Spotlight SAR Processing Using the Extended Chirp Scaling Algorithm Josef Mittermayer and Alberto Moreira Institute of Radio Frequency Technology German Aerospace Research Establishment (DLR) D-82234 Oberpfaffenhofen, Germany T: +49-8 153-28-2373. e-mail:
[email protected] Abstract -- This paper presents a new processing algorithm for spotlight SAR data processing. The spotlight mode offers the potential of achieving very high geornetric resolution. The Extended Chirp Scaling (ECS) processing performs a subaperture approach combined with azimuth scaling and a new frequency scaling for range cell migration correction (RCMC). The subaperture processing and the effect of the frequency scaling are discussed. Simulation results demonstrate the precision processing in high resolution mode. I. INTRODUCTION Spotlight SAR offers a very high geometric resolution in azimuth [ I ] . In order to obtain a similar resolution in range, a high bandwidth chirp is transmitted. Due to the small range extension of spotlight scenes, dechirp on receive is used to reduce the range bandwidth before ND conversion. Dechirp means to multiply the received range ecihoes by a chirp signal with inverted modulation rate centered at ‘scene center position rret, Some processing algorithms suitabk for spotlight SAR processing are Chirp Scaling Algorithm, Polar Format Algorithm and Range Migration Algorithm. An advantage of the Chirp Scaling Algorithm is that it requires no interpolations. However, a linear frequency modulated range signal is necessary and must be recovered before processing. The Polar Format Algorithm is attractive since lit requires only two FFT’s, but two interpolations were needed in azimuth and range. The Range Migration Algorithm is able to process raw data dechirped in range by using three FFT’s. The major advantage is thc complete RCMC. One disadvantage is the need of the Stolt interpolation. The ECS algorithm proposed in this paper works with chirped or dechirped raw data in range. Here we assume dechirped raw data. By means of a new frequency scaling, the RCMC is performed without interpolation and without the need of chirped signals in range. During range processing the spotlight aperture is divided into subaperiures. This allows the use of short azimuth FFT’s. Azimuth compression is performed using azimuth scaling and SPECAN. This combination overcomes the need of a very long reference function for azimuth compression without interpolation.
11. THE ECS ALGORITHM FOR SPOTLIGHT MODE Fig. I shows the block diagram of the ECS algorithm. The spotlight SAR signal after dechirp, down-conversion and A/D-conversion can be expressed by ( 1 ). The distance be-
0-7803-3836-7/97/$10.000 1997 IEEE
tween antenna and target at closest approach is To, r is the azimuth dependent distance to the target, h is the wavelength and co the velocity of light. t, --
s(ta,tr;ro)=C.exp
The azimuth time is ta and the range time is L, while the range chirp rate is denoted by kr and C is a complex constant. The processing starts with the subaperture formation. The raw data are divided into separate blocks with original range, but smaller azimuth extension. The subaperture processing is discussed in more detail in the next section. After subaperture formation the raw data are transformed into the range Doppler domain by means of short azimuth FFT’s. Here, the signals are range compressed but range cell migration is not yet corrected. This is performed by a new frequency scaling function ( 2 ), which is more explained in section 4. The frequency scaling function Hf has the same function as the well known chirp scaling function. 2.x.k (2) H (fa,t r ; ro) = exp j . -2 ro .. a( f a ) . t,
[
]
CO
The frequency scaling factor a(f,) in ( 3 ) is calculated similarly to the linear chirp scaling factor [ 3 ] . In equation ( 3 ) V is platform velocity and fa is Doppler frequency.
Next, the data are transformed into two dimensional frequency domain by means of short range FFT’s. This means, the full number of range samples, corresponding to the required range frequency resolution, is required just before the last range FFT. Then the residual video phase (RVP) correction is performed. The RVP arises during dechirp on receive and is discussed in section 4. The next step is to transform the data again into range Doppler domain. Here, a small linear frequency modulation arising during frequency scaling is removed in order to avoid defocusing of the impulse response function (IRF) after the full range FFT. This full range FFT must have enough points to obtain a frequency sampling distance adequate for the range resolution. Next, the azimuth scaling function Ha ( 4 ) transfers the hyperbolic phase history from the azimuth signals into a pure
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quadratic one [2]. The resulting final Doppler rate ka,scl means a linear frequency modulation constant with range. No resampiing is needed after deramping and final azimuth FFT. More, the final sampling distance in azimuth can be adjusted by selecting a proper final Doppler rate. H,(f,,f,;r,)=exp
1[
[ "=
.p
j-,ro
exp j-.
fq
k:sc,
(4)
After azimuth scaling a range dependent azimuth phase is corrected which arises during the frequency scaling operation. The recombination of the subapertures is performed after short azimuth IFFT's in the range Doppler domain. After deramping, the data are finally transformed into the two dimensional frequency domain by full azimuth FFT's. As the length of the full range FFT's, the length of the full azimuth FFT's is determined by the azimuth resolution.
During range processing the instantaneous azimuth bandwidth Ba, which is the bandwidth of a single point target, has to be properly sampled. The maximum instantaneous azimuth bandwidth Ba,, is the spotlight aperture Tspottimes the near range Doppler rate ka,near. The total azimuth bandwidth Ba,totai is higher than Ba,,, since the azimuth position of the targets results in a frequency offset. Thus, the total azimuth bandwidth Ba,total is dependent on Aa: ( 5 ) Ba,total = ',,ma, + k a , n e a '4' The spotlight raw data are separated into sub-blocks with duration T s u b at the beginning of the processing. For each subaperture processing the according fDC value is used. After range processing including RCMC, the subapertures are recombined and the bandwidth Ba of each target is restored before azimuth processing. As can be seen in Fig. 2, the duration of the subapertures Tsubis determined by ( 6 ).
Spotlight.Raw Data
I
Subaperture Formation
I
+
Ka,near
To avoid a deterioration of the impulse response function there should be a small overlap between the subapertures.
I
Short AzimuthFFT
Frequency Scaling
I
I
Short Range FIT
RVP Correction
I
I
Short Range IFFT
Inverse Freq. Scaling
I
I
I
Full Range FFT
1
-
I
. I
'
T
Azimuth Scaling
Fig. 2: Subaperture formation
Phase Correction
IV. FREQUENCY SCALING
Short Azimuth IFFT
+
I
Final Image Fig. 1 : Block diagram of the ECS algorithm 111. SUBAPERTURE FORMATION The subaperture formation is shown in Fig. 2. The azimuth signals A and B with the Doppler rate k,,n,ar belong to the azimuth end points of the imaged scene in near range. Boresight geometry is assumed and the scene size in azimuth Aa equals arbitrarily the spotlight aperture.
+i
soot
In F . 3 the frequency scaling-~operation is shown graphically. Plot 1 shows the range signals of three point targets after dechirp on receive. The targets are in near, reference and far range. The range time shift of the signals corresponds to the RVP. Plot 2 shows the frequency scaling function which is azimuth frequency dependent. The bold function is used for the range signals in the first plot. The result of the frequency scaling can be seen in plot 3. The center frequencies of the range signals are shifted dependent on their range and azimuth positions. The azimuth position of a target results in an azimuth frequency and the frequency scaling is performed dependent on a(fa). In addition to the scaling of the center frequencies, a small linear frequency modulation is introduced which has to be removed later. The range signals after frequency scaling are represented in continuous line style while the range signals before frequency scaling are in dotted line style. Next, the RVP is removed. This can be interpreted as a scaling operation in
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range frequency direction. The function for the removal is shown in plot 4. After the removal, the irange signals are located at the same range time position as shown in plot 5. By multiplication with the inverse frequency scaling function, shown in plot 6, the small linear frequency modulation mentioned above is removed. Plot 7 shows the resulting range signals after complete frequency scaling. The frequency of the sinusoidal signal in far range is increased, in near range the frequency is decreased and the frequency at reference range is not changed (remains 0 Hz). After frequency scaling the range cell migration at all ranges is equalized to reference range. The bulk shift in range frequency for correcting the range cell migration of this reference range is already included in ( 2 ). I ) raw data --+ tr
+ 2
-
3 ) raw data after freq scaling 4) RVP corr S) raw data after RVPcorr 6) inverse freq scaling 7) raw data after complete fieq.
-
---T 2
range chirp length range chirp bandwidth sampling freq. transmitted sampling freq. after dechirp reference range dechirp reference range azimuth scaling range scene size aircraft velocity PRF wavelength length of spotlight aperture
I
ISLR [dB] I resolution[m] I res. Deviation 3500 -9.93 0.23 8 4500 -9.98 0.304 Tab. 1 : Results of point target analysis in azimuth
I I
range [m]
I
I
I
1
I ISLR [dB] I
I
resolution[m]
I
res. Deviation
4500 -10.08 0.733 Tab. 2: Results of point target analysis in range
185 MHz 200 MHz 40 MHz 4000 m 4000 m 1000 m
100 m/s 500 Hz 0.03 m 2.003 s
The ECS algorithm leads to a very precise and efficient
4 -
of the proposed algorithm. The parameters during raw data generation and processing are listed in Tab..?. At the top in Fig. 4 a image gray level representation of six targets after processing is shown. At the bottom a contour plot of a single processed point target can be seen. The point target analysis results for the targets located at the right side are listed in Tab. 1 and Tab. 2.
I range [m] I
38.5 ps
I
1.7 %
The SLR of the first three sidelobes left and right are -13.2, - 17.8 and -20.8 dB (f0. I dB) for all targets.
. .
of DLR) data. The E-SAR has a very wide beam in azimuth and thus allows the simulation of spotlight mode. The phase errors in the different steps of the processing will be calculated in order to explore the limitations of the algorithm. The computational complexity will be evaluated and compared with other approaches suitable for spotlight processing. REFERENCES [I] G. Carrara, R. S. Goodman, R. M. Majewski, "Spotlight Synthetic Aperture Radar", Artech House Boston, 1995. [2] Moreira, J. Mittermayer and R. Scheiber, " Extended Chirp Scaling Algorithm for Air- and Spaceborne SAR Data Processing in Stripmap and ScanSAR Imaging Modes", IEEE Trans. on Geosci. and Remote Sensing, Vol. 34, NO. 5, September 1996. [3] K. Raney, Runge, H., Bamler, R. Cumming, I. and Wong, F.:"Precision SAR Processing without Interpolation for Range Cell Migration Correction". IEEE Trans. on Geosci. and Remote Sensing, V01.32, No.4, July 1994.
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