An X-band radar has the following specifications: received peak power 10-10 W, probability of detection P = 0.95, time of false alarm Tya = 8min, pulse width = 2s, operating bandwidth B = 2MHz, operating frequency fo=10GHz, and detection range R = 100Km. Assume single pulse processing.

(a) Compute the probability of false alarm Pfa.

(b) Determine the SNR at the output of the matched filter.

(c) At what SNR would the probability of detection drop to 0.9 (Pfa does not change)?

(d) What is the increase in range that corresponds to this drop in the probability of detection?