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Pulse Compression for Different Types of Radar Signals Thesis no: MCS-2012-09 Pulse compression for different types of radar signals. This thesis is presented as of Bachelor Science in Electrical Engineering with Emphasis on Telecommunication Blekinge Institute of Technology September 2012 Blekinge Institute of Technology School of Engineering Department of Electrical Engineering Supervisor: Mats Pettersson Authors: Tomás Garnacho Aparicio & Alberto Trejo Roldán 2 2 3 Abstract The aim of our project is to compare pulse compression of different waveforms using correlation of real signals or matched filter for analytic signals. In this thesis a set of programs is developed for this comparison. The characteristic of the matched filter is that it processes the highest possible Signal to Noise ratio (SNR) under the assumption of white noise. The implementation of the algorithm is made in Matlab. Radar signal processors are usually carried out over a specified range window. Returns from all targets within the received window are collected and passed through the matched filter to perform the pulse compression. Because of the recent development of digital signal processors (DSPs), this process is often performed digitally. The aim of this work is to get better quality in the radar images, including SAR (Synthetic Aperture Radar) and to explain the characteristics of each waveform. The thesis also includes an appendix, where the implemented programs and program code are attached. The work also aims at illustrative and didactic purposes. The programs have been developed so as to be easily understood and therefore useful for engineering students. 3 4 4 5 Gracias a todos aquellos que me han acompañado en este camino. A mi madre. “Si caes, levántate... si vuelves a caer, levántate otra vez... Y si vuelves a caer levántate una y otra vez... Sólo en la lucha, la fe, la constancia y la fuerza de voluntad llegaremos al triunfo...” “If you fall, get up... If you fall back again, then get up again... and if you fall back once more, get up again and again. In struggle, faith, perseverance and power are the ways to achieve the victory..." Tomás 5 6 6 7 Firstly, I would like to thank to everyone who helped us with our thesis during our stay as exchange students in Blekinge Tekniska Högskola. I especially want to mention our project supervisor Mats Pettersson for his help and support from the very beginning of the project. Furthermore I also want to give thanks to all the classmates I met during my studies as well as all the friends that were not studying with me but giving me their support, though. Additionally I am grateful for meeting so many great persons during my stay, especially Tamara, and I want to thank them for the help they were during my time in Sweden. Finally I want to thank my family, especially my parents and my sister who gave me the possibility to study abroad and their endless support and help. Alberto 7 8 8 9 Table of contents Abstract ................................................................................................................................... 3 Table of contents .................................................................................................................... 9 List of Figures ....................................................................................................................... 11 List of Acronyms .................................................................................................................. 13 Chapter 1 Introduction .......................................................................................................... 15 Chapter 2 Matched Filter ...................................................................................................... 17 2.1. Fundamentals of the Matched Filter................................................................... 17 2.2. Range Resolution Properties .............................................................................. 20 Chapter 3 Analysis Matched Filter Response of Linear Frequency Modulated Waveforms (chirp) ................................................................................................................................... 25 3.1. Basics of Linear FM Waveforms ....................................................................... 25 3.2. Frequency analysis of Linear FM Waveforms ................................................... 27 3.3. Pulse Compression Process ................................................................................ 33 Chapter 4 Cross-Correlation ................................................................................................. 37 Chapter 5 Analytic Signal .................................................................................................... 43 5.1. Definition of Hilbert transforms. ........................................................................ 43 5.2. Analytic Signal Application ............................................................................... 44 Chapter 6 Different types of radar signals ............................................................................ 53 6.1. Binary phase coded pulse ................................................................................... 53 6.2. Square pulse ....................................................................................................... 61 Chapter 7 Conclusions .......................................................................................................... 67 9 10 References ............................................................................................................................ 69 Appendix .............................................................................................................................. 73 Program code ................................................................................................................ 73 10 11 List of Figures Figure 1.Matched Filter maximizes the signal peak to mean noise ratio. ................................................... 20 Figure 2. llustration of a square pulse and its corresponding spectra. ........................................................ 21 Figure 3. Square Pulse compressed ............................................................................................................ 22 Figure 4. Comparison between the ultimate resolution of a rectangular constant frequency and a chirp pulse ................................................................................................................................................. 23 Figure 5. Output pulse compression filter. ................................................................................................. 24 Figure 6. Real part and imaginary part of signal chirp ................................................................................ 26 Figure 7. Signal chirp in the frequency domain by the use of FFT ............................................................... 28 Figure 8. Graphical Representation of signal delay. ................................................................................... 29 Figure 9. Signal chirp delayed in the frequency domain by the use of FFT .................................................. 30 Figure 10. Ramp function to implement the delayed signal. ...................................................................... 31 Figure 11. Comparison of signal chirp and signal chirp delayed in the frequency domain .......................... 32 Figure 12. Comparison of signal chirp and signal chirp delayed in the time domain ................................... 33 Figure 13. Fast Convolution Processor ....................................................................................................... 34 Figure 14. Response in frequency after after the matched filter ................................................................ 35 Figure 15. Output of the matched filter ..................................................................................................... 36 Figure 16. Convolution of Reflected echo and Time reversed pulse ........................................................... 38 Figure 17. Convolution of Reflected echo and Time reversed pulse. Intermediate step ............................. 38 Figure 18. Convolution of Reflected echo and Time reversed pulse. Finished convolution ......................... 39 Figure 19. Matched filter by cross-correlation process ............................................................................... 40 Figure 20. Comparison of the responses of matched filter and cross-correlation process for a transmitted signal ................................................................................................................................................ 41 11 12 Figure 21. Comparison of the envelopes of the responses of matched filter and cross-correlation process for a transmitted signal .................................................................................................................... 42 Figure 22. Real part and imaginary part of analytic signal. Orthogonal vectors .......................................... 44 Figure 23. Analytic signal property Hilbert ................................................................................................. 46 Figure 24. Diagram of the generation of the analytic signal ....................................................................... 47 Figure 25. Comparison between the original chirp signal and the recovered signal ..................................
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