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SAR Case Study

2.0 Overview of the Problem with the Synthetic Aperture Array System

2.1 Synthetic Aperture Array System

For more details, go to the Lincoln Laboratory website

The ADTS radar is a fully polarimetric, air-to-ground SAR that operates stripmap mode with a +90-degree squint angle; that is, the radar points +90 degrees relative to the velocity vector. The transmitter alternates between H-pol and V-pol, while H-pol and V-pol are simultaneously processed in the receiver. The radar transmits at a 3-kHz rate, so that the same-polarization pulse repetition frequency (PRF) is 1.5 kHz. The resolution is 0.3 meters.

The system de-ramped, down-converted, and filtered the linear frequency modulated (LFM) pulses, providing inputs to the A/D (analog to digital) converters that were real, uncompressed (i.e., frequency domain) data. The data corresponded to a 375-meter range swath. The system sampled pulse data using 8-bit A/D converters at a 125-MHz rate, yielding 4064 real samples per pulse. The range window for the radar was 468.4 meters with a 375-meter range swath at the center of the range window. After digitization, the system compensated the phase and frequency for non- linear motion of the aircraft and timing errors in the de-ramp process. Pulses were also processed for Doppler and re- sampled (interpolated) to yield a constant spatial interval of 0.2287 meters along the flight path. This represented a PRF of 437 Hz for a nominal aircraft velocity of 100 meters/second. The output of the re-sampling process was pulse data with 11 bits of precision.

Figure 2- 2 shows the proposed ADTS SAR processing system. Data was recorded from the original system after azimuth re-sampling and A/D conversion. With a real-time processor, the data would be sent to the SAR signal processor as 40-bit words transmitted serially over a fiber-optic link. In the laboratory, the recorded data was supplied to the SAR processor from real-time source/sink test equipment. The functions implemented in the benchmark SAR processor were those inside the dashed lines of Figure 2- 2. The Team did not implement the other post-processing functions at that time, but it did size the SAR processor to provide future upgrade capability to include these functions.

2.2 Synthetic Aperture Radar Processing Algorithms

During operation, the SAR processor continuously formed images for up to three, user selectable, polarizations. Figure 2- 3 shows the processing flow. In addition to the continuous process of image formation, there was a setup process prior to processing the first PRI of data that loaded the required parameters.

Figure 2- 3: SAR processing flow.

The SAR signal processor received channels of polarized pulse, header , and auxiliary (Aux) data. A 20-word sequence indicated the start of pulse data. This sequence was a 13-word Barker code, five leading zeros, and two trailing don't-care words. This sequence was followed by 2032 words of 11-bit even-pulse samples and 11-bit odd-pulse samples, sign extended to 12 bits. Included with the pulse samples were header and Aux data recorded in bit-serial fashion and duplicated in bit positions 3, 16, 19, and 32 of the 40-bit data word. Header data described the polarization of the pulse data, and Aux data contained ancillary navigation and radar data. Pulse data for the four polarizations were outputted in a repeated sequence; that is, ... HH, HV, VH, VV, HH, ... Aux data was only written for the leading pulse of the sequence; that is, HH. There was arbitrary length-filler data between the end-of-data for one pulse and the start sequence for the next pulse.

Because the HV and VH polarizations ideally contain the same information, the system used at most three of the four polarizations to form images. Generally, images were formed for the HH and VV polarizations and either the HV or the VH polarization, as established by the operator through the RS- 232 control interface. Therefore, it was necessary to process and retain pulse polarization information from the header. Aux data also had to be processed to extract slant range information used by the processing.

Prior to pulse compression, the system converted 4064 real video samples of each polarization to be imaged to in- phase and quadrature or I/Q data at baseband. The system created the basebanding operation by forming sequences of even/odd pulse samples and then modulating each sequence by (- 1)ⁿ. This yielded two real-value sequences for each pulse:

• An even sample sequence, { s₀, -s₂, s₄, -s₆, ... , - s₄₀₆₂ },
• An odd sample sequence { s₁, -s₃, s₅, -s₇, ... , - s₄₀₆₃ },
  where s_n is the nth real sample.
  A detailed description of the processing is contained in in the MIT Lincoln Laboratory paper [Zuerndorfer94]

The system then passed the sequence through a FIR (Finite Impulse Response) filter, which had from 8 to 48 taps. For example, an 8- coefficient FIR filter yielded the sequence{ si₀, si₁, si₂, ..., si₂₀₂₃}. The FIR filter output sequence was 8 samples shorter than the FIR input sequence because the system had to initialize the filter before valid data samples were obtained. Similarly, the odd sequence was passed through the FIR filter to yield the sequence{ sq₀, sq₁, sq₂, ..., sq₂₀₂₃}. These sequences were combined to form the sequence of complex samples { (si₀, sq₀), (si₁, sq₁), ..., (si₂₀₂₃, sq₂₀₂₃)}.

During pulse compression, the system transformed the 2024 uncompressed I/Q samples of each pulse into a compressed-range pulse with 2048 samples. Each of the 2048 samples constituted a range-gate. Pulse compression began by applying weighting to the complex valued I/Q data. Weighting reduced the sidelobes of the compressed pulse and was applied to the 2024 complex input samples with trailing zero-pads to expand the data to 2048 samples. The system modulated the complex input data by (- 1)ⁿ , where n = 0, ... , 2047, so that the compressed range pulses were centered in the range window. The complex equalization weights were down -loaded via the control interface to the SAR processor prior to real-time operation. These weights were polarization-specific. Polarization designations, extracted from the data header, had to be used to establish which set of equalization weights to apply to a given set of data.

Weighted I/Q data was transformed to compressed range data using a 2048-point DFT. To compensate for radar cross- section (RCS) variations from elevation beam-shape modulation and for losses across the range swath, amplitude weights were applied to samples of the compressed pulse. The RCS weights were down-loaded via the control interface to the SAR processor prior to real-time operation.

Compressed pulses were placed in time sequence in a 2-D array called a frame. Each row of the frame contained 512 pulses and each column contained 2048 range gates. Each frame, then, was a 2048 x 512 array. Once 512 pulses had accumulated to form a frame, the frame was shifted into the processing array. The processing array was a 2-D array, where azimuth compression processing was performed. The processing array consisted of two frames and was a 2048 x 1024 array. As each new frame was shifted into the processing array, the oldest frame was shifted out. A convolution was performed along each row of the processing array. The convolution processing was performed using DFTs with the overlap-save method. A 1024-point DFT of each row was multiplied with the 1024-point DFT of the associated convolution kernel. The convolution kernels were 512 points long, but trailing zeros were used to pad-out the kernel to 1024 points. Each vector product was inverse transformed, and the last 512 samples of each inverse transform represented valid convolution outputs and were saved in an image array. A new frame was shifted into the processing array, the convolution process was repeated, and more data was added to the image array, thereby generating the output SAR image.

The convolution kernel used for each row was selected from a database of 31 pre-calculated kernels, where the kernels had been Taylor weighted, zero padded, and Fourier transformed. The choice of kernel was determined by the slant range to the middle of the most recent frame in the processing array. This slant range was contained in the Aux record of the 256th pulse of the most recent frame. The kernels were calculated based on the slant range to the middle of the first frame of data obtained for a given pass, and they were stored for use throughout the pass. Only 16 of the 31 stored kernels were used at one time in azimuth compression, but the 16 vary with each frame. See Figure 2- 4 for an example SAR image output.

2.3 Form Factor Constraints

The maximum allowable dimensions for the processor were 10.5," 20.5," and 17.5." These dimensions encompass chassis, cooling fans, power supply, and cable headers and were consistent with the use of the processor on board the Amber UAV. The Amber is a long endurance UAV produced by Leading Systems, Inc., during the 1980s. It is approximately 18 feet long (Figure 2- 5) and has a demonstrated flight endurance of 30 to 35 hours.

Figure 2- 5: Amber UAV.

The system architecture had to be scalable to support at least twice the processing and twice the aggregate communication bandwidth as that implemented in the initial configuration. In addition to space for future expansion in the algorithm, room also had to be available in the processor box for the addition of a 4-slot 6U VME chassis. The provision for a VME chassis, or availability of four contiguous slots in an existing internal chassis, was to enable the use of commercial VME boards for display or subsequent processing of the images.

The weight for a fully loaded chassis, including the 4 slot VME chassis, was not to exceed 60 pounds. Air cooling in a non-condensing environment was used, and the temperature range of the ambient air was 0^o C to 40^o C.

The SAR processor power supply had an input voltage of 24 to 32 volts DC, with average input power not exceeding 500 watts in the baseline system and 750 watts in the fully expanded system.

2.4 Accuracy

2.5 Latency

2.6 Data Interfaces

2.7 Control and Diagnostic Interface

2.8 Summary