MIT16_36s09_lec08_09

MIT16_36s09_lec08_09 - MIT OpenCourseWare http:/ocw.mit.edu...

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MIT OpenCourseWare http://ocw.mit.edu 16.36 Communication Systems Engineering Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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Lectures 8 - 9 : Signal Detection in Noise and the Matched Filter Eytan Modiano A ero- A stro Dept. Eytan Modiano Slide 1
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Noise in communication systems S(t) Channel r(t) r(t) = S(t) + n(t) n(t) Noise is additional “unwanted” signal that interferes with the transmitted signal Generated by electronic devices The noise is a random process Each “sample” of n(t) is a random variable Typically, the noise process is modeled as “Additive White Gaussian Noise” (AWGN) White: Flat frequency spectrum Gaussian: noise distribution Eytan Modiano Slide 2
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The auto-correlation of a random process x(t) is defined as R xx (t 1 ,t 2 ) = E[x(t 1 )x(t 2 )] A random process is Wide-sense-stationary (WSS) if its mean and auto-correlation are not a function of time. That is m x (t) = E[x(t)] = m R xx (t 1 ,t 2 ) = R x ( τ ), where τ = t 1 -t 2 If x(t) is WSS then: R x ( τ ) = R x (- τ ) | R x ( τ )| <= |R x ( 0 )| (max is achieved at τ = 0) The power content of a WSS process is: P x = E [lim t !" 1 T x 2
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MIT16_36s09_lec08_09 - MIT OpenCourseWare http:/ocw.mit.edu...

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