Unformatted text preview: Digital Modulation 1 - Problem Set 6
Problem 1 (MPSK)
1ยท Derive an upper bound for the symbol error probability of 8PSK by using the union bound and assuming that X = s1 was transmitted. a) Determine the squared Euclidean distance between the transmitted symbol s1 and the other symbols sm , m = 1. b) For each sm , m = 1, write the symbol error probability ห P (X = sm |X = s1 ) = P (Y โ Dm |X = s1 ) using the Q-function (similar to BPSK). c) Use the result from b) to express the union bound for the symbol error probability. Hint: The union bound for P (Y โ D1 |X = s1 ) is P (Y โ D1 |X = s1 ) โค
i=1 P (Y โ Di |X = s1 ). d) Why is the union bound an upper bound? 2ยท Derive an approximation of the bit error probability of MPSK for high values of Eb when Gray codes are used. N0 a) Determine a simple union bound for the symbol error probability of MPSK. b) Take into account the Gray encoding and relate Pb and Ps . 3ยท Simulate the BER of 8PSK versus obtained in 2.
Eb N0 and compare it with the approximation Problem 2 (QPSK)
The symbol error probability of QPSK reads Ps = 2Q Es N0 โ Q2 Es . N0 Relate the two summands in the right-hand expression to the conditional probabilities that Y lies in some sub-regions outside the decision region of the transmitted symbol. BFl, TPe. Digital Modulation 1 NavCom ...
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This note was uploaded on 12/29/2010 for the course UAE 605 taught by Professor Ttttt during the Spring '10 term at University of Arkansas โ Fort Smith.
- Spring '10