Q5. A receiver in a multiuser communication system accepts K binary signals from K independent transmitters,...

 

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Q5. A receiver in a multiuser communication system accepts K binary signals from K independent transmitters, i.e., Y = [Y, Y2, ..., YK], where Y is the received signal from the Kth transmitter. In an ideal system the received vector is given by Y = Ab+N where A=[a] is a diagonal matrix of positive channel gains, b=(b, b, ..., bx) is the vector of bits from each of the transmitters where b = 1, and N is a vector of K independent zero-mean, unit-variance Gaussian random variables. Assume the transmitted bits by are independent and equally likely to be +1 or -1. (a) Find the ML and MAP estimators for b given the observation Y. (b) Find the minimum mean square linear estimator for b given the observation Y. How can this estimator be used in deciding what were the transmitted bits? Q5. A receiver in a multiuser communication system accepts K binary signals from K independent transmitters, i.e., Y = [Y, Y2, ..., YK], where Y is the received signal from the Kth transmitter. In an ideal system the received vector is given by Y = Ab+N where A=[a] is a diagonal matrix of positive channel gains, b=(b, b, ..., bx) is the vector of bits from each of the transmitters where b = 1, and N is a vector of K independent zero-mean, unit-variance Gaussian random variables. Assume the transmitted bits by are independent and equally likely to be +1 or -1. (a) Find the ML and MAP estimators for b given the observation Y. (b) Find the minimum mean square linear estimator for b given the observation Y. How can this estimator be used in deciding what were the transmitted bits?