A radar system transmits a signal and recieves reflected signals from the background and, on occasion, targets. If no target is present, the PDF of the reflected signal is N 0, s2 and if a target is present the reflected signal is N 1, s2 .

(a) Derive a formula for the log likelihood ratio for the received signal.

(b) Use the Neyman Pearson criteria to find a formula for the threshold value that produces a false alarm (false positive) rate of a.

(c) For s = 1, 0 = 1, 1 = 4, and a = 104, find the threshold value and the probability of hit (true positive).