Reference no: EM131083862
In the radar system of Example 8.4, the probability that a target is present is P[H1] = 0.01. In the case of a false alarm, the system issues an unnecessary alert at the cost of C10 = 1 unit. The cost of a miss is C10= 104 units because the target could cause a lot of damage. When the target is present, the voltage is X = 4 + N, a Gaussian (4, 1) random variable. When there is no target present, the voltage is X = N, the Gaussian (0, 1) random variable. In a binary hypothesis test, the acceptance sets are A0 = {X ≤ x0} and A1 = {X > x0}.
(a) What is x0 = xMAP, the decision threshold of the maximum a posteriori probability hypothesis test?
(b) What are the error probabilities PFA and PMISS of the MAP test?
Example 8.4
The noise voltage in a radar detection system is a Gaussian (0, 1) random variable, N. When a target is present, the received signal is X = v + N volts with v ≥ 0. Otherwise the received signal is X = N volts. Periodically, the detector performs a binary hypothesis test with H0 as the hypothesis no target and H1as the hypothesis target present. The acceptance sets for the test are A0 = {X ≤ x0} and A1 = {X > x0}. Draw the receiver operating curves of the radar system for the three target voltages v = 0, 1, 2 volts.
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