Lower bound on MSE of sparse vector estimation in additive white Gaussian noise

The lower MSE bound on a sparse vector estimation from observations corrupted by additive white Gaussian noise, when the sparsity s is unknown, is investigated. The optimal support in the MSE sense is derived as a function of the noise variance and leads to an interval-wise expression of the MSE lower bound. The obtained reduction with respect to the Cramér-Rao Bound is shown to be an increasing function of the noise variance.