An X-band radar has the following specifications: received peak power (10^{-10} mathrm{~W}), probability of detection (P_{D}=0.95), time
Question:
An X-band radar has the following specifications: received peak power \(10^{-10} \mathrm{~W}\), probability of detection \(P_{D}=0.95\), time of false alarm \(T_{f a}=8 \mathrm{~min}\), pulse width \(\tau=\) \(2 \mu \mathrm{s}\), operating bandwidth \(B=2 \mathrm{MHz}\), operating frequency \(f_{0}=10 \mathrm{GHz}\), and detection range \(R=100 \mathrm{~km}\). Assume single pulse processing.
(a) Compute the probability of false alarm \(P_{f a}\).
(b) Determine the \(S N R\) at the output of the matched filter.
(c) At what SNR would the probability of detection drop to 0.9 ( \(P_{f a}\) does not change)? (d) What is the increase in range that corresponds to this drop in the probability of detection?
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