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Analysis of Fisher Information and the Cram\'{e}r-Rao Bound for Nonlinear Parameter Estimation after Compressed Sensing

Authors :
Pakrooh, Pooria
Pezeshki, Ali
Scharf, Louis L.
Cochran, Douglas
Howard, Stephen D.
Publication Year :
2015

Abstract

In this paper, we analyze the impact of compressed sensing with complex random matrices on Fisher information and the Cram\'{e}r-Rao Bound (CRB) for estimating unknown parameters in the mean value function of a complex multivariate normal distribution. We consider the class of random compression matrices whose distribution is right-orthogonally invariant. The compression matrix whose elements are i.i.d. standard normal random variables is one such matrix. We show that for all such compression matrices, the Fisher information matrix has a complex matrix beta distribution. We also derive the distribution of CRB. These distributions can be used to quantify the loss in CRB as a function of the Fisher information of the non-compressed data. In our numerical examples, we consider a direction of arrival estimation problem and discuss the use of these distributions as guidelines for choosing compression ratios based on the resulting loss in CRB.<br />Comment: 12 pages, 3figures

Subjects

Subjects :
Mathematics - Statistics Theory

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.1504.01081
Document Type :
Working Paper
Full Text :
https://doi.org/10.1109/TSP.2015.2464183