Signal Detection in Non-Gaussian Noise

This book contains a unified treatment of a class of problems of signal detection theory. This is the detection of signals in addi­ tive noise which is not required to have Gaussian probability den­ sity functions in its statistical description. For the most part the material developed here can be classified as belonging to the gen­ eral body of results of parametric theory. Thus the probability density functions of the observations are assumed to be known, at least to within a finite number of unknown parameters in a known functional form. Of course the focus is on noise which is not Gaussian; results for Gaussian noise in the problems treated here become special cases. The contents also form a bridge between the classical results of signal detection in Gaussian noise and those of nonparametric and robust signal detection, which are not con­ sidered in this book. Three canonical problems of signal detection in additive noise are covered here. These allow between them formulation of a range of specific detection problems arising in applications such as radar and sonar, binary signaling, and pattern recognition and classification. The simplest to state and perhaps the most widely studied of all is the problem of detecting a completely known deterministic signal in noise. Also considered here is the detection random non-deterministic signal in noise. Both of these situa­ of a tions may arise for observation processes of the low-pass type and also for processes of the band-pass type.

Contenu

1 Elements of Statistical Hypothesis Testing.- 1.1 Introduction.- 1.2 Basic Concepts of Hypothesis Testing.- 1.3 Most Powerful Tests and the Neyman- Pearson Lemma.- 1.4 Local Optimality and the Generalized Neyman-Pearson Lemma.- 1.5 Bayes Tests.- 1.6 A Characterization of the Relative Performance of Tests.- 1.6.1 Relative Efficiency.- 1.6.2 Asymptotic Relative Efficiency and Efficacy.- Problems.- 2 Detection of Known Signals in Additive Noise.- 2.1 Introduction.- 2.2 The Observation Model.- 2.2.1 Detection of a Pulse Train.- 2.2.2 Statistical Assumptions.- 2.3 Locally Optimum Detection and Asymptotic Optimality.- 2.3.1 Locally Optimum Detectors.- 2.3.2 Generalized Correlator Detectors.- 2.3.3 Asymptotic Optimality.- 2.3.4 Asymptotic Optimality of LO Detectors.- 2.4 Detector Performance Comparisons.- 2.4.1 Asymptotic Relative Efficiency and Efficacy.- 2.4.2 Finite-Sample-Size Performance.- 2.5 Locally Optimum Bayes Detection.- 2.6 Locally Optimum Multivariate Detectors.- Problems.- 3 Some Univariate Noise Probability Density Function Models.- 3.1 Introduction.- 3.2 Generalized Gaussian and Generalized Cauchy Noise.- 3.2.1 Generalized Gaussian Noise.- 3.2.2 Generalized Cauchy Noise.- 3.3 Mixture Noise and Middleton Class A Noise.- 3.4 Adaptive Detection.- Problems.- 4 Optimum Data Quantization in Known-Signal Detection.- 4.1 Introduction.- 4.2 Asymptotically Optimum Quantization.- 4.3 Asymptotically Optimum Generalized Quantization.- 4.4 Maximum-Distance Quantization.- 4.5 Approximations of Locally Optimum Test Statistics.- Problems.- 5 Detection of Known Narrowband Signals in Narrowband Noise.- 5.1 Introduction.- 5.2 The Observation Model.- 5.3 Locally Optimum Detection.- 5.4 Asymptotic Performance Analysis.- 5.5 Asymptotically Optimum Envelope Quantization.- 5.6 Locally Optimum Bayes Detection.- Problems.- 6 Detection of Narrowband Signals with Random Phase Angles.- 6.1 Introduction.- 6.2 Detection of an Incoherent Signal.- 6.2.1 The Observation Model.- 6.2.2 The Locally Optimum Detector.- 6.3 Detection of a Noncoherent Pulse Train.- 6.3.1 The Observation Model.- 6.3.2 The Locally Optimum Detector.- 6.4 Asymptotically Optimum Quantization.- 6.4.1 M-Interval Envelope Quantization.- 6.4.2 Optimum Envelope Quantization for Gaussian Noise.- 6.4.3 A/-Region Generalized Quantization.- Problems.- 7 Detection of Random Signals in Additive Noise.- 7.1 Introduction.- 7.2 The Observation Model.- 7.3 Locally Optimum Array Detection.- 7.3.1 General Form of the LO Test Statistic.- 7.3.2 LO Statistic for White Signal Sequence.- 7.3.3 LO Statistic for Correlated Signal Sequence.- 7.4 Asymptotic Performance Characteristics.- 7.5 Asymptotically Optimum Quantization.- 7.6 Detection of Narrowband Random Signals.- Problems.- References.