PS04 - University of Illinois Spring 2011 ECE 361 Problem...

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Unformatted text preview: University of Illinois Spring 2011 ECE 361: Problem Set 4 M-ary Orthogonal and Trans-Orthogonal Signaling Due: Thursday February 17 at 9:30 a.m. Reading: Lecture Notes: Lectures 5-9.1 Reminder: The First MidSemester Exam is scheduled for Tuesday February 22, 9:30 a.m. to 10:50 a.m. Coverage of material is up to and including M-ary orthogonal and trans-orthogonal signaling but not bi-orthogonal signaling, that is, everything through the lecture of February 15, or equivalently, Problem Sets 0-4. One 8.5” × 11” sheet of notes is permitted; both sides may be used. 1. [Hadamard matrices] A Hadamard matrix is a n × n matrix A = [ a ij ] in which each a ij has value ± 1, and the rows are orthogonal to one another, that is, ∑ j a ij a kj = 0 for all i 6 = k . It is obvious that n must be a multiple of 2 for a Hadamard matrix to exist. But in fact, if n ≥ 3, then n must be a multiple of 4....
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