Unformatted text preview: University of Illinois Spring 2011 ECE 361: Problem Set 4 Mary Orthogonal and TransOrthogonal Signaling Due: Thursday February 17 at 9:30 a.m. Reading: Lecture Notes: Lectures 59.1 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 Mary orthogonal and transorthogonal signaling but not biorthogonal signaling, that is, everything through the lecture of February 15, or equivalently, Problem Sets 04. 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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