  A sparse or compressible signal can be recovered from a certain number of
noisy random projections, smaller than what dictated by classic Shannon/Nyquist
theory. In this paper, we derive the closed-form expression of the mean square
error performance of the oracle receiver, knowing the sparsity pattern of the
signal. With respect to existing bounds, our result is exact and does not
depend on a particular realization of the sensing matrix. Moreover, our result
holds irrespective of whether the noise affecting the measurements is white or
correlated. Numerical results show a perfect match between equations and
simulations, confirming the validity of the result.
