Estimation, Optimization, and Detection

Abstract

Signals are transmitted by pulses or by sinusoidal waveforms. These signals pass through a propagation channel and are received in the presence of atmospheric, optical, or electronic noise. The received signals may differ from the original signals in terms of amplitude, phase, frequency, timing or any combination because of the propagation medium, interference from other sources, and additive noise. Extraction of signals from the noise constitutes the study of statistical interference. Statistics are functions of samples of random signals. Any decisions based on the observed (received) samples and their statistics are the subject of statistical decision theory, which involves (a) estimation theory and (b) detection (decision or hypothesis testing) theory. In this chapter we will deal with estimation theory and elements of binary hypothesis testing.