Optimum Receiver for AWGN Channel Needs M Correlators (or Matched Filters) So(t) Samples at t=T r(t) [.dr SM-1(t) Detector Oytput Decision .od rM-1 5=∫0r0s,()d,i=0,l,M-1
Optimum Receiver for AWGN Channel ◼ Needs M Correlators (or Matched Filters) 0 ( ) ( ) , 0,1,., 1 T i i r r t s t dt i M = = − 0 ( ) t d r(t) s0(t) Samples at t=T 0 ( ) t d sM-1(t) Detector Output Decision r0 rM-1
Signal Correlators Let so(t)is transmitted (dt+[so(n()dt =+n ■5=∫rus,)dh=s,④+n0}s,0M -ss (di+s.(n()di=ni Orthogonal Noise component(Gaussian Process) Zero mean and Variance o-)
Signal Correlators ◼ Let s0 (t) is transmitted ◼ ◼ ◼ Noise component (Gaussian Process) ◼ Zero mean and Variance 0 0 0 0 0 0 2 0 0 0 0 0 ( ) ( ) { ( ) ( )} ( ) ( ) ( ) ( ) T T T T r r t s t dt s t n t s t dt s t dt s t n t dt n = = + = + = + 0 0 0 0 0 0 0 ( ) ( ) { ( ) ( )} ( ) ( ) ( ) ( ) ( ) , 0 T T i i T T i i i r r t s t dt s t n t s t dt s t s t dt s t n t dt n i = = + = + = Orthogonal 2 2 2 0 0 0 ( ) ( ) 2 2 T i i N N E n s t dt = = =