Statistical Detection Theory Random Signal Wenhui Xiong NCL UESTC whxiong@uestc.edu.cn
whxiong@uestc.edu.cn Statistical Detection Theory Random Signal Wenhui Xiong NCL UESTC
Outline Signal Model Estimator-correlator whxiong@uestc.edu.cn 2
whxiong@uestc.edu.cn Signal Model Estimator-correlator 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 WGN with zero mean and known variance .wIn]:awgn rww[k]=E(w[njwin+k)=026(k) whxiong@uestc.edu.cn 4
whxiong@uestc.edu.cn System Model 4 Assumption: s[n] is WGN with zero mean and known variance w[n]: awgn 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)
System Model Binary Hypo.Test:Ho or Hi Ho xIn]wln] n=0,1..N-1 H cln]=sIn]+wlnl 。Assumption: s[n]is WGN with zero mean and known variance .wIn]:awgn rww[k]=E(w[njwin+k)=026(k) P(x;H1) L(x)=Px;Ho) whxiong@uestc.edu.cn 5
whxiong@uestc.edu.cn System Model 5 Assumption: s[n] is WGN with zero mean and known variance w[n]: awgn 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) L(x) = P(x; H1) P(x; H0) > °