along the x-axis using the parameter xvar, based on (0.1 m, 0 m). Table 1 shows the range and spacing of the parameters for the downscaled model. The antenna’s coordinates were set to x = 0.1 m + xvar and y = 0 m, while the moving antenna was implemented by varying xvar.
3. Near-Field Gain Analysis
The parameters of the horn antenna employed in this study to calculate the near-field gain are presented in Fig. 2. This antenna was configured to operate at 30 GHz. Notably, the far-field distance Rff can be calculated using Eq. (2) [10]:
where L is the length of the horn antenna and λ is the wavelength. In general, the length of the antenna is used to calculate the far-field distance. Therefore, L was used as the horn antenna length, and it was used as is because it does not lose its validity in near-field analysis [11]. Since L = 39 mm and λ = 10 mm, Rff was calculated to be approximately 0.3 m. In the configured scenario, the distance between the target and the horn antenna remained within Rff, thus necessitating a redefinition of the near-field gain. Eq. (3) presents the formula for calculating the near-field gain G [3] of the horn antenna:
where Go is the far-field gain, while
R H ′ R E ′
and
where the path length errors δH(x) and δE(x) can be obtained using Eq. (5):
and
with
where a is the width of the horn antenna’s aperture, measuring 29 mm, and b is the height of the aperture, measuring 22 mm. Furthermore, R refers to the distance from the antenna, and
k = 2 π λ R H ′ R E ′
Considering that the far-field distance of the horn antenna is 0.3 m, we conducted analyses and measurements for distances up to 0.35 m between the target and the antenna. Notably, for the analysis of near-field RCS discussed in the following sections, the measurement range is defined as the radiative near-field region, which is located between the antenna’s reactive near-field and the far-field region [10]. As shown in Fig. 3, the region outside about 0.05 m exhibits an almost constant gain for the horn antenna. Therefore, based on the given scenario, we expected the impact of variation in the near-field gain of the horn antenna to be very small.
4. Near-Field Radar Cross-Section Analysis
and
where
E s → H s → | E s → × H s * → |
Numerical Results
1. Case 1: Plate Model
Fig. 5 illustrates the PEC plate model designed using HFSS, measuring 140 mm by 140 mm (14λ × 14λ). Fig. 6 presents a graph depicting the near-field RCS as a function of distance when the antenna moves along the x-axis for the PEC plate, with the dashed line representing the far-field RCS. Notably, the incident wave in the near-field was assumed to be the electromagnetic field radiated from the horn antenna located near the target, while the incident wave in the far-field was assumed to be a uniform plane wave.
In Fig. 6, the calculated near-field and far-field RCS exhibit a difference of more than 20 dB. Even near the far-field distance of the horn antenna—0.3 m—the calculated near-field and far-field RCS show a significant difference. This result can be attributed to the incident wave not being a uniform plane wave near the far-field region of the horn antenna.
Fig. 7 shows the surface current distribution on the PEC plate in the case of horn antenna incidence (left) and uniform plane wave incidence (right). Notably, the surface currents in Fig. 7 were simulated using the physical optics technique, and diffraction was not accounted for. In the case of horn antenna incidence, the surface current is highest at the center of the PEC plate, where the horn antenna directs its waves. In the case of uniform plane wave incidence, the surface current is uniformly and strongly distributed over the entire PEC plate. These results imply that owing to the differences in surface current distribution, the near-field RCS is lower when waves from the horn antenna is incident compared to when a uniform plane wave is incident.
2. Case 2: Missile Model
Fig. 8 shows the PEC missile-shaped target model designed using HFSS. The larger model has a length of 20 mm (22λ) and a central diameter of 56 mm (5.6λ), while the smaller model has a length of 110 mm (11λ) and a central diameter of 28 mm (2.8λ).
Fig. 9 presents the near-field RCS as a function of distance when the antenna moves along the x-axis for the PEC missile-shaped targets (large and small), with the dashed lines representing the far-field RCS. As in the case of the PEC plate, a significant difference is observed between the calculated near-field and far-field RCS. This discrepancy resulted in a major difference in the calculation of received power in the near-field compared to the far-field.
Fig. 10(a) and 10(b) illustrate the surface current distribution for the large and small missile-shaped target models, respectively. In the case of horn antenna incidence, the surface current for both models is highest at the center of the PEC missile-shaped targets, where the horn antenna directs its waves. Similarly, for both models, the surface current is relatively uniform and strongly distributed along the curved surface of the PEC missile-shaped targets in the case of uniform plane wave incidence compared to horn antenna incidence. For the same reasons as in the case of the PEC plate, these differences in surface current distribution contributed to differences between the near-field and far-field RCS.
Measurement
1. Sample and Antenna Setup
To validate the proposed method of calculating received power by analyzing the near-field gain and near-field RCS, the received power (S11) was measured using a vector network analyzer (VNA). A horn antenna (model SAV-0367312429-VF-21; Eravant Inc.) and PEC targets were also employed. Fig. 11 illustrates the overall measurement setup. The jig, target, and antenna were installed on a rail that could move in the x-axis direction. The targets were mounted on a custom-made jig. The reflection signal was measured based on various distances between the target and the antenna.
As shown in Fig. 12, the PEC targets used in this experiment included a PEC plate made of aluminum and a missile-shaped structure, which was fabricated using a 3D printer and then covered with copper tape to create a copper-taped missile-shaped structure. Notably, the PEC plate and PEC missile-shaped targets were manufactured with identical dimensions to the PEC plate model and the model for the PEC missile-shaped targets discussed in Section III. The jig was designed to offer stable support to the targets, thereby ensuring precise measurements. Both the skeleton of the missile-shaped targets and the jig were created by a 3D printer using polylactic acid with carbon fiber (PLA-CF) with a relative permittivity of 20 and a loss tangent of 0.1, as measured in our laboratory [12]. Holes were added to the PEC plate to fix it to the jig. Notably, the jig was placed behind the PEC plate to minimize any reflected signals from the jig. Meanwhile, the PEC missile-shaped target jig was designed to be cylindrical in shape to minimize reflection. In the presence of only the PEC missile-shaped target jig, the reflection ranged from −50 dB to −60 dB, indicating that the influence of the jig was very low compared to that of the target.
2. Measurement Method
The measurement setup comprised a VNA (model ZVA67; Rohde & Schwarz, Munich, Germany) equipped with phase-stable cable connections. Prior to measurement, one-port calibration was performed using open-short-load standards for the VNA and cable. The VNA frequency range was configured to span from 25 to 35 GHz, which was essential for the subsequent time-gating analysis [13].
The calibrated measurement cable was then connected to the antenna mounted on the test fixture. To analyze the reflected signals, the frequency-domain data were transformed into time-domain data using the VNA’s built-in function. The resulting time-domain response, as shown in Fig. 13, revealed three distinct zones of reflection. Zone 1 represents the reflections from the antenna and cable assembly, while Zone 2 contains the target-induced reflections. The distinction between these zones was established by converting the round-trip time into distance and then correlating it with the known physical separation between the antenna and the target. Meanwhile, Zone 3 features multiple reflection signals occurring between the target and antenna.
To isolate the target response, time gating was applied to Zone 2. As a result, only those reflection effects caused by the target could be analyzed, thus mitigating noise even when conducting measurements in a standard laboratory environment [14, 15]. Furthermore, a flat-top window function was implemented during the time-gating process to minimize ripple effects in the frequency domain [12]. The gated time-domain response was then transformed back to the frequency domain for analysis at the target frequency of 30 GHz. The magnitude of the reflected signal was quantified by measuring the S11 parameter at this frequency, thereby achieving a precise characterization of the target reflection.
3. Measurement Results
Fig. 14 depicts the received power calculated using the radar equation by substituting the near-field gain and near-field RCS (labeled “Near”), the received power considering the far-field gain and far-field RCS (labeled “Far”), the received power obtained through HFSS SBR+ simulation (labeled “Sim(SBR+)”), and the actual measured reflection coefficient (labeled “Meas”) as the antenna moves along the x-axis, with the PEC plate as the target.
Notably, since the measured reflected signal represents a relative value, it is expressed as the received power by assuming an initial transmission power of 0 dBm for easier comparison with the actual received power. The “Near” graph exhibits a difference of more than 20 dB compared to the “Far” graph, reflecting the previously analyzed difference of more than 20 dB between the near-field RCS and the far-field RCS. The “Near” graph also presents an error of less than 1–2 dB compared to the “Meas” and “Sim” graphs despite the target not being a perfect PEC, indicating that the near-field RCS had been configured well.
Fig. 15 depicts the calculated, simulated, and measured received power as the antenna moves along the x-axis when using the PEC missile-shaped targets (large and small). As in the case of the PEC plate, the “Near” and “Far” graphs show a relatively large difference. The “Near” graph also presents an error of less than 1–2 dB compared to the “Meas” and “Sim” graphs. With regard to the PEC missile-shaped targets, which were fabricated by applying copper tape on a curved surface, the target surface was not perfectly smooth, and the copper itself was not a perfect PEC. Nevertheless, the near-field RCS had been accurately configured, as indicated by the very small discrepancy compared with the measured and simulated results.
Conclusion
In this paper, the downscaled model of a scenario where a PGM encounters a target was set up in a simple laboratory measurement environment to devise a method for calculating the power received through the PGM’s antenna by analyzing near-field gain and near-field RCS. It was found that the proposed method allows for the calculation of received power using near-field gain and near-field RCS, providing more accurate results in the near-field compared to traditional methods that use far-field gain and far-field RCS to conduct the same calculation. The received power calculated using the proposed method showed only a small difference of 1–2 dB compared to the HFSS SBR+ simulation data and the actual measurement data, confirming the validity of the configured near-field gain and near-field RCS. Moreover, the successful analysis of the near-field RCS of the target and the received power between the target and the antenna using the SBR+ technique in a simple laboratory environment, as depicted in this study, suggests that the proposed method could also be applicable in scenarios where actual-sized targets and guided weapons are involved. Overall, the proposed downscaled model approach is expected to improve the accuracy of PGM and radar system analyses in target encounter scenarios.
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