p)= xF530 p( ardw-酊M1r-g到s3n The vector likelihood ratio is L()= D -eyw了与r-0wg宁w Do UESTC 6
6 UESTC 1 0 0 0 1 1 ( ) exp [ ] [ ] (5.36) (2 ) det( ) 2 T k p y y u y u − = − − − M M 1 1 1 1 1 1 ( ) exp [ ] [ ] (5.37) (2 ) det( ) 2 T k p y y u y u − = − − − M M The vector likelihood ratio is 1 0 1 1 * * 1 1 1 0 1 0 0 0 1 1 ( ) 1 1 1 1 exp ( ) ( ) 2 2 2 2 D T T T T B D L y u u y y u u u u u u − − − − = − + − + − M M M M
The log-likelihood ratio 0)=Re付M'-+方M-买MG之n,= D The optimum digital detector in additive Gaussian noise can be represented as D e它万}：-对M元+方M元540) Do UESTC 万=M(-)or方=(d-,)TM1 7
7 UESTC 1 0 1 1 1 1 0 0 0 1 1 0 1 1 ( ) Re ( ) ln 2 2 D T T T B D y y u u u u u u − − − = − + − = M M M The optimum digital detector in additive Gaussian noise can be represented as 1 0 1 1 0 0 0 1 1 1 1 Re (5.40) 2 2 D T T T D y h u u u u − − = − + M M The log-likelihood ratio 1 1 1 0 1 0 ( ) or ( ) T T h u u h u u − − = − = − M M
/936 MAC forms dot Real 0 product part Figure 5.1.Functional block diagram of general optimal detector in additive Gaussian noise UESTC 8
8 UESTC
Example 5.3 For ML criterion,the log-likelihood ratio threshold is 0.0.From Eq.(5.40): D RelM RelMM Do U.=ReM元]-)M'或 (5.44) The largest U,determines the decision. UESTC 9
9 UESTC Example 5.3 For ML criterion, the log-likelihood ratio threshold is 0.0. From Eq.(5.40): 1 0 1 1 1 1 1 1 1 0 0 0 1 1 Re[ ] Re[ ] 2 2 D T T T T D y u u u y u u u − − − − − − M M M M 1 1 1 Re[ ] (5.44) 2 T T U y u u u i i i i − − = − M M The largest determines the decision. Ui
36 MAC forms dot Real product part 宿=M动 号M-1 Choose largest MAC forms dot Real product part 福= (M16) 是裙M-1话 5.2.Alternative functional block diagram of optimal detector in additive Gaussian noise UESTC 10
10 UESTC