This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: ECE 562 Fall 2011 October 10, 2011 HOMEWORK ASSIGNMENT 4 Due Date: October 18, 2011 (in class) 1. SemiOrthogonal Signal Set. Consider the signal set with M = 2 N signals given by: s m ( t ) = E g m ( t ) m = 1 ,...,N j E g m N ( t ) m = N + 1 ,...,M. where { g k ( t ) } N k =1 are realvalued orthonormal functions. Clearly this signal set satis fies: Re [ k,` ] = 0, for k 6 = ` . (a) Argue that R k = h r ( t ) ,g k ( t ) i ,k = 1 ,...,N , form sufficient statistics for optimal decision making at the receiver for an AWGN channel. (b) Now define the M realvalued statistics y m = r m,I m = 1 ,...,N r ( m N ) ,Q m = N + 1 ,...,M. Show that the MPE decision rule is given by m MPE = arg max m y m (c) Find an expression for P e for the MPE decision rule 2. In this problem you will show the following result for Mary orthogonal modulation lim M P c = 1 b > ln 2 b < ln 2 where P c is the probability of correct decision making. Recall that we showed in class that P c = Z  h 1 Q ( x + p 2 b log 2 M ) i M 1 1 2 e x 2 / 2 dx (a) Show that for any...
View
Full
Document
 Fall '09

Click to edit the document details