This text is the second volume of a series of books addressing statistical signal processing. The first volume,
Fundamentals of Statistical Signal Processing: Estimation Theory, was published in 1993 by Prentice-Hall, Inc.
Henceforth, it will be referred to as Kay-I 1993.
This second volume, entitled Fundamentals of Statistical Signal Processing: Detection Theory, is the application
of statistical hypothesis testing to the detection of signals in noise. The series has been written to provide
the reader with a broad introduction to the theory and application of statistical signal processing. Hypothesis
testing is a subject that is standard fare in the many books available dealing with statistics.
These books range from the highly theoretical expositions written by statisticians to the more practical treatments
contributed by the many users of applied statistics.
This text is an attempt to strike a balance between these two extremes. The particular audience we have in mind
is the community involved in the design and implementation of signal processing algorithms. As such, the primary
focus is on obtaining optimal detection algorithms that may be implemented on a digital computer. The data sets
are therefore assumed to be samples of a continuous-time waveform or a sequence of data points. The choice of topics
reflects what we believe to be the important approaches to obtaining an optimal detector and analyzing its performance.
As a consequence, some of the deeper theoretical issues have been omitted with references given instead. It is
the author's opinion that the best way to assimilate the material on detection theory is by exposure to and working
with good examples. Consequently, there are numerous examples that illustrate the theory and others that apply
the theory to actual detection problems of current interest.
We have made extensive use of the MATLAB scientific programming language (Version 4.2b) Footnote: MATLAB is a registered
trademark of The MathWorks, Inc. for all computer-generated results. In some cases, actual MATLAB programs have
been listed where a program was deemed to be of sufficient utility to the reader.
Additionally, an abundance of homework problems has been included. They range from simple applications of the theory
to extensions of the basic concepts. A solutions manual is available from the author. To aid the reader, summary
sections have been provided at the beginning of each chapter. Also, an overview of all the principal detection
approaches and the rationale for choosing a particular method can be found in Chapter 11.
Detection based on simple hypothesis testing is described in Chapters 3--5, while that based on composite hypothesis
testing (to accommodate unknown parameters) is the subject of Chapters 6--9.
Other chapters address detection in nonGaussian noise (Chapter 10), detection of model changes (Chapter 12), and
extensions for complex/vector data useful in array processing (Chapter 13). This book is an outgrowth of a one-semester
graduate level course on detection theory given at the University of Rhode Island. It includes somewhat more material
than can actually be covered in one semester. We typically cover most of Chapters 1--10, leaving the subjects of
model change detection and complex data/vector data extensions to the student. It is also possible to combine the
subjects of estimation and detection into a single semester course by a judicious choice of material from Volumes
I and II.
The necessary background that has been assumed is an exposure to the basic theory of digital signal processing,
probability and random processes, and linear and matrix algebra. This book can also be used for self-study and
so should be useful to the practicing engineer as well as the student.
The author would like to acknowledge the contributions of the many people who over the years have provided stimulating
discussions of research problems, opportunities to apply the results of that research, and support for conducting
research.
Thanks are due to my colleagues L. Jackson, R. Kumaresan, L. Pakula, and P. Swaszek of the University of Rhode
Island, and L. Scharf of the University of Colorado.
Exposure to practical problems, leading to new research directions, has been provided by H. Woodsum of Sonetech,
Bedford, New Hampshire, and by D. Mook and S. Lang of Sanders, a Lockheed-Martin Co., Nashua, New Hampshire.
The opportunity to apply detection theory to sonar and the research support of J. Kelly of the Naval Undersea Warfare
Center, J. Salisbury, formerly of the Naval Undersea Warfare Center, and D. Sheldon of the Naval Undersea Warfare
Center, Newport, Rhode Island are also greatly appreciated.
Thanks are due to J. Sjogren of the Air Force Office of Scientific Research, whose support has allowed the author
to investigate the field of statistical signal processing. A debt of gratitude is owed to all my current and former
graduate students. They have contributed to the final manuscript through many hours of pedagogical and research
discussions as well as by their specific comments and questions. In particular, P. Djuri'{c} of the State University
of New York proofread much of the manuscript, and S. Talwalkar of Motorola, Plantation, Florida proofread parts
of the manuscript and helped with the finer points of MATLAB.
Steven M. Kay, University of Rhode Island Kingston, RI 02881 Email: [email protected]
Summary
The most comprehensive overview of signal detection available.
This is a thorough, up-to-date introduction to optimizing detection algorithms for implementation on digital
computers. It focuses extensively on real-world signal processing applications, including state-of-the-art speech
and communications technology as well as traditional sonar/radar systems.
Start with a quick review of the fundamental issues associated with mathematical detection, as well as the most
important probability density functions and their properties. Next, review Gaussian, Chi-Squared, F, Rayleigh,
and Rician PDFs, quadratic forms of Gaussian random variables, asymptotic Gaussian PDFs, and Monte Carlo Performance
Evaluations.
Three chapters introduce the basics of detection based on simple hypothesis testing, including the Neyman-Pearson
Theorem, handling irrelevant data, Bayes Risk, multiple hypothesis testing, and both deterministic and random signals.
The author then presents exceptionally detailed coverage of composite hypothesis testing to accommodate unknown
signal and noise parameters. These chapters will be especially useful for those building detectors that must work
with real, physical data. Other topics covered include:
Detection in nonGaussian noise, including nonGaussian noise characteristics, known deterministic signals, and
deterministic signals with unknown parameters
Detection of model changes, including maneuver detection and time-varying PSD detection
Complex extensions, vector generalization, and array processing
The book makes extensive use of MATLAB, and program listings are included wherever appropriate. Designed for
practicing electrical engineers, researchers, and advanced students, it is an ideal complement to Steven M. Kay's
Fundamentals of Statistical Signal Processing, Vol. 1: Estimation Theory.
Table of Contents
(NOTE: Most chapters begin with an Introduction and Summary.) 1. Introduction.
Detection Theory in Signal Processing.
The Detection Problem.
The Mathematical Detection Problem.
Hierarchy of Detection Problems.
Role of Asymptotics.
Some Notes to the Reader.
2. Summary of Important PDFs.
Fundamental Probability Density Functionshfil Penalty - M and Properties.
Quadratic Forms of Gaussian Random Variables.
Asymptotic Gaussian PDF.
Monte Carlo Performance Evaluation.
Number of Required Monte Carlo Trials.
Normal Probability Paper.
MATLAB Program to Compute Gaussian Right-Tail Probability and its Inverse.
MATLAB Program to Compute Central and Noncentral c 2 Right-Tail Probability.
MATLAB Program for Monte Carlo Computer Simulation.
