Springer Texts in Electrical Engineering Consulting Editor: John B. Thomas Springer TextsinElectricalEngineering Multivariable Feedback Systems P.M.Callier/C.A.Desoer Linear Programming M.Sakarovitch Introduction to Random Processes E.Wong Stochastic Processesin Engineering Systems E.Wong/B.Hajek Introduction to Probability J.B.Thomas Elements of Detection and Signal Design C.L.Weber An Introduction toCommunication Theory and Systems J.B.Thomas Signal Detection in Non-GaussianNoise S.A.Kassam An Introduction to Signal Detection and Estimation,2nd Edition H.V.Poor Introduction toShannon Sampling and Interpolation Theory RJ.MarksII Random Point Processes in Time and Space, 2nd Edition D.L.SnyderlM.I.Miller Linear System Tl,Jeory P.M.Callier/CA Desoer Advanced Topics in Shannon Sampling and Interpolation Theory RJ.MarksII(ed.) H. Vincent Poor An Introduction to Signal Detection and Estimation Second Edition With 48Illustrations Springer-Verlag Berlin Heidelberg GmbH H. Vincent Poor Department of Electrical Engineering School of Engineering/ Applied Science Princeton University Engineering Quadrangle Princeton, NJ 08544-5263 USA Library of Congress Cataloging-in-Publication Data Poor, H. Vincent. An introduction to signal detection and estimation /H. Vincent Poor.- [2nd ed.J p.cm.- (Springer texts in electrical engineering) "A Dowden &Culver book." Includes bibliographical references and index. 1.Signal detection.2.Signal theory (Telecommunication). 3.Estimation theory.I. Title.II.Series. TK5102.5.P6541994 621.382 '2-dc2093-21312 1994,1988by Springer-Verlag Berlin Heidelberg Originally published by Springer-Verlag Berlin Heidelberg New York in 1994 Softcover reprint of the hardcover 1st edition 1994 Allrights reserved.This workmay not be translated or copied in whole or in part without the written permission of the copyright holder, except for brief excerpts in connection with reviews or scholarly analysis.Usein connection withanyformof information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed isforbidden. The use of generaldescriptive names,trade names,trademarks,etc.,in this publication,even if theformerarenotespeciallyidentified,isnottobetakenasasignthatsuchnames,as understood by the Trade Marks and Merchandise Marks Act,may accordingly be used freely by anyone. Production managed by Hal Henglein;manufacturing supervised by Jacqui Ashri. Camera-ready copy prepared from the author's LaTeX file. 987654321 ISBN 978-1-4419-2837-5ISBN 978-1-4757-2341-0 (eBook) DOI 10.1007/978-1-4757-2341-0 Tomy family Preface Thepurposeof thisbookistointroducethereadertothebasictheory of signaldetectionandestimation.It isassumedthatthereaderhasa workingknowledgeofappliedprobabilityandrandomprocessessuchas that taught in atypical first-semestergraduate engineering course on these subjects. This material is covered, for example, in the book by Wong(1983) in this series.More advanced concepts in these areasare introduced where needed,primarily in Chapters VI and VII, where continuous-time problems are treated. Thisbookisadaptedfromaone-semester,second-tiergraduatecourse taughtat theUniversityof IllinoisandatPrincetonUniversity.However, this material can also be used for a shorter or first-tier course by restricting coverage to Chapters I through V,which for the most part can be read with abackgroundof onlythebasicsof appliedprobability,includingrandom vectorsandconditionalexpectations.Sufficientbackgroundforthelatter optionisgivenforexampleinthebookbyThomas(1986),alsointhis series. Thistreatmentisalsosuitableforuseasatextinothermodes.For example,twosmallercourses,oneinsignaldetection(ChaptersII,III, andVI)andoneinestimation(ChaptersIV,V,andVII),canbetaught from the materials as organized here. Similarly, an introductory-level course (Chapters Ithrough IV)followedby amoreadvancedcourse(Chapters V through VII)isanotherpossibility. In preparing this second edition, the suggestions and comments of many readers have been incorporated.Although these individuals are too numer-ous to be listedhere,theauthor isgratefulfortheir valuable advice. Contents Preface IIntroduction IIElements of Hypothesis Testing II.AIntroduction.......... II.BBayesianHypothesis Testing.. II. CMinimaxHypothesisTesting.. II.DNeyman-PearsonHypothesis Testing II.EComposite Hypothesis Testing. II.FExercises............. . IIISignal Detection in Discrete Time lILAIntroduction........... . III.BModelsandDetectorStructures. III.CPerformance Evaluation of SignalDetectionProcedures. III.C.1DirectPerformance Computation III.C.2Chernoff and Related Bounds. III.C.3AsymptoticRelativeEfficiency III.DSequential Detection......... . III.ENonparametricand RobustDetection. III.E.1Nonparametric Detection III.E.2RobustDetection III.FExercises............. . IVElements of Parameter Estimation IV.AIntroduction....................... . IV.BBayesianParameter Estimation............ . IV.CNonrandom Parameter Estimation:GeneralStructure IV.DMaximum-LikelihoodEstimation........... . IV.EFurtherAspectsandExtensionsofMaximum-Likelihood Estimation................ . IV.E.1Estimation of VectorParameters... . IV.E.2Estimation of SignalParameters... . IV.E.3Robust Estimation of SignalParameters IV.E.4RecursiveParameter Estimation IV.FExercises..................... . vii 1 5 5 5 13 22 29 39 45 45 45 82 83 86 91 97 111 112 124 132 141 141 142 157 173 185 185 186 193 195 197 xContents VElements of Signal Estimation V.AIntroduction..... . V.BKalman-Bucy Filtering... . V.CLinearEstimation...... . V.DWiener-KolmogorovFiltering V.D.lNoncausal Wiener-KolmogorovFiltering V.D.2Causal Wiener-KolmogorovFiltering V.EExercises..................... . VISignal Detection in Continuous Time VI.AIntroduction.. ............ VI.BMathematical Preliminaries..... VI.B.lDensitiesin Function Spaces. VI.B.2Grenander's Theorem and the Karhunen-Loeve Expansion..................... . VI.CThe Detection of Deterministicand Partly Determined SignalsinGaussianNoise................. VI.C.lCoherentDetection.............. . VI.C.2Detection of Signals with Unknown Parameters. VI.DThe Detection of RandomSignals in Gaussian Noise.. VI.D.lPreliminary Results on WienerProcesses..... VI.D.2The Detection of Gaussian Signals in White Noise VI.D.3The Estimator-Correlator Representation of the LikelihoodRatio forStochastic Signals VI.EExercises....................... VIISignal Estimation in Continuous Time VII.AIntroduction............ VII.BEstimation of SignalParameters.. VII.CLinear/Gaussian Estimation.... VII.C.1Estimation in White Noise. VII.C.2The Linear Innovations Process VII.C.3The Continuous-Time Kalman-Bucy Filter. VII.C.4Further Aspects of the Linear/Gaussian Problem VII.DNonlinearFiltering.................... . VII.D.1Basic Equations of NonlinearFiltering..... . VII.D.2A Derivation of the NonlinearFiltering Equations. VII.D.3PracticalApproximationstoOptimumNonlinear Filters VII.EExercises. References Index 205 205 206 221 233 234 239 258 263 263 264 264 272 278 278 294 298 299 303 310 323 327 327 327 333 333 336 340 349 352 358 365 374 383 387 393