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Sponsored By

Abstract1

Ritamar Siurano – Undergraduate Student Prof. Domingo Rodriguez – AdvisorAbigail Fuentes – Graduate Student Prof. Ana B. Ramirez – Collaborator RASP Group, ECE Department, AIP Group - UPRM, ICPS Group - UIS University of Puerto Rico at Mayaguez E-mail: domingo@ece.uprm.edu

Rapid Systems Prototyping Laboratory (RASP) www.ece.uprm.edu/rasp

This work presents the design of DSP support algorithms for synthetic aperture radar (SAR) image formation operations. Computational results are presented for fast Fourier transforms (FFTs), matrix corner turning operations and the convolution process based on FFTs. Correlation implementation of transmitted and received SAR signals are also presented in this work.

Introduction2Synthetic aperture radar (SAR) image formation is a technique for obtaining images of the Earth’s surface through pulsed microwave transmitted and received signals. This system transmits a series of pulses at a fixed repetition rate and it collects the backscattered signals.

Through signal processing techniques the transmitted and received signals are treated by a SAR image formation system to produce an image that is usually enhanced in the azimuth direction when compared with standard real (vs. synthetic) aperture images. The main benefit of using a SAR instead of a RAR is that the length of the antenna is significantly reduced to obtain a more detailed image.

Methodology3The following procedure was used for the implementation of the algorithms: i) A TMS320C6713 DSP Starter Kit (DSK) was utilized as development platform; ii) The TMS320C6713 DSP(figure2) was configured to test the various FFT algorithms; iii) These FFT algorithms were used to develop the indirect convolution process, the correlation algorithm(figure3) and corner turning implementation; iv) Computational results were obtained in terms of number of cycles and execution times; v) Range and Azimuth compression algorithms were developed using MATLAB.

Results4

Conclusions5This work presents the results for implementation efforts of FFT and of corner turning algorithms on the TMS320C6713 DSP unit. For these algorithms, the execution times obtained on the DSP unit were faster using internal memory. It also validates correlation algorithm results from CCS, and presents the image formation algorithms using range and azimuth compression in MATLAB.

References6[1] A. Ramirez, M. Rodriguez, D. Rodriguez, “TMS320C6713 User’s Guide, ”University of Puerto Rico Mayaguez Campus, Mayaguez, Puerto Rico, 2007.

[2] R. Chassaing, Digital Signal Processing and Application with the C6713 and C6416 DSK, Wiley-Interscience, John Wiley & Sons, Inc., NY, 2005.

DSP Implementation of SAR Support Algorithms

Figure 2 (a) – TMS320C6713 Board

sin2

}{c

Rres

Range ResolutionRange Resolution

Azimuth ResolutionAzimuth Resolution

RADARTRAJECTORY

RADARFOOTPRINT

RADAR PULSE

L

swath

Courtesy of RADARSAT

r

L

rAres r

}{RAR

2}{L

Ares s SAR

Figure 1 – SAR Imaging Infrastructure

TI’s Complex FFT Function

Table 1: Internal Memory (196KB)

Table 2: External Memory (16MB)

Blind Test Correlation

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Figure 4: MATLAB

Figure 5: Code Composer Studio

Corner Turning Operation

Table 3: Corner Turning Execution Times

*Clock Frequency 225MHz

*Clock Frequency 225MHz

TI’s Complex FFT functionC

TI’s Complex FFT functionAssembly

Number of Points

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Cycles

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32 4102 1.82E-05 504 2.24E-0664 9369 4.16E-05 974 4.33E-06128 21164 9.41E-05 2061 9.16E-06256 47303 2.10E-04 4579 2.04E-05512 105850 4.70E-04 11528 5.12E-051024 239697 1.07E-03 32860 1.46E-042048 522636 2.32E-03 71934 3.19E-044096 1130999 5.03E-03 155658 6.92E-04

TI’s Complex FFT functionC

TI’s Complex FFT functionAssembly

Number of Points

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Time(s)

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Average Execution

Time(s)

32 32391 1.44E-04 17735 7.88E-0564 78381 3.48E-04 39666 1.76E-04128 180840 8.04E-04 89046.39 3.96E-04256 412667 1.83E-03 199190.27 8.85E-04512 928654 4.13E-03 443742 1.96E-031024 2045460 9.09E-03 966894 4.30E-032048 4502977 2.00E-02 2114933.3 9.40E-034096 9829573 4.37E-02 4595090 2.04E-02

Corner TurningIRAM (196Kb)

Corner TurningSDRAM (16Mb)

Number of Points

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Average Execution

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Average Number of

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Average Execution

Time(s)

32x32 29976 1.3323E-04 80676.8 3.59E-0464x64 118264 5.2562E-04 321115.5 1.427E-03128x128 469944 2.08864E-03 1280994 5.693E-03256x256 -- -- 5117224 2.2743E-02512x512 -- -- 20455588 9.0914E-021024x1024 -- -- 73543745 3.26861E-01

Zero-padding DFT

DFT

IDFT

rT,R [n]

Zero-padding

sR

sT Index Reversal

Figure 3 – FFT Based Correlation Algorithm

Image Formation Results in MATLABFigure 6 128X128 Image

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