QR SIGNAL DETECTION IN THE PRESENCE OF AM NOISE

Transcription

1 The Pennsylvania State University The Graduate School Department of Electrical Engineering QR SIGNAL DETECTION IN THE PRESENCE OF AM NOISE A Dissertation in Electrical Engineering by Abdullah G. Almahri c 2013 Abdullah G. Almahri Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy December 2013

2 The dissertation of Abdullah G. Almahri was reviewed and approved* by the following: Constantino C. Lagoa Professor of Electrical Engineering Dissertation Adviser Chair of Committee Jeffrey Schiano Professor of Electrical Engineering David Miller Professor of Electrical Engineering Patrick M. Lenahan Professor of Engineering Science and Mechanics Kultegin Aydin Professor of Electrical Engineering Head of the Department of Electrical Engineering *Signatures are on file in the Graduate School.

3 iii Abstract The thesis proposes a matched filter approach to detect quadrupole resonance (QR) signals in the presence of disturbance from AM stations. Detecting QR signals is a challenge due to several reasons. One is the amplitude of a QR signal is typically on the same level of thermal noise, which makes it very susceptible to noise interferences. External Radio Frequency (RF) interferences, such as AM signals, and internal RF interferences, ones from inside the search volume, pose another challenge and contribute to the low SNR values observed. AM stations broadcast within the same frequency band of QR signals, which is a problem for QR detection. A third important challenge we face is the uncertainty in the QR signal characteristics. To motivate the use of a matched filter approach, a matched filter (under the assumption that the QR signal is known) was compared to the generic energy detector in theory and it resulted in a performance improvement. The work proposes a detector referred to as the batch matched filter, which uses a gridding technique to search for unknown QR signal parameters and attempts to match the filter to the shape of the QR signal present. This approach resulted in a performance gain when compared to the generic energy detector using simulation and experimental data, where the QR signal is unknown. To further improve performance we introduced an approach that would also match the filter to the noise present in addition to the QR signal. This approach is referred to as the batch whitened matched filter and when properly matched to the noise outperforms both the batch matched filter and energy detector.

4 iv Table of Contents List of Tables vii List of Figures ix Acknowledgments xviii Chapter 1. Introduction Motivation Literature Review Approach Chapter 2. QR Spectroscopy QR Physics Quadrupole Interaction Relaxation Mechanisms Observed Signals RF Excitation Pulse Sequences QR Detection Procedure Chapter 3. Challenges, Signal Characteristics and Data Generation Challenges Challenges Due to Uncertainty QR Signal Challenges Due to External and Internal RFI Signals RFI Mitigation Methods QR Signals Noise Characteristics Thermal Noise AM Signals Averaged N m Trials Aggregating N m Trials Experimental Data Versus Simulation Data Experimental Data Collected Simulation Data Generated Chapter 4. Motivation for Using Matched Filter Energy Detector Matched Filter Detection Algorithm Comparison Under Noise Assumptions Energy Detector in the Presence of Thermal Noise Energy Detector in the Presence of AM and Thermal Noise Matched Filter in the Presence of Thermal Noise

5 4.3.4 Matched Filter in the Presence of AM and Thermal Noise Thermal Noise Comparison AM and Thermal Noise Comparison Algorithm Comparison, No Noise Assumptions Band and Low pass Filtered Thermal Noise Band and Low pass Filtered AM and Thermal Noise Conclusion Chapter 5. Batch Matched Filter Error in the QR signal Description Batch Matched Filter Batch Matched Filter versus Energy Detector, Unknown QR signal Simulation Data Experimental Data The Effect of Finer Gridding on the Performance of the Batch Matched Filter Adaptive Grid Batch Matched Filter Simulation Data Experimental Data Alternative Detection Decisions Chapter 6. Batch Whitened Matched Filter Whitened Matched Filter Estimating Whitening Matrix using the Autocorrelation Method Estimating Whitening Matrix using the Covariance Method The Effect of All Zero Filters On a QR Signal Batch Whitened Matched Filter Batch Whitened Matched Filter versus Energy Detector, Unknown QR signal Simulation Data Experimental Data Batch Adaptive Whitened Matched Filter Whitening Filter Order that Least Effects the QR Signal Whitening Filter Order, Minimum Description Length Algorithm Simulation Data Experimental Data Chapter 7. Batch Whitened Robust Matched Filter Robust Matched Filter Analytical Solutions For Robust Matched Filters Over Particular Uncertainty Sets Spherical Signal Set and Noise Uncertainty Bounded by a Matrix Norm v

6 7.2.2 Elliptic Signal Set and Noise Uncertainty Bounded by the Frobenius Matrix Norm or the 2-Norm The Scenario Approach Characterizing a Set of QR Signals Through Sampling Smallest Sphere Containing the Set of QR Signals Spherical Set Central Signal Examples Robust Matched Filter by Maximizing SNR Using Sampling Robust Matched Filter Examples in the presence of Thermal Noise, Maximizing SNR Batch Whitened Robust Matched Filter Batch Robust Matched Filter in Presence of Thermal Noise Frequency Robust Batch Matched Filters in the Presence of Thermal Noise Robust Batch Matched Filters in the Presence of Thermal Noise Batch Whitened Robust Matched Filter in the Presence of AM and Thermal Noise Simulation Data in the Presence of AM and Thermal Noise Experimental Data in the Presence of AM and Thermal Noise 237 Chapter 8. Conclusion Future Work Appendix A. Mean and Variance of Energy Detector Test Statistic, in the Presence of AM and Thermal Noise Appendix B. Mean and Variance of Matched Filter Test Statistic, in the Presence of AM and Thermal Noise Appendix C. MATLAB Code C.1 Data Generation Function Bibliography vi

7 vii List of Tables 6.1 Simulation, SNR = -22 db, Performance Comparison on Simulation Data, Band-passed White Gaussian AM, with the QR and AM at 2.5 khz Simulation, SNR = -22 db, Performance Comparison on Simulation Data, Band-passed White Gaussian AM, with the QR and AM at 5 khz Simulation, SNR = -22 db, Performance Comparison on Simulation Data, Band-passed White Gaussian AM, with the QR and AM at 7.5 khz Simulation, SNR = -22 db, Performance Comparison on Simulation Data, Band-passed White Gaussian AM, with the QR and AM at 10 khz Simulation, SNR = -22 db, Performance Comparison on Simulation Data, Band-passed White Gaussian AM, with the QR and AM at 12.5 khz Simulation, SNR = -22 db, Performance Comparison on Simulation Data, Band-passed White Gaussian AM, with the QR and AM at 15 khz Performance Comparison on Experimental Data A, BP White Gaussian AM, with the QR and AM at 6.25 khz Performance Comparison on Experimental Data B, BP White Gaussian AM, with the QR and AM at 10 khz Performance Comparison on Experimental Data C, BP White Gaussian AM, with the QR and AM at -8 khz Performance Comparison on Experimental Data D, BP White Gaussian AM, with the QR and AM at 12.5 khz Simulation, SNR = -22 db, Performance Comparison on Simulation Data, Band-passed White Gaussian AM, with the QR and AM at 2.5 khz. Adaptive Whitening Filter Order Selection Simulation, SNR = -22 db, Performance Comparison on Simulation Data, Band-passed White Gaussian AM, with the QR and AM at 5 khz. Adaptive Whitening Filter Order Selection Simulation, SNR = -22 db, Performance Comparison on Simulation Data, Band-passed White Gaussian AM, with the QR and AM at 7.5 khz. Adaptive Whitening Filter Order Selection Simulation, SNR = -22 db, Performance Comparison on Simulation Data, Band-passed White Gaussian AM, with the QR and AM at 10 khz. Adaptive Whitening Filter Order Selection Simulation, SNR = -22 db, Performance Comparison on Simulation Data, Band-passed White Gaussian AM, with the QR and AM at 12.5 khz. Adaptive Whitening Filter Order Selection

8 6.16 Simulation, SNR = -22 db, Performance Comparison on Simulation Data, Band-passed White Gaussian AM, with the QR and AM at 15 khz. Adaptive Whitening Filter Order Selection Performance Comparison on Experimental Data A, BP White Gaussian AM, with the QR and AM at 6.25 khz. Adaptive Whitening Filter Order Selection Performance Comparison on Experimental Data B, BP White Gaussian AM, with the QR and AM at 10 khz. Adaptive Whitening Filter Order Selection Performance Comparison on Experimental Data C, BP White Gaussian AM, with the QR and AM at -8 khz. Adaptive Whitening Filter Order Selection Performance Comparison on Experimental Data D, BP White Gaussian AM, with the QR and AM at 12.5 khz. Adaptive Whitening Filter Order Selection viii

9 ix List of Figures 2.1 Simplified block diagram of QR detection system QR energy levels and transition frequencies for nitrogen-14, an I=1 nucleus with η 0 [17] QR frequencies of different explosives/chemicals [3] Lorentzian distribution of transition frequencies [17] Block diagram of QR spectrometer QR Signal with a Frequency of MHz and T 2 of 500e Comparison of QR+AM and QR: (Top) QR Signal with a Frequency of MHz and T 2 of 500e-6 (Center) AM Signal with Carrier Frequency of MHz (Bottom) QR plus AM Signal, SNR = -12 db Illustration of Phase Cycling on SLSE sequences Energy Detector s Theoretical PDF plots vs Simulation PDF plots for Thermal Noise, SNR = 20 log 10 ( A σ tn ) = -50 db Energy Detector s, Theoretical ROC plot vs Simulation ROC plot for Thermal Noise, SNR = 20 log 10 ( A σ tn ) = -50 db Energy Detector s Theoretical PDF plots vs Simulation PDF plots for AM and Thermal Noise, SNR = 20 log 10 ( A A η ) = -66 db Energy Detector s, Theoretical ROC plot vs Simulation ROC plot for AM and Thermal Noise, SNR = 20 log 10 ( A A η ) = -66 db Matched Filter s Theoretical PDF plots vs Simulation PDF plots for Thermal Noise, SNR = 20 log 10 ( A σ tn ) =-50 db Theoretical ROC plot vs Simulation ROC plot for Thermal Noise, SNR = 20 log 10 ( A σ tn ) = -50 db Matched Filter s Theoretical PDF plots vs Simulation PDF plots for AM and Thermal Noise, SNR = 20 log 10 ( A A η ) = -66 db Theoretical ROC plot vs Simulation ROC plot for AM & Thermal Noise, SNR = 20 log 10 ( A A η ) = -66 db Energy of noise signals vs number of averages, Log scale Energy Detector PDF plots in the presence of Thermal Noise, SNR = 20 log 10 ( A σ tn ) =-12 db, Theoretical PDF plots vs Simulation and Experiment without Noise Assumptions Matched Filter PDF plots in the presence of Thermal Noise, SNR = 20 log 10 ( A σ tn ) = -12 db, Theoretical PDF plots vs Simulation and Experiment without Noise Assumptions Energy Detector PDF plots in the presence of band-passed white gaussian AM and Thermal Noise, SNR = 20 log 10 ( A A η ) = -30 db, Theoretical PDF plots vs Simulation and Experiment without Noise Assumptions. N m = 10, Number of experiments =

10 4.13 Energy Detector ROC plots in the presence of band-passed white gaussian AM Thermal Noise, SNR = 20 log 10 ( A A η )= -30 db, Theoretical PDF plots vs Simulation and Experiment without Noise Assumptions. N m = 10, Number of experiments = Matched Filter PDF plots in the presence of band-passed white gaussian AM and Thermal Noise, SNR = 20 log 10 ( A A η ) = -30 db, Theoretical PDF plots vs Simulation and Experiment without Noise Assumptions Matched Filter PDF plots in the presence of band-passed white gaussian AM and Thermal Noise, SNR = 20 log 10 ( A A η ) = -30 db, Theoretical PDF plots vs Simulation and Experiment without Noise Assumptions Inner Product versus Frequency Error of the Filter Inner Product versus Phase Error of the Filter Inner Product versus Decaying Parameter Error of the Filter Uncertain Frequency Matched Filter ROC plots in the presence of Bandpassed White Gaussian AM, SNR = -30 db Batch Matched Filter with 1 khz Frequency gridding, ROC plots in the presence of Different QR Frequencies and Band-passed White Gaussian AM, Simulation SNR = -22 db Simulation SNR = -22 db, Performance Comparison, BP White Gaussian AM, with the QR and AM at 2.5 khz Simulation SNR = -22 db, Performance Comparison, BP White Gaussian AM, with the QR and AM at 5 khz Simulation SNR = -22 db, Performance Comparison, BP White Gaussian AM, with the QR and AM at 7.5 khz Simulation SNR = -22 db, Performance Comparison, BP White Gaussian AM, with the QR and AM at 10 khz Simulation SNR = -22 db, Performance Comparison, BP White Gaussian AM, with the QR and AM at 12.5 khz Simulation SNR = -22 db, Performance Comparison, BP White Gaussian AM, with the QR and AM at 15 khz Experiment A, Performance Comparison on Experiment Data, BP White Gaussian AM, with the QR and AM at 6.25 khz Experiment B, Performance Comparison on Experiment Data, BP White Gaussian AM, with the QR and AM at 10 khz Experiment C, Performance Comparison on Experiment Data, BP White Gaussian AM, with the QR and AM at -8 khz Experiment D, Performance Comparison on Experiment Data, BP White Gaussian AM, with the QR and AM at 12.5 khz Simulation SNR = -22 db, Adaptive versus Brute Force Gridding Performance Comparison, BP White Gaussian AM, with the QR and AM at 2.5 khz Simulation SNR = -22 db, Adaptive versus Brute Force Gridding Performance Comparison, BP White Gaussian AM, with the QR and AM at 5 khz x

11 5.18 Simulation SNR = -22 db, Adaptive versus Brute Force Gridding Performance Comparison, BP White Gaussian AM, with the QR and AM at 7.5 khz Simulation SNR = -22 db, Adaptive versus Brute Force Gridding Performance Comparison, BP White Gaussian AM, with the QR and AM at 10 khz Simulation SNR = -22 db, Adaptive versus Brute Force Gridding Performance Comparison, BP White Gaussian AM, with the QR and AM at 12.5 khz Simulation SNR = -22 db, Adaptive versus Brute Force Gridding Performance Comparison, BP White Gaussian AM, with the QR and AM at 15 khz Experiment A, Adaptive versus Brute Force Gridding Performance Comparison on Experiment Data, BP White Gaussian AM, with the QR and AM at 6.25 khz Experiment B, Adaptive versus Brute Force Gridding Performance Comparison on Experiment Data, BP White Gaussian AM, with the QR and AM at 10 khz Experiment C, Adaptive versus Brute Force Gridding Performance Comparison on Experiment Data, BP White Gaussian AM, with the QR and AM at -8 khz Experiment D, Adaptive versus Brute Force Gridding Performance Comparison on Experiment Data, BP White Gaussian AM, with the QR and AM at 12.5 khz Simulation SNR = -22 db, Comparing Detection Decision Methods, BP White Gaussian AM, with the QR and AM at 2.5 khz Simulation SNR = -22 db, Comparing Detection Decision Methods, BP White Gaussian AM, with the QR and AM at 5 khz Simulation SNR = -22 db, Comparing Detection Decision Methods, BP White Gaussian AM, with the QR and AM at 7.5 khz Simulation SNR = -22 db, Comparing Detection Decision Methods, BP White Gaussian AM, with the QR and AM at 10 khz Simulation SNR = -22 db, Comparing Detection Decision Methods, BP White Gaussian AM, with the QR and AM at 12.5 khz Simulation SNR = -22 db, Comparing Detection Decision Methods, BP White Gaussian AM, with the QR and AM at 15 khz Experiment A, Comparing Detection Decision Methods on Experiment Data, BP White Gaussian AM, with the QR and AM at 6.25 khz Experiment B, Comparing Detection Decision Methods on Experiment Data, BP White Gaussian AM, with the QR and AM at 10 khz Experiment C, Comparing Detection Decision Methods on Experiment Data, BP White Gaussian AM, with the QR and AM at -8 khz Experiment D, Comparing Detection Decision Methods on Experiment Data, BP White Gaussian AM, with the QR and AM at 12.5 khz xi

12 6.1 The output of a 6 th order FIR filter applied to a simulated 12.5 khz QR signal is compared to the input signal Magnitude of the Frequency Response of an 8 pole Butterworth filter with a 20 khz cutoff Magnitude (db) of the Frequency Response of an 8 pole Butterworth filter with a 20 khz cutoff Simulation, SNR = -22 db, Performance Comparison on Simulation Data, Band-passed White Gaussian AM, with the QR and AM at 2.5 khz. Autocorrelation Whitening Method Simulation, SNR = -22 db, Performance Comparison on Simulation Data, Band-passed White Gaussian AM, with the QR and AM at 2.5 khz. Covariance Whitening Method Simulation, SNR = -22 db, Performance Comparison on Simulation Data, Band-passed White Gaussian AM, with the QR and AM at 5 khz. Autocorrelation Whitening Method Simulation, SNR = -22 db, Performance Comparison on Simulation Data, Band-passed White Gaussian AM, with the QR and AM at 5 khz. Covariance Whitening Method Simulation, SNR = -22 db, Performance Comparison on Simulation Data, Band-passed White Gaussian AM, with the QR and AM at 7.5 khz. Autocorrelation Whitening Method Simulation, SNR = -22 db, Performance Comparison on Simulation Data, Band-passed White Gaussian AM, with the QR and AM at 7.5 khz. Covariance Whitening Method Simulation, SNR = -22 db, Performance Comparison on Simulation Data, Band-passed White Gaussian AM, with the QR and AM at 10 khz. Autocorrelation Whitening Method Simulation, SNR = -22 db, Performance Comparison on Simulation Data, Band-passed White Gaussian AM, with the QR and AM at 10 khz. Covariance Whitening Method Simulation, SNR = -22 db, Performance Comparison on Simulation Data, Band-passed White Gaussian AM, with the QR and AM at 12.5 khz. Autocorrelation Whitening Method Simulation, SNR = -22 db, Performance Comparison on Simulation Data, Band-passed White Gaussian AM, with the QR and AM at 12.5 khz. Covariance Whitening Method Simulation, SNR = -22 db, Performance Comparison on Simulation Data, Band-passed White Gaussian AM, with the QR and AM at 15 khz. Autocorrelation Whitening Method Simulation, SNR = -22 db, Performance Comparison on Simulation Data, Band-passed White Gaussian AM, with the QR and AM at 15 khz. Covariance Whitening Method xii

13 6.16 Top: Frequency Response of Modulating Signal (Bandpassed Gaussian Noise). Bottom: Frequency Response of an AM Signal with a Carrier Frequency of f c < 10 khz. 0 = 0 Hz, 1 = f c - 40 Hz, 2 = f c +40 Hz, 3 = 10 khz - f c and 4 = f c +10 khz Frequency Response of Whitening Filter When the AM Signal s Carrier Frequency is f c < 10 khz. 1 = f c - 40 Hz, 2 = f c +40 Hz, 3 = 10 khz - f c and 4 = f c +10 khz Fast Fourier Transform of a 2.5 khz QR signal Frequency Response of the N e = 5 Whitening Filters of Order 3, Designed Using the Covariance Method. Simulation Data, SNR = -22 db, Experiment 1 of Band-passed White Gaussian AM, with the QR and AM at 2.5 khz Data Set Frequency Response of the N e = 5 Whitening Filters of Order 4, Designed Using the Covariance Method. Simulation Data, SNR = -22 db, Experiment 1 of Band-passed White Gaussian AM, with the QR and AM at 2.5 khz Data Set Frequency Response of the N e = 5 Whitening Filters of Order 5, Designed Using the Covariance Method. Simulation Data, SNR = -22 db, Experiment 1 of Band-passed White Gaussian AM, with the QR and AM at 2.5 khz Data Set Frequency Response of the N e = 5 Whitening Filters of Order 6, Designed Using the Covariance Method. Simulation Data, SNR = -22 db, Experiment 1 of Band-passed White Gaussian AM, with the QR and AM at 2.5 khz Data Set Frequency Response of the N e = 5 Whitening Filters of Order 7, Designed Using the Covariance Method. Simulation Data, SNR = -22 db, Experiment 1 of Band-passed White Gaussian AM, with the QR and AM at 2.5 khz Data Set Filter Lock Frequency for Different Experiments, When Using A Covariance Whitening Filter of Order 3. Simulation Data, SNR = -22 db, Band-passed White Gaussian AM, with the QR and AM at 2.5 khz Filter Lock Frequency for Different Experiments, When Using A Covariance Whitening Filter of Order 4. Simulation Data, SNR = -22 db, Band-passed White Gaussian AM, with the QR and AM at 2.5 khz Filter Lock Frequency for Different Experiments, When Using A Covariance Whitening Filter of Order 5. Simulation Data, SNR = -22 db, Band-passed White Gaussian AM, with the QR and AM at 2.5 khz Filter Lock Frequency for Different Experiments, When Using A Covariance Whitening Filter of Order 6. Simulation Data, SNR = -22 db, Band-passed White Gaussian AM, with the QR and AM at 2.5 khz Filter Lock Frequency for Different Experiments, When Using A Covariance Whitening Filter of Order 7. Simulation Data, SNR = -22 db, Band-passed White Gaussian AM, with the QR and AM at 2.5 khz xiii

14 6.29 Frequency Response of the N e = 5 Whitening Filters of Order 3, Designed Using the Autocorrelation Method. Simulation Data, SNR = -22 db, Experiment 1 of Band-passed White Gaussian AM, with the QR and AM at 2.5 khz Data Set Frequency Response of the N e = 5 Whitening Filters of Order 4, Designed Using the Autcorrelation Method. Simulation Data, SNR = -22 db, Experiment 1 of Band-passed White Gaussian AM, with the QR and AM at 2.5 khz Data Set Frequency Response of the N e = 5 Whitening Filters of Order 5, Designed Using the Autcorrelation Method. Simulation Data, SNR = -22 db, Experiment 1 of Band-passed White Gaussian AM, with the QR and AM at 2.5 khz Data Set Frequency Response of the N e = 5 Whitening Filters of Order 6, Designed Using the Autcorrelation Method. Simulation Data, SNR = -22 db, Experiment 1 of Band-passed White Gaussian AM, with the QR and AM at 2.5 khz Data Set Frequency Response of the N e = 5 Whitening Filters of Order 7, Designed Using the Autcorrelation Method. Simulation Data, SNR = -22 db, Experiment 1 of Band-passed White Gaussian AM, with the QR and AM at 2.5 khz Data Set Filter Lock Frequency for Different Experiments, When Using An Autocorrelation Whitening Filter of Order 3. Simulation Data, SNR = -22 db, Band-passed White Gaussian AM, with the QR and AM at 2.5 khz Filter Lock Frequency for Different Experiments, When Using An Autocorrelation Whitening Filter of Order 4. Simulation Data, SNR = -22 db, Band-passed White Gaussian AM, with the QR and AM at 2.5 khz Filter Lock Frequency for Different Experiments, When Using An Autocorrelation Whitening Filter of Order 5. Simulation Data, SNR = -22 db, Band-passed White Gaussian AM, with the QR and AM at 2.5 khz Filter Lock Frequency for Different Experiments, When Using An Autocorrelation Whitening Filter of Order 6. Simulation Data, SNR = -22 db, Band-passed White Gaussian AM, with the QR and AM at 2.5 khz Filter Lock Frequency for Different Experiments, When Using An Autocorrelation Whitening Filter of Order 7. Simulation Data, SNR = -22 db, Band-passed White Gaussian AM, with the QR and AM at 2.5 khz Performance Comparison on Experiment Data, BP White Gaussian AM, with the QR and AM at 6.25 khz. Autocorrelation Method Performance Comparison on Experiment Data, BP White Gaussian AM, Covariance Method, with the QR and AM at 6.25 khz Performance Comparison on Experiment Data, BP White Gaussian AM, with the QR and AM at 10 khz. Autocorrelation Method Performance Comparison on Experiment Data, BP White Gaussian AM, with the QR and AM at 10 khz. Covariance Method Performance Comparison on Experiment Data, BP White Gaussian AM, with the QR and AM at -8 khz. Autocorrelation Method xiv

15 6.44 Performance Comparison on Experiment Data, BP White Gaussian AM, with the QR and AM at -8 khz. Covariance Method Performance Comparison on Experiment Data, BP White Gaussian AM, with the QR and AM at 12.5 khz. Autocorrelation Method Performance Comparison on Experiment Data, BP White Gaussian AM, with the QR and AM at 12.5 khz. Covariance Method Simulation, SNR = -22 db, Performance Comparison on Simulation Data, Band-passed White Gaussian AM, with the QR and AM at 2.5 khz. Whitened with either the Autocorrelation Method or the Covariance Method using an Adaptive Filter Order that either Minimizes the Effect on the QR Signal or based on the MDL algorithm Simulation, SNR = -22 db, Performance Comparison on Simulation Data, Band-passed White Gaussian AM, with the QR and AM at 5 khz. Whitened with either the Autocorrelation Method or the Covariance Method using an Adaptive Filter Order that either Minimizes the Effect on the QR Signal or based on the MDL algorithm Simulation, SNR = -22 db, Performance Comparison on Simulation Data, Band-passed White Gaussian AM, with the QR and AM at 7.5 khz. Whitened with either the Autocorrelation Method or the Covariance Method using an Adaptive Filter Order that either Minimizes the Effect on the QR Signal or based on the MDL algorithm Simulation, SNR = -22 db, Performance Comparison on Simulation Data, Band-passed White Gaussian AM, with the QR and AM at 10 khz. Whitened with either the Autocorrelation Method or the Covariance Method using an Adaptive Filter Order that either Minimizes the Effect on the QR Signal or based on the MDL algorithm Simulation, SNR = -22 db, Performance Comparison on Simulation Data, Band-passed White Gaussian AM, with the QR and AM at 12.5 khz. Whitened with either the Autocorrelation Method or the Covariance Method using an Adaptive Filter Order that either Minimizes the Effect on the QR Signal or based on the MDL algorithm Simulation, SNR = -22 db, Performance Comparison on Simulation Data, Band-passed White Gaussian AM, with the QR and AM at 15 khz. Whitened with either the Autocorrelation Method or the Covariance Method using an Adaptive Filter Order that either Minimizes the Effect on the QR Signal or based on the MDL algorithm Performance Comparison on Experiment Data A, BP White Gaussian AM, with the QR and AM at 6.25 khz. Whitened with either the Autocorrelation Method or the Covariance Method using an Adaptive Filter Order that either Minimizes the Effect on the QR Signal or based on the MDL algorithm xv

16 6.54 Performance Comparison on Experiment Data B, BP White Gaussian AM, with the QR and AM at 10 khz. Whitened with either the Autocorrelation Method or the Covariance Method using an Adaptive Filter Order that either Minimizes the Effect on the QR Signal or based on the MDL algorithm Performance Comparison on Experiment Data C, BP White Gaussian AM, with the QR and AM at -8 khz. Whitened with either the Autocorrelation Method or the Covariance Method using an Adaptive Filter Order that either Minimizes the Effect on the QR Signal or based on the MDL algorithm Performance Comparison on Experiment Data D, BP White Gaussian AM, with the QR and AM at 12.5 khz. Whitened with either the Autocorrelation Method or the Covariance Method using an Adaptive Filter Order that either Minimizes the Effect on the QR Signal or based on the MDL algorithm Central Signal, For the Set of QR Signals with Fixed Phase and T 2 and Frequency Values Between khz and khz Central Signal, For the Set of QR Signals with Fixed Phase and T 2 and Frequency Values Between 11.5 khz and 12.5 khz Central Signal, For the Set of QR Signals with Fixed Phase and T 2 and Frequency Values Between 12 khz and 14 khz Central Signal, For the Set of QR Signals with Fixed Frequency and Phase and T Values Between 400e-6 and 800e Central Signal, For the Set of QR Signals with Fixed Frequency and T 2 and Phase Values Between -0.4 and 0.4 Radians Central Signal, of the Smallest Sphere Containing the Set of QR Signals with Frequency Values Between khz and 12.5 khz, T Values Between 400e-6 and 800e-6, and Phase Values Between -0.4 and 0.4 Radians Robust Matched Filter, For Thermal Noise and the Samples from the Set of QR Signals with Fixed Phase and T and Frequency Values Between khz and khz Robust Matched Filter, For Thermal Noise and the Samples from the Set of QR Signals with Fixed Phase and T and Frequency Values Between khz and 12.5 khz Robust Matched Filter, For Thermal Noise and the Samples from the Set of QR Signals with Fixed Phase and T and Frequency Values Between 2 12 khz and 14 khz Robust Matched Filter, For Thermal Noise and the Samples from the Set of QR Signals with Fixed Frequency and Phase and T Values Between 2 400e-6 and 800e Robust Matched Filter, For Thermal Noise and the Samples from the Set of QR Signals with Fixed Frequency and T and Phase Values Between and 0.4 Radians xvi

17 xvii 7.12 Robust Matched Filter, For Thermal Noise and the Samples from the Set of QR Signals with Frequency Between 11.5 khz and 12.5 khz, T 2 Between 400e-6 and 800e-6 and Phase Between -0.4 and 0.4 Radians Robust Matched Filter, For Thermal Noise and the Set of QR Signal Samples Versus the Robust Matched Filter, For Thermal Noise and the SmallestSphere Containing the QR Signal Samples Comparing the Robust Matched Filter for the set covering the frequencies 11.5 khz to 12.5 khz, to the sample signals with the largest and smallest frequencies Simulation, SNR = -16 db, Thermal Noise, Batch of Robust Matched Filters versus using a Batch Matched Filter, The QR signal parameters, decaying parameter, T, and phase,φ, remained constant while the frequency varied between 5 khz to 15 khz Simulation, SNR = -12 db, Thermal Noise, Batch of Robust Matched Filters versus using a Batch Matched Filter, The QR signal parameters varied as follows, frequency between 5 khz to 15 khz, decaying parameter T between 400e-6 and 800e-6, and phase φ between π/2 to π/ Simulation, SNR = -18 db, BPWGAM Noise, Batch of Robust Matched Filters versus using a Batch Matched Filter, The QR signal parameters varied as follows, frequency between 5 khz to 15 khz, decaying parameter T between 400e-6 and 800e-6, and phase φ between π/2 to π/ Simulation, SNR = -18 db, BPWGAM Noise, Batch of Whitened Robust Matched Filters versus Batch Whitened Matched Filters, QR signal parameters varied as follows, frequency between 5 khz to 15 khz, decaying parameter T between 400e-6 and 800e-6, and phase φ between π/2 to 2 π/

18 xviii Acknowledgments I would like to thank everybody who influenced the completion of this thesis in one way or another. First and foremost, I would like to thank the source of all knowledge and reason, the Almighty Allah, for making things work out for me. On the personal side, this thesis is the end product of unwavering support from my loving family. My parents, my father who I look to as a role model and my mother who never stops praying for me, constantly pushed me towards the pursuit of knowledge and wisdom. My brother, Faisal, and two sisters, Ghalia and Sara, have always inspired me and supported in my strive for success. I would also like to express immeasurable gratitude to my adviser, Dr. Constantino M. Lagoa, for his invaluable, scholarly insights, guidance, encouragement and unfailing support. In addition to being an outstanding teacher and a seasoned scholar, Dr. Lagoa was a caring coach, a morale booster, and a supporter at times when I was about to falter. I would also like to thank each one of my committee members, Dr. Jeffrey Schiano, Dr. David Miller and Dr. Patrick M. Lenahan for their valuable input and comments that helped fine tune this document. The many students, teachers, and social supervisors who gave me their trust and their time and shared their deeply-felt beliefs and attitudes with me, made a qualitative contribution to the development of this thesis. I have learned a lot from them, and understand

19 them to be sources of knowledge in their own right. Furthermore, I m grateful to the many friends who have supported me and encouraged me throughout the years. xix I also acknowledge, for the record and from the heart, my debt to the Abu-Dhabi National Oil Company for sponsoring my graduate studies at the Pennsylvania State University. I also thank in particular the dedicated staff of the Scholarship Department at ADNOC, for their assistance and support throughout my academic journey.

20 1 Chapter 1 Introduction 1.1 Motivation The idea of using quadrupole resonance (QR) spectroscopy as an explosive detection technology started more than 30 years ago in an attempt to detect improvised explosive devices used against American soldiers during the Vietnam war [36; 29]. The North Vietnamese forces would recycle American munitions as satchel charges and seed roadways with them. Metal detectors were unable to detect these satchels loaded with explosives. Hirschfeld proposed that NQR might provide a means for directly detecting the explosive material, and therefore provide a means for discriminating between the explosive satchels and decoys [30]. Marino [36] was the first to detect NQR signals in RDX (which makes up approximately 91% of C4 [1]), and he later presented a review paper on NQR spectroscopy of explosive materials that included TNT, PETN (which has been used by both the underwear and shoe bombers [33; 2]), RDX, and HMX. Research funding diminished after the withdrawal of American forces from Vietnam in Fifteen years later, the destruction of a Pan AM Flight 103 over Scotland restored interest in explosive detection.

21 2 1.2 Literature Review Researchers at the Naval Research Laboratory (NRL) noted that x-ray detection systems and magnetometers used at aviation security points are unable to detect plastic explosives. This led to the development of NQR technology for civil aviation security. Buess showed that a pulsed NQR spectrometer can detect sub-kilogram quantities of explosives [34; 35]. At least two commercial NQR detection systems have been developed. Quantum Magnetics, now a subsidiary of Morpho, in San Diego, California, and British Technology Group (BTG) in conjunction with Smith et al., at King s College in London, have produced NQR detection systems for narcotics and explosives detection in airline baggage. Recently, the SEE Corporation in Perth, Australia, has also started work on NQR detection systems for aviation, landmine, and postal applications. With funding from DARPA, Quantum Magnetics also conducted field trials of an NQR system for detection of mines containing RDX. Researchers in the former Soviet Union began investigating NQR as a means to detect AT landmines during the war in Afghanistan. Grechishkin, at the Kaliningrad State University in Russia, developed an NQR detection system that could sweep a one-square meter area in ten seconds with a detection rate over ninety percent for mines buried within 10 cm of the surface [63]. His group also demonstrated that the NQR system could detect 2.5 kg of RDX buried 35 cm underground using a RF power level of 1 kw [25]. Recently, Grechishkin described a method for determining the burial depth based on finding the optimal frequency offset in a RF pulse sequence [26].

22 3 In addition to the mentioned systems, there are several other QR explosive detection prototypes such as the chemical sniffers and others that even combine x-ray and QR detection technology. While the technology has progressed significantly in the last three decades, present day detectors still suffer from high false alarm rates [9]. The physical basis for QR detection is the electrical properties of atomic nuclei and their surrounding electronic environment [52]. Atomic nuclei with spin angular momentum greater than one-half possess both an electric quadrupole moment and a magnetic dipole moment, and are referred to as quadrupolar nuclei. If a quadrupolar nucleus experiences an electric-field gradient tensor due to the surrounding electric charges, the resulting electrostatic interaction energy produces preferred orientations of the nucleus. It is possible to perturb the orientation of quadrupolar nuclei by subjecting them to an external radio frequency (RF) magnetic field, at a resonant frequency that is material dependent. As the resonant frequency is strongly dependent on the electric field gradient tensor, different chemical compounds containing the same quadrupolar nuclei will have distinct resonant frequencies [19]. As of now, no QR system has been approved for civil aviation security by the Transportation Security Administration.The low success rate of these explosive detection machines is due to the several challenges presented next. Threat quantities of explosives are not easy to detect, due to four main obstacles. The first, is that the amplitude of a QR signal is typically on the same level if not smaller than the amplitude of thermal noise, which makes it very susceptible to noise interference [9]. External RF interferences such as AM signals pose another challenge, and they are another source of noise that contributes to

23 4 the low SNR values. AM stations broadcast within the same frequency band of QR signals, which is a problem for QR detection. Internal noise sources (ones from within the search volume such as RF interferences) which include ringing produced by the search coil [9; 45] and piezoelectric responses, pose another challenge. The excitation of a QR response requires the application of a pulsed RF magnetic field within the search volume. Currents induced within conductive materials located in the search volume cause decaying magnetic fields that lead to unacceptable false alarm rates. The fourth challenge we face is uncertainty in the QR signal characteristics. The signal may contain more than a single frequency, depending on the temperature and strains of the explosive material. Explosive material within a bomb is required to have a uniform temperature to obtain a signal with a very narrow bandwidth. We also face uncertainty in the decaying shape of the QR signal. The envelope of the QR signal is often thought of as a Lorentzian distribution, though at times it may look more Gaussian. To overcome these challenges, several attempts at increasing the SNR ratio have been made. Some sought to increase the SNR ratio by increasing the amplitude of the QR signal. Smith et al. attempted this through interweaving of different pulse sequences [54]. Schiano et al. used feedback optimization to optimize the pulse parameters and gain an increase in the QR signal [31]. Schiano also used narrowband superconducting HTS coils to gain an increase in SNR [49]. The HTS coils managed to amplify the QR signal by orders of magnitude and at the same time suppress noise due to their narrow passband. Unfortunately, the HTS coil also amplifies any noise that falls within its passband as much as it would amplify the QR signal. Another approach to increasing the SNR,

24 5 is to try to decrease the noise. Ernst, [21], showed that, for the case of uncorrelated and stationary noise, signal averaging is an efficient and simple method to decreasing the noise. Signal averaging decreases the standard deviation of the noise by the square root of the number of averages. Another way to decrease the noise is to shield from external RF interferences, which is impractical when attempting to detect explosives in land mines and on humans at aviation security check points due to claustrophobic experiences. Suits proposed using a gradiometer [56], which is sensitive only to spatial gradients of the magnetic fields, as another approach to limiting the level of interference which enters the receiver. Others have used signal processing methods to improve detection and false alarm rates. Since this work focuses on signal processing algorithms, only literature with a common focus will be reviewed. The most widely used signal detection method is the energy detector, due to its simplicity. The detector transforms the collected QR signal into the frequency domain and the power at the frequency bin of interest is calculated. Then, using a preset threshold, the presence of the target of interest is determined. According to [45] this method works well when the signal-to-interference-plus-noise ratio (SNR) is high. Although in the more practical scenario of land mine detection, where the SNR ratio is usually low [4; 5], it becomes difficult to obtain a good performance rate using this method alone. Other signal processing algorithms focused on RFI mitigation. Tantum et al. [46] used an adaptive noise cancellation method to reduce the RFI s for QR. This method is used in a similar fashion in QM s active approach for RFI reduction [9]. By using a 1-tap

25 6 least mean squares algorithm, it has been reported that the adaptive noise cancellation method [64; 60] can reduce the RFI s by almost 40 db [46]. The drawback however, is that this method may amplify noise from signal cancellation, [64]. RFI mitigation for landmine detection by QR was also investigated in Liu et al. [22]. They exploited both the spatial and temporal correlation of the RFI s and proposed a combined approach to mitigate the RFI s efficiently and effectively improve the TNT detection performance. They first considered only exploiting the spatial correlation of the RFI s and proposed a maximum likelihood (ML) estimator for signal amplitude estimation and a constant false alarm rate (CFAR) detector for TNT detection. Then, they used a multi-channel autoregressive (MAR) model to take into account the temporal correlation of the RFI s. Third, they made use of the spatial and temporal correlations of the RFI s using a (2- D) robust Capon beamformer (RCB) followed by the ML method for improved RFI mitigation. Finally, they combined the merits of all the three methods and applied it to TNT detection. Using experimental results they showed that the combined method outperforms all the three proposed methods but still does not provide enough of an SNR improvement to robustly detect a QR signal. Another group focused on estimation as an approach for QR detection. One example is the average power detector based on a power spectral estimation algorithm, which has been proposed by Tan et al. in [69]. It has been reported in [69] that this detector outperforms the non-adaptive Bayesian detector by using distinguishable features of the QR signal and RFI in the frequency domain [59]. However, just like the energy detector, the average power detector suffers from low SNR and, therefore it is preferably used after

26 7 RFI mitigation. Tan et al. [70] have derived a Cramer-Rao lower bound by considering the RFI as a colored non-gaussian process. A two-step adaptive Kalman filter to estimate and detect a QR signal in the post-mitigation signal [59; 71] has been proposed by Tan et al. It has been shown in [71] that this method can provide robust landmine detection performance. However, to obtain the coefficient and covariance matrices, this method requires training data, which might not be available. Signal amplitude estimation, with known signal waveform and phase delays, is another method that has been used for landmine detection by Jiang et al. [68; 67]. In [68] they proposed a maximum likelihood (ML) estimator and a Capon estimator and derived closed-form expressions for the bias and mean-squared errors of both estimators in the the presence of spatially colored but temporally white interference and noise [68]. Both of these estimators have also been shown to be asymptotically statistically efficient for large data snapshots. To consider the more general case where the interference and noise are both temporally spatially colored, an alternative least square (ALS) method has also been proposed. Using numerical simulations, in [68], Jiang et al. showed that in most cases the ALS approach outperforms the model-mismatched maximum likelihood (M 3 L) method, which ignores the temporal correlation of the interference noise. On the other hand the M 3 L is slightly better in worst cases, when the desired signal and the interference are closely spaced in the temporal frequency domain. Both these methods work well in the particular situations mentioned, though neither of them can robustly detect a QR signal.