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20072ee132A_1_hwk6

20072ee132A_1_hwk6 - EE132A Spring 2007 Prof John...

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EE132A, Spring 2007 Communication Systems Prof. John Villasenor Handout # 14 TA: Choo Chin (Jeffrey) Tan Homework 6 Assigned: Monday, May 14, 2007 Due: Monday, May 21, 2007 Reading Assignment: Chapter 8 (8.5), Chapter 10 (10.1 – 10.3), Chapter 9 (9.1, 9.2) 1. Consider the signal space depicted below: Assume that each symbol has transmitted energy E and that ( ) t 1 ϕ and ( ) t 2 ϕ are given by ( ) < = elsewhere , 0 0 , 2 cos / 2 1 T t t f T t c π ϕ , ( ) < = elsewhere , 0 0 , 2 sin / 2 2 T t t f T t c π ϕ (a) Find the time domain expressions for the 8 signals ( ) t s i , 8 , , 1 midhorizellipsis = i . (b) Determine the bit error probability (as a function of E b / N 0 ), considering only the nearest neighbors. (c) Provide a labeling using Gray coding. 2. Consider an 8-PSK system and a 16-PSK system. (a) Find an expression for the probability of symbol (not bit) error for the 8-PSK system, as a function of E and N 0 , where E is the transmitted symbol energy. (b) Give an expression for the BER, as a function of E b and N 0 .
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