HW04 - University of Illinois Spring 2011 ECE 361: Problem...

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: University of Illinois Spring 2011 ECE 361: Problem Set 4: Solutions M-ary Orthogonal and Trans-Orthogonal Signaling 1. [Hadamard matrices] Let h 1 ,h 2 ,h 3 denote three different rows of the matrix. Let a denote the number of coordinates where the three rows are identical, and let a i ,i { 1 , 2 , 3 } denote the number of coordinates in which the i-th row differs from the other two. Then we have h h 1 ,h 2 i = a- a 1- a 2 + a 3 = 0 h h 1 ,h 3 i = a- a 1 + a 2- a 3 = 0 h h 2 ,h 3 i = a + a 1- a 2- a 3 = 0 which, when added in pairs, give a = a 1 = a 2 = a 3 , and since a + a 1 + a 2 + a 3 = n , we conclude that n must be a multiple of 4. 2. [Bit Error Probabilities for M-ary orthogonal signaling] (a) The first bit is in error if the output is any of 100, 101, 110, 111. Hence we have that P ( A 1 | a = 011) = 4 p/ 7. Similarly, the last bit is is in error if the output is any of 000, 010, 100, 110 and hence P ( A 3 | a = 011) = 4 p/ 7 also. Note that both the first and last bits are in error if the...
View Full Document

Page1 / 2

HW04 - University of Illinois Spring 2011 ECE 361: Problem...

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