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Unformatted text preview: ECE 562 Fall 2011 Coherent Detection of Orthogonally Modulated Signals ◦ The signal set is described as: s m ( t ) = √ E g m ( t ) , m = 1 , 2 ,...,M, ≤ t ≤ T s Here we consider the case where { g m } are orthonormal signals, i.e., ρ k` = 0, for k 6 = ` (both in real and imaginary parts). For the case where only Re [ ρ k` ] = 0, for k 6 = ` , see HW 4. ◦ The signal s m ( t ) = √ E g m ( t ) belongs to span( g 1 ( t ) ,...,g M ( t )), and hence R k = h r ( t ) ,g k ( t ) i , k = 1 ,...,M , form sufficient statistics. ◦ If symbol m is sent, then the vector of sufficient statistics is given by R = [ W 1 ··· √ E + W m ··· W M ] > where { W k } are easily seen to be i.i.d. CN (0 ,N ) random variables. ◦ The likelihood function is given by: p m ( r ) = 1 πN exp " ( r m,I √ E ) 2 + r 2 m,Q N # Y k 6 = m 1 πN exp " r 2 k,I + r 2 k,Q N # ◦ We showed in class that for equal priors, ˆ m MPE ( r ) = ˆ m ML ( r ) = arg max m p m ( r ) = arg max m r m,I Note that only the real part of...
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This document was uploaded on 02/08/2012.
 Fall '09

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