Question

Problem 3 Consider the linear MMSE estimator to the case where our estimation of a random variable Y is based on observations of multiple random variables, say XXX. Then, our linear MMSE estimator can be e written in the following fom: (a) Show that the optimal values of aa,a.a for the linear LMSE estimator is given as where E(X, a, Cxx is an covariance matrix of X,,X,...Xv and cxy is a cross-correlation vector, which is defined as E(x,r EtXyY (b) Show the minimum mean square error is given as (c) Considering the following noisy measurements, and Y. Y. where N and N are additive noise. Assume that X, N.and N2 are mutually uncorrelated, and Ni and N2 have zero means and unit variances. Assuming that X has zero mean and unit variance, find the linear MMSE estimator for X in terms of the measurements, and ·Then, find the minimum MMSE value of the current estimator

Answer 1

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