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

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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 0 / 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 0 / 2. Let A i denote the event that the number i is transmitted, and E the event that the number transmitted is received incorrectly. (a) Find P ( E | A i ), 0 i 3 and then use the law of total probability to find P ( E ).

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

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