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