  Recently, it has been proved in Babadi et al. that in noisy compressed
sensing, a joint typical estimator can asymptotically achieve the Cramer-Rao
lower bound of the problem.To prove this result, this paper used a lemma,which
is provided in Akcakaya et al,that comprises the main building block of the
proof. This lemma is based on the assumption of Gaussianity of the measurement
matrix and its randomness in the domain of noise. In this correspondence, we
generalize the results obtained in Babadi et al by dropping the Gaussianity
assumption on the measurement matrix. In fact, by considering the measurement
matrix as a deterministic matrix in our analysis, we find a theorem similar to
the main theorem of Babadi et al for a family of randomly generated (but
deterministic in the noise domain) measurement matrices that satisfy a
generalized condition known as The Concentration of Measures Inequality. By
this, we finally show that under our generalized assumptions, the Cramer-Rao
bound of the estimation is achievable by using the typical estimator introduced
in Babadi et al.
