Introduction
In the past 60 years, since the launch of Sputnik 1, the number of objects in orbit around the Earth has increased tremendously. A good part of these objects are classified as space debris representing a significant hazard for all current and future satellite missions [1]. In addition, the growing traffic is increasing the probability of collisions also among functioning satellites as the Iridium–Cosmos collision in 2009 demonstrated.
Even collisions with very small objects (a few centimetres in size) at orbital speed can cause catastrophic consequences. Each explosion or collision with space junk produces additional debris, which can lead to a cascade of more collisions. This chain reaction is known as Kessler syndrome, and some argue it has already started. Very large objects, such as defunct satellites, rocket bodies, and large fragments, can represent a threat even for people on the ground since they may hit the ground at unpredictable locations after reentry. In addition to trackable space debris, millions of nontrackable small fragments, with the size of a grain of salt, exist that can penetrate the spacesuit of an astronauts or a window on a space vehicle with tragic consequences.
Information about space debris comes from a combination of ground-based and space-based measurements. One of the entities that identifies, tracks, and categorizes space objects is the United States Space Command [2], which consists of Space-Based Space Surveillance satellites and a network of radars and optical telescopes [3]. In 2009, the European Space Agency started a program for a European Space Situational Awareness System, which required the design of a radar system able to detect small targets with size in the order of one decimetre in LEO [3]. Moreover, in Europe, a number of radar systems are used to monitor space debris. An example is the bistatic radar (BR) system Grand Rseau Adapt la Veille Spatiale that has been operating in France since 2005. In Russia, 20 radars and telescopes are positioned in 8 different sites. In Germany, the Tracking and Imaging Radar system of Fraunhofer FHR allows for the estimation of target's characteristics as orbital elements, intrinsic motion parameters, target shape and size, and ballistic coefficient thanks to new signal processing techniques based on radar observations [3].
Among all sensors deployed to detect an track space debris radar systems represent an important contribution for their ability to provide high detection probabilities at very large ranges in addition to a range of target's characteristics.
The feasibility of tracking space debris by using a passive bistatic radar (PBR) was investigated in [4]. Specifically, [4] proposes a system, which comprises a ground-based receiver for space object tracking with low-power scattering observations of any objects above the horizon. The underlying principle is to estimate the radarcross section (RCS) of an object by measuring the received forward scattering (FS). The paper proposes several solutions to achieve a suitable signal-to-noise ratio (SNR) at the receiver, such as the use of multiple receiving elements and the integration of the received signal over time. One of the principal problem is represented by the Doppler offset of the received signal due to relative motion between transmitter, receiver, and target. Jayasimha and Jyothendar in [5] show the capability to detect small space debris by using a large-antenna earth-station communicating with a geo-stationary satellite, exploiting self-interference cancellation. Specifically, when a space debris is at near-LOS, the output of self-interference cancellation may contain the return from one or two debris, which can be used for detection. However, the presented method is dependent on weather conditions, since the debris signature can be affected by inadequate cancellation of direct-path caused by the clutter from weather. In [6], a novel multistep processing strategy is proposed with the aim of reducing computational costs for extracting target signature to an affordable level for a PBR. The first step comprises correlation with a replica of the expected signal for relative short integration times. After integrate and dump (I&D), the full length coherent integration is obtained by summing the outcomes from the two operations with the necessary phase adjustments.
The FS radar configuration represents a suitable countermeasure also to stealth technology. With an FS radar, one can detect objects with very small RCS, built with absorbing material [7]. In fact, the FS RCS of a target depends only on the size and the shape of its silhouette. Recently, FS radars have been exploited in many different scenarios to perform radar tasks, e.g., detection, tracking, and imaging. In [8], an algorithm for the classification of vehicles with different size is proposed based on different frequency Doppler shifts characterizing the target signature. In [9], the capability to detect an aircraft by a FS radar using the Global Navigation Satellite System (GNSS) satellites as illuminator of opportunity was demonstrated experimentally. Moreover, target classification was performed by evaluating the shadow inverse synthetic aperture radar image from received signals. Abdullah et al. in [10] show experimentally the capability of extracting microDoppler information due to target secondary motions, e.g., rotation or vibration, which may be used for target classification using FS configuration [11]. In this paper, the concept of FS is exploited for space situational awareness. A novel radar system for the detection of very small space debris, which may allow the development of target tracking and classification capabilities, is proposed. Specifically, the feasibility of a new space-borne PBR system for space target detection is investigated.
In the proposed system, the PBR is installed on one or more cubeSats flying at low altitude and receiving the RF signals transmitted by noncooperative illuminators at higher altitudes. The main motivation for a space-borne PBR is that:
it reduces the distance between transmitter and receiver;
allows for a lower relative velocity between illuminator and receiver;
bypasses the atmosphere and the sources of error and attenuation that come with it.
The long distance has an impact on the required gain of the antenna, while the relative velocity has an impact on the integration time, and thus the ability to detect small objects. A cubeSat-based PBR offers a low-cost alternative solution since the shorter distances and smaller relative velocities allow one to achieve suitable SNR with a simpler hardware and lower costs. The proposed system can provide higher integration times by conveniently selecting the system illuminator. Moreover, a space-borne receiver in LEO avoids the detection of other flying objects, and the degradations of the signal due to atmospheric effects. Finally, by using two or more cubeSats, one can observe the same target for different parts of its orbit improving temporal and spatial resolution. The paper will consider technologies that are compatible with mass and dimensions of cubeSats and a wide range of illuminators. The key performance metric, for the proposed system, is the minimum size of detectable target.
The remainder of the paper is organized as follows. Section II describes the proposed radar system configuration. In Section III, the capabilities of proposed system are evaluated in terms of minimum detectable target's size while Section IV concludes the paper.
cubeSat-Based Space-Borne Radar System
In this section, a new system for space debris detection and monitoring is introduced. The idea is to fly a receiver at low-altitude, collect, and analyze the radio waves coming from any satellite flying at higher altitudes and broadcasting toward the Earth. Such a system can be defined and operated as a PBR. In fact, PBRs are radar systems composed of only the receiver, which exploits RF energy transmitted by other noncooperative systems (generally a communication system) to perform radar tasks such as target detection, parameter estimation, imaging, and classification. PBRs are an interesting solution in many applications with tight power and weight constrains because they do not need a dedicated transmitter, are low cost, have low-power requirements, lighter payloads, and no dedicated frequency allocation requirement. PBR systems are, therefore, suitable to be installed on low-cost power-limited platforms like cubeSats. One or more cubeSats in LEO would form a low-cost detection system with a sufficient lifetime to collect enough data on the existing debris population but not long enough to increase such a population.
A. Radar Range Equation in Bistatic Configuration
A radar system is considered to be bistatic if there is sufficient separation between the transmitter and receiver antennas such that the angles or ranges to the target are sufficiently different [12]. The angle defined by the positions of transmitter, target, and receiver is known as bistatic angle,
\begin{equation}
\text{SNR} = \frac{P_t G_t G_r \sigma \lambda ^2 L_s}{(4\pi)^3 R_t^2 R_r^2}\frac{1}{P_n} \tag{1}
\end{equation}
\begin{equation}
P_n = k T_0 B_r F \tag{2}
\end{equation}
In this paper, the FS configuration is proposed to guarantee better performance in terms of SNR in the case of a specific class of targets of interest.
B. Forward Scattering Configuration
FS occurs when
Two diffraction types are possible: Fraunhofer diffraction and Fresnel diffraction. In the former case, the target is electromagnetically far from both the transmitter and receiver, while in the latter case, the target is close to one of the two. Considering the following coefficients:
\begin{align}
&F_t = \frac{a^2}{R_t \lambda } &F_r = \frac{a^2}{R_r \lambda } \tag{3}
\end{align}
\begin{align}
&F_t<<1 &F_r<<1. \tag{4}
\end{align}
\begin{equation}
\sigma _{\rm FS} = \frac{4\pi A^2}{\lambda ^2} = G_{\rm FS} A \tag{5}
\end{equation}
C. Proposed Configuration
As illustrated in Fig. 2, the sensing platform comprises essentially three principal components: a software defined radio (SDR) as a PBR receiver, a low noise amplifier (LNA), and one or more antennas. The LNA is introduced to enhance the sensing capability by increasing the receiver gain.
Any satellite transmitting radio waves toward the Earth within the frequency band of the antenna on the sensing platform represents a suitable illuminator. The source of RF illumination can be selected statically or dynamically among the available platforms (e.g., existing constellations such as Iridium, GNSS, HY2A). One of the main features considered in this work for the illuminator selection, is the satellite altitude. In fact, the RF source has to fly at higher orbits with respect to the cubeSat, such that the FS region between transmitter and receiver can be exploited for the detection of space debris. By using the FS configuration, an object can be detected by measuring the variation in received power. When there is no object along the Line of sight (LOS) between transmitter and receiver, the received power is almost constant in time. When an object approaches the LOS, the FS field starts to shadow the receiver leading to a loss of received power. The proposed system configuration is described in Fig. 3.
The peak FS RCS is reached when the target crosses the LOS and it is given by (5). This peak value can be used as a signature for the detectability of an object. Note, however, that even in the case in which the bistatic angle never reachesOne of the critical drawbacks of FS radar is that this system does not allow one to estimate directly the target range. Nevertheless, the absence of range resolution is compensated by the advantage of absence of signal fluctuation because of the target's natural swinging, which represents a limit for coherent signal processing time in conventional radar. Furthermore, the FS radar allows power budget improvements as it allows for long integration intervals.
Notice that, in order to obtain the maximum benefit from a long coherent processing interval, the received signal must have a zero frequency offset with respect to the matched filter. By using a PBR on a cubeSat, the Doppler offset can be very small in case of transmitter, receiver, and target move along similar directions. Moreover, the attenuation and delays introduced into received signal by the atmosphere (e.g., by troposphere) are avoided.
In case the signal transmitted by the illuminator is known (e.g., GNSS), a way to achieve a good performance from a such passive system is to create a replica of the expected scattered signal from the debris for the receiving system, assuming a preliminary knowledge of system kinematic. However, since the Doppler effect that affects the received signal result from the relative movement of transmitter, receiver, and target (which can be about thousands of metres per second in the worst case of opposite fly directions), it is not guaranteed to yield a constant Doppler offset during the acquisition time interval. For this reason, a bank of matched filters could also be used, in case of small deviations from the expected Doppler, assuming linear variation [4].
An alternative approach is proposed in [6], where a multistep processing strategy is described for reducing the computational cost. First, the received signal is correlated with a replica of the expected signal over a relative short integration period. The latter is taken short enough such that the phase error between the received signal and the replica is approximately constant. Through I&D operations, complex observations of the beat signal between the replica and the actual indirect arrival are obtained. Finally, the full length coherent integration is obtained by adjusting the phase of the samples of I&D operations and summing over the observation period. This second step is robust against phase errors that are inconsistent over the observation period. This approach, which has been demonstrated in case of GNSS signals, can be potentially adapted for decoding other weak signals as well [6].
Another possible solution is the crystal video detector (CVD). The CVD consist into widely used detection scheme, based on the square law detector, followed by mean level cancellation and matched filter. Ustalli et al. in [16] present a full characterization of the performance of the CVD for a FS radar in presence of a moving target onto linear trajectory against Additive White Gaussian Noise. Specifically, it is shown that the CVD has limited losses with respect to the ideal detector, when the target is in far field. For this reason, this kind of detector can be used for the proposed system for monitoring a specific set of orbits at suitable distance from the cubeSat's orbits and the selected illuminator's ones.
Detection Capability Analysis
In this section, the detection capabilities of the proposed radar system are evaluated. Before extracting the desired radar information, the SNR is generally increased by processing the received signal, e.g., matched filtering. Specifically, the signal processing gain,
\begin{equation}
\overline{\text{SNR}} = \frac{P_t G_t G_r \sigma \lambda ^2 L_s}{(4\pi)^3 R_t^2 R_r^2 k T_0 B_r F} \sqrt{N} G_{sp}. \tag{6}
\end{equation}
A. Integration Time
The integration time is defined as the time interval needed to transmit and receive the integrated pulses to perform the radar detection. For a FS PBR, the maximum possible integration time is the interval during which the target is approximately along the LOS between the transmitter and the receiver.
The maximum integration time for the proposed system depends on the orbits of transmitter, receiver, and space target and on both transmitter and receiver antenna's pointing and patterns. In this subsection, we analze the maximum and minimum possible integration times assuming different orbit geometries. For simplicity, only circular orbits are considered. Furthermore, the bore sight of the transmitter is expected to be aligned with the nadir direction and the bore sight of the receiver antenna is aligned with the zenith direction.
Let us consider that at
Considering the three orbit radii
\begin{align*}
&{\boldsymbol {p}}_{rx}(t) = d_{rx} \left[ \begin{array}{c}\cos (\omega _{rx} t) \\
\sin (\omega _{rx} t) \\
0 \end{array} \right]\\
&{\boldsymbol {p}}_{st}(t) = d_{st} \left[ \begin{array}{c}\cos (\omega _{st} t)\\
\sin (\omega _{st} t)\cos (\alpha _{st})\\
\sin (\omega _{st} t)\sin (\alpha _{st}) \end{array} \right]\\
&{\boldsymbol {p}}_{tx}(t) = d_{tx} \left[ \begin{array}{c}\cos (\omega _{tx} t)\\
\sin (\omega _{tx} t)\cos (\alpha _{tx})\\
\sin (\omega _{tx} t)\sin (\alpha _{tx}) \end{array} \right]
\end{align*}
The angular velocity
\begin{equation}
\omega = \omega (d) = \sqrt{\frac{\mu }{d^3}} \tag{7}
\end{equation}
\begin{align}
l_1(t) &= \Vert {\boldsymbol {p}}_{tx}(t) - {\boldsymbol {p}}_{rx}(t) \Vert \tag{8}\\
l_2(t) &= \Vert {\boldsymbol {p}}_{tx}(t) - {\boldsymbol {p}}_{st}(t) \Vert \tag{9}\\
l_3(t) &= \Vert {\boldsymbol {p}}_{st}(t) - {\boldsymbol {p}}_{rx}(t) \Vert . \tag{10}
\end{align}
\begin{equation}
\beta (t) = \cos ^{-1}\left(\frac{l_2^2(t) - l_1^2(t) + l_3^2(t)}{2l_2(t)l_3(t)}\right). \tag{11}
\end{equation}
Representation of the bistatic angle
It is highlighted that since the Earth has not a perfect spherical shape, the transmitter and the receiver at different altitudes experience different precession of the line of the nodes [18]. Therefore, the orbits of transmitter, target, and receiver cannot remain coplanar, and the illuminator (the transmitter) needs to be selected dynamically to allow higher integration times.
B. Figure of Merit
The key performance indicator for the proposed PBR system is the minimum detectable target's size. From (6), the RCS can be written as a function of the system parameters and SNR as follows:
\begin{equation}
\sigma = \frac{(4\pi)^3 R_t^2 R_r^2 k T_0 B_r F}{P_t G_t G_r \lambda ^2 L_s}\frac{\overline{\text{SNR}}}{ \sqrt{N} G_{sp}}. \tag{12}
\end{equation}
From (12), it is noted that the RCS is a function of the target's altitude. In particular,
\begin{align}
\sigma _{\rm min} \propto R_t^2 R_r^2 &= f(\rho _{st}|\rho _{rx},\rho _{tx}) \nonumber\\
&= (\rho _{st} - \rho _{rx})^2(\rho _{tx}- \rho _{st})^2 \tag{13}
\end{align}
\begin{equation}
\overline{\rho _{st}} = \frac{\rho _{rx} + \rho _{tx}}{2}. \tag{14}
\end{equation}
From (5), it follows that, for a FS system, the minimum target silhouette's area
\begin{align}
\bar{A} &= \sqrt{\frac{\lambda ^2\sigma _{\rm min}}{4\pi }}\nonumber\\
&= \frac{4\pi R_t R_r}{\lambda }\sqrt{\frac{k T_o B_r F \,\,\widehat{\text{SNR}}}{P_t G_t G_r G_{sp} L_s \sqrt{N}}} \tag{15}
\end{align}
C. Observation Zone of Interest
From the current distribution of space objects in Fig. 5, one can see that the peak density in LEO is at an altitude of around 800 km.
Spatial density of objects in LEO, according to the 2011 NASA report to the United Nations Office for Outer Space Affairs [19].
Given the high density of objects in this orbit regime, without loss of generality, in this paper, we will consider targets flying in that region.
D. Selection of the Illuminators
The choice of the illuminators is driven by a number of parameters that concur to increase the SNR. For the design of the proposed system, the key selection criteria are the EIRP of the RF sources, their distance from the target and receiver, the carrier frequency (or wavelength), the system bandwidth, which determines the power of noise at the receiver, and the modulation scheme used by the source, which determines the signal processing gain and gain of the integration time.
In this paper, a set of two illuminators is considered for the analysis of performance. The first is the Haiyang-2A (HY2A), which is a second generation satellite series for ocean monitoring approved by the China National Space Administration, Beijing [21]. The satellite has been placed at an altitude of 971 km, on a near sun-synchronous frozen orbit, with an inclination of
The second set of illuminators is the global star (GS) constellation. GS is a LEO satellite constellation dedicated to satellite phone and low-speed data communications. Specifically, the system broadcasts with a C-to-S band transponder and receives with an L-to-C band transponder, respectively. The GS payloads have been placed at an altitude of about 1400 km, with an orbit inclination of about
The GS Canada mobile-satellite network primary modulation and multiplexing method is Code-Division Multiple Access. The system operates in four distinct frequency bands [22], which are as follows.
The forward or down-link service from satellite to user terminal operates in a band of 16.5 MHz between
MHz and\text{2483.5} MHz where there are 13 frequency-division multiplexed channels, each 1.23 MHz wide.\text{2500} The return or up-link service from user terminal to satellite operates in the band between 1610 MHz and 1626.5 MHz.
The forward feeder link from feeder-link earth station to satellite occupies the band from 5091 MHz to 5250 MHz where there are eight channels 16.5 MHz wide in right-hand circular polarization and additional eight channels 16.5 MHz wide transmitted in LHCP.
The return feeder link from satellite to feeder-link earth station occupies the band
MHz with 16 frequency-division multiplexed RF channels, each one 16.5 MHz wide and associated with a separate antenna-pattern beam in the\text{6875}-\text{7055} MHz band.\text{1610}-\text{1626.5}
For the system proposed, in this paper, the 16.5 MHz wide downlink, from satellite to user, in
E. Numerical Results
For the numerical simulations, in this paper, we will consider a cubeSat equipped with a SDR with a noise figure of
\begin{equation}
G_r = \frac{4\pi \eta _p A_p}{\lambda ^2} = \eta _e\left(\frac{\pi D}{\lambda }\right)^2 \tag{16}
\end{equation}
Fig. 6 show the minimum silhouette's area of detectable object as a function of the integration time, for Ku-band and C-band transmitted chirp signals from a HY2A satellite to cubeSats at different altitudes. Specifically, the receiver is placed at 300 km, 400 km, 500 km, and 600 km of altitude with the target at 800 km.
Minimum silhouette's area of detectable target. (a) Ku-band. (b) C-band transmitted signal from a HY2A satellite to cubeSats at different altitudes.
Fig. 7(a) and (b) show the minimum silhouette's area of detectable object as a function of the integration time for a C-band and S-band transmitted signal from a GS satellite to cubeSats at different altitudes.
Minimum silhouette's area of detectable target. (a) S-band. (b) C-band transmitted signals from a GS satellite as a function of cubeSat's altitude and integration time.
In the GS case, which involves continuous transmission, sequential segments of 10 ms are incoherently integrated such that
From Figs. 6(b) and 7(a), it is apparent the HYA2 illuminator allows for the detection of smaller targets, compared to the GS illuminator, since the latter is at higher altitude and transmits with a lower EIRP.
A measure of maximum integration time is obtained evaluating the duration of time interval during which the configuration of radar system is such that the bistatic angle is around
Example of bistatic angle variation from the instant of alignment of transmitter, receiver, and target for different values of couple
All the results can be reproduced using the methods and the information provided in the paper.
Conclusion
In this paper, a feasibility study of a new space-based passive radar system for SSA was described. The proposed system comprises of a PBR deployed on a cubeSat, equipped with a SDR, and a passive antenna to perform radar task for space surveillance. The analysis of performance showed that the proposed system can represent a low-budget solution for the detection even of very small space objects with sizes of few centimetres. One of the most important aspect is that the relative shorter distances between transmitter, target, and space-based receiver with respect to a ground-based receiver guarantees higher SNR for the radar tasks. Moreover, the performance of the proposed system is not affected by atmospheric absorption due to the system geometry. For the same reason, the system functionality is independent of weather conditions and interference factor represented by flying man-made vehicles or bird flock.
The paper demonstrated that, with integration times shorter than 10 s and an appropriate choice of the illuminator, the system can detect objects with section areas as small as 50 cm2 with a cubeSat positioned at 300 km and as small as 20 cm2 if the cubeSat is at 600 km. Arguably, at the altitude of the space station or above the injection of cubeSats can potentially cause additional problems. Nonetheless, at the altitudes, considered in this paper, the expected lifetime of the receiver is such to limit the risk to increase the debris population. The capabilities of the system can be further improved by integrating signals from several illuminators. To this aim, wide-band antennas and suitable receiver filters have to be considered in order to recover all the received channels. Since the system capabilities depend on the distance between transmitter and receiver, the use of LEO emitters at higher orbits as illuminator of opportunity is most suitable for achieving better detection performance. The expected increase in LEO emitters, such as OneWeb, could represent an important factor for improving the performance of such a system. The proposed system may be used for a primary detection and identification of sensitive targets. FS radar has been used with success in literature for target discrimination based on Doppler analysis of echoes. Therefore, it is possible to classify targets by considering their microDoppler signature as a result of micromotions exhibited while orbiting.
Moreover, it is possible to use several cubeSat receivers working together in order to perform target localization and ranging. All this is the subject of a current investigation and will appear in future publications.