The Pennsylvania State University The Graduate School THE DESIGN AND IMPLEMENTATION OF A COGNITIVE RADAR FOR THE STUDY OF PLASMA INSTABILITIES AT

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1 The Pennsylvania State University The Graduate School THE DESIGN AND IMPLEMENTATION OF A COGNITIVE RADAR FOR THE STUDY OF PLASMA INSTABILITIES AT EQUATORIAL AND MID-LATITUDE REGIONS A Dissertation in Electrical Engineering by Robert Sorbello c 2015 Robert Sorbello Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy May 2015

2 The dissertation of Robert Sorbello was reviewed and approved by the following: Julio V. Urbina Associate Professor of Electrical Engineering Dissertation Advisor, Co-Chair of Committee John D. Mathews Professor of Electrical Engineering Co-Chair of Committee James K. Breakall Professor of Electrical Engineering Matthew R. Kumjian Assistant Professor of Meteorology Kultegin Aydin Professor of Electrical Engineering Head of the Department of Electrical Engineering Signatures are on file in the Graduate School.

3 Abstract Cognitive radar is envisioned to be the future of remote sensing systems. The idea proposed by Simon Haykin in [1] details that a cognitive radar will be have the ability to learn about the sensing environment and, over time, optimize returns from targets of interest by altering the transmitted pulse waveform. Although military applications were initially the most prominent field for this new paradigm of radar systems, additional benefits were realized in the ionospheric radar community. In Huancayo, Peru, located along the geomagnetic equator, a cognitive imaging radar system is to be installed to continuously monitor the generation of the three different plasma instabilities observed throughout the course of a day, namely Spread F, Electrojet, and 150 km echoes. This system has been given the name Cognitive Interferometric Radar Imager (CIRI) based on the described characteristics, and has also been replicated close to the Pennsylvania State University campus to serve as a test system. The first step of the cognitive process is to automatically recognize the current plasma instability forming in the ionosphere, and then switch to a transmission waveform that is able to improve the study of certain aspects of the event. This dissertation discusses in detail both the hardware configuration and signal processing aspects of the CIRI system. A major section is then dedicated toward the development of a cognitive routine that has potential to be utilized for optimizing the returns from the mentioned plasma instabilities. Finally, results of the two systems located at Pennsylvania State University and Huancayo will be provided along with the future work anticipated for this topic of research. iii

4 Table of Contents List of Figures List of Tables List of Abbreviations Acknowledgments viii xv xvi xix Chapter 1 Introduction The Concept of Cognitive Radar Brief Overview of Radar Systems Waveforms for Radar Systems Cognitive Radar Introduction to CIRI Brief Overview of the Ionosphere The Equatorial Electrojet km echoes The Equatorial Spread F Cognitive Interferometric Radar Imager Chapter 2 Hardware Configuration For CIRI Introduction Clock Signal Generator Radar Pulse Generator Transmitter Chain Transmitter iv

5 2.6 Antennas RF Front End Universal Software Radio Peripheral Software: Sauron Chapter 3 Radar Signal Processing Introduction Radar Signal Fundamentals Interpulse Period Radar Equation Range Resolution Binary Phase Coding Inphase and Quadrature Sampling Matched Filter Doppler Effect and the Ambiguity Function Radar Signal Processing for Ionospheric Observations Range-Time Intensity Plot Sky Noise Spectra Doppler Map Spectrogram Interferometry Cross Spectra Phase Plots Radar Imaging Introduction Radar Configuration Radar Imaging Theory The Fourier Method Phase Calibration Practical Implementation of Fourier Method Chapter 4 Cognitive Processing Routine for CIRI Introduction Classification Theory Introduction Implementation of a Classifier v

6 Gaussian Mixture Model Expectation Maximization Implementation Waveform Diversity Optimal Transmission Envelope Introduction Derivation of Optimal Transmission Envelope Numerical Method to Solve for Optimal Transmission Envelope Optimal Transmission Envelope for CIRI Data Frequency Selection Introduction Global Optimization of Signal to Noise Ratio Classical Simulated Annealing and Fast Simulated Annealing Adaptive Simulated Annealing Implementation of Simulated Annealing Algorithms Application of Adaptive Simulated Annealing for Cognitive Radar Systems Summary of Cognitive Routine Aside: Waveform Diversity with CIRI at PSU Chapter 5 Observations with CIRI at PSU Introduction Quasi-Periodic Echo RTI Plot Doppler Map Spectrogram Phase Plot Miscellaneous Echo # RTI Plot Doppler Map Spectrogram Phase Plot Miscellaneous Echo # RTI Plot Doppler Map Spectrogram Phase Plot vi

7 5.5 Meteor Events Meteor Shower Sky Noise Chapter 6 Observations with CIRI at Huancayo Introduction Equatorial Electrojet RTI Plots Doppler Maps Spectrograms Phase Plots Meteor Events Comparisons with JRO Antenna and Radar Configurations Results and Discussion Chapter 7 Summary and Future Work Summary Future Work Bibliography 160 vii

8 List of Figures 1.1 Conceptual block diagram of a cognitive radar system Photographs of Ionospheric radar observatories: (Top Left) Jicamarca Radio Observatory, Lima, Peru. (Top Right) Arecibo Observatory, Arecibo, Puerto Rico. (Bottom Left) Resolute Bay Incoherent Scatter Radar, Nunavut, Canada. (Bottom Right) Poker Flat Incoherent Scatter Radar, Fairbanks, Alaska An Equatorial Electrojet observed with the Radar de Espalhamento Coerente in Sao Luis, Brazil during an equinox (Denardini, 2005) An 150 km Echo layer observed at Jicamarca Radio Observatory on May 1, An Equatorial Spread F layer observed at Jicamarca Radio Observatory on February 13, Map showing the location of geomagnetic equator along with the locations of Jicamarca Radio Observatory and the Huancayo Observatory System block diagram displaying interconnection of hardware components for both CIRI at PSU and CIRI at Huancayo (Hackett, 2013) Clock Signal Generator for CIRI - Novatech 409B Radar Pulse Generator High Power Transmitter used for CIRI, developed by Genesis Software Coaxial-Collinear antenna array layout utilized for CIRI at PSU (Hackett, 2013) Simulated radiation pattern of CIRI at PSU antenna array. The slice of the radiation pattern is taken perpendicular to Coaxial- Collinear lines Simulated radiation pattern of CIRI at Huancayo antenna array. The slice of the radiation pattern is taken perpendicular to Coaxial- Collinear lines viii

9 2.8 Block Diagram of RF Front End for both CIRI at PSU and CIRI at Huancayo (Hackett, 2013) Picture of the assembled RF front end, using a combination off-theshelf components Software Defined Radio utilized for CIRI - USRP N Flow diagram of the Sauron real time processing software A time domain voltage sequence of a Barker 13 code Matched Filter output of a Barker 13 sequence Ambiguity Function Surface for Barker 13 sequence (Levanon, 2004) Sky Noise Measurements collected at Jicamarca Radio Observatory on February 1, Spectra Plot of Equatorial Electrojet collected at Jicamarca Radio Observatory on July 26, 2005 (Hysell, 2007) Doppler Map of Equatorial Spread F observed by Jicamarca Radio Observatory on January 1, Spectrogram of Sporadic E Layer observed with the Cornell University Portable Radar Interferometer on May 7, 1983 (Riggen, 1986) Classical example of a single baseline interferometer Antenna configuration of a meteor interferometer installed in Buckland Park, South Australia (Holdsworth, 2004) Meteor distribution map produced at Jicamarca Radio Observatory on November 19, 2002 (Chau, 2004) Cross Spectra measurements of ion-acoustic enhancements collected at the EISCAT Svalbard radar on January 17, 2002 (Grydeland, 2005) Phase Plot produced by an observation of an Equatorial Spread F at Jicamarca Radio Observatory on January 25, 1980 (Kudeki, 1981) Radar Image of Equatorial Spread F observed with Sao Luis Radar in Brazil on October 25, 2005 (Rodrigues, 2008) Antenna configuration for imaging experiments with Sao Luis Radar in Brazil (Rodrigues, 2008) Antenna configuration for imaging experiments at Jicamarca Radio Observatory (Chau, 2008) Comparison of the three commonly used imaging algorithms: Fourier, Capon, and Maximum Entropy. Simulation performed by using a predefined model. (Yu, 2000) Flow diagram illustrating the processing steps for implementing the Fourier Method during a radar imaging experiment Results of Preliminary Tests Using Gaussian Mixture Models ix

10 4.2 Linear system demonstrating the link between the transmitted and received signal Simulated impulse response from target Kernel matrix for simulated impulse response Optimal transmission envelope for simulated impulse response Measured impulse response from detected plasma instability Optimal transmission envelope for detected plasma instability using CIRI at PSU Comparison of the Cauchy and Gaussian sampling probability distribution Flow Diagram of the Adaptive Simulated Annealing algorithm (Chen, 1998) Adaptive Simulated Annealing sampling distribution at different annealing times Arbitrary signal to noise ratio distribution as a function of frequency. Generated to apply Simulated Annealing algorithms Global Optimization Results of Classical Simulated Annealing Algorithm Global Optimization Results of Fast Simulated Annealing Algorithm Global Optimization Results of Adaptive Simulated Annealing Algorithm Range-Time-Intensity Plot illustrating the transition of the transmitted waveform from the default mode to a higher average power and resolution mode. Detected event was meteor trail observed at approximately 3:02 LT Range-Time-Intensity Plot illustrating the transition of the transmitted waveform from the higher average power and resolution mode to the default mode. Detected meteor trail subsided at approximately 3:04 LT Range-Time-Intensity Plot illustrating the transition of the transmitted waveform from the default mode to a higher average power and resolution mode. Detected event was meteor trail observed at around 3:10 LT Range-Time-Intensity Plot illustrating the transition of the transmitted waveform from the higher average power and resolution mode to the default mode. Detected meteor trail subsided at approximately 3:12 LT x

11 5.1 RTI Plot of a Quasi-Periodic Echo observed on June 29, The transmitted waveform was a Barker 13 code with a 10 µs baud length, and frequency of 49.5 MHz Doppler Map of Quasi-Periodic Echo. The returns illustrate that the motion of the plasma instabilities were primarily away from the radar system Spectrogram of Quasi-Periodic Echo processed at km. The particular echo contains a large spread of Doppler content covering both positive and negative values, with the majority weighted toward negative Doppler shifts Phase Plot of Quasi-Periodic Echo processed at km. The sequence of linear slopes corresponded to East-West drift velocity each exceeding 150 m/s RTI Plot of an ionospheric echo observed on June 30, The transmitted waveform was a Barker 13 code with a 10 µs baud length, and frequency of 49.5 MHz Doppler Map of ionospheric echo. The event transitions to a larger negative Doppler shift toward the events completion. DC content is also prominent intermittently at the lower ranges Spectrogram of ionospheric echo processed at km. The plot illustrates a narrow spread of Doppler content, with the majority of the power containing negative values. The negative Doppler content increases at the end of the event Phase Plot of ionospheric echo processed at km. The slope of the two major linear portions correspond to an East-West drift velocity both exceeding 55 m/s. Note the phase wrapping at approximately 22:12 LT RTI Plot of an ionospheric echo observed on July 10, The transmitted waveform was a Barker 13 code with a 10 µs baud length, and frequency of 49.5 MHz. Note that this was a rare daytime event Doppler Map of daytime ionospheric echo. The event presents all positive Doppler content throughout its duration Spectrogram of daytime ionospheric echo processed at 300 km. A large spread is apparent with majority of the power confined on the positive Doppler spectrum Phase Plot of daytime ionospheric echo processed at 300 km. The slope of the portions exhibiting linear phase correspond to an East- West drift velocity exceeding 55 m/s xi

12 second RTI plot of observation on June 6, The transmitted waveform was a 28 baud code, with a 5 µs baud length, and frequency of 49.8 MHz. A meteor head echo and trail is observed starting at approximately 05:19:21 LT second RTI plot of observation on August 19, The transmitted waveform was Barker 13 code, with a 10 µs baud length, and frequency of 49.5 MHz. The displayed event was a nonspecular meteor with an exceptionally long trail minute RTI plot of Quadrantids meteor shower occurring on January 3, The transmitted waveform was a Barker 3 code, with a 55 µs baud length, and frequency of 49.8 MHz. A vast increase in meteors was observed this night with frequent occurrences of meteors with long trails. Note that the range resolution is quite poor due to the chosen waveform Additional 15 minute RTI plot during peak of Quadrantids meteor shower occurring on January 3, Events occurring below the range 150 km are not considered as meteors and are typically considered to be airplanes or cars illuminated from one of the antennas sidelobes Sky noise level measured for 24 hours on June 20, The noise level was computed every 2 seconds using the Hilbrand-Sekon Method. In order to smooth the curve, the noise level was averaged for 10 minute intervals. The noise level predominately depreciates throughout the morning hours and then increases during the nighttime hours. Occasionally short spikes in the noise level occur, which could be caused by radio stars. A more thorough analysis and understanding of the radio star locations must be performed to draw better reasoning behind the daily trends RTI Plot of an Equatorial Electrojet observed during the daytime on March 2, RTI Plot of same Equatorial Electrojet presented in Figure 6.1 but spotlighting the hours between 12:00 and 15:00 LT. Note that greater detail of the plasma structure is noticable with the shorter time window RTI Plot of same Equatorial Electrojet presented in Figure 6.1 but spotlighting the hours between 16:00 and 19:00 LT. Note that greater detail of the plasma structure is noticable with the shorter time window xii

13 6.4 Doppler Map of the Equatorial Electrojet during the hours 12:00-15:00 LT. A significant portion of the plot is occupied by Doppler corresponding to zero Doppler, which is thought to have been external interference. However, a thin layer of high negative Doppler is discernible within the Electrojet Doppler Map of the Equatorial Electrojet during the hours 16:00-19:00 LT. A significant portion of the plot is occupied by Doppler corresponding to zero Doppler, which is thought to have been external interference, and abruptly disappears around 17:15 LT. Doppler within the Electrojet is still discernible, with a continued high negative Doppler that reverses to a high positive Doppler at the event s conclusion Spectrogram of the Equatorial Electrojet during the hours 12:00-15:00 LT at km. The returns illustrate that periods of the Electrojet contained a large spread Doppler content, that slowly compressed to a smaller spectral width. This characteristic repeated several times during these hours Spectrogram of the Equatorial Electrojet during the hours 16:00-19:00 LT at km. The returns illustrate large spread of Doppler content, that slowly compresses toward the conclusion of the Electrojet Phase Plot of the Equatorial Electrojet during the hours 12:00-15:00 LT at km. The measured phase at this range tended to cluster within -1 and -2 radians, with some periods of linearity. Unfortunately the linear sections were too short to compute an accurate East-West Drift velocity Phase Plot of the Equatorial Electrojet during the hours 16:00-19:00 LT at km. The measured phase at this range tended to cluster within -1 and -2 radians, with some periods of linearity. Unfortunately the linear sections were too short to compute an accurate East-West Drift velocity second RTI plot of observed meteor event on March 2, The event starting approximately 3:47:17 LT has a short trail confined within a smaller range window at the beginning, then revives shortly after with a longer trail and occupying a larger range. Meteors displaying this characteristic could be classified as fragmenting One minute RTI plot of observed meteor event on March 3, The event starting approximately 4:19:40 LT is known as a meteor head echo because of the sharp initiation, followed by a long trail xiii

14 6.12 Comparisons of RTI Plots between JRO and CIRI at Huancayo for an Equatorial Electroject during the nighttime hours on March 1, Similar structure is evident for the duration of the event, especially during period of high SNR at JRO. One subtle difference is the range of detection with each system. Note: The color scales are different for the two plots Comparisons of RTI Plots between JRO and CIRI at Huancayo for an Equatorial Spread F during the early morning hours on March 2, Similar structure is evident for the duration of the event, especially during period of high SNR at JRO. One subtle difference is the range of detection with each system. Note: The color scales are different for the two plots Comparisons of RTI Plots between JRO and CIRI at Huancayo for an Equatorial Spread F during the nighttime hours on March 2, Similar structure is evident for the duration of the event, especially during period of high SNR at JRO. One subtle difference is the range of detection with each system. However, a major discrepancy is the time at which the event was detected, with an approximately 15 minute delay with CIRI at Huancayo. Note: The color scales are different for the two plots Comparisons of 24 hour Sky Noise Plots between JRO and CIRI at Huancayo during March 2, Sky Noise was averaged every 10 minutes with CIRI at Huancayo. Major sources of sky noise at JRO are similarly found with CIRI at Huancayo, including the center of the galaxy (approximately 8:00 LT) and the back of the galaxy (approximately 20:00 LT). Throughout the daytime hours, heavy interference was detected with CIRI at Huancayo between the hours of 9:00-17:00 LT, causing many disparities during this time Proposed antenna layout of CIRI at Huancayo with imaging capabilities xiv

15 List of Tables 2.1 Receive RF front-end components used by CIRI (Hackett, 2013) Specifications of CIRI at Huancayo, and Daytime / Nighttime JU- LIA modes xv

16 List of Abbreviations ADC: ASA: CIRI: CoCo: CSA: CW: DC: DDC: DFT: EISCAT: EM: FCC: FFT: FM: FSA: GMM: GPS: Analog to Digital Converter Adaptive Simulated Annealing Cognitive Interferometric Radar Imager Coaxial Collinear Classical Simulated Annealing Continuous Wave Direct Current Digital Downconverter Discrete Fourier Transform European Incoherent Scatter Scientific Association Expectation Maximization Federal Communications Commission Fast Fourier Transform Frequency Modulation Fast Simulated Annealing Gaussian Mixture Model Global Positioning System xvi

17 I: Inphase IID: IPP: ISR: JRO: JULIA: PDF: PSU: PRF: PRI: PTM: Independent and Identically Distributed Inter Pulse Period Incoherent Scatter Radar Jicamarca Radio Observatory Jicamarca Unattended Long-term Investigations of the Ionosphere and Atmosphere Probability Distribtuion Function Pennsylvania State University Pulse Repetition Frequency Pulse Repetition Interval Pulse Transmitter Module Q: Quadrature RAID: RADAR: RCS: RF: RGB: RTI: RX: SAR: SNR: SVM: TR: Redundant Array of Independent Disks RAdio Detection And Ranging Radar Cross Section Radio Frequency Red Green Blue Range Time Intensity Receiver Synthetic Aperture Radar Signal to Noise Ratio Support Vector Machine Transmit/Receive xvii

18 TX: USRP: VHF: VSWR: Transmitter Universal Software Radio Peripheral Very High Frequency Voltage Standing Wave Ratio xviii

19 Acknowledgments The work presented in this dissertation could not have been possible without the countless support and assistance from others. Needless to say, I would like to extend my sincere gratitude to everyone involved during the course of my graduate school studies, especially to the following: Dr. Julio Urbina - For welcoming me into his lab, being a firm supporter of my work and helpful advisor. It is due to him that I was assigned this engaging research project in which this thesis is based upon. He was always available to assist me in any way possible to advance in my research, and always insisted for me to strive for best, while continuing to be patient throughout the entire process. I would also like to thank him for providing me with numerous travel opportunities to radar facilities around the world, in order to facilitate in my educational and professional growth. Lastly, he was always a good friend where discussions could be made about any topic, within or outside the engineering field. I look forward to keeping in touch and possibly collaborating on future projects. Dr. Jim Breakall - For his guidance toward the installation of the antennas for CIRI at PSU. His experience in the antenna engineering field really helped me draw the link between the theory and practical implementation. He was also always willing to spend time with me if any issue would arise in my research. Dr. John Mathews - For his continued support during my graduate studies, and being my thesis co-chair. I would also like to thank him for nominating me to be his teaching assistant during two separate semesters. Dr. Erhan Kudeki and Dr. Steve Franke (University of Illinois at Urbana- Champaign) - For their contributions with the hardware aspect of the CIRI system, and taking the time to thoroughly explain their system during a visit to the University of Illinois campus. xix

20 Dr. Fabiano Rodrigues (The University of Texas at Dallas)- For guiding me toward the understanding of the radar imaging process. It is greatly appreciated the time he took from his day, on multiple occasions, to sequentially explain the theory and practical implementation. Dr. Burak Tuysuz - For his help and support throughout his time at Penn State. He was always willing to spend time helping me understand the foundations of Linux and GNURadio, which were essential toward advancing in my research. Alex Hackett - For his contributions and continued support of the CIRI radar system. He also on many occasions spent time to teach me about Linux, GNURadio, and numerous aspects of hardware. Whenever any issue occurred in either the hardware or software, he was able to explain in detail what the problem was, and what needed to be done to fix it. Zach Stephens - For his contributions toward the development of the CIRI software. To this date, the basis of what he wrote is still in use. I also would like to thank him for assisting in the development of the classification portion of the cognitive routine. Jicamarca Radio Observatory - For providing me with the opportunity to stay in Lima, Peru for three months during the JIREP program, and also the continued support of the CIRI radar system. Everybody at JRO was friendly and welcoming from the beginning of my stay. I would like to personally thank Dr. Marco Milla and Sandra Mendieta for helping organize the logistics of installing the CIRI system in Huancayo. Also I would like to thank Marcos Inonan for the constant interactions and advise during the JIREP program. Karim Kuyeng - For her many contributions toward the planning of the CIRI system in Huancayo. Only through her constant interactions with JRO and IGP, was the installation of CIRI made possible. I would also like to thank her for allowing me to stay in her home during the three months in Peru. Her family was very hospitable and the food was amazing. Freddy Galindo - For his continued support and contributions of the CIRI system. With his extensive experience in radar he helped improve the software portion of the system. I would also like to thank him for taking the time to explain many aspects of ionospheric research to me. Hakan Arslan, Salih Bostan, Yolian Amaro, Jack Kurth, and Lauren Donohoe - For all the support during the time we overlapped in the lab. Although xx

21 our research topics were different, we were always able to discuss the details of our projects, and at times I attempted to implement some of their ideas toward my project. I wish each of them the best for the rest of their time at Penn State and for every future endeavor. Family and Friends - For all the love and support during the course of my graduate school studies. They were always there to provide positive reinforcement and kept me moving forward toward to achieve my goals. I also would like to thank my family for instilling in me the value of hard work. This work is supported by the National Science Foundation under grants: ATM and ATM to Penn State University. xxi

22 Chapter 1 Introduction 1.1 The Concept of Cognitive Radar Brief Overview of Radar Systems The formulation of Maxwell s Equations in 1861 revolutionized the field of physics and engineering to date by defining a closed form solution that provided a connection between the electric and magnetic fields. One major conclusion made by the four sets of equations proposed by James Clerk Maxwell was the presence of an electromagnetic wave that was proven to propagate through space in any direction [2]. As a consequence of this scientific development, many areas of research were initiated, including the development of a system that could apply an electromagnetic wave to determine an object s location. After approximately a century of researching this concept, the first practical application was utilized in World War II for the purpose of gathering a map of all surrounding aircrafts. Considered to be an extension of the human vision, Radar, meaning Radio Detection and Ranging, has the ability to detect targets at distant locations and observe targets through opaque material, all the while extracting precise information in fractions of a second [3,4]. Radar is a popular field of interest in both academia and industry where projects expand a variety of purposes from military to a range of scientific applications. Understanding modern radar systems require a well rounded knowledge of many subjects in electrical engineering, including hardware, software, electromagnetism, and antenna theory.

23 2 During operation, a radar transmits an electromagnetic wave of a selected frequency into a specific medium, in most cases free space. Upon transmission via an antenna, the electromagnetic signal travels approximately at the speed of light (3x10 8 m/s), and reflects off of surfaces consisting of electrical properties different from the current medium. Depending on the electrical properties of the material and the angle of incidence, the signal continues to propagate and reflects from subsequent transitions in material. The reflections caused by the material, scatter in an anisotropic manner, with the surface roughness altering the pattern of the electromagnetic wave. Finally, a portion of the reflected wave is received by an antenna where the processing and analysis is performed. The antenna for reception in some applications is shared with the antenna used for transmission. Radar systems having this property are called monostatic. On the other hand, if a second antenna is used for reception, the radar system is called bistatic. Radars can also be extended to multistatic applications, in which multiple antennas are used for transmission or reception. The frequency of the received signal will remain constant unless the target contains a relative velocity with respect to the radar system. If the target is moving toward or away from the incoming electromagnetic wave, the frequency of the wave will increase or decrease respectively. This phenomenon is known as the Doppler effect. Although the physics of the chosen electromagnetic signal is immutable upon transmission, hardware implementation for radar systems are flexible and are designed strategically to maximize the information received. Since the development of the aircraft detection system during World War II, hardware configurations have become more complex resulting in substantial improvement in the sensitivity of the systems. Depending on the application, the transmitter, receiver hardware, and antennas are installed in a variety of configurations. A passive radar is the only type of system where a transmitter is not utilized in the hardware design. In order to accomplish the systems goal however, it relies on third party transmitters such as Frequency Modulation (FM) radio signals or cellular phone signals. The processing for passive radar encompasses the difference in time of arrivals between the direct transmission signal uninterrupted between the third party transmitter and receiver, and the reflection off the target of interest. A comparison of the time of arrivals between the two incomings signals then leads to an estimated location

24 3 of the target. Another type of Radar system is called Synthetic Aperture Radar (SAR). Analogous to an optical camera, SAR involves using an array of receiving antennas with the goal of reconstructing an image of the area illuminated by the transmitted antenna. Each receiver in the multistatic system collects a similar incoming signal, but with slight phase offsets due to the location of the antennas. The phase differences between each of the received antennas are essential toward the image development. The ability to gather information about a target s range and velocity with great accuracy in fractions of a second gives radar an advantage over many alternatives and is therefore commonly used in practice Waveforms for Radar Systems A primary component of a radar system is the selection of the waveform used for transmission [5]. Not only does determination of the waveform affect the types of returns the user should expect, but consequently affects all of the hardware involved in the design. The waveform selected for each application is different depending on the information wanted to be studied by the target of interest. For radar purposes, waveforms are separated into two distinct categories, continuouswave (CW) and pulsed. A CW signal is an unmodulated sinusoidal wave of a specific frequency. The advantage of CW is the ability to isolate the Doppler frequency, therefore providing a sufficient estimate of the target s radial velocity relative to the radar system [3, 4]. The limitation of a single frequency CW signal however is resolving range information of the target. In order to estimate a target s location, time information of the transmitted signal must be recorded in some manner. Since target returns are located many wavelengths from the system, recording time information for a single frequency CW signal leads to many uncertainties. To provide an improved range estimate, periodic frequency or phase modulations are included, with a modulation period long enough to eliminate any range uncertainties. The particular frequency or phase modulation scheme used for transmission is known to the user in advance, therefore time information is kept indirectly for each modulation period. A pulsed waveform on the other hand is capable of extracting range and doppler information without the use of frequency and phase modulation. The conceptual

25 4 difference between a single frequency CW and pulsed signal, is the pulse contains a duty cycle less than 100%. In practice however, the duty cycle of a radar pulsed signal will in most cases be less than 10%. The inactive period of the pulsed signal is used to listen for returning signals. The amount of elapsed time between the beginning of the pulse signal and the arrival of the returning signal corresponds to a specific range. The characteristics that define a pulsed signal include the Pulse Repetition Frequency (PRF) and the pulse width. The PRF is given in term of Hertz (Hz) and represents the number of iterations per second the pulse is transmitted. The inverse of this number is called the Interpulse Period (IPP) which is defined in seconds. If the PRF is set to a low value, the maximum unambiguous range of a target is large and vice versa. PRFs are needed to be selected with caution in order to avoid range aliasing. Range aliasing occurs when a return from an earlier pulse arrives after the subsequent pulse is transmitted, resulting in a processed range smaller than the true value. The pulse width is the length of time the selected frequency will be triggered. The wider the pulse width, the greater the power transmitted. This results in acquiring returns from farther distances or weaker scatterers. The shortcoming of a large pulse width is the large range resolution associated with it. The range resolution is defined as the minimum distance at which two separated targets can be resolved. With a large range resolution multiple individual targets can potentially be processed to look like one. Coding schemes are used in pulse waveforms to involve a long pulse length, while also obtaining a low range resolution. Doppler information about the target is also obtainable through use of pulsed waveforms. Spectral analysis is a common technique applied for pulsed radar signals to provide a relation between the Doppler frequency versus range. The spectral content of a target is calculated after a selected number of IPPs, and then taking the Discrete Fourier Transform (DFT) over each sampled range bin. The value of the PRF is proportional to the maximum unambiguous frequency or velocity that can be measured. Given a large PRF, the time elapsed between measurements of the same range bin is a small value relative to a low PRF. Therefore if a target is moving at a fast rate, it is more feasible to determine the velocity with a high PRF than a low PRF. Finally, the choice of frequency of transmission is a major aspect of a radar

26 5 system. Low frequency signals are proficient for propagating through various media because of the large wavelength. Wavelengths that are large compared to the medium of incidence experience insignificant attenuation when compared to higher frequency signals. To the contrary, high frequency signals are able to determine a better estimate of the target velocity. In addition, the physical size of the components comprising the system are manufactured in smaller dimensions. It should be noted that majority of the concepts outlined in this section will be explained in further detail in Chapter Cognitive Radar As advancement in computing and algorithms continue to develop, radar systems are also at a crossroad toward taking the functionality to a new level of approaches. Waveform diversity is the integral piece for this transition [6, 7]. The traditional radar system described in Section does not consist of a connection that allows an exchanging of information between the received and transmission end. Consequently, a traditional radar system is limited to only applying a single transmission waveform, hence operating in a feedforward manner. Unless the transmitted waveform is manually altered by the user, radar returns cannot be improved upon with the current system configuration. In [1, 8, 9], Haykin separates the present and forthcoming radars into three classes, one including the traditional radar system. A second category is classified as a Fore-active radar. This type of radar system brings this proposed connection between the receiver and the transmission stage. With this design, waveforms are selected from a predefined list and are adjusted automatically based on processed results. The purpose of reconfiguring the transmitted waveform is to optimally improve return parameters such as the Signal-to-Noise Ratio (SNR) of the target. Although this system does proceed in the direction of waveform diversity, it contains no memory of the previous results and hence does not improve in the long term. The final category defined by Haykin includes this additional facet and was coined as a cognitive radar. The cognitive radar idea was introduced by Haykin as being a radar system that will be able to function without any human interaction and automatically perform waveform diversity techniques [1]. The traditional radar typically transmits a

27 6 modulated pulse, then receives and processes the returns in the same manner throughout the duration of the experiment. By contrast, a cognitive radar system is composed of three components: 1) intelligent signal processing, which builds on radar interactions from the surrounding environment, 2) receiver feedback which is utilized by the transmitter to facilitate an intelligent response to detected signals, and 3) preservation of radar echo information contents. Figure 1.1 presents a conceptual block diagram that demonstrates the integration and functionality of these three components. The prior knowledge and preservation of information components are the foundations for making the cognitive radar a completely self sufficient system. After gaining experience in the observed echoes, the cognitive radar will be able decide on the most advantageous waveform to track targets of interest automatically and focus on details essential to the user. A real world example of how a cognitive radar should operate in practice is analogous to an echo-locating bat [1]. While flying in dark caves, bats use sonar to navigate to help avoid collisions with other bats, walls, etc. In addition, they are able to pinpoint small insects while scanning large areas. During the process of searching for food, the bat transmits a variety of waveforms that help optimize the return and provide a precise location of the insect. The procedure of maneuvering through caves and hunting for food becomes more efficient as the bat grows older and more experienced. So far in literature, there has not been any practical implementation of a cognitive radar system, but many theoretical papers have been published on how the processing techniques are envisioned [8 11]. This dissertation provides the initial steps taken toward the development of a system named CIRI (Cognitive Interferometric Radar Imager) in Huancayo, Peru, to study plasma instabilities at the magnetic equator.

28 7 Figure 1.1. Conceptual block diagram of a cognitive radar system 1.2 Introduction to CIRI Brief Overview of the Ionosphere The ionosphere is defined as the region of the atmosphere ranging from 90 km to altitudes greater than 1000 km [12]. It is in this area that the boundary between Earth s atmosphere and space is located. The ionosphere is categorized as a distinct region in the atmosphere because of the appreciable amount free electrons and positive ions. The ionosphere is further partitioned into two main regions: The E region ( km) and F region (150 km and above), based on the electron densities and temperature [13]. The densities of the ionized particles and free electrons have a distribution that fluctuate depending on the altitude and time of the day. The ionization process occurs when highly energized photons are emitted by the Suns ultraviolet rays, removing an electron from the neutral particles namely nitric oxide and oxygen. Following ionization, the positive ions and electrons attempt to recombine due to their opposite polarities. However, the continuous stream of the strong ultraviolet rays prevent the molecules from holding a truly neutral state, resulting in a plasma. A strong geomagnetic field is generated around the Earth s surface because of the molten iron in the core. The magnetic field lines cause the plasma and ionized particles in the ionosphere to move in a spiral pattern due to the Lorentz Force, and solar wind [14]. In addition, along the field lines plasma instabilities develop for reasons that are still not completely understood. Besides the scientific contributions to understanding the plasma instabilities, these events are also known to cause real world issue, mostly disrupting the use of radio communications and

29 8 Global Positioning Systems (GPS). These plasma instabilities tend to have different structures depending on the latitude at which observations are made, one reason being that the strength of the magnetic field lines are not consistent around the Earth. Since the plasma irregularities occur only along the magnetic field, in order to make observations with a radar system, the boresight of the antenna beam must be pointed perpendicular to the magnetic field lines. The angle relative to Earth s surface that directs at normal incidence to the magnetic field also depend on the latitude of observation. Around the world there are many radar observatories at different latitudes that study plasma irregularities. The European Incoherent Scatter Scientific Association (EISCAT) is located in northern Scandinavia and observes instabilities developing along the polar region, and Arecibo Observatory in Puerto Rico studies the mid-latitude irregularities. Jicamarca Radio Observatory (JRO), located outside of Lima, Peru, studies the unique events that occur at the magnetic equator. Figure 1.2 includes photographs taken of these ionospheric observatories in addition to a couple others. The plasma instabilities occurring along magnetic equator is the topic of much ionospheric research since the magnetic field is perpendicular the Earth s surface and hence causing the plasma to drift in the East-West direction. The plasma instabilities developed in this region will be studied by the CIRI system, and a brief description of each event is outlined in Sections

30 9 Figure 1.2. Photographs of Ionospheric radar observatories: (Top Left) Jicamarca Radio Observatory, Lima, Peru. (Top Right) Arecibo Observatory, Arecibo, Puerto Rico. (Bottom Left) Resolute Bay Incoherent Scatter Radar, Nunavut, Canada. (Bottom Right) Poker Flat Incoherent Scatter Radar, Fairbanks, Alaska The Equatorial Electrojet The equatorial electrojet is an E region plasma instability that occurs at the magnetic dip equator. An electrical current is generated by ions and electrons along the magnetic field lines because of the solar driven wind. An analogy made in [15] mentions that this electrodynamic process is similar to the current generated by a conductive coil passing through a magnetic field. The electrojet current is typically flowing in the East-West direction, but has also been discovered to reverse directions, which is known as the counterelectrojet. The East-West current typically flows in the morning hours after sunrise from 07:00 to 20:00 while the counterelectrojet flows after sunset between the hours of 20:00 to 07:00 [16]. Seasonal trends were first reported by [17], which observed that the counterelectrojet is present much earlier during the fall and winter time with respect to the summer and spring. The electrojet however did not tend to vary over the course of different seasons. The main aspect of this irregularity studied with Incoherent Scatter Radar (ISR) systems is the plasma drift producing the East-West current. A result of an Equatorial Electrojet radar observation is provided in Figure 1.3 [18].

31 10 Figure 1.3. An Equatorial Electrojet observed with the Radar de Espalhamento Coerente in Sao Luis, Brazil during an equinox (Denardini, 2005) km echoes 150 km echoes occur at the boundary between the E region and the F region. The source that generates the 150km echoes is still under investigation, but literature has studied many aspects of the event. The facts known about the 150km echoes are that it is only a daytime irregularity. All observations show multiple scattering layers, approximately 3-5 km thick, descending in altitude in the morning and reaching a minimum around noon local time. In the afternoon, the plasma layers begin to ascend and disappear around 17:00 local time. The typical necklace shape of the 150km echo occurs in the altitude ranges between 130 and 170 kms. In [19, 20] a long term study of the yearly statistics of the events show that there is a clear seasonal variability in the strength of the echoes and the occurrence rate. Rodrigues performed statistics with the Sao Luis Radar in Brazil and concludes that stronger returns are more present in the periods between June and September, while during the March Equinox the occurrence rate drops significantly [19]. In [20], Chau performed similar experiments at JRO but discovered different results. To the contrary of Rodrigues, Chau observed that the occurrence frequency is highest during the March Equinox and the December Solstice period. The geo-

32 11 graphical latitude at which each independent paper was published could potentially be a factor to be considered when analyzing these statistics. Figure 1.4. An 150 km Echo layer observed at Jicamarca Radio Observatory on May 1, The Equatorial Spread F The Equatorial Spread F occurs in the F region of the ionosphere, defined by the altitudes ranging between 150 km and 800 km. This event displays one of the more dynamic processes occurring the ionosphere because variability of structures that result and the broad range of altitude values that the event transpires. This is due to the horizontal electron density fluctuations that results in the plasma to flow upward [21]. A prime example of this is more random pattern is shown in Figure 1.5. The Spread F is a nighttime layer that generates between the hours of [ ], and is examined to have seasonal trends that depend on the solar flux and geomagnetic activity [22, 23]. Even with the diversity of forms of the Spread F, Hysell categorized the echoes into four types called bottom-type, bottom side, topside, and post-midnight based on various features [22]. In addition to radar, the winds that affect the evolution of the Spread F also are examined using rockets

33 12 and satellites. The main aspects of the event studied to comprehend the physical nature are the east-west drift velocities, in addition to the vertical velocities of the plasma. Figure 1.5. An Equatorial Spread F layer observed at Jicamarca Radio Observatory on February 13, Cognitive Interferometric Radar Imager The basis of this dissertation is to provide an initial approach toward the implementation of a cognitive Very High Frequency (VHF) coherent imaging radar, called CIRI, in Huancayo, Peru. The radar system, which is located near the Peruvian Andes, is to initiate continuous monitoring of the plasma structuring in the equatorial ionosphere. The new radar system will utilize cognitive sensing techniques and complement the ionospheric observations conducted by the JRO ISR, located about 170 km to the west of Huancayo along the geomagnetic equator. Locations of JRO and the Huancayo Observatory with respect to the geomagnetic equator are shown in Figure 1.6. The main purpose of the new system will be to obtain uninterrupted images of ionospheric structuring and drifts from Huancayo, which are only probed and sampled intermittently from Jicamarca due to the operation costs

34 13 and scheduling issues of the more powerful incoherent scatter system. CIRI is to provide an alternative view of the equatorial plasma instabilities because current radar systems conducting ionospheric studies contain a fixed transmission waveform. In depth images, statistics, and trajectories of these events will be produced that will contribute to a better understanding of the underlying physics than that of a traditional radar. The proposed system will work in two stages: 1.) classifying the occurrences observed in the atmosphere, and 2.) transmitting an optimal waveform to illuminate and process areas of interest. Figure 1.6. Map showing the location of geomagnetic equator along with the locations of Jicamarca Radio Observatory and the Huancayo Observatory. The layout of this dissertation is divided into six separate sections. Chapter 2 discusses the hardware design for the proposed system along with background information on each of the subsystems. Chapter 3 gives an overview of basic radar concepts along with critical processing techniques used for ionospheric research. The processing techniques will be critical toward the understanding of later chap-

35 14 ters. Chapter 4 presents the design of the cognitive algorithm to ultimately apply with CIRI or any alternative cognitive radar application. The chapter is divided into two major sections. The primary section introduces the theory and implementation of a classification technique to correctly identify the following geophysical equatorial echoes: Spread-F, electrojet, and 150 km echoes. These events are each categorized by signal parameters with known distributions, e.g., signal-to-noise ratio, changes in range, instantaneous frequency, periodicity, etc. The subsequent section in Chapter 4 presents the waveform diversity technique composed to search for a transmitted signal that will optimize signal parameters of echoes from each of the mentioned plasma instabilities. Chapters 5 and 6 respectively provide radar processing results from a test radar system built approximately 10 miles away from the Pennsylvania State University campus, and from CIRI in Huancayo. Finally, Chapter 7 discusses the future work that is to be carried out to improve the implementation of CIRI.

36 Chapter 2 Hardware Configuration For CIRI 2.1 Introduction The foundation of virtually all modern radar system consists of two major parts, the hardware side and software side. The hardware configuration for CIRI uses a combination of analog and digital circuitry that provides the necessary signals to transmit the selected waveform and manipulate the received signal in a manner that improves the quality of extracted information. The software side of the CIRI handles the output of the hardware stage to process the returns and present the user with the current conditions in the ionosphere. A test system approximately ten miles from the Penn State campus has been installed and operational for the past two years, studying the ionospheric events at mid-latitudes, mostly consisting of meteors and occasional plasma instabilities. The name of this test system was given as CIRI at Pennsylvania State University (PSU). The hardware configuration for CIRI at PSU and CIRI at Huancayo are identical for the exception of couple components due to alternate frequencies of transmission and antenna beam pointing direction. A block diagram of the hardware design is provided in Figure 2.1 and will be a valuable reference for the remainder of the chapter toward the comprehension of the interconnects of all the components [24].

37 16 Ionosphere Reflections Pulsed RF Reflections West Array East Array RF Front End Filtering TX Blanking Downconversion Transmitter Power Amplification Phase Coding TR Switch TX Chain RF Gating Filtering Amplification Trigger TX Gate LO RF Carrier TX Blank Radar Pulse Generator Clock Clock Signal Generator Clock USRP N210 Receiver IF A/D Sampling Filtering and Decimation Digital Down- Conversion Ethernet RS-485 Host Computer Data Collection Data Processing and Display Data Storage TX/RX Control Receive Segment Transmit Segment Figure 2.1. System block diagram displaying interconnection of hardware components for both CIRI at PSU and CIRI at Huancayo (Hackett, 2013) 2.2 Clock Signal Generator A clock is a signal generator used as the input for digital hardware to coordinate the timing of the systems particular function. Clock signals can either be a square wave of a given frequency with a 50% duty cycle, or a sinusoidal function. In modern radar systems, synchronization of both the transmission and reception chain is necessary for the preservation of phase information to perform various processing techniques. Therefore an external clock is used as a separate subsystem to generate the necessary signals to all the digital hardware, meaning that the clock must

38 17 contain more than one output. An important specification of an effective external clock is the phase stability of the multiple outputs. Over time, the outputs of clocks tend to drift and lose phase alignment resulting in the digital hardware components to lose synchronization. The external clock used for CIRI serves a dual purpose, to generate the clock signals for the radar pulse generator and Universal Software Radio Peripheral (USRP) while also providing the necessary signals for the Radio Frequency (RF) front end and Transmitter (TX) Chain. The radar pulse generator and USRP are both digital systems located on transmission and reception stage respectively. Both contain an internal clock, but have the option for the application an external signal. Therefore with an external clock, synchronization of these hardwares system can be achieved. Without synchronization, these systems would be operating at arbitrary times, which could provide misleading processed results. Further explanation of these systems will be discussed in the sections to follow. The model of the selected clock for CIRI is a Novatech 409B, shown in Figure 2.2 which outputs up to four programmable sinusoidal signals. Some of the specifications of this particular clock are that is has a programable precision of <±1.5 ppm (.00015%) of the selected frequency. The outputs can be programmed to any sinusoidal frequency up to 171 MHz in steps of 0.1 Hz and can contain an amplitude up to 5 dbm. All four outputs are utilized for the CIRI systems, with 20 MHz used for the radar pulse generator, and 10 MHz for the USRP. Due to the transmission frequency differences between CIRI at PSU and CIRI at Huancayo, the final two outputs are adjusted for each system. For CIRI at PSU the final sinusoidal outputs are 49.8 MHz for the TX Chain, and 71.2 MHz RF front end, while CIRI at Huancayo outputs MHz and MHz respectively. The clock has its own internal oscillator used to generate each of the four output and assure each are locked in phase. To improve the stability of the clock even further, an external GPS clock signal can be used as an input. The GPS signals are constantly transmitted via satellite and are used for synchronization in a variety of hardware applications.

39 18 Figure 2.2. Clock Signal Generator for CIRI - Novatech 409B 2.3 Radar Pulse Generator The radar pulse generator is a completely programmable system that is used for the generation of signals for the transmitter and RF front end. There are 16 outputs obtainable by this system, each of which are periodic binary signals, either logic high or low. Logic high corresponds to 5 volts while logic low is 0 volts. These outputs are independently programmed for a particular radar operating mode requested by the user. Within a particular mode, each of the 16 outputs have to contain the same PRF, but are capable of being programed to have alternative logic variations throughout the periodic interval. The radar pulse generator also has the capability of switching through a set of predefined operating modes, therefore a variety of waveforms could potentially be utilized for a cognitive routine. For the particular case of CIRI two out of the 16 potential outputs are needed to operate the system. One of the outputs serves as a trigger for the transmitter, to notify when to transmit the selected waveform. Older transmitters were not capable of being programmed, therefore the entire pulsed RF for transmission was essential to function properly. For the new programmable transmitter used by CIRI, a only rising edge at every inter pulse period is required. Therefore a short pulse of typically 1µs is the output for this case. Other specifications of the transmitter will be discussed in Section 2.5. The other output provided by the radar pulse generator is a blanking pulse for the RF front end. This contains the

40 19 opposite logic of the transmission pulse and will be further explained in Section 2.7. A 20 MHz sinusoidal clock stemming from the clock signal generator ensures the synchronization between the radar pulse generator and the USRP. A picture of the radar pulse generator used for CIRI is shown below in Figure 2.3. Figure 2.3. Radar Pulse Generator 2.4 Transmitter Chain The TX Chain is a simple subsystem that aids in the generation of the transmitted pulsed signal. The principal component of the TX Chain is an RF switch, which is used for amplitude modulation. The clock inputs the frequency of transmission (49.8 MHz for CIRI at PSU or MHz for CIRI at Huancayo) to the common port of the switch. The output of the transmitter due to the 1µs trigger pulse sent from the radar pulse generator is the entire pulse envelope needed for transmission, which is programmed by the user. The RF switch uses the combination of these two inputs to pass the frequency of transmission only when the pulsed binary envelope is logic high. When the transmission pulse is logic low, the frequency input from the clock is impeded, causing the output at the corresponding times to be 0 volts. In addition to the switch, a filter is connected to prevent extra noise from corrupting the modulated signal, and an amplifier to ensure the power level

41 20 is sufficient to activate the transmitter. The pulsed RF signal is the output of this block and is sent to the transmitter to initiate the high power signals. 2.5 Transmitter The high power transmitter selected for the the operation of CIRI is developed by Genesis Software, and is shown in Figure 2.4. The transmitter contains four independent Pulse Transmitter Modules (PTMs) that serve as the source for amplification of the selected transmitted waveform. Each PTM amplifies the input pulsed RF signal up to 7.5 kw provided that the duty cycle of the pulsed signal is less than 5%. With the combined power of the four PTMs, the total output peak power is maximized around 30 kw. The output of each of the PTMs can be supplied to separate antennas, if the radar system is designed to have four antennas for transmission. If two antennas are used for transmission, then the output of two PTMs can be combined to generate additional power to a single antenna, while still utilizing all four PTMs. The transmitter also contains a Transmit/Receive (TR) switch, that passes the transmitted signal for the given pulse length, then switches to reception to listen for echoes upon completion of the pulse. The Genesis transmitter is programmed via the host computer in two stages. The first step involves turning on the high voltage power supply used to activate each of the PTMs. The following step is to send a specific command to the transmitter with the parameters of the selected transmitted waveform. Only one transmission pulse can be emitted at one time, but up to two different pulses can be saved in memory for the case that the user wants to switch operating modes during an experiment. Each mode has the capability to be programmed to have binary phase coding, with a minimum baud of 1µs. Chapter 3 explains these two terms in detail for those unfamiliar with the concepts. The maximum pulse length the transmitter can handle is 400 µs given that the power level is tolerable with the hardware. If transmission bandwidth requirements are restricted due to hardware or communication regulations, the shape of each baud in the selected pulse can be formed into a Gaussian shape instead of the typical square pulse. The Gaussian shape for long pulse lengths significantly reduces the transmitted signal bandwidth, at the cost of a reduction of average power. In order to protect

42 21 the transmitter hardware, the maximum Voltage Standing Wave Ratio (VSWR) of the antennas must be less than 1.4. For antennas measured to have a VSWR larger than 1.4, the transmitter will decline operation to avoid damaging reflections within the transmitting cables. The flexibility of the described transmitter is ideal for the purposes of CIRI because of the ability to program a variety of waveforms, and the capability to switch modes in a timely manner. Figure 2.4. High Power Transmitter used for CIRI, developed by Genesis Software.

43 Antennas The selection for antennas used to transmit and receive the radar waveforms are called Coaxial-Collinear (CoCo). These narrowband antennas consist of multiple sections of coaxial cable fused together by alternating the connection of the inner and outer conductor [25]. Each element of the CoCo antenna is cut at lengths equal to the half of the transmission wavelength multiplied by the velocity factor of the cable, typically around 0.67, to account for the difference in propagation speed between free space and the cable. Since sections are cut based on the transmission wavelength, CoCo antennas have limited bandwidths, where 1 MHz is a desirable value. Increasing the number of elements reduces the beamwidth of the radiation pattern while multiple lines being fed in parallel significantly increases the gain and sensitivity. The advantage of the CoCo antennas include the feasibility of the manufacturing, inexpensive to construct, and easily portable. CoCo antennas are commonly used for radars examining the ionosphere, including large aperture arrays such at JRO. For CIRI at PSU, eight CoCo antennas are used in total, with four being used for each channel of transmission. The two channels are adjacent to one another and aligned along the magnetic East - West plane. Due to the alignment, the two arrays are accordingly named the East array and West array. Each CoCo contains 26 elements sectioned by half wavelengths of 49.8 MHz. The array was designed such that the main beam would be narrow in the magnetic East-West direction and angled perpendicular to the geomagnetic field at E-regions heights. At the specific latitude of Penn State, this required the antenna boresight to be angled at approximately 18 relative to the Earth s Surface, in order to be perpendicular to the geomagnetic field. The array consists of a front and back plane to correctly steer the beam, while also canceling out the backlobe. The front and back plane each have CoCo antennas elevated at 3 and 6 meters, which were erected with a simple pulley system. Figure 2.5 shows the antenna layout while Figure 2.6 shows the simulated radiation pattern on the antenna array. Since the antenna boresight is steered to a low elevation angle, the presence of sidelobes are more apparent. The sidelobes of the antenna beam occasionally lead to altitude ambiguities of the detected events, because the sidelobes illuminate the ionosphere at angles dissimilar

44 23 to the boresight. Further processing needs to be performed to interpret which beam a target was illuminated by, leading to a more accurate evaluation of the altitude. For CIRI at Huancayo, the installment of the CoCo lines is more straightforward because the antenna main beam is required to radiate normal to Earth s surface rather than an inconvenient angle. Consequently, the lines will only be elevated at one distance above the ground with a value of half the wave length in free space. The initial antenna configuration consists of an East and West array, with each array having four lines of 26 element CoCo antennas installed parallel to one another. Figure 2.7 shows the simulated radiation pattern for this setup. Notice that sidelobes are still present. Eventually, CIRI at Huancayo is proposed to have up to 16 CoCo lines for each array, which would significantly reduce the beam width of the antenna array, leading to a narrower portion of the ionosphere to be illuminated. 3 m East Array West Array 3 m 6 m ~50 m N Figure 2.5. Coaxial-Collinear antenna array layout utilized for CIRI at PSU (Hackett, 2013)

45 24 Figure 2.6. Simulated radiation pattern of CIRI at PSU antenna array. The slice of the radiation pattern is taken perpendicular to Coaxial-Collinear lines.

46 25 Figure 2.7. Simulated radiation pattern of CIRI at Huancayo antenna array. The slice of the radiation pattern is taken perpendicular to Coaxial-Collinear lines. 2.7 RF Front End For each IPP, analog voltages of the reflected returns are collected upon completion of the transmission pulse initially via the antennas and TR switch. The output of the TR switch is then directly sent to the RF front end in order to improve the quality of the analog signal. In addition to containing vital information of the current condition of the ionosphere, the returns input to the RF front end are corrupted with excess noise and are typically low in amplitude. In order to effectively perform analysis on the reflections, it is essential to remove as much of the noise as possible. Therefore, before any further digital processing is implemented, the RF front end governs the incoming analog signal. This complete subsystem consists of a chain of multiple filters and amplifiers to restrict the frequency content to a

47 26 narrow band, and increase the overall power level. Narrow band signals are ideal for further processing because of the guaranteed removal the unavoidable ultra wideband white noise. A block digram of the RF Front end is shown in Figure 2.8. Receive RF Front End RF Ch. 1 from Transmitter 49.8 MHz BPF 50 MHz Tx Blanking RF BPF Limiter +24 db 70 MHz LPF 21.4 MHz BPF 21.4 MHz BPF +24 db RF Ch. 1 to USRP TX Blanking from Radar Controller Local Oscillator from DDS Splitter RF Ch. 2 from Transmitter 49.8 MHz BPF 50 MHz RF BPF Tx Blanking Limiter +24 db 70 MHz LPF 21.4 MHz BPF 21.4 MHz BPF +24 db RF Ch. 2 to USRP Figure 2.8. Block Diagram of RF Front End for both CIRI at PSU and CIRI at Huancayo (Hackett, 2013) The RF front end consists of a few additional features that benefit in the protection of the hardware and the use of the USRP. A blanking pulse, generated by the radar pulse generator, is a binary signal input to the RF front end to assure no hardware damages occur from strong returns due to the coupling of the two antenna arrays upon transmission. Hardware components generally can handle an input signal up to a certain voltage level, but once exceeded, the internal circuitry will become defective. As briefly explained in Section 2.3, the blanking pulse contains the opposite logic of the transmission pulse. The signal input is connected directly to an RF switch, which passes the returns only when the blacking pulse is logic high. Hence strong returns from the direct transmission pulse are avoided as the blanking pulse is logic low at those instants. Further protection is made with an RF limiter, that only passes signals with amplitudes below a designed value. The other feature of the RF front end is to mix the center frequency of the returned signal down to MHz. For this reason, the additional input of MHz is included. The reason for selection of these precise frequencies are due in part because availably of corresponding filters through vendors, and for reasons to be explained in Section 2.8. Supplementary information about the RF front end includes the characterization of the gain being measured to be around 49 db and an output bandwidth of 5 MHz. Also, the theoretical noise figure for the system was calculated to be approximately 8 db. The output of the two received channels are sent to the USRP, primarily used as the digital receiver. An actual picture of

48 27 the assembled front end is shown below in Figure 2.9, along with a component list in Table 2.1. Figure 2.9. Picture of the assembled RF front end, using a combination off-the-shelf components. Table 2.1. Receive RF front-end components used by CIRI (Hackett, 2013). Manufacturer Part Number Description TTE, Inc. KB8-49.8M-5M A 49.8-MHz Band-pass Filter MiniCircuits SIF MHz Band-pass Filter MiniCircuits ZX80-DR230-S+ RF Gating Switch MiniCircuits VLM-33-S+ RF Limiter MiniCircuits ZFL-500LN+ +24-dB RF Amplifier MiniCircuits SLP MHz Low-pass Filter MiniCircuits ZX05-1L-S+ RF Mixer MiniCircuits SIF MHz Band-pass Filter MiniCircuits SBP MHz Band-pass Filter MiniCircuits ZFL-500LN+ +24-dB RF Amplifier

49 Universal Software Radio Peripheral The digital receiver used for CIRI is a Software Defined Radio called the USRP with the specific version being N210, shown in Figure The primary purpose of the USRP is to digitize the incoming analog signal via an Analog-to-Digital Converter (ADC). The USRP has a built in 14 bit ADC that can sample up to a rate of 100MHz. The motherboard contains two configurable ports for daughterboards desired for the reception and transmission of analog signals. For the purposes of CIRI, only a receive daughterboard is used and is called BasicRX. Other receive daughterboards are available for the USRP where the frequency band of operation is the main specification of interest. The BasicRX is used for direct sampling of any signal with frequency content between 1 MHz and 250 MHz. Figure Software Defined Radio utilized for CIRI - USRP N210 Once the BasicRX daughterboard samples the signal from the RF front end, the Digital Downconverter (DDC) on the motherboard converts the signal to baseband. The DDC has a resolution of Hz, and can therefore be tuned to any integer multiple of this value. For this reason, the frequency content of the RF front end is mixed to be centered at MHz before transferring to the USRP. The

50 29 phase information of the baseband signal is preserved by sampling the Inphase (I) and Quadrature (Q) values, before sending this data to the host computer via ethernet. For those unfamiliar in I and Q sampling, more details are provided in Chapter 3. The digital samples are scheduled to be synchronized with binary signals from the radar pulse generator because of the 10 MHz sinusoidal clock originating from the clock signal generator. 2.9 Software: Sauron Sauron is name of the python script that handles the incoming I and Q data from the USRP, and processes and displays the results in real time. To accomplish this task, the user must manually input specifications about the current waveform such as the IPP, baud width, coding sequence, and sample rate. Other plotting parameters are included in the input file and must be entered before the program is executed. The processing techniques performed with Sauron will be discussed in detail in Chapter 3. The current program can also perform meteor detection and classification using a similar procedure described in Chapter 4. It is with this program that the detection of the ionospheric events in Huancayo will be detected and as a result provide a command to alter the waveform configuration. A flow diagram is presented below in Figure 2.11 to illustrate the steps toward the data collection and real time processing for CIRI. The tables on the left most side are the necessary inputs for effectively running the program.

51 30 General Parameters Input Directory Output Directory Freq of Transmission Sampling Rate Number of Chans Data Type Baud Length Binary Code Process Amount Raw Data File Size Data Collection Real Time Plotter Plotting Parameters Locate New File Time Averaging Amount Range Averaging Amount Decimation type Size of RTI Window Read Raw Data and Reshape Roll data to synchronize with transmitter pulse Meteor Detection and Classification Repeat Until End of File Average Raw Data Calculate Power and Convert to Decibals Calculate Noise Level and SNR Plot Figure Flow diagram of the Sauron real time processing software.

52 Chapter 3 Radar Signal Processing 3.1 Introduction To complement the baseband RF signal output by the hardware section of a radar system, the essential proceeding action involves the software portion. The beginnings of any modern software stage involves the digitization of the RF signal via the ADC. Following the digital sampling, the data is further utilized for various selected processing techniques. The purpose of any signal processing algorithm is to manipulate the incoming digitized signal in a logical manner for a human user to interpret. For radar signal processing algorithms, the chosen techniques allow the user to decipher if anything of significance transpired in the transmitted media. For the purposes of the original radar system during World War II, without proper signal processing techniques, the location of a nearby aircraft could be misconstrued toward being in an alternate position. As computing speeds continue to rise, advanced processing techniques anticipated to further improve data interpretation becomes more practical. Depending on the computational complexity and the urgency, some radar processing algorithms can be chosen to be performed after the system has completed taking measurements. For most ionospheric radar systems this statement holds true, since the radar is used for observations and analysis can be done offline without any setbacks. In the case of CIRI however, processing algorithms are required to be executed in real time. In order to make changes in the transmitted radar waveform with the purpose of enhancing returns, observations of the ionosphere must

53 32 be processed as fast as possible to accomplish CIRI s goals. To understand the software portion of CIRI, this chapter first introduces the fundamentals concepts of radar signals, which are relevant toward any application of radar systems. Then the processing techniques commonly used to analyze returns from the ionosphere will be explained in Section Radar Signal Fundamentals Interpulse Period As mentioned in Section 1.1.2, the selection of a transmitted waveform for radar systems require consideration toward the aspects of the targets to be studied. For ionospheric studies, both doppler and range information are critical components to the scientific community toward proper understanding of the plasma instabilities. Therefore the commonly selected type of transmission waveform is a pulsed signal. To review, the two major features of a pulsed signal are the pulse length and the IPP (also called Pulse Repetition Interval (PRI)). Selection of a fixed IPP defines the maximum unambiguous range of a target to be detected by the radar. Targets located outside of the maximum unambiguous range will be ranged aliased to the proceeding IPP, leading to interpreting the range to be smaller than the reality. If approximated range information about the target is known in advance, the selection of the maximum unambiguous range should be selected to be slightly larger than its location. This leads to more frequent samples of the target, rather than the alternative of having a larger IPP and not gathering optimal amount of measurements. For a pulsed radar signal decided to have a maximum unambiguous range, R max, while transmitting an electromagnetic wave traveling in free space at a velocity of 3x10 8 m/s, c, the resulting IPP in seconds is: IP P = 2R max c (3.1) Since the plasma instabilities in the ionosphere mainly occur around the 100 km to 300 km region, a suitable IPP to study the events would be around 2 µs at the magnetic equator. For ionospheric radars located not along the magnetic equator, the radar beam is not pointed perpendicular to Earth s surface. Therefore

54 33 to study similar targets, the selected IPPs must be larger than 2 µs Radar Equation Within a pulsed radar signal, the transmitter is active for a specified time less than the length of the IPP. In other words, the duty cycle is less than 100%. While active, the transmitter emits the chosen frequency within the pulse shape, or envelope. The length in time of the pulsed envelope, or duty cycle, is proportional to the amount of average power being transmitted. The greater the amount of average power the greater the likelihood of receiving a signal from a target from distance locations or of low detectability, also known as Radar Cross Section (RCS). Due to electromagnetic theory, while an electromagnetic wave is propagating in free space and reflects off a target at a distance, R, from the transmission antenna, 1 the power of the signal decreases by a factor of after transmission and after R 2 reflecting off the target. Therefore the total power loss in the signal once received is on the order of 1 R 4. Since the plasma instabilities develop at distances far away from the radar system, the signal received by ionospheric radars are typically very low. To properly detect low incoming signals, the gain of the antennas must be very large to compensate. The gain of an antenna is proportional to the physical size of the antenna, which is why most ionospheric radars require much real estate. For example, the antenna aperture at Jicamarca Radio Observatory and Arecibo Observatory are 84,100 m 2 and 70,685 m 2, while transmitting at a peak power of 4 MW and 2.5 MW respectively [26]. The radar equation takes each of the described factors into account to provide an estimate of the received power from a target at a distance, R, and with a RCS, σ: P r = P tg t G r λ 2 σ (4π) 3 R 4 (3.2) Where P r and P t are the received and transmitted power, G r and G t are the antenna gains for reception and transmission respectively. The variable λ is the wavelength of the transmitted signal due to the frequency selection, and is defined by c. For a full derivation of Equation 3.2 see [3]. Generally for monostatic f radar systems the antenna gains for reception and transmission are equal, therefore Equation 3.2 can be simplified to only include a factor of G 2.

55 Range Resolution While collecting radar measurements, depending on the size of the target and the amount of targets the user is expecting in the media, the selected waveform plays a major role in ensuring each target is individually detected. Range resolution is defined as the minimum distance in which two targets can be individually identified. Without a proper selection of range resolution two targets located in close proximity to one other can be observed as one instead of two. For pulsed radar signals with a pulse length of τ the range resolution, δr, in meters is defined as: δr = cτ 2 (3.3) Ideally any radar operator would like to choose the range resolution to be as small as possible, however many restrictions are involved with this decision. In Fourier theory [27], the bandwidth, B, occupied by a rectangular pulse is inversely proportional to the length of the pulse, generally estimated by the reciprocal ( B 1 ). Therefore, a small pulse hoping to obtain a tiny range resolution will τ occupy a very large bandwidth in the frequency domain. In practical applications of radar, the hardware used on the transmission and received end only operate properly in a finite bandwidth of the spectrum. Signals exceeding this bandwidth will get corrupted by the hardware limitation. For the case of ionospheric radars, operation bandwidths are typically regulated by federal committees due to the high transmitted power, and for the prevention of causing interference to other communication operators. Other considerations made when choosing a range resolution is the sampling rate used to collect the received data. The sampling rate must satisfy the Nyquist criterion in order to properly recover the received signal. The Nyquist criterion states that the sampling rate, F s, used on the received signal must be greater than or equal to twice the occupied bandwidth of the signal ( F s 2B ). If the occupied bandwidth is too large for the Nyquist criterion to be met, then selected pulse length must be made larger Binary Phase Coding Based on the previous two sections, the dilemma when selecting a simple pulsed waveform arrives at the trade off between higher average power and smaller range

56 35 resolution. Higher average power (longer pulse width) will be able to detect low RCS targets more comfortably, while a short pulse width (small range resolution) will be able to decipher between multiple targets nearly adjacent to one another. The development of coding schemes for radar signals refrains from this situation by generating a waveform that is able to achieve an optimal range resolution while still emitting a large average transmitted power. The foundation of binary phase coding is a sequence of binary numbers (1 s and 0 s) that correspond to a particular phase of the transmitted signal. Each binary digit in the sequence also represents an interval at which the phase designation is made. The set of subpulses or bauds, τ B, can be viewed as a large pulse partitioned into M equal segments, where M is the length of the binary sequence ( τ B = τ M ). The significance of the binary digits is the phase of the transmitted sinusoidal frequency at the beginning of each baud. A binary digit of 1 corresponds to an initial phase of 0 while 0 corresponds to a phase of 180. A table of known binary sequences ranging from 2 to 105 can be found in [3, 5]. Each sequence was individually designed to achieve a range resolution equivalent to a pulse of length τ B because of the output response of the matched filter, a topic to be discussed in Section As a result, a short baud length can be coded with a long sequence to acquire quality returns from targets while maintaining a suitable range resolution. Binary phase coding is routinely used for ionospheric research because of the simplicity of programming the selected waveform. Other coding scheme that are occasionally used for radar signals are Huffman Codes, Ipatov codes, quadrature coding [5] Inphase and Quadrature Sampling The initial step toward applying any processing techniques on the software side is to digitize the voltage samples received by the radar. In addition to the magnitude of the received voltage reflected from a target, the phase of the incoming signal contains critical information for analysis, especially if the radar contains multiple receiver channels. The phase of the baseband signal also important when recovering the code of the transmitted signal, which will be discussed in Section Therefore a common sampling technique used for radar systems is to ac-

57 36 quire both magnitude and phase information. To obtain both requirements, the incoming analog signal is first split into two channels. Since the incoming signal is modulated, a digital downconverter is required to convert the signal to baseband, meaning to center the frequency content around Direct Current (DC). After splitting the incoming signal, one channel is immediately mixed to baseband, while the other is phase delayed by 90 before mixing is performed. The result is two orthogonal samples which are called the Inphase (I) and Quadrature (Q). It can be imagined for these samples to be plotted on a complex plane, with the inphase representing the real component and the quadrature representing the imaginary. If the baseband signal contains any frequency content, the phase will rotate at the value of the frequency. Due to the described relations of the I and Q samples, the phase, θ, and the magnitude of the voltage, V, of the signal are calculated by: ( ) Q θ = tan 1 (3.4) I V = I 2 + Q 2 (3.5) The power of the baseband signal is derived from Equation 3.5, by simply squaring the value. This is due to the relation described in introductory circuit theory textbooks [28] Matched Filter Once sampled, the essential subsequent step taken for a phase coded radar signal is to apply a matched filter. Match filtering is used in a variety of applications in addition to radar systems, including communications. The basis of the matched filter is the understanding that the user has prior knowledge of baseband envelope of the transmitted signal. Assuming that the radar target is stationary, the received baseband envelope will have a similar envelope as the transmitted signal, with the only difference being that they are mirror images on one another. The received baseband envelope undergoes many phase and amplitude fluctuations in the transmitted medium, but the general shape of the envelope can always be extracted. The purpose of the matched filter is to take advantage of knowing the shape of

58 37 the received baseband signal, and design a linear filter whose output will maximize the Signal-to-Noise Ratio. Maximizing the SNR will increase the likelihood of the detection of a target, in addition to understanding specific information about the target. For an incoming baseband signal, h(t), the impulse response of a linear filter guaranteed to maximize the SNR in time domain notation is h ( t), where the * means the complex conjugate. A full derivation leading to the mentioned conclusion can be found in [3,5]. Given a baseband envelope generated by a binary phase coded sequence, the matched filter is applied by convolving this signal with a mirror image version of itself. This is in essence an autocorrelation function. To give an example, a binary sequence of length 13, also known as the Barker 13, will produce a baseband envelope as shown in Figure 3.1, assuming no phase change. Figure 3.1. A time domain voltage sequence of a Barker 13 code The binary sequence of the shown Barker 13 is Due to the phase value of the corresponding binary numbers mentioned in Section the resulting voltages in the complex plane are completely real. A phase of 0 corresponding to 1 while 180 corresponding to -1, hence resulting in a voltage sequence shown in Figure 3.1. The autocorrelation of this time sequence results in a matched

59 38 filter response displayed in Figure 3.2. As a result the match filter provides a peak to side lobe ratio of 13, signifying a special case of the Barker sequences. Each Barker sequence was designed to have a maximum side lobe of 1, therefore the peak to maximum side lobe ratio is always the length of the sequence. Figure 3.2. Matched Filter output of a Barker 13 sequence Figure 3.2 is a simulated example of a radar return processed for a point target, with radar returns causing no amplitude or phase changes. The normalized delay represents the number of baud lengths from complete overlap of the two mirror imaged signals. One feature of significance displayed in Figure 3.2 is the main lobe of the matched filter response being one baud length. Returning to the concept of range resolution, since the main lobe peaks for one baud length and the surrounding samples are considerably lower in amplitude, the baud length, τ B, is the value used for the pulse length in Equation 3.3. As a consequence, the range resolution can continue to be small while the overall pulse length can obtain large values. The list of sequences shown in [3, 5] are the ideal binary phase code sequence for specific lengths, since the autocorrelation of these sequences maintain a main lobe lasting one baud length, while suppressing the size of the subsequent sidelobes. The peak

60 39 to maximum sidelobe ratio is important toward deciphering between targets. The reason for the necessity of not having high sidelobes or a main lobe lasting many bauds lengths is because the resolution will become larger and hence masking potential neighboring targets Doppler Effect and the Ambiguity Function A major assumption made in order for the matched filter to work optimally is for the target to be stationary meaning that there is no frequency content in the baseband signal. In reality however, targets will be moving with some velocity with respect to the radar system causing the baseband signal to contain some frequency content. As briefly mentioned in Section 1.1.2, the phenomena that causes the transmitted signal to shift in frequency due to a moving target is called the Doppler effect. If the target s motion is toward the radar system, then the transmitted frequency will increase, while a target moving away relative to the radar will decrease the value of the transmitted frequency. If the transmitted electromagnetic signal has an original wavelength of λ before reflecting from a moving target traveling with velocity, v r, relative to the radar system, the resulting baseband Doppler frequency is: f d = 2v r λ (3.6) Before baseband conversion, the frequency computed in Equation 3.6 is added to the transmitted frequency for a incoming target and subtracted for an outgoing target. If there prior knowledge of the targets radial velocity, than an additional mixing process can be applied to bring the received signal to baseband. However, in most cases the radial velocity of a target is never known to the user and in certain applications can only be estimated using complex methods. Because of this uncertainty, the matched filter output for Doppler shifted signals would not be ideal, resulting in a distorted response with a reduced peak to maximum sidelobe ratio. The ambiguity function is a three dimensional surface plot of the output of the matched filter as a function of Doppler frequency. The ambiguity function provides an idea of how distorted the matched filter output will become due to the different Doppler shifts. The surface plot of the ambiguity function, χ(τ, f d ) is

61 40 calculated by: χ(τ, f d ) = h(t)h (t + τ)exp(j2πf d t)dt (3.7) where h(t)h (t + τ) provides the time sequence of the matched filter output for different delays, τ, while exp(j2πf d t) induces the complex sinusoidal signal of Doppler shift, f d. The variable, t, is a dummy variable needed for integration purposes. An example of the ambiguity function for a Barker 13 radar signal is provided below. Figure 3.3. Ambiguity Function Surface for Barker 13 sequence (Levanon, 2004) From Figure 3.3, is it evident that for only small Doppler shifts provide a close to optimal response for the matched filter. A Doppler shift above a nominal range completely alters the shape of the match filter, leading to a misinterpretation of the return. The Barker 13 waveform shown in Figure 3.3 is a waveform that is a common selection for ionospheric research. The plasma instabilities that develop in the ionosphere do have motion relative to the radar system, but not large enough to distort the match filter response dramatically.

62 Radar Signal Processing for Ionospheric Observations Range-Time Intensity Plot For ionospheric radars, a Range-Time Intensity (RTI) plot is commonly used to display information about the plasma activity. As the name suggests, the plot provides information about the radar returns in terms of range from the system over a period of time. Typical RTI plots for equatorial plasma instabilities were shown in Figures The time evolution of the plasma instabilities is the main purpose for generating these plots, which had led to conclusions about underlying physics driving the resulting structure. To construct an RTI plot each digitized sample for a single IPP are aligned adjacent to the subsequent IPP creating was is called a data cube. The data cube consists of one axis corresponding to the fast sampling rate, where each sample is a designated range away from the radar system. The other axis illustrates the slow sampling rate, which is determined by the length of the IPP. For one specific range the slow sampling rate generates a time domain representation of the returns. The third dimension in an RTI plot is the intensity, usually represented by a color or grey scale. The colors correspond to the magnitude of the power or SNR received by the target. The power can be determined by squaring the result of Equation 3.5 since power is proportional to V 2. The calculation of the SNR requires a little more processing, but the resulting RTI plot provides greater significance about the targets than the power plot. The essence behind the determination of the SNR is the estimation of the noise floor. An approximation of the noise floor is calculated in periodic intervals, by using a data cube of a specified duration selected by the user. Once the noise floor is known for a specific window of data, the SNR is simply calculated by: SNR = P N N (3.8) Where P is the power of the data samples and N in the estimated value noise of the floor. There are several developed techniques used to provide an approximate measure of the noise floor, each varying in complexity. For ionospheric research one of the more straightforward algorithms begins by sorting a data cube of a

63 42 specific time interval (ex. 2 seconds) in ascending order of power. The noise level can then be determined by taking the average of the lowest 25% of the data for the specific window. The process then proceeds to the next data cube with equivalent size. A more complex technique used for a better estimation of the noise floor is the Hilbrand-Sekon Method, which is fully explained in [29]. The resulting linearly scaled SNR can be further converted to decibels to reduce the possibility of large dynamic ranges. Decibel conversion from linear scale is performed by: SNR db = 10 log 10 (SNR) (3.9) RTI plots for ionospheric radars typically provide results for events lasting several hours, so the need to display each IPP individually is a bit of an overkill. To avoid the abundance of data, a processing technique called integration can be performed. Integration is the process of adding several IPPs together to degrade the time resolution, but consequently obtaining an increase in SNR from target echoes. There are two different types of integration: coherent and incoherent. The difference between the two techniques is that coherent integration maintains signal phase information while incoherent integration only uses magnitude information. Full proofs on how coherent and incoherent integration provide an increased SNR can be found in [3] Sky Noise Throughout the course of a day, the estimated noise level of the ionosphere does not retain a constant value. To the contrary, the noise level tends to vary significantly due to radio sources that pass through the beam of the antenna. The center of our galaxy is a major source of noise that emits energy all the way to Earth s ionosphere. Due to the Earth s rotation, once a day the beam of an ionospheric radar antenna will be pointed directly toward the center of the galaxy resulting in a significant increase in noise. In addition to the center of the galaxy, certain stars in space also generate enough energy to cause a spike in the noise level. Although these radio sources may be viewed as a hindrance toward observing quality ionospheric data, measuring variability of the sky noise is a common ap-

64 43 proach to calibrate the sensitivity of an ionospheric radar. At ionospheric radar facilities around the world, the time of the day at which the beam is pointed to the center of the galaxy and other radio stars can vary. If the system is not able to detect the changes in the sky noise throughout the course of the day than the plasma instabilities, occurring above the noise level, would not be able to be observed. The proper way to collect sky noise measurements is to run a radar system similar to any typical observation, except for the fact that no transmitter is to be in use. Without the use of a transmitter, the only data that is to be collected is noise received by the antenna. Running the observation for 24 hours and calculating the noise level with similar techniques as explained in Section 3.3.1, the full diurnal distribution of the sky noise can be plotted. A typical sky noise plot produced by JRO is shown below in Figure 3.4. Figure 3.4. Sky Noise Measurements collected at Jicamarca Radio Observatory on February 1, 2013 Since the antenna beamwidth at JRO is very narrow because of the size of the array, the precision of the sky noise measurements is high enough to see minor fluctuations. For antennas with larger beams, a similar pattern in the sky noise would be observed, but the precision would be degraded causing the minor abrupt changes to be smoothed out. From Figure 3.4, it is observed that the sudden changes in noise occur around 1AM and 9AM. These are results of the radio star

65 44 Hydra A and the center of the galaxy respectively [30]. The sky noise measurements generally are the same everyday besides about a four minute daily shift, because the rotation of the Earth is not exactly 24 hours Spectra Spectra and cross spectra are alternative processing techniques used to analyze pulsed radar signals. With a RTI plot, the user is mostly concerned with the activity of the targets for a specified period in time. With spectra and cross spectra however the frequency or Doppler content of the events are studied in order to learn more about the motion of the targets relative to the radar system. To calculate the spectra, the process begins the same way as calculating the noise floor for an RTI plot. A specified time window of adjacent complex samples of IPPs are formed into a data cube, then are transformed into frequency domain by taking the Fast Fourier Transform (FFT) for each range bin. Due to Fourier theory, since the I and Q samples are considered complex, the resulting Fourier transform will not be symmetric around the origin, therefore frequency content of the target can be analyzed for positive and negative Doppler shifts. For each range bin the following manipulation is performed: S(f d ) = F F T SHIF T {F F T {V IQ (t)}} (3.10) where V IQ (t) are the I and Q complex samples acquired as a function of the slow sampling rate, namely the IPP. The FFT shift is used to unwrap the FFT coefficients in order to be symmetric around the DC (0 Hz) axis. Typically the phase of the samples are not needed, while the power is the main measurement of interest. Therefore the spectra measurement in Equation 3.10 is modified to calculate power by squaring the magnitude, i.e. S(f d ) 2. The phase information is important for calculating the cross spectra, which is discussed in Section Since the spectra analyzes the doppler frequency with respect to each range, ionospheric radars use this data to observe how the plasma instabilities are moving perpendicular to the magnetic field lines. This motion is also called vertical drift velocity. To convert the FFT samples to the Doppler frequency axis one must first determine the maximum unambiguous Doppler frequency. As briefly described in

66 45 Section the PRF or IPP in pulsed radar signals determines the maximum unambiguous frequency and the value is calculated by the following equation: f max d = ± P RF 2 = ± 1 2 IP P (3.11) Once the extreme values of fd max are determined, the frequency axis is simply divided out evenly based on the number of samples used to generate the Spectra. Coherent or incoherent integration can be used increase SNR of returns, similarly to its application in RTI plots. The frequency axis can subsequently be scaled to velocity, in meters per second, by using Equation 3.6. Another conclusion from Fourier theory states that the power of the FFT coefficients will be proportional to the power of the I and Q samples that generated them. Therefore the RTI plot can be regenerated using spectra by simply adding each of the range bins independently. This results in a integrated RTI with time resolution of the amount of IPPs used for the spectra. A typical spectra plot generated by ionospheric research is shown below in Figure 3.5 [31]. Figure 3.5. Spectra Plot of Equatorial Electrojet collected at Jicamarca Radio Observatory on July 26, 2005 (Hysell, 2007)

67 46 Figure 3.5 shows two returns from the Equatorial Electrojet one from the main lobe and the other from a side lobe in the radar beam. The main lobe return is between the ranges km. As is shown, the plasma generating the electrojet has a spread of motion between -500 and 500 m/s in vertical drift velocity Doppler Map A Doppler map is a variant of the standard RTI Plot in which the color intensity corresponds to Doppler information instead of the SNR or Power. For ionospheric research, Doppler maps are primarily generated for long term plasma instabilities to associate the developed structure to a vertical drift velocity. The information extracted from these plots lead to conclusions on the evolution of the plasma instabilities over the duration of the event. Generating a Doppler map initially requires the computation of the spectra in order to provide sufficient vertical drift information for successive short periods. Hence, the resulting RTI plot will have a degraded time resolution. For long term events however, a larger time resolution contributes a minute loss of information. For each range bin in spectra data, the distribution produced by the FFT coefficients will maximize at some Doppler velocity, whether it is a positive velocity, negative velocity, or DC. The Doppler velocity corresponding to the maximum FFT coefficient is then selected and occupies one time resolution sample on the Doppler Map. The process is then repeated for successive spectra data, and each range bin. Figure 3.6 displays the Doppler Map for a Equatorial Spread F observed at JRO. One point to note about the color scale in Figure 3.6, the vertical velocity is referenced to changes in range rather than the change in frequency. For example, a positive vertical velocity defined by the Doppler Map concludes that the plasma is moving up or away from the radar system. For Doppler measurements, this would constitute in a negative velocity. The observed Equatorial Spread F reveals that majority of the plasma in the event are moving away from the radar which results in the very extended structure in range.

68 47 Figure 3.6. Doppler Map of Equatorial Spread F observed by Jicamarca Radio Observatory on January 1, Spectrogram In addition to Doppler maps, spectrograms also require spectra data to produce a time dependent display of the plasma activity. Spectrograms however do not provide information about all of the sampled ranges, but only reveal measurements for one specific range bin. The selected range bin is chosen by the user and typically at a range where the plasma activity is most dynamic. Even though spectrograms are only concerned about one range bin, the plots are still three dimensional with the vertical axis corresponding to the entire spread of Doppler velocities/frequencies, the horizontal axis representing the time, and the color scale displaying a normalized power. Often these plots are called also frequency time intensity plots to give an analogous nomenclature of the RTI plots. Ultimately, these plots provide facts about how the Doppler content of the plasma alters over time for a specific range. Therefore further conclusions can be made about the generation of the event structure. To produce a spectrogram, the spectrum of the chosen range bin must be calculated by using Equation Over time, each ensuing spectrum is plotted adjacent to the preceding spectrum, adding an additional slice on the time

69 48 axis. Once the entire plotting duration is compiled, the color scale is initially normalized by dividing all of the computed FFT coefficients by the maximum value of the entire plot resulting in a dynamic range between 0 and 1. For aesthetic purposes, the normalized values are further converted to decibels. Figure 3.7 is an example of a Spectrogram provided in literature of a Sporadic E Layer at a range of km [32]. The Doppler axis is displayed in meters per second, with the normal convention of positive values representing movement toward the radar system. Due to the content of the spectrogram, it is clear that the motion of the plasma in the Sporadic E Layer was mainly descending, with only a short duration shifting to ascending. Figure 3.7. Spectrogram of Sporadic E Layer observed with the Cornell University Portable Radar Interferometer on May 7, 1983 (Riggen, 1986) Interferometry So far, the description of the radar processing techniques have only been concerned with the analysis of one receiver or channel. If the hardware installation of the radar involves multiple receivers, each sampled channel is treated independently to produce the previously described plots. However for multichannel radars, the amount of processing techniques can be further extended in order to compare the returns from each of the receivers. A major reason for using multiple channels is to provide an estimate of the reflected signals angle of arrival, which leads to a more precise determination of the targets position. For ionospheric radar systems, multichannel radars are a necessity in order to extract vital information about the plasma instabilities that cannot be achieved alone with a single channel. Some examples of additional information are East-West drift, Imaging, and meteor distributions. These topics will be discussed in detail throughout the remainder of the chapter.

70 49 The simplest example of multichannel radar system is given in Figure 3.8. This radar setup is also called a single baseline interferometer because target location information can only be determined in the one plane along the antennas. As shown, the configuration just requires two antennas separated by a distance, d. For a simple demonstration, a point target is located at a distance, R, away from the antennas and at an angle of, θ, relative to the middle of the two antennas. For a radar system of this configuration, the transmitted signal can either be emitted by both of the antennas used for reception, or an alternate antenna located in close proximity to the others. The antenna beam occupies a large area in space, especially at far distances, therefore an angle of arrival estimate is possible for targets not completely with the antenna boresight. Upon reflection of the transmitted electromagnetic wave, the reflected wave scatters in all directions and is assumed to be a plane wave by the time the signal reaches the antennas. Due to this assumption, the signal first arrives at the left most antennas then arrives at the rightmost antenna after a short duration. This assumption also implies that the signals contains the same voltage information, with amplitude differences being insignificant. However, the phase of the two signals are different because of the non identical receiving times. Using geometry, the extra distance the reflected signal needs to travel in order to arrive at the right channel is shown by δr. Knowing the frequency of transmission, the phase difference, φ, between the two signals can also be calculated. The wavenumber, k, is necessary to calculate the phase difference. The wavenumber is a factor heavily used in electromagnetics giving a ratio of the number of radians covered per wavelength. The wavenumber for a electromagnetic wave with wavelength, λ, is found by: k = 2π λ (3.12) Then using the small angle approximation where sin(θ) θ the estimation for φ is determined by: φ = k δr = kd sin(θ) kdθ (3.13) A single baseline interferometer is a standard technique used in ionospheric research to study the East-West drift velocity of the plasma. The plasma insta-

71 50 Figure 3.8. Classical example of a single baseline interferometer bilities that are observed by pointing perpendicular to the geomagnetic field are not stationary in the vertical direction as shown by Figures 3.6 and Figure 3.7. In addition, the plasma instabilities propagate along the magnetic field lines. Since the geomagnetic field lines are in the East West direction, this motion is therefore called the East-West drift velocity. To properly study the East-West drift, the antennas for the single baseline interferometer need to alined along the magnetic East-West plane to achieve a proper angle of arrival estimate. Through a series of measurements, the phase of the plasma instabilities can be tracked, resulting in an approximation of the East-West drift velocity. The derivative of the phase will provide an estimate of this velocity. To derive this value, taking the derivative of both sides of Equation 3.13 with respect to time, the following relation occurs: dφ dt = kddθ dt (3.14) When processing the phase information as a function of time, the user is only concerned with a particular range because the East-West drift is variant at different altitudes. If both sides of Equation 3.14 are multiplied by the range of interest, r, the relation is further reduced. The right side of Equation 3.14 takes the form of the tangential velocity of a rotating object. Since the ranges are so large and the angle of arrival is assumed to be small, we can assume the surface illuminated for EW drift measurements is flat. Once the kd term is divided to the opposite side,

72 51 the East-West velocity, v EW at a distance, r, is equated by: r dφ dt = rkddθ dt (3.15) v EW = r dθ dt = r kd dφ dt (3.16) This is the theory behind calculating the East-West drift, further processing details will be explained in Section To further extend the capabilities of the single baseline interferometry system, an additional baseline can be included perpendicular to the original, such as in Figure 3.9 [33]. Notice that this configuration includes an antenna in the center of each baseline, and the spacing between the antennas on a single baseline are different lengths. For ionospheric research this is mainly used for meteor observations since these targets occur anywhere in the ionosphere, not necessarily perpendicular to the geomagnetic field. Therefore the antenna used for transmission typically has a very wide beam in order to illuminate a large area of the ionosphere. With the addition of the second baseline, and using the phase differences in both the East-West and North-South direction, an estimated three dimensional location can be made about where the meteor originated from because meteors are considered as point targets. After many meteor events, a map of all the occurrence can be constructed to make evaluations of locations of meteor sources. An example of this meteor map is shown in Figure 3.10 [34]. Each point represents one meteor event and the color corresponds to the incoming velocity. As shown the meteors for the particular observation tended to cluster around the North East section at JRO. For further details about meteor interferometers see [33, 34] Cross Spectra For single baseline interferometers used to study the East-West drift velocity of the plasma instabilities, the standard processing approach is to initially calculate the cross spectra. This technique is used to discover the phase differences between the receivers for short increments in time, leading toward an estimate of the angular location of a target. Similar to spectra, the cross spectra shows information in terms of range and doppler frequency. The processing technique was first proposed

73 52 Figure 3.9. Antenna configuration of a meteor interferometer installed in Buckland Park, South Australia (Holdsworth, 2004) in [35]. In the practical radar setting, the user does not expect to receive echoes from a single point target, hence the cross spectra is used to determine the position of a highly localized scattering region [35]. The spectra of the two channels must initially be determined in order to proceed with solving for the cross spectra. For spectra content achieved by Equation 3.10 for two channels named i and j, the cross-spectra is equated and normalized for one specific range as follows: CS ij (f d ) = S i (f d )Sj (f d ) (3.17) S i (f d ) 2 N i S j (f d ) 2 N j Where the noise levels for channel i and j are N i and N j respectively. The noise level for each channel is calculated independently using the technique outlined in Section The result of Equation 3.17 is a complex valued signal as a function of Doppler frequency, where the phase is relative to channel i. Contrary to the analysis of spectra, both the magnitude and phase of the cross-spectra contain relevant information toward the advancing of the processing techniques. Due to the normalization, the magnitude of all the cross spectra coefficients acquire values between 0 and 1. The magnitude, also called the coherence, is a relation of how prominent the scattering regions are. A coherence value close to 1 can be regarded

74 53 Figure Meteor distribution map produced at Jicamarca Radio Observatory on November 19, 2002 (Chau, 2004) as large point target, and values close to zero correspond to either no echoing region or a very diffuse target. The angle of each of the coefficients correspond to the angular position of the target relative to the center of the interferometer. Equation 3.17 is generalized for two antennas i and j for case that more than two antennas are used for cross-spectra measurements, a necessary requirement to perform radar imaging, a topic to be discussed in Section Figure 3.11 below shows a typical example of the two Spectra plots along with the coherence and phase information [36]. The figure shows larger coherence value measurements for the targets located at higher ranges, meaning the plasma is confined to a certain region of the ionosphere. On the other hand, the lower range targets exhibit low coherence, concluding the plasma is spread over a large area. It is also evident that the phase content is more structured in the range and frequency values corresponding to the large coherence, while in areas of low coherence, the phase is highly randomized.

75 54 Figure Cross Spectra measurements of ion-acoustic enhancements collected at the EISCAT Svalbard radar on January 17, 2002 (Grydeland, 2005) Phase Plots A single cross-spectra measurement alone provides limited information about the motion parallel to the antennas of reception. For the case of ionospheric radars, determination of the East-West drift velocity is only possible after a series of crossspectra measurements. Phase plots are a scatter plot providing a graphical display of the cross spectra phase information for extended periods of time. If a highly localized target is within the beam for multiple cross-spectra measurements, a phase plot is able to capture the progression of the phase, leading to an estimate of the East-West drift velocity. This is typically a post processing technique because the entire development of the plasma instabilities needs to be observed to provide the best estimate of the drift. Since East-West drift velocities are known to vary at different altitudes, phase plots only provide phase information for one specific range. Therefore the axes of the generated plot display the phase value or location relative the center antenna on one axis, and the time progression on the other axis. The selection of the phase

76 55 values requires also knowledge of the coherence values. If the selected range for the phase plots have low coherence values, then the determination of the East- West drift velocity is near impossible, since a linear progression is unlikely. In order to filter out the noise and diffuse targets resulting in low coherence values, typical phase plots only present phase information for coherence values exceeding 0.7. For one particular time instant, multiple phase values can be shown because the frequency content of the cross-spectra is ignored. The resolution of the phase plot is determined by the duration of time used to calculate the spectra. If the collection of all the phase content exceeding a coherence value of 0.7 results in scatter plot with a clear linear progression, estimating the slope leads toward the East-West drift velocity. Considering the slope represents the derivative of the phase with respect to time, this value is substituted into Equation 3.16 to achieve the derived velocity. There will inevitably be times where the phase plots behave arbitrarily, even with the filtering out of small coherence values. This could lead to the conclusion that the echo came from a broad region or from many dispersed localized regions. An example of a phase plot is shown below in Figure 3.12 [37]. Figure Phase Plot produced by an observation of an Equatorial Spread F at Jicamarca Radio Observatory on January 25, 1980 (Kudeki, 1981) The figure shows a clear linear relationship for the entire duration of the event.

77 56 The calculated East-West drift velocity for this particular Equatorial Spread F was around 60 m/s in an Eastward direction. The phase in this particular plot wraps around about halfway through because of the 2π phase ambiguity. Since the content of the phase can only retain values between 0 and 2π, if the progression eventually falls below or exceeds these extremes, the next scatter points will get wrapped around. Being aware of the possibility of the 2π phase ambiguity is critical towards interpreting the location of the scattering region. This effect is more common for radars operating at higher frequencies because the wavelength is shorter, therefore small changes in target angular location leads to larger phase differences. For calculating the East-West drift velocity however, this ambiguity not have any effect since only the slope is main parameter of interest Radar Imaging Introduction Recall from Section that a RTI plot provides the user with a range distribution of the plasma instabilities over a select amount of time. To those new to radar development, the echoes received from a single IPP would suggest that the plasma instabilities are confined to a one dimensional plane directly perpendicular the the magnetic field lines, which is the pointing direction of the antenna. The plasma instabilities in reality occupy a volume in space along the magnetic field lines, that still induce reflections even if the illuminated by the antenna beam off perpendicular. For all cases of ionospheric radars, the plasma instabilities located slightly off perpendicular to the magnetic field are illuminated because antennas do not have the ideal radiation pattern of a infinitesimally narrow beam pointed in the direction of interest. They instead have a main lobe containing a finite beam width, at which majority of the transmitter power is allocated. For large aperture arrays such as JRO, the half power beam width is around 1 degree, depending on the antenna configuration. In addition to the main lobe, antennas also have unavoidable side lobes that radiate at angles typically not of interest to the users observation. Since ionospheric radars are concerned with the returns from very distant ranges, even antennas with small main lobes cover a significant portion of the ionosphere. For example, the arc length occupied by the JRO antenna main-

78 57 lobe at 150 km is approximately 2.62 km. Based on the conditions for practical implementation of radar systems, the processed RTI plots are helpful for determining the range of targets, but are misleading toward the actual spatial structure of the plasma instabilities contained in the ionosphere. Radar imaging is a processing technique used to reconstruct the spatial distribution of the plasma instabilities located perpendicular and off perpendicular to the magnetic field. Generally, the images produced from this technique are concerned with the distribution in the East-West direction, but not the North-South, since the aspect angle of the plasma instabilities are small [38, 39]. Therefore, a typical imaging result displays the range distribution as a function of the angle off perpendicular to the magnetic field, i.e. zenith angle. An example of a radar image displaying the structure of an Equatorial Spread F is shown in Figure 3.13 [40]. The color scheme used to generate the image is based on two factors: the SNR and the vertical velocity. The intensity of the color is related to the magnitude of the SNR. The color green is assigned for echoes displaying zero or insignificant vertical velocity, while red and blue are associated with negative and positive Doppler shift respectively. As seen, combination of these primary colors are possible, and will a topic of discussion later in the section. Similar to RTI plots, images are produced using short segments of radar returns. Subsequent images are not concatenated with previous data, as with RTI plots, therefore the images are treated independently from one another. A sequence of images are combined to generate movies that illustrate exactly how the plasma instabilities achieved the given structure. Measurable parameters such as the East-West drift are not only enhanced by the compilation of movies, but a better understanding of the underlying physics of the events is possible. In [40], the sequence of Equatorial Spread F images lead to the conclusion that large scale waves were present in the bottom side of the F-region. In addition, presence of large scale plasma depletions were observed at the topside of Equatorial Spread F measurements in [41]. Needless to say, imaging is extremely beneficial toward the advancement of ionospheric studies. However, the major drawback of running imaging experiments is the complexity of the radar system configuration.

79 58 Figure Radar Image of Equatorial Spread F observed with Sao Luis Radar in Brazil on October 25, 2005 (Rodrigues, 2008) Radar Configuration The radar configuration setup to perform imaging is an extension of the single baseline interferometry technique described in Section For the case of imaging, more than two receivers are essential, and are installed along the plane of interest, usually in the East-West direction for measuring plasma instabilities. Not only are the amount of receivers important, but also the placement. An important parameter for an effective setup of imaging experiments is baselines. The number of baselines are equivalent to the integer value of unique distances between each of the receivers. If carefully chosen the maximum number of non-redundant base- P (P 1) lines for a set of P receivers is. The larger the number of baselines, the 2 higher the quality of processed images in terms of zenith resolution. Analogous to single baseline interferometry, the addition of multiple receivers constitutes to more comparisons of the phase of the incoming returns in each receiver, leading to a greater determination of the location of the plasma instabilities. The reason for the number of baselines being an important factor will be explained in the coming paragraphs. Some examples of radar configurations used for imaging experiments are shown

80 59 in Figures 3.14 and 3.15 [40, 42]. These display the antenna spacings installed for the Sao Luis Radar in Brazil and JRO respectively. The Sao Luis radar has four antennas for reception, and is optimized for imaging experiments. With four antennas, the maximum number of obtainable baselines is six, and this is achieved at Sao Luis due to the antenna spacing. The JRO configuration is more complicated by involving eight channels. This configuration is also optimized for imaging experiments resulting in the maximum number of baselines of 28. Comparing the two described setups, the JRO configuration has a clear advantage for obtaining quality images due to the size of the system, and number of baselines. Notice that some of the antennas used for JRO setup are not exactly along the East-West plane. In order to achieve 28 baselines, these receivers were necessary, but are noted to be outside the East-West plane when performing the processing. Also notice in Figure 3.15 the receiver located outside of the main array. The purpose of this final receiver is to achieve the longest baseline possible, also beneficial for creating a quality images. Figure Antenna configuration for imaging experiments with Sao Luis Radar in Brazil (Rodrigues, 2008) Radar Imaging Theory The theory behind the processing algorithm for radar imaging begins by introducing two terminologies: brightness distribution and visibility function. These terms

81 60 Figure Antenna configuration for imaging experiments at Jicamarca Radio Observatory (Chau, 2008) were originated from the radio astronomy field, where imaging techniques were first applied for observations far beyond the ionospheric region, for example the Milky Way [43]. Considering only a single range bin, the brightness distribution is defined by the backscattered power from the target as a function of arrival angle. Taking into account potential motion of the targets, the brightness distribution also analyzes the backscattered power as a function of the Doppler content. The visibility function is the spatial cross correlation function for the given range, where the spatial distance is defined by the antenna separations, i.e. length of the baselines between the receivers. Practically, the visibility function uses the cross spectra measurements for the particular range as a function of frequency and baseline. For ionospheric research, the overall goal of imaging is to obtain the brightness distribution for each range bin of the plasma instabilities, as displayed in Figure Obtaining the brightness distribution is only possible with the measurement of the visibility function. It has been shown in literature that the visibility function, g(kd, ω), and the brightness distribution, f(ψ, ω) are Fourier pairs of one another, where kd is the radial distance between the antennas, ψ is the zenith angle relative to the radar system, and ω is the Doppler frequency [43 45]. Since the brightness distribution is a measurement of power, this function is real valued. On the other hand, the visibility function is complex valued due to the cross correlation analysis. The Fourier relationship relating these two functions is defined as follows:

82 61 g(kd, ω) = 1 1 ψ 2 f(ψ, ω)a(ψ)eikdψ dψ (3.18) where A(ψ) is the gain of the antenna as a function of zenith angle. For simplicity in implementation, the antenna radiation pattern is often ignored. However, it has been shown in literature to greatly enhance the produced images if considered [46]. One assumption made by the Fourier relationship defined in Equation 3.18 is the continuous structure of both the visibility function and brightness distribution. Due to all modern radar systems dealing with digital data, the continuous assumption is impractical, but close approximations are still possible. The biggest impact of the made assumption falls on the visibility function. In order to have a near continuous visibility function, practically this entails an infinite amount of antennas where cross spectra measurements for any baseline are attainable. In reality, this function can only be discretely sampled for a very limited amount of baselines. Therefore maximizing the number of baselines are ideal for achieving the best estimate of the visibility function, and subsequently, the brightness distribution. Obtaining the largest baseline possible, within the bounds of the radar facility, is also beneficial to aid in the range of discrete samples. Another point worth noting about Equation 3.18 is that the radar imaging problem involves the inverting of the Fourier transform. The practical measurements, i.e. the visibility function, are set to equal the result on the right hand side of the equation, and information about the brightness distribution is to be determined. Therefore inversion techniques are needed to convert the observed measurements toward obtaining the brightness distribution, which is underneath the integral. Some inverse techniques first developed and applied for radio astronomy observations, are called the Capon and Maximum Entropy Methods [47, 48]. Each algorithm has its own computational complexity, with the larger computational cost resulting in highly enhanced images. Recently, these radio astronomy techniques were also applied to ionospheric research [40, 41, 45, 46, 49, 50]. Some additional algorithms are in development for ionospheric imaging using the ideas proposed by compressed sensing [51].

83 The Fourier Method One of the more intuitive methods used for imaging is called the Fourier method. As the name suggests, this method uses the fact that the visibility function and brightness distribution are Fourier pairs in order to proceed with the inversion process. However, since the visibility function is discretely sampled, only an estimate of the inverse Fourier Transform can be performed. The Fourier method was the first technique used to implement ionospheric imaging where the development of the Equatorial Electrojet along the East-West plane was observed [44]. The derivation of the Fourier method disregards some of the variables introduced in Equation 3.18, and reduces the relationship between the visibility function and brightness distribution to be the classical arrangement of a Fourier Transform. g(kd, ω) = f(ψ, ω)e ikdψ dψ (3.19) Using this simplified version, the inverse Fourier transform is easily derived using concepts from system theory and mathematics [27]. f(ψ, ω) = g(kd, ω)e ikdψ d(kd) (3.20) If a continuous visibility function was feasible, Equation 3.20 provides the necessary relation to solve for the brightness distribution in terms of the visibility function, completing the inversion process. Provided that the visibility function is discretely and non-uniformly sampled, the integrals need to be substituted by a summation over a finite amount of baselines. For a configuration containing M baselines, the estimated brightness distribution for a particular zenith angle, ψ, is: M ˆf(ψ, ω) = g(kd m, ω)e ikdmψ (3.21) m=1 where d 1... d M is the discrete set corresponding to the M baseline lengths. For producing images similar to Figure 3.13, Equation 3.21 is applied numerous times depending on the amount of Doppler bins, and Zenith angle bins. Since the estimated brightness distribution, ˆf(ψ, ω), is not a function of range, each range bin is treated independently from one another. Discussion of the entire imaging process, involving Equation 3.21 will be discussed in the coming paragraphs.

84 63 Although the closed form solution of the Fourier Method results in a convenient form, the inversion process has tradeoffs when applying in practice. The draw back of this method involves the baseline, kd m, samples not available for the selected antenna configuration. These samples, since unavailable, are not interpolated based on the attainable baseline measurements, but are all assumed to equal zero. This issue greatly effects the quality of the inversion process, since majority of the visibility function will naturally be zero. As a result, the Fourier method generally produces the least quality images when compared to the other commonly used algorithms, i.e. Capon and Maximum Entropy. Figure 3.16 shows a comparison between each of these mentioned techniques [52]. Yu performed a simulation where the true image was known a priori. Knowing the correct image in advance allowed Yu to work backwards to solve for the visibility function via the optimal brightness distribution. Then each method was subsequently executed utilizing the obtained visibility function, resulting in a suboptimal image. Notice that these images are not concerned with the range of the target, but present spatial distribution in two dimensions. Clearly it is shown that the Fourier method reconstructs the least quality of the images due to the large spreading effect. The Capon and Maximum Entropy method provide better estimates for the model, with Maximum Entropy performing the best. More information about the derivation and application of the Capon and Maximum Entropy Method are outlined in [45, 48, 49]. Figure Comparison of the three commonly used imaging algorithms: Fourier, Capon, and Maximum Entropy. Simulation performed by using a predefined model. (Yu, 2000) An advantage of the Fourier method however is the small computational cost required to generate the processed images. As previously indicated, Equation 3.21 is independent of the range. Hence for a particular Doppler frequency and zenith angle, the same mathematical procedure can be enforced to solve for brightness

85 64 distribution on every range bin simultaneously, no matter the values of each visibility function. The other inversion techniques used for radar imaging also treat all ranges independently, but simultaneous evaluations of the brightness distribution cannot be accomplished because the arithmetic process adjusts based on the samples of the visibility function. Consequently, the computational cost for these methods are larger, and have a noticeable effect as the number of baselines for an experiment increases. Other factors taken into account for the computational cost are the Doppler resolution in the spectra/cross-spectra, and zenith resolution. The Doppler resolution, similar to the amount of baselines, can dramatically enhance the quality of the image. However, the computational cost significantly increases for high Doppler resolutions. The zenith resolution does not effect the cost as much as the other factors, but should be chosen with consideration based on the quality of the inversion technique. For example, selecting a very high frequency resolution for the Fourier method would add unnecessary iterations to the algorithm because produced images are typically far from optimal. The small computational cost for the Fourier method make this the ideal choice to process radar images in real time, while the other techniques are typically performed offline Phase Calibration Appending to the concepts developed by a single baseline interferometer, the phase of the complex valued visibility function is critical toward determining the angular distribution of the plasma instabilities. The addition of multiple receivers aids in the increase of angular resolution. However, greater challenges arise with calibrating these sets of receivers. In the ideal case, each of the receivers would be phase locked with one another, hypothetically meaning that if a sinusoidal signal is fed synchronously to each of the receiving antennas, continuous identical phases are recorded at the output of every receiving channel, i.e. after digitization. Obtaining phase locked channels in practice are difficult due to various cable lengths, aging of components, and RF front end responses, each inducing phase lags of different values [42,53,54]. Therefore, a crucial preliminary test needed to be performed before any radar imaging experiment is the determination of the phase offsets at the output of each receiver. Typically the phase offsets are measured relative to one of the receivers, and can be easily expanded toward determining the phase offset for

86 65 every baseline. Without proper phase calibration, the imaging experiments would not operate effectively, and processed images would be inaccurate. For ionospheric research, various techniques have been developed to accurately calibrate the phase of each receiver. In [42], Chau implements a phase calibration technique at JRO by using natural sources such as radio stars and meteor trails. Radio stars are considered point targets with a determinable location, therefore the angle of arrival is known in advance. Knowing the angle of arrival allows the user to work backwards to conclude the phase offsets of the receivers. Alternate techniques apply similar ideas but with artificial sources. Chen in [53], tracks the movements of airplanes for calibration, while Valentic in [54] places a transmitter at alternate locations in the far field of the antennas. The evaluation of the hardware configuration is fulfilled upon assessing the phase offsets relative to one receiver, while the remaining steps of the imaging algorithm explicitly involve the software processing. Within the software portion of the imaging experiment, adjustment of the phases are accounted for Practical Implementation of Fourier Method In order to produce the optimal image with the selected imaging algorithm, a few preprocessing techniques are performed on the spectra and the cross-spectra. The initial step of any imaging experiment is to gather a block of data and compute the spectra for the number of receiving channels, using Equation Before proceeding with determining the cross-spectra for every baseline, an additional step is utilized to remove an effect of the hardware. The RF portion of the receiving channels typically leak a unavoidable strong DC signal through the entire front end stage. Therefore, the software side assists in eliminating this DC bias with a simple manipulation in the spectra. The DC removal technique involves using the spectra samples from the smallest positive frequency component and smallest negative frequency component, each being adjacent to the DC sample. Using the power of these two samples, the technique reduces the DC component by averaging the samples. For a spectra with frequency resolution of f d, the following is performed for every range bin on the power scaled spectra.

87 66 Ŝ(0) 2 = S( f d ) 2 + S( f d ) 2 2 (3.22) Once the DC bias is removed, the pre-processing steps proceed with determining the cross-spectra for every baseline by initially calculating and removing the noise level in each spectra, then by normalizing using Equation Recall that the cross-spectra is complex valued and can be analyzed in two forms, the coherence and the phase. At first, the phase in every cross spectra is skewed because of the hardware issues causing various phase lags between the receivers. Therefore the phase offsets measured prior to the experiment serve to modify the cross-spectra and provide a more accurate assessment of the phase differences. For an imaging experiment containing P receivers, the calibration results in a list of phase offsets expressed in terms of radian, i.e. θ 1, θ 2,..., θ P. Since the phase offsets need to be relative to a receiver, one value of θ will be equal to zero, typically θ 1. To correct the phase of a cross-spectra comparing channel i and channel j, application of these offsets are utilized by properly scaling with the use of Euler s equation. ĈS ij (f d ) = CS ij (f d ) exp(1j (θ j θ i )) (3.23) The 1j inside the exponential function represents the basic form of an imaginary number, and is not to get confused with channel j. Since the phase of the cross spectra always relative to channel i, the calibrated phase difference is determined by subtracting the phase of channel j and channel i accordingly. Equation 3.23 essentially just rotates the phase on the complex plane relative to channel i, while having no effect on the coherence. The coherence is held constant because fixing the phase does not help improve or degrade the understanding of the structure of the target, only the angle at which target was illuminated. After fixing every cross-spectra appropriately, the channels are then indirectly assumed to be phase locked, so proper angle of arrival estimates are possible, and ultimately, accurate images. The final step in the pre-processing section is somewhat independent from the previous procedures, and involves calculating the average SNR of the spectra for each Doppler and range bin. The resulting values are applied during the the Fourier inversion with the intention of enhancing the brightness distribution for large SNR

88 67 values and vice versa. Details of scaling the brightness distribution via the SNR will be discussed later in the section. Determining the average SNR of the spectra is a two step process. For a single range bin, the average power across each Doppler frequency is simply an average over the P number of channels. S(f d ) = P p=0 S p(f d ) 2 P (3.24) S p (f d ) 2 corresponds to the spectra power of a single channel p. To complete the average spectra, Equation 3.24 is subsequently repeated for all the range bins. Note that S(f d ) represents the power of the spectra, which deviates from the previous form for notational simplicity. Analogous to working with time domain data, the SNR is similarly computing by using Equations 3.8 and 3.9. In the case of the average spectra, the noise level is the average value taken from the channels. Additionally, since the power of the spectra is real valued, it can be converted to decibels using Equation 3.25, where N is the average noise level power. ( S(fd ) S db (f d ) = 10 log N ) 10 N (3.25) To apply any of the radar imaging techniques, one must first recognize that the brightness distribution and visibility function are both dependent on two variables. Therefore, to accumulate the full array of values comprising these functions generally takes multiple iterations. The common variable between the visibility function and brightness distribution is the Doppler frequency, so each imaging process begins by selecting one of the finite Doppler bins. The inversion process solves for each brightness distribution for a particular Doppler frequency independently, then repeats the same process for another Doppler frequency. Typically the initial selection begins with largest positive or negative Doppler frequency, then iterates in descending or ascending order respectively. Upon selection of a particular Doppler frequency, the imaging algorithm utilizes the cross-spectra in order to generate the visibility function. With columns given in ascending order of baseline length or kd value, the visibility function results in a R M complex matrix where R is the number of range bins in the cross-spectra and M is the number of non-redundant baselines. Given the particular Doppler frequency, a R 1 vector is extracted from every cross-spectra and inserted to the

89 68 column of the visibility matrix corresponding to the correct kd value. Occasionally a baseline length of zero is included in the visibility function in order to obtain more samples. The content from this baseline is achieved by calculating the crossspectra with only one receive channel, usually resulting in values of high coherence. Recall that the brightness distribution estimates the power backscattered from a series of zenith angles, therefore the value of this function must be completely real. The subsequent step is specific to the Fourier method in order to guarantee this condition. In Fourier theory, one of the properties states that an even function is assured to have a Fourier transform that is completely real valued [27]. Consequently, this property is applied to the visibility matrix to make the samples even around the kd = 0 column. This is resolved by concatenating the original matrix with a mirror image of itself, resulting in a final matrix of dimensions R (2M 1). The subtraction of one is only included if the zero lag is a sample in the visibility matrix. Application of the Fourier Method, shown in Equation 3.21, is finally possible once attaining the expanded visibility matrix. The output of the Fourier method is the brightness distribution for a particular Doppler frequency and zenith angle, and each range on the visibility matrix can be computed simultaneously. amount of discrete zenith angles, K, are selected by the user in advance, and the result of the Fourier inversion after iterating through each angle is a completely real R K matrix. To properly enhance or degrade the brightness distribution, the average SNR computed previously using Equation 3.25 is used to scale the result of the Fourier method as follows: ( M ) ˆf(ψ k, ω d ) = g(kd m, ω d )e ikdmψ k m=1 The 10 S db (ω d ) 10 (3.26) Note that the average SNR is a function of ω d, and is converted to linear scale for consistency. Alternative methods for scaling have been applied in practice, where additional variables such as the number of baselines are included. Once the R K matrix is obtained, the entire imaging process is repeated for another Doppler frequency. Upon iterating through all Doppler frequencies, the resulting matrices can be formed into a three dimensional matrix of dimensions R K N, where N is the number of Doppler frequency bins.

90 69 The final step of the imaging process is to manipulate the resulting three dimensional matrix, to compute the total brightness distribution for each range. Two techniques are typically used in practice. The first technique generates strictly the power of the brightness distribution, and does not take into account the Doppler content. Images applying this technique are formed by summing the matrix over the third dimension, essentially performing a discrete integration. The brightness distribution is then only a variable of the zenith angle, i.e. ˆf(ψk ). The alternate technique partitions the three dimensional matrix into three segments: low Doppler frequency content around DC, positive Doppler, and negative Doppler. The resulting individual segments are combined similar to the previous technique, and the values obtained are applied for a weighted summation of the Red-Green-Blue (RGB) color model. The weights for the red, green and blue colors correspond to negative Doppler, DC, and positive Doppler respectively. The result of this technique enhances the physical interpretation of the images, by not only resolving the plasma structure, but also the motion of the plasma within the structure. Due to the complexity of applying the imaging algorithm, a flow chart of each step is given in Figure Keep in mind, the description given in this section discusses the generation of a single image. In order to produce a sequence of images, the same process is repeated after acquiring a new set of spectra measurements.

91 70 Calculate Spectra Remove DC Component Calculate and Remove Noise Level for Each Spectra Calculate Average Signal- to- Noise RaFo of Spectra Fix Phase of Cross- Spectra Calculate Normalized Cross- Spectra Select a Doppler Frequency (f 1 - f N ) Select a Baseline (d 1 - d M ) Insert Column to Visibility Matrix for Corresponding Baseline Iterated Through Each Baseline? No Yes Concatenate Visibility Matrix with Mirror Image Select a Zenith Angle (ψ 1 - ψ K ) No No Perform the Fourier Method for Fixed Zenith Angle Iterated Through Each Zenith Angle? Yes Iterated Through Each Doppler Frequency? Yes Calculate Total Brightness DistribuFon or ParFFoned RGB Image Figure Flow diagram illustrating the processing steps for implementing the Fourier Method during a radar imaging experiment

92 Chapter 4 Cognitive Processing Routine for CIRI 4.1 Introduction The processing techniques described in Chapter 3 are typically used for ionospheric radars operating with a fixed pulsed waveform. No matter what the radar observes, the processing continues to work monotonously until the end of the campaign. The proposed implementation of CIRI on the other hand will break the standard by transmitting a diversity of waveforms to help improve the radar returns and the indirectly constitute to the advancement of physical understanding of the plasma instabilities. To apply any waveform diversity technique, the primary prerequisite is to have real time processing software, and a mean to communicate to the transmitter via the host computer. The real time software will program the transmitter to emit a variety of waveforms depending on the current activity in the ionosphere. In order to make the radar cognitive, the returns must be attempted to be continually improved based upon certain criterion. The criterion selected to be optimized by the cognitive routine for CIRI is the SNR. If the SNR of a target has reached maximum potential with a specific waveform, a more comprehensive analysis is feasible, thus leading to an enhanced physical interpretation of the event. In addition, maximizing the SNR would also potentially allow the detection of small reflective targets. In a traditional radar operating mode, a small

93 72 reflective target would induce a low return power, and typically fall beneath the noise floor. Depending on the application of the cognitive radar, other signal parameters can be considered for optimization. However, for ionospheric research, plasma instabilities are comprehended best if the SNR is maximized because the described processing techniques are less noisy and hence more meaningful. The proposed cognitive routine will essentially work in three stages. The first step is first decide in real time if one of the three long term equatorial plasma instabilities (i.e. 150 km echoes, Equatorial Electrojet, and Equatorial Spread F) is present in the ionosphere. If a plasma instability is present, the processed returns are analyzed to determine which particular event it is. Once the event is known, a customized envelope for transmission is computed based on the returns from the plasma instability. The customized envelope is utilized for maximizing the SNR on the output of the matched filter. Embedded within the envelope is a frequency that regularly modifies to explore the VHF spectrum. Over time, the algorithm will compile a list of frequencies ideal for optimizing the SNR of the plasma instabilities. The assumption for applying this technique is a transmitter that contains a large bandwidth of operation, and is flexible toward programming an envelope that is not square or Gaussian. This technique is not restricted just to ionospheric radars, and can easily be extended toward any application that observe targets viewable by the radar for long periods of time. 4.2 Classification Theory Introduction The classification process is a branch of machine learning and pattern recognition that exploits statistical properties of data to emulate an every day human occurrence [55, 56]. Daily, we subconsciously make classification decisions on various items based on observable parameters. A classifier dealing with data has the objective to identify a particular object or class out of a group of alternative classes. Reasons for implementing a classifier vary on the application, but the overall goal is to add an additional voice to the human element in the process of dealing

94 73 with large amounts of data. Although there are diverse approaches to implement this idea, the general procedure is usually very similar. In practice, the procedure is initiated by recognizing that at least one out of the set of known classes has transpired. From the detected event or events, information is extracted that can best distinguish one event from another with a very low probability of false alarm. This information is provided to the classifier where an automatic decision process is performed based on statistical characteristics of the classes Implementation of a Classifier Over the past two decades, the design of novel classification algorithms has become a heavily researched topic. Presently, there are several techniques used in practice each containing various complexities that attempt to optimize performance. Implementation of a k-means classifier was presented in [57] to distinguish between the different fingerprint structures. Classification techniques are seldom used for ionospheric research, and only once were results shown in literature. [58] presents a novel approach to studying the statistics of meteors by employing a Support Vector Machine (SVM) model to detect and determine occurrences of overdensed, underdensed, and nonspecular events. Using this algorithm, seasonal trends of the meteor fluxes are much easier to analyze rather than the tedious alternative of counting each event manually. The implementation of a classifier in practice requires a couple essential steps to assure that the performance criterion is met. Initially, a detection process must be developed to isolate potential events of interest in the data from noise and other unwanted occurrences. Without a detection system in place, an overwhelming amount of processing would occur, causing the classification results to be evaluated significantly after the occurrence of a potential event. For a real time detection systems, this is a deterrence. In addition, with the detection of unwanted events, the amount of false positives will inevitably increase. Once a probable desired event has been detected, specific information about the event is extracted to best conclude which class it belongs to. For example, if the classifier is to differentiate between US coins, the criterion analyzed from a detected coin could be the radius and the weight. The list of extracted parameters is formed into a one-dimensional array called a feature vector. Detection strategies are distinct for each application,

95 74 therefore numerous algorithms have been developed. In [58] a threshold level was set on the SNR in addition to utilizing a time-frequency detector [59] to determine if any type meteor event has occurred. In [60] a neural network is iterated over an entire image in small window increments for the recognition of a human face. A further action required before classification is performed on unobserved data is to train the classifier. For training, a table of feature vectors is compiled from previously collected data using the chosen detection algorithm. This table of training data is the input to determine patterns between each of the classes and hence striving for maximum performance. The training data is partitioned into two sets: a training set and testing set. The training set is used to optimize the classifier, while the testing set is used to measure how well the trained classifier performed. There are three commonly used training processes that are applied in machine learning: supervised learning, unsupervised learning, and reinforcement learning. In supervised learning, supplementary to the training data, each feature vector is labeled with the corresponding class. The idea behind this method is to produce a generalization for each class, which avoids the use of needing a large amount of training data. On the other hand, unsupervised learning uses unlabeled training and testing data, therefore the algorithm discovers similarities in the feature vectors in order to best separate the classes. This idea is defined as clustering. Lastly, with reinforcement learning, an unlaced training and testing set is used, but the classifier is only notified by the testing set when the result is incorrect. Through a series of trial and error the misclassifications are attempted to be minimized by continually making adjustments. Classification is a necessary step toward the development of CIRI. In the proposed cognitive routine, the primary goal is to process real time ionospheric returns, and automatically decide whether the Spread F, 150 km echoes, or the Electrojet are present. For the case of multiple events occurring simultaneously, the classification algorithm will be capable of recognizing this as well. The approach taken was to estimate the probability distribution for each event with a Gaussian Mixture Model (GMM) over the dimension of the selected feature vector, or feature space. To be explained in greater detail in the next section, a supervised learning training process called the Expectation-Maximization algorithm was used to generate the Gaussian Mixture Model for each ionospheric event.

96 Gaussian Mixture Model A probability density function (pdf) is a statistical function used to describe the characteristics of a random variable. Although the value of a random variable is not known a priori, the pdf is used to estimate the likelihood of a certain value occurring. A pdf can either be a discrete or continuous function depending on whether the random variable can obtain a finite or infinite amount of values. The Gaussian distribution is a pdf frequently used in practice for many applications. The two parameters that define this function are the mean and variance represented by µ and σ, respectively. Equation 4.1 provides the function defining a Gaussian pdf. N(x µ, σ) = 1 2πσ e (x µ)2 2σ 2 (4.1) The mean is the value of the pdf where the random variable tends to form around, while the variance parameterizes how far around the mean the values tend to spread. Adjusting the mean of any pdf will cause the distribution to shift along the axis representing the value of the random variable, represented by x. A Gaussian distribution has a special case where the mean is also equal to the mode of the function, meaning that the majority of random variable samples will occur around the mean. Increasing or decreasing the variance of the distribution results in a wider or thinner bell curve respectively. A large variance concludes that the random variable has a greater uncertainty than a small variance. Supplemental to Equation 4.1 where the Gaussian distribution is defined for a single, or univariate, random variable, multivariate statistics involve the use of defining a joint pdf for the outcome of multiple random variables. A multivariate pdf is used to discover relationships between the chosen random variables. Equation 4.2 generalizes the Gaussian distribution for a D-dimensional random vector, x by: N(x µ, Σ) = ( 1 exp 1 ) (2π) D/2 Σ 1/2 2 (x µ)t Σ 1 (x µ) (4.2) The name of this distribution is called the multivariate Gaussian. In Equation 4.2, Σ, is the covariance matrix and Σ signifies the determinant. The co-

97 76 variance matrix is a D D dimensional matrix that measures how each random variable varies with each other. Along the diagonal is the variance of each individual random variable. Adding extra dimensions to the Gaussian distribution still gives the general shape with a single peak located at the mean vector µ, with a surrounding bell curve. The Gaussian distribution is regularly chosen for statistical models, however there are limitations that arise in practice. As previously discussed, the Gaussian distribution, whether univariate or multivariate, has a single peak, which is termed unimodal. Multimodal hence means the pdf has multiple peaks or modes. Multimodal distributions appear in applications where samples of the random variable(s) cluster in several areas. Each independent distribution used in probability theory typically has only one mode, and therefore would not be able to incorporate any additional modes. Mixture models are a procedure to eliminate this issue. In general, a mixture model is a linear combination of a finite set of any weighted pdf. The Gaussian mixture model is a common selection, and is defined by: K f(x) = π k N(x µ k, Σ k ) (4.3) k=1 where the π k are weights assigned to each of the K Gaussian distributions. From Equation 4.3, K Gaussian pdfs with independent means and covariances are summed together making the estimation of arbitrary distributions feasible. The only constraint with any mixture model is that the weights π k must sum to one in order to satisfy the integral conditions for the pdf. Because of this constraint, the variable π is considered to be a random variable with each π k representing a probability of occurrence of the associated Gaussian pdf.the applications for GMM span a wide range of field. In [61] a GMM is implemented to classify the voice of multiple speakers. With any mixture model, difficulty arises when the specific values for π k, µ k, and Σ k need to be selected. Given a sufficient amount of training vectors for a class, the Expectation-Maximization algorithm optimizes these parameters.

98 Expectation Maximization The Expectation-Maximization (EM) algorithm is a supervised learning training process used to generate a GMM for every selected class, therefore the training data is required to have the feature vectors labelled with the correct class. Each feature vector for a specific class is assumed to be independent and identically distributed (iid), meaning they are derived from a common pdf and contain no correlation between each other. A likelihood function is defined by the joint probability of the training data. From probability theory, the joint pdf of N iid random variables is the product of the individual pdfs. Therefore the likelihood function of a GMM is: { N K } p(x µ, Σ, π) = π k N(x n µ k, Σ k ) (4.4) n=1 k=1 Taking the natural logarithm of Equation 4.4 is a commonly selected alternative in practice to replace the product over the random vectors with a summation. Additionally, the log-likelihood makes dealing with smaller probabilities possible without under flowing the numerical precision. Given a set of training vectors, Equation 4.4 and the log-likelihood become a function of the unknown parameters π 1...π k,µ 1...µ k, and Σ 1...Σ k. The foundation of the EM algorithm is to maximize the likelihood function over these parameters, resulting in the optimal pdf for the class. However, given amount of unknowns this turns out to be quite complex. Solving for the maximum likelihood of a univariate or multivariate Gaussian pdf is accomplished by using the log-likelihood function, and setting the partial derivatives over the mean and variance respectively to equal to zero. A closed form solution for optimal mean and variance is easily determined. To maximize the log-likelihood of a GMM however requires a more involved process due to the additional π k coefficients. The Expectation-Maximization algorithm is an iterative technique to maximize the likelihood function of any mixture model. The derivation for the algorithm is extensive, but the EM for GMMs is applied by the following procedure [55,56]. After each subsequent iteration, the log-likelihood function is guaranteed to increase and converge at a local maximum, but not necessarily the global maximum. To achieve the local maximum, steps 2 to 4 are iterated until the difference between successive log-likelihoods fall below a selected threshold.

99 78 Step 1: Initialization the parameters µ k, Σ k and π k Step 2: Calculate the weight for feature vector x n that provides the strength of association with mixture k γ(z nk ) = π k N(x n µ k, Σ k ) K j=1 π jn(x n µ j, Σ j ) (4.5) Step 3: Recalcuate µ k, Σ k and π k Σ new k = µ new k = N n=1 γ(z nk)x n N n=1 γ(z nk) N n=1 γ(z nk)(x n µ new k )(x n µ new k N n=1 γ(z nk) π new k = N n=1 γ(z nk) N ) T (4.6) (4.7) (4.8) Step 4: Calculate Log-Likelihood { N K } ln p(x µ, Σ, π) = ln π k N(x n µ k, Σ k ) n=1 k=1 (4.9) Implementation CIRI in Huancayo has yet to be installed, therefore alternatives to generate the GMM associated with the Spread F, 150 km, and Electrojet were developed using data from JRO. JRO is located at a lower elevation than the Huancayo Observatory, but the same plasma instabilities of interest to CIRI are studied on a daily basis with a radar configuration known as Jicamarca Unattended Long-term Investigations of the Ionosphere and Atmosphere (JULIA). Instead of saving the all of the Inphase and Quadrature voltages for every channel, integrated spectral and cross-spectral data are stored in order to maintain hard drive space for data collected over many years. Spectral data is a processed form of the I and Q voltages where the Fast Fourier Transform (FFT) is taken across each range bin for a specified window of data. Data displayed in this format can be transformed to

100 79 power in each range by summing over the FFT points. Furthermore, the SNR is calculated by first determining the noise floor. There are several techniques used in practice to calculate the noise level, but the one selected for this specific test was to average the lowest quartile of the data over each IPP. Four weeks of radar measurements were provided by JRO in order to develop, train and test a GMM classifier on collected data. All of the data was stored in spectral format, and consisted of one week from each season of the year. Each season has been shown to produce different trends for plasma instabilities in terms of the structure in the ionosphere [17,20,22]. Therefore to properly minimized the false positives for the trained classifier, a wide variety of their formations must be used. Upon completion of these tests, the classifier developed will be more efficient once CIRI is established in Huancayo. In order to follow the classification procedure, the initial step was to devise a detection technique to separate the events of interest from noise and other unwanted instabilities. The JRO spectral data was used to generate RTI plots of the SNR. Instead of plotting the entire duration of the event, the data was plotted in five minute sections to simulate close to real time detection. The thought process behind the detection algorithm was the observation that each of the three ionospheric events are present for multiple hours at a time and, for the exception of the Spread F, tend to be restricted to a specific altitude of the ionosphere. For the case of the Spread F, occasionally the event can span a large portion of the ionosphere, but takes multiple hours to achieve this form. To begin the detection process, each of the five minute RTI windows were averaged across the time domain, with each range bin being treated independently. The result was a vector of average SNR values as a function of range. Each range bin above a selected average SNR threshold was considered to be a probable event. Ranges exceeding the threshold were very rarely isolated, and usually occurred in clusters of multiple range bins. As a result, each detected event contained a lower bound and an upper bound in range. Using these two values in addition to the local time of the detected layer, a feature vector was produced. Knowing that each ionospheric plasma instability occurs at certain times of the day and cover a select portion of the ionosphere, the optimal feature vector applied to separate the detected events from each other was:

101 80 [Hour, M inute, LowerBound, U pperbound] (4.10) The selected feature vector was the input for each of the trained GMMs representing the Spread F, Electrojet, and 150km echoes. Two separate days of labeled feature vectors were used to train and optimize the GMM parameters for the Spread F, 150km echoes, and Electrojet classes. The output of the GMM for each class was the estimated probability of the input feature vector extracted from the spectral data. The labeled feature vectors were initially separated by class and normalized to have each value in the feature vector be between 0 and 1. Using the normalized feature vectors, the EM algorithm was applied to compute the GMM parameters. A primary assessment to be made was to decide the maximum number of independent Gaussian distributions the GMM will contain. Provided that the length of the feature space is four elements, logically the maximum number of means the optimal GMM will contain would be four. Therefore the EM algorithm was programmed to find the optimal GMM from one to four mixtures. Whichever of the four resulting GMMs performed the best on the testing set was the selected GMM for that specific class. Before performing steps 2 to 4 in the algorithm defined in Section , the vectors of π k, µ k, and Σ k needed to be given initial values. Each Gaussian in the mixture model was assumed to be independent, therefore the covariance matrix Σ k contained non-zero values only along the diagonal. All of the initial diagonal components for testing purposes were set to one, while the off diagonal components remained zero. Given that the values of the feature vectors were normalized prior to training, the mean vector µ k was initiated to have each component contain random values between 0 and 1. Lastly, all the mixture coefficient π k were initiated to consist of equal values depending on how many mixtures were involved during the current training process. To avoid convergence of the algorithm falling on a local maximum of the likelihood function, the EM algorithm was executed several time and output parameters containing the largest log-likelihood was selected. Using the resulting GMMs provided by the EM process, a classification procedure was devised to test the performance on data not used in the training process. Radar measurements from each season of the year were used to analyze if the various structures of the plasma instabilities effected the performance of the clas-

102 81 sifier. The feature vectors resulting from an unknown detected event served as the input to each of the three generated GMMs. Following normalization of the feature vector, the output of each GMM provided a probability of certainty that the feature vector belong to that class. The class resulting in the highest probability was selected to the be classifier output. In the end, the classifier achieved promising results, which are displayed in Figure 4.1. As shown, the Spread F had the lowest percentage of correct classifications at 89.66%, which can be justified by the tendency of the event to behave more arbitrarily in range, than the 150 km echo and Electrojet. Even though each of the events performed well on the testing data, the most encouraging result was the absence of misclassifying one event for another. The unknown category was included when manually checking the results to account for some events that were above the SNR threshold, but did not look to be part of any of the particular classes. Figure 4.1. Results of Preliminary Tests Using Gaussian Mixture Models 4.3 Waveform Diversity Optimal Transmission Envelope Introduction In Section the matched filter was introduced and described as a commonly used processing technique for radar systems. The foundation of the match filter

103 82 utilizes the knowledge of the transmitted pulse envelope in order to maximum the SNR of the returns. An additional advantage of the matched filter is the capability of obtaining small range resolutions while maintaining a large transmitted average power via the use of coding schemes. For the use of binary coding schemes, the peak of the matched filter response occurs when the baseband envelopes are fully overlapped, i.e. the zero lag of the autocorrelation function. The value of the peak occurring at the zero lag is a function of the power of the received signal and the length of the chosen code. Since the peak is proportional to the SNR, the larger the value of the matched filter at the zero lag, the greater the corresponding SNR of the target. Therefore the optimal transmitted envelope would provide a matched filter response with the maximum possible peak at the zero lag. Various coding schemes could be applied to approach this goal, however the optimum peak is only achieved upon knowledge of the target. Pillai states in [6] that the fundamental measurement needed to optimize the peak value of the match filter response is the impulse response of the target. To visualize the impulse response, consider the simple linear system presented in Figure 4.2 where the transmitted pulse is defined by f(t), the targets impulse response by q(t), and the received signal by s(t). Each of the time domain signals in the linear system is given in terms of volts. The targets impulse response is hence the time domain signal that, once convolved with the transmitted signal, outputs the received signal collected at the hardware portion of the radar system. Figure 4.2. Linear system demonstrating the link between the transmitted and received signal. For the case of CIRI, the impulse response can be restricted to the returns from ranges containing the detected events, instead of from the whole ionosphere. This condition will greatly reduce the amount of computations and focus the optimal waveform specifically to the plasma instabilities. The algorithm to be explained

104 83 in detail this section is very advantageous for CIRI because of the duration of the plasma instabilities. Given the impulse response of the target, q(t), the algorithm derives the optimal transmitted signal, f(t), to illuminate the target on the subsequent pulse. For slow developing targets like the plasma instabilities, the process of solving for the best transmitted envelope can be repeated occasionally, and is unnecessary to apply after every IPP. Solving for the envelope finalizes the first of two steps of the cognitive algorithm with the intention of discovering an optimal waveform to study the plasma instabilities Derivation of Optimal Transmission Envelope The beginning of the algorithm discovering a transmission envelope optimizing the matched filter output utilizes an equation attained in the derivation of the original matched filter problem. The derivation states that the maximum SNR is truly achieved if the impulse response is matched to the deterministic received signal, s(t) [6]. Assuming the corruption of white noise with power density σ 2, the maximum attainable SNR at the peak time, t 0, is proportional to the power of the noiseless signal s(t). t 0 SNR max = ρ(t 0 ) = 1 s(t) 2 dt (4.11) σ 2 Equation 4.11 is easily obtained based on the concepts of matched filtering. The matched filter response at the peak time, t 0, involves applying the autocorrelation function for two signals that are completely overlapped. Therefore, to compute the response at this time would just be the summation of the received signal s squared magnitude An additional equation to set up the main derivation relates the received signal to the transmitted signal and impulse response. Assuming each of the time domain signals are causal and induced in a linear system, s(t) is the convolution between q(t) and f(t). 0 t s(t) = f(t) q(t) = f(τ)q(t τ)dτ (4.12) 0

105 84 If the medium illuminated by the transmitted signal is considered to be static, the measured impulse response of the medium would always maintain a constant time domain sequence. Consequently, an intuitive method that could be applied to improve the SNR would simply involve increasing the average power of f(t). Hence the output of the convolution in Equation 4.12 would result in an increased scaled version of s(t). To avoid the trivial case, Pillai forms a constraint stating that the power of the optimal transmitted envelope must be restricted to a specific value. For simplicity it was selected that the signal power must always equal to 1. Therefore the resulting transmitted envelope is optimal for the selected power constraint. t 0 0 f(t) 2 dt = 1 (4.13) Assuming a known target impulse response, the crux of the derivation initiates by expanding Equation 4.11 with the use of Equation 4.12 in order to replace s(t). The noise power, σ 2, is assumed not be dependent on the resulting transmitted signal, therefore it is set to maintain a constant value of 1. This assumption is held for the remainder of the derivation. After some mathematical manipulation the following form results in Equation Note that all of the integrations are definite between 0 and t 0 because of the causality condition and the objective of solving for the maximum SNR at the peak time. ρ(t 0 ) = = = t 0 0 t 0 0 t 0 0 t 0 f(τ)q(t τ)dτ t 0 t f (τ 1 )dτ dt f (τ 1 )q (t τ 1 )f(τ 2 )q(t τ 2 )dτ 1 dτ 2 dt (4.14) t 0 t 0 q (t τ 1 )q(t τ 2 )dt f(τ 2 )dτ 2 To reduce the mathematical complexity in the final form of Equation 4.14, a new variable is introduced replacing the integral between the parentheses. This function is called a Kernel because it is a weighting function essential for the

106 85 remainder of the derivation. The Kernel function is symmetric and positivedefinite based on two lags of the target impulse response and the fulfillment of non-negativity conditions [62]. To reiterate, the Kernel function, K(τ 1, τ 2 ), is defined as: t 0 K(τ 1, τ 2 ) = q (t τ 1 )q(t τ 2 )dt (4.15) 0 Equation 4.14 can be further reduced by defining a new variable ψ(τ 1 ), which comprises of the entire second integral with K(τ 1, τ 2 ) and f(τ 2 ). The new variable is only a function of τ 1 because the τ 2 is integrated out of both elements inside the integral. This step leaves the maximum SNR in Equation 4.14 being an integral of two variables, i.e f (τ 1 ) and ψ(τ 1 ), both a function of τ 1. The Cauchy- Schwarz inequality provides a relation for integrals involving the multiplication of two functions, where the result of the integral is proven to be less than or equal to the product of two individual integrations [6, 63]. Applying the Cauchy-Schwarz inequality to the reduced form Equation 4.14 is given as follows: ρ(t 0 ) t 0 f (τ 1 ) 2 dτ 1 t 0 ψ(τ 1 ) 2 dτ = t 0 ψ(τ 1 ) 2 dτ (4.16) With the simplification on right side coming from Equation The intention of using the Cauchy-Schwarz inequality is to solve for the solution where equality holds, i.e. the optimal value for the maximum SNR. Any solution below equality would be considered sub-optimal. Equivalence of the Cauchy-Schwarz inequality is possible if the two concerned function are scalar multiples of each other [63]. Therefore, the maximum value of ρ(t 0 ) is achieved if ψ(τ 1 ) = λf (τ 1 ), where λ is a constant of real or complex value. Expanding the definition of ψ(τ 1 ), the maximum SNR is a solution of the following relation. t 0 ψ(τ 1 ) = K(τ 1, τ 2 )f(τ 2 )dτ 2 = λf (τ 1 ) (4.17) 0

107 86 Notice that the undetermined function, f(τ 2 ), appears inside the integral, which constitutes Equation 4.17 as an integral equation. The particular form of this integral equation is classified as a homogeneous Fredholm Equation of Second Kind, since the unknown function appears also on the righthand side of the relation [64]. Solutions for integral equations are not unique because of the various forms potentially taken by the undetermined function, hence a problem of this form leads to a set of eigenvalues and eigenfunctions, where λ is considered a particular eigenvalue. Utilizing both Equation 4.16 and Equation 4.17, equality holds in the Cauchy-Schwarz inequality when the maximum SNR is the largest positive eigenvalue resulting from the integral equation, λ max. ρ(t 0 ) λ max t 0 f (τ 1 ) 2 dτ = λ max (4.18) 0 Therefore the optimal transmission envelope resulting in the maximum possible SNR of the given target impulse response is equivalent to the eigenfunction corresponding the the maximum eigenvalue. f(t) = Λ max (t) (4.19) Numerical Method to Solve for Optimal Transmission Envelope The approaches applied to solve for the eigenvalues and eigenvectors of Equation 4.17 are explicit toward the content of data involved, i.e continuous or discrete. Since processed radar data is digitized, numerical methods must be implemented to solve for a set of discrete eigenfunctions. An essential step toward converting Equation 4.17 to a form able to be handled by numerical methods is to replace the integral with a finite summation. The general form implementing any numerical integration technique includes a weighting vector, w, inside the summation to account for discrete area accumulation. For a target impulse response discretized in N samples, the discrete form of Equation 4.17 is represented as follow: λf(τ i 1) = N w j K(τ1, i τ2)f(τ j 2) j (4.20) j=1

108 87 where the superscripts i and j represent the sample number for the two time delays, τ 1 and τ 2. To simplify the expression and notational significance of Equation 4.20, the parentheses are removed to convert the functions to vectors or matrices. The Kernel function is dependent on two variables, hence it takes a matrix form, K ij. On the other hand, the transmitted envelope is only a function of one variable, so a vector is used for replacement. Compressing the matrix notation takes into account the knowledge of the weighting vector and Kernel matrix in advance. The weighting vector scales each column identically, updating the value of each cell of the matrix, i.e K ij = K ij w j. This manipulation reduces the expression to a standard eigenvalue, eigenvector problem. K f = λ f (4.21) With the bold letters representing a matrix K of dimensions N N and vector f of length N 1. equivalent to the value of N. The number of resulting eigenvalues and eigenfunction are Reducing the computational complexity for the eigenvalue problem requires making the updated Kernel Matrix, K, symmetric. The original form of the Kernel matrix was symmetric, but the multiplication of the weighting vector removed this characteristic. To generate a symmetric matrix, the weighting vector is initially constructed into a diagonal matrix, where all the off-diagonal terms are zero. The values of the weighting vector are derived by selecting one of the known Newton- Cotes or Quadrature rules [65, 66]. For an example, the resulting diagonal matrix, D, for weights using the trapezoidal method are set as follows: D = diag([w 1,..., w N ]) = t ( 0 1 N 1 diag 2, 1, 1,..., 1, 1, 1 ) 2 where t 0 is the duration of the impulse response sequence. (4.22) Symmetry is achieved by applying matrix multiplication properties between the diagonal matrix and original Kernel Matrix, K. The final form of the eigenvalue, eigenvector problem is given in Equation 4.23 below where the expression D 1 2 = diag( w j ) and h = D 1 2 f [66].

109 88 ( ) D K D 2 h = λ h (4.23) After computing the eigenvalues and eigenvectors with standard techniques [63], the optimal transmission envelope is found by exploiting the solution arrived in the previous section. Upon selection of the largest resulting eigenvalue, the corresponding eigenvector, Λ max, is proportional to the vector representing the the transmission envelope proven to maximize the SNR of the measured target. where the f = ( D 1 2 ) 1 Λmax (4.24) ( D 1 2 ) 1 is included due to the definition of h. For a quick demonstration of the described method, a target impulse response was chosen to be a sinusoidal function of frequency 2 Hz, shown in Figure 4.3. The impulse response was windowed to a duration of one second, which represents the amount of time the measured target was illuminated by the antenna beam. A duration of one second corresponds to a target occupying an area of 150x10 3 km, which is obviously unlikely. The values were chosen for convenience, and do not effect the shape of the resulting transmission pulse. Given the impulse response, the Kernel matrix is assembled by using the definition in Equation Each cell in the matrix is individually evaluated for the different values of the delays, τ 1 and τ 2, and integration is performed with the trapezoidal method. The resulting Kernel matrix of the sinusoidal impulse response is shown in Figure 4.4. Note that provided Kernel matrix fulfills the requirement of being symmetric, i.e K(τ 1, τ 2 ) = K(τ 2, τ 1 ). Applying the procedure outlined in Equations 4.23 and Equation 4.24 the optimal transmission envelope for the given target impulse response was found to have an irregular shape with a couple local maximums and minimums. The resulting transmission envelope is shown in Figure Optimal Transmission Envelope for CIRI Data The optimal transmission envelope for ionospheric targets can be determined utilizing the measurements of the received signal and the knowledge of the transmitted signal. With these two time domain signals, the impulse response can be computed

110 89 Figure 4.3. Simulated impulse response from target and used as the input for the completion of the algorithm. The theory for estimating the impulse response uses the assumption that the medium for transmission is a linear system. Therefore, applying properties of Fourier Theory, the impulse response is resolved by initially computing the frequency content of the received signal and the transmitted signal. Dividing the frequency domain signals results in the frequency domain representation of the impulse response. Q(ω) = S(ω) F (ω) (4.25) The time domain sequence of the target impulse response is then computed by taking the inverse Fourier Transform of the outcome of Equation Although the algorithm has yet to be performed in real time, the optimal transmission envelope for ionospheric targets has been examined offline using data from CIRI at PSU. The proposed design can either be performed using spectra data or time domain content, with the intention of providing an estimate of the received signal from only the target, s(t). Upon measuring s(t), the impulse response can then be computed since the transmission pulse is known in advance. For the described implementation, only spectra data, representing the frequency content for a two second window, was used to calculate the optimal transmission envelope.

111 90 Figure 4.4. Kernel matrix for simulated impulse response A single spectra was chosen based on the prior knowledge that a plasma instability was present at the time of collection. The addition over the frequency domain in each range results in the integrated power of the signal for the two second window. Applying a threshold detector to the integrated power, the region of the ionosphere containing the event is isolated and set to equal the time domain sequence of the target. The time domain sequence in this case also corresponds to the signal as a function of range. The transmission signal for this data collection was a Barker 13 code with a 10µs baud. The FFT of both signals were computed and divided according to Equation 4.25 leading to the time domain sequence of the impulse response by computation of the inverse FFT. The resulting impulse response and optimal transmission envelope for the detected plasma instability are shown in Figures 4.6 and 4.7 and respectively. At the time of the detection, the plasma instability occupied approximately 56 km in the ionosphere, which produces time domain sequences of both the impulse response and optimal transmission pulse to last 375µs. As shown in Figure 4.6, the estimated impulse response was measured to be a rectangular function. This function was normalized with respect to the maximum value of the original measured impulse response for display purposes. Although not apparent, slight variations around the normalized value are embedded in the

112 91 Figure 4.5. Optimal transmission envelope for simulated impulse response signal, but are insignificant due to the large DC content that resulted from the FFT calculations. Consequently, the impulse response appears to be noiseless which enhances the quality of the algorithm output. The optimal transmission envelope for the particular case of a rectangular function impulse response took the form of a downward parabola. In order to confirm the effectiveness of the outlined algorithm, the essential next step of the cognitive process would be to alter the transmission envelope to the shape given in Figure 4.7. However in practice, there are limitations that come with the hardware, and more specifically the high power transmitters. As mentioned in Section 2.5 the selected transmitter for CIRI can emit two shapes of waveforms, square or Gaussian pulse. The hardware design of the transmitter is not capable of emitting a customized envelope resulting from the algorithm. Therefore, practical implementation of CIRI would require transmitting the pulse shape that is most correlated to the output of the algorithm. In the provided result, the Gaussian pulse would be a better selection for the subsequent transmitted signal than the square pulse. In either case however, the selection between Gaussian and square pulse would still provide a large range resolution. To make use of the proposed method, more thorough analysis of the types of optimal transmission envelopes needs to be performed. The analysis would need to consider the tradeoff between

113 92 Figure 4.6. Measured impulse response from detected plasma instability the range resolution and the output SNR of the matched filter. Alternatives can be developed to emit a similar shape to the algorithm s output, but compressed to a smaller baud length to maintain a small range resolution Frequency Selection Introduction The two pieces that define an optimal waveform consists of the transmission envelope, and the transmission frequency. In Section 4.3.1, the optimal transmission envelope providing maximum SNR on the matched filter output is outlined in a numerical algorithm. The subsequent step in the cognitive process is to select an optimal frequency to embed within the transmission envelope. An optimal frequency is chosen to further enhance the resulting SNR of the target, and for the particular case of ionospheric research, the plasma instabilities. The major ionospheric observatories stationed around the globe typically have fixed frequencies, but the selected frequency at each observatory is unique. The frequency selection of the observatories primarily fall within the VHF spectrum, which is defined by the range 30 MHz to 300 MHz. Occasionally however there are exceptions for observatories going beyond this frequency range. Some examples of operating frequencies

114 93 Figure 4.7. Optimal transmission envelope for detected plasma instability using CIRI at PSU at ionospheric observatories are MHz at JRO, 430 MHz at Arecibo, and 224 MHz EISCAT VHF [26, 67]. The antennas at the observatories are designed and constructed to be tuned to these specific frequencies, and therefore do not have the capability to emit significantly distant frequencies in the VHF spectrum. Since these facilities are located geographically far from one another, a comparison of observations of the same ionospheric plasma instability cannot never be provided. Furthermore, since the observatories cannot change the transmission frequency far from the selected value, a study of an optimal frequency to maximize the SNR of the ionospheric layers has never been performed. Occasionally, radar observatories perform a technique called Frequency Domain Interferometry, where two slightly different frequencies (differences on the order of 0.5 MHz) are transmitted and are alternated between each IPP [68 70]. The objective of emitting two frequencies in close proximity has been proven to improve the range resolution of the observations. In an ideal circumstance, ionospheric radars would have an option to scan a wide band of frequencies during the development of a plasma instability, eventually leading to a select number of frequencies that optimize the SNR. Not only will these studies improve the processed results, but also will be a catalyst toward a better understanding of the physics behind the events. In addition, future obser-

115 94 vatories designed for a single operating frequency would have improved scientific reasoning behind the selection process. The plasma instabilities that develop along the magnetic field lines in the ionosphere are categorized as soft targets because they occupy a large portion of the ionosphere and generally fill the entire antenna beam illuminated by the radar system. Since the entire main lobe of the antenna beam is filled, soft targets induce volume scattering back toward the radar system, which have vastly different return properties than hard targets such as meteors. The plasma instabilities are triggered due to electron density fluctuations in the ionosphere that contain spherical or plane wave characteristics. The spherical or plane waves emitted by the electron density fluctuations can either consist of a single wavelength or be a superposition of a number of different wavelengths. Kudeki in [71], derived that a radar observing a soft target with transmitted wavelength, λ, receives the most prominent reflections from the electron density fluctuations comprising of half the transmitted wavelength. This wavelength detected by the radar is also called the Bragg wavelength, and is typically represented by λ B. In short, electron density fluctuations of the Bragg wavelength prompt the strongest response back to the radar, provided it is half the wavelength of the carrier, i.e λ B = λ. 2 During observations of plasma instabilities with current ionospheric radars, the user knows in advance that the processed reflections are caused by the Bragg wavelength associated with the operating frequency. However, since the electron density fluctuations can emit a variety of wavelengths, the optimal Bragg wavelength contributing to the largest received power cannot be determined without examining alternate frequencies. In a practical setting, modifying the transmitted frequency will affect the power aperture of the antenna. The two way antenna power aperture, A e, is proportional the square of the antenna gain, G, and the square of the transmission wavelength, i.e A e = G 2 λ 2 [3]. Therefore selection of the an alternate frequency is influenced by the design of the antenna, and can occasionally negatively adjust the potential received power. Subsequently, upon implementation of a frequency scan technique, the Bragg wavelength that maximizes the SNR is not necessary the optimal Bragg wavelength. Nevertheless, identifying the Bragg wavelength maximizes the SNR still will provide many implications on the underlying physical processes of the plasma instabilities.

116 Global Optimization of Signal to Noise Ratio Since research on the optimal frequency of plasma instabilities has not been applied in practice, some intuition needs to be made in order to design an effective searching algorithm. At a particular instant, if acquiring a function that displays how the SNR varies with frequency was possible, one could speculate in advance that the distribution would fall into one of two categories. If limited to a finite bandwidth, one option would be that the SNR of the plasma instability maximizes once at a particular frequency, meaning that the distribution is smooth and concave down for the entire band. The other assumption would that the SNR versus frequency function would behave more arbitrarily within the operating band, resulting in many local maximums, but one global maximum at a certain frequency. Practically obtaining this function at one instant is not feasible, but can be compiled over time if the bandwidth is properly sampled. The user clearly does not know the shape of the distribution in advance, therefore an frequency searching algorithm needs to be applied to not only discover the global maximum within the entire operating band, but in an efficient manner. For the simple case that assumes the SNR distribution contains a single maximum point, a few algorithms are typically implemented in practice to discover the optimal point. One common approach is called hill climbing. Given a known computable function of any number of dimensions, the hill climbing method initially selects a point at random within the function space. For a known function the hill climbing technique searches for any incremental step thats results in an increased state value. Over time, the algorithm converges when when all incremental steps decrease the value of the current state, meaning a local maximum has been obtained. A similar procedure is applied to discover the local minimum of a given function. Some uses of the hill climbing technique in practice are meant to verify written signatures and optimize the server configuration for web applications [72]. The limitation of this algorithm is assumption that the distribution has one maximum. If the function turns out to have many local maximums, the algorithm would very rarely converge on the global maximum and generally fall on a local maximum. Therefore selecting a hill climbing techniques requires some background information about the function to be analyzed. The more general case of the SNR distribution is to speculate that the function

117 96 contains multiple extrema along the frequency axis. This consequently requires a more complex algorithm to search for the global maximum. Two efficient algorithms used heavily in practice for global optimization are the Genetic Algorithm and Simulated Annealing. The genetic algorithm tries to simulate a searching technique by using the ideas developed by the scientific process of natural selection. Simulated annealing on the other hand uses probability distributions to efficiently sample the parameter space and accept or reject samples based on the value of the current state. Charbonneau implemented the genetic algorithm to model processes in the universe such as the rotation of the galaxies [73]. Kilpatrick in [74] applied the simulated annealing algorithm to the classical traveling salesman problem. Given a set of N cities and locations in a finite dimensional space, the traveling salesman problem attempts to discover the shortest path in which all cities can be visited once. For this particular case of the Simulated Annealing algorithm, the application is solving for the global minimum, which requires minor alterations from the global maximum. As with most algorithms, limitations inevitably during its implementation. Applying the Genetic algorithm requires some knowledge about the shape of the distribution, or cost function, in advance, while the Simulated Annealing algorithm takes longer to converge because information about the cost function is not known. In addition, programming efficiency plays a part in the convergence time. For the case of CIRI, convergence time is essential toward discovering the optimal frequency in a minimum amount of iterations. Given a background on the two categories that can potentially represent the SNR of the plasma instability versus frequency, the most rational choice would be to consider that the distribution possesses multiple local maximums. Provided that no information about the distribution is known, selection of the worst case situation is essential toward developing an effective algorithm. Even if the SNR function ends up consisting of only one maximum point, implementing a global optimization technique still will converge on the correct value. However, the opposite does not hold true for applying a hill climbing technique for a function containing multiple extrema. For CIRI, the simulated annealing algorithm was selected to be a better choice over the Genetic algorithm for discovering an optimal frequency for studying the plasma instabilities. The major advantage that the simulated annealing algorithm has over the genetic algorithm is that no prior knowledge about

118 97 the cost function is needed, therefore the algorithm is very generalized. Applying a genetic algorithm requires some background information and is specific toward each application. Since measurements of the SNR for a single event at various frequencies has yet to be implemented, a generalized algorithm is initially more beneficial. Once a better understanding of the distribution is obtained, specific global optimization techniques such as the genetic algorithm can be applied. Before proceeding toward the details of the simulated annealing algorithm, it must be noted of an assumption being made for the distribution of the plasma instabilities. Although the events are typically very dynamic with regards to the range covered in the ionosphere, it is assumed for each independent event that the optimal frequency that maximizes the SNR does not change throughout the development. The SNR at a specific frequency will vary over time, but the optimal frequency is remains the same. Significance of this assumption will become more apparent in Section and Classical Simulated Annealing and Fast Simulated Annealing The idea of simulated annealing was taken from a physical process used to discover the minimum energy state of a metal [75]. The minimum energy state is found by initially heating the metal with a high temperature, then slowly cooling the temperature until a crystal is formed. A similar strategy is used find the global extrema of a cost function. Typically, simulated annealing is applied for solving the global minimum of a cost function, but the application can be easily adjusted to find the global maximum. The algorithm in practice has a user defined input variable representing a starting temperature, which after each iteration is cooled or in other words reduced. It is necessary for this algorithm to have a known computable cost function that can be randomly sampled over the function space. The random sampling is conducted by applying known probability distributions, where the variance is proportional to the current temperature. For global maximization, once a point on the function space is sampled, the point can be either accepted or rejected depending if the current state is inferior to the previous sample. Inferior states are frequently accepted while the temperature is at a large value. As the temperature cools the sampling variance is reduced and the acceptance probability is also reduced. Given a sufficient amount of samples in the function space, the

119 98 algorithm is guaranteed to converge on the global maximum or global minimum. The initial application of simulated annealing for global optimization purposes was presented in [76], and since then adjustments have been made to improve the performance. A commonly regarded downfall of the algorithm is the amount of iterations needed to converge to the optimum state value. Therefore the main priority toward improving the algorithm entails the speed of convergence. To date, there are three distinct versions of the simulated annealing algorithm, Classical Simulated Annealing (CSA), Fast Simulated Annealing (FSA), and Adaptive Simulated Annealing (ASA). Respectively, the algorithms have been proven to increase the convergence speed by altering the sampling probability distribution and the cooling process of the temperature. Algorithmically, the CSA and FSA are closely related therefore the implementation is described in conjunction. The Simulated Annealing algorithm for each version begins by randomly selecting a point in the function space and determining the value of the function at that particular state. The subsequent step is to sample another point in the function space utilizing a predefined probability distribution. The probability distribution is a function of the distance from the original sampled point. For a parameter vector, x, associated with a particular cost function of dimension, D, the sampling probability distribution of the CSA and FSA are respectively shown in Equation 4.26 and Equation ( ) g( x) = (2πT SA ) D x 2 2 exp 2T SA (4.26) g( x) = T F A π( x 2 + TF 2 A ) D+1 2 (4.27) The variables T SA and T F A in Equations 4.26 and 4.27 are the initial temperature values set by the user for the CSA and FSA respectively. The resulting form of the sampling distribution following a Gaussian distribution for the CSA and a Cauchy distribution for the FSA. Initially, the temperature is high which corresponds to a large sampling variance where large values of x generally result. Over time however, the temperature cools and the sampling distribution becomes restricted to values of small x. The reason why the Cauchy distribution has been shown to be more effective than the Gaussian distribution will be discussed in the

120 99 coming paragraphs. Once a new sample has been obtained with the mentioned distributions, the value of the cost function at the new point is determined. In global maximization, if the value of the cost function at the newly acquired sample is larger than the previous sample, then the algorithm continues without further analysis. If the value of the cost function is less than the previous sample however, then the new sample can either be accepted or rejected with a computable probability of acceptance. If we define the cost function to be f(x), the difference in subsequent samples, x k+1 and x k, is represented by E, i.e. E = f(x k+1 ) f(x k ). The probability of acceptance for an inferior point is a function of E and the current temperature. ( ) E P accept = exp (4.28) T The value of the temperature, T, is kept generic in Equation 4.28 because the same function is applied for all the versions of Simulated Annealing. Since P accept is only computed if a decrease in the cost function occurs, the value of E is always a negative. Therefore the resulting probability is guaranteed to be between 0 and 1. In practice, once obtaining a value for P accept, a uniform random variable is generated. If the value of the uniform random variable is less than P accept, the new sample is accepted, otherwise it is rejected. If rejected, the preceding point is maintained. The final step before repeating the given process is to reduce or anneal the current temperature. The purpose of this step is to allow a gradual decay in the temperature which slowly reduces the sampling variance and the probability of acceptance of inferior samples. If the cooling process is too fast, an insufficient amount of samples of the cost function will be attained, meaning the algorithm would rarely converge on the global optimum. For each iteration, k, the following procedure is performed to anneal the temperature for the CSA and FSA. T SA (k) = T 0 Ln(k + 1) (4.29) T F A (k) = T 0 k + 1 (4.30)

121 100 T 0 in Equation 4.29 and 4.30 is the initial temperature chosen by the user. Provided that T 0 is large enough, the CSA and FSA are guaranteed to converge provided a adequate amount of samples of the cost function. After annealing the temperature, the algorithm repeats by generating a new sample with the probability distributions in Equation 4.26 and The process continues until a convergence criterion is met, typically set by the user. Some common convergence criterion is to stop the algorithm once T SA or T F A fall below a certain value, or the algorithm has completed a predefined number of iterations. In [77], it was mathematically proven that the FSA is faster to converge on the global optimum than the CSA. Observing the implementation of both algorithms, the difference lies in the sampling distribution and the annealing schedule. The sampling distribution is the main contributor toward the quicker convergence. Comparing the Gaussian and Cauchy distribution, the noticeable difference is the extent of the tails that continue for large values of x. A visual comparison of the two distributions is shown below in Figure 4.8 for the case of T 0 = 1. Figure 4.8. Comparison of the Cauchy and Gaussian sampling probability distribution As shown, the Cauchy distribution is far more likely to sample bigger values of x than the Gaussian distribution. This is advantageous for the simulated annealing algorithm because the tails provide opportunities to escape local minimums or maximums. Without a widespread distribution, the function space is finely sampled and will inevitably converge on a local maximum. In addition,

122 101 small displacements in the sampling process will result in only a finite portion of the function space being explored, while majority of the function space needs to be sampled in order to converge on a global maximum. Even as the temperature decreases the tails in the Cauchy distribution are maintained while the Gaussian would continue to rarely sample outside of two standard deviations. One way deal with this issue for CSA would be to increase the starting temperature, T 0. The major drawback of this adjustment would be an even longer time to converge. The annealing schedule also plays a role in the speed of convergence for CSA and FSA. The schedule shown in Equation 4.29 for CSA has a much slower decay rate than the schedule for FSA in Equation Intuitively this is necessary because it allows a larger number of iterations to explore the function space, while the FSA can cover a larger area of the function space in less samples. The initial temperature values are selected so the majority of the function space can be covered within the distribution, therefore large hops can result in the beginning of the algorithm. In [77] a mathematical derivation is given, showing that when the samples are infinite in the function space the CSA and FSA are guaranteed to converge. For the theoretical case of when T SA or T F A reaches zero, the algorithm becomes a hill climbing technique in which no inferior points can be accepted Adaptive Simulated Annealing The CSA and FSA algorithms described have the advantage that they require a minimal amount of input variables in order to discover the global optimum of a given cost function. The essential input variables for applying both algorithms are the initial temperature and the stopping criterion. However, with a few extra parameters, the speed of convergence can be vastly improved. This is with the Adaptive Simulated Annealing algorithm. The algorithm was first presented by Lester Ingber in [78,79] and has been typically used for cost functions with a very large function space containing one or multiple dimensions [75, 80, 81]. The overall algorithm is slightly more involved than the CSA and FSA, but the general idea is maintained. A flow diagram of the ASA algorithm is shown in Figure 4.9 [80]. From the flow diagram it is evident that the ASA algorithm follows a similar procedure to the CSA and FSA, for the exception of the reannealing step. The primary idea for the reannealing step is to counteract the temperature reduction

123 102 Figure ) Flow Diagram of the Adaptive Simulated Annealing algorithm (Chen, and reset the temperature to a higher value. Essentially this allows the algorithm to successfully cover the function space an additional time, for the chance that the global maximum or minimum was missed. This procedure is only applied after a certain amount of accepted points, N accept, therefore it is more common to reanneal toward the beginning stages of the algorithm than at a point close to convergence. The sampling distribution and annealing schedules for the ASA are also different from the CSA and FSA. Instead of sharing the same temperature for the probability distribution and the acceptance probability, ASA defines two separate input variables for these temperatures, i.e T gen and T accept. The annealing of these temperatures are not applied after every iteration, but after a user defined amount of samples, N gen. Once all input variables are set, the algorithm is initiated by selecting a random point in the function space and evaluating the cost function.

124 103 The rest of the described procedure follows the outline of [75, 80] with necessary changes made for global maximization purposes instead of the literatures global minimization application. Generating the ensuing sample in the function space is a three-fold process. For a cost function containing n dimensions, a uniform random variable between 0 and 1 is initially produced for each dimension. Represented by, v i, the random sample is input into the following equation for each dimension, i. ( q i = sgn v i 1 ) ( ( ) ) 2vi 1 1 T i,gen (k i ) T i,gen (k i ) (4.31) T i,gen (k i ) is the generating temperature for dimension, i, and iteration k. The result of Equation 4.31 is an updated random variable containing a value between -1 and 1. A visual presentation of the distribution resulting from Equation 4.31 is provided in Figure 4.10 for three consecutive iterations or temperature annealings. Notice that the tails of the distribution are still prominent even with the temperature greatly reduced. This consequently allows the algorithm to rarely get stuck in a local maximum even at low temperatures. Figure Adaptive Simulated Annealing sampling distribution at different annealing times The newly acquired random variable is then used to compute the new sample in the function space, a new i.

125 104 a new i = a old i + q i (U i L i ) (4.32) where U i and L i represent the upper and lower bounds of the cost function in each dimension respectively. The resulting sample, a new i, can occasionally fall outside of the bounds because of the values of a old i and q i. In this situation, q i is reevaluated with a new set of values for v i until the Equation 4.32 is valid within the function space. Once the new sample or parameter vector is set, the difference between the subsequent cost functions are computed, i.e E = f(a new ) f(a old ). If the value of the cost function increased, then the new sample is automatically accepted. If a decrease occurred, the probability of acceptance is defined as: ( ) E P accept = exp T accept (k a ) (4.33) The acceptance probability is essentially the same relation used for CSA and FSA in Equation However, since ASA utilizes two different temperature values, Equation 4.33 is a function of the specific input T accept. Once a value of P accept is computed, the practical implementation is the same as CSA and FSA, where a uniform random variable between 0 and 1 in generated. If the uniform random variable is less than P accept than a new is accepted, otherwise the algorithm repeats with a old as the parameter vector. After N accept acceptances, the ASA algorithm reanneals the temperatures in order to ensure the parameter space was properly sampled. If the cost function contains more than one dimension, the reannealing process is two fold process which resets both the generating temperature and the acceptance temperature. For one dimensional cost functions however, only acceptance temperature is reset. Keeping note of the parameter vector that resulted in the largest cost function value, a best, the first step of reannealing is to determine the derivative of this parameter vector along each dimension. The absolute value of these derivatives are called sensitivities and is denoted by s i. s i = f(a best + e i δ) f(a best ) δ (4.34) In Equation 4.34, e i is a unit vector for each dimension, i, and δ is an infinites-

126 105 imal step that depends on the function space resolution. For a cost function of dimension n, the maximum value from the set of computed sensitivities is defined as s max. s max is used for rescaling the current generating temperature along each dimension and the annealing time, k i, by: T i,gen (k i ) = s max s i T i,gen (k i ) (4.35) k i = ( 1 ( )) n c log Ti,gen (k i ) (4.36) T i,gen (0) where T i,gen (0) is the initial value of the generating temperature set by the user, and c is an additional user defined control parameter. In Equation 4.35 the dimension that resulted in the smallest sensitivity is subjected to the largest increase to the generating temperature. To interpret this relation, if a best was nearly a local maximum along a particular dimension, then the sudden increase in temperature would guarantee the subsequent samples to be far outside of that region. The acceptance temperature is also rescaled by first resetting the value of T accept (0) to the reciprocal of the last accepted cost function value, while T accept (k a ) is reset to the reciprocal of the best cost function value found at the particular time. In a similar manner to Equation 4.36 the annealing time is then calculated by: k a = ( 1 ( )) n c log Taccept (k a ) (4.37) T accept (0) If a large difference is determined between the value of T accept (k a ) and T accept (0), meaning the ratio is much less than 1, than the resulting annealing time is a large number. If the ratio is around 1, the annealing time is reset to 0. Significance of the annealing time for both the generating temperature and the acceptance temperature will be apparent in the coming paragraphs. Notice that rescaling the acceptance temperature and corresponding annealing time do not require knowledge about the other dimensions, therefore a one dimensional cost function can be involved in this step. Involving a one dimensional cost function for rescaling the generating temperature has no affect since the ratio s max /s i will always be unity.

127 106 Continuing to follow Figure 4.9, the next step after reannealing is the annealing process. The purpose of the annealing process for ASA is the same for CSA and FSA where the temperature is decreased to narrow the generating distribution and prevent an abundance of inferior samples toward being accepted. After N gen generated samples, the annealing process is initiated by increasing the most current value of k a and k i by one. The ensuing annealed generating and acceptance temperatures are then computed by: T i,gen (k i ) = T i,gen (0)exp( ck 1/n i ) (4.38) T accept (k a ) = T accept (0)exp( ck 1/n a ) (4.39) where T accept (0) is the most updated value as a result of the reannealing process. After temperature annealing, the described process is repeated for additional samples of the parameter space. The algorithm has reached convergence if the largest found cost function value has remained the same for a number of consecutive iterations or reannealings Implementation of Simulated Annealing Algorithms To demonstrate the effectiveness of the simulated annealing algorithm, each of the variants were applied to a cost function that represented the SNR of a simulated target versus the transmission frequency. In a practical setting, this distribution would not be known in advance, otherwise the optimal frequency would already be known. Therefore an arbitrary shape was generated which contained a number of local maximums in order to ensure the algorithm is proficient at finding the global maximum at a user selected frequency. The cost function used for the simulation is shown in Figure As shown, the frequency band used to represent the simulated target was selected to be between 10 MHz and 100 MHz. The lower bound of the distribution was chosen based on physical limitations of ionospheric research. Due to the plasma density of the ionosphere, frequencies lower than 10 MHz typically will not be able propagate through this region and consequently all the energy is reflected. For this reason, frequencies lower than 10 MHz are used generally for Radio communica-

128 107 Figure Arbitrary signal to noise ratio distribution as a function of frequency. Generated to apply Simulated Annealing algorithms. tion. The upper bound of the frequency band however could have been selected to any number, but was set to 100 MHz based on the consideration of realistic antenna operating bands. The cost function was generated with seven independent Gaussian distributions each encompassing a different mean and variance. The global maximum for the simulation occurs at 40 MHz on the Gaussian distribution containing the smallest variance in order to test the algorithms searching technique. The value of the SNR at the global maximum was chosen to be 50 db. Because of the narrow variance, the peak has a larger likelihood of being overlooked during the sampling process. Even though the user knows in advance the SNR distribution and the optimal frequency, the simulated annealing algorithm for this purpose resembles a practical setting where the optimal frequency is only discovered by methodically sampling the bandwidth of operation. The implementation of the CSA and FSA algorithm require two user inputs to properly run the global optimization simulation, the starting temperature and the convergence criterion. The algorithms were presumed to satisfy the convergence criterion once the current temperature drops below a selected value. At that instant, the temperature would be low enough such that the sampling distribution covers a narrow band in the frequency domain, meaning there is a small chance of escaping out of a local maximum. The starting temperature

129 108 for the CSA and FSA algorithms respectively were 30 and 1000, while associated threshold temperatures were 3 and 0.1. Based on Equation 4.29 and 4.30 the resulting number of iterations for the entire process is 22,026 and 10,000. With FSA, it is more feasible to cover a wide range of temperatures because of the fast annealing schedule, while CSA generally needs to be limited to a small variety. Because of the slow annealing time, CSA hence requires much more iterations for guaranteeing a convergence on the true global maximum. Initiating the ASA algorithm for the simulation required a few additional input parameters, namely the starting generating and acceptance temperatures, the number of accepted samples needed for reannealing (N accept ), number of generated samples for annealing (N gen ), the control parameter (c), and stopping criterion. The selected input values followed a similar setup given in [75] with the initial generating temperature set to 1, initial acceptance temperature set to the reciprocal of the first cost function value, N accept to 50, N gen to 500, and c to 2. The criterion for convergence was selected to cease once the cost function value has remained unchanged for 500 consecutive samples. Occasionally the algorithm continues to reject inferior cost function values for multiple iterations, even at lower temperatures, therefore the stopping criterion must be set to a excessive amount of samples to confirm the global maximum was achieved. The selected inputs could be altered slightly for fine tuning the performance, but a significant improvement is unlikely [75]. Figures below display the performance for a single trial of the simulated annealing algorithms. The curve represents the cost function value or SNR as a function of the iteration of the algorithm, hence the SNR generally improves as the iteration increases due to the global optimization structure. A drop in SNR value is apparent throughout the plots because of accepted inferior samples. This happens regularly at the beginning stages of the algorithm due to the temperature being high. The provided plots demonstrate the order of efficiency of the described simulated annealing algorithms. Each converged on the global optimum of 50 db, but at a vastly diverse number of iterations. The CSA, FSA, and ASA respectively converged on the global maximum after approximately 16,000, 2,000, and 500 samples. Notice that the once the global maximum was achieved, the accepted

130 109 Figure Global Optimization Results of Classical Simulated Annealing Algorithm Figure Global Optimization Results of Fast Simulated Annealing Algorithm inferior points did not degrade the SNR by a significant amount since typically the temperature was low at the current iteration. Every time the algorithm is executed, the resulting plots are unique because of the random nature behind the sampling process. However, given the mentioned input parameters, each of the simulated annealing algorithms consistently converged on the global maximum. The convergence times varied slightly from trial to trial, but CSA would always be out performed by the ASA and FSA. ASA would regularly better the perfor-

131 110 Figure Global Optimization Results of Adaptive Simulated Annealing Algorithm mance of FSA. Sporadically, each of the three methods would get caught in a local maximum presumably because the sampling process overlooked the narrow bandwidth containing the global solution. The significance of the results prove that an optimal frequency leading to a maximum SNR is achievable for an unknown cost function. Since the simulation was an offline process, the amount of iterations required for convergence would not enhance any interpretation of a time dependent plasma instability. However, for a real time radar system such as CIRI, the optimal frequency would need to be discovered in the least amount of samples so the maximum SNR is measured for the majority of the event s duration. Hence the concepts originating from the ASA algorithm is the basis toward developing a real time frequency selection technique for a cognitive radar system Application of Adaptive Simulated Annealing for Cognitive Radar Systems The fundamental difference between the simulated implementation of ASA discussed in the previous section and the practical implementation for a radar system is the computation of the unknown cost function. For simulated purposes the cost function was an input to the algorithm, therefore the SNR at a particular frequency was easily determined. For a real time radar system this convenience is not available, so each selected frequency must collect and process the radar returns

132 111 from the detected event in order to resolve the associated SNR. Therefore the applied frequency selection algorithm is a time consuming process where a minimal amount of samples are preferred for the interest of locating the optimal frequency. For the intention of CIRI, the plasma instabilities observed at a fixed frequency additionally do not maintain a constant SNR throughout the event s development. Referring back to Figures , the RTI plots illustrate that the SNR for the Electrojet, 150 km echos and Spread F naturally increase and decrease arbitrarily due to physical reasons. These changes in SNR must be taken into consideration to avoid misinterpreting the differences in SNR between two transmitted frequencies. Given the challenges and unknowns that emanate with applying the ASA algorithm for ionospheric radars, a few assumptions about the plasma instabilities are made to simplify the process. The first assumption was mentioned previously concerning the optimal frequency. Throughout the development of any individual plasma instability, the optimal frequency that maximizes the SNR is presumed to be constant. If the optimal frequency was given the freedom to shift, than the cost function would need to be time dependent, meaning that there is a independent cost function for each time instant. Considering that no two plasma instabilities are the same, having a time dependent cost function would be illogical, and would greatly increase the computational complexity. Another assumption made about the plasma instabilities acknowledges the natural increases and decreases that occur over time. If the SNR at one particular frequency was observed to increase then it is speculated that the SNR for all other frequencies increased as well. The same idea is included for observing a decrease in SNR. This assumption further reduces the complexities that would be involved if the cost function could stochastically modify as a function of time. A necessary requirement for applying this technique for radars is to have access to real time processing software. The software would need to have the capability of processing the radars returns close to real time and triggering a command that adjusts the transmitted frequency. The real time software would also generate the resulting RTI plot, and update with the latest data after a user defined plotting interval. An example of a plotting interval could be every 10 seconds. After a sequence of plotting intervals the software would analyze the changes in SNR of the detected event and make a decision to maintain the current frequency or to

133 112 continue to sample the band of operation. With the presented requirements and assumptions, a step by step procedure for applying a modified version of the ASA algorithm for determining the optimal frequency with a radar system is summarized as follows:

134 113 Step 1: Initialize algorithm by selecting input parameters N gen, N accept, initial temperatures (T gen and T accept ), and control parameter (c). Operating at a fixed frequency, process returns in RTI format with a user defined plotting interval. Step 2: After each processed plotting interval, apply the detection scheme explained in Section to find an average SNR for every range bin. Continue to Step 3, upon the detection and classification for any of the three known plasma instabilities, while preserving the SNR measured during the detection process. Step 3: Utilize Equation 4.31 and 4.32 to compute new operating frequency. The upper and lower bounds (U and L) are set by the user based on hardware constraints. Note that the dimension, i, in the given equations is 1 because this is a one dimensional optimization problem. Step 4: Switch to new frequency of transmission and sample returns for several plotting intervals. Two different measurements are conducted at the new fixed frequency: The average SNR for the combined RTI plot containing several plotting intervals, and the average SNR for each individual plotting interval. The former is used to represent the value of the cost function for the chosen frequency. The difference in average SNR between the first individual plotting interval and final plotting interval is represented by SN R, and is necessary for computing the probability of acceptance of new frequency. This value signifies the natural increase or decrease in SNR for the observed plasma instability. Step 5: Compute the value of E by subtracting the cost function value of the new frequency from the previously sampled frequency. In addition, compute SNR. If E is a positive number than accept the new frequency of transmission because a larger cost function value was discovered. To the contrary, if E is negative than accept new frequency with probability P accept. ( ) E SNR P accept = exp T accept (4.40)

135 114 The only exception to computing P accept occurs if SNR is less than zero. For this case, automatically reject the new frequency. Step 6: After N gen generated samples or N accept accepted samples proceed with the annealing or reannealing process respectively using the appropriate equations outlined in Equations Note that Equation are ignored since this is a one dimensional optimization problem. If the new frequency is accepted, then return to Step 3. Otherwise select the previous frequency and return to Step 4. Step 7: At the completion of the event, if convergence is not made, make note of the best frequency found to that point. For the next occurrence of the detected event, initiate the sampling on this frequency and continue with Step 3. If convergence to an optimal frequency is found, then always initiate sampling on this frequency, and occasionally return to Step 3 to discover if multiple ideal frequencies exist. Over time, gradually reduce the starting temperatures that were set in Step 1 so convergence is inevitable after long observation campaigns. In general, the given procedure follows the ideas of the ASA algorithm but necessary changes were made to allow the process to work in a real time environment. One important modification to the algorithm was the relation of the acceptance probability. As mentioned in Step 4, SN R was incorporated to the acceptance probability to take into account the natural fluctuations in SNR during the development of the plasma instabilities at a single frequency. For a large positive SN R the previous frequency would intuitively be more ideal, so P accept should result in a low value. This is due to the made assumption than an increase in SNR in one frequency would imply an increase in SNR for all other frequencies. Since applying Equation 4.40 already assumes E is less than zero, the previous frequency is guaranteed to maintain a larger SNR than the new frequency. This same reasoning is made for case of setting P accept to zero if SNR is negative valued since no improvement in the optimization process is achieved. On

136 115 the other hand, if the event is more stable at the current iteration, SNR is low and P accept would be higher. Accepting a frequency that returns an inferior SNR is reasonable at low SN R because the cost function is stationary, and escaping out of local maximums is more likely. Overall, the provided algorithm is not time dependent, meaning that each detected event is assumed to have an independent cost function. However, trends are explored for each particular plasma instability (Electrojet, 150 km Echoes, and Spread F) so past returns will build off each other to find a set of ideal frequencies. After a period of time, if a select number of frequencies have been discovered to maximize the SNR, the algorithm would be adjusted to restrict the observations to just these values. The one disadvantage with the algorithm currently, is that only one event can be optimized at a time. For the case of multiple event occurring simultaneously in the ionosphere, multiple cost functions would exist and the radar system can only emit one frequency at a time. In this situation, a choice would have to be made for which event to focus on. For current ionospheric radars, the presented algorithm has some limitations due to the hardware typically used for the system. The bandwidth of operation for both the high power transmitter and the antennas are generally very narrowband and are of the order of 2-3 MHz. Therefore a large portion of the VHF spectrum would not be possible to sample during the development of the ionospheric events. However, even with the hardware constraints, an optimal frequency within the band is still achievable and could potentially result in an advancement of the physical interpretation. Furthermore, as hardware designs continue to improve the bandwidth of operation for high power transmitters and antennas, future ionospheric radars would have the capability to explore a larger portion of the VHF spectrum, leading to a more deserving scientific contribution. Although the CIRI hardware will be only operational within a narrow band, the impact of the proposed algorithm will only be recognized upon its implementation. Once a contribution is made, the algorithm can then be similarly applied at radars at alternate locations.

137 Summary of Cognitive Routine To summarize the contents outlined in this chapter, the proposed cognitive routine for studying the plasma instabilities operates in three stages with the intention of seeking for an optimal waveform to maximize the SNR. The first stage is to detect and classify the plasma instabilities of interest. This technique needs to initially be performed offline to train the corresponding GMM distributions for each event. The training requires a list of labelled feature vectors extracted from previously collected data. Once trained, the feature extraction and classification is performed in real time to determine which event is generating in the ionosphere. The second step uses the received signal from the ranges containing the plasma instability to estimate an optimal transmission envelope. Assuming the ionosphere behaves as a linear system, the impulse response of the target can be determined by using concepts from Fourier Theory. The information needed to calculate the impulse response is the received signal from the target and the original envelope of the transmission signal. Upon resolving the target impulse response, an algorithm is presented to compute the optimal transmission envelope that maximizes the matched filter output. Since the plasma instabilities are generally slow to develop in the ionosphere, the optimal transmission envelop needs only to be determined occasionally. The essence of the cognitive routine involves searching for the optimal frequency to embed within the transmission envelope. Assuming that the optimal frequency is constant while the plasma instability is present, a frequency selection algorithm is presented with the objective of discovering the wavelength that maximizes the SNR from the target. In practice, the operating frequency will regularly change until a maximum SNR is achieved, but also continue to explore any further changes. The approach of the algorithm was based off a global optimization technique called ASA. Although hardware limitations do exist for practical implementation of the provided algorithm, slight alternatives are possible to sequentially enhance the returns from the plasma instabilities. Ultimately, the designed algorithm is the preliminary attempt toward building a stronger foundation for interpreting the physics behind the plasma instabilities, which is a major interest to the scientific community.

138 Aside: Waveform Diversity with CIRI at PSU An initial attempt toward applying the cognitive design with CIRI at PSU culminated in many challenges due to the selected hardware and restrictions to the bandwidth of operation. The major limitation prompted by the hardware was the inability for the high power transmitter to dynamically change the frequency of operation. The transmitter has an operation bandwidth of approximately 2 MHz, but a frequency switch is only possible by shutting down the component and reprogramming the frequency offline. Performing this task in real time would result in a significant loss of information about the plasma instabilities. Subsequently, the bandwidth of operation for CIRI at PSU is limited to 200 KHz because of Federal Communications Commission (FCC) regulations. Even if a dynamic change to the operating frequency was possible, only a narrow portion of the VHF spectrum would be explored. In addition, all transmission pulses occupy a finite bandwidth around the frequency of operation, reducing the potential portion of the VHF spectrum further. As a result of the mentioned drawbacks with the hardware, an alternative approach was designed to adaptively improve the SNR of long duration ionospheric targets with CIRI at PSU. The fundamental idea behind the design was that, although the high power transmitter does not allow dynamic frequency switching, it does tolerate dynamic changes to the waveform envelope. Therefore the potential to transmit different coding schemes is feasible. The initial design involved the transmission of two different waveforms that both contain the same IPP. While the processed returns from the ionosphere present only the occasional short duration meteor event, the radar will continue to operate in a default mode. Once a long duration event is detected however, the transmitter is reprogrammed to switch operating modes to a higher average power and higher resolution i.e longer coding sequence. The higher average power guarantees a stronger return from the target resulting in an increased SNR. Moreover, if chosen properly, the longer coding sequence also enhances the SNR because peak to sidelobe ratio of the matched filter output. Upon completion of the long term ionospheric event, the radar is reprogrammed to switch back to the default mode. The described approach was implemented for a couple days in August 2014 with

139 118 CIRI at PSU, using a default mode of a Barker 13 and a baud length of 10 µs. With the real time software, returns from the ionosphere were digitized, processed, and plotted in a RTI format. The RTI plot would update with the latest returns every 10 seconds. In each 10 second window, the detection technique discussed in Sections was applied to determine if a sequence of altitudes exceeded a predefined average SNR threshold. If the average SNR threshold was exceeded for three consecutive plotting updates, than it was decided that a potential long term plasma instability was present. This then triggered the reprogramming of the transmitter and the matched filter coefficients. The waveform selected to improve the SNR of the plasma instability was a 28 baud sequence with a 5 µs baud length. This waveform was chosen to improve the SNR because it satisfied both requirements outlined in the previous paragraph. CIRI would continue to operate in the new transmission mode until the average SNR threshold was not surpassed for two consecutive plotting intervals, consequently reprogramming the transmitter back to the original mode. Figures are the RTIs illustrating the results of the waveform transition for a couple detected events. The only detected events during the two day observation were long duration meteor trails. Plasma instabilities specific to the mid-latitude region occasionally generate during night time periods, but unfortunately did not occur during the experiment. Figures 4.15 and 4.17 both show the transition from the default waveform to the higher average power and resolution waveform. The time of transition is noticeable by observing the pulse shape at low ranges. At approximately 03:02:02 and 03:11:24 LT respectively, the SNR of the transmission pulse increases significantly as a result of a higher average power. The transitions are not synchronized with the plotting intervals because of the processing time required to analyze the received data. The change in transmission waveform consequently increased the SNR of the detected meteor trails, with the enhancement more evident in Figure The sidelobes of the 28 baud sequence are also more conspicuous than the Barker 13 sequence because of the enhanced SNR. For completion, the RTIs displaying the transition back to the default mode are provided in Figures 4.16 and The adjustment occurs once the meteor trail subsided, approximately a minute later for both detected events. Although the initial adaptive method proved successful in temporarily improv-

140 119 ing the SNR of the detected meteors, improvements can still be incorporated. Instead of the radar alternating between two waveforms, additional waveforms would help to further analyze the ionospheric targets. Since the ionosphere is more dynamic in the equatorial region, a potential improvement for CIRI in Huancayo could be to select a specific waveform for each of the three plasma instabilities. Once the event is detected and classified using the described method in Section 4.2.2, the software will reprogram the transmitter in a similar manner to the experiment performed with CIRI at PSU. Figure Range-Time-Intensity Plot illustrating the transition of the transmitted waveform from the default mode to a higher average power and resolution mode. Detected event was meteor trail observed at approximately 3:02 LT.

141 120 Figure Range-Time-Intensity Plot illustrating the transition of the transmitted waveform from the higher average power and resolution mode to the default mode. Detected meteor trail subsided at approximately 3:04 LT.

142 121 Figure Range-Time-Intensity Plot illustrating the transition of the transmitted waveform from the default mode to a higher average power and resolution mode. Detected event was meteor trail observed at around 3:10 LT.

143 122 Figure Range-Time-Intensity Plot illustrating the transition of the transmitted waveform from the higher average power and resolution mode to the default mode. Detected meteor trail subsided at approximately 3:12 LT.

144 Chapter 5 Observations with CIRI at PSU 5.1 Introduction Since the summer of 2012, CIRI at PSU has been operating intermittently to obtain measurements of the ionosphere for mid-latitude regions. For the past year however, observations have been conducted more regularly. The majority of ionospheric activity during the course of a single day is caused by meteor events, typically falling into the category of specular overdensed or underdensed [82, 83]. As a result of the antenna boresight being directed perpendicular to the geomagnetic field, the formation of non-specular meteors and head echoes are also occasionally observed [84, 85]. In addition to short duration meteor events, long duration plasma instabilities were sporadically observed in the ionosphere because of the antenna pointing direction. Typically at mid-latitudes, the most frequently detected plasma instability is called a Quasi-Periodic Echo. These events have a distinct signature when analyzed in an RTI plot, each containing a short descending layer that reappears steadily for around or above an hour [86, 87]. Other plasma instabilities were observed in addition to Quasi-Periodic layers, but due to the arbitrary structure, a particular name has yet to be designated for every individual. After over a year of consistent ionospheric measurements, a fair assessment can be drawn that the plasma activity at mid-latitudes does not follow a repetitive daily routine. Therefore some very preliminary analysis can be made on the diurnal and seasonal trends of the meteors and plasma instabilities. For meteor occurrences, it is well known that the peak hours are generally in the early morning because of the

145 124 pointing direction of the Earth s surface [88]. This tendency was confirmed using a detection and classification algorithm incorporated into the CIRI at PSU software. However, the amount of meteors detected daily varied throughout the course of the year, with a large increase of activity appearing in the summer months. For the plasma instabilities, the time of development would consistently take place during night time periods. On a few rare occasions however, a plasma instability was present during the daytime hours. Annual trends were also apparent during the year long observation, where the layers were more frequent during the late fall and early summer months, and became dormant during the late winter to early spring. In order to perform a more comprehensive physical interpretation of the daily and annual trends of the ionosphere, a compilation of multiple years of data would need to be processed. With the current data collected with CIRI at PSU, only a single annual sample is acquired, leading only to initial conclusions. For the exception of a few experiments implementing the initial approach toward waveform diversity, CIRI at PSU has been operating in the traditional radar mode by the selection of a fixed pulsed transmitted signal. Over the course of the two years, the chosen signal was altered a couple times. However, each pulsed signal contained an IPP of 4 ms, and a peak transmit power of 30 kw. Since the boresight of the antenna beam is approximately 18, the IPP had to be fixed to a value that would encompass a major portion of the ionosphere. The maximum unambiguous altitude with a 4 ms IPP is approximately 185 km ( c 4ms 2 sin (18 ) ). The initial transmitted waveform selected was a 28 baud code, with a 5 µs baud length, and transmission frequency of 49.8 MHz. This waveform was ideal in terms of the range resolution and average transmitted power. However, because of the short baud length, the bandwidth of operation was extensive and therefore interfered with other communication systems located in close proximity to CIRI at PSU. As a result, the operation bandwidth had to be reduced leading to a subsequent transmitted waveform holding the same frequency, but switching to a Barker 3 code, with a 55 µs baud length. The average power for this waveform was larger than the initial signal, but the range resolution was very poor, making it occasionally difficult to properly decipher the returns. Eventually, a new license was acquired to move the frequency of operation further away from the other communication systems, meaning more transmission bandwidth was tolerated. The

146 125 current frequency of transmission is 49.5 MHz, while the waveform is a Barker 13 code, with a baud length of 10 µs. During the course of the observations with CIRI at PSU, the raw data is processed and saved on the host computer in order to perform further analysis offline. The processing techniques outlined in Chapter 3 are each implemented upon the occurrence of any plasma instability or long duration meteor trail. This chapter begins by presenting three interesting plasma instabilities observed by CIRI at PSU. In addition to the conventional RTI plot, each plasma instability is also further processed in a doppler map, spectrogram, and phase plot. Following the plasma instabilities, RTI plots that contain selected meteor events are shown along with an observations of a meteor shower that occurred in early Finally, the daily variation of the sky noise is provided for a single day. 5.2 Quasi-Periodic Echo RTI Plot Figure 5.1. RTI Plot of a Quasi-Periodic Echo observed on June 29, The transmitted waveform was a Barker 13 code with a 10 µs baud length, and frequency of 49.5 MHz.

147 Doppler Map Figure 5.2. Doppler Map of Quasi-Periodic Echo. The returns illustrate that the motion of the plasma instabilities were primarily away from the radar system Spectrogram Figure 5.3. Spectrogram of Quasi-Periodic Echo processed at km. The particular echo contains a large spread of Doppler content covering both positive and negative values, with the majority weighted toward negative Doppler shifts.

148 Phase Plot Figure 5.4. Phase Plot of Quasi-Periodic Echo processed at km. The sequence of linear slopes corresponded to East-West drift velocity each exceeding 150 m/s. 5.3 Miscellaneous Echo # RTI Plot Figure 5.5. RTI Plot of an ionospheric echo observed on June 30, The transmitted waveform was a Barker 13 code with a 10 µs baud length, and frequency of 49.5 MHz.

149 Doppler Map Figure 5.6. Doppler Map of ionospheric echo. The event transitions to a larger negative Doppler shift toward the events completion. DC content is also prominent intermittently at the lower ranges Spectrogram Figure 5.7. Spectrogram of ionospheric echo processed at km. The plot illustrates a narrow spread of Doppler content, with the majority of the power containing negative values. The negative Doppler content increases at the end of the event.

150 Phase Plot Figure 5.8. Phase Plot of ionospheric echo processed at km. The slope of the two major linear portions correspond to an East-West drift velocity both exceeding 55 m/s. Note the phase wrapping at approximately 22:12 LT.

151 Miscellaneous Echo # RTI Plot Figure 5.9. RTI Plot of an ionospheric echo observed on July 10, The transmitted waveform was a Barker 13 code with a 10 µs baud length, and frequency of 49.5 MHz. Note that this was a rare daytime event

152 Doppler Map Figure Doppler Map of daytime ionospheric echo. The event presents all positive Doppler content throughout its duration Spectrogram Figure Spectrogram of daytime ionospheric echo processed at 300 km. A large spread is apparent with majority of the power confined on the positive Doppler spectrum.

153 Phase Plot Figure Phase Plot of daytime ionospheric echo processed at 300 km. The slope of the portions exhibiting linear phase correspond to an East-West drift velocity exceeding 55 m/s.

154 Meteor Events Figure second RTI plot of observation on June 6, The transmitted waveform was a 28 baud code, with a 5 µs baud length, and frequency of 49.8 MHz. A meteor head echo and trail is observed starting at approximately 05:19:21 LT.

155 134 Figure second RTI plot of observation on August 19, The transmitted waveform was Barker 13 code, with a 10 µs baud length, and frequency of 49.5 MHz. The displayed event was a nonspecular meteor with an exceptionally long trail.

156 Meteor Shower Figure minute RTI plot of Quadrantids meteor shower occurring on January 3, The transmitted waveform was a Barker 3 code, with a 55 µs baud length, and frequency of 49.8 MHz. A vast increase in meteors was observed this night with frequent occurrences of meteors with long trails. Note that the range resolution is quite poor due to the chosen waveform.

157 136 Figure Additional 15 minute RTI plot during peak of Quadrantids meteor shower occurring on January 3, Events occurring below the range 150 km are not considered as meteors and are typically considered to be airplanes or cars illuminated from one of the antennas sidelobes.

158 Sky Noise Figure Sky noise level measured for 24 hours on June 20, The noise level was computed every 2 seconds using the Hilbrand-Sekon Method. In order to smooth the curve, the noise level was averaged for 10 minute intervals. The noise level predominately depreciates throughout the morning hours and then increases during the nighttime hours. Occasionally short spikes in the noise level occur, which could be caused by radio stars. A more thorough analysis and understanding of the radio star locations must be performed to draw better reasoning behind the daily trends.

159 Chapter 6 Observations with CIRI at Huancayo 6.1 Introduction In March 2015, the installation of CIRI at Huancayo was finalized, therefore continuous monitoring of the activity in the equatorial ionosphere commenced. Since the designed cognitive routine required some changes with the hardware, the initial observations were made by running CIRI at Huancayo in the traditional radar mode. During the beginning stages, the Equatorial Electrojet was the plasma irregularity that was detected consistently throughout the course of the day. The Equatorial Spread F generated occasionally, but the echoes were typically weak because of the range of occurrence. Unfortunately, CIRI at Huancayo is not yet sensitive enough to sense a 150 km echo, since large aperture and high power radars such as JRO are essential. This chapter presents the initial observations collected with CIRI at Huancayo by first presenting one of the Equatorial Electrojets in Section 6.2, and analyzing the echo with the various processing techniques described in Chapter 3. In Section 6.3, two interesting meteor events are provided. An additional benefit of CIRI at Huancayo is the ability to perform simultaneous observations with JRO, which can potentially lead to an enhanced physical interpretation behind the equatorial field-aligned plasma irregularities. This asset was utilized shortly after the installation of CIRI at Huancayo, and this chapter reports the initial comparisons of radar echoes detected with each system in Section 6.4. Section describes the antenna and chosen radar configuration at each facility, along with processing performed on the collected raw data. Section

160 then goes on to present the comparisons of results observed with each system during the synchronized experiment. 6.2 Equatorial Electrojet RTI Plots Figure 6.1. RTI Plot of an Equatorial Electrojet observed during the daytime on March 2, 2015.

161 140 Figure 6.2. RTI Plot of same Equatorial Electrojet presented in Figure 6.1 but spotlighting the hours between 12:00 and 15:00 LT. Note that greater detail of the plasma structure is noticable with the shorter time window. Figure 6.3. RTI Plot of same Equatorial Electrojet presented in Figure 6.1 but spotlighting the hours between 16:00 and 19:00 LT. Note that greater detail of the plasma structure is noticable with the shorter time window.

162 Doppler Maps Figure 6.4. Doppler Map of the Equatorial Electrojet during the hours 12:00-15:00 LT. A significant portion of the plot is occupied by Doppler corresponding to zero Doppler, which is thought to have been external interference. However, a thin layer of high negative Doppler is discernible within the Electrojet.

163 142 Figure 6.5. Doppler Map of the Equatorial Electrojet during the hours 16:00-19:00 LT. A significant portion of the plot is occupied by Doppler corresponding to zero Doppler, which is thought to have been external interference, and abruptly disappears around 17:15 LT. Doppler within the Electrojet is still discernible, with a continued high negative Doppler that reverses to a high positive Doppler at the event s conclusion.

164 Spectrograms Figure 6.6. Spectrogram of the Equatorial Electrojet during the hours 12:00-15:00 LT at km. The returns illustrate that periods of the Electrojet contained a large spread Doppler content, that slowly compressed to a smaller spectral width. This characteristic repeated several times during these hours. Figure 6.7. Spectrogram of the Equatorial Electrojet during the hours 16:00-19:00 LT at km. The returns illustrate large spread of Doppler content, that slowly compresses toward the conclusion of the Electrojet.

165 Phase Plots Figure 6.8. Phase Plot of the Equatorial Electrojet during the hours 12:00-15:00 LT at km. The measured phase at this range tended to cluster within -1 and -2 radians, with some periods of linearity. Unfortunately the linear sections were too short to compute an accurate East-West Drift velocity. Figure 6.9. Phase Plot of the Equatorial Electrojet during the hours 16:00-19:00 LT at km. The measured phase at this range tended to cluster within -1 and -2 radians, with some periods of linearity. Unfortunately the linear sections were too short to compute an accurate East-West Drift velocity.

166 Meteor Events Figure second RTI plot of observed meteor event on March 2, The event starting approximately 3:47:17 LT has a short trail confined within a smaller range window at the beginning, then revives shortly after with a longer trail and occupying a larger range. Meteors displaying this characteristic could be classified as fragmenting.

167 146 Figure One minute RTI plot of observed meteor event on March 3, The event starting approximately 4:19:40 LT is known as a meteor head echo because of the sharp initiation, followed by a long trail. 6.4 Comparisons with JRO Antenna and Radar Configurations CIRI at Huancayo was designed to transmit at a frequency of MHz via an array of CoCo Antennas [25]. Frequency selection was decided based on having a transmission wavelength comparable to JRO, while also being sufficiently outside the band of operation, hence, avoiding any possible interference. The CoCo array is subdivided into two channels, where the antennas are aligned along the Magnetic East-West Plane. Each channel consists of 4 lines of 24-element half wave dipoles, providing an antenna aperture of approximately m 2. Simulated results of this antenna array compute a half-power beamwidth of 2.6 in the East-West plane, and 26.7 in the North-South plane. Since the radar is located in the equatorial region, the boresight of the antenna beam is pointed perpendicular to the Earth s

168 147 surface, and was simulated to have a gain of 22.6 dbi. One transmitter is utilized during operation of CIRI at Huancayo, where 15 kws of peak power are separated between the two channels. The initially chosen pulsed radar configuration contained an IPP of 4 ms, corresponding in a maximum unambiguous range of 600 km. The transmission pulse used a 28-baud binary sequence, with each baud-length lasting 5 µs. Thus, a large average power (3.5 %) is achieved through the use of the selected pulsed configuration, while a small range resolution (0.75 km) is still maintained. On the processing side, both channels are involved for reception and the entire IPP is oversampled by a factor of 2. An integrated power profile is eventually saved every 2 seconds. The JRO antenna is a 290m x 290m cross half-wave dipole array that operates at a frequency of MHz. For low power, coherent scatter radar observations, the frequently used mode at JRO is known as JULIA [89,90]. For this mode, only two quarters of the array are exercised, which provide a total antenna aperture of 42.05x10 3 m 2. Each quarter (or channel) contains 48 lines of 48-element CoCo antennas. JULIA is partitioned into a daytime mode (between the hours of 7:00 and 18:00 LT), and a nighttime mode (between the hours of 18:00 and 7:00 LT) in order to study different features of the ionosphere throughout the course of a day. For each mode, the antenna quarters used for transmission and reception vary, and will be discussed in the coming paragraphs. Both the daytime and nighttime modes contain one 11 kw transmitter, where power is distributed evenly between the North and South quarters of the array. The IPP is the main specification that alters between the daytime and nighttime modes, because of the Spread F, which often is detected at large ranges. Hence, the duration of the IPP for the daytime JULIA mode is 2.5 ms (or 375 km) while the nighttime IPP is 6.25 ms (or km). Both JULIA modes use an uncoded pulse, lasting 20 µs in the daytime and 25 µs for the nighttime mode. Upon reception, the daytime mode also uses the North and South quarters, but switches to the East and West quarters for the nighttime mode. This switch is typically performed to measure the East-West drift of the Spread F [90]. The processing of JULIA is also executed differently for the two modes. The daytime mode oversamples the pulse width by a factor of 2, while there is no oversampling in the nighttime mode. Finally, the saved integrated power profiles

169 148 Table 6.1. Specifications of CIRI at Huancayo, and Daytime / Nighttime JULIA modes. JULIA CIRI 7:00-18:00 LT 18:00-7:00 LT - Antenna Parameters Frequency of Operation (MHz) Channels # of Dipoles (per CoCo) # of Lines of CoCos (per Channel) Effective Area (m 2 ) Radar Configuration Peak Power (kw) IPP (km / ms) 375 / / / 4 Duty Cycle (%) Range Resolution (km) Code None None Binary 28 Processing Sampling Resolution (km) Integrated Time Resolution (s) for the daytime correspond to seconds in order to overly enhance the SNR of the typically very weak 150 km echoes. These echoes do not appear during the nighttime hours, therefore the integrated power profiles are performed in shorter intervals during nighttime JULIA mode and saved every 3 seconds. For a summary of the major specifications for both JULIA modes and CIRI at Huancayo, please refer to Table Results and Discussion Beginning March 1st, 2015, the first ionospheric observations with CIRI at Huancayo were acquired by using the described setup presented in Section For a two day period starting on this date, the JULIA mode operated intermittently due to maintenance, but was mostly consistent during the nighttime hours. Hence, the possibility of performing a comparative study with observatories installed in close proximity was accomplished for the first time. The two day simultaneous observation resulted in three independent plasma irregularities that achieved similar structure at the two sites. The comparable events consisted of one nighttime Electrojet and two Spread F s. The resulting RTI plots for each event at both ob-

170 149 servatories are provided in Figures , along with a Sky Noise comparison in Figure Although the JULIA mode and CIRI at Huancayo were able to operate simultaneously, there are vast systematic differences between the two observatories that contribute to varying sensitivities of the detected ionospheric irregularities. The principle factor causing the sensitivity difference is the aperture of the antenna arrays used for the observations. As shown in Table 6.1, the CIRI at Huancayo CoCo array has an antenna aperture of m 2 while the CoCo array used for the JU- LIA mode is 42.05x10 3 m 2. The fundamental concepts of antenna theory states that the size of the antenna array relative to the wavelength is proportional to the gain of the system [91, 92]. Since the wavelengths are similar for both systems, the gain of the CoCo array for JULIA is much larger than the CIRI at Huancayo array, which is apparent in Figures with the measured SNR. It should be noted that the color scales in the SNR are compressed significantly for the CIRI at Huancayo RTI Plots in order to allow the returns from the plasma irregularities to be discernible. Consequently, many more features of the plasma irregularities are observed with JULIA during periods of low SNR, at which time, the event seemed to conclude with the CIRI at Huancayo radar. Despite the greater peak power and average power of the CIRI at Huancayo system, the observations prove that the size of the antenna aperture still overshadows these specifications when comparing the sensitivity. One difference between the detected plasma irregularities in favor of the CIRI at Huancayo system was the chosen range resolution. The range resolution was selected to be 5 times greater than the JULIA nighttime mode, therefore finer details of the plasma structure is noticeable, especially during the Electrojet event in Figure This difference in range resolution, after extended periods of observations, can eventually lead to better implications behind development of the plasma irregularities. With only three events, it is evident that the two observatories located approximately 170 km apart are able to sense the same plasma irregularities developing in the ionosphere. It is very rare that two radar facilities are so close in proximity, therefore the outcome of this experiment is unique. In each figure, periods of strong SNR in the JULIA mode typically align with similar features with the

171 150 observations with CIRI at Huancayo. Further physical analysis must be performed to gain a better understanding behind some of subtle differences however. For example, there are clear discrepancies with the range of the detected irregularities, with differences being approximately between km. It should be noted that Huancayo, Peru is located within the Peruvian Andes, therefore the physical elevation of the observatories are approximately 3,000 km apart. Nevertheless, this does not compensate for the range differences of the irregularities. The other noteworthy characteristic was the time of detection for the nighttime Spread F event in Figure Out of the three events, this was lone irregularity that was observed at noticeably different times with the two systems, with around a 15 minute delay to fall within the beam of CIRI at Huancayo. This potentially can be due to the drift of the event, but questions arise with why the Electrojet and the morning time Spread F did not display similar qualities. With CIRI at Huancayo making continued observations of the ionosphere alongside the occasional JULIA operation mode, a larger dataset of comparisons is inevitable. Thus, with an extended investigation, a more concrete statistical analysis of the differences can be resolved, leading toward the development of the physical explanation.

172 151 Figure Comparisons of RTI Plots between JRO and CIRI at Huancayo for an Equatorial Electroject during the nighttime hours on March 1, Similar structure is evident for the duration of the event, especially during period of high SNR at JRO. One subtle difference is the range of detection with each system. Note: The color scales are different for the two plots.

173 152 Figure Comparisons of RTI Plots between JRO and CIRI at Huancayo for an Equatorial Spread F during the early morning hours on March 2, Similar structure is evident for the duration of the event, especially during period of high SNR at JRO. One subtle difference is the range of detection with each system. Note: The color scales are different for the two plots.

174 153 Figure Comparisons of RTI Plots between JRO and CIRI at Huancayo for an Equatorial Spread F during the nighttime hours on March 2, Similar structure is evident for the duration of the event, especially during period of high SNR at JRO. One subtle difference is the range of detection with each system. However, a major discrepancy is the time at which the event was detected, with an approximately 15 minute delay with CIRI at Huancayo. Note: The color scales are different for the two plots.

175 154 Figure Comparisons of 24 hour Sky Noise Plots between JRO and CIRI at Huancayo during March 2, Sky Noise was averaged every 10 minutes with CIRI at Huancayo. Major sources of sky noise at JRO are similarly found with CIRI at Huancayo, including the center of the galaxy (approximately 8:00 LT) and the back of the galaxy (approximately 20:00 LT). Throughout the daytime hours, heavy interference was detected with CIRI at Huancayo between the hours of 9:00-17:00 LT, causing many disparities during this time.

176 Chapter 7 Summary and Future Work 7.1 Summary At this point, the design and development of two ionospheric pulsed radars named CIRI have been accomplished in order to continuously make observations of the frequently occurring plasma instabilities. CIRI at PSU studies the plasma instabilities at mid-latitude regions such as the QP echoes presented in Chapter 5, while CIRI at Huancayo observes the equatorial region events such as the Spread F, 150 km echoes, and electrojet. Both radars are capable of taking measurements for extended periods of time, with only the occasional maintenance. Ionospheric radars with this feature are seldom for these specified regions. Additional high power radars reside in these regions, but are sporadically implemented due to high operational costs. Therefore, a more in depth statistical analysis of the activity in these two regions can be conducted with CIRI s uninterrupted measure of the ionosphere. The two CIRI radars were assembled with a robust hardware and software design in order to effectively perform the necessary observations. The hardware configuration, outlined in Chapter 2, involves a combination of digital and analog systems on both the transmission and receive end. On the transmission side, a variety of binary phase coding is included to improve the quality of the processed results. The receive end on the other hand, ensures the incoming reflected signal is properly filtered and amplified in order to perform the processing techniques in software. The software portion of CIRI includes a multitude of technique that were

177 156 discussed in Chapter 3. With the digitized data given at the output of the receive hardware, the chosen processing techniques are essential toward extracting the maximum amount of information to analyze the developments in the ionosphere. To further improve the provided processing techniques, an initial attempt toward a cognitive routine was designed for ionospheric radars in order to optimize the SNR received from the plasma instabilities, which is introduced in three steps in Chapter 4. Finally, the results for both CIRI at PSU and CIRI at Huancayo are presented in Chapter 5 and Chapter 6 respectively. Although much has been presented in this dissertation, there are still many undertakings that can be included to improve the quality of the system on both the hardware and software side. The addition of these improvements will ensure a significant impact in the scientific community. The future work for this project is explained in the ensuing section. 7.2 Future Work Although CIRI at PSU and CIRI at Huancayo have both been calibrated and implemented, some additional assessments should be accounted for. One initial test that was not performed on either system was the reconstruction of the antenna beam pattern. The theoretical beam pattern for both systems were presented in Section 2.6. However, theoretical and practical implementation always contain subtle differences. Due to the large physical size of the array, many imperfections exist that do not occur in the ideal simulations. With the measurement of the antenna radiation pattern, a clearer picture of the area illuminated in the ionosphere would be known. Subsequently, the antennas could then be further altered if slightly off perpendicular to the magnetic field. To measure the radiation pattern is not a simple task, because the array is too larger to fit into any anechoic chamber, therefore measurements must be made by alternative methods. One solution is to coordinate the use of an airplane to fly around the far field of the antenna beam. While in flight, a real time GPS tracker should be synchronized with a receive antenna that is measuring the power transmitted by the array. The GPS location with an associated power level, would then aid with slowly reconstructing the antenna beam.

178 157 Another aspect that should be included in both systems is the ability to perform radar imaging, a processing technique discussed in Section In order to implement this technique, vast improvements must be included on the hardware side to fulfill the basic requirements. To perform an effective imaging experiment, the radar should have at least four receivers, and be installed in such a way that six baselines are possible, i.e the maximum with four receivers. The inclusion of two more receivers involves adding two more antennas to both systems along the East-West plane. Along with these antennas, the RF front end, shown in Section 2.7, would need to be replicated for these additional channels. Furthermore, on the received end of the hardware, an extra USRP must be included because a single USRP can only collect up to two channels simultaneously. Needless to say, these two USRPs must be synchronized in order to properly keep track of phase information. Prior to the running the imaging experiment, a phase calibration should be performed in order to correct the offsets in each channel on the software side. An envisioned setup of CIRI in Huancayo with imaging capabilities is shown in Figure 7.1. Notice that this setup has a total of five antennas to enhance the quality of the potential images even farther. Figure 7.1. Proposed antenna layout of CIRI at Huancayo with imaging capabilities. A further major piece to be included in the CIRI system is the implementation