Page 79 - Fundamentals of Radar Signal Processing

range (fast time) for a single transmitted pulse. It crosses the threshold at three

different times, suggesting the presence of three targets at different ranges.

FIGURE 1.24 Illustration of threshold detection.

Because they are the result of a statistical process, threshold detection
decisions have a finite probability of being wrong. For example, a noise spike
could cross the threshold, leading to a false target declaration, commonly called
a false alarm. These errors are minimized if the target spikes stand out strongly
from the background interference, i.e., if the SIR is as large as possible. If this is
the case the threshold can be set relatively high, resulting in few false alarms
while still detecting most targets. This fact also accounts for the importance of
matched filtering in radar systems. The matched filter maximizes the SIR, thus

providing the best threshold detection performance. Furthermore, the achievable
SIR increases monotonically with the transmitted pulse energy E, thus
encouraging the use of longer pulses to get more energy on the target. Since
longer simple pulses reduce range resolution, the technique of pulse
compression is also important so that fine resolution can be obtained while

maintaining good detection performance.
The concept of threshold detection can be applied to many different radar
signal processing systems. Figure 1.24 illustrates its application to a fast-time
(range) signal trace, but it can be equally well applied to a signal composed of
measurements at different Doppler frequencies for a fixed range, or in a two-
dimensional form to combined range-Doppler data or to SAR imagery.
There are numerous significant details in implementing threshold detection.

Various detector designs work on the magnitude, squared-magnitude, or even
log-magnitude of the complex signal samples. The threshold is computed from
knowledge of the interference statistics so as to limit false alarms to an
acceptable rate. However, in real systems the interference statistics are rarely
known accurately enough to allow for precomputing a fixed threshold. Instead,