Detection of Signals

Abstract

In digital communications, information is transmitted using a finite number of symbols, say Os and Is. These symbols, if passed through a disturbed channel such as ionosphere or if they are corrupted by a random noise, may be received erroneously at the destination. A signal S T (t) when transmitted through, for example, a scattering or turbulent medium (see Fig. 4.0-la, b) becomes a signal with random phase or amplitude. It is desired to make a decision on the correct value of the transmitted symbols based on the received values of the signal. For example, in a radar system, it is desired to measure the range and velocity of a target (air-craft, ships, or tanks) by processing the reflected pulse. However, the reflected pulse may be due to a cluttered environment and may not be due to a target. In this chapter we will deal with detection of signals in the presence of noise by using methods of testing hypotheses. Hypothesis testing will be discussed in Section 2. Sections 2 and 3 are concerned with detection of signals with known and random parameters. Detection of binary signals in the presence of colored noise is treated in Section 4. Section 5 covers detection of multiple signals. Sequential detection will be described in Section 6. In Section 7, nonparametric methods will be considered. We will deal with, in this chapter, signals with random or unknown phase, frequency, doppler shift, amplitude, and arrival time delay.