MIT16_36s09_lec11

# MIT16_36s09_lec11 - 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 11: Hypothesis Testing and BER analysis Eytan Modiano Eytan Modiano Slide 1
Signal Detection After matched ﬁltering we receive r = S m + n S m {S 1 ,..S M } How do we determine from r which of the M possible symbols was sent? Without the noise we would receive what sent, but the noise can transform one symbol into another Hypothesis testing Objective: minimize the probability of a decision error Decision rule: Choose S m such that P(S m sent | r received) is maximized This is known as Maximum a posteriori probability (MAP) rule MAP Rule: Maximize the conditional probability that S m was sent given that r was received Eytan Modiano Slide 2

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MAP detector Notes: MAP rule requires prior probabilities MAP minimizes the probability of a decision error ML rule assumes equally likely symbols With equally likely symbols MAP and ML are the same MAP detector: max S 1 ... S M P ( S m | r ) P ( S m | r )= P ( S m , r ) P ( r ) = P ( r | S m ) P ( S m ) P ( r ) P ( S m | r ) = f r | s ( r | S m ) P ( S m ) f r ( r ) f r ( r f r | s ( r | S m ) P ( S m ) m=1 M !
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MIT16_36s09_lec11 - MIT OpenCourseWare http/ocw.mit.edu...

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