Question: Consider a communication system in which the random variable Y is transmitted through a channel with a random gain W, so that the received variable

Consider a communication system in which the random variable Y is transmitted through a channel with a random gain W, so that the received variable X = WY. Assume that Y and W are independent, and that both of them are uniformly distributed in the range [1,2]

a) suppose you are sitting at the receiver and want to estimate the transmitted value Y from a measurement of the received value X, using the LMMSE estimator y = d1X +d2. Determine what d1 and d2 should be, and compute the associated MMSE

b) Suppose instead that you are sitting at the transmitter and want to estimate what the received value X will be from a measurement of the transmitted value Y. Find the (unconstrained) MMSE estimator X(y)

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