Page 542 - Fundamentals of Radar Signal Processing

α
χ /x = N . What would be the value of α for coherent integration? Which
1
nc
is more efficient (obtains more gain for the same number of samples
integrated), coherent or noncoherent integration?

17. Consider 3-out-of-5 (M = 3, N = 5) binary integration. Determine the
required values of the single-trial probabilities P and P such that the
D
FA
–8
cumulative probabilities are P CFA = 10 and P = 0.99. A small-
CD
probability approximation can be used to solve for P , but finding P will
FA
D
require some numerical trial-and-error; the estimate of P should be
D
accurate to two decimal places. (Hint: The correct answer lies in the range
0.87 ≤ P ≤ 0.92.)
D
18. A single noncoherently detected sample of a nonfluctuating target in
complex Gaussian noise with power is to be tested for the presence
of a target. A square-law detector is used. Assuming the interference
power level exactly, what ideal value of threshold T is required to obtain
–4
P = 10 ? If the SNR is χ = 10 dB, what is P ? MATLAB® and one of
D
FA
the computer functions mentioned in Prob. 8 or their equivalent will be
needed to evaluate the Marcum Q function Q .
M
19. Now assume that the interference level is not known a priori, so a cell-
averaging CFAR is used to perform the detection test. Choose N = 30
reference cells. What will be the threshold multiplier α such that the
–4
average false alarm probability remains at 10 ? It turns out that if the
SNR is χ = 10 dB, the value of P using the ideal threshold in the previous
D
problem is 0.616. Assuming the SNR is still χ = 10 dB, what will be the

average detection probability using the CA-CFAR?

20. Suppose the threshold in a standard (non-CFAR) threshold detector
–6
designed using the Neyman-Pearson approach is chosen to give P = 10 .
FA
If the interference power level increases by 6 dB, what will be the new
value of P ?
FA
21. Consider a detector designed to give an average false alarm probability of

. What is the SNR χ in dB required to achieve = 0.9 when using
∞
the ideal Neyman-Pearson threshold? What SNR χ in dB is required when
N
using a cell-averaging CFAR with N = 16 reference cells? What is the
CFAR loss for this case, in dB?

22. Consider a CA-CFAR with a single interfering target (the “target masking”
problem). Assume the SNR χ of the target of interest in the cell under test

is 15 dB. What is the approximate “target masking loss” in dB if the SNR χ i
of the interferer is 10 dB? Repeat for χ = 15 dB. Assume the number of
i
averaging cells is N = 20. Compute the results numerically and show all
work. Figure 6.23 can be used as an approximate check of the results.

23. Consider an order statistic CFAR in exponentially-distributed interference