PS03 - University of Illinois Spring 2011 ECE 361: Problem...

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Unformatted text preview: University of Illinois Spring 2011 ECE 361: Problem Set 3 M-ary Amplitude Shift Keying; Repetition Coding Due: Tuesday February 15 at 9:30 a.m. Reading: Lecture Notes: Lectures 2-6 1. [Average energy in M-ary amplitude shift keying] In class, it was stated that the maximum energy in M-ary amplitude shift keying was E max = ( M- 1) 2 E while the average energy was E = (( M 2- 1) / 3) E . Prove the latter claim. Remember to consider both the cases M odd and M even. 2. [Bit error probabilities in 4-ASK systems] Consider a 4-ASK system operating in additive white Gaussian noise with two-sided power spectral density N / 2. The (equally likely) numbers 0, 1, 2, 3 are (Gray-)coded into data bits 00, 01, 11, and 10 and produce signal levels +3 E , E ,- E , and- 3 E at the output of the receiver filter. As usual, the noise variance at the filter output is N / 2. Let A i denote the event that the number i is transmitted, and E the event that the number transmitted is received incorrectly....
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PS03 - University of Illinois Spring 2011 ECE 361: Problem...

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