Page 175 - Fundamentals of Radar Signal Processing

exponential PDF is a good model for the RCS statistics, and again when a

fourth-degree chi-square is a good model for the statistics. What is the
ratio of the exponential PDF value to the chi-square PDF value? Repeat for
σ > 10.

13. A ground-based airport surveillance radar has an antenna that rotates at 10
rpm (revolutions per minute). The 3-dB azimuth bandwidth of the antenna
is 3º. Assume the PRF is chosen to give an unambiguous range of 150 km.
How many pulses will be transmitted during the time a given target is
within the antenna mainbeam during a single rotation? (This is the number

of “hits” the radar gets on the target on each rotation.)

14. Consider a complex target with dimensions of 2 m by 4 m. What is the
maximum change in aspect angle needed to decorrelate the target RCS,
assuming the radar frequency remains fixed at F = 3 GHz? Repeat for F =
35 GHz.

15. For the same target considered in the previous problem, what is the
maximum frequency step needed to decorrelate the target RCS, regardless
of radar-target aspect angle?

16. A stationary, fixed-frequency radar collects several CPIs of data, each
consisting of several pulses, from a stationary complex target. What is an
appropriate correlation model for this data within a CPI? What is the

appropriate model from one CPI to the next? Justify the answers.

17. Consider a radar at a fixed height above the ground of h m, with the
boresight intercepting the ground at a slant range of R m. Show that in this
scenario, the constant-gamma model for σ given by Eq. (2.64) implies that
0
the received clutter power will be proportional to R if the clutter echo is
–2
beam-limited. What will be the proportionality if σ is independent of
0
grazing angle?

18. Use the GTRI clutter model of Eq. (2.65) with λ = 3 cm and the X-band
data in Table 2.6 to compute and plot or sketch on a single graph the
0
variation in σ in dBsm for grass, trees, and urban clutter as the grazing
angle δ varies from 10° to 70°. Assume σ = 10λ.
h
0
19. Show that the GTRI model predicts that σ becomes independent of surface
roughness when σ 10λ.
h
20. Consider the four radar system parameters of antenna azimuth plane size,
antenna elevation plane size, transmitter power, and pulse length. Which of
these affect the signal-to-clutter ratio (SCR) in a beam-limited area clutter
scenario? Repeat for a pulse-limited area clutter scenario. Justify the

answers.

21. Use the Billingsley clutter model to estimate the time lag required for the