Signal Detection and Estimation Theory

Introduction to Detection and Estimation

Hierarchy of Detection Problems

The detection problem in its simplest form assumes that both signal and noise characteristics are completely known. If the characteristics of signal and/or noise are unknown or not known completely it leads to detection problem becoming more challenging as well as complex. The hierarchy of the detection problems along with their typical applications are listed in Table 1.2.

Conditions Applications
Level 1: Known signals in noise 1. Synchronous digital communication
2. Pattern recognition
Level 2: Signals with unknown parameters in noise 1. Digital communication system without phase reference
2. Digital communication over slowly fading channels
3. Conventional pulse radar and sonar, target detection
Level 3: Random signals in noise 1. Digital communication over scatter link
2. Passive sonar
3. Radio astronomy (detection of noise sources)

Table 1.2: Hierarchy of signal detection problems

1.1.3 Organization of the Material

The signal detection and parameter estimation problems are closely linked and often we are required to address both problems in the same system. But they both have their separate applications. As the detection theory employes many concepts and techniques developed for the estimation theory, we first present the estimation theory concepts and then the detection theory concepts. Further most of the real world problems involve analog observations; so traditionally the detection and the estimation theories were developed for the continuous-time domain. But nowadays as most of the signal processing is done on digital computers, the detection and the estimation theories are analogously developed for the discrete-time domain. In this material, only the discrete-time cases are considered.

In this material, we begin with classical estimation methods which include: minimum variance unbiased estimator (MVUE), best linear unbiased estimator (BLUE), maximum likelihood estimator (MLE) and least squares estimator (LSE). These estimators are discussed in Modules 2-5. It is followed by the Bayesian estimation methods. These techniques are discussed in Modules 6-7. In detection theory, we first describe different types of dection criteria in Modele 8. It is followed by brief introduction to non-parametric detection methods in Module 9. Finally we describe a detection of deterministic and random signals in white Gaussian noise in Modules 10-11. At the end of this material some long answer and multiple-choice type questions are given in Module 12.

1.1.4 References

The material presented in this web-course is majorly adapted from following two books which are among the best resources on this topic.

In addition to above, some of the other noted references on this topic are:

  1. H. Vincent Poor, “An Introduction to Signal Detection and Estimation”, 2e, Springer, 1998.
  2. Harry L. Van Trees, “Detection , Estimation and Modulation Theory ”, Part- I, II, & III, John Wiley & Sons, 2004
  3. Louis L. Scharf, “Statistical Signal Processing: Detection, Estimation and Time Series Analysis”, Prentice Hall, 1991.
  4. Carl W. Helstrom, “Elements of Signal Detection & Estimation”, Prentice Hall, 1994.
  5. M. D. Srinath, P. K. Rajasekaran and R. Visawanath, “Introduction to Statistical Signal Processing with Applications”, Prentice Hall, 1995.