Page 436 - Fundamentals of Radar Signal Processing

percentage by which the total range-velocity coverage, defined as the

product of the unambiguous range and first blind Doppler, increased in the
staggered case as compared to the unstaggered case? In other words,
compute R F /R F . Show that the numerical results agree with the result
ua b
uas
bs
predicted by Eq. (5.46).
14. Assume a set of integer staggers {k } is mutually prime. Show that
p
lcm{1/k } = 1. Hint #1: For any set of numbers β, α ·lcm(β , …, β } =
p
p
1
lcm(αβ , …, αβ }. Hint #2: Use hint #1 with a = β · β · … · β and the
2
1
p
1
p
prime factorization method for finding the least common multiple.
15. Consider a three-pulse canceller; thus the filter coefficients are h[m] = {1,
–2, 1}. Suppose the clutter c[m] at the canceller input has an
autocorrelation function given by

a. Find the clutter power spectrum on a normalized radian frequency
scale, S (ω).
c
b. The improvement factor I was expressed as the product of “gain” and
“clutter attenuation,” I = G·CA, in Eq. (5.48). Find the gain G for the
three-pulse canceller using Eq. (5.49).

c. Use the autocorrelation method to find the improvement factor I for the
three-pulse canceller with this clutter process.

16. Repeat Prob. 15(c) using the frequency domain approach. The value of G
from Prob. 15(b) can be reused.

17. Repeat Prob. 15(c) using the vector matched filter approach. Recompute
both G and CA using the vector method.

18. Compute the clutter attenuation CA when using a two-pulse canceller,
assuming the clutter Doppler power spectrum is of the form

Assume F ≤ PRF/2 and express the answer in terms of F .
co
co
19. Consider an M = 32 pulse sequence of slow-time data collected with PRF

= 10 kHz. A radix 2 FFT algorithm is used to compute the Doppler
spectrum of the data. If the Doppler frequency samples are to have a
spacing of 100 Hz or less, what is the minimum FFT size K that should be
used? What is the resulting spacing of the Doppler frequency samples in
hertz?