Mathematical Foundations for Signal Processing, Communications, and Networking

Chapter 11  Fundamentals of Detection Theory

Venugopal V. Veeravalli^‡

^‡ University of Illinois at Urbana-Champaign, USA

11.1    Introduction

Detection problems arise in a number of engineering applications such as radar, communications, surveillance, and image analysis. In the basic setting of the problem, the goal is to detect the presence or absence of a signal in noise. This chapter will provide the mathematical and statistical foundations for solving such problems.

11.1.1    Statistical Decision Theory Framework

Detection problems fall under the umbrella of statistical decision theory [1], where the goal is to make a right (optimal) choice from a set of alternatives in a noisy environment. There are five basic ingredients in a typical decision ...