{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

19CorrelationRx

19CorrelationRx - The Correlation Receiver Jeffrey B Burl...

This preview shows pages 1–6. Sign up to view the full content.

EE 3180 Probability and Random  Signal Anaysis,  © 2009 by J. B. Burl The Correlation Receiver Jeffrey B. Burl

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
EE 3180 Probability and Random  Signal Anaysis,  © 2009 by J. B. Burl Introduction We have talked about making decisions  based on sampled data. Here, we will extend these results to  continuous-time data with additive white  noise.
EE 3180 Probability and Random  Signal Anaysis,  © 2009 by J. B. Burl Solution With Additive White  Noise Consider the example: Under H 0 :  r(t) = s 0 (t) + n(t), t 0    t   t f Under H 1 :  r(t) = s 1 (t) + n(t), t 0    t   t f where R n ( τ ) = S n δ ( τ ), n(t) is Gaussian. We can sample the data so that we can use  previous results: Under H 0 :  r k  = r(t 0  + kT) = s 0k  + n k , 1   k   N Under H 1 :  r k  = r(t 0  + kT) = s 1k  + n k , 1   k   N where n k    N(0,S n /T)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
EE 3180 Probability and Random  Signal Anaysis,  © 2009 by J. B. Burl Solution With Additive White  Noise, Cont. We can form the likelihood ratio: The likelihood ratio test is then ( 29 ( 29 ( 29 ( 29 2 2 1 1 1 2 2 0 0 0 1 1 2 / 2 / 1 | 1 1 1 1 | 0 2 / 2 / 1 1 1 ( | ) 2 / ( ) ( | ) 1 2 / k k k k n n k k k k n n r s r s N N S T S T k H n k r s r s N N H S T S T k k n e e f H S T f H e e S T π π - - - - = = - - - - = = Λ = = = r r r r r 1 10 00 0 01 11 1 0 ( ) ( ) ( ) H C C P C C P H η - Λ = < - r
EE 3180 Probability and Random  Signal Anaysis,  © 2009 by J. B. Burl Solution With Additive White  Noise, Cont.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 18

19CorrelationRx - The Correlation Receiver Jeffrey B Burl...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online