On the Analysis of the Fisher Information of a Perturbed Linear Model After Random Compression

The impact of random compression on the Fisher information matrix (FIM) and the Cramér-Rao bound (CRB) is studied when estimating unknown complex parameters in the perturbed linear model. A random compression matrix is considered whose elements are i.i.d. standard complex normal random variables. The FIM averaged over compression is equal to a scalar of the FIM before compression plus an additional term. The upper and lower bounds of the CRB averaged over the random compression matrix are also given. Finally, numerical results are conducted to verify our theoretical results.

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