Bistatic parasitic SAR processor evaluation - UBC ECE
Bistatic parasitic SAR processor evaluation Jesus Sanz-Marcos, Jordi J. Mallorquí, Antoni Broquetas Signal Theory and Communications Department Universitat Politecnica de Catalunya Barcelona, Spain {jsanz,mallorqui,toni}@tsc.upc.es Abstract— Bistatic radar systems will pay a great role in the coming decade since a large number of radar missions are being foreseen. Using existing transmitters, formations of small passive receivers will enhance our capability to gather backscatter information from earth. A bistatic SAR system operates with separated transmitting and receiving antenna and both antennas can follow independent trajectories. In this paper, the recently developed imaging algorithm for the case where the transmitting antenna follows a rectilinear trajectory while the receiver remains in a fixed position and orientation will be evaluated. This new imaging algorithm is based on a projecting the bistatic geometry onto the chirp scaling algorithm which results on a scaling factor in the azimuth compression function. This scaling factor is derived from the bistatic configurations and assumes a flat topography. The main purpose of this paper is to determine the accuracy of the algorithm when used with real case simulated scenarios such as the airborne case where the transmitter is onboard an airplane while the receiver will be installed in the top of a high tower.
Figure 1. Bistatic system geometry with static reveicer (left) and bistatic ambiguity for two targets at the same bistatic distance (right)
and target positions. The B factor will allow us to maintain a same expression for the transfer function for both monostatic two-way (B = 2) and bistatic one-way (B = 1) paths. The starting expression for the impulse response of a given target as a function of its bistatic parameters is:
Keywords- bistatic; sar; processor;algorithm; fixed receiver
I.
II.
λ
R
(1)
2
As shown in Figure 1 right, there is an implicit ambiguity for targets at the same bistatic distance (r1+ r2); however, it is possible to distinguish them by observing their respective range curvatures. Using the same formulation that in [3] and after several variable transformations, we obtain the expression of the impulse response of the system, due to an abstract bistatic unitary point target: BX L g (") = PR r '−r1 − r2 ( x, r1 ) − ∆X ·exp − jaB ∆R (2) λ cτ
where P(t ) represents the time-limited signal modulation and has the duration of the transmitted pulse and where r2 is now expressed as a function of target azimuth and slant range coordinates. Normalization and intermediate variables are described in the following expressions: X = λr0 / L, a = 2πX / L, b = Kτ 2
(
)
PR (r ) = exp jbr 2 rect (r )
(x − xR )2 + [ y(r1 ) − yR ]2 + (h − hR )2
r2 ( x, r1 ) =
STRIP MODE BISTATIC TRANSFER FUNCTION
y (r1 ) = r − (hT − h ) 2 1
Consider the geometry depicted in Figure 1 left, where instead of the usual cylindrical coordinate system ( x, r , ϕ ) a Cartesian coordinate system has been used to define transmitter, receiver
2
r1 , r2 , r ' norm → cτ / B
This work has been financed by the Spanish MCYT and EU FEDER funds under project TIC2002-04451-C02-01, and by the Catalan Commission for Research (CIRIT).
0-7803-8742-2/04/$20.00 (c) 2004 IEEE
−j
∆R = r12 + ( x − xT ) − r1
INTRODUCTION
Past and current SAR missions, such as SIR-C, ERS-1/2, Envisat, SRTM, E-SAR, etc. had in common that the signal transmitter and the receiver were located at the same moving platform. New missions are being planned based on the bistatic concept, where transmitter and receiver subsystems are located at different locations and thus follow different trajectories [1]. One of the first attempts in this direction is the joint mission carried out by DLR and Onera, where E-SAR and Ramsés SAR sensors flew in formation and experimented with some bistatic geometries. This paper presents an approach in the characterization of a different bistatic configuration, where the transmitter follows a rectilinear path while the receiver remains in a fixed position. First, an evaluation of the strip mode bistatic function is derived, both in time and frequency domain. Then the hybrid monostatic/bistatic [2] simulator will be introduced. Finally, a SAR processing algorithm for this bistatic configuration will be explained and its accuracy will be evaluated over a wide range of possible scenarios.
2π
R P t − B c R (x − xT , r1 , r2 ) = r1 + r2 + ∆R g ( xT , t ; x, r1 , r2 ) = e
3666
x ' , x, ∆R norm → X
(3)
Next step is to compute the transfer function of the SAR system by considering the 2D Fourier transform of the impulse response. The stationary phase method is applied for integrals evaluation leading to:
G (ξ ,η ; x, r ) = Gmono (ξ ,η ; r ) B =1 exp[ηr2 (x, r )]
(4)
This result gives an idea of the specific characteristics of the bistatic case, where the response of a single target depends not only on its slant range but also on its azimuth absolute position. III.
RAW-DATA BISTATIC SIMULATOR
To test the validity of expression (4), a bistatic simulator was build for the airborne ideal case where the transmitter follows a rectilinear path and trajectory inaccuracies has not been taken into consideration. The simulation parameters used in the paper are shown in Table 1. The simulator has also been used to develop the bistatic SAR processor as it is possible to generate sets of raw data for different types of configurations in a parameter sweep mode and thus have a clear knowledge of the impact of transfer functions approximations verifying the processing capabilities of the algorithm under study. The simulator works in time domain emulating transmitter and receiver operations and thus Fourier transforms are not used. To be able to adapt an existent monostatic SAR algorithm to the bistatic case, the simulator can, for a given configuration, generate both the monostatic and the bistatic response. This is done by carefully selecting gating times for monostatic and bistatic receivers. The software architecture has been the same that in [4]. Further steps will allow the simulation of Digital Elevation Models (DEMs) together with ideal targets to get a more accurate idea of the usefulness of bistatic systems. The scene that will be processed, and which results are shown in the next section, has nine targets distributed over it in such a way that targets’ impulse responses fit inside the processing area. Given the geometry presented in Table 1, targets are 1345 m separated in azimuth and 5500 m in ground range. First attempts simulated targets that lie in the ground (z coordinate set to zero) and future studies will examine the effect of targets at different heights. TABLE I.
SIMULATION PARAMETERS
Instrument f0 9.6 GHz PRF 1000 Hz fs 160 MHz v 386 m/s Chirp bandwidth 72% Doppler bandwidth 72% Lines 4096 Samples 2048
Geometry hT 4000 m hR 500 m Look angle 50 º Squint angle 0º xR, yR, yT, h 0m r0 6222 m Targets 9
Figure 2. Monostatic vs. Bistatic projection. Bistatic two-way distance and bistatic distance (transmitter to target + target to receiver) are shown for three different targets located a near, middle and far range.
attempts to process a bistatic simulated image with two monostatic algorithms (wave number [5] and chirp scaling [6]) gave the same results. The image was well focused for the reference range but aberrations appeared only in the azimuth direction as targets were located away from this reference range. Therefore, monostatic algorithms modified for one-way slant range act as narrow algorithms when are used to focus bistatic raw data. However, and as will be shown in the rest of this section, these algorithms can be modified in order to properly process bistatic data. It is possible to visualize the effect of a bistatic configuration versus the monostatic one by studying the slant range projection of three different targets, located, for sake of simplicity, at the same azimuth coordinate than the receiver. The relation between the projection of a target in the bistatic slant range and the monostatic slant range appears to be the clue for a correct bistatic raw data focusing. Figure 2 shows this projection and it can be seen how the bistatic slant range is compressed respect to the reference range. First modifications to current monostatic algorithms included an autofocus block which was able to estimate the correct azimuth compression phase factor for the bistatic case. We found that it was proportional to the monostatic azimuth compression phase factor µ’(ξ) and had a strong dependence on look angle and on receiver height. Deep analysis of the geometry of Figure 3, leads to an analytical formulation of the proportionality (that we cal azimuth compression bistatic factor β) as a function of transmitter and receiver heights, and look angle (or range of reference). This factor is approximate by Taylor’s expansion as follows: β (r´) =
r '→0
lim β (r´) =
NARROW BISTATIC PROCESSOR
In the process of designing a processing algorithm for the bistatic case and given the similarities between monostatic and bistatic transfer functions, the first step was to adapt a monostatic algorithm from two-way to one-way. This was accomplished by substituting the B factor from 2 to 1. First
0-7803-8742-2/04/$20.00 (c) 2004 IEEE
h + (r´+ r0 ) − h + r´− hR2 + r02 − hT2 2
2 T
∂ β (r´) ∂r´
β ( r´) ≅ lim β (r´) + r´lim
r '→ 0
IV.
r´ 2 R
r '→ 0
(5)
hR2 + r02 − hT2 hR2 + r02 − hT2 + r0
It is important to notice that the azimuth compression factor is not defined for the reference range. We are using the linear approximation instead of its exact value to be able to properly correct raw data with more samples per line as the azimuth compression factor looses its linearity when the near range approaches the value of the receiver height. Other curve fitting
3667
Figure 3 shows three graphs corresponding to cross sections of zero padded interpolated targets responses, in azimuth and in range and a contour plot is also provided. In the three graphs, responses for the nine targets have been superposed in order to easily visualize the overall processing accuracy. When targets do not lie in the ground, they are not perfectly focused and this gets worse as target height increases in comparison to the size of the receiver position. However, for a “real case”, where the receivers would be located in the top of a mountain (lets say, at 500 m) and illuminated targets (buildings, city topography) would have a mean height of about 25-40 m, the presented algorithm keeps in good shape and the worst decrease in PLSR is only 0.163 dB. To illustrate the limitations of this algorithm, and more specifically, the limitations of the bistatic scaling factor some simulations have been performed. Three cases have been studied. The first one considers the effect of target height in the azimuth response and its results are shown in the below figure.
Figure 3. Chirp Scaling Algorithm for Bistatic Fixed Receiver (top) and Processing output superposed contour plot and azimuth and range sections for a 9 target scene (bottom).
strategies are under study even though the presented approximation is good enough for accurate bistatic processsing. We have chosen the Chirp Scaling Algorithm because of its efficiency and accuracy but the same modification can be added to other SAR processing algorithms such as the wavenumber, the Omega-K or the Chirp-Z transform. The modification is applied by multiplying the phase factor µ(ξ)r by the presented new bistatic azimuth compression factor β(r’). This operation is shown in Figure 3. Values for the expressions that appear in the CSA algorithm diagram block are given by: Gmono (ξ ,η , r ) ≅ G0 (ξ ,η ) +
µ ( ξ ) + ηv(ξ ) + η 2ζ (ξ )] (r − r0 )[
Ω(ξ ) = 1 + v(ξ ) D(ξ ) =
~ K (ξ ,η )
b 1 + 4ζ (ξ )r0b
(6)
C (ξ ) = D(ξ )[1 − Ω(ξ )] B(ξ ) = − D(ξ )Ω(ξ ) A(ξ ) = B(ξ )[1 − Ω(ξ )]
V.
RESULTS The presented algorithm has demonstrated its usefulness over a wide range of bistatic geometries by using the parameter sweep capabilities and automatic impulse response evaluation of the previously mentioned bistatic SAR simulator. For instance, we present the results of the processor for a typical bistatic geometry based on the use, for example, of the E-SAR airborne sensor. Simulation parameters are shown in Table 1.
0-7803-8742-2/04/$20.00 (c) 2004 IEEE
Figure 4. Evolution of the worst azimuth response of nine focused targets at different heights (top) and level of aberration at the theorical null position as a function of target height (bottom).
We can notice that the response gets worst linearly as target height increases. For targets at heights lower than 30 meters the algorithm is still working well because the null is at the same level than the rest of secondary lobes. However in the bistatic case it is very ambiguous to define a slant range as in the monostatic case and there is not a simple way to transform from the ground range topography to the acquisition geometry. In monostatic processing we talk about “narrow” processors when they are only able to properly focus the image in the
3668
vicinity of a given reference slant range. In the same way, we can consider this algorithm to be a narrow focusing algorithm in the sense that only targets located at a determined height are well focused. This conclusion, although pessimistic, gives us a hint of what is happening. Probably, we must find the way to equalize the height effect for a reference range before processing the image.
Figure 5. Evolution of the worst azimuth response of nine focused targets at different scene look angles with a transmitter height of 9000 m.
The second case under study shows the effect of the acquisition geometry. Nine targets are again located at zero height while transmitter look angle is swept from 35 degrees to 65 degrees (and so does near, middle and far range). We can notice that the higher the look angle the better the algorithm performs due to small variations in the range curvature for all targets. However, we can observe that null values are acceptable for the given range of look angles.
VI.
Bistatic systems will play an important role in incoming missions. However, even the ideal target definition can not be easily extrapolated from the monostatic case to the bistatic one. In this paper we have shown that system geometry has a great impact in the design of imaging algorithms to process data acquired in these new missions. For instance, the case where the transmitter is moving in a straight line while the receiver remains in a fixed position has been studied, from the definition of the target impulse response to the implementation of a focusing algorithm. Future steps in this direction will expand this processor to the orbital case in order to evaluate the feasibility of bistatic systems where transmitters are located at existing or future satellite platforms, such as Envisat or TerraSAR-X, and receivers are located at high buildings or towers. The benefits of single pass interferometry with the use of several bistatic fixed receivers will be also studied. Finally, the correctness of both the simulator and the processor will be evaluated in the near future using real measurements of a bistatic system inside an anechoic chamber. ACKNOWLEDGMENT The authors wish to thank Marc Rodríguez Cassolà and Dr. Josef Mittermayer, both from the DLR, for some challenging conversations and comments. REFERENCES [1]
[2] [3] [4]
[5] [6]
Fiedler, H., Krieger, G., Jochim, F., Kirschner, M., Moreira, A.: “Analysis of bistatic configurations for spaceborne SAR interferometry”. Proceedings of EUSAR, 2002. Sanz-Marcos, J., Mallorqui, J.J.: A Bistatic Simulator and Processor; Proceedings of EUSAR, 2004. Franceschetti, G., Lanari, R.: Synthetic Aperture Radar Processing. CRC Press, 1999 Sanz J., Prats, P., Mallorqui, J.J.: Platform and mode independent SAR data processor based on the Extended Chirp Scaling Algorithm. IGARSS proceedings, 2003. Bamler, R.:A comparison of range-Doppler and wave number domain SAR focusing algorithms. TGARS, 1992. Raney, R.K., Runge, H., Bamler, R., Cumming, I.G., and Wong, F.H.: Precision SAR processing using chirp scaling. TGARS, 1994.G. Eason, B. Noble, and I. N. Sneddon, “On certain integrals of Lipschitz-Hankel type involving products of Bessel functions,” Phil. Trans. Roy. Soc. London, vol. A247, pp. 529–551, April 1955. (references)
Figure 6. Evolution of the worst azimuth response of nine focused targets located at the corners of an azimuth size-increasing scene.
In the last studied case, the scene size was simulated from 200 m to 2 km and targets were located at the scene limits. This study shows another important limitation of the proposed algorithm as aberrations start to become severe when scene size reaches the first km. Therefore, the implemented chirp scaling algorithm with the bistatic scaling factor can only be used in small to middle size scenes.
0-7803-8742-2/04/$20.00 (c) 2004 IEEE
CONCLUSIONS
3669
Figure 1. Bistatic system geometry with static reveicer (left) and bistatic ambiguity for two targets at the same bistatic distance (right)
and target positions. The B factor will allow us to maintain a same expression for the transfer function for both monostatic two-way (B = 2) and bistatic one-way (B = 1) paths. The starting expression for the impulse response of a given target as a function of its bistatic parameters is:
Keywords- bistatic; sar; processor;algorithm; fixed receiver
I.
II.
λ
R
(1)
2
As shown in Figure 1 right, there is an implicit ambiguity for targets at the same bistatic distance (r1+ r2); however, it is possible to distinguish them by observing their respective range curvatures. Using the same formulation that in [3] and after several variable transformations, we obtain the expression of the impulse response of the system, due to an abstract bistatic unitary point target: BX L g (") = PR r '−r1 − r2 ( x, r1 ) − ∆X ·exp − jaB ∆R (2) λ cτ
where P(t ) represents the time-limited signal modulation and has the duration of the transmitted pulse and where r2 is now expressed as a function of target azimuth and slant range coordinates. Normalization and intermediate variables are described in the following expressions: X = λr0 / L, a = 2πX / L, b = Kτ 2
(
)
PR (r ) = exp jbr 2 rect (r )
(x − xR )2 + [ y(r1 ) − yR ]2 + (h − hR )2
r2 ( x, r1 ) =
STRIP MODE BISTATIC TRANSFER FUNCTION
y (r1 ) = r − (hT − h ) 2 1
Consider the geometry depicted in Figure 1 left, where instead of the usual cylindrical coordinate system ( x, r , ϕ ) a Cartesian coordinate system has been used to define transmitter, receiver
2
r1 , r2 , r ' norm → cτ / B
This work has been financed by the Spanish MCYT and EU FEDER funds under project TIC2002-04451-C02-01, and by the Catalan Commission for Research (CIRIT).
0-7803-8742-2/04/$20.00 (c) 2004 IEEE
−j
∆R = r12 + ( x − xT ) − r1
INTRODUCTION
Past and current SAR missions, such as SIR-C, ERS-1/2, Envisat, SRTM, E-SAR, etc. had in common that the signal transmitter and the receiver were located at the same moving platform. New missions are being planned based on the bistatic concept, where transmitter and receiver subsystems are located at different locations and thus follow different trajectories [1]. One of the first attempts in this direction is the joint mission carried out by DLR and Onera, where E-SAR and Ramsés SAR sensors flew in formation and experimented with some bistatic geometries. This paper presents an approach in the characterization of a different bistatic configuration, where the transmitter follows a rectilinear path while the receiver remains in a fixed position. First, an evaluation of the strip mode bistatic function is derived, both in time and frequency domain. Then the hybrid monostatic/bistatic [2] simulator will be introduced. Finally, a SAR processing algorithm for this bistatic configuration will be explained and its accuracy will be evaluated over a wide range of possible scenarios.
2π
R P t − B c R (x − xT , r1 , r2 ) = r1 + r2 + ∆R g ( xT , t ; x, r1 , r2 ) = e
3666
x ' , x, ∆R norm → X
(3)
Next step is to compute the transfer function of the SAR system by considering the 2D Fourier transform of the impulse response. The stationary phase method is applied for integrals evaluation leading to:
G (ξ ,η ; x, r ) = Gmono (ξ ,η ; r ) B =1 exp[ηr2 (x, r )]
(4)
This result gives an idea of the specific characteristics of the bistatic case, where the response of a single target depends not only on its slant range but also on its azimuth absolute position. III.
RAW-DATA BISTATIC SIMULATOR
To test the validity of expression (4), a bistatic simulator was build for the airborne ideal case where the transmitter follows a rectilinear path and trajectory inaccuracies has not been taken into consideration. The simulation parameters used in the paper are shown in Table 1. The simulator has also been used to develop the bistatic SAR processor as it is possible to generate sets of raw data for different types of configurations in a parameter sweep mode and thus have a clear knowledge of the impact of transfer functions approximations verifying the processing capabilities of the algorithm under study. The simulator works in time domain emulating transmitter and receiver operations and thus Fourier transforms are not used. To be able to adapt an existent monostatic SAR algorithm to the bistatic case, the simulator can, for a given configuration, generate both the monostatic and the bistatic response. This is done by carefully selecting gating times for monostatic and bistatic receivers. The software architecture has been the same that in [4]. Further steps will allow the simulation of Digital Elevation Models (DEMs) together with ideal targets to get a more accurate idea of the usefulness of bistatic systems. The scene that will be processed, and which results are shown in the next section, has nine targets distributed over it in such a way that targets’ impulse responses fit inside the processing area. Given the geometry presented in Table 1, targets are 1345 m separated in azimuth and 5500 m in ground range. First attempts simulated targets that lie in the ground (z coordinate set to zero) and future studies will examine the effect of targets at different heights. TABLE I.
SIMULATION PARAMETERS
Instrument f0 9.6 GHz PRF 1000 Hz fs 160 MHz v 386 m/s Chirp bandwidth 72% Doppler bandwidth 72% Lines 4096 Samples 2048
Geometry hT 4000 m hR 500 m Look angle 50 º Squint angle 0º xR, yR, yT, h 0m r0 6222 m Targets 9
Figure 2. Monostatic vs. Bistatic projection. Bistatic two-way distance and bistatic distance (transmitter to target + target to receiver) are shown for three different targets located a near, middle and far range.
attempts to process a bistatic simulated image with two monostatic algorithms (wave number [5] and chirp scaling [6]) gave the same results. The image was well focused for the reference range but aberrations appeared only in the azimuth direction as targets were located away from this reference range. Therefore, monostatic algorithms modified for one-way slant range act as narrow algorithms when are used to focus bistatic raw data. However, and as will be shown in the rest of this section, these algorithms can be modified in order to properly process bistatic data. It is possible to visualize the effect of a bistatic configuration versus the monostatic one by studying the slant range projection of three different targets, located, for sake of simplicity, at the same azimuth coordinate than the receiver. The relation between the projection of a target in the bistatic slant range and the monostatic slant range appears to be the clue for a correct bistatic raw data focusing. Figure 2 shows this projection and it can be seen how the bistatic slant range is compressed respect to the reference range. First modifications to current monostatic algorithms included an autofocus block which was able to estimate the correct azimuth compression phase factor for the bistatic case. We found that it was proportional to the monostatic azimuth compression phase factor µ’(ξ) and had a strong dependence on look angle and on receiver height. Deep analysis of the geometry of Figure 3, leads to an analytical formulation of the proportionality (that we cal azimuth compression bistatic factor β) as a function of transmitter and receiver heights, and look angle (or range of reference). This factor is approximate by Taylor’s expansion as follows: β (r´) =
r '→0
lim β (r´) =
NARROW BISTATIC PROCESSOR
In the process of designing a processing algorithm for the bistatic case and given the similarities between monostatic and bistatic transfer functions, the first step was to adapt a monostatic algorithm from two-way to one-way. This was accomplished by substituting the B factor from 2 to 1. First
0-7803-8742-2/04/$20.00 (c) 2004 IEEE
h + (r´+ r0 ) − h + r´− hR2 + r02 − hT2 2
2 T
∂ β (r´) ∂r´
β ( r´) ≅ lim β (r´) + r´lim
r '→ 0
IV.
r´ 2 R
r '→ 0
(5)
hR2 + r02 − hT2 hR2 + r02 − hT2 + r0
It is important to notice that the azimuth compression factor is not defined for the reference range. We are using the linear approximation instead of its exact value to be able to properly correct raw data with more samples per line as the azimuth compression factor looses its linearity when the near range approaches the value of the receiver height. Other curve fitting
3667
Figure 3 shows three graphs corresponding to cross sections of zero padded interpolated targets responses, in azimuth and in range and a contour plot is also provided. In the three graphs, responses for the nine targets have been superposed in order to easily visualize the overall processing accuracy. When targets do not lie in the ground, they are not perfectly focused and this gets worse as target height increases in comparison to the size of the receiver position. However, for a “real case”, where the receivers would be located in the top of a mountain (lets say, at 500 m) and illuminated targets (buildings, city topography) would have a mean height of about 25-40 m, the presented algorithm keeps in good shape and the worst decrease in PLSR is only 0.163 dB. To illustrate the limitations of this algorithm, and more specifically, the limitations of the bistatic scaling factor some simulations have been performed. Three cases have been studied. The first one considers the effect of target height in the azimuth response and its results are shown in the below figure.
Figure 3. Chirp Scaling Algorithm for Bistatic Fixed Receiver (top) and Processing output superposed contour plot and azimuth and range sections for a 9 target scene (bottom).
strategies are under study even though the presented approximation is good enough for accurate bistatic processsing. We have chosen the Chirp Scaling Algorithm because of its efficiency and accuracy but the same modification can be added to other SAR processing algorithms such as the wavenumber, the Omega-K or the Chirp-Z transform. The modification is applied by multiplying the phase factor µ(ξ)r by the presented new bistatic azimuth compression factor β(r’). This operation is shown in Figure 3. Values for the expressions that appear in the CSA algorithm diagram block are given by: Gmono (ξ ,η , r ) ≅ G0 (ξ ,η ) +
µ ( ξ ) + ηv(ξ ) + η 2ζ (ξ )] (r − r0 )[
Ω(ξ ) = 1 + v(ξ ) D(ξ ) =
~ K (ξ ,η )
b 1 + 4ζ (ξ )r0b
(6)
C (ξ ) = D(ξ )[1 − Ω(ξ )] B(ξ ) = − D(ξ )Ω(ξ ) A(ξ ) = B(ξ )[1 − Ω(ξ )]
V.
RESULTS The presented algorithm has demonstrated its usefulness over a wide range of bistatic geometries by using the parameter sweep capabilities and automatic impulse response evaluation of the previously mentioned bistatic SAR simulator. For instance, we present the results of the processor for a typical bistatic geometry based on the use, for example, of the E-SAR airborne sensor. Simulation parameters are shown in Table 1.
0-7803-8742-2/04/$20.00 (c) 2004 IEEE
Figure 4. Evolution of the worst azimuth response of nine focused targets at different heights (top) and level of aberration at the theorical null position as a function of target height (bottom).
We can notice that the response gets worst linearly as target height increases. For targets at heights lower than 30 meters the algorithm is still working well because the null is at the same level than the rest of secondary lobes. However in the bistatic case it is very ambiguous to define a slant range as in the monostatic case and there is not a simple way to transform from the ground range topography to the acquisition geometry. In monostatic processing we talk about “narrow” processors when they are only able to properly focus the image in the
3668
vicinity of a given reference slant range. In the same way, we can consider this algorithm to be a narrow focusing algorithm in the sense that only targets located at a determined height are well focused. This conclusion, although pessimistic, gives us a hint of what is happening. Probably, we must find the way to equalize the height effect for a reference range before processing the image.
Figure 5. Evolution of the worst azimuth response of nine focused targets at different scene look angles with a transmitter height of 9000 m.
The second case under study shows the effect of the acquisition geometry. Nine targets are again located at zero height while transmitter look angle is swept from 35 degrees to 65 degrees (and so does near, middle and far range). We can notice that the higher the look angle the better the algorithm performs due to small variations in the range curvature for all targets. However, we can observe that null values are acceptable for the given range of look angles.
VI.
Bistatic systems will play an important role in incoming missions. However, even the ideal target definition can not be easily extrapolated from the monostatic case to the bistatic one. In this paper we have shown that system geometry has a great impact in the design of imaging algorithms to process data acquired in these new missions. For instance, the case where the transmitter is moving in a straight line while the receiver remains in a fixed position has been studied, from the definition of the target impulse response to the implementation of a focusing algorithm. Future steps in this direction will expand this processor to the orbital case in order to evaluate the feasibility of bistatic systems where transmitters are located at existing or future satellite platforms, such as Envisat or TerraSAR-X, and receivers are located at high buildings or towers. The benefits of single pass interferometry with the use of several bistatic fixed receivers will be also studied. Finally, the correctness of both the simulator and the processor will be evaluated in the near future using real measurements of a bistatic system inside an anechoic chamber. ACKNOWLEDGMENT The authors wish to thank Marc Rodríguez Cassolà and Dr. Josef Mittermayer, both from the DLR, for some challenging conversations and comments. REFERENCES [1]
[2] [3] [4]
[5] [6]
Fiedler, H., Krieger, G., Jochim, F., Kirschner, M., Moreira, A.: “Analysis of bistatic configurations for spaceborne SAR interferometry”. Proceedings of EUSAR, 2002. Sanz-Marcos, J., Mallorqui, J.J.: A Bistatic Simulator and Processor; Proceedings of EUSAR, 2004. Franceschetti, G., Lanari, R.: Synthetic Aperture Radar Processing. CRC Press, 1999 Sanz J., Prats, P., Mallorqui, J.J.: Platform and mode independent SAR data processor based on the Extended Chirp Scaling Algorithm. IGARSS proceedings, 2003. Bamler, R.:A comparison of range-Doppler and wave number domain SAR focusing algorithms. TGARS, 1992. Raney, R.K., Runge, H., Bamler, R., Cumming, I.G., and Wong, F.H.: Precision SAR processing using chirp scaling. TGARS, 1994.G. Eason, B. Noble, and I. N. Sneddon, “On certain integrals of Lipschitz-Hankel type involving products of Bessel functions,” Phil. Trans. Roy. Soc. London, vol. A247, pp. 529–551, April 1955. (references)
Figure 6. Evolution of the worst azimuth response of nine focused targets located at the corners of an azimuth size-increasing scene.
In the last studied case, the scene size was simulated from 200 m to 2 km and targets were located at the scene limits. This study shows another important limitation of the proposed algorithm as aberrations start to become severe when scene size reaches the first km. Therefore, the implemented chirp scaling algorithm with the bistatic scaling factor can only be used in small to middle size scenes.
0-7803-8742-2/04/$20.00 (c) 2004 IEEE
CONCLUSIONS
3669
