Chapter 6 Detection of signals with random parameters UESTC 1
1 UESTC Chapter 6 Detection of signals with random parameters
Detection of binary hypothesis:One of two possible signals is transmitted by source where a valid continuous-time representation is s,(t)=a,(t)Cos[2π(f+fe)t+(t)];i=0,1;0≤t≤T s④=Re[a（)eew]6.2) 4,(t)=a,(t)e2+;i=0,1; 0≤t≤T UESTC 2
2 UESTC Detection of binary hypothesis: One of two possible signals is transmitted by source where a valid continuous-time representation is ( ) ( )cos[2 ( ) ( )]; 0,1;0 i i i c i s t a t f f t t i t T = + + = (2 ( )) ( ) ( ) ; 0,1; 0 i i J f t t i i u t a t e i t T + = = ( ) (2 ) ( ) Re (6.2) c J f t i i s t u t e =
u,(t)=a,(t)e2+a;i=0,1;0≤t≤T C Amplitude attenuation H Frequency alteration A Phase shifting N Time delay N E y(t)= aa,(t-to)exp[J[2π(f+fa)(t-t)+g(t-to)+β] +z(t),i=0,l;t≤t≤T+to (6.4) UESTC 3
3 UESTC 0 0 0 0 0 ( ) ( )exp[ [2 ( )( ) ( ) ]] ( ), 0,1; 4) (6. i i i d z t y t a t J f t t t f T t i t t t t = − + − + − + + = + (2 ( )) ( ) ( ) ; 0,1; 0 i i J f t t i i u t a t e i t T + = = C H A N N E L Amplitude attenuation Frequency alteration Phase shifting Time delay
/936 If above parameters are all known: CT+to Re() 4 y④ aui(t-to) 2 e-j2m(B+fdt-to)) CT+to Re() a6t-0) eo UESTC 4
4 UESTC If above parameters are all known:
6.1 Chapter highlights Composite hypothesis testing. ·Unknown phase.. 。Unknown amplitude. 。Unknown frequency. Unknown time of arrival UESTC 5
5 UESTC 6.1 Chapter highlights • Composite hypothesis testing. • Unknown phase. • Unknown amplitude. • Unknown frequency. • Unknown time of arrival