Probability and Information Theory, with Applications to Radar

Editor's Preface

Author's Prefaces


1 An Introduction to Probability Theory


1.1 The Rules of Probability


1.2 Bernoulli's Theorem


1.3 Moments and Generating Functions


1.4 Convolution


1.5 Events at Random in Time


1.6 Probability Density and the Convolution Integral


1.7 The Delta-Function


1.8 Characteristic Functions and the Normal Distribution


1.9 The Rayleigh Distribution


1.10 Entropy as a Measure of Spread


2 Waveform Analysis and Noise


2.1 The Complex Spectrum of Positive and Negative Frequencies0


2.2 The Rectangular Function and its Spectrum


2.3 Parseval's Theorem


2.4 Sampling Analysis


2.5 Sampling of High-Frequency Waveforms


2.6 Poisson's Formula


2.7 Vector Representation of Waveforms


2.8 Uniform Gaussian Noise


2.9 Complex Representation of Real Waveforms


3 Information Theory


3.1 Hartley's Measure of Information Capacity


3.2 Shannon's Measure of Information Content


3.3 Information Gain


3.4 The Symmetrical Formulation of Information Transfer


3.5 Average Expressions


3.6 The Capacity of a Noisy Communication Channel


3.7 Information-Destroying Processes


3.8 Guesswork


4 The Statistical Problem of Reception


4.1 The Ideal Receiver


4.2 Inverse Probability


4.3 Reception of a Steady Voltage in Gaussian Noise


4.4 Sufficiency and Reversibility


4.5 Correlation Reception


4.6 Signals with Unknown Parameters


4.7 Observation Systems and the a Priori Difficulty


4.8 Reception of High-Frequency Signals


4.9 The Complex Formulation


5 Simple Theory of Radar Reception


5.1 The Measurement of Delay


5.2 Threshold Effects


6.3 Continuous Observation and Filtering


5.4 Signals of Doubtful Strength or Existence


5.5 Detection


5.6 Conclusion


6 The Mathematical Analysis of Radar Information


6.1 Introduction


6.2 Complex Signal and Noise Functions


6.3 Range Accuracy


6.4 Noise Ambiguity


6.5 Information Gain


6.6 Discussion of the Threshold Effect


7 The Transmitted Radar Signal


7.1 Accuracy Resolution and Signal Ambiguity


7.2 Ambiguity in Range and Velocity


7.3 The Gaussian Pulse-Train


7.4 Frequency Modulation


7.5 Conclusion


8 Direct Probabilities


8.1 Introduction


8.2 Errors in Binary Decisions


8.3 Signal-to-Noise Ratio


8.4 Envelope Probabilities


8.5 Coherent Versus Incoherent Integration

References

Index