RCS measurements and ISAR images of small UAVs

Currently small unmanned aerial vehicles (UAV) pose a serious threat for the safety of flights. The Aviation Authorities are dealing with this issue worldwide. Recently (October 2015), the U.S. Federal Aviation Administration gave permission to test antidrone technology that would counter rogue drones flying within a fivemile radius of selected airports [1]. Airport safety is only one of the problems that the increasing number of UAVs can pose. A critical issue is to prevent UAVs being used for terrorist attacks, espionage, or other malicious activities against sites with critical infrastructure. Last but not least, UAVs flying in private area pose privacy concerns [2].


INTRODUCTION
Currently small unmanned aerial vehicles (UAV) pose a serious threat for the safety of flights. The Aviation Authorities are dealing with this issue worldwide. Recently (October 2015), the U.S. Federal Aviation Administration gave permission to test antidrone technology that would counter rogue drones flying within a fivemile radius of selected airports [1]. Airport safety is only one of the problems that the increasing number of UAVs can pose. A critical issue is to prevent UAVs being used for terrorist attacks, espionage, or other malicious activities against sites with critical infrastructure. Last but not least, UAVs flying in private area pose privacy concerns [2].
Radar could be the technology of choice for detecting them, but standard air defense is ill-prepared for UAV detection: UAVs are low-velocity aircraft with a very weak radar signature. Despite this, the scientific literature lacks detailed experimental studies on the radar cross section (RCS) of small UAVs [3], [4], [5], especially for quadcopters that are the most popular civil UAVs. Therefore, the first aim of this article is to carry out RCS measurements of small drones, in particular of a toy drone and a professional quadcopter.
The RCS measurements give global information on a target, but they do not provide information on which features are mainly responsible for the radar response. Inverse Synthetic Aperture Radar (ISAR) [6], [7], [8] processing provides just this kind of information.

THE MEASUREMENT EQUIPMENT
A sketch of the measurement equipment is shown in Figure 1. A vector network analyzer (HP 8720A) operates as Continuous Wave Step Frequency transceiver. It is linked through microwave cables to a radar front-end held on a tripod.
The front-end is provided with a pair of single-pole doublethrow switches that provides a direct path (through a −40 dB attenuator) between the transmitter and the receiver in order to perform calibrated measurements. The antennas are two equal horns linearly polarized, with a rectangular aperture 5.5 cm × 7.5 cm, designed for operating in the 8-12 GHz band. Their measured efficiency has been η = 0.446 ± 0.040.
As shown in Figure 1, the target under test was positioned on a platform that can be rotated step-by-step. For each k angular position, the equipment carried out a sweep of N f frequencies between 8 GHz and 12 GHz with the switches connected to antennas and a second sweep with the switches connected to the attenuator (−40 dB). The ratio, frequency by frequency, gives a calibrated measurement. A complete acquisition is a matrix of complex numbers E i,k , with i index relative to the frequency and k index relative to the angular position. After the radar acquisition, the target under test was removed and a single frequency sweep was performed. This later acquisition (called empty room) was subtracted to each column of matrix E i,k (background removal).
Before the measurements session of the targets under test, the equipment was calibrated using three known targets positioned at 17 m in front of the antennas: a metallic sphere of 0.45 m diameter, a corner reflector of 0.30 m side, and a second corner reflector of 0.50 m side. From the radar equation [9], the RCS (σ) can be obtained from the following equation: where A is the physical area of RX antenna, η is the antenna efficiency, λ wavelength, u k is peak amplitude of the inverse fast Fourier transform (IFFT) (along the i-index) of E i,k , γ power attenuation of the calibration path (−40 dB), and F padding factor of IFFT. The α factor takes into account the decreasing of the peak

THE UAVS UNDER TEST
As a representative toy drone we selected a SYMA X5SC-1 quadcopter ( Figure 2). Although it is provided with a 2.0 Megapixel camera, it is intended to be a low-cost toy not for professional use. It is powered by a built-in 500 mAh Li-Poli battery. The distance from the motors is 16 cm. Their height from the ground is 4.5 cm. The frame and the blades are made of plastic material.
We selected a NT4Contra quadcopter, manufactured by Air-Vision (Figure 6), as representative professional UAV. It has four pairs of engines with counter-rotating blades. The frame is made of carbon. It is powered by two 4,600 mAh Li-Poli batteries housed in the legs. Below the head there is a dock for a camera (not provided). The distance from the motors is 36 cm. The height of the motors from ground is 22 cm (Figure 3).

RCS MEASUREMENTS
The SYMA quadcopter was placed over the platform and a complete measurement with antennas in vertical polarization was car-ried out. The distance between the antennas and the rotation center was 156 cm. The angular step was 1 deg. By using a Kaiser window with β = 5, a 500 MHz bandwidth gives a Full Width at Half Maximum (FWHM) equal to 0.54 m (larger than the size of the quadcopter). The measured angular pattern of RCS is shown in Figure 4. The largest values are in correspondence of the four motors. The measured main value of the RCS was 0.0312 m 2 .
By rotating the antennas, the RCS of the SYMA quadcopter was also measured in horizontal polarization. The obtained main value has been 0.0229 m 2 . There are not substantial differences with respect to the RCS pattern in vertical polarization.
The same measurements have been performed with the AirVision quadcopter. The measured angular pattern of RCS in vertical polarization is shown in Figure 5. For this quadcopter, the largest RCS values are in front and back. The main value is 0.271 m 2 .
By rotating the antennas, the RCS of AirVision quadcopter was also measured in horizontal polarization. The obtained main value has been 0.2759 m 2 . There are no substantial differences between the RCS patterns in horizontal and vertical polarizations. Table 1 summarizes the obtained results.
Just a note about the distance between antenna and target: for both the UAVs it was 156 cm. The RCS of a target should be measured in the far field both of antenna and of target. The first

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condition is always respected, But the latter condition is not respected in the measurements with the bigger UAV (AIRVISION NT4CONTRAS). Fortunately this is not a serious issue, as suitable algorithms have been developed for transforming near-field data in far-field data [10], [11]. In particular, we used the well-known algorithm by Mensa and Vaccaro as described in [11].

ISAR PROCESSING
The ISAR processing allows to obtain a two-dimensional (2D) (or even a three-dimensional (3D)) image of the RCS distribution. It is particularly useful to identify the features of the target that contribute most to the radar signal. The basic idea of ISAR is to exploit the spatial diversity of data acquired for focusing a high-resolution image.
Using the above-mentioned equipment, the result of a measurement session is a matrix N f × N p of complex numbers: where I i,k and Q i,k are the in-phase and the quadrature components acquired at ith frequency (1 < i < N f ) and at the kth angular position (1 < k < N p ). The basic formula for focusing in a generic point identified by the coordinate (x, y, z) is [6]: where R k (x, y, z) is the distance between the image-point (x, y, z) and the kth angular position of the antenna. Equation (8) is computationally very heavy, but several faster algorithms have been developed [6], [7], [8].

2D ISAR IMAGES
The SYMA quadcopter was placed on the platform as shown in Figure 1. The antennas operated in vertical polarization. The distance between the antennas and the rotation center was 202 cm. The angular step was 1 deg. The bandwidth was B = 4GHz; that Table 1.   gives a FWHM in range equal to 0.136 m, using a Kaiser window with β = 5. The obtained RCS image is shown in Figure 6. The shape of a quadcopter can be easily recognized. The four motors give a clear, high signal. The same measurements were performed with the AirVision quadcopter. The obtained RCS image is shown in Figure 7. Also in this case the shape of quadcopter can be easily recognized but, unlike SYNA quadcopter, the motors do not give the highest RCS signal.

3D ISAR IMAGES
The focusing formula in (3) can be applied to the 3D case by carrying out radar measurement at different height of the rotation plane. With this aim, the height of the platform was varied of 18 cm at step of 1.0 cm. The contour plot of the obtained 3D image of the smaller UAV is shown in Figure 8. The four blades are clearly recognizable, as well as the central body.

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IEEE A&E SYSTEMS MAGAZINE 31 Figure 9 shows the contour plot of the 3D image of the bigger UAV. The height of the platform was varied of 26 cm at step of 1.0 cm. The shape of the motors (a couple of motors in line to be more precise) are clearly recognizable, as well as the legs and the head of quadcopter.
Finally, by using the whole measurement set (9,270 single acquisitions), we calculated the RCS statistical distribution, as shown in Figure 10, that resulted in very good agreement with the wellknown Swerling Case I distribution [12]: where σ is the mean value of RCS. Indeed the χ 2 goodness-of-fit test rejected the null hypothesis at the 1% significance level.

CONCLUSIONS
RCS measurement of a toy drone and a professional quadcopter has been carried out. A significant finding of this work is that Swerling distribution is in very good agreement with the RCS statistical distribution of the quadcopters we tested. This is not an obvious fact. Swerling Case I distribution was obtained in a very heuristic hypothesis (a random set of equal scatters on a planar surface) and-at least in the open literature-it has never been tested with quadcopters or other small UAVs. Another finding that is worth mentioning is that mean RCS in vertical and horizontal polarization are nearly equal.  Aerospace and Electronic m a g a z i n e