Page 122 - Fundamentals of Radar Signal Processing

desired result for the change in angle or frequency required to decorrelate the

echo amplitude:

(2.62)

Note that L cosθ is the projection of the target extent orthogonal to the radar
boresight, while Lsinθ is the projection along the radar boresight. Thus, the
decorrelation interval in aspect angle is driven by the width of the target as
viewed from the radar, while the interval in frequency is driven by the depth. A
more general pair of expressions that can be applied to more arbitrary many-

scatterer targets is then

(2.63)

where L and L are the target width and depth, respectively, as viewed from the
w
d
radar.
As an example, consider a target the size of an automobile, about 5 m long.
At L band (1 GHz), the target signature can be expected to decorrelate in (3 ×
8
9
10 )/(2 × 5 × 10 ) = 30 mrad of aspect angle rotation relative to a broadside
view (so the width is 5 m), about 1.7°, while at W band (95 GHz), this is
reduced to only 0.018°. The frequency step required for decorrelation from a

head-on aspect (depth of 5 m) is 30 MHz. This result does not depend on the
nominal transmitted frequency.
As another example, Fig. 2.13a shows the autocorrelation function in
angle for many-scatterer targets similar to that of Fig. 2.8, using only the data
for aspect angles over a range ±3°. Each of the two autocorrelation functions
shown is the average of the autocorrelations of 20 different random targets, 6
each having 20 randomly placed scatterers in a 5 m by 10 m box. The black

curve is the autocorrelation of the data around a nominal boresight orthogonal to
the 5 m side of the target, while the gray curve is the autocorrelation of the data
viewed from the 10-m side. These look angles correspond to viewing the target
nominally from the right and from the top in Fig. 2.8. At F = 10 GHz, the
expected decorrelation interval in angle when viewed from the right is 0.34°;
while when viewed from the top it is 0.17°. These expected decorrelation

intervals are marked by the vertical dashed lines in Fig. 2.13a. In both cases, the
first minimum of the correlation function occurs the predicted amount of change
in the aspect angle. Figure 2.13b shows the average autocorrelation function in
frequency over 30 similar random targets. The autocorrelation in this simulation
does not have a distinct minimum, but the predicted decorrelation intervals
closely approximate the first zero crossing.