Page 435 - Fundamentals of Radar Signal Processing

2
i.e., assume σ = 0. Assume the stationary clutter c[m] has power and
n
first autocorrelation lag . Use the vector approach to find the
coefficients of the optimum two-pulse (N = 2) matched filter for this case.
Compare to the N = 2 vector matched filter for the stationary radar. Explain
how the shift in the clutter power spectrum center frequency changes the
coefficients. Interpret the resulting coefficients as in the previous problem.

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

interference is white noise plus a pure complex sinusoid at some specific
normalized radian frequency ω , and (b) target velocity is uniform random
J
over the entire spectrum. Specifically, the interference signal becomes

where n[m] is a stationary white noise process with power . This could
be a simple model for a jammer at frequency ω . What is the frequency
J
response H(ω) of the filter having the resulting coefficients? Explain how
this frequency response will affect the jammer and target signals.

11. Consider a pulse-to-pulse staggered PRF system using a series of P = 3
PRIs, namely .

a. What are the base interval T and the set of staggers {k }?
p
g
b. What is the average PRI, T ?
avg
c. What is the first blind Doppler frequency, F , of the staggered system?
bs
d. What is the ratio F /F of the first blind Doppler of the staggered
bs
b
system to the first blind speed of a constant-PRF system having the
average PRI T ?
avg
12. Now consider the effect of the staggered PRIs of the previous problem on
range coverage.

a. What is the unambiguous range, R , corresponding to the average PRI
us
from Prob. 11? (This would be the unambiguous range of a constant-

PRI system that used the same amount of time to collect N pulses as
the staggered-PRF system.)
b. For the three PRFs in Prob. 11, what is the maximum unambiguous

range R ?
uas
c. What is the factor by which the range coverage (unambiguous range) is
reduced in the staggered PRF system of Prob. 11 relative to the
unstaggered system?

13. Using the numerical results from the previous two problems, determine the