In a BPSK communication system, a source wishes to communicate a random bit X {- 1, 1}
Question:
(a) After n transmissions of X, you observe Y = y = [y1 ... yn]ʹ. Find P[X = 1|Y = y]. Express your answer in terms of the likelihood ratio
(b) Suppose after n transmissions, the receiver observes Y = y, and decides
Find the probability of error Pe = P[X* X] in terms of the Φ function.
(c) Now suppose the system uses ARQ as follows. If |n(y)| n(y) > 1 - ϵ, the receiver guesses X* = 1. If n(y) ϵ1 ¤ Pe ¤ ϵ2
Transcribed Image Text:
fyix(y1-1) fyix (y1) X* ={-1 otherwise-yl > 1/2,
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a Since Y is continuous the conditioning event is y Y y dy We then write P X 1y Y y dy We co...View the full answer
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Related Book For
Probability and Stochastic Processes A Friendly Introduction for Electrical and Computer Engineers
ISBN: 978-1118324561
3rd edition
Authors: Roy D. Yates, David J. Goodman
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