相干检测: BPSKX{+ad p(yIh,a) ex 丌N P(ylh,-a)=exp 9/~1y+ha exp piH, +a 丌N + ha-ly-hal ( h,-a = exp TN p/-/+ha y片+10+2Re(y)- hal-2arelh exp a 4a rely exp 信号检测与估值2017年春
信号检测与估值 2017年春 季 6 相干检测：BPSK ( ) 2 0 0 1 | , exp y ha p y h a N N − + = − ( ) 2 0 0 1 | , exp y ha p y h a N N + − = − ( ) ( ) ( ) ( ( )) ( ) 2 2 2 0 0 2 0 0 0 2 2 2 2 * * 0 * 0 1 exp | , exp | , 1 exp 2 Re 2 Re exp 4 Re exp 1 y ha p y h a N N y ha y ha p y h a N y ha N N y ha a h y y ha a h y N a a h y N a − − + + − − = = − + − + + − + − = + = − X== , + − a a
ML检测 /=Re(hy)=Reh(hx+w))=h/x+Re(h w h"x+Re((hr-jh,)(WR+jw ) =hx+hWR+h, w,=h x+z h.w. th E(=)=E(h2+b)=h2E(g)+hE(v)=0 Var (+)] E(y)2+(1)+2 =hE(v0)+2E()+2bE() +: 2 信号检测与估值2017年春 7
信号检测与估值 2017年春 季 7 ML检测 ( ) ( ) ( ) (( )( )) 2 * * * 2 2 2 Re Re ( ) Re Re R I R I R R I I l h y h hx w h x h w h x h jh w jw h x h w h w h x z = = + = + = + − + = + + = + R R I I z h w h w = + ( ) ( ) ( ) ( ) 0 E z E h w h w h E w h E w R R I I R R I I = + = + = ( ) ( ) (( ) ( ) ) ( ) ( ) ( ) ( ) 2 2 2 2 2 2 2 2 2 2 0 0 2 2 2 2 R R I I R R I I R I R I R R I I R I R I R I Var z E h w h w E h w h w h h w w h E w h E w h h E w w N N h h h = + = + + = + + = + = 2 0 0, 2 N z N h
ML检测 N|0 x+z 1|dN(a.N/2) 1-a-N(ha, Nol (E(|-a)-E(|+a)(-ha-hla)82b2 Var(!1-a) a P()=9 SNR SNR=a/No snR per symbol time 信号检测与估值2017年春 8
信号检测与估值 2017年春 季 8 ML检测 ( ( ) ( )) ( ) ( ) 2 2 2 2 2 0 0 | | 8 | 2 E l a E l a h a h a a h d Var l a N N − − + − − = = = − z z h = 0 0, 2 N z N l l h h x z = = + l a N h a N | , 2 + ( 0 ) l a N h a N | , 2 − −( 0 ) ( ) ( ) 2 0 2 2 2 e d a h P h Q Q Q h SNR N = = = 2 0 SNR a N = ,SNR per symbol time
BER Proof p()=c()=en会 P()=(V24NR) 信号检测与估值2017年春
信号检测与估值 2017年春 季 9 BER Proof ( ) 2 2 2 , ( ) , h u p h e p u e u h − − = = P h Q uSNR e ( ) = ( 2 )
BER Proof P(u)()du=f e( 2u uSNr du exp NR exp t' t/2snro-u dudt exp √2丌 2 SNR SNR snr 信号检测与估值2017年春 10
信号检测与估值 2017年春 季 10 BER Proof ( ) ( ) 2 0 0 2 0 2 2 2 0 0 2 0 ( ) 2 1 exp 2 2 1 exp 2 2 1 1 1 exp 1 2 2 2 1 1 2 1 u e e u uSNR t SNR u P P u p u du Q uSNR e du t e dtdu t e dudt t dt SNR SNR SNR − − − = = = − = − = − − + = − +