The Analysis of Effects of Random Compression on the Cramér-Rao Bound of a Perturbed Linear Model

In this paper, the analysis results of random compression on the Cramér-Rao bound (CRB) and the Fisher information matrix (FIM) are provided of a perturbed linear model for estimating unknown complex parameters, where the elements of the random compression matrix are independent and identically distributed (i.i.d.) standard complex normal random variables. Particularly, the relationships between the FIMs and CRBs before and after compression are given. And the upper and lower bounds of the CRB and FIM averaged over compression are analyzed. At last, numerical results are implemented to validate theoretical results, which shows the effectiveness of upper and lower bound of the CRB.