  We consider the estimation of a sparse parameter vector from measurements
corrupted by white Gaussian noise. Our focus is on unbiased estimation as a
setting under which the difficulty of the problem can be quantified
analytically. We show that there are infinitely many unbiased estimators but
none of them has uniformly minimum mean-squared error. We then provide lower
and upper bounds on the Barankin bound, which describes the performance
achievable by unbiased estimators. These bounds are used to predict the
threshold region of practical estimators.
