Non-Gaussian Statistical Communication Theory / Edition 1

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The book is based on the observation that communication is the central operation of discovery in all the sciences. In its "active mode" we use it to "interrogate" the physical world, sending appropriate "signals" and receiving nature's "reply". In the "passive mode" we receive nature's signals directly. Since we never know a prioriwhat particular return signal will be forthcoming, we must necessarily adopt a probabilistic model of communication. This has developed over the approximately seventy years since it's beginning, into a Statistical Communication Theory (or SCT). Here it is the set or ensemble of possible results which is meaningful. From this ensemble we attempt to construct in the appropriate model format, based on our understanding of the observed physical data and on the associated statistical mechanism, analytically represented by suitable probability measures. Since its inception in the late '30's of the last century, and in particular subsequent to World War II, SCT has grown into a major field of study. As we have noted above, SCT is applicable to all branches of science. The latter itself is inherently and ultimately probabilistic at all levels. Moreover, in the natural world there is always a random background "noise" as well as an inherent a priori uncertainty in the presentation of deterministic observations, i.e. those which are specifically obtained, a posteriori. The purpose of the book is to introduce Non-Gaussian statistical communication theory and demonstrate how the theory improves probabilistic model. The book was originally planed to include 24 chapters as seen in the table of preface. Dr. Middleton completed first 10 chapters prior to his passing in 2008. Bibliography which represents remaining chapters are put together by the author's close colleagues; Drs. Vincent Poor, Leon Cohen and John Anderson.

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Meet the Author

David Middleton, PhD, graduated from Harvard Universitywhere he began his career at the institution's Radio ResearchLaboratory—working on radar countermeasures as well aspassive and active jamming during World War II—beforeteaching there. A recipient of numerous prizes and awards relatedto his work on communication theory, Dr. Middleton was a fellow ofthe IEEE, the American Physical Society, the Acoustical Society ofAmerica, and the American Association for the Advancement ofScience.

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Table of Contents

Foreword xv

Visualizing the Invisible xvii

Acknowledgments xxi

About the Author xxiii

Editor's Note xxv

Introduction 1

1 Reception as a Statistical Decision Problem 15

1.1 Signal Detection and Estimation, 15

1.2 Signal Detection and Estimation, 17

1.3 The Reception Situation in General Terms, 22

1.4 System Evaluation, 27

1.5 A Summary of Basic Definitions and Principal Theorems,35

1.6 Preliminaries: Binary Bayes Detection, 40

1.7 Optimum Detection: On–Off Optimum ProcessingAlgorithms, 46

1.8 Special On–Off Optimum Binary Systems, 50

1.9 Optimum Detection: On–Off Performance Measures andSystem Comparisons, 57

1.10 Binary Two-Signal Detection: Disjoint and OverlappingHypothesis Classes, 69

2 Space-Time Covariances and Wave Number Frequency Spectra:I. Noise and Signals with Continuous and Discrete Sampling77

2.1 Inhomogeneous and Nonstationary Signal and Noise Fields I:Waveforms, Beam Theory, Covariances, and Intensity Spectra, 78

2.2 Continuous Space-Time Wiener-Khintchine Relations, 91

2.3 The W–Kh Relations for Discrete Samples in theNon-Hom-Stat Situation, 102

2.4 The Wiener–Khintchine Relations for Discretely SampledRandom Fields, 108

2.5 Aperture and Arrays-I: An Introduction, 115

2.6 Concluding Remarks, 138

3 Optimum Detection, Space-Time Matched Filters, and BeamForming in Gaussian Noise Fields 141

3.1 Optimum Detection I: Selected Gaussian Prototypes-CoherentReception, 142

3.2 Optimum Detection II: Selected GaussianPrototypes-Incoherent Reception, 154

3.3 Optimal Detection III: Slowly Fluctuating Noise Backgrounds,176

3.4 Bayes Matched Filters and Their Associated Bilinear andQuadratic Forms, I, 188

3.5 Bayes Matched Filters in the Wave Number–FrequencyDomain, 219

3.6 Concluding Remarks, 235

4 Multiple Alternative Detection 239

4.1 Multiple-Alternative Detection: The Disjoint Cases, 239

4.2 Overlapping Hypothesis Classes, 254

4.3 Detection with Decisions Rejection: Nonoverlapping SignalClasses, 262

5 Bayes Extraction Systems: Signal Estimation and Analysis,p(H1) = 1 271

5.1 Decision Theory Formulation, 272

5.2 Coherent Estimation of Amplitude (Deterministic Signals andNormal Noise, p(H1) = 1), 287

5.3 Incoherent Estimation of Signal Amplitude (DeterministicSignals and Normal Noise, p(H1) = 1), 294

5.4 Waveform Estimation (Random Fields), 300

5.5 Summary Remarks, 304

6 Joint Detection and Estimation, p(H1) ≤ 1: I.Foundations 307

6.1 Joint Detection and Estimation under Prior Uncertainty[p(H1)≤ 1]: Formulation, 309

6.2 Optimal Estimation [ p(H1) ≤ 1]: No Coupling, 315

6.3 Simultaneous Joint Detection and Estimation: General Theory,326

6.4 Joint D and E: Examples–Estimation of SignalAmplitudes [p(H1) ≤ 1], 350

6.5 Summary Remarks, p(H)1 ≤ 1: I-Foundations, 378

7 Joint Detection and Estimation under Uncertainty, pk(H1)< 1.
II. Multiple Hypotheses and Sequential Observations 381

7.1 Jointly Optimum Detection and Estimation under MultipleHypotheses, p(H1) ≤ 1, 382

7.2 Uncoupled Optimum Detection and Estimation, MultipleHypotheses, and Overlapping Parameter Spaces, 400

7.3 Simultaneous Detection and Estimation: Sequences ofObservations and Decisions, 407

7.4 Concluding Remarks, 428

8 The Canonical Channel I: Scalar Field Propagation in aDeterministic Medium 435

8.1 The Generic Deterministic Channel: Homogeneous UnboundedMedia, 437

8.2 The Engineering Approach: I-The Medium and Channel asTime-Varying Linear Filters (Deterministic Media), 465

8.3 Inhomogeneous Media and Channels-Deterministic Scatter andOperational Solutions, 473

8.4 The Deterministic Scattered Field in Wave Number-FrequencySpace: Innovations, 494

8.5 Extensions and Innovations, Multimedia Interactions, 499

8.6 Energy Considerations, 509

8.7 Summary: Results and Conclusions, 535

9 The Canonical Channel II: Scattering in Random Media;"Classical" Operator Solutions 539

9.1 Random Media: Operational Solutions-First- and Second-OrderMoments, 541

9.2 Higher Order Moments Operational Solutions for The LangevinEquation, 565

9.3 Equivalent Representations: Elementary Feynman Diagrams,580

9.4 Summary Remarks, 598

References, 599

Appendix A1 601

Index 617

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