Passive 3D interferometric ISAR using target‐borne illuminator of opportunity

IET Radar, Sonar & NavigationVolume 13, Issue 2 p. 190-197 Special Section: Passive High Resolution and Imaging RadarFree Access Passive 3D interferometric ISAR using target-borne illuminator of opportunity Elisa Giusti, Corresponding Author Elisa Giusti elisa.giusti@cnit.it RaSS (Radar and Surveillance System) Laboratory, CNIT, Galleria Gerace, Pisa, ItalySearch for more papers by this authorMarco Martorella, Marco Martorella orcid.org/0000-0002-8985-5069 RaSS (Radar and Surveillance System) Laboratory, CNIT, Galleria Gerace, Pisa, Italy Department of Information Engineering, Universita degli Studi di Pisa, Via Caruso 16, Pisa, ItalySearch for more papers by this author Elisa Giusti, Corresponding Author Elisa Giusti elisa.giusti@cnit.it RaSS (Radar and Surveillance System) Laboratory, CNIT, Galleria Gerace, Pisa, ItalySearch for more papers by this authorMarco Martorella, Marco Martorella orcid.org/0000-0002-8985-5069 RaSS (Radar and Surveillance System) Laboratory, CNIT, Galleria Gerace, Pisa, Italy Department of Information Engineering, Universita degli Studi di Pisa, Via Caruso 16, Pisa, ItalySearch for more papers by this author First published: 28 January 2019 https://doi.org/10.1049/iet-rsn.2018.5162Citations: 4AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract This study proposes a new idea for forming three-dimensional (3D) passive inverse synthetic aperture radar (ISAR) images. Two main innovations are presented, the first that is related to the use of a dual interferometer and the second that considers the illuminator of opportunity (IO) located on the target to be imaged. A theoretical approach was proposed in a previous study that demonstrated passive ISAR imaging with a target-borne IO in the 2D domain. In the present study, such approach is extended to a full 3D case. A complete theoretical derivation is proposed for the formation of point-like 3D ISAR images when using target-borne IOs. Simulations are used to produce some examples. Practical issues and limitations are also discussed. 1 Introduction Passive radar is an advancing technology that is gaining ground, thanks to its advantageous features with respect to active radars, in particular, the ability to perform radar functions without transmitting electromagnetic signals, enabling, therefore, covert operations as well being a green technology. Although passive radar does not always perform at the same level of scattering mechanism must be formulated active radar, it is able to implement almost all radar functionalities that are typically available with active systems [1]. One of such is the ability to form radar images. Passive ISAR imaging has been proven feasible provided that enough bandwidth and integration time are available for ISAR images to be formed with a reasonable resolution [2-4]. Such ISAR images, though they do not produce similar results as dedicated active radar systems, are valuable for coarse classification purposes. Passive bistatic radar (PBR) imaging at low frequencies may also provide the means for imaging low-observable targets, due to the inherent bistatic configuration and to the possibility to use low-frequency emissions. Illuminators of opportunity that are typically chosen to enable passive radar are broadcast radio and TV transmitters, which have a large equivalent isotropically radiated power, and therefore provide wide coverage [2, 5-9]. Nevertheless, several other types of illuminators of opportunity have been used in a number of passive radar applications such as mobile phone communications [10] and wireless fidelity [11] among others. As such, illuminator of opportunities (IOs) are typically installed on land and often only in populated areas. This constraint makes passive radar viable only closely to IOs installation points, which limits passive radar applications, especially when it comes to open sea and deserted area surveillance. To overcome this issue, space-borne IOs have been considered such as satellite digital TV broadcast [12], global positioning system/global navigation satellite system [13, 14], space-borne SAR systems [15] etc., which offer continental scale coverage. Despite the great effort made in this direction, due to power limitation, the range coverage of passive radar based on space-borne illuminators still remains very limited. A recent paper investigated the possibility of forming ISAR images when the IO is on the target itself [16]. This could be the case of a target that uses communication systems, jammers or even its own radar. With the transmitter in the same place as the target, the power budget becomes very favourable and, as far as such signals can be detected, an image of the target could be formed. Passive ISAR imaging with target-borne IOs may become then a complement to electronic warfare systems as they would provide extra information that may be used to identify the target based on its shape and size. In this geometry, the bistatic angles relative to a scatterer may be small or large enough to enable both the back-scattering or forward-scattering, respectively [17, 18]. In this particular application, an algorithm that applies independently of the scattering mechanism must be formulated, as in [16]. In [16], the theoretical means to form ISAR images using target-borne IOs have been provided. However, the application of the proposed scheme was limited to the planar case [two-dimensional (2D) geometry]. The transmitter proximity to the scatterers is the reason for the non-linear relationship between the range–Doppler (RD) and the range/cross-range coordinates. This non-linearity affects the interpretation of a 2D ISAR image as it is no longer interpretable as a planar projection. To make such images interpretable, 3D reconstruction must be enabled. In this paper, 3D passive radar image formation is dealt with by introducing a dual interferometric system, which allows for orthogonal dual baseline interferometric phases to be exploited in conjunction with more traditional 2D passive radar imaging for extracting target scatterers and positioning them in a 3D space. It must be mentioned that a similar concept has been proposed and demonstrated by the same authors for monostatic and bistatic active radar systems [19-21]. 3D ISAR images that are obtained by combining interferometry and ISAR imaging, namely 3D indium ISAR (InISAR), appear as a cloud of points that are distributed in a 3D space. Such a cloud of points carries both geometrical and radiometric information of a region of the target that reflects enough energy toward the radar. Such information allows for geometrical (e.g. the target size as those of the smallest parallelepiped that contains the cloud of points) and radiometric features (e.g. the estimated single or fully polarimetric radar cross section (RCS) of each scatterer) to be easily extracted from a target that can be used to classify or even recognise it [22, 23]. Two important facts must be pointed out when comparing 3D target reconstructions to 2D ISAR images. This first is related to the amount of information that can be extracted from a 3D ISAR image when compared with the 2D case such as 3D target sizing (L×W×H), or more, in general, 3D geometrical features, e.g. ship masts, superstructure etc. The second fact concerns an important and very performance-limiting problem that afflicts 2D ISAR imaging when it comes to image interpretation and feature extraction. Specifically, 2D ISAR images are the result of a target projection onto the image projection plane. Such a projection is neither controllable nor known a priori leading to a very hard image interpretation problem. It is sufficient to think of a simple case, where a ship can be projected from the top, side or front. Each of these cases is completely different from the others and poses the problem of having huge databases, where for each target, several templates must be obtained to allow for any potential projection to be matched to a database element for the target to be recognised correctly. This paper is organised as follows. Section 2 introduces the passive ISAR geometry and signal model. The 2D RD passive radar image formation is then presented in Section 3. Section 4 details the scatterers extraction method, whereas the 3D passive ISAR image reconstruction technique is dealt with in Section 5. Section 6 defines the implementation steps that are necessary for implementing 3D reconstruction with a dual interferometric passive radar system and also suggests methods to implement the 'direct signal separation' step. Section 7 shows some simulation results. Conclusion is finally drawn in Section 8. 2 Received signal model Let the geometry of an interferometric ISAR system be as represented in Fig. 1 [20]. The receiver is composed of an 'L'-shaped antenna formed by three receiving elements located in a plane perpendicular to the line of sight (LoS) of the central element (C), and and are the two orthogonal baselines forming the 'L' shape. Fig. 1Open in figure viewerPowerPoint System and target geometry Let and be the target rotation vector and the effective target rotation vector, respectively. is the component of that is responsible for the synthetic aperture formation and it is obtained by projecting onto the plane orthogonal to the LoS. Mathematically, this can be obtained by using equation below: (1) Let be a reference system that is fixed on the target such that is aligned with and with the LoS at the central time instant (t = 0) within the coherent processing interval (CPI). Let be another reference system that is rotated with respect to of an angle , which is the angle identifying the target effective rotation vector orientation with respect to a reference system that is fixed on the radar receiver. According to this geometry, the receiver coordinates can be written with respect to the reference system as follows: (2) where is the target–receiver distance at the central time instant, which is going to be assumed equal to . Therefore, the LoS unit vectors can be derived as follows: (3) , and are the distance between the target and the radar over time, the distance between the pth receiver (where ) and the kth scatterer over time, and the distance between the transmitter and the kth scatterer, respectively. It should be noted that is independent of either time or the receiver's position. The angle is the angle identifying the orientation of in the plane orthogonal to the radar LoS, namely . The signal transmitted by the IO can be modelled as follows: (4) where is the transmitted signal, is a complex amplitude and is the one way delay-time measured between the centre of the reference system from the central antenna, as shown in Fig. 1. The generic component reflected toward the pth receiver by a scatterer can be written as follows: (5) where is the complex amplitude related to the kth scatterer and . The signal received by the pth receiver can be written as follows: (6) From now on, we will assume that the direct signal, namely , is known and available at the receiver. Discussion on methods that can be used to estimate it and extracted from the received signal will be found in Section 6. By following the 'batches' algorithm [24] idea, both the received signal and the reference signal are divided into batches of fixed time length, as depicted in Fig. 2 and specified in the equation below: (7) where (8) (9) and corresponds to the maximum non-ambiguous range. Fig. 2Open in figure viewerPowerPoint Graphical representation of the batches algorithm approach Then, the cross-correlation is performed at each batch between and . The result can be written as follows: (10) where is the batch index, is the number of batches such that , and are the observation time and the time length of a batch, is the fast time variable, is the auto-correlation function of the transmitted signal centred at , as defined in the equation below: (11) and is defined as in the equation below: (12) By Fourier transforming along t, the spectrum of , , can be derived, as follows: (13) where is the Fourier transform of the transmitted signal within the nth batch, (such an assumption is similar to the 'stop & go' for SAR systems), and (14) In far-field condition (which now applies to the receivers), the 'straight-iso-range' approximation holds, then can be defined as (15) and therefore (16) can be rewritten as follows: (16) By observing (16), it can be noted that the radial motion compensation is not needed as it is embedded in the RD map formation. In fact, the term associated with the target's radial motion, which is typical in all the cases where the IO is not on the target itself, is not present in the signal model after the received signal is matched filtered. 3 2D ISAR image reconstruction By assuming a constant target rotation vector during the CPI, and following the results in [20], (13) can be approximated as follows: (17) where and (18) where is the slow-time variable, measures the distance between the scatterer and the radar at a time instant and measures how the scatterer radial distance varies over the slow-time variable. can be expressed as a function of the scatterer coordinates and as follows: (19) More details on how and are derived can be found in [20]. A 2D ISAR image can be obtained at the receiver by applying a 2D Fourier transform to (17), thus obtaining (20) where , and . When (it corresponds to the transmitter location), both and equal 0. When the baselines, and , are small if compared with the target–receiver distance, , the RD coordinates in the argument of the sinc functions can be approximated as follows: (21) (22) where and are the cross-range and range coordinates of the kth scatterer and is the scatterer radial velocity with respect to the C receiver. The radial velocity of a scatterer with respect to the central channel can be derived as follows: (23) This assumption does not apply for the phase term in (5) (24) As can be noted, the complex ISAR images are the composition of complex 2D sinc functions centred on the scatterer coordinates in the RD map. The phases of each sinc function depend on the path of the echo to go from the transmitter to the scatterer and then to a receiver. Then, it is worth remarking that when the 2D ISAR images are co-registered and the baselines are small if compared with the target–radar distance, the RD coordinates of the scatterers do not vary among the receivers. This is because the path differences are small if compared with the RD resolutions. This assumption does not apply to the phase term since the path differences are not negligible with respect to the wavelength . 4 Scatterer extraction Equation (24) shows that a 2D ISAR image is obtained at each receiver. The scattering centre extraction is a fundamental step as it allows the formation of 3D point clouds starting from a number of 2D point clouds. As pointed out in [20], a 'continuous' 3D target reconstruction, i.e. a pixel-by-pixel approach, would not be effective as the interferometric phase information can be considered accurate enough only for bright scatterers, where the signal-to-noise ratio (SNR) and the signal-to-clutter ratio are sufficiently high. The scatterer extraction algorithm adopted here is the multichannel CLEAN algorithm [20]. Such an algorithm aims at extracting the scatterers RD coordinates as well as their complex amplitude. Such features will be used to recover the scatterer 3D Cartesian coordinates in a fully spatial coordinate system. As expressed in (17), the matched-filtered signal (implemented in this framework through a cross-correlation) in the frequency/slow-time domain can be modelled as the product of two terms, the former depending on the slow-time variable and the latter depending on the frequency only. The two terms depend on unknown parameters that the algorithms aim at estimating, namely the Doppler frequency, the time delay and the complex amplitude of each scatterer. The estimation of these unknown parameters allows for the scatterer point spread function (PSF) to be estimated and then removed from the ISAR images at each iteration and for each receiving channel. The Monte Carlo (MC)-CLEAN algorithm works iteratively by: locating the brightest scatterer in one of the receiving channels and finding its coordinates. Such coordinates are used as initial estimates of the RD coordinates of the scatterer; the scatterer unknown parameters, namely the range, Doppler coordinates and complex amplitude, are jointly estimated following an optimisation approach. The optimisation approach is based on the minimisation of the residual energy, namely the energy after the scatterer cancellation from the RD map. This step is applied to each receiving channel separately; scatterer PSF cancellation. Once the scatterer parameters have estimated the scatterer PSF is also estimated for each receiving channel and then removed from the ISAR images; and steps 1–3 are then repeated until a stop condition is reached. The algorithm stops when the residual energy in the ISAR image at the hth iteration is lower than a preset threshold. Such a threshold is typically set to a percentage of the initial energy but it can also be set according to noise and clutter signal statistics, as detailed in [25]. More details about how to implement the multichannel CLEAN technique can be found in [20]. 5 3D target model reconstruction The use of only the RD estimates extracted from the amplitude of the 2D ISAR images are not sufficient to recover the scatterer position in the reference system. In fact, the range coordinate depends on [see (21)] which corresponds to the scatterer Euclidean distance with respect to the centre of the reference system, namely . To estimate the 3D scatterer coordinates, we need to use also the phase of the ISAR images, and specifically the interferometric phases, defined as follows: (25) The phase terms in (25) are a measure of the difference between the distance between the target and the AV and AH receivers with respect to that of the target and the AC receiver. The interferometric phases can be rewritten by using (3) and (15) and by noting that is the same for all the three receivers. Therefore, following the derivation for the monostatic case as suggested in [20], we obtain: (26) The scatterer's cross-range, , and height, , can be derived by manipulating (26), as follows: (27) Equations (21) and (22) can be inverted to obtain the RD coordinates as a function of the geometrical and dynamical parameters, as follows: (28) (29) The effective target rotation vector can be estimated by combining (28) and the first equation in (27) as follows: (30) Equation (30) can be rewritten as follows: (31) where , , , and . Equation (31) represents the equation of a 2D regression plane, where , and are measured for each kth scatterer, and a and b have to be estimated. The two unknowns, namely a and b, can be estimated via a least square error, where the function to be minimised is expressed in (32). Further details can be found in [20] (32) 6 Target-borne IO passive 3D processing block scheme Fig. 3 shows the functional block scheme of the proposed processing. Fig. 3Open in figure viewerPowerPoint Functional block scheme of the proposed processing The first step that must be performed is the 'direct signal separation', which aims at isolating the direct signal, namely , from the received signal, . This is a necessary step to implement a matched filter, and therefore to produce an RD map. Details about such a task are out of the scope of this paper, which focuses instead on the development and analysis of the imaging algorithm. However, some indications about methods that can be used to recover the direct signal from the surveillance signal are produced below that may direct the reader to other sources in the literature that address this specific problem. To identify the techniques that may be used for the estimation of the reference signal, it is first necessary to spend some words on typical ship-borne IOs. Ship-borne IO may be of different types and can be sketchily categorised as follows: Tactical communication: Link-16 is a radio communications system, designed to meet the most stringent requirements of modem combat – providing reliable situational awareness for fast-moving forces. It works at L-band and employs a set of frequencies within this band by implementing frequency hopping and direct sequence techniques. It operates in an omnidirectional broadcast mode. Communications: Many antennas system covering high-frequency (HF), very/ultra-HF (V/U-HF) and X/Ku/Ka bands are typically used for ship-to-air and ship-to-ship communications. Their operative bandwidth and beamwidth change according to the frequency band in which they operate. Communication systems at HF and V/U-HF are typically designed to operate in an omnidirectional broadcast mode. Conversely, communication systems at X/Ku/Ka typically used for satellite communications have directive beams (few degrees). Signals transmitted at HF or V/U-HF are typically narrow-band signals. Conversely, communications at higher frequencies make use of wide-band signal (of the order of hundreds of MHz) that make passive radar imaging more effective. Active electronically scanned array (AESA) system: AESA systems are typically installed on the main mast of modern naval fleets to implement scalable multifunction radio-frequency systems. Such systems are able to perform different tasks at the same time (as, for example, detection and tracking) by transmitting different radar waveforms at the same time in different antenna beams. Such radar waveforms have typically large enough instantaneous bandwidth. Jammer: Military ship is equipped with electronic suppression system designed to intercept emissions from airborne and ship-borne radars and to provide jamming in threat directions, also simultaneously. To be efficient, a jammer should transmit high power, wide bandwidth and possibly constant power spectral density jamming signals. Moreover, it should be able to work on a wide range of frequencies. These are all attractive features for a system employing the technique proposed in this paper. IO can be divided into digital transmitters and analogue ones. Modern digital IOs transmit orthogonal frequency division multiplexing (OFDM)-based signals. When a digital IO is installed and used by moving targets, the direct signal separation can be performed by decoding the transmitted symbols and remodulating the signal, thus generating a synthetic version of the transmitted signal at the receiver [7, 26]. In case of moving platforms, the channel temporal variation must be taken into account when decoding the transmitted symbols, as proposed in [27] for OFDM signals. In the case of analogue signals, the direct signal separation is not straightforward but it can be implemented by means of algorithms that are typically used in PBR systems to clean the reference signal when it is affected by multipath. Analogue signals are typically constant power waveform since they are frequency/phase-modulated signal. Under such a hypothesis, the constant modulus algorithm (CMA) algorithm can be used to estimate the direct signal from the surveillance one [28, 29]. When a single antenna element is used at the receiver, the CMA algorithm acts as an finite impulse response (FIR) filter with L taps in the temporal domain. The algorithm estimates the weight taps that better suppress the additive interference signal from the received one. In this framework, the additive interference is the contributions from all the scatterers which compose the target. CMA can also be implemented in the case of multichannel systems by exploiting spatial diversity. Such an implementation is even more effective than the time-only approach. More details can be found in [7], Chapter 17. Another way to estimate the direct signal may be found among those used by the electronic measurement support (ESM) receivers to identify the transmitted waveform. Such techniques are applied to both digital or analogue signals. Recently proposed algorithms based on the time–frequency analysis are able to identify the transmitted signal waveform and its phase/frequency modulation [30, 31]. Once the direct signal is extracted from the received signal, an ISAR image can be formed by applying the cross-ambiguity function batch algorithm. As demonstrated in Section 2, the target radial motion compensation step, namely, the autofocusing step, is embedded in the RD map reconstruction. Therefore, an RD map is inherently also a perfectly focused ISAR image of the target in the RD domain. After having formed a 2D ISAR image at each receiving channel, the dominant scatterers are extracted as well as their delay-time and Doppler coordinates, namely , and their interferometric phases, and . This set of values is then used to estimate and by minimising (32) and to estimate the scatterer coordinates, namely by using (29) and (27). As a final remark on the practical implementation of the proposed technique, it can be said that passive radar imaging that exploits target-borne IO may become an add-on capability of ESM receivers. ESM receivers have had a great boost of growth due to the development of software define radars. Modern ESM systems are able to not only detect transmitters and estimates parameters such as direction of arrival, time of arrival, pulse repetition interval (PRI), pulse duration etc. but also to identify the pulse modulation. Recent papers have proposed methods based on time–frequency and ambiguity function analysis to identify the phase modulation used among P1, P2, P3, P4 and Frank codes [30, 31]. Such papers concentrate on low probability of intercept radars but the same algorithms can be applied to other radar systems and all types of modulations. If the sensed waveform is correctly recognised and its modulation parameters correctly estimated the proposed techniques can be used to estimate information on the target carrying the transmitter that may help in recognising it. 7 Simulation results This section illustrates results obtained by processing simulated data. The main simulation parameters are summarised in Table 1. The radar receiver is an L-shape array composed of three receiving antennas as depicted in Fig. 1. The target is a point-like target that resembles a ship and that moves with respect to the receiver along the -axis and with motion parameters that are shown in Table 1. The point-like target is also depicted in Fig. 4 for the sake of clarity. For each receiving channel, the signal at the output of the cross-correlator in the frequency/slow-time domain has been simulated as in (13). Table 1. Simulation parameters Parameter Value roll pitch yaw v 30 m/s 6000 m B 300 MHz 1 m 1 m Fig. 4Open in figure viewerPowerPoint 3D view, top view and side view of the point-like target The algorithm performance has been tested in terms of visual inspection by comparing the target model and the reconstructed target model and also by evaluating the normalised root-mean-square error (NRMSE) for both the modulus and the angle of the target effective rotation vector as in (33) and (34). In fact, the accuracy with which such a rotation vector is estimated is a strong indication of the ability of this algorithm to also correctly estimate the position of the extracted scattering centre in the 3D spatial domain. The NRMSEs are defined in (33) and (34) for the magnitude and orientation, respectively. It is worth reminding the reader that a single angle is sufficient to represent the orientation of the effective rotation vector as this is confined to lie on the 2D plane that is orthogonal to the receiver LoS. The angle is in fact defined in that same 2D plane (33) (34) where and are the true values of the magnitude and angle of the target effective rotation vector. For the sake of completeness, the orientation of is taken with respect to the (vertical) direction. After the direct signal separation, the ISAR images at the three receiving antennae are obtained by means of the cross-correlation between the received signal and the direct signal (matched filter operation). The 2D ISAR images in the RD domain at each receiving channel are shown in Fig. 5. Fig. 5Open in figure viewerPowerPoint ISAR images in the RD domain obtained the three receiving channels, (top) AV, (centre) AC and (bottom) AH As can be noted by looking at the three images, each RD ISAR image appears to be geometrically distorted in this domain. This is because the range coordinate depends on both the cross-range and height coordinates, as found in (29). Therefore, to completely restore the scatterer coordinates we have to estimate the coordinates and and then decouple them from . To estimate the scatterer 3D coordina