A binary communication system

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A binary communication system has transmitted signal X, a Bernoulli (p = 1/2) random variable. At the receiver, we observe Y = V X + W, where V is a "fading factor" and W is additive noise. Note that X, V and W are mutually independent random variables. Moreover V and W are exponential random variables with PDFs

Given the observation Y, we must guess whether X = 0 or X = 1 was transmitted. Use a binary hypothesis test to determine the rule that minimizes the probability P_ERR of a decoding error. For the optimum decision rule, calculate P_ERR.

Reference no: EM131083889

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