20072ee132A_1_ca2sol

20072ee132A_1_ca2sol - EE132A, Spring 2007 Prof. John...

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EE132A, Spring 2007 Communication Systems Prof. John Villasenor Handout# 17 TA: Choo Chin (Jeffrey) Tan Computer Assignment #2 Solution (a) QPSK System: The probability of bit error in a coherent QPSK system is approximately given by = 0 erfc 2 1 N E P b B Let x = 0 N E b in dB. So, the argument of ( ) erfc should be replaced by 10^(x/10). See the plot and MATLAB code that follows. (b) One-dimensional constellation: This one-dimensional constellation has the following properties: - The average symbol energy is E - The probability of occurrence of each symbol is equal. i.e., ( ) ( ) ( ) ( ) 4 1 = = = = D P C P B P A P The probability of symbol error is given by: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) [ ] D E P C E P B E P A E P D P D E P C P C E P B P B E P A P A E P P E | | | | 4 1 | | | | + + + = + + + = By symmetry: ( ) ( ) ( ) ( ) C E P B E P D E P A E P | | and | | = = Thus, ( ) ( ) [ ] B E P A E P P E | | 2 1 + = Since ( ) A E P | and ( ) B E P
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20072ee132A_1_ca2sol - EE132A, Spring 2007 Prof. John...

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