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SAR [1] is a technique for computing high-resolution radar returns that exceed the traditional resolution limits imposed by the physical size, or aperture, of an antenna. SAR exploits antenna motion to synthesize a large "virtual" aperture, as if the physical antenna were larger than it actually is. In this example, the SAR technique is used to form a high-resolution backscatter image of a distant area using an airborne radar platform.

This model shows the following concepts:

Processing of realistic, synthesized SAR data

Implementation of important signal processing operations, including matched filtering

Combining DSP System Toolbox™ blocks and MATLAB® code in a system context

The model used in this example is based on a benchmark developed by MIT Lincoln Laboratory called the High-Performance Embedded Computing (HPEC) Challenge benchmark. The benchmark shows a simplified SAR processing chain. The simplifications made by this benchmark that differ from a real SAR system are given by MIT Lincoln Laboratory as follows [2]:

The area under observation is at exactly 90 degrees from the aircraft flight path

The aperture is made equal to the cross-range (Y-dimension) of the area under observation

The benchmark includes both image formation and pattern recognition. The Simulink® model only implements the 'genSARImage' image formation function (kernel #1) from the benchmark. See the HPEC Challenge benchmark web site [3] for more details.

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Step 1: Digital Filtering and Spotlight SAR Processing Step 2: Two-Dimensional Matched Filtering Step 3: Polar-to-Rectangular Interpolation |

The SAR system is gathering data about a 6x8 grid of reflectors placed on the ground that is being imaged by an aircraft flying overhead. The final image produced by the MATLAB® code for the benchmark is shown here. The demonstration model reproduces this image.

Examine the (synthetic) raw SAR data returns. A SAR system transmits a series of pulses, then collects a series of samples from the antenna for each transmitted pulse. It collects these samples into a single two-dimensional data set. The data set dimension corresponding to the samples collected in response to a single pulse is referred to as the *fast-time* or *range* dimension. The other dimension is referred to as the *slow-time* dimension. On the ground, the slow-time dimension corresponds to the direction of the plane's motion, also called the *cross-range* dimension. The input to this model is a single collected data set representing the unprocessed data that comes from the sensor. This unprocessed data has no discernable patterns that would allow you to infer what is actually being viewed.

**Step 1: Digital Filtering and Spotlight SAR Processing**

The first subsystem in the model performs three operations.

Fast-time filtering transforms the returns from each pulse into the frequency domain and convolves them with the expected return from a unit reflector.

Digital spotlighting focuses the returns in cross-range.

Bandwidth expansion increases the cross-range resolution using FFTs and zero-padding in the image frequency domain.

Forward and inverse FFTs form the bulk of this portion of the processing. Equation numbers in the model refer to the equations in the benchmark description document [2].

**Step 2: Two-Dimensional Matched Filtering**

Two-dimensional matched filtering convolves the output of the previous stage with the impulse response of an ideal point reflector. Matched filtering is performed by multiplication in the frequency domain, which is equivalent to convolution in the spatial domain.

**Step 3: Polar-to-Rectangular Interpolation**

Run the model to process the data. In the matched-filtered image, although the reflectors are all present, the returns from the nearest and farthest rows of reflectors in range are smeared. Furthermore, although the reflectors are evenly spaced on the ground, they are not evenly spaced in the processed image. Also, we wish to focus more on the area of the returns that actually contains objects.

Polar-to-rectangular interpolation of the image corrects for these issues. When you run the model, the image on the left is the matched-filtered image (before interpolation), and the image on the right is the final output. Each of these images have been transformed to the spatial domain using a two-dimensional inverse FFT. The final output of the SAR system focuses on the 6x8 grid of reflectors and shows crisp peaks that are not smeared.

**Polar-to-Rectangular Interpolation Details**

Polar-to-rectangular interpolation involves upsampling and interpolating to increase the range resolution of the output image. The interpolation operation takes the frequency-domain matched-filtered image as an input. It maps each row in the input image to several rows in the output image. The number of output rows to which each input row is mapped is determined by the number of sidelobes in the sinc function that is used for interpolation. The following figure shows, for each point in the matched filtered image, the central coordinate of the row it contributes to in the output image. The curvature in the figure shows the translation from a polar grid to a rectangular grid. The polar to rectangular interpolation is performed by MATLAB® code, which can effectively express the looping and indexing operations required with a minimum of temporary storage space.

[1] Soumekh, Mehrdad. *Synthetic Aperture Radar Signal Processing With MATLAB Algorithms.* John Wiley and Sons, 1999.

[2] MIT Lincoln Laboratory. "HPCS Scalable Synthetic Compact Application #3: Sensor Processing, Knowledge Formation, and Data I/O," Version 1.03, 15 March 2007.

[3] MIT Lincoln Laboratory. "High-Performance Embedded Computing Challenge Benchmark."

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