  The estimation of a sparse vector in the linear model is a fundamental
problem in signal processing, statistics, and compressive sensing. This paper
establishes a lower bound on the mean-squared error, which holds regardless of
the sensing/design matrix being used and regardless of the estimation
procedure. This lower bound very nearly matches the known upper bound one gets
by taking a random projection of the sparse vector followed by an $\ell_1$
estimation procedure such as the Dantzig selector. In this sense, compressive
sensing techniques cannot essentially be improved.
