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Sector imaging radar for enhanced vision
Aerospace Science and Technology 7 (2003) 147–158 www.elsevier.com/locate/aescte
Sector imaging radar for enhanced vision Vorwärtssicht-Radar für erweitertes Blickfeld Gerhard Krieger ∗ , Josef Mittermayer, Stefan Buckreuss, Michael Wendler, Thomas Sutor, Franz Witte, Alberto Moreira Institut für Hochfrequenztechnik und Radarsysteme, Deutsches Zentrum für Luft- und Raumfahrt (DLR) e.V., P.O. Box 1116, 82230 Wessling, Germany Received 28 January 2002; received in revised form 12 August 2002; accepted 2 September 2002
Abstract SIREV (Sector Imaging Radar for Enhanced Vision) is an innovative airborne radar system which can supply high-quality images in any desired direction under almost every weather condition. In contrast to synthetic aperture radar (SAR) systems, no relative motion between sensor and targets is required in SIREV. The high frame repetition frequency in SIREV allows to detect even very rapid changes in the imaged scenes. Besides providing a map of the earth’s surface, the complex-valued radar images can be further processed to supply additional information about the topography and objects in the field of view. A fast processing algorithm has been developed for SIREV which allows a very accurate, phase preserving and efficient image formation. A prototype of a forward-looking SIREV system has been built up at the German Aerospace Center and raw data were obtained by a first demonstration flight using a helicopter as a moving platform. Motion errors of the platform could be extracted from the range compressed raw data avoiding the need of an inertial navigation system. The data processing results show good agreement with the theory. After image formation, coherent and incoherent image averaging processes have been applied to improve the image quality. The evaluation of the computational effort shows that a real-time hardware realization can be carried out using off-the-shelf digital components. 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. Zusammenfassung SIREV (Sector Imaging Radar for Enhanced Vision) ist ein innovatives Radarsystem, das auch bei schlechten Witterungsbedingungen eine hochauflösende Abbildung der Umgebung ermöglicht. Im Gegensatz zu einem Radar mit synthetischer Apertur wird in SIREV keine Relativbewegung zwischen dem Sensor und dem abzubildenden Zielgebiet benötigt. Die hohe Bildwiederholfrequenz ermöglicht die Aufzeichnung von schnellen dynamischen Veränderungen in der abgebildeten Szene. Zur phasentreuen Verarbeitung und Fokussierung der Rohdaten wird ein effizienter Prozessierungsalgorithmus vorgestellt. Neben einer Abbildung der Erdoberfläche können die komplexwertigen Radarbilder weiterverarbeitet werden, um beispielsweise zusätzliche Informationen über Topographie oder andere spezifische Objekteigenschaften zu gewinnen. Ein Funktionsmodell für SIREV wurde am Deutschen Zentrum für Luft- und Raumfahrt aufgebaut und erste Testflüge mit einem Hubschrauber durchgeführt. Hierbei kann auf ein kostenintensives Trägheitsnavigationssystem verzichtet werden, da Bewegungsfehler aus den aufgezeichneten Rohdaten extrahiert werden. Die erzielte Auflösung von Punktzielen zeigt eine gute Übereinstimmung mit der Theorie. Zur Rauschunterdrückung werden kohärente und inkohärente Mittelungsverfahren eingesetzt. Aufgrund seiner Systemarchitektur eignet sich SIREV besonders zur kostengünstigen Realisierung eines Radarsystems mit Vorwärtssicht, das beispielsweise zur Hindernisvermeidung und als Landehilfe in der Luftfahrt eingesetzt werden kann. 2002 Éditions scientifiques et médicales Elsevier SAS. Alle Rechte vorbehalten. Keywords: Forward-looking radar; Enhanced vision; Near field digital beamforming; Synthetic aperture radar Schlüsselwörter: Vorwärtssicht-Radar; Erweitertes Blickfeld; Nahfeld-Antennendiagramm-Synthese; Radar mit synthetischer Apertur
* Corresponding author.
E-mail address: [email protected] (G. Krieger). 1270-9638/02/$ – see front matter 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. doi:10.1016/S1270-9638(02)01189-6
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1. Introduction Adverse weather conditions affect both flight safety and the operational area of airborne platforms. This problem becomes most evident during take-off, landing and taxiing, but reliable collision warning in airspace gains also increasing importance. In all these cases it would be highly desirable to provide the pilot with visual information about the surrounding environment independent of weather and daylight. An imaging sensor for enhanced vision will also substantially increase the situation awareness of the crew without the necessity to recourse to an external electronic guidance system. Imaging radar systems, like synthetic aperture radar (SAR, [4,6,17,22]), have proved as a valuable tool in many applications where weather independent imaging is required, but, inherent to the underlying principle, these systems suffer from a visualization gap with respect to the forward looking direction [6,17]. In order to fill this blind spot a new real aperture array radar called Sector Imaging Radar for Enhanced Vision (SIREV) has been developed at the German Aerospace Center [3,11,20]. This innovative system has the potential to supply high quality radar images of a sector in front of the aircraft as shown in Fig. 1. In principle, it is possible to scan the complete sector in Fig. 1 sequentially by using a mechanically steered antenna with a narrow pencil beam. Since such an antenna has to be very large for high resolution imaging, it will become bulky and the necessary mechanics will be very complicated. This drawback may be avoided by electronically steered arrays which allow for inertia-free beamsteering and thereby substantially facilitate the integration into the aircraft. A common technique to form a narrow pencil beam in the desired direction is analog beamforming where the signals from (and to) the antenna elements are phase-shifted, weighted and summed (e.g. by an active phased array with T/R modules).
Fig. 1. SIREV is an innovative radar system which has the capability to provide high quality images of a sector in front of an aircraft independent of the weather conditions. Since SAR or Squint SAR systems have no azimuth resolution in flight direction their operational area is restricted to applications where boresight vision is sufficient.
The required phase-shifts are usually determined by the farfield approximation where the wavefront at the antenna array is regarded as planar. A common criterion for the applicability of this approximation is that the maximum phase error across the antenna array should not exceed π/8 , which re2 /λ where sults in a minimum focusing distance rmin 2dant dant is the antenna length and λ the wavelength [1]. For an antenna length of 3 m the minimum distance rmin is 581 m in X-Band (λ = 3.1 cm), 2118 m in Ka-Band (λ = 0.85 cm), and 5625 m in W-Band (λ = 0.32 cm). These values exclude conventional analog beamforming techniques from high-resolution mapping of close image sectors as required for aircraft landing and taxiing. An alternative to analog beamforming is digital beamforming [2,19,21] where the recorded raw data signals are separately digitized for each element. The focusing is then performed in a special purpose digital processor. Since the total information available at the antenna aperture is preserved in digital beamforming, it is possible to apply rangedependent phase functions which allows a focusing of the recorded signal array to different ranges (cf. Section 3). Further potentials of such an (a posteriori) digital beamforming are antenna self-calibration and element pattern correction (cf. Section 5.1), simultaneous high-resolution imaging of a large field of view, ambiguity reduction by an adaptive weighting of the sensor signals, the efficient compensation of array element failures, and the suppression of interferences by pattern nulling (see also [19]). In principle, digital beamforming is applicable both on transmit and receive, and the antenna array may be arranged and operated in many different ways (see also [8,18]). One example is the sequential switching of a linear array, where the individual antenna elements transmit and record the radar signals in successive order [24]. Since the recorded data in such a system closely resemble the raw data of a monostatic SAR, both near-field and far-field image formation may be achieved by a coherent processing with standard SAR processing algorithms [4,6,17]. Alternatively, the radar echoes for each of the sequentially transmitted pulses may be recorded simultaneously by all array elements which will improve the performance of the system due to the increased receptive antenna area. In this case, a hybrid of digital beamforming techniques [12,13,21,23] and conventional SAR focusing algorithms has to be developed in order to take full advantage of the potentials hidden in the recorded raw data. The disadvantage of the operational modes mentioned above is that a T/R module (or at least a T/R switch) is required for each array element which increases the complexity and costs of the necessary hardware. A more cost-efficient realization may be achieved by using a bistatic configuration with a dedicated transmit antenna illuminating the complete SIREV sector of Fig. 1 and recording the backscattered signals with a passive receive-only array of antenna elements. The drawback of such a bistatic configuration with one single transmit antenna is, that it achieves only half of the image resolution as compared to the
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monostatic case. In principle, it is also possible to combine the advantages of the monostatic and bistatic configurations by using a small number of dedicated transmit antennas in conjunction with the full receiving array. The bistatic configuration can again be operated in either a simultaneous or a sequential reception mode. The simultaneous recording allows for a very high image repetition frequency, which may be used, for example, to detect very fast moving objects, or, as outlined in Section 5.3, to coherently integrate across several image frames. In the latter case, the signal-to-noise ratio is expected to be comparable to active phased arrays since the loss in antenna transmit gain due to the broad illumination is compensated by the gain resulting from the coherent image combination. This is due to the fact that the higher allowed PRF by simultaneous reception compensates for the gain decrease of the transmitting antenna. Taking into account the low efficiency of current T/R modules and the possibility to increase the sensitivity of receiveonly array antennas (e.g. by direct integration of MMICs into the antenna), the imaging performance of SIREV may even become superior to that of an active phased-array radar. The disadvantages of the simultaneous reception mode are the large data rate as well as the required receive modules and analog-to-digital converters for each antenna element. The hardware and processing requirements may be minimized by a serial sampling of the received wavefronts, which is easily achieved by sequentially switching the array elements of the passive receive-only antenna. It is evident, that such an approach will enable a very cost-efficient implementation of a
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forward-looking radar, which is especially attractive for the mapping of sectors in the near field where the SNR requirements are less critical.
2. SIREV geometry and data acquisition The current SIREV system consists of one transmit antenna and a linear array of receiving patch elements as shown in Fig. 2. The receive antennas are centered around the across-track position y = 0 at height z = h, while the transmit antenna is at position x = 0, y = 0 and z = h − zoffset . The direction parallel to the receiving array is termed azimuth and the direction orthogonal to azimuth in forward direction, slantwise to the ground, is denoted as slant range. Correspondingly, the direction of the x-axis is termed ground range. For a point target at ground range position xp and azimuth position yp the transmit and receive paths RTX and RRX of the radar signal are given by RTX = = RRX = =
Fig. 2. Basic SIREV geometry.
xp2 + yp2 + (h − zoffset )2 2 rp2 + yp2 + zoffset − 2 · h · zoffset ,
xp2 + (yp − yi )2 + h2 rp2 + (yp − yi )2 ,
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wherefor convenience the point target slant range position rp = xp2 + h2 has been introduced. The variables yi denote the positions of the receiving antenna elements. Using the definitions for the signal transmit and receive paths, the SIREV signal modulation of a point target at position rp and yp can be written as RTX + RRX 2 s(yi , τ ; yp , rp ) = C exp j πke τ − c0 2π × exp −j (RTX + RRX ) λ where τ denotes the range time, c0 is the velocity of light, and λ is the wavelength. The first exponential term describes the linear frequency modulation of a range chirp with modulation rate ke = Br /τp , chirp bandwidth Br , and pulse duration τp . The azimuth modulation is given by the second exponential term. The contributions from the pulse envelope and the antenna weighting have been omitted in this equation since the phase functions are more important for the development of the processing algorithms.
3. SIREV processing 3.1. Spatial domain focusing In general, the focusing of the SIREV raw data may be achieved by a space-variant 2-D correlation +∞ Na u(y, r) = h(yi , τ ; y, r)s(yi , τ ) dτ i=1 0
where s(yi , τ ) is the unfocused raw data signal recorded by the Na antenna elements and u(y, r) is the processed complex image expressed in terms of azimuth y and slant range r. According to the matched filter concept [5], the space-variant 2-D kernel h(yi , τ ; y, r) is given by the complex conjugate of the predicted response of an ideal point scatterer located at (y, r), i.e., h(yi , τ ; y, r) = s ∗ (yi , τ ; y, r). While such a 2-D focusing approach maximizes the signalto-noise ratio under the reasonable assumption of secondorder white background noise, it is also most expensive from a computational point of view, since a two-dimensional integration has to be performed for each pixel of the final image. A computationally more efficient focusing algorithm may be derived, if the received raw data signals are first compressed in range by a 1-D convolution: Tp urc (yi , r) = 0
2r hr (τ )s yi , − τ dτ . c0
Here, hr (τ ) is the time-reversed complex conjugate of the transmitted chirp of duration Tp . The range compressed signal is denoted by urc (yi , r). Since the convolution in this equation is time-invariant, it may efficiently be implemented in the frequency domain by taking advantage of the Fast Fourier Transform (FFT). After range compression, the response of a point scatterer located at (yp , rp ) may well be approximated by a set of δ-impulses at r(yi ; yp, rp ) = RTX (yp , rp ) + RRX (yi ; yp , rp ). Thus, azimuth beamforming is achieved by the 1-D space variant correlation: u(y, r) =
Na
ha (yi ; y, r)urc yi , r(yi ; y, r)
(1)
i=1
where the kernel ha is given by 2π 2 ha (yi ; y, r) = exp j r 2 + y 2 + zoffset − 2hzoffset λ + r 2 + (yi − y)2 . In this approach, the inseparable and shift-variant 2-D correlation has been approximated by two 1-D correlations, resulting in a considerably reduced computational effort. Note that application of Eq. (1) may require an interpolation in range in order to extract the correct values from the range compressed array urc . Such an interpolation can be neglected for ‘narrow-band systems’ with small range migration (i.e. Br dant c0 · 2 · sin(θmax ) 1) like the SIREV functional model of Section 5. For a large number of antenna elements, the efficiency may be further increased by an appropriate adaptation of the Extended Chirp Scaling Algorithm [14,16], which is introduced in the next section. 3.2. Extended chirp scaling algorithm for SIREV An efficient processing algorithm for SIREV has been derived from a reformulation of the Extended Chirp Scaling (ECS) algorithm for ScanSAR [14–16]. Algorithms for ScanSAR focusing may be adapted to the processing of SIREV raw data due to the similarity of a ScanSAR raw data burst with the recorded data from the limited number of receiving antennas in SIREV. The block diagram of the modified ECS algorithm is shown in Fig. 3. The derivation of the ECS for SIREV is based on the following assumptions: • The azimuth modulation is only caused by the variation of the receiving path. This means half of the azimuth phase variation in SIREV compared to ScanSAR. • For SIREV a scanning velocity is defined by the product of receiving element spacing and pulse repetition frequency, which is used in the ECS processing like a platform velocity. • The range cell migration in SIREV has been approximated by the range cell migration of ScanSAR. This assumption is reasonable for an antenna array which is much smaller than the minimum observed range in the imaged scene.
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Fig. 3. Extended Chirp Scaling algorithm for SIREV (for a detailed description see [15]).
In Table 1, the resulting equations of the ECS for SIREV are compared with the ECS for ScanSAR. For a detailed explanation of the equations please refer to [16] and [15]. The table shows in bold style the differences in the equations caused by the halved azimuth phase variation in SIREV. The difference in the azimuth phase causes changes in all equations of the ECS processing, either directly visible in the ECS phase functions H1 to H6 or via the chirp scaling factor a(fa ) and the modified modulation rate keff .
4. Image quality estimation by simulation In order to obtain a reference for the SIREV image data processing and to get a first impression of the SIREV mapping capabilities, a SIREV image simulation has been carried out based on X-Band data from the Experimental SAR system of DLR (E-SAR) [10]. The results of this simulation are shown in Table 2 (see also [15] and [3]). As a main parameter, the wavelength decreases from left to right. From the simulations it becomes
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Table 1 Comparison of equations of the extended chirp scaling algorithm for ScanSAR and SIREV. The differences are shown in bold style Extended chirp scaling for ScanSAR (monostatic) H1 (fa , τ, r0 ) = exp −j · π · keff (fa , rref,cs ) · a(fa )
Chirp scaling
Range compression Range cell migration correction Chirp scaling phase correction
Azimuth scaling
Deramping ta azimuth time keff effective chirp modulation rate λ wavelength τ range time rref,cs reference range for chirp scaling
Extended chirp scaling for SIREV (bi-static) H1 (fa , τ, r0 ) = exp −j · π · keff (fa , rref,cs ) · a(fa )
2 · R(fa , rref,cs ) 2 2 · R(fa , rref,cs ) 2 × τ− × τ− c c
2 2 λ · fa λ · fa β(fa ) = 1 − β(fa ) = 1 − V 2V −1 2 1 4 · r0 · λ (β 2 (fa ) − 1) −1 1 2 · r0 · λ (β (fa ) − 1) keff (fa , r0 ) = − keff (fa , r0 ) = − ke c2 β 3 (fa ) ke c2 β 3 (fa ) r0 r0 R(fa , r0 ) = = r0 · (1 + a(fa )) R(fa , r0 ) = = r0 · (1 + a(fa )) β(fa ) β(fa ) 2 · rref,cs · a(fa ) −j · π · fe2 · exp +j · 2π · · fe H2 (fa , fe , rref,cs ) = exp keff (fa , rref,cs ) · (1 + a(fa )) c 2 2 H3 (fa , r0 ) = exp j · π · keff (fa , rref,cs ) · (1 + a(fa )) · a(fa ) · · (r0 − rref,cs ) c 4π 2π H5 (fa , r0 ) = exp +j · H5 (fa , r0 ) = exp +j · · r0 · (β(fa ) − 1) · r0 · (β(fa ) − 1) λ λ λ · rscl λ · rscl 2 2 × exp j · π · × exp j · π · · f · f a a V2 2V2 2 2 2V V H6 (ta , r0 ) = exp j · π · H6 (ta , r0 ) = exp j · π · · ta2 · ta2 λ · rscl λ · rscl a chirp scaling factor fa azimuth frequency c velocity of light rscl scaling range for azimuth scaling fe range frequency
V platform/scanning velocity r0 slant range distance R range migration in range-Doppler domain
apparent that the image quality will substantially improve for higher carrier frequencies if the antenna length is kept constant. To avoid ambiguities, the number of antenna elements has also to increase as indicated in the table.
reflector as the main scattering element and data from this recording were used for a calibration of the system. The second raw data set was obtained during a flight across the river ‘Lech’. The recording parameters of these two flights are summarized in Table 3.
5. Results from an experimental model
5.1. Raw data analysis
A functional model for SIREV has been built up at the German Aerospace Center [3]. The major goal of this hardware demonstration was to prove the feasibility of the SIREV principle in a short period of time with a minimum amount of effort. To reduce the costs it was preferable to use existing radar hardware even with specifications that were not optimized for this purpose. For example, a sequential switching of the 56 receiving antenna elements was necessary and the experimental model had to be built up in X-Band notwithstanding the poor image resolution to be expected due to the short antenna length of 2.85 m. Details of the radar hardware and the antenna system may be found in [3] and [25]. Fig. 4 illustrates the antenna system and its attachment to the helicopter. In the following, we will report our experimental results from two helicopter flights in the vicinity of Oberpfaffenhofen (Germany). The first scene contained a large corner
To test the integrity of the recorded raw data set we first investigated the response to the large corner reflector. An excerpt of the demodulated complex format raw data is shown in Fig. 5 on the left, where the dominant chirp signals from the corner reflector are easily recognized. From a visual inspection of the raw data an important aspect becomes immediately apparent: the recorded azimuth phases suffer from substantial discontinuities, which manifest themselves as disruptions between the individual range lines. These phase errors, which are mainly caused by the different wiring and radiation properties of the individual antenna elements, are a major concern, since they will substantially degrade the image quality. To quantify the phase errors, we first compressed the received radar signals in range and then extracted the azimuth phase response of the corner reflector (Fig. 5(b) and (c)). In this representation, large phase discontinuities up to ±π become apparent. For comparison,
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Table 2 SIREV image simulations for X-Band (left), Ka-Band (middle) and W-Band (right) X-Band
Ka-Band
W-Band
Wavelength: 0.031 m
Wavelength: 0.0085 m Antenna length: 3.0 m Look angle: 45◦ Chirp bandwidth: 100 MHz Chirp length: 1.5 µs Processed azimuth width: 24◦ Required array elements: 196 (for illuminated sector with 32◦ ) 707 (for illuminated sector with 180◦ ) Valid near range: 396 m Valid far range: 1698 m Range resolution: 2.2 m Azimuth extension near range: 169 m Azimuth resolution near: 1.6 m Azimuth extension far range: 722 m Azimuth resolution far: 6.7 m
Wavelength: 0.0032 m
Required array elements: 55 (for illuminated sector with 32◦ ) 195 (for illuminated sector with 180◦ )
Azimuth resolution near: 6 m Azimuth resolution far: 24 m
the analytically derived azimuth phase function of an ideal point target at azimuth position y0 = 0 m and slant range r0 = 761,5 m is also plotted in this figure using a dashed curve. Improved focusing will be achieved for all recorded frames by multiplying each recorded range line with a complex phasor, which is immediately derived from the difference of the measured azimuth phase and its theoretical prediction. The successful focusing by this method is demonstrated in Fig. 6, where we compare an example of one compressed corner reflector response with the impulse response function of an ideal point target located at y0 = 9,6 m and r0 = 681,8 m. The raw data frame was recorded approx. 3 seconds after the frame from which the phase correction has been derived.
Required array elements: 518 (for illuminated sector with 32◦ ) 1876 (for illuminated sector with 180◦ )
Azimuth resolution near: 0.6 m Azimuth resolution far: 2.5 m
In the phase compensation algorithm introduced above, we have implicitly assumed that all phase errors are both time- and space-invariant. In order to test this hypothesis we have extracted the compressed corner reflector responses for a sequence of 10.000 frames corresponding to a flight period of 37,9 seconds. A visualization of the azimuth profiles of these corner reflector responses is shown in Fig. 7 as a 3-D surface plot. From the temporal sequence of the azimuth profiles in Fig. 7 it becomes apparent, that the focusing is almost independent of both the azimuth angle and the frame number, thus supporting the hypothesis of space- and time-invariant phase errors. However, a closer look into the corner reflector responses revealed some small but systematic space-variant errors, which are presumably due to variations in the phase
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Table 3 Recording parameters
Center frequency Chirp bandwidth Antenna length Number of receive antenna elements PRF (sequential switching) Chirp duration Average helicopter velocity Average helicopter altitude Average ground level
Recorded scene corner river reflector “Lech” 9.5 GHz 100 MHz 2.85 m 56 (equally distributed) 14793 Hz 1.3 µs 1.3 µs 28 m/s 21 m/s 1056 m 927 m 556 m 645 m
Section 3.1, where we apply for each pixel in the output image a different reference function. Since an accurate implementation of this technique requires knowledge of a large number of phase response curves for a densely sampled grid of azimuth and elevation angles, we have restricted the phase error correction to the space-invariant phase shift of the range lines as described before. 5.2. Image processing results Fig. 4. Top: Antenna system attached to the skids of the helicopter. Bottom: RF side of the SIREV antenna with the 56 2 × 2 patch receiving subarrays. A detailed description of antenna hardware may be found in [25].
pattern of the receiving array antenna. In principle, a compensation of these space-variant azimuth phase errors may be incorporated in the correlation algorithms introduced in
In the preceding subsection we have demonstrated that a successful focusing of the recorded SIREV raw data is achieved, if the phase disruptions between the individual range lines are appropriately compensated. Using the phase corrections derived from the corner reflector response, we have also processed the raw data of the flight across the river
Fig. 5. Raw data analysis of the corner reflector response. (a) Excerpt of the recorded raw data in complex format. (b) Magnitude of the range compressed data. (c) Comparison of the measured (solid line) and the simulated (dashed line) azimuth phase response curves for a corner reflector located at an azimuth angle of zero degrees and a slant range distance of 761.5 m.
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Fig. 7. Temporal sequence of corner reflector responses obtained as the helicopter moved forward. The normalised azimuth profile of the focused radar image is shown as a function of azimuth angle and frame number.
Fig. 6. Comparison of the theoretical (top) and measured corner reflector response (bottom).
‘Lech’. An example of an image obtained by the SIREV processing is shown in Fig. 8(a). The displayed image has an extension of 1150 m in slant range. The azimuth extensions are 163 m in near range and 790 m in far range. From the processed image it becomes apparent, that system noise is a major concern. The low SNR was mainly caused by the sequential switching and the low gain of the receiving antenna elements. 5.3. Noise suppression As we have seen in the preceding section, the processed SIREV images suffer from a substantial contamination with noise. To alleviate these deteriorating effects, we took advantage of the high image repetition frequency (fimg = PRF/56 = 264 Hz) by appropriately combining the information of consecutively recorded frames. Most conveniently, this is achieved by a linear summation over several frames. In order to compensate for systematic phase shifts
induced by the helicopter movement, an appropriate phase correction has to be applied prior to complex summation. In our algorithm, which will be explained in detail below, this phase correction is automatically extracted from the image sequence. As an alternative, the necessary phase offsets could be deduced from the motion parameters of the helicopter. The block diagram in Fig. 9 summarizes the algorithm, which consists of three processing steps. The coherent SIREV smoother starts with a set u = {u1 (y, r), . . . , uN (y, r)} of N complex valued images denoted by ui (y, r). From this set phase differences "ϕi (y, r) between successive image pairs are computed using complex multiplication and taking the argument (phase) of the result: "ϕi (y, r) = arg ui (y, r) · u∗i+1 (y, r) . This yields a set of N − 1 phase differences which may be visualized in 2-D space by N − 1 vectors of unit length. An illustration of this processing step is shown within the first block of Fig. 9. Taking advantage of the vector representation of complex numbers, an average phase offset may be computed using 2-D vector summation as illustrated in the second block of Fig. 9. Analytically, this can be written as
N−1 "ϕ(y, r) = arg exp j "ϕi (y, r) , i=1
where "ϕ(y, r) denotes the two-dimensional average phase offset. An example of the spatial phase distribution obtained by this 2-D phase smoothing process is provided in Fig. 8(b), where "ϕ(y, r) has been computed for a set of N = 50 complex images. The average phase offset function "ϕ(y, r) is now used to correct the phase of the individual complex images for possible shifts due to movements of both the transmit and the
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Fig. 8. Results of SIREV processing: (a) Focused image. (b) Average phase offset. (c) Coherent smoothing with N = 50. (d) Hybrid smoothing. N
receive antennas. This can be achieved by multiplying each input image ui (y, r) with a complex phase factor ϕ i (y, r) which is immediately derived from the average phase offset "ϕ(y, r): ϕ i (y, r) = exp −j (i − 1)"ϕ(y, r) .
u(y, r) =
In this equation, a linear motion of both the receiving and the transmitting antennas has been assumed, resulting in an approximately linear decrease of the phase values as the helicopter moves forward. In a final step, the N phase aligned complex images are coherently summed according to the formula
which yields the smoothed image u(y, r). An example of the resulting image obtained by this complex averaging process is shown in Fig. 8(c), where the number of coherently summed images is N = 50. It becomes apparent that the coherent smoothing technique substantially improves both the image contrast and the SNR.
ui (y, r) · ϕ i (y, r)
i=1
=
N
ui (y, r) · exp −j (i − 1)"ϕ(y, r) ,
i=1
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The coherent smoothing process described above may also be combined with an incoherent average, as given by a linear summation of several detected images after coherent summation. The result of this hybrid smoothing technique is shown in Fig. 8(d) for a total of 50 coherently and 50 incoherently averaged images. As can be seen from the last image in Fig. 8 the incoherent summation further reduces the noise at the cost of a slightly impaired image resolution. The deterioration in geometric resolution may be avoided by an appropriate spatially inhomogeneous shift of the individual images which basically compensates for the helicopter movement. This ‘co-registration’ allows also the number of averaged images to be increased, which will further improve the quality of the resulting image. 5.4. Display geometries The images shown in Fig. 8 are represented as a function of azimuth and slant range. More natural from a pilot’s point of view is a representation in ‘optical coordinates’ which may be obtained by an appropriate central perspective projection (Fig. 10, see also [3]). An example for this geometrical image transformation is given in Fig. 11 together with an optical image of the recorded scene.
Fig. 9. Block diagram of coherent SIREV image smoothing procedure.
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6. Conclusion This paper has given a short overview of the data acquisition, modeling and processing of SIREV raw data. The final result of the experimental model was an image sequence animation, composed of several thousands of successive images as in Fig. 8(c), which demonstrates the validity and applicability of the SIREV principle. An excerpt of the movie is accessible on the SIREV Internet homepage [9]. SIREV has a great potential for applications where a radar mapping with short to moderate range distances with a forward looking geometry is required. The image formation is based on a digital beam forming on receive which allows a great flexibility for correcting phase and amplitude errors caused by the radar system or platform induced motion errors. By this, the side-lobes of the impulse response function can efficiently be suppressed even in the case of extremely high phase errors. Additionally, a coherent averaging process can be used to improve the signal-to-noise ratio of the processed images. The SIREV principle can also be combined with the SAR principle for a very high squinted imaging geometry. Although it is not possible to improve the azimuth resolution in the middle of the imaging sector, the Doppler effect can be exploited to improve the resolution in the forward direction by forming a synthetic aperture orthogonal to the SIREV antenna. In this case, several image frames have to be stored and the Doppler history can be used due to the coherent nature of the data acquisition scheme. This resolution improvement assumes, however, that the platform has a forward movement which is not necessarily the case for an imaging with the SIREV principle. A downward looking
Fig. 10. ‘Cyclopean’ projection from ground coordinates to screen coordinates.
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Fig. 11. Comparison of the ‘cyclopean’ SIREV image representation with an optical image. Left: Excerpt of the pilot’s view obtained from the SIREV image shown in Fig. 8(c). Right: Optical image recorded during a separate flight from a slightly different height and viewing angle.
geometry can also be considered in the case of a moving platform [7]. Interferometry or even tomography may be implemented by adding additional transmit antennas or by taking advantage of the forward movement. The same array of receiving antennas as for two-dimensional imaging can be used so that the additional hardware requirements are minimized. In this case, however, an inertial navigation system as well as a precise positioning system like differential GPS is required for accurate height determination. The feasibility of such a system using longer wavelength radar, e.g. for forest biomass estimation, will be investigated in a future work.
Acknowledgements We thank the anonymous reviewer for the valuable comments and hints. The fruitful collaboration with M. Younis, Y. Venot and W. Wiesbeck from the University of Karlsruhe is greatly appreciated. We thank Rolf Scheiber for helpful discussions. The SIREV project has been partially funded by STN Atlas.
References [1] C.A. Balanis, Antenna Theory: Analysis and Design, Wiley, New York, 1997. [2] P. Barton, Digital beam forming for radar, IEE Proc. Pt. F 127 (1980) 266–277. [3] S. Buckreuss, G. Krieger, J. Mittermayer, A. Moreira, R. Scheunemann, T. Sutor, M. Wendler, F. Witte, M. Younis, Y. Venot, W. Wiesbeck, SIREV – Development of a functional model, DLR Forschungsbericht 2000-44, 2000. [4] W.G. Carrara, R.S. Goodman, R.M. Majewski, Spotlight Synthetic Aperture Radar: Signal Processing Algorithms, Artech House, Norwood, MA, 1995. [5] C.E. Cook, M. Bernfeld, Radar Signals, Academic Press, New York, 1967. [6] J.C. Curlander, R.N. McDonough, Synthetic Aperture Radar: Systems and Signal Processing, Wiley, New York, 1991.
[7] C.H. Gierull, Combining the idea of a downward-looking with a forward-looking airborne imaging radar, in: Proc. EUSAR 2000, Munich, 2000, pp. 377–380. [8] R.C. Heimiller, J.E. Belyea, P.G. Tomlinson, Distributed array radar, IEEE Trans. Aerospace Electronic Systems 19 (1983) 831–839. [9] http://www.dlr.de/hr/sirev/home.html. [10] R. Horn, The DLR airborne SAR project E-SAR, in: Proc. IGARSS, 1996, pp. 1624–1628. [11] G. Krieger, J. Mittermayer, M. Wendler, F. Witte, A. Moreira, SIREV – Sector imaging radar for enhanced vision, in: Proc. of the 2nd International Symposium on Image and Signal Processing and Analysis Pula, Croatia, 2001, pp. 377–382. [12] H. Krim, M. Viberg, Two decades of array signal processing research, IEEE Signal Processing Magazine 13 (1996) 67–94. [13] R.E. McIntosh, S.J. Frasier, J.B. Mead, FOPAIR: A focused array imaging radar for ocean remote sensing, IEEE Trans. Geosci. Remote Sensing 33 (1995) 115–124. [14] J. Mittermayer, A. Moreira, O. Loffeld, Spotlight SAR data processing using the frequency scaling algorithm, IEEE Trans. Geosci. Remote Sensing 37 (1999) 2198–2214. [15] J. Mittermayer, M. Wendler, G. Krieger, A. Moreira, T. Sutor, S. Buckreuss, Data processing of an innovative forward looking sar system for enhanced vision, in: Proc. EUSAR 2000, Munich, 2000, pp. 733–736. [16] A. Moreira, J. Mittermayer, R. Scheiber, Extended chirp scaling algorithm for air- and spaceborne SAR data processing in Stripmap and ScanSAR imaging modes, IEEE Trans. Geosci. Remote Sensing 34 (1996) 1123–1136. [17] R.A. Ryerson, Manual of Remote Sensing, Wiley, New York, 1998. [18] B.D. Steinberg, E. Yadin, Distributed airborne array concepts, IEEE Trans. Aerospace Electronic Syst. 18 (1982) 219–227. [19] H. Steyskal, Digital beamforming at Rome laboratory, Microwave J. (1996) 100–126. [20] T. Sutor, F. Witte, A. Moreira, A new sector imaging radar for enhanced vision – SIREV, in: Proc. SPIE, Vol. 3691, 1999, pp. 39– 47. [21] B.D. Van Veen, K.M. Buckley, Beamforming: A versatile approach to spatial filtering, IEEE ASSP Magazine 5 (1988) 4–24. [22] D.R. Wehner, High-Resolution Radar, Artech House, Norwood, MA, 1995. [23] W.D. Wirth, Radar Techniques using Array Antennas, The Institution of Electrical Engineers, London, UK, 2001. [24] F. Witte, Forward looking radar (coherent), Deutsches Patent Nr. 4007612, 1990, US Patent Nr. 5182562, 1993. [25] M. Younis, W. Wiesbeck, Antenna system for a forward looking SAR using digital beamforming on-receive-only, in: Proc. IGARSS 00, Honululu, 2000.
Sector imaging radar for enhanced vision Vorwärtssicht-Radar für erweitertes Blickfeld Gerhard Krieger ∗ , Josef Mittermayer, Stefan Buckreuss, Michael Wendler, Thomas Sutor, Franz Witte, Alberto Moreira Institut für Hochfrequenztechnik und Radarsysteme, Deutsches Zentrum für Luft- und Raumfahrt (DLR) e.V., P.O. Box 1116, 82230 Wessling, Germany Received 28 January 2002; received in revised form 12 August 2002; accepted 2 September 2002
Abstract SIREV (Sector Imaging Radar for Enhanced Vision) is an innovative airborne radar system which can supply high-quality images in any desired direction under almost every weather condition. In contrast to synthetic aperture radar (SAR) systems, no relative motion between sensor and targets is required in SIREV. The high frame repetition frequency in SIREV allows to detect even very rapid changes in the imaged scenes. Besides providing a map of the earth’s surface, the complex-valued radar images can be further processed to supply additional information about the topography and objects in the field of view. A fast processing algorithm has been developed for SIREV which allows a very accurate, phase preserving and efficient image formation. A prototype of a forward-looking SIREV system has been built up at the German Aerospace Center and raw data were obtained by a first demonstration flight using a helicopter as a moving platform. Motion errors of the platform could be extracted from the range compressed raw data avoiding the need of an inertial navigation system. The data processing results show good agreement with the theory. After image formation, coherent and incoherent image averaging processes have been applied to improve the image quality. The evaluation of the computational effort shows that a real-time hardware realization can be carried out using off-the-shelf digital components. 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. Zusammenfassung SIREV (Sector Imaging Radar for Enhanced Vision) ist ein innovatives Radarsystem, das auch bei schlechten Witterungsbedingungen eine hochauflösende Abbildung der Umgebung ermöglicht. Im Gegensatz zu einem Radar mit synthetischer Apertur wird in SIREV keine Relativbewegung zwischen dem Sensor und dem abzubildenden Zielgebiet benötigt. Die hohe Bildwiederholfrequenz ermöglicht die Aufzeichnung von schnellen dynamischen Veränderungen in der abgebildeten Szene. Zur phasentreuen Verarbeitung und Fokussierung der Rohdaten wird ein effizienter Prozessierungsalgorithmus vorgestellt. Neben einer Abbildung der Erdoberfläche können die komplexwertigen Radarbilder weiterverarbeitet werden, um beispielsweise zusätzliche Informationen über Topographie oder andere spezifische Objekteigenschaften zu gewinnen. Ein Funktionsmodell für SIREV wurde am Deutschen Zentrum für Luft- und Raumfahrt aufgebaut und erste Testflüge mit einem Hubschrauber durchgeführt. Hierbei kann auf ein kostenintensives Trägheitsnavigationssystem verzichtet werden, da Bewegungsfehler aus den aufgezeichneten Rohdaten extrahiert werden. Die erzielte Auflösung von Punktzielen zeigt eine gute Übereinstimmung mit der Theorie. Zur Rauschunterdrückung werden kohärente und inkohärente Mittelungsverfahren eingesetzt. Aufgrund seiner Systemarchitektur eignet sich SIREV besonders zur kostengünstigen Realisierung eines Radarsystems mit Vorwärtssicht, das beispielsweise zur Hindernisvermeidung und als Landehilfe in der Luftfahrt eingesetzt werden kann. 2002 Éditions scientifiques et médicales Elsevier SAS. Alle Rechte vorbehalten. Keywords: Forward-looking radar; Enhanced vision; Near field digital beamforming; Synthetic aperture radar Schlüsselwörter: Vorwärtssicht-Radar; Erweitertes Blickfeld; Nahfeld-Antennendiagramm-Synthese; Radar mit synthetischer Apertur
* Corresponding author.
E-mail address: [email protected] (G. Krieger). 1270-9638/02/$ – see front matter 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. doi:10.1016/S1270-9638(02)01189-6
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1. Introduction Adverse weather conditions affect both flight safety and the operational area of airborne platforms. This problem becomes most evident during take-off, landing and taxiing, but reliable collision warning in airspace gains also increasing importance. In all these cases it would be highly desirable to provide the pilot with visual information about the surrounding environment independent of weather and daylight. An imaging sensor for enhanced vision will also substantially increase the situation awareness of the crew without the necessity to recourse to an external electronic guidance system. Imaging radar systems, like synthetic aperture radar (SAR, [4,6,17,22]), have proved as a valuable tool in many applications where weather independent imaging is required, but, inherent to the underlying principle, these systems suffer from a visualization gap with respect to the forward looking direction [6,17]. In order to fill this blind spot a new real aperture array radar called Sector Imaging Radar for Enhanced Vision (SIREV) has been developed at the German Aerospace Center [3,11,20]. This innovative system has the potential to supply high quality radar images of a sector in front of the aircraft as shown in Fig. 1. In principle, it is possible to scan the complete sector in Fig. 1 sequentially by using a mechanically steered antenna with a narrow pencil beam. Since such an antenna has to be very large for high resolution imaging, it will become bulky and the necessary mechanics will be very complicated. This drawback may be avoided by electronically steered arrays which allow for inertia-free beamsteering and thereby substantially facilitate the integration into the aircraft. A common technique to form a narrow pencil beam in the desired direction is analog beamforming where the signals from (and to) the antenna elements are phase-shifted, weighted and summed (e.g. by an active phased array with T/R modules).
Fig. 1. SIREV is an innovative radar system which has the capability to provide high quality images of a sector in front of an aircraft independent of the weather conditions. Since SAR or Squint SAR systems have no azimuth resolution in flight direction their operational area is restricted to applications where boresight vision is sufficient.
The required phase-shifts are usually determined by the farfield approximation where the wavefront at the antenna array is regarded as planar. A common criterion for the applicability of this approximation is that the maximum phase error across the antenna array should not exceed π/8 , which re2 /λ where sults in a minimum focusing distance rmin 2dant dant is the antenna length and λ the wavelength [1]. For an antenna length of 3 m the minimum distance rmin is 581 m in X-Band (λ = 3.1 cm), 2118 m in Ka-Band (λ = 0.85 cm), and 5625 m in W-Band (λ = 0.32 cm). These values exclude conventional analog beamforming techniques from high-resolution mapping of close image sectors as required for aircraft landing and taxiing. An alternative to analog beamforming is digital beamforming [2,19,21] where the recorded raw data signals are separately digitized for each element. The focusing is then performed in a special purpose digital processor. Since the total information available at the antenna aperture is preserved in digital beamforming, it is possible to apply rangedependent phase functions which allows a focusing of the recorded signal array to different ranges (cf. Section 3). Further potentials of such an (a posteriori) digital beamforming are antenna self-calibration and element pattern correction (cf. Section 5.1), simultaneous high-resolution imaging of a large field of view, ambiguity reduction by an adaptive weighting of the sensor signals, the efficient compensation of array element failures, and the suppression of interferences by pattern nulling (see also [19]). In principle, digital beamforming is applicable both on transmit and receive, and the antenna array may be arranged and operated in many different ways (see also [8,18]). One example is the sequential switching of a linear array, where the individual antenna elements transmit and record the radar signals in successive order [24]. Since the recorded data in such a system closely resemble the raw data of a monostatic SAR, both near-field and far-field image formation may be achieved by a coherent processing with standard SAR processing algorithms [4,6,17]. Alternatively, the radar echoes for each of the sequentially transmitted pulses may be recorded simultaneously by all array elements which will improve the performance of the system due to the increased receptive antenna area. In this case, a hybrid of digital beamforming techniques [12,13,21,23] and conventional SAR focusing algorithms has to be developed in order to take full advantage of the potentials hidden in the recorded raw data. The disadvantage of the operational modes mentioned above is that a T/R module (or at least a T/R switch) is required for each array element which increases the complexity and costs of the necessary hardware. A more cost-efficient realization may be achieved by using a bistatic configuration with a dedicated transmit antenna illuminating the complete SIREV sector of Fig. 1 and recording the backscattered signals with a passive receive-only array of antenna elements. The drawback of such a bistatic configuration with one single transmit antenna is, that it achieves only half of the image resolution as compared to the
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monostatic case. In principle, it is also possible to combine the advantages of the monostatic and bistatic configurations by using a small number of dedicated transmit antennas in conjunction with the full receiving array. The bistatic configuration can again be operated in either a simultaneous or a sequential reception mode. The simultaneous recording allows for a very high image repetition frequency, which may be used, for example, to detect very fast moving objects, or, as outlined in Section 5.3, to coherently integrate across several image frames. In the latter case, the signal-to-noise ratio is expected to be comparable to active phased arrays since the loss in antenna transmit gain due to the broad illumination is compensated by the gain resulting from the coherent image combination. This is due to the fact that the higher allowed PRF by simultaneous reception compensates for the gain decrease of the transmitting antenna. Taking into account the low efficiency of current T/R modules and the possibility to increase the sensitivity of receiveonly array antennas (e.g. by direct integration of MMICs into the antenna), the imaging performance of SIREV may even become superior to that of an active phased-array radar. The disadvantages of the simultaneous reception mode are the large data rate as well as the required receive modules and analog-to-digital converters for each antenna element. The hardware and processing requirements may be minimized by a serial sampling of the received wavefronts, which is easily achieved by sequentially switching the array elements of the passive receive-only antenna. It is evident, that such an approach will enable a very cost-efficient implementation of a
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forward-looking radar, which is especially attractive for the mapping of sectors in the near field where the SNR requirements are less critical.
2. SIREV geometry and data acquisition The current SIREV system consists of one transmit antenna and a linear array of receiving patch elements as shown in Fig. 2. The receive antennas are centered around the across-track position y = 0 at height z = h, while the transmit antenna is at position x = 0, y = 0 and z = h − zoffset . The direction parallel to the receiving array is termed azimuth and the direction orthogonal to azimuth in forward direction, slantwise to the ground, is denoted as slant range. Correspondingly, the direction of the x-axis is termed ground range. For a point target at ground range position xp and azimuth position yp the transmit and receive paths RTX and RRX of the radar signal are given by RTX = = RRX = =
Fig. 2. Basic SIREV geometry.
xp2 + yp2 + (h − zoffset )2 2 rp2 + yp2 + zoffset − 2 · h · zoffset ,
xp2 + (yp − yi )2 + h2 rp2 + (yp − yi )2 ,
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wherefor convenience the point target slant range position rp = xp2 + h2 has been introduced. The variables yi denote the positions of the receiving antenna elements. Using the definitions for the signal transmit and receive paths, the SIREV signal modulation of a point target at position rp and yp can be written as RTX + RRX 2 s(yi , τ ; yp , rp ) = C exp j πke τ − c0 2π × exp −j (RTX + RRX ) λ where τ denotes the range time, c0 is the velocity of light, and λ is the wavelength. The first exponential term describes the linear frequency modulation of a range chirp with modulation rate ke = Br /τp , chirp bandwidth Br , and pulse duration τp . The azimuth modulation is given by the second exponential term. The contributions from the pulse envelope and the antenna weighting have been omitted in this equation since the phase functions are more important for the development of the processing algorithms.
3. SIREV processing 3.1. Spatial domain focusing In general, the focusing of the SIREV raw data may be achieved by a space-variant 2-D correlation +∞ Na u(y, r) = h(yi , τ ; y, r)s(yi , τ ) dτ i=1 0
where s(yi , τ ) is the unfocused raw data signal recorded by the Na antenna elements and u(y, r) is the processed complex image expressed in terms of azimuth y and slant range r. According to the matched filter concept [5], the space-variant 2-D kernel h(yi , τ ; y, r) is given by the complex conjugate of the predicted response of an ideal point scatterer located at (y, r), i.e., h(yi , τ ; y, r) = s ∗ (yi , τ ; y, r). While such a 2-D focusing approach maximizes the signalto-noise ratio under the reasonable assumption of secondorder white background noise, it is also most expensive from a computational point of view, since a two-dimensional integration has to be performed for each pixel of the final image. A computationally more efficient focusing algorithm may be derived, if the received raw data signals are first compressed in range by a 1-D convolution: Tp urc (yi , r) = 0
2r hr (τ )s yi , − τ dτ . c0
Here, hr (τ ) is the time-reversed complex conjugate of the transmitted chirp of duration Tp . The range compressed signal is denoted by urc (yi , r). Since the convolution in this equation is time-invariant, it may efficiently be implemented in the frequency domain by taking advantage of the Fast Fourier Transform (FFT). After range compression, the response of a point scatterer located at (yp , rp ) may well be approximated by a set of δ-impulses at r(yi ; yp, rp ) = RTX (yp , rp ) + RRX (yi ; yp , rp ). Thus, azimuth beamforming is achieved by the 1-D space variant correlation: u(y, r) =
Na
ha (yi ; y, r)urc yi , r(yi ; y, r)
(1)
i=1
where the kernel ha is given by 2π 2 ha (yi ; y, r) = exp j r 2 + y 2 + zoffset − 2hzoffset λ + r 2 + (yi − y)2 . In this approach, the inseparable and shift-variant 2-D correlation has been approximated by two 1-D correlations, resulting in a considerably reduced computational effort. Note that application of Eq. (1) may require an interpolation in range in order to extract the correct values from the range compressed array urc . Such an interpolation can be neglected for ‘narrow-band systems’ with small range migration (i.e. Br dant c0 · 2 · sin(θmax ) 1) like the SIREV functional model of Section 5. For a large number of antenna elements, the efficiency may be further increased by an appropriate adaptation of the Extended Chirp Scaling Algorithm [14,16], which is introduced in the next section. 3.2. Extended chirp scaling algorithm for SIREV An efficient processing algorithm for SIREV has been derived from a reformulation of the Extended Chirp Scaling (ECS) algorithm for ScanSAR [14–16]. Algorithms for ScanSAR focusing may be adapted to the processing of SIREV raw data due to the similarity of a ScanSAR raw data burst with the recorded data from the limited number of receiving antennas in SIREV. The block diagram of the modified ECS algorithm is shown in Fig. 3. The derivation of the ECS for SIREV is based on the following assumptions: • The azimuth modulation is only caused by the variation of the receiving path. This means half of the azimuth phase variation in SIREV compared to ScanSAR. • For SIREV a scanning velocity is defined by the product of receiving element spacing and pulse repetition frequency, which is used in the ECS processing like a platform velocity. • The range cell migration in SIREV has been approximated by the range cell migration of ScanSAR. This assumption is reasonable for an antenna array which is much smaller than the minimum observed range in the imaged scene.
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Fig. 3. Extended Chirp Scaling algorithm for SIREV (for a detailed description see [15]).
In Table 1, the resulting equations of the ECS for SIREV are compared with the ECS for ScanSAR. For a detailed explanation of the equations please refer to [16] and [15]. The table shows in bold style the differences in the equations caused by the halved azimuth phase variation in SIREV. The difference in the azimuth phase causes changes in all equations of the ECS processing, either directly visible in the ECS phase functions H1 to H6 or via the chirp scaling factor a(fa ) and the modified modulation rate keff .
4. Image quality estimation by simulation In order to obtain a reference for the SIREV image data processing and to get a first impression of the SIREV mapping capabilities, a SIREV image simulation has been carried out based on X-Band data from the Experimental SAR system of DLR (E-SAR) [10]. The results of this simulation are shown in Table 2 (see also [15] and [3]). As a main parameter, the wavelength decreases from left to right. From the simulations it becomes
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Table 1 Comparison of equations of the extended chirp scaling algorithm for ScanSAR and SIREV. The differences are shown in bold style Extended chirp scaling for ScanSAR (monostatic) H1 (fa , τ, r0 ) = exp −j · π · keff (fa , rref,cs ) · a(fa )
Chirp scaling
Range compression Range cell migration correction Chirp scaling phase correction
Azimuth scaling
Deramping ta azimuth time keff effective chirp modulation rate λ wavelength τ range time rref,cs reference range for chirp scaling
Extended chirp scaling for SIREV (bi-static) H1 (fa , τ, r0 ) = exp −j · π · keff (fa , rref,cs ) · a(fa )
2 · R(fa , rref,cs ) 2 2 · R(fa , rref,cs ) 2 × τ− × τ− c c
2 2 λ · fa λ · fa β(fa ) = 1 − β(fa ) = 1 − V 2V −1 2 1 4 · r0 · λ (β 2 (fa ) − 1) −1 1 2 · r0 · λ (β (fa ) − 1) keff (fa , r0 ) = − keff (fa , r0 ) = − ke c2 β 3 (fa ) ke c2 β 3 (fa ) r0 r0 R(fa , r0 ) = = r0 · (1 + a(fa )) R(fa , r0 ) = = r0 · (1 + a(fa )) β(fa ) β(fa ) 2 · rref,cs · a(fa ) −j · π · fe2 · exp +j · 2π · · fe H2 (fa , fe , rref,cs ) = exp keff (fa , rref,cs ) · (1 + a(fa )) c 2 2 H3 (fa , r0 ) = exp j · π · keff (fa , rref,cs ) · (1 + a(fa )) · a(fa ) · · (r0 − rref,cs ) c 4π 2π H5 (fa , r0 ) = exp +j · H5 (fa , r0 ) = exp +j · · r0 · (β(fa ) − 1) · r0 · (β(fa ) − 1) λ λ λ · rscl λ · rscl 2 2 × exp j · π · × exp j · π · · f · f a a V2 2V2 2 2 2V V H6 (ta , r0 ) = exp j · π · H6 (ta , r0 ) = exp j · π · · ta2 · ta2 λ · rscl λ · rscl a chirp scaling factor fa azimuth frequency c velocity of light rscl scaling range for azimuth scaling fe range frequency
V platform/scanning velocity r0 slant range distance R range migration in range-Doppler domain
apparent that the image quality will substantially improve for higher carrier frequencies if the antenna length is kept constant. To avoid ambiguities, the number of antenna elements has also to increase as indicated in the table.
reflector as the main scattering element and data from this recording were used for a calibration of the system. The second raw data set was obtained during a flight across the river ‘Lech’. The recording parameters of these two flights are summarized in Table 3.
5. Results from an experimental model
5.1. Raw data analysis
A functional model for SIREV has been built up at the German Aerospace Center [3]. The major goal of this hardware demonstration was to prove the feasibility of the SIREV principle in a short period of time with a minimum amount of effort. To reduce the costs it was preferable to use existing radar hardware even with specifications that were not optimized for this purpose. For example, a sequential switching of the 56 receiving antenna elements was necessary and the experimental model had to be built up in X-Band notwithstanding the poor image resolution to be expected due to the short antenna length of 2.85 m. Details of the radar hardware and the antenna system may be found in [3] and [25]. Fig. 4 illustrates the antenna system and its attachment to the helicopter. In the following, we will report our experimental results from two helicopter flights in the vicinity of Oberpfaffenhofen (Germany). The first scene contained a large corner
To test the integrity of the recorded raw data set we first investigated the response to the large corner reflector. An excerpt of the demodulated complex format raw data is shown in Fig. 5 on the left, where the dominant chirp signals from the corner reflector are easily recognized. From a visual inspection of the raw data an important aspect becomes immediately apparent: the recorded azimuth phases suffer from substantial discontinuities, which manifest themselves as disruptions between the individual range lines. These phase errors, which are mainly caused by the different wiring and radiation properties of the individual antenna elements, are a major concern, since they will substantially degrade the image quality. To quantify the phase errors, we first compressed the received radar signals in range and then extracted the azimuth phase response of the corner reflector (Fig. 5(b) and (c)). In this representation, large phase discontinuities up to ±π become apparent. For comparison,
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Table 2 SIREV image simulations for X-Band (left), Ka-Band (middle) and W-Band (right) X-Band
Ka-Band
W-Band
Wavelength: 0.031 m
Wavelength: 0.0085 m Antenna length: 3.0 m Look angle: 45◦ Chirp bandwidth: 100 MHz Chirp length: 1.5 µs Processed azimuth width: 24◦ Required array elements: 196 (for illuminated sector with 32◦ ) 707 (for illuminated sector with 180◦ ) Valid near range: 396 m Valid far range: 1698 m Range resolution: 2.2 m Azimuth extension near range: 169 m Azimuth resolution near: 1.6 m Azimuth extension far range: 722 m Azimuth resolution far: 6.7 m
Wavelength: 0.0032 m
Required array elements: 55 (for illuminated sector with 32◦ ) 195 (for illuminated sector with 180◦ )
Azimuth resolution near: 6 m Azimuth resolution far: 24 m
the analytically derived azimuth phase function of an ideal point target at azimuth position y0 = 0 m and slant range r0 = 761,5 m is also plotted in this figure using a dashed curve. Improved focusing will be achieved for all recorded frames by multiplying each recorded range line with a complex phasor, which is immediately derived from the difference of the measured azimuth phase and its theoretical prediction. The successful focusing by this method is demonstrated in Fig. 6, where we compare an example of one compressed corner reflector response with the impulse response function of an ideal point target located at y0 = 9,6 m and r0 = 681,8 m. The raw data frame was recorded approx. 3 seconds after the frame from which the phase correction has been derived.
Required array elements: 518 (for illuminated sector with 32◦ ) 1876 (for illuminated sector with 180◦ )
Azimuth resolution near: 0.6 m Azimuth resolution far: 2.5 m
In the phase compensation algorithm introduced above, we have implicitly assumed that all phase errors are both time- and space-invariant. In order to test this hypothesis we have extracted the compressed corner reflector responses for a sequence of 10.000 frames corresponding to a flight period of 37,9 seconds. A visualization of the azimuth profiles of these corner reflector responses is shown in Fig. 7 as a 3-D surface plot. From the temporal sequence of the azimuth profiles in Fig. 7 it becomes apparent, that the focusing is almost independent of both the azimuth angle and the frame number, thus supporting the hypothesis of space- and time-invariant phase errors. However, a closer look into the corner reflector responses revealed some small but systematic space-variant errors, which are presumably due to variations in the phase
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Table 3 Recording parameters
Center frequency Chirp bandwidth Antenna length Number of receive antenna elements PRF (sequential switching) Chirp duration Average helicopter velocity Average helicopter altitude Average ground level
Recorded scene corner river reflector “Lech” 9.5 GHz 100 MHz 2.85 m 56 (equally distributed) 14793 Hz 1.3 µs 1.3 µs 28 m/s 21 m/s 1056 m 927 m 556 m 645 m
Section 3.1, where we apply for each pixel in the output image a different reference function. Since an accurate implementation of this technique requires knowledge of a large number of phase response curves for a densely sampled grid of azimuth and elevation angles, we have restricted the phase error correction to the space-invariant phase shift of the range lines as described before. 5.2. Image processing results Fig. 4. Top: Antenna system attached to the skids of the helicopter. Bottom: RF side of the SIREV antenna with the 56 2 × 2 patch receiving subarrays. A detailed description of antenna hardware may be found in [25].
pattern of the receiving array antenna. In principle, a compensation of these space-variant azimuth phase errors may be incorporated in the correlation algorithms introduced in
In the preceding subsection we have demonstrated that a successful focusing of the recorded SIREV raw data is achieved, if the phase disruptions between the individual range lines are appropriately compensated. Using the phase corrections derived from the corner reflector response, we have also processed the raw data of the flight across the river
Fig. 5. Raw data analysis of the corner reflector response. (a) Excerpt of the recorded raw data in complex format. (b) Magnitude of the range compressed data. (c) Comparison of the measured (solid line) and the simulated (dashed line) azimuth phase response curves for a corner reflector located at an azimuth angle of zero degrees and a slant range distance of 761.5 m.
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Fig. 7. Temporal sequence of corner reflector responses obtained as the helicopter moved forward. The normalised azimuth profile of the focused radar image is shown as a function of azimuth angle and frame number.
Fig. 6. Comparison of the theoretical (top) and measured corner reflector response (bottom).
‘Lech’. An example of an image obtained by the SIREV processing is shown in Fig. 8(a). The displayed image has an extension of 1150 m in slant range. The azimuth extensions are 163 m in near range and 790 m in far range. From the processed image it becomes apparent, that system noise is a major concern. The low SNR was mainly caused by the sequential switching and the low gain of the receiving antenna elements. 5.3. Noise suppression As we have seen in the preceding section, the processed SIREV images suffer from a substantial contamination with noise. To alleviate these deteriorating effects, we took advantage of the high image repetition frequency (fimg = PRF/56 = 264 Hz) by appropriately combining the information of consecutively recorded frames. Most conveniently, this is achieved by a linear summation over several frames. In order to compensate for systematic phase shifts
induced by the helicopter movement, an appropriate phase correction has to be applied prior to complex summation. In our algorithm, which will be explained in detail below, this phase correction is automatically extracted from the image sequence. As an alternative, the necessary phase offsets could be deduced from the motion parameters of the helicopter. The block diagram in Fig. 9 summarizes the algorithm, which consists of three processing steps. The coherent SIREV smoother starts with a set u = {u1 (y, r), . . . , uN (y, r)} of N complex valued images denoted by ui (y, r). From this set phase differences "ϕi (y, r) between successive image pairs are computed using complex multiplication and taking the argument (phase) of the result: "ϕi (y, r) = arg ui (y, r) · u∗i+1 (y, r) . This yields a set of N − 1 phase differences which may be visualized in 2-D space by N − 1 vectors of unit length. An illustration of this processing step is shown within the first block of Fig. 9. Taking advantage of the vector representation of complex numbers, an average phase offset may be computed using 2-D vector summation as illustrated in the second block of Fig. 9. Analytically, this can be written as
N−1 "ϕ(y, r) = arg exp j "ϕi (y, r) , i=1
where "ϕ(y, r) denotes the two-dimensional average phase offset. An example of the spatial phase distribution obtained by this 2-D phase smoothing process is provided in Fig. 8(b), where "ϕ(y, r) has been computed for a set of N = 50 complex images. The average phase offset function "ϕ(y, r) is now used to correct the phase of the individual complex images for possible shifts due to movements of both the transmit and the
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Fig. 8. Results of SIREV processing: (a) Focused image. (b) Average phase offset. (c) Coherent smoothing with N = 50. (d) Hybrid smoothing. N
receive antennas. This can be achieved by multiplying each input image ui (y, r) with a complex phase factor ϕ i (y, r) which is immediately derived from the average phase offset "ϕ(y, r): ϕ i (y, r) = exp −j (i − 1)"ϕ(y, r) .
u(y, r) =
In this equation, a linear motion of both the receiving and the transmitting antennas has been assumed, resulting in an approximately linear decrease of the phase values as the helicopter moves forward. In a final step, the N phase aligned complex images are coherently summed according to the formula
which yields the smoothed image u(y, r). An example of the resulting image obtained by this complex averaging process is shown in Fig. 8(c), where the number of coherently summed images is N = 50. It becomes apparent that the coherent smoothing technique substantially improves both the image contrast and the SNR.
ui (y, r) · ϕ i (y, r)
i=1
=
N
ui (y, r) · exp −j (i − 1)"ϕ(y, r) ,
i=1
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The coherent smoothing process described above may also be combined with an incoherent average, as given by a linear summation of several detected images after coherent summation. The result of this hybrid smoothing technique is shown in Fig. 8(d) for a total of 50 coherently and 50 incoherently averaged images. As can be seen from the last image in Fig. 8 the incoherent summation further reduces the noise at the cost of a slightly impaired image resolution. The deterioration in geometric resolution may be avoided by an appropriate spatially inhomogeneous shift of the individual images which basically compensates for the helicopter movement. This ‘co-registration’ allows also the number of averaged images to be increased, which will further improve the quality of the resulting image. 5.4. Display geometries The images shown in Fig. 8 are represented as a function of azimuth and slant range. More natural from a pilot’s point of view is a representation in ‘optical coordinates’ which may be obtained by an appropriate central perspective projection (Fig. 10, see also [3]). An example for this geometrical image transformation is given in Fig. 11 together with an optical image of the recorded scene.
Fig. 9. Block diagram of coherent SIREV image smoothing procedure.
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6. Conclusion This paper has given a short overview of the data acquisition, modeling and processing of SIREV raw data. The final result of the experimental model was an image sequence animation, composed of several thousands of successive images as in Fig. 8(c), which demonstrates the validity and applicability of the SIREV principle. An excerpt of the movie is accessible on the SIREV Internet homepage [9]. SIREV has a great potential for applications where a radar mapping with short to moderate range distances with a forward looking geometry is required. The image formation is based on a digital beam forming on receive which allows a great flexibility for correcting phase and amplitude errors caused by the radar system or platform induced motion errors. By this, the side-lobes of the impulse response function can efficiently be suppressed even in the case of extremely high phase errors. Additionally, a coherent averaging process can be used to improve the signal-to-noise ratio of the processed images. The SIREV principle can also be combined with the SAR principle for a very high squinted imaging geometry. Although it is not possible to improve the azimuth resolution in the middle of the imaging sector, the Doppler effect can be exploited to improve the resolution in the forward direction by forming a synthetic aperture orthogonal to the SIREV antenna. In this case, several image frames have to be stored and the Doppler history can be used due to the coherent nature of the data acquisition scheme. This resolution improvement assumes, however, that the platform has a forward movement which is not necessarily the case for an imaging with the SIREV principle. A downward looking
Fig. 10. ‘Cyclopean’ projection from ground coordinates to screen coordinates.
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Fig. 11. Comparison of the ‘cyclopean’ SIREV image representation with an optical image. Left: Excerpt of the pilot’s view obtained from the SIREV image shown in Fig. 8(c). Right: Optical image recorded during a separate flight from a slightly different height and viewing angle.
geometry can also be considered in the case of a moving platform [7]. Interferometry or even tomography may be implemented by adding additional transmit antennas or by taking advantage of the forward movement. The same array of receiving antennas as for two-dimensional imaging can be used so that the additional hardware requirements are minimized. In this case, however, an inertial navigation system as well as a precise positioning system like differential GPS is required for accurate height determination. The feasibility of such a system using longer wavelength radar, e.g. for forest biomass estimation, will be investigated in a future work.
Acknowledgements We thank the anonymous reviewer for the valuable comments and hints. The fruitful collaboration with M. Younis, Y. Venot and W. Wiesbeck from the University of Karlsruhe is greatly appreciated. We thank Rolf Scheiber for helpful discussions. The SIREV project has been partially funded by STN Atlas.
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