Non-Gaussian Statistical Communication Theory

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. email href="mailto:pressbooks@ieee.org">pressbooks@ieee.org to request Ch.10

Autorentext

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.

Zusammenfassung
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 priori*what 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.

email pressbooks@ieee.org to request Ch.10

Inhalt

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: OnOff Optimum Processing Algorithms, 46

1.8 Special OnOff Optimum Binary Systems, 50

1.9 Optimum Detection: OnOff 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 WKh Relations for Discrete Samples in the Non-Hom-Stat Situation, 102

2.4 The WienerKhintchine 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 NumberFrequency 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 309

6.2 Optimal Estimation Coupling, 315

6.3 Simultaneous Joint Detection and Estimation: General Theory, 326

6.4 Joint D and E: ExamplesEstimation 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)