Composite Test The detection statistics Constant False Alarm,e.g.,PrA=P(H1;Ho) Under Ho I(x)~N(0,02/N) PrA=P(T()>Y;Ho)=fH(t)dt=Q(Y/V2TN Po)-(P- Pp is a function of the unknown parameter A For each value of A,this detector is optimal Uniform Most Powerful(UMP) whxiong@uestc.edu.cn 11whxiong@uestc.edu.cn Composite Test 11 The detection statistics Constant False Alarm, e.g., T(x) = 1 N Xx[n] PFA = P(H1; H0) Under H0 T(x) » N(0; ¾ 2 =N) PFA = P(T(x) > ° 0 ; H0) = Z 1 °0 fH0 (t)dt = Q ³ ° 0 = p ¾2 =N ´ ° 0 = r ¾2 N Q ¡1 (PFA) PD = P(T(x) > ° 0 ; H1) = Q Ã °0 ¡ A p ¾2 =N ! = Q µ Q ¡1 (PFA) ¡ q NA 2 =¾2 ¶  PD is a function of the unknown parameter A  For each value of A, this detector is optimal Uniform Most Powerful (UMP)