APMA 3100, Class Work 25 - Section 11.2 1
1. 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= 6 + Nvolts, a Gaussian (6,1)
random variable. Otherwise, the received signal is X=Nvolts.
Periodically, the detector performs a binary hypothesis test with null hypothesis H0: no
target is present, and alternative hypothesis H1: a target is present.
The acceptance sets for the test are A0={X≤x0}and A1={X > x0}. The probability
of a target is P[H1]=0.05.
For the MAP hypothesis test, answer the following questions.
(a) Find the decison threshold x0=xMAP.
(b) Find the probability of a false alarm PFA.
