A SAR image-formation algorithm that compensates for the spatially-variant effects of antenna motion Page: 4 of 16
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Azimuth correlation consists of a vector multiplication followed by a chirp-z transform (CZT). Use of the CZT here instead
of an FFT improves the geometric quality of the image, by keeping the azimuth pixel spacing constant as a function of range.
In what follows, we describe the OSA algorithm and its limitations in more detail. The hardware implementation of the
algorithm and quality of the images are interesting topics, but they are not the main subject. This paper emphasizes the
aspects of the algorithm that make it tolerant to flight-path deviations. The initial section discusses the parts of motion
compensation that are done in real time. The remaining sections deal with the three algorithm stages: coarse-resolution
azimuth processing, fine-resolution range processing, and fine-resolution azimuth processing. Figure 1 is a simple block
diagram of the OSA method.
COARSE- RNEFINE-
A/D CTMO RES AZ CTM1 PROCESS CTM2 RES AZ Image Output
Figure 1. Overlapped Subaperture Block Diagram
3. REAL-TIME MOTION COMPENSATION
The amount of digital processing is reduced if the radar performs some motion-compensation operations before digitizing the
return signal. This involves changing the frequency and phase of the transmit and receive chirps and varying the sample
rate of the A/D, all as functions of antenna motion. A digital waveform synthesizer generates the chirp signals. For the nth
pulse, both signals have the form
w(t,n)= g(t)cos(2nfnt + nyt2 + n) (I)
where fn is the starting frequency, n is the starting phase, y is the chirp rate, and g(t) is a gating function.
To see why it is useful to vary fn and fn, consider the geometry in Figure 2. Let rs be the range from the radar to some point
s in a ground patch, and let rc be the range to the parch center. Also let y be the depression angle between the XY plane and
the line joining the radar and patch center. If fn and 4n are constant, the dechirped return signal has Doppler-frequency and
range components that are proportional to rc. These components need to be removed eventually, since the algorithm
estimates the range and azimuth coordinates of a point s by operating on the difference
rsc = rs - re. (2)
A signal processor can accomplish the subtraction in (2) by multiplying the sampled return by appropriate vectors. The
disadvantage is that the radar needs to have excess bandwidth to accommodate the variation in rc. A much better approach
is to change the dechirp waveform as a function of rc. By appropriately incrementing the starting frequency and phase of the
receiver chirp, the radar produces the baseband point-target response
j4nr. f, y( t
xs(t,n)=e c , (3)
where fo,n is the radar center frequency, and to is a constant. For simplicity, we have omitted from (3) the signal amplitude
and a phase expression that varies slowly with n.
This first motion-compensation step is adequate for many situations. However, for fine-resolution and/or squint-mode
imaging two other steps are helpful to reduce the variation in xs(t,n) due to rsc. Let s = (sa.sr,sz) denote the azimuth,
ground-range, and vertical coordinates of s measured with respect to the patch center. Then the first few terms in an
expansion for rsc can be written as
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Burns, B. L. & Cordaro, J. T. A SAR image-formation algorithm that compensates for the spatially-variant effects of antenna motion, article, March 1, 1994; Albuquerque, New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc1313819/m1/4/: accessed April 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.