Page 125 - Fundamentals of Radar Signal Processing

many radars operate on the magnitude-squared of the echo amplitude, rather than

the magnitude as has been assumed in this derivation. A square law detector
produces a correlation function proportional to the square of Eq. (2.60)
(Birkmeier and Wallace, 1963). The first zero therefore occurs at the same
value of ΔK , and the previous conclusions still apply. However, if a different
θ
definition of the correlation interval is used (such as the 50 percent
decorrelation point), the required change in ΔK is less for the square law than
θ
for the linear detector.

2.2.6 Target Fluctuation Models
It is common in radar detection algorithms to make a detection decision based
not on one, but on a set of N noncoherently combined measurements from a
given resolution cell. One way such a set of measurements can arise, and
possibly the original motivation for this model, is based on the operation of a
ground-based surveillance radar. Consider a radar with an antenna that rotates

at a constant angular velocity Ω radians per second with an azimuth beamwidth
of θ radians and a pulse repetition frequency of PRF pulses per second (hertz).
Suppose that a target is present at a particular location. The geometry is shown
in Fig. 2.15a. Assume that significant returns are received only when the target
is in the antenna mainlobe. Every complete 360° scan of the antenna results in a
new set of N = (θ/Ω)PRF mainbeam pulses containing an echo of the target as

the beam scans past. Consequently, it would seem to make sense to integrate the
measurements from the same range bin over N successive pulses in an attempt to
improve signal-to-noise ratio before performing a detection test. Early radars
could only do this noncoherently.

FIGURE 2.15 Sample scenarios for collection of multiple noncoherently related
measurements: (a) rotating surveillance antenna with noncoherent radar, (b)
multiple CPIs with a coherent radar.