1. Sponsored By Abstract 1 Ritamar Siurano – Undergraduate Student Prof. Domingo Rodriguez – Advisor Abigail Fuentes – Graduate StudentProf. Ana B. Ramirez - Collaborator Inerys Otero – Graduate Assistant AIP Group – UPRM, ICPS Group - UIS RASP Group, ECE Department, E- mail:domingo@ece.uprm.edu University of Puerto Rico at Mayaguez 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), corner turning operations for NxN dimensional matrices, and the convolution process based on FFTs. Correlation implementation results of transmitted and received SAR signals are also presented in this work. Introduction 2 Synthetic 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. Methodology 3 The 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 (figure 2) was configured to test the various FFT algorithms, correlation and corner turning operations; iii) Computational results were obtained in terms of number of cycles and execution times. Results 4 Conclusions and Future Work 5 This work presented results for implementation efforts of correlation based on FFT and of corner turning algorithms on the TMS320C6713 DSP unit. It also presents the equivalence of the different correlation methods by using MATLAB. Future work for this project includes image formation with SAR data using these algorithms. References 6 [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 Figure 1 – SAR Imaging Infrastructure Figure 3: Correlation Calculation Methods Implemented in MATLAB The correlation was calculated using MATLAB in order to determine the similitude between a transmitted and received signal and the number of targets in range. TI’s Complex FFT Function Table 1: Internal Memory (196KB) Table 2: External Memory (16MB) Blind Test Correlation Figure 4: MATLAB Figure 5: Code Composer Studio Corner Turning Operation Table 3: Corner Turning Execution Times *Clock Frequency 225MHz In the Blind test for the correlation code all targets were correctly detected within the noise in the received signal data. In the FFT algorithm the internal memory execution ties were faster than those when using external memory. Still using internal memory is only possible for a very small amount of sampling points. In addition to this the FFT code in assembly language had faster execution times then that of the FFT written in C language. The Corner Turning operation also resulted to be faster when using internal memory, yet the algorithm produced a memory overflow error when used for anything larger than 128x128 complex variable matrix. Figure 2 (b)– TMS320C6713 Block Diagram TI’s Complex FFT function C TI’s Complex FFT function Assembly Number of Points Average Number of Cycles Average Execution Time (s) Average Number of Cycles Average Execution Time (s) 3241021.82E-055042.24E-06 64 93694.16E-059744.33E-06 128211649.41E-0520619.16E-06 256473032.10E-0445792.04E-05 5121058504.70E-04115285.12E-05 10242396971.07E-03328601.46E-04 20485226362.32E-03719343.19E-04 409611309995.03E-031556586.92E-04 TI’s Complex FFT function C TI’s Complex FFT function Assembly Number of Points Average Number of Cycles Average Execution Time (s) Average Number of Cycles Average Execution Time (s) 32323911.44E-04177357.88E-05 6478381 3.48E-04 39666 1.76E-04 1281808408.04E-0489046.393.96E-04 2564126671.83E-03199190.278.85E-04 5129286544.13E-034437421.96E-03 102420454609.09E-039668944.30E-03 204845029772.00E-022114933.39.40E-03 409698295734.37E-0245950902.04E-02 Corner Turning IRAM (196Kb) Corner Turning SDRAM (16Mb) Number of Points Average Number of Cycles Average Execution Time (s) Average Number of Cycles Average Execution Time (s) 32x32299761.3323E-0480676.83.59E-04 64x641182645.2562E-04321115.51.427E-03 128x1284699442.08864E-0312809945.693E-03 256x256-- 51172242.2743E-02 512x512-- 204555889.0914E-02 1024x1024-- 735437453.26861E-01