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ISSN : 2093-5587(Print)
ISSN : 2093-1409(Online)
Journal of Astronomy and Space Sciences Vol.34 No.4 pp.303-313
DOI : https://doi.org/10.5140/JASS.2017.34.4.303

# Performance Analysis of Sensor Systems for Space Situational Awareness

Eun-Jung Choi1, Sungki Cho1, Jung Hyun Jo1,2, Jang-Hyun Park1, Taejin Chung3, Jaewoo Park3, Hocheol Jeon3, Ami Yun3, Yonghui Lee3
1Korea Astronomy and Space Science Institute, Daejeon 34055, Korea
2Korea University of Science and Technology, Daejeon 34133, Korea
3Radar&Space Co., Ltd., Daejeon 34016, Korea
Corresponding Author +82-42-865-3275, eunjung@kasi.re.kr
20171021 20171122 20171124

## Abstract

With increased human activity in space, the risk of re-entry and collision between space objects is constantly increasing. Hence, the need for space situational awareness (SSA) programs has been acknowledged by many experienced space agencies. Optical and radar sensors, which enable the surveillance and tracking of space objects, are the most important technical components of SSA systems. In particular, combinations of radar systems and optical sensor networks play an outstanding role in SSA programs. At present, Korea operates the optical wide field patrol network (OWL-Net), the only optical system for tracking space objects. However, due to their dependence on weather conditions and observation time, it is not reasonable to use optical systems alone for SSA initiatives, as they have limited operational availability. Therefore, the strategies for developing radar systems should be considered for an efficient SSA system using currently available technology. The purpose of this paper is to analyze the performance of a radar system in detecting and tracking space objects. With the radar system investigated, the minimum sensitivity is defined as detection of a 1-m2 radar cross section (RCS) at an altitude of 2,000 km, with operating frequencies in the L, S, C, X or Ku-band. The results of power budget analysis showed that the maximum detection range of 2,000 km, which includes the low earth orbit (LEO) environment, can be achieved with a transmission power of 900 kW, transmit and receive antenna gains of 40 dB and 43 dB, respectively, a pulse width of 2 ms, and a signal processing gain of 13.3 dB, at a frequency of 1.3 GHz. We defined the key parameters of the radar following a performance analysis of the system. This research can thus provide guidelines for the conceptual design of radar systems for national SSA initiatives.

## 1.INTRODUCTION

The need to develop technology for space situational awareness (SSA) initiatives is on the rise, to protect people and assets from space hazards. The main purpose of an SSA system is the surveillance and tracking of space objects that are likely to re-enter the Earth’s atmosphere, or collide with satellites and space debris. In particular, obtaining knowledge of the position and orbits of space objects is one of the most important aspects of SSA (Donath et al. 2010; Kalden & Bodemann 2011; Kennewell & Vo 2013). In recent years, surveillance systems based on radar have provided more comprehensive information regarding space objects under observation, compared to that obtained by optical systems. Radar systems have high detection probabilities for objects in low earth orbit (LEO) by two way distance due to the active illumination they perform using electromagnetic radio waves. In addition, radar systems are advantageous as they can be operated independent of meteorological and daytime conditions. Hence, radar systems configured for SSA are required for the assessment of the general condition of space objects, and to perform risk assessments for reentering space objects.

In Korea, the development of SSA systems has been considered, according to the preparedness plan for space hazards (Choi et al. 2014; Choi et al. 2015a, 2015b). At present, the optical wide-field patrol network (OWL-Net), with five optical telescopes in different locations around the world, is the only infrastructure for Korean SSA programs (Park et al. 2015; Lee et al. 2017). However, due to the dependence of this network on weather conditions and observation time, it is not reasonable to use optical systems alone for SSA activities, as they have limited operational availability (Bae et al. 2016). The development of radar systems should thus be considered, to create an efficient SSA system with currently-available technology. Accordingly, the National Space Situational Awareness Organization (NSSAO) initiated a conceptual study of the operation of a space objects observation system using the existing optical system, and the radar system necessary for efficient operation. A preliminary study considering the development of efficient SSA radar systems is being conducted by the NSSAO. The work summarized in this paper was conducted as part of this study, to analyze the performance of radar systems in detecting and tracking space objects in LEO. This paper presents a comparative study of several reference radar parameters for various frequencies, as well as design of the power budget, by means of simulation. These results provide the basis for development of future SSA radar systems.

## 2.SPACE SITUATIONAL AWARERNESS SYSTEM

The purpose of an SSA system is to observe, analyze, and predict the location of natural and man-made objects in orbit around the Earth. Fig. 1 illustrates a schematic block diagram of the typical architecture of an SSA system (Bobrinsky & Del Monte 2010; Kalden & Bodemann 2011). The overall SSA system comprises sensors, database, and user interface. The core of this system is the database of trackable space objects, which must be updated continuously. The data is based on observations from ground-based and space-based sensors, and information from external sources from international cooperation networks. Table 1 provides a summary of representative sensors, available currently, which are capable of performing SSA tasks.

In addition to ground-based radars, optical systems are essential contributors to the SSA mission. The ground-based electro-optical deep space surveillance (GEODSS) system plays a vital role in tracking space objects, particularly those in deep space. The Air Force Maui Optical Station (AMOS) is a state-of-the-art electro-optical facility for detecting and tracking orbital debris. AMOS includes a 1.6-meter telescope, and a 3.67-meter advanced electro-optical system (AEOS) telescope with an adaptive optics (AO) system. This system can perform surface characterization and identification of space objects (Africano et al. 2004).

Space-based optical telescopes provide a number of advantages over ground-based systems, primarily, the absence of interference from weather and atmosphere, and the mitigation of limitations relating to the time of day, and are increasingly being considered as an important component of SSA systems. The space-based surveillance system (SBSS) program is a planned constellation of satellites for tracking space objects in orbit, and accomplishing space situational awareness for future space control operations. This satellite system, with space-based visible (SBV) sensors, will operate constantly (24 hours a day, 7 days a week).

### 3.1.Operational Scenario

Radar systems for use in SSA initiatives are required to be able to detect space objects up to a height of 2,000 km, because, as shown in Fig. 3, approximately 78 % of trackable space objects are distributed in this region. The maximum range required to observe objects at this height is a function of the maximum elevation of the system (Ender et al. 2011; Liebschwager et al. 2013; Eilers et al. 2016). Fig. 4 illustrates how the maximum range of the radar affects the observable altitude. The requisite operational range of the radar system is determined from the desired range of elevation angles, and the maximum orbit altitude.

In general, the position of an orbiting object can be represented using a topocentric coordinate system, with the angles defined as right ascension (α) and declination (δ). With optical systems, the vector representing the observed data is given, without range, ρ, and range rate, $ρ ˙$, as $A opt = ( α , δ , α ˙ , δ ˙ )$, where the ̇ operator indicates a rate of change. In contrast, with radar systems, the vector representing the observed data is given as $A rad = ( α , δ , ρ , ρ ˙ )$. To determine orbital parameters, the observed data must be represented as $X = ( α , δ , α ˙ , δ ˙ , ρ , ρ ˙ )$. At observer position vector q, the Cartesian position vector of an orbital object is $r = q + ρ ρ ^$, where $ρ ^$ is a unit vector. Therefore, orbital elements can be calculated from the Cartesian state vectors, using the orbit algorithms shown in Fig. 5.

Three different utilization modes can be defined for SSA radar, depending on the operation scenario. In ‘Staring mode’ all objects passing through the antenna beam width, with the antenna position fixed to a certain azimuth and elevation angle, are detected. In ‘Search mode’, all space objects passing through the sensor’s FoV during scanning can be detected. If some objects of interest are identified during search mode, ‘Track mode’ is activated, where the radar beam focuses on designated objects by continuously controlling the antenna direction. More accurate position and angle data can be obtained for tracked objects using this mode. Fig. 6 depicts a flow diagram illustrating control and selection of the radar operation scenario. We define parameters controlling the observability of space objects, including pulse width (PW), pulse repetition frequency (PRF), and modulation bandwidth (Mod. BW) as well as parameters for signal processing. This conceptual scenario can lead to efficient operation of SSA radar systems.

In general, there are two types of radar configuration: monostatic and bistatic configurations. In the monostatic configuration the transmitter and receiver are situated in the same location, whereas in the bistatic configuration, they are situated in different locations, separated by a considerable distance. To estimate radar performance in terms of the maximum range, we consider the detection probability and beam extension in different frequency bands, for a given target position. As we used the radar range equation to estimate the maximum theoretical detection range for a particular target, it is fundamental to determining radar performance (Patyuchenko et al. 2011).

The performance of a radar system can be estimated using the simplified radar range equation for a monostatic pulsed radar (Skolnik 1980). For such configurations, the received power, Pr, is expressed as,(1)

$P r = p t G t G r λ 2 ( 4 π ) 2 L S ( | F | 4 L p ) σ R 4 G p ,$
(1)

where Pt is the peak power of the transmitter, Gt is the gain of the transmitting antenna, Gr is the gain of the receiving antenna, λ is the wavelength of the radio wave, σ is the radar cross section (RCS), Ls is the loss factor of the total system, and Lp is the propagation loss due to the absorption of the electromagnetic wave by O2 and H2O molecules in the atmosphere, which is dependent on the radar frequency. |F|4 is the propagation factor, where $F = | E → E → 0 |$, which is the ratio of the actual magnitude of the electric field to the magnitude of the electric field in free space, R is the radar range to the target, and Gp is the gain from signal processing, which is usually implemented in the form of a pulse integration technique.

The noise power, Pn, is expressed as,(2)

$P n = k T s B n$
(2)

where k is Boltzmann’s constant (1.38 × 10−23 J/K), Ts is the noise temperature of the system, which is usually defined as Ts = T0F, where T0 is 290 K and F is the noise factor of the receiver, and Bn is the receiver’s noise bandwidth. The noise figure of the receiver, NF, is expressed in dB unit as NF = 10 log10(F). It should be noted that the noise factor, F, is different from the propagation factor, |F|.

The signal-to-noise ratio is defined as,(3)

$SNR = P r P n .$
(3)

The radar constant, K, can be determined by the parameters of the hardware subsystem of the radar system as follows:(4)

$K = p t G t G r λ 2 ( 4 π ) 2 P n L s .$
(4)

From the radar range equation, the SNR can be expressed in terms of K as follows:(5)

$SNR = K σ R 4 G p .$
(5)

Alternatively, the maximum radar range, Rmax, can be expressed as,(6)

$R max = K σ SNR min G p , 4$
(6)

where SNRmin is the minimum SNR.

The maximum detection range can thus be computed as a function of RCS. RCS is dependent on the radar frequency and the size of the target, which is usually modeled as a conductive sphere with radius, r. For space surveillance and tracking radar systems, the NASA size estimation model (SEM), which is based on the results of measurements performed in the 2.4 GHz–18 GHz frequency range (encompassing the S, C, X, and Ku bands), is typically used for calculation of the RCS. The RCS of a sphere is calculated differently in three scattering regions: Rayleigh, Mie, and optical. NASA SEM curves are calculated as follows (Stokely et al. 2006):(7a)(7b)(7c)

$x = 4 z π , for z > 5 , optical region$
(7a)

$x = 4 z 9 π 5 6 , for z > 5 , optical region$
(7b)

(7c)

where x = d/λ, d is the diameter of the object, and z = σ/λ2. In the Mie resonance region, the smooth function, g(z), can be expressed using curve fitting.

### 3.3.Reference Performance Analysis

In this paper, to analyze the performance of the radar system, we defined detection of a target with a diameter of 1 m at a distance of 2,000 km, as the benchmark sensitivity. Key radar reference parameters for all frequency bands considered are shown in Table 2. Atmospheric attenuation was assumed to be constant above the troposphere. The values of atmospheric attenuation are 1.2 dB, 1.5 dB, 1.7 dB, 2.4 dB, and 5.5 dB at 1.3 GHz, 3.0 GHz, 5.5 GHz, 10 GHz, and 16.7 GHz, respectively (Mahafza & Elsherbeni 2003). We defined the signal to noise ratio of a single pulse, SNR1, using a 1-m2 RCS at a range of 1,000 km.

For phased-array antennas with an element spacing of λ/2, the antenna gain and 3-dB beamwidth can be estimated using the following formulas (Skolnik 1980):(8)(9)

$G ≈ π N η$
(8)

$θ 3dB ≈ 100 N ,$
(9)

where the units of θ3dB are in degrees, N is the number of elements, and η is antenna efficiency.

When η = 0.65 and N = 5,000, the antenna gain is 40 dBi, with a beamwidth of 1.4°. A peak transmit power of 100 kW can be obtained with a single element power, P0, of 20 W, since Pt = N × P0.

The probability of detection, Pd, can be calculated in terms of SNR1 and the probability of false alarm, Pfa. The approximate relation between these parameters is (Mahafza & Elsherbeni 2003):(10)

$P d = 0.5 ⋅ erfc( − ln ( P fa ) - SNR + 0.5$
(10)

The requisite SNR for Pd = 80 % when Pfa = 10−6, is 12.6 dB.

Fig. 7shows the results of simulations using the reference radar parameters. From this figure, we can observe the frequency dependence of detection ability for the same set of parameters. Although the detection range decreases with frequency, radar systems operating at higher frequencies have some advantages, such as the reduced dimensions of the hardware, and detection of smaller target sizes in some applications, due to the shorter wavelength.

Table 3 summarizes the reference radar performance at different frequencies. A higher transmit power and antenna gain is necessary when increasing the frequency. However, as increases in power and antenna gain are challenging problems in the relevant frequency bands, some technical compromises must be made.

### 3.4.Power Budget Design

The power budget was designed based on the reference performance analysis, by taking into account practical radar components. Although we considered the L-band frequency in this paper, the same method can be applied for radar systems operating at other frequencies. We assume a phasedarray radar system, which has many advantages compared to conventional radars with large parabolic antennas. These systems allow the surveillance of large angular sectors in a short amount of time, and can detect and track numerous targets simultaneously, offering multi-functional operation. It has been suggested that continuous surveillance of LEO can only be guaranteed using high performance groundbased phased-array systems (Ender et al. 2011).

An example of a power budget design is summarized in Table 4. While Gt was fixed to 40 dB, P0 was increased from 20 W to 100 W, delivering a total peak power of 500 kW. The receive antenna, with the increased gain, is usually separated from the transmit antenna, for bistatic or pseudo-monostatic operation. The signal processing techniques used in radar systems are also very important. The most commonly used method is pulse integration, which can be coherent or noncoherent. In space surveillance radars, 16 or 64 pulses are typically used for non-coherent integration, which gives processing gains of 9.5 dB and 13.3 dB, respectively (Mahafza & Elsherbeni 2003). The average transmit power, Pav, is calculated as Pav = Pt × τ × PRF, where PRF is the pulse repletion frequency and τ is the pulse width. Hence, a longer pulse width yields a higher average power. We included an additional SNR margin of 10 dB, to account for unmodeled losses. As incrementing individual parameters may be accompanied by high costs, a tradeoff analysis of cost and performance is needed.

The results of simulations are shown in Fig. 8. As can be seen in this figure, the maximum range of 2,000 km can be achieved for a target size of 1 m2 with a transmit power of 900 kW. The detection capabilities of the radar system, in terms of range and target diameter, can be estimated easily, using Table 5. For example, for a range of 1,000 km and a target diameter of 50 cm, the SNR is 27.3 dB when Pt = 500 kW. As the SNR is greater than the detection threshold of 22.6 dB (blue dotted line in Fig. 8), the target size can be detected at 1,000 km for the given radar parameters. Doubling the detection range reduces the SNR by 12 dB, since SNR is inversely proportional to the fourth power of the range.

An SNR contour map with respect to range and RCS is shown in Fig. 9. The range extends from 200 km to 2,000 km, with 5 km intervals, and RCS is plotted from −27.07 dBsm to 4.97 dBsm, corresponding to object diameters of 5 cm to 2 m, which are separated by 5 cm intervals. The radar parameters are, Pt = 900 kW, Gt = 40 dBi, Gr = 43 dBi, and pw = 2 ms, at a frequency of 1.3 GHz. The processing gain, Gp, was set to 13.3 dB. Since the detection threshold, including the 10 dB margin, was calculated to be 22. 6 dB, the detection region is to the right of the 20-dB SNR contour line. This map can thus easily illustrate radar performance in terms of range and the size of the space object or RCS.

## 4.CONCLUSION

The behavior of a radar system for detecting and tracking space objects was simulated, to analyze its detection capability in terms of frequency, transmit power, and target size (measured in diameter). Two principal types of system are available with current radar technology: systems with mechanically steered reflector antennas, and phased-array antennas. Continuous space situational awareness can be guaranteed using a high-performance ground-based phased-array radar system with electronic beam-steering, enabling tracking of multiple space objects simultaneously. In general, a higher transmitted power and antenna gain results in the detection of smaller space objects, and a longer detection range. This demonstrates that the detection performance of a radar system is heavily dependent on hardware. Therefore, for an efficient SSA system using current technology, a relevant strategy that takes cost and performance into consideration is needed.

We applied non-coherent pulse integration as a simple radar signal processing technique, during simulation. The results of power budget analysis showed that the maximum detection range of 2,000 km could be achieved with a transmit power of 900 kW, transmit and receive antenna gains of 40 dB and 43 dB, respectively, a 2-millisecond pulse width, and a signal processing gain of 13.3 dB, at a frequency of 1.3 GHz. The SNR required for an 80 % probability of detection with a false alarm rate 10−6, was assumed to be 12.6 dB. An additional SNR margin of 10 dB was included, to account for unmodeled losses. In order to further improve the SNR, coherent signal processing techniques, such as pulse compression, constant false alarm rate (CFAR) detectors, and other advanced algorithms, will be necessary in the base band, which usually require complex systems, and incur higher costs. The key parameters of the radar system were designed through a performance analysis and tradeoff study. We also showed that phased-array radar systems are the most suitable technology for detecting and tracking space objects in combination with OWL-Net. These results will be expected to be used for the conceptual design of SSA radar system. In particular, the analysis of the detection capabilities of the radar can provide guidelines for the development of radar systems for SSA programs.

## ACKNOWLEDGMENTS

This study was supported by the Korea Astronomy and Space Science Institute (KASI) with the research project of “Development of Space Situational Awareness Technology”.

## Figure

Block diagram of the typical architecture of a space situational awareness (SSA) system.

Primary SSA ground sensors and operations centers for the U.S. Space Surveillance Network.

Distribution of space objects with respect to orbital altitudes in the LEO region.

Zenith passage of a space object at an altitude of 500 km above ground. The object flies along an arc of 4,930 km in 650 seconds, modifying the radar range required for constant detection (Ender et al. 2011).

Combined measurement and data processing flow for optical and radar systems.

Control flow diagram for different radar operation scenarios.

Reference radar performance: (a) single pulse signal to noise ratio (SNR1) vs. range, (b) altitude vs. radar cross section (RCS) for various frequencies, when SNR1 = 1 dB (Pt = 100 kW, Gt = Gr = 40 dBi).

SNR with respect to range for a target diameter of 1 m, for varying transmit powers (the red and blue dotted lines indicate 12.6 dB and 22.6 dB, respectively).

SNR contour map with respect to range and RCS (range step: 5 km, RCS step: 5 cm), with Pt = 900 kW, Gt = 40 dBi, Gr = 43 dBi, pw = 2 ms, f = 1.3 GHz, and non-coherent integration with 64 pulses.

## Table

Overview of global space situational awareness sensors

Note 1: Antenna beam elevation is assumed to be 75°.
Note 2: Additional SNR is required to detect target RCS of 1 m2 at 2,000 km with threshold SNR of 12.6 dB.

Power budget design for an L-band radar with the following detection requirements: RCS = 1 m2, range = 2,000 km, and SNR = 12.6 dB

SNR versus target diameter and transmit power at 1,000 km (f = 1.3 GHz, Gt = 40 dB, Gr = 43 dB, Gp = 13.3 dB, τ = 2 ms)

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