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 University where he began his career at the institution's Radio Research Laboratory—working on radar countermeasures as well as passive and active jamming during World War II—before teaching there. A recipient of numerous prizes and awards related to his work on communication theory, Dr. Middleton was a fellow of the IEEE, the American Physical Society, the Acoustical Society of America, and the American Association for the Advancement of Science.

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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 Processing Algorithms, 46

1.8 Special On–Off Optimum Binary Systems, 50

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

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

2 Space-Time Covariances and Wave Number Frequency Spectra: I. Noise and Signals with Continuous and Discrete Sampling 77

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 the Non-Hom-Stat Situation, 102

2.4 The Wiener–Khintchine Relations for Discretely Sampled Random Fields, 108

2.5 Aperture and Arrays-I: An Introduction, 115

2.6 Concluding Remarks, 138

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

3.1 Optimum Detection I: Selected Gaussian Prototypes-Coherent Reception, 142

3.2 Optimum Detection II: Selected Gaussian Prototypes-Incoherent Reception, 154

3.3 Optimal Detection III: Slowly Fluctuating Noise Backgrounds, 176

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

3.5 Bayes Matched Filters in the Wave Number–Frequency Domain, 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 Signal Classes, 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 and Normal Noise, p(H1) = 1), 287

5.3 Incoherent Estimation of Signal Amplitude (Deterministic Signals 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 Signal Amplitudes [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 Multiple Hypotheses, p(H1) ≤ 1, 382

7.2 Uncoupled Optimum Detection and Estimation, Multiple Hypotheses, and Overlapping Parameter Spaces, 400

7.3 Simultaneous Detection and Estimation: Sequences of Observations and Decisions, 407

7.4 Concluding Remarks, 428

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

8.1 The Generic Deterministic Channel: Homogeneous Unbounded Media, 437

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

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

8.4 The Deterministic Scattered Field in Wave Number-Frequency Space: 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-Order Moments, 541

9.2 Higher Order Moments Operational Solutions for The Langevin Equation, 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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