Homework_5_2007

# Homework_5_2007 - s /N in db. 3. Find an expression for the...

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ECE 154B Winter 2007 Homework #5: Due February 28, 2007 1. Consider that the Voronoi region for a 2-D signal is a hexagon centered at the signal point with shortest distance from the center to any of the edges of the hexagon equal to 2. Assume AWGN with zero mean and power spectral density equal to N 0 /2 for all frequencies. Calculate exact expressions for tight upper and lower bounds for the conditional probability that the received point falls within the Voronoi region given that that signal was sent. (Hint: Consider two circles, one of which is of radius 2 and the other of which passes through the vertices of the hexagon.) Evaluate your bounds for N 0 = 0.1. 2. Again consider problem 1 of the midterm exam. a. Find an exact expression for the symbol probability of error. b. Find the union bound for the probability of symbol error. c. Plot the results found in parts a and b versus E
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Unformatted text preview: s /N in db. 3. Find an expression for the union bound for the probability of symbol error for a 32 point QAM signal constellation. Make the usual assumptions about AWGN, equally likely signals, optimal receiver, etc. Plot your result versus E b /N in db. (Note: Now we use E b / N .) 4. Do a simulation to verify the result found in problem 3 for an E b /N that gives a symbol error rate of about 10-3 . 5. For M even, consider a signal set of M signal consisting of M/2 equi-energy orthogonal signals and their negatives. Make the usual assumptions about AWGN, equally likely signals, optimal receiver, etc. Derive an expression for the probability of symbol error versus E s /N in db. Like in the case of M orthogonal signals, you can leave your result in terms of a multi-dimensional integral....
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## This note was uploaded on 11/11/2009 for the course ECE 670377 taught by Professor Wolf during the Winter '07 term at UCSD.

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