notes9 - ECE 562 Fall 2011 Coherent Detection of...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This document was uploaded on 02/08/2012.

Page1 / 2

notes9 - ECE 562 Fall 2011 Coherent Detection of...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online