**ABSTRACT**

A time-domain back projection processor for airborne synthetic aperture radar (SAR) has been developed at the University of Massachusetts’ Microwave Remote Sensing Lab (MIRSL). The aim of this work is to produce a SAR processor capable of addressing the motion compensation issues faced by frequency-domain processing algorithms, in order to create well focused SAR imagery suitable for interferome- try.

The time-domain backprojection algorithm inherently compensates for non-linear platform motion, dependent on the availability of accurate measurements of the motion. The implementation must manage the relatively high computational burden of the back projection algorithm, which is done using modern graphics processing units (GPUs), programmed with NVIDIA’s CUDA language.

An implementation of the Non-Equispaced Fast Fourier Transform (NERFFT) is used to enable efficient and accurate range interpolation as a critical step of the processing. The phase of time domain processed imagery is different than that of frequency-domain imagery, leading to a potentially different approach to interferometry.

This general purpose SAR processor is designed to work with a novel, dual-frequency S- and Ka-band radar system developed at MIRSL as well as the UAVSAR instrument developed by NASA’s Jet Propulsion Laboratory. These instruments represent a wide range of SAR system parameters, ensuring the ability of the processor to work with most any airborne SAR. Results are presented from these two systems, showing good performance of the processor itself.

**SAR SIGNAL MODEL**

Linear-frequency modulated radar systems are commonly used on airborne and spaceborne platforms. These systems transmit a pulse whose frequency changes linearly with time. In such a configuration, there are two main dimensions of importance. There is the azimuth dimension corresponding to the flight track of the platform, and the range dimension which is measured orthogonal to the azimuth dimension.

** Platform Attitude:**

Relevant to the discussion of most synthetic aperture radar systems is a note about the attitude, or spatial orientation, of the radar platform. Especially for airborne systems, the orientation of the platform will not always be aligned with its direction of travel. It shows a depiction of this. The x-,y- and z-axes and flight track are defined the same, but here the current platform location is on the z axis. The TCN, or Track, Cross-Track, Nadir, coordinate system is defined relative to the platform motion such that T is aligned with the platform velocity vector.

**PROCESSING ALGORITHMS**

The signals recorded by a radar’s data acquisition system will be discrete versions of the received signals

sif[n,tm] = sif(n,mTs)

Note that tm is now a discrete time index, m, and that the brackets denote the entire signal as being discrete. From this point, it is the goal of the SAR processor to take these recorded signals and generate high resolution output imagery. The task is to generate a map (Rd) of backscatter values (σ) which amounts to inverting (2.5)or (2.14) forσ( ̄x).

**Frequency-Domain Algorithms:**

One approach to improve the speed of processing is to perform some of the processing in the frequency-domain. Algorithms such as range-Doppler, ωK or chirp scaling, fall into this category. These algorithms all begin with range / pulse compression, involving the start-stop approximation. From here, the range-Doppler algorithm performs the azimuth compression in the range-time, azimuth frequency domain.

**BACK PROJECTION INTERFEROMETRY**

**Traditional Interferometry:**

Traditional interferometry aims to use the residual processed phase to precisely measure the ncidence angle of the scatterer,θ′0. The major assumption made in this case is that the look vectors ̄ρ′0and ̄ρ′1are parallel. This assumption derives from the fact that B ρ (whereρ may be any of the involved ranges). By making this assumption, the difference in length between the look vectors (ρ′0−ρ′1) is simply one side of the right triangle.

**Backprojection Interferometry:**

Duersch develops another approach to interferometry based on backprojection processing. This development starts with the geometry and imagery of a back-projection processed scene, but for the generic case the same result may also be derived from the two-dimensional geometry.

**IMPLEMENTATION DETAILS**

This thesis presents details of the SAR Processor under development at UMass. It has the goal of creating highly accurate focused imagery from both the UAVSAR platform developed and operated by NASA’s Jet Propulsion Laboratory as well as two radar platforms under development at UMass Amherst. These two platforms are both side-looking cross-track interferometers. One operates at Ka-band using slotted waveguide antennas and the other at S-band using microstrip patch antennas.

**GPU Hardware:**

While the backprojection algorithm is a large improvement in speed over the time-domain correlation algorithm, it still has trouble keeping up with frequency-domain based approaches. A unique feature of the algorithm developed in this thesis is that it performs almost exactly the same computation for each output pixel. In fact, a trivial implementation would include a loop over every pixel which performs the sum.

**Motion Estimation and Autofocus:**

Since the backprojection processor requires precise knowledge of the antenna position and attitude, effort must be taken to ensure that they are measured accurately. Generally, these are measured using a combination of a GPS unit for position information, and an inertial navigation unit (INU) for attitude information.

**COORDINATE SYSTEMS**

There are several different coordinate systems in use by the processor. This chapter serves as a reference to them and their relations.

The core of the processing uses the earth-centered, earth-fixed (ECEF) Cartesian1 coordinate system. Here, the ECEF coordinate system is also referred to as the XYZ system. This system is a right-handed Cartesian coordinate system centered at the center of the earth’s mass. The x-axis points toward the intersection of the prime meridian and the equator. The y-axis points toward the intersection of the 90 degrees longitude and the equator. Thus the z-axis points (approximately) toward the north pole.

**PROCESSOR DESCRIPTION**

What is presented here is intended to provide the clearest understanding of how this processor works. In this discussion, the processor chain is defined to start with the data inputs, which have been recorded and made ready for the processor, and end with the focused SAR data outputs. Some system specific processing is done prior to running the processor, which includes any data format handling and potential GPS/INU motion post-processing. In the case of UAVSAR, the raw data is pulse-compressed externally from this processor, using existing tools.

**RESULTS**

Using this processor, preliminary results have been obtained with the two UMass systems and the UAVSAR instrument. Additionally, simulated data were processed to help evaluate the quality and accuracy of the processor itself.

Corner reflectors, due to their well behaved impulse response, are commonly used as point targets for radar system calibration. The system impulse response is often quantified by several measures, as described by Cumming. The first is resolution, or impulse response width, IRW, defined as the half-power beamwidth of the main lobe of the impulse response.

**Simulated Data:**

Using a simulator developed at the Jet Propulsion Laboratory, SAR data was generated with radar and flight parameters similar to a typical UAVSAR deployment. The simulation contains a number of corner reflectors on the ellipsoid surface (i.e.there is no DEM).

**CONCLUSION**

The majority of this work entailed the development of a time-domain backprojection processor, designed to use GPU hardware to improve runtime performance, and to work with a wide variety of airborne radar systems. The goal of the processor is to enable accurate processing in the face of non-linear aircraft motion, which is difficult to avoid, especially in low altitude aircraft.

Time-domain backprojection makes only minor assumptions about aircraft motion, much of which is correctable as described, making it particularly suitable for the application. To achieve good results, the processor must have good knowledge of the motion of the aircraft, which is not always easy to obtain. The motion data may be estimated and/or refined, using the Doppler information in the recorded radar data.

A critical step of the backprojection algorithm is the interpolation of the pulse-compressed data. Here, the NERFFT method is used, for both FMCW and pulsed systems. This method is able to provide high accuracy with limited computational cost.

Another important aspect of the algorithm is the substantial computational complexity. Though much less than that of pure time-domain correlation, the complexity is still significant when compared to traditional frequency-domain approaches. While this processor generally stresses accuracy, flexibility and usability the implementation medium was chosen to provide high performance. Interferometry is an important aspect of the relevant radar systems.

There has been limited work using backprojection processed imagery for interferometry and its ultimate suitability may be uncertain. Theoretically, it is shown to provide different performance over traditional methods, which generally use frequency-domain processing algorithms. Preliminary interferometric results have been shown using the backprojection processor and show promise.

**FUTURE WORK**

Further improvements may be made to the processor. One option to correct for unknown platform motion is to perform some type of autofocusing during data processing. This is commonly done with frequency-domain algorithms and has the potential to be extended to time-domain backprojection.

The unknown motion may also be corrected before processing. This can be done using estimation procedures that rely on Doppler information in the radar data. This is in part what is currently done with the UMass radar systems, but is very basic. Another option is to improve the motion measurement system itself, to improve the initial platform motion estimation.

Source: University of Massachusetts

Author: Dustin Lagoy