ece4305_L11

ece4305_L11 - Optimal Detection ECE4305 Software-Defined...

Info iconThis preview shows pages 1–5. 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

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: Optimal Detection ECE4305: Software-Defined Radio Systems and Analysis Professor Alexander M. Wyglinski Department of Electrical and Computer Engineering Worcester Polytechnic Institute Lecture 11 Professor Alexander M. Wyglinski ECE4305: Software-Defined Radio Systems and Analysis Optimal Detection Signal Vector Framework Probability Density Function of n Decision Rules Recall Simple Digital Transceiver Model I Receiver only observes the corrupted version of s ( t ) by n ( t ), namely r ( t ) I Usually n ( t ) represents the culmination of all noise sources into a single variable I Detection problem: Given r ( t ) for 0 ≤ t ≤ T , determine which s i ( t ), i = 1 , 2 , . . . , M , is present in r ( t ) Figure: Simple Digital Transceiver Model. Professor Alexander M. Wyglinski ECE4305: Software-Defined Radio Systems and Analysis Optimal Detection Signal Vector Framework Probability Density Function of n Decision Rules Mathematical Formulation I Decompose waveforms s i ( t ), n ( t ), and r ( t ) into a collection of weights applied to a set of orthonormal basis functions: s i ( t ) = N X k =1 s ik φ k ( t ) , r ( t ) = N X k =1 r k φ k ( t ) , n ( t ) = N X k =1 n k φ k ( t ) I Thus, waveform model r ( t ) = s i ( t ) + n ( t ) now becomes r ( t ) = s i ( t ) + n ( t ) N X k =1 r k φ k ( t ) = N X k =1 s ik φ k ( t ) + N X k =1 n k φ k ( t ) r = s i + n → Vector Model Professor Alexander M. Wyglinski ECE4305: Software-Defined Radio Systems and Analysis Optimal Detection Signal Vector Framework Probability Density Function of n Decision Rules n ( t ) is Gaussian I We know that the noise vector element n k is equal to: n k = T Z n ( t ) φ k ( t...
View Full Document

This note was uploaded on 01/13/2011 for the course ECE 4305 taught by Professor Wy during the Spring '10 term at WPI.

Page1 / 13

ece4305_L11 - Optimal Detection ECE4305 Software-Defined...

This preview shows document pages 1 - 5. Sign up to view the full document.

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