Page 454 - Fundamentals of Radar Signal Processing

FIGURE 6.3 Two ways to modify the PDFs of Fig. 6.1 to improve the tradeoff
between detection and false alarms: (a) increasing the signal power, (b)
reducing the noise power.

The second way to improve the performance tradeoff is to reduce the

overlap of the PDFs by reducing their variance. Reducing the noise power
will reduce the variance of both PDFs, leading to the situation shown in Fig.
6.3b (where the area corresponding to P is too small to be seen) and again
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improving performance. As with the first technique of increasing m, reducing

again constitutes increasing the SNR. Thus, consistent with Eq. (6.25),
improving the tradeoff between P and P requires increasing the SNR χ. This
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is a fundamental result that will arise repeatedly.
Radar systems are designed to achieve specified values of P and P FA
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subject to various conditions, such as specified ranges, target types, interference
environments, and so forth. The designer can work with antenna design,
transmitter power, waveform design, and signal processing techniques, all
within cost and form factor constraints. The job of the designer is therefore to

develop a radar system design which ultimately results in a pair of “target
absent” and “target present” PDFs at the point of detection with a small enough
overlap to allow the desired P and P to be achieved. If the design does not
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do this, the designer must redesign one or more of these elements to reduce the
variance of the PDFs, shift them further apart, or both until the desired

performance is obtained. Thus, a significant goal of radar system design is
controlling the overlap of the two PDFs analogous to those in Fig. 6.1, or
equivalently, maximizing the SNR.

6.2 Threshold Detection in Coherent Systems

The Gaussian problem considered so far is useful to introduce and explain the
major elements of Neyman-Pearson detection such as the likelihood ratio test,
probabilities of detection and false alarm, receiver operating characteristics,
and the major design tradeoffs that follow. The problem seems “radar-like”:

under one hypothesis, only Gaussian noise is observed; under the other, a
constant was added to the noise, which could be interpreted as the echoes from
a steady target. Figure 6.4 summarizes the design and analysis strategy that was
used. Beginning with models of the PDF of the data under hypotheses H and H ,
0
1
the LRT or log-LRT is written down and manipulated to isolate the terms
involving the measured data. If necessary or useful, a simplified detector law is
substituted (see Section 6.2.3). The sufficient statistic is then identified and its

PDF under each hypothesis determined. The PDF under H is integrated to get a
0
relationship between the threshold T and the P which is solved analytically or
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