Signal Detection and Estimation, Second Edition
Packed with over 2,100 equations, 230 figures and 183 problems, this authoritative resource helps you apply the material to projects in the field involving signal processing, radar, and communications.
TABLE OF CONTENTS Signal Detection and Estimation, Second Edition
10.2: BINARY DETECTION
10.2 BINARY DETECTION
In a binary communication problem, the transmitter may send a deterministic signal s 0( t) under the null hypothesis H 0, or a deterministic signal s 1( t) under the alternate hypothesis H 1. At the receiver, the signal is corrupted by W(t), which is an additive white Gaussian noise process. Assume that the additive noise is zero mean and has a double-sided power spectral density of N 0/2. The goal is to design an optimum receiver that observes the received signal Y( t) over the interval t ? [0, T], and then decides whether hypothesis H 0 or hypothesis H 1 is true.
10.2.1 Simple Binary Detection
In a simple binary detection problem, the transmitted signal under hypothesis H 1 is s( t), and no signal is transmitted under the null hypothesis H 0. At the receiver, we have
Note that the signal is a continuous time function. In order to obtain a set of countable random variables so that we may apply the concepts developed in Chapter 5, we need to take K samples, where K may be infinite. However, in Chapter 8, we saw that a continuous time signal may be represented by Karhunen-Lo ve expansion using a set of K complete orthonormal functions. The coefficients in the series expansion are the desired set of random variables.
The energy of the known deterministic signal...
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