Page 434 - Fundamentals of Radar Signal Processing

below the aircraft, (d) on the ground directly to the left or right of the

aircraft (azimuth angle of ±90°), and (e) directly behind the aircraft?

5. Verify all of the calculations regarding Fig. 5.4 given in the text. These
include boresight range to the ground, component of velocity along the
boresight, Doppler shift at the middle of the mainlobe clutter, maximum
Doppler shift of clutter, and maximum radial velocity of clutter.

6. For the aircraft in Prob. 4, sketch the approximate unaliased slant range-
velocity distribution of the ground clutter (mainlobe + sidelobe) in a
“bird’s-eye” format similar to that of Fig. 5.36a. The slant range axis of the
sketch should cover 0 to 100 km and the velocity axis should cover ±v max ,

where v max is the maximum possible radial velocity in meter per second
that could be observed from scatterers in front of the radar. It is not
necessary to represent antenna gain effects; concentrate on indicating
where the mainlobe clutter will be centered and the intervals in range and
velocity where clutter energy will be seen.

7. Suppose the radar in the previous problem has an operating frequency of 10
GHz and a PRF of 3 kHz. What are the unambiguous slant range R and
ua
blind velocity interval v ? Sketch the approximate aliased range-velocity
b
distribution of the ground clutter (mainlobe + sidelobe) in a format similar
to that of “bird’s-eye” format similar to that of Fig. 5.36c. The slant range
axis of the sketch should cover 0 to R and the velocity axis should cover
ua
±v = ±v /2. Concentrate on indicating where the mainlobe clutter will be
ua
ub
centered and the intervals in range and velocity where clutter energy will
be seen.

8. Use the vector form of the matched filter to find the coefficients of an
optimum two-pulse (N = 2) MTI filter under the assumptions that (a) the

interference is white noise only, and (b) only approaching targets are of
interest, that is, those with positive Doppler shifts; however, targets can be
approaching with any positive velocity between 0 and λ · PRF/4
(corresponding to F = PRF/2) being equally likely. Repeat for receding
D
targets. Interpret the result: that is, explain how the particular form of the
filter coefficients will maximize the SIR at the filter output for this target
and interference model.

9. Suppose an MTI radar is placed on a moving platform such that the clutter

spectrum, rather than being centered at normalized radian frequency ω = 0,
is instead centered on ω = π/2. If the clutter observed by a stationary
platform was c[m], the new clutter process can be modeled crudely as
c′[m] = c[m]exp(jπm/2). (This is an oversimplified model because it does
not account for the broadening of the clutter spectrum caused by platform
motion, but that effect is ignored in this problem for simplicity.) Assume
the target can be at any velocity with equal likelihood. Ignore the noise,