WWrriigghhtt SSttaattee UUnniivveerrssiittyy CCOORREE SScchhoollaarr Browse all Theses and Dissertations Theses and Dissertations 2015 DDiirreeccttiioonn ooff AArrrriivvaall EEssttiimmaattiioonn uussiinngg WWiiddeebbaanndd SSppeeccttrraall SSuubbssppaaccee PPrroojjeeccttiioonn Majid Shaik Wright State University Follow this and additional works at: https://corescholar.libraries.wright.edu/etd_all Part of the Electrical and Computer Engineering Commons RReeppoossiittoorryy CCiittaattiioonn Shaik, Majid, "Direction of Arrival Estimation using Wideband Spectral Subspace Projection" (2015). Browse all Theses and Dissertations. 1635. https://corescholar.libraries.wright.edu/etd_all/1635 This Thesis is brought to you for free and open access by the Theses and Dissertations at CORE Scholar. It has been accepted for inclusion in Browse all Theses and Dissertations by an authorized administrator of CORE Scholar. For more information, please contact [email protected]. Direction of Arrival Estimation using Wideband Spectral Subspace Projection A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Engineering by Majid Shaik Bachelor of Engineering, Osmania University, 2013 2015 Wright State University WrightStateUniversity GRADUATESCHOOL January19,2016 I HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MY SUPER- VISION BY Majid Shaik ENTITLED Direction of Arrival Estimation using Wideband Spectral Subspace Projection BE ACCEPTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTSFORTHEDEGREEOFMasterofScienceinEngineering. ArnabK.Shaw ThesisDirector BrianD.Rigling Chair,DepartmentofElectricalEngineering Committeeon FinalExamination ArnabK.Shaw,Ph.D JoshAsh,Ph.D HenryChen,Ph.D RobertE.W.Fyffe,Ph.D VicePresidentforResearchand DeanoftheGraduateSchool ABSTRACT Shaik, Majid. M.S.Egr., Department of Electrical Engineering, Wright State University, 2015. Di- rectionofArrivalEstimationusingWidebandSpectralSubspaceProjection. Many areas such as Wireless Communication, Oil Mining, Radars, Sonar, and Seismic Exploration require direction of arrival estimation (DOA) of wideband sources. Most ex- isting wideband DOA estimation algorithms decompose the wideband signals into several narrowbandfrequencybins,followedbyeitherfocusingortransformingtoareferencefre- quency bin, before estimating the DOAs. The focusing based methods are iterative and their performance is affected by the choice of preliminary DOA estimates and the number of source DOAs to be estimated. The existing method requiring transformation to a ref- erence frequency bin exhibits spurious peaks in the spatial spectrum and is not reliable in general. Inthisthesis,anovelWidebandSpectralSubspaceProjection(WSSP)approachispre- sented. WSSP exploits the properties of projected subspaces to estimate the wideband DOAs. The proposed method is non-iterative and it does not require any prior DOA es- timates, focusing, beamforming or transformation to reference frequency bin. Theoretical small perturbation analysis has been conducted that confirms the ability of WSSP to pro- ducelargepeaksatcorrectDOAs. The validity of the proposed algorithm has been tested using a variety of typical wide- band sources encountered in radar and wireless communication applications, including Chirp,QPSKandMC-CDMA.Theperformanceoftheproposedalgorithmhasbeencom- paredwiththoseofpreviouslyexistingalgorithmsviaextensivesimulationstudies,interms of bias and root mean square error (RMSE). The simulation results demonstrate that when compared to the existing methods, the performance of proposed method is accurate over a wide range of SNRs and it is not affected by the number of the source DOAs to be esti- mated. iii Contents 1 Chapter1: Introduction 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 OverviewoftheThesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Chapter2: OverviewofDOAEstimationAlgorithms 4 2.1 SignalandArrayModel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 NarrowbandAlgorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2.1 MultipleSignalClassification(MUSIC) . . . . . . . . . . . . . . . 7 2.2.2 Root-MUSIC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2.3 Estimation of Signal Parameter via Rotational Invariance Tech- niques(ESPRIT) . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3 WidebandAlgorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3.1 IncoherentMUSIC(IMUSIC) . . . . . . . . . . . . . . . . . . . . 14 2.3.2 CoherentSignalSubspace(CSS) . . . . . . . . . . . . . . . . . . . 15 2.3.3 WeightedAverageofSignalSubspace(WAVES) . . . . . . . . . . 18 2.3.4 TestofOrthogonalityofProjectedSubspace(TOPS) . . . . . . . . 19 3 Chapter3: WidebandSpectralSubspaceProjection(WSSP) 25 3.1 ProjectionofSignalSubspaceontoNoiseSubspace . . . . . . . . . . . . . 26 3.2 FrequencySelection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.3 ErrorAnalysisusingNoiseSubspaceProjection . . . . . . . . . . . . . . . 31 3.4 WSSPAlgorithmSteps . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4 Chapter4: Simulation 35 4.1 SignalGeneration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.1.1 ChirpSignalGeneration . . . . . . . . . . . . . . . . . . . . . . . 36 4.1.2 QuadraturePhaseShiftKey(QPSK)SignalGeneration . . . . . . . 39 4.1.3 Multi-CarrierCodeDivisionMultipleAccess(MC-CDMA)Signal Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.2 SimulationResultsforChirpSources . . . . . . . . . . . . . . . . . . . . 43 4.3 SimulationforQPSKSignal . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.4 SimulationofMC-CDMASources . . . . . . . . . . . . . . . . . . . . . . 62 iv 4.5 ComparisonofTOPSandWSSPford = λ /2 . . . . . . . . . . . . . . . . 71 c 5 Chapter5: ConcludingRemarks 78 Bibliography 81 v List of Figures 2.1 SensorArray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 MUSICandRoot-MUSICComparison . . . . . . . . . . . . . . . . . . . . 10 2.3 TOPSProjectionMatrix . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.4 TOPSProjectionMatrix . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.1 EigenvalueDifferenceVsSNR . . . . . . . . . . . . . . . . . . . . . . . . 30 3.2 Frequencyselectionat10dBforβ = 0.9 . . . . . . . . . . . . . . . . . . . 31 3.3 Frequencyselectionat10dBforβ = 0.9 . . . . . . . . . . . . . . . . . . . 31 3.4 Frequencyselectionat10dBforβ = 0.8 . . . . . . . . . . . . . . . . . . . 32 4.1 UpChirp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.2 DownChirp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4.3 ConvexChirp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 4.4 QPSKConstellationPlot . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.5 BlockDiagramforQPSK . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.6 BlockDiagramforMC-CDMA . . . . . . . . . . . . . . . . . . . . . . . . 42 4.7 ChirpSpectrumatSensor . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.8 ChirpTwoSourceCSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.9 ChirpTwoSourceWAVES . . . . . . . . . . . . . . . . . . . . . . . . . . 46 4.10 ChirpTwoSourceTOPS . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 4.11 ChirpTwoSourceWSSP . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 4.12 ComparisonofmethodsatSNR=10dB . . . . . . . . . . . . . . . . . . . . 47 4.13 ChirpThreeSourceCSS . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.14 ChirpThreeSourceWAVES . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.15 ChirpThreeSourceTOPS . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.16 ChirpThreeSourceWSSP . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.17 ChirpThreeSourceCombinedspectrum . . . . . . . . . . . . . . . . . . . 50 4.18 BiasPlotforChirpsourceatangle9degrees . . . . . . . . . . . . . . . . . 51 4.19 BiasPlotforChirpsourceatangle12degrees . . . . . . . . . . . . . . . . 52 4.20 RMSEPlotforChirpsourceatangle12degrees . . . . . . . . . . . . . . . 52 4.21 RMSEPlotforChirpsourceatangle12degrees . . . . . . . . . . . . . . . 52 4.22 QPSKSpectrumatSensor . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.23 QPSKTwoSourceCSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 vi 4.24 QPSKTwoSourceWAVES . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.25 QPSKTwoSourceTOPS . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.26 QPSKTwoSourceWSSP . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.27 QPSK2sourcecombinedspectrum . . . . . . . . . . . . . . . . . . . . . 56 4.28 QPSKThreeSourceCSS . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.29 QPSKThreeSourceWAVES . . . . . . . . . . . . . . . . . . . . . . . . . 58 4.30 QPSKThreeSourceTOPS . . . . . . . . . . . . . . . . . . . . . . . . . . 58 4.31 QPSKThreeSourceWSSP . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.32 QPSKthreeSourceCombinedspectrum . . . . . . . . . . . . . . . . . . . 59 4.33 BiasPlotforChirpsourceatangle9degrees . . . . . . . . . . . . . . . . . 60 4.34 BiasPlotforChirpsourceatangle12degrees . . . . . . . . . . . . . . . . 61 4.35 RMSEPlotforChirpsourceatangle12degrees . . . . . . . . . . . . . . . 61 4.36 RMSEPlotforChirpsourceatangle12degrees . . . . . . . . . . . . . . . 62 4.37 MC-CDMASpectrumatSensor . . . . . . . . . . . . . . . . . . . . . . . 63 4.38 MC-CDMATwoSourceCSS . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.39 MC-CDMATwoSourceWAVES . . . . . . . . . . . . . . . . . . . . . . 64 4.40 MC-CDMATwoSourceTOPS . . . . . . . . . . . . . . . . . . . . . . . . 65 4.41 MC-CDMATwoSourceWSSP . . . . . . . . . . . . . . . . . . . . . . . 65 4.42 MC-CDMATwoSourceCombinedSpectrum . . . . . . . . . . . . . . . . 66 4.43 MC-CDMAThreeSourceCSS . . . . . . . . . . . . . . . . . . . . . . . . 66 4.44 MC-CDMAThreeSourceWAVES . . . . . . . . . . . . . . . . . . . . . . 67 4.45 MC-CDMAThreeSourceTOPS . . . . . . . . . . . . . . . . . . . . . . . 67 4.46 MC-CDMAThreeSourceWSSP . . . . . . . . . . . . . . . . . . . . . . . 68 4.47 MC-CDMAThreeSourceCombinedSpectrum . . . . . . . . . . . . . . . 68 4.48 BiasPlotforMC-CDMAsourceatangle9degrees . . . . . . . . . . . . . 69 4.49 BiasPlotforMC-CDMAsourceatangle12degrees . . . . . . . . . . . . 70 4.50 RMSEPlotforMC-CDMAsourceatangle12degrees . . . . . . . . . . . 70 4.51 RMSEPlotforMC-CDMAsourceatangle12degrees . . . . . . . . . . . 71 4.52 ChirpTOPSandWSSPatSNR=10dB . . . . . . . . . . . . . . . . . . . . 72 4.53 Chirp-3SourceTOPSandWSSPatSNR=20dB . . . . . . . . . . . . . . . 72 4.54 Chirp-4SourceTOPSandWSSPatSNR=30dB . . . . . . . . . . . . . . . 73 4.55 QPSK-2SourceTOPSandWSSPatSNR=10dB . . . . . . . . . . . . . . 74 4.56 QPSK-3SourceTOPSandWSSPatSNR=20dB . . . . . . . . . . . . . . 75 4.57 QPSK-4SourceTOPSandWSSPatSNR=30dB . . . . . . . . . . . . . . 75 4.58 MC-CDMA-2SourceTOPSandWSSPatSNR=10dB . . . . . . . . . . . 76 4.59 MC-CDMA-3SourceTOPSandWSSPatSNR=20dB . . . . . . . . . . . 77 4.60 MC-CDMA-4SourceTOPSandWSSPatSNR=30dB . . . . . . . . . . . 77 vii Acknowledgment Firstly, I would like to take this opportunity to express my sincere gratitude to my Thesis advisor and mentor Dr. Arnab K. Shaw for his Support of my Masters study and Thesis at Wright State University, for his motivation, patience and immense knowledge. He guided me all the time of research and writing of this thesis. I could not have imagined having a betteradvisorandmentorformyThesisandMastersstudy. Besides my advisor, I would like to thank my thesis committee: Dr. Joshua Ash, and Dr. Henry Chen, for their insightful comments and encouragement which incented me to widenmyresearchfromvariousperspectives. I would like to take this opportunity to express gratitude to all of the Department facultymembersfortheirhelpandsupport. Lastly, I would like to thank my Parents, Uncle and brothers for their unconditional supportandlovethroughoutmyjourneyandlifeingeneral. IalsothankmyfriendsSalman Shaik, Syed Abdul Zabi and Arjuman Afreen Khan at Wright State University and my fellowroommatesfortheirsupport. viii Dedicatedto MyParentsandUncle ix