In the radar system of Example 8.4, show that the ROC in Figure 8.2 is the result of a Neyman-Pearson test. That is, show that the Neyman-Pearson test is a threshold test with acceptance set A0 = {X ≤ x0}. How is x0 related to the false alarm probability α?
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.
Figure 8.2
