Digital Programmable Gaussian Noise Generator WPI – MIT Lincoln Laboratory A Major Qualifying Project Submitted to the faculty of the WORCESTER POLYTECHNIC INSTITUTE in partial fulfillment of the requirements for the Degree of Bachelor of Science in Electrical and Computer Engineering by ________________________________ Karen L. Fitch Date: October 30, 2015 ________________________________ Kathryn A. Gillis Date: October 30, 2015 ________________________________ Abby W. Harrison Date: October 30, 2015 Approved: ________________________________ Edward A. Clancy, Faculty Advisor, WPI Date: October 30, 2015 This work is sponsored by the Department of the Air Force under Air Force Contract #FA8721- 05-C-0002. Opinions, interpretations, conclusions, and recommendations are those of the authors and not necessarily endorsed by the United States Government. 1 Abstract Electronic countermeasures are critical to air vehicle survivability. Noise jamming is a technique used to prevent radar from tracking targets by taking advantage of a radar’s sensitivity to noise. Gaussian noise is preferred for this purpose because it is more difficult to eliminate than structured noise. This project produced a digital Gaussian noise generator based around a field programmable gate array (FPGA) with programmable bandwidth, center frequency, and amplitude to be used by Group 108 within MIT Lincoln Laboratory. Noise produced by the generator is band limited white in frequency with a Gaussian probability density function, as verified both visually and via statistical tests. The device is a strong improvement over existing technology used by Group 108 and it will be used in laboratory and over-the-air testing for researching the effects of Gaussian noise on various radar systems. 2 Statement of Authorship In this project, all three group members contributed to work on all parts of the design and implementation of the final device. All members also contributed to editing all sections of the paper, but sections were written individually as follows: Karen Fitch: Sections 1.0, 2.5, 3.1, 3.2, Chapter 6 Kathryn Gillis: Sections 2.1, 2.3, 3.4.1, 3.4.3, Chapter 4 Abby Harrison: Sections 2.2, 2.4, 3.3, 3.4.2, 3.4.3, Chapter 5 All members wrote the Abstract and Executive Summary 3 Acknowledgements We would like to thank Lisa Basile, Sarah Curry, Emily Fenn and Chris Massa for mentoring us throughout our time at MIT Lincoln Laboratory and for assisting us in understanding and completing our project. We would also like to thank Professor Edward Clancy, our WPI advisor, for guiding us and consistently encouraging us to improve our project. Additional thanks go to Dave Baur, Jim Burke, Bob Giovanucci, Dave McQueen and Andy Messier for their important contributions to our project. 4 Table of Contents Abstract ........................................................................................................................................... 1 Statement of Authorship ................................................................................................................. 3 Acknowledgements ......................................................................................................................... 4 Table of Contents ............................................................................................................................ 5 Table of Figures .............................................................................................................................. 7 Table of Tables ............................................................................................................................... 9 Executive Summary ...................................................................................................................... 10 2.0 Background ............................................................................................................................. 15 2.1 Gaussian Noise and Radar ................................................................................................... 15 2.1.1 Radar Overview ............................................................................................................ 15 2.1.2 Radar Pulse Generation ................................................................................................ 16 2.1.3 Effects of Noise on Radar ............................................................................................. 19 2.1.4 Jamming Techniques .................................................................................................... 19 2.1.5 Effectiveness of White Gaussian Noise in Jamming .................................................... 20 2.2 Gaussian Characteristics ..................................................................................................... 20 2.2.1 Defining Characteristics ............................................................................................... 20 2.2.2 How to Test Characteristics .......................................................................................... 24 2.3 Group 108 Testing Environment ......................................................................................... 27 2.3.1 Radar Open Systems Architecture ................................................................................ 27 2.3.2 Existing Noise Sources in Group 108 ........................................................................... 28 2.4 Digital Generation of Gaussian Noise ................................................................................. 28 2.4.2 Pseudorandom Number Generation .............................................................................. 29 2.4.3 Techniques for Digitally Generating Gaussian Distributions ....................................... 29 2.5 Digital Programmability ...................................................................................................... 33 2.5.1 Center Frequency and Bandwidth ................................................................................ 33 2.5.2 Amplitude ..................................................................................................................... 37 3.0 Methods................................................................................................................................... 38 3.1 Project Requirements .......................................................................................................... 38 3.2 Gaussian Test Suite ............................................................................................................. 39 3.3 Hardware Selection ............................................................................................................. 39 3.4 Implementation .................................................................................................................... 40 3.4.1 Random Number Algorithm Selection and Implementation ........................................ 40 3.4.2 Programmability ........................................................................................................... 48 Determining Center Frequency and Bandwidth .................................................................... 48 User Interface ........................................................................................................................ 51 5 4.0 Results ..................................................................................................................................... 54 4.1 Simulation Results .............................................................................................................. 54 4.2 Output Test Results ............................................................................................................. 60 4.3 ROSA Data .......................................................................................................................... 64 5.0 Discussion ............................................................................................................................... 66 6.0 Conclusion .............................................................................................................................. 70 Works Cited .................................................................................................................................. 72 Appendix A – Hardware Platform Value Analysis ....................................................................... 75 Appendix B – MATLAB Simulation of Uniform Data Through ROSA ...................................... 76 6 Table of Figures Figure 1: Comparison of KC705 Noise Generator to WhiteBox Lite Noise ................................ 13 Figure 2: IQ Data .......................................................................................................................... 16 Figure 3: Mixing a signal to a desired center frequency ............................................................... 17 Figure 4: IQ data generation by digital mixing (top) and analog mixing (bottom) ...................... 18 Figure 5: MATLAB-generated autocorrelation of white Gaussian noise vs. band-limited Gaussian noise ....................................................................................................................... 21 Figure 6: MATLAB-generated power spectral density plots of white vs. band-limited noise ..... 22 Figure 7: Gaussian distribution with zero-mean and standard deviation of 1 .............................. 23 Figure 8: Rayleigh distribution with