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eigenvalue-estimations
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Eigenvalue estimation of the exponentially windowed sample covariance matrices
, Article IEEE Transactions on Information Theory ; Volume 62, Issue 7 , 2016 , Pages 4300-4311 ; 00189448 (ISSN) ; Gazor, S ; Bastani, M. H ; Sharifitabar, M ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2016
Abstract
In this paper, we consider an exponentially windowed sample covariance matrix (EWSCM) and propose an improved estimator for its eigenvalues. We use new advances in random matrix theory, which describe the limiting spectral distribution of the large dimensional doubly correlated Wishart matrices to find the support and distribution of the eigenvalues of the EWSCM. We then employ the complex integration and residue theorem to design an estimator for the eigenvalues, which satisfies the cluster separability condition, assuming that the eigenvalue multiplicities are known. We show that the proposed estimator is consistent in the asymptotic regime and has good performance in finite sample size...
Source Enumeration and Identification in Array Processing Systems
, Ph.D. Dissertation Sharif University of Technology ; Bastani, Mohammad Hasan (Supervisor)
Abstract
Employing array of antennas in amny signal processing application has received considerable attention in recent years due to major advances in design and implementation of large dimentional antennas. In many applications we deal with such large dimentional antennas which challenge the traditional signal processing algorithms. Since most of traditional signal processing algorithms assume that the number of samples is much more than the number of array elements while it is not possible to collect so many samples due to hardware and time constraints.
In this thesis we exploit new results in random matrix theory to charachterize and describe the properties of Sample Covariance Matrices...
In this thesis we exploit new results in random matrix theory to charachterize and describe the properties of Sample Covariance Matrices...
Analysis of Wave Propagation Eigenproblem in Periodic Structures
, Ph.D. Dissertation Sharif University of Technology ; Akbari, Mahmood (Supervisor)
Abstract
The Fourier modal method is one of the most important methods in the analysis of flat periodic structures (gratings). Using this method, the problem of wave propagation in the periodic medium leads to an eigenproblem, in which eigenvalues represent the propagation constants and eigenvector or eigenfunctions determine the filed distribution of the modes. On the other side, considering all the generalizations and modifications reported so far, the Fourier modal method still faces two fundamental problems. First, for problems involving large dielectric constants or high contrasts, the matrix form of the eigenproblem (the modal matrix) can be large, dense, and require a high computational cost....