Therefore,D is chosen when p(B )IC(B)-C(B)dB Po(Bo)p(BIC(B)-Coo(B)1dB 元1 If the costs are independent of B,and B,then D,is chosen if Bp(B)dB π(Ci0-Co) JEp,G川B)p(A)Mg π(Co1-C1) UESTC
11 UESTC Therefore, D1 is chosen when 1 0 1 1 1 01 1 11 1 1 0 0 0 0 10 0 00 0 0 1 ( | ) ( )[ ( ) ( )] ( | ) ( )[ ( ) ( )] p y p C C d p y p C C d − − If the costs are independent of and , then D1 is chosen if 0 1 1 0 1 1 1 1 0 10 00 0 0 0 0 1 01 11 ( | ) ( ) ( ) ( ) ( | ) ( ) ( ) p y p d C C L y p y p d C C − = −
6.2.2 Unknown density functions Maximum-Likelihood technique p川B) max (6.15) B-Bo po(yBo) Generalized LG) max p(yB) (6.16 likelihood- maxp,(y|B)） ratio test (GLRT) LG)=G) (6.17) Po(yB) where B.,i=0,1 is the ML estimate of B,i=0,1 UESTC 12
6.2.2 Unknown density functions • Maximum-Likelihood technique 12 UESTC 1 0 1 1 , 0 0 ( | ) max (6.15) ( | ) p y p y 1 0 1 1 0 0 max ( | ) ( ) (6.16) max ( | ) p y L y p y = ^ 1 1 ^ 0 0 ( | ) ( ) (6.17) ( | ) p y L y p y = where , i=0,1 is the ML estimate of , i=0,1. ^ i i Generalized likelihoodratio test (GLRT)
936 ML estimator e ReO⊕ 0 aui(t-io) 2e1 er✉i+20-》 Re( o audt -1o) Peo UESTC 13
13 UESTC
5 Least favorable density function technique Another technique that is used is to assume least favorable density functions. Conditional likelihood-ratio technique L(川R,R)=D1B) po(yBo) If the decision test is independent of the specific density function,it is called a uniformly most powerful test (UMPT). UESTC 14
• Least favorable density function technique Another technique that is used is to assume least favorable density functions. • Conditional likelihood-ratio technique If the decision test is independent of the specific density function, it is called a uniformly most powerful test (UMPT). 14 UESTC 1 1 0 1 0 0 ( | ) ( | , ) ( | ) p y L y p y =
6.3 Unknown phase The received signal can be expressed as: y(t)= aa,(t-to)exp[J2(f+fa)(t-to)+(t-t)+B]+z(t). i=0,l;t≤t≤T+to f=to=0,Sampling ↓au)bexplJ2z/,+,川 aa,(t)exp[J2ft(tB.]+z(t)=au,exp(JB,)+ i=0,1; j=1,…k (6.22) UESTC 15
6.3 Unknown phase The received signal can be expressed as: 15 UESTC 0 0 0 0 0 ( ) ( )exp[ [2 ( )( ) ( ) ]] ( ), 0,1; i i i d i y t a t J f t t f t t z t t t T t i t = − + − + − + + = + ( )exp[ [2 ( ) ]] exp( ) , ( ) 0,1; 1, (6.22) j i j i j i j i j i j ij y a t J f t t z t J z i j u k = + + + = + = = 0 0 d f t = = ， ( )exp[ [2 ( )]] i j i j i j a t J f t t + Sampling