Detection in Noise

Abstract

Detection is the process by which the presence of the sought-after object, or target, is sensed in the presence of competing indications which arise from background echoes (clutter), atmospheric noise, or noise generated in the radar receiver. The characteristics and effects of background clutter are discussed in Chapter 10. Atmospheric and receiver noise voltages result from random electron movement in the atmosphere and in electrically conducting radar components, respectively. These time-varying voltages are called random processes and are described by a well-defined mathematical formula. When the target return is added to the noise voltage, the result is also a random process. Random processes are defined by statistical measures such as the probability density and autocorrelation functions. Sometimes the power density spectrum (PDS) is used to define random processes in addition to or instead of the autocorrelation function.

The noise power present at the output of the radar receiver can be minimized by using a filter that passes most of the target return energy while rejecting much of the noise energy. Such a filter, whose frequency response function maximizes the output peak-signal to mean-noise (power) ratio is called a matched filter. Matched filter approximations are used extensively in radar systems. The rule of thumb in radar practice is that the matched filter bandwidth should be approximately equal to the reciprocal of the pulse width. This is a reasonable approximation for pulse radars.

Correlation detection is mathematically equivalent to matched filter detection but is implemented differently. In correlation detection, the input signal is multiplied by a delayed replica of the transmitted signal, and the product is passed through a low-pass filter. The matched filter receiver, or an approximation, is generally preferred to the cross-correlation receiver in the vast majority of applications.

The envelope of an IF carrier within a radar receiver contains the information that is used to determine if a target is present or not. The radar detection process is almost always described in terms of threshold detection. If the envelope of the receiver output exceeds a preestablished threshold, a target is said to be present. Of course, with this type of detection, errors are made. Sometimes a target that is present is missed, and sometimes a target is declared to exist when none is present. These two situations are called missed targets and false alarms, respectively. The threshold detector is sometimes called a Neyman-Pearson detector. Other statistical criteria usually discussed when considering detection of targets in noise are the likelihood ratio and inverse probability, but these two types of receivers are seldom implemented in practice.

The portion of the radar receiver that extracts the modulation from the carrier is called the detector. One form of detector is the envelope detector, which recognizes the presence of the signal on the basis of the amplitude of the carrier envelope. When this detector is used, all phase information is ignored. It is also possible to design a detector which utilizes only phase information for detecting targets.

The most efficient detector is the coherent detector. With this detector, the reference oscillator signal is assumed to have the same frequency and phase as the input signal and simply provides a translation of the carrier frequency to DC. This detector does not ignore phase information, as does the envelope detector, but passes all of the modulation information to the detector output. Thus, it is not surprising that the coherent detector provides better performance than other detectors. Since the phase of the received signal is usually not known, a variation of the coherent detector called the synchronous detector, or I&Q detector, is usually utilized. The performance of the I&Q detector is equivalent to that of a coherent detector.

The rate of information production inherent in a typical radar signal is considerably greater than can be handled by a human operator. Thus, the function of the radar display is to aid the operator in efficiently extracting the information that is important to the task. In some radar systems, automatic detection is employed to overcome the limitations of an operator due to fatigue, boredom, or overload. In addition, automatic detection allows the radar output to be transmitted over communication links.