TABLE OF CONTENTS The radar signal can be represented by a sinusoidal RF carrier with (usually) narrowband modulation of its amplitude and phase superimposed by the transmitter, the antenna, and the target. Narrowband here means that the modulation bandwidth is a small fraction of the carrier frequency. Detection of a target requires that the receiver output, consisting of signals, noise, and other interference, be processed in such a way that the desired signal causes an output (an alarm) with a specified (usually high) probability, while noise and interference produce random false alarms with low probability. The probabilities of detection and false alarm are determined by the amplitude distribution (probability density function, or pdf) of the noise and interference, and that of the signal accompanied by these unwanted components. In this chapter, we will consider primarily the pdf which results from thermal (Gaussian) noise, added to a sinusoidal signal.
Procedures will be developed by which the detection probability P d can be calculated when the available SNR and false-alarm probability P fa are known. Other procedures will be given to find the required SNR, or detectability factor D, when the required values of P d and P fa are given. The basic definition of detectability factor is, from [1, p. 277]:
In pulsed radar, the ratio of single-pulse signal energy to noise power per unit bandwidth that provides stated probabilities of detection and false alarm, measured in the intermediate-frequency amplifier and using an intermediate-frequency filter matched to...
