Page 471 - Fundamentals of Radar Signal Processing

unknown, which again is the only realistic assumption that can be made in radar.

It is therefore necessary to resort to a generalized likelihood ratio test (GLRT),
in which the likelihood ratio is written as a function of the unknown signal delay
Δ, and then the value of D that maximizes the likelihood ratio is found. Details
are given in Dudgeon and Johnson (1993). The problem of estimating the time
delay or range that maximizes the likelihood ratio is a major topic in Chap. 7.
The result simply requires evaluation of the matched filter output to identify the

range that produces the maximum output. In practice, each matched filter output
sample is compared to a threshold. If the threshold is crossed, a detection is
declared and the value of Δ at which the threshold crossing occurs is taken as an
estimate of the target delay.
If the target is moving, an unknown Doppler shift will be imposed on the
incident signal. The received echo will then be proportional not to , but to a
modified signal where the samples of the reference signal have been

multiplied by the complex exponential sequence exp(jω n), where ω is the
D
D
normalized Doppler shift. The required matched filter impulse response is now
; if is replaced by in the derivations of Sec. 6.2.2, the same performance
results as before will be obtained. Because ω is unknown, however, it is
D
necessary to test for different possible Doppler shifts by conducting the
detection test for multiple possible values of ω , similar to the procedure used
D
to test for unknown range. If a set of K potential Doppler frequencies uniformly
spaced from –PRF/2 to +PRF/2 is to be tested, the matched filter can be
implemented for all K frequencies at once using the pulse Doppler processing
techniques described in Chap. 5.

6.3 Threshold Detection of Radar Signals
The results of the preceding sections can now be applied to some reasonably
realistic scenarios for detecting radar targets in noise. These scenarios will

almost always include unknown parameters of the signal to be detected (the
target), specifically, its amplitude, absolute phase, time of arrival, and Doppler
shift. Both detection using a single sample of the target signal and, when
available, multiple samples are of interest. In the latter case, as discussed in
Chap. 2, the target signal is often modeled as a random process, rather than a
simple constant; the discussion in this chapter will be limited to the four
Swerling models to illustrate both the approach and the classical, and still very

useful, results obtained in these cases. Furthermore, it will be seen that the idea
of pulse integration is needed in the case of multiple samples. Finally, a square-
law detector will be assumed, though one important approximation that applies
to linear detectors will also be introduced. Figure 6.10 represents one possible
taxonomy of the most common variations on the radar detection problem.