DOCSLIB.ORG

Digital Programmable Gaussian Noise Generator

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Digital Programmable Gaussian Noise Generator 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
Load more

Recommended publications
  • EN 300 676 V1.2.1 (1999-12) European Standard (Telecommunications Series)
    Draft ETSI EN 300 676 V1.2.1 (1999-12) European Standard (Telecommunications series) Electromagnetic compatibility and Radio spectrum Matters (ERM); Ground-based VHF hand-held, mobile and fixed radio transmitters, receivers and transceivers for the VHF aeronautical mobile service using amplitude modulation; Technical characteristics and methods of measurement 2 Draft ETSI EN 300 676 V1.2.1 (1999-12) Reference REN/ERM-RP05-014 Keywords Aeronautical, AM, DSB, radio, testing, VHF ETSI Postal address F-06921 Sophia Antipolis Cedex - FRANCE Office address 650 Route des Lucioles - Sophia Antipolis Valbonne - FRANCE Tel.:+33492944200 Fax:+33493654716 Siret N° 348 623 562 00017 - NAF 742 C Association à but non lucratif enregistrée à la Sous-Préfecture de Grasse (06) N° 7803/88 Internet [email protected] Individual copies of this ETSI deliverable can be downloaded from http://www.etsi.org If you find errors in the present document, send your comment to: [email protected] Important notice This ETSI deliverable may be made available in more than one electronic version or in print. In any case of existing or perceived difference in contents between such versions, the reference version is the Portable Document Format (PDF). In case of dispute, the reference shall be the printing on ETSI printers of the PDF version kept on a specific network drive within ETSI Secretariat. Copyright Notification No part may be reproduced except as authorized by written permission. The copyright and the foregoing restriction extend to reproduction in all media. © European
    [Show full text]
  • Blind Denoising Autoencoder
    1 Blind Denoising Autoencoder Angshul Majumdar In recent times a handful of papers have been published on Abstract—The term ‘blind denoising’ refers to the fact that the autoencoders used for signal denoising [10-13]. These basis used for denoising is learnt from the noisy sample itself techniques learn the autoencoder model on a training set and during denoising. Dictionary learning and transform learning uses the trained model to denoise new test samples. Unlike the based formulations for blind denoising are well known. But there has been no autoencoder based solution for the said blind dictionary learning and transform learning based approaches, denoising approach. So far autoencoder based denoising the autoencoder based methods were not blind; they were not formulations have learnt the model on a separate training data learning the model from the signal at hand. and have used the learnt model to denoise test samples. Such a The main disadvantage of such an approach is that, one methodology fails when the test image (to denoise) is not of the never knows how good the learned autoencoder will same kind as the models learnt with. This will be first work, generalize on unseen data. In the aforesaid studies [10-13] where we learn the autoencoder from the noisy sample while denoising. Experimental results show that our proposed method training was performed on standard dataset of natural images performs better than dictionary learning (K-SVD), transform (image-net / CIFAR) and used to denoise natural images. Can learning, sparse stacked denoising autoencoder and the gold the learnt model be used to recover images from other standard BM3D algorithm.
    [Show full text]
  • A Comparison of Delayed Self-Heterodyne Interference Measurement of Laser Linewidth Using Mach-Zehnder and Michelson Interferometers
    Sensors 2011, 11, 9233-9241; doi:10.3390/s111009233 OPEN ACCESS sensors ISSN 1424-8220 www.mdpi.com/journal/sensors Article A Comparison of Delayed Self-Heterodyne Interference Measurement of Laser Linewidth Using Mach-Zehnder and Michelson Interferometers Albert Canagasabey 1,2,*, Andrew Michie 1,2, John Canning 1, John Holdsworth 3, Simon Fleming 2, Hsiao-Chuan Wang 1,2 and Mattias L. Åslund 1 1 Interdisciplinary Photonics Laboratories (iPL), School of Chemistry, University of Sydney, 2006, NSW, Australia; E-Mails: [email protected] (A.M.); [email protected] (J.C.); [email protected] (H.-C.W.); [email protected] (M.L.Å.) 2 Institute of Photonics and Optical Science (IPOS), School of Physics, University of Sydney, 2006, NSW, Australia; E-Mail: [email protected] (S.F.) 3 SMAPS, University of Newcastle, Callaghan, NSW 2308, Australia; E-Mail: [email protected] (J.H.) * Author to whom correspondence should be addressed; E-Mail: [email protected]; Tel.: +61-2-9351-1984. Received: 17 August 2011; in revised form: 13 September 2011 / Accepted: 23 September 2011 / Published: 27 September 2011 Abstract: Linewidth measurements of a distributed feedback (DFB) fibre laser are made using delayed self heterodyne interferometry (DHSI) with both Mach-Zehnder and Michelson interferometer configurations. Voigt fitting is used to extract and compare the Lorentzian and Gaussian linewidths and associated sources of noise. The respective measurements are wL (MZI) = (1.6 ± 0.2) kHz and wL (MI) = (1.4 ± 0.1) kHz. The Michelson with Faraday rotator mirrors gives a slightly narrower linewidth with significantly reduced error.
    [Show full text]
  • Pink Noise Generator
    PINK NOISE GENERATOR K4301 Add a spectrum analyser with a microphone and check your audio system performance. H4301IP-1 VELLEMAN NV Legen Heirweg 33 9890 Gavere Belgium Europe www.velleman.be www.velleman-kit.com Features & Specifications To analyse the acoustic properties of a room (usually a living- room), a good pink noise generator together with a spectrum analyser is indispensable. Moreover you need a microphone with as linear a frequency characteristic as possible (from 20 to 20000Hz.). If, in addition, you dispose of an equaliser, then you can not only check but also correct reproduction. Features: Random digital noise. 33 bit shift register. Clock frequency adjustable between 30KHz and 100KHz. Pink noise filter: -3 dB per octave (20 .. 20000Hz.). Easily adaptable to produce "white noise". Specifications: Output voltage: 150mV RMS./ clock frequency 40KHz. Output impedance: 1K ohm. Power supply: 9 to 12VAC, or 12 to 15VDC / 5mA. 3 Assembly hints 1. Assembly (Skipping this can lead to troubles ! ) Ok, so we have your attention. These hints will help you to make this project successful. Read them carefully. 1.1 Make sure you have the right tools: A good quality soldering iron (25-40W) with a small tip. Wipe it often on a wet sponge or cloth, to keep it clean; then apply solder to the tip, to give it a wet look. This is called ‘thinning’ and will protect the tip, and enables you to make good connections. When solder rolls off the tip, it needs cleaning. Thin raisin-core solder. Do not use any flux or grease. A diagonal cutter to trim excess wires.
    [Show full text]
  • Estimation from Quantized Gaussian Measurements: When and How to Use Dither Joshua Rapp, Robin M
    1 Estimation from Quantized Gaussian Measurements: When and How to Use Dither Joshua Rapp, Robin M. A. Dawson, and Vivek K Goyal Abstract—Subtractive dither is a powerful method for remov- be arbitrarily far from minimizing the mean-squared error ing the signal dependence of quantization noise for coarsely- (MSE). For example, when the population variance vanishes, quantized signals. However, estimation from dithered measure- the sample mean estimator has MSE inversely proportional ments often naively applies the sample mean or midrange, even to the number of samples, whereas the MSE achieved by the when the total noise is not well described with a Gaussian or midrange estimator is inversely proportional to the square of uniform distribution. We show that the generalized Gaussian dis- the number of samples [2]. tribution approximately describes subtractively-dithered, quan- tized samples of a Gaussian signal. Furthermore, a generalized In this paper, we develop estimators for cases where the Gaussian fit leads to simple estimators based on order statistics quantization is neither extremely fine nor extremely coarse. that match the performance of more complicated maximum like- The motivation for this work stemmed from a series of lihood estimators requiring iterative solvers. The order statistics- experiments performed by the authors and colleagues with based estimators outperform both the sample mean and midrange single-photon lidar. In [3], temporally spreading a narrow for nontrivial sums of Gaussian and uniform noise. Additional laser pulse, equivalent to adding non-subtractive Gaussian analysis of the generalized Gaussian approximation yields rules dither, was found to reduce the effects of the detector’s coarse of thumb for determining when and how to apply dither to temporal resolution on ranging accuracy.
    [Show full text]
  • Image Denoising by Autoencoder: Learning Core Representations
    Image Denoising by AutoEncoder: Learning Core Representations Zhenyu Zhao College of Engineering and Computer Science, The Australian National University, Australia, [email protected] Abstract. In this paper, we implement an image denoising method which can be generally used in all kinds of noisy images. We achieve denoising process by adding Gaussian noise to raw images and then feed them into AutoEncoder to learn its core representations(raw images itself or high-level representations).We use pre- trained classifier to test the quality of the representations with the classification accuracy. Our result shows that in task-specific classification neuron networks, the performance of the network with noisy input images is far below the preprocessing images that using denoising AutoEncoder. In the meanwhile, our experiments also show that the preprocessed images can achieve compatible result with the noiseless input images. Keywords: Image Denoising, Image Representations, Neuron Networks, Deep Learning, AutoEncoder. 1 Introduction 1.1 Image Denoising Image is the object that stores and reflects visual perception. Images are also important information carriers today. Acquisition channel and artificial editing are the two main ways that corrupt observed images. The goal of image restoration techniques [1] is to restore the original image from a noisy observation of it. Image denoising is common image restoration problems that are useful by to many industrial and scientific applications. Image denoising prob- lems arise when an image is corrupted by additive white Gaussian noise which is common result of many acquisition channels. The white Gaussian noise can be harmful to many image applications. Hence, it is of great importance to remove Gaussian noise from images.
    [Show full text]
  • Generating Realistic City Boundaries Using Two-Dimensional Perlin Noise
    Generating realistic city boundaries using two-dimensional Perlin noise Graduation thesis for the Doctoraal program, Computer Science Steven Wijgerse student number 9706496 February 12, 2007 Graduation Committee dr. J. Zwiers dr. M. Poel prof.dr.ir. A. Nijholt ir. F. Kuijper (TNO Defence, Security and Safety) University of Twente Cluster: Human Media Interaction (HMI) Department of Electrical Engineering, Mathematics and Computer Science (EEMCS) Generating realistic city boundaries using two-dimensional Perlin noise Graduation thesis for the Doctoraal program, Computer Science by Steven Wijgerse, student number 9706496 February 12, 2007 Graduation Committee dr. J. Zwiers dr. M. Poel prof.dr.ir. A. Nijholt ir. F. Kuijper (TNO Defence, Security and Safety) University of Twente Cluster: Human Media Interaction (HMI) Department of Electrical Engineering, Mathematics and Computer Science (EEMCS) Abstract Currently, during the creation of a simulator that uses Virtual Reality, 3D content creation is by far the most time consuming step, of which a large part is done by hand. This is no different for the creation of virtual urban environments. In order to speed up this process, city generation systems are used. At re-lion, an overall design was specified in order to implement such a system, of which the first step is to automatically create realistic city boundaries. Within the scope of a research project for the University of Twente, an algorithm is proposed for this first step. This algorithm makes use of two-dimensional Perlin noise to fill a grid with random values. After applying a transformation function, to ensure a minimum amount of clustering, and a threshold mech- anism to the grid, the hull of the resulting shape is converted to a vector representation.
    [Show full text]
  • ECE 417 Lecture 3: 1-D Gaussians Mark Hasegawa-Johnson 9/5/2017 Contents
    ECE 417 Lecture 3: 1-D Gaussians Mark Hasegawa-Johnson 9/5/2017 Contents • Probability and Probability Density • Gaussian pdf • Central Limit Theorem • Brownian Motion • White Noise • Vector with independent Gaussian elements Cumulative Distribution Function (CDF) A “cumulative distribution function” (CDF) specifies the probability that random variable X takes a value less than : Probability Density Function (pdf) A “probability density function” (pdf) is the derivative of the CDF: That means, for example, that the probability of getting an X in any interval is: Example: Uniform pdf The rand() function in most programming languages simulates a number uniformly distributed between 0 and 1, that is, Suppose you generated 100 random numbers using the rand() function. • How many of the numbers would be between 0.5 and 0.6? • How many would you expect to be between 0.5 and 0.6? • How many would you expect to be between 0.95 and 1.05? Gaussian (Normal) pdf Gauss considered this problem: under what circumstances does it make sense to estimate the mean of a distribution, , by taking the average of the experimental values, ? He demonstrated that is the maximum likelihood estimate of if Gaussian pdf Attribution: jhguch, https://commons. wikimedia.org/wik i/File:Boxplot_vs_P DF.svg Unit Normal pdf Suppose that X is normal with mean and standard deviation (variance ): Then is normal with mean 0 and standard deviation 1: Central Limit Theorem The Gaussian pdf is important because of the Central Limit Theorem. Suppose are i.i.d. (independent and identically distributed), each having mean and variance . Then Example: the sum of uniform random variables Suppose that are i.i.d.
    [Show full text]
  • Topic 5: Noise in Images
    NOISE IN IMAGES Session: 2007-2008 -1 Topic 5: Noise in Images 5.1 Introduction One of the most important consideration in digital processing of images is noise, in fact it is usually the factor that determines the success or failure of any of the enhancement or recon- struction scheme, most of which fail in the present of significant noise. In all processing systems we must consider how much of the detected signal can be regarded as true and how much is associated with random background events resulting from either the detection or transmission process. These random events are classified under the general topic of noise. This noise can result from a vast variety of sources, including the discrete nature of radiation, variation in detector sensitivity, photo-graphic grain effects, data transmission errors, properties of imaging systems such as air turbulence or water droplets and image quantsiation errors. In each case the properties of the noise are different, as are the image processing opera- tions that can be applied to reduce their effects. 5.2 Fixed Pattern Noise As image sensor consists of many detectors, the most obvious example being a CCD array which is a two-dimensional array of detectors, one per pixel of the detected image. If indi- vidual detector do not have identical response, then this fixed pattern detector response will be combined with the detected image. If this fixed pattern is purely additive, then the detected image is just, f (i; j) = s(i; j) + b(i; j) where s(i; j) is the true image and b(i; j) the fixed pattern noise.
    [Show full text]
  • Adaptive Noise Suppression of Pediatric Lung Auscultations with Real Applications to Noisy Clinical Settings in Developing Countries Dimitra Emmanouilidou, Eric D
    IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 62, NO. 9, SEPTEMBER 2015 2279 Adaptive Noise Suppression of Pediatric Lung Auscultations With Real Applications to Noisy Clinical Settings in Developing Countries Dimitra Emmanouilidou, Eric D. McCollum, Daniel E. Park, and Mounya Elhilali∗, Member, IEEE Abstract— Goal: Chest auscultation constitutes a portable low- phy or other imaging techniques, as well as chest percussion cost tool widely used for respiratory disease detection. Though it and palpation, the stethoscope remains a key diagnostic de- offers a powerful means of pulmonary examination, it remains vice due to its portability, low cost, and its noninvasive nature. riddled with a number of issues that limit its diagnostic capabil- ity. Particularly, patient agitation (especially in children), back- Chest auscultation with standard acoustic stethoscopes is not ground chatter, and other environmental noises often contaminate limited to resource-rich industrialized settings. In low-resource the auscultation, hence affecting the clarity of the lung sound itself. high-mortality countries with weak health care systems, there is This paper proposes an automated multiband denoising scheme for limited access to diagnostic tools like chest radiographs or ba- improving the quality of auscultation signals against heavy back- sic laboratories. As a result, health care providers with variable ground contaminations. Methods: The algorithm works on a sim- ple two-microphone setup, dynamically adapts to the background training and supervision
    [Show full text]
  • Lecture 18: Gaussian Channel, Parallel Channels and Rate-Distortion Theory 18.1 Joint Source-Channel Coding (Cont'd) 18.2 Cont
    10-704: Information Processing and Learning Spring 2012 Lecture 18: Gaussian channel, Parallel channels and Rate-distortion theory Lecturer: Aarti Singh Scribe: Danai Koutra Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal publications. They may be distributed outside this class only with the permission of the Instructor. 18.1 Joint Source-Channel Coding (cont'd) Clarification: Last time we mentioned that we should be able to transfer the source over the channel only if H(src) < Capacity(ch). Why not design a very low rate code by repeating some bits of the source (which would of course overcome any errors in the long run)? This design is not valid, because we cannot accumulate bits from the source into a buffer; we have to transmit them immediately as they are generated. 18.2 Continuous Alphabet (discrete-time, memoryless) Channel The most important continuous alphabet channel is the Gaussian channel. We assume that we have a signal 2 Xi with gaussian noise Zi ∼ N (0; σ ) (which is independent from Xi). Then, Yi = Xi + Zi. Without any Figure 18.1: Gaussian channel further constraints, the capacity of the channel can be infinite as there exists an inifinte subset of the inputs which can be perfectly recovery (as discussed in last lecture). Therefore, we are interested in the case where we have a power constraint on the input. For every transmitted codeword (x1; x2; : : : ; xn) the following inequality should hold: n n 1 X 1 X x2 ≤ P (deterministic) or E[x2] = E[X2] ≤ P (randomly generated codebits) n i n i i=1 i=1 Last time we computed the information capacity of a Gaussian channel with power constraint.
    [Show full text]
  • Noisecom UFX-Ebno Datasheet (Pdf)
    Full-service, independent repair center -~ ARTISAN® with experienced engineers and technicians on staff. TECHNOLOGY GROUP ~I We buy your excess, underutilized, and idle equipment along with credit for buybacks and trade-ins. Custom engineering Your definitive source so your equipment works exactly as you specify. for quality pre-owned • Critical and expedited services • Leasing / Rentals/ Demos equipment. • In stock/ Ready-to-ship • !TAR-certified secure asset solutions Expert team I Trust guarantee I 100% satisfaction Artisan Technology Group (217) 352-9330 | [email protected] | artisantg.com All trademarks, brand names, and brands appearing herein are the property o f their respective owners. Find the NoiseCom UFX-NPR-22 at our website: Click HERE Data Sheet UFX-EbNo Series Precision Generators Count on the Noise Leader. Count on Noise Com. Artisan Technology Group - Quality Instrumentation ... Guaranteed | (888) 88-SOURCE | www.artisantg.com UFX-EbNo Series Precision Eb/No (C/N)Generators The UFX-EbNo is a fully automated instrument that sets and maintains a highly accurate ratio between a user- supplied carrier and internally generated noise, over a wide range of signal power levels and frequencies. The UFX-EbNo gives system, design, and test engineers in the cellular/PCS, satellite and military communica- tion industries a cost-effective means of obtaining higher yield through automated testing, plus increased confidence from repeatable, accurate test results. Features Multiple Operating Modes True RMS Power Meter The UFX-EbNo provides five operating modes: carrier- The digital power meter is custom designed to cover tonoise (C/N), carrier-to-noise density (C/No), bit ener- the frequency range of the particular instrument.
    [Show full text]