<p>The Cramer-Rao Bound (CRB) is a fundamental tool for assessing estimator performance, but its application in compressive sensing is limited on the ability to reliably detect the signal in the domain of estimator. This paper demonstrates that below a critical number of available samples <i>M</i>, the probability of signal misdetection renders the CRB meaningless. We derive a closed-form expression for this critical <i>M</i>. Thus the performance of unbiased estimators in the compressive sensing scenario is considered using the Cramer-Rao bound. Based on the general equation for Fisher information, the expression for minimum variance is provided in terms of the number of available signal samples. However, missing samples produce noise components in the sparsity domain that degrades the estimation efficiency, and may prevent signal components estimation. Without loss of generality, we observe the case of complex sinusoid in order to derive the minimum number of available samples, such that the Cramer-Rao bound for minimum variance holds. In that sense, when dealing with compressive sensing scenario, it is necessary to take into account certain limitations in all equations used to derive the Cramer-Rao bound. This results in modified expressions and new constraints within the Cramer-Rao bound framework, which is provided in the paper. The theory is generalized for the windowed signals and its optimal estimator, namely the short-time Fourier transform, being the basic tool for time-frequency representation. The theoretical results are illustrated and proven by numerical examples, showing constraints of Cramer-Rao bound theory in the missing samples scenario.</p>