Statistical Detection Theory Deterministic Signal Wenhui Xiong NCL UESTC whxiong@uestc.edu.cn
whxiong@uestc.edu.cn Statistical Detection Theory Deterministic Signal Wenhui Xiong NCL UESTC
Outline Signal Model 。Matched Filter 。Review:NP theorem Development of the Detector Performance of Matched Filter Generalized Matched Filter 。Multiple Signal 。M-ary Detector whxiong@uestc.edu.cn 2
whxiong@uestc.edu.cn Signal Model Matched Filter Review: NP theorem Development of the Detector Performance of Matched Filter Generalized Matched Filter Multiple Signal M-ary Detector Outline 2
System Model Binary Hypo.Test:Ho or H Ho xIn]wln] n=0,1..N-1 H cIn]sIn]+wln] whxiong@uestc.edu.cn 3
whxiong@uestc.edu.cn System Model 3 H0 Binary Hypo. Test: H0 or H1 H0 x[n] = w[n] H1 x[n] = s[n] + w[n] n=0,1…N-1
System Model Binary Hypo.Test:Ho or Hi Ho xIn]wln] n=0,1..N-1 H cln]=sIn]+wlnl 。Assumption: 。S[n]is known .WIn]:awgn rww[=E(w[n]w[n+k)=028(k) 。Noise power is known whxiong@uestc.edu.cn
whxiong@uestc.edu.cn System Model 4 Assumption: S[n] is known W[n]: awgn Noise power is known H0 Binary Hypo. Test: H0 or H1 H0 x[n] = w[n] H1 x[n] = s[n] + w[n] n=0,1…N-1 rww[k] = E(w[n]w[n + k]) = ¾ 2 ±(k)
Review:NP theorem NP Theorem:Likelihood ratio test(LRT) maximize Pp while a given PrA=a,decide H if whxiong@uestc.edu.cn
whxiong@uestc.edu.cn Review: NP theorem NP Theorem: Likelihood ratio test (LRT) • maximize PD while a given PFA =α , decide H1 if
Review:NP theorem NP Theorem:Likelihood ratio test(LRT) .maximize Pp while a given PrA=a,decide H if L(x) P(x;H) P(x;Ho) The threshold y is determined from PEA as whxiong@uestc.edu.cn 6
whxiong@uestc.edu.cn Review: NP theorem NP Theorem: Likelihood ratio test (LRT) • maximize PD while a given PFA =α , decide H1 if 6 L(x) = P(x; H1) P(x; H0) > ° The threshold γ is determined from PFA as
Review:NP theorem NP Theorem:Likelihood ratio test(LRT) .maximize Pp while a given PrA=a,decide H if L(x)= P(x;H) P(x;Ho) The threshold y is determined from PrA as p(x;Ho)dx =a whxiong@uestc.edu.cn
whxiong@uestc.edu.cn Review: NP theorem NP Theorem: Likelihood ratio test (LRT) • maximize PD while a given PFA =α , decide H1 if 7 L(x) = P(x; H1) P(x; H0) > ° The threshold γ is determined from PFA as PFA = Z x:L(x)>° p(x; H0)dx = ®
Review:NP theorem NP Theorem:Likelihood ratio test(LRT) maximize Pp while a given PrA=a,decide H if L(x)= P(x;H) P(x;Ho) The threshold y is determined from PrA as p(x;Ho)dx a L(x):the likelihood ratio n-xaxH放 whxiong@uestc.edu.cn 8
whxiong@uestc.edu.cn Review: NP theorem NP Theorem: Likelihood ratio test (LRT) • maximize PD while a given PFA =α , decide H1 if 8 L(x) = P(x; H1) P(x; H0) > ° The threshold γ is determined from PFA as PFA = Z x:L(x)>° p(x; H0)dx = ® L(x): the likelihood ratio PD = Z x:L(x)>° p(x; H1)dx
Review:NP theorem { W-1 pxo)=了 N-1 p(x:H）=7 m{2w- whxiong@uestc.edu.cn
whxiong@uestc.edu.cn Review: NP theorem p(x; H1) = 1 (2¼¾2) N=2 exp ( ¡ 1 2¾2 N X¡1 n=0 [x(n) ¡ s(n)] 2 ) p(x; H0) = 1 (2¼¾2) N=2 exp ( ¡ 1 2¾2 N X¡1 n=0 [x(n)] 2 )
Review:NP theorem W-1 pxHo)=了 N-1 p(x;H)= w四{2-} Follow the NP rule W-1 L(x)=4 -{和三-ar-2可} n=0 whxiong@uestc.edu.cn 10
whxiong@uestc.edu.cn Review: NP theorem 10 p(x; H1) = 1 (2¼¾2) N=2 exp ( ¡ 1 2¾2 N X¡1 n=0 [x(n) ¡ s(n)] 2 ) p(x; H0) = 1 (2¼¾2) N=2 exp ( ¡ 1 2¾2 N X¡1 n=0 [x(n)] 2 ) Follow the NP rule L(x) = p(x; H1) p(x; H0) = exp ( ¡ 1 2¾2 N X¡1 n=0 £ (x[n] ¡ s[n]) 2 ¡ x 2 [n] ¤ )