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**Search for:**sample-covariance-matrix

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#### Limiting spectral distribution of the sample covariance matrix of the windowed array data

, Article Eurasip Journal on Advances in Signal Processing ; Volume 2013, Issue 1 , 2013 ; 16876172 (ISSN) ; Gazor, S ; Bastani, M. H ; Sharif University of Technology
2013

Abstract

In this article, we investigate the limiting spectral distribution of the sample covariance matrix (SCM) of weighted/windowed complex data. We use recent advances in random matrix theory and describe the distribution of eigenvalues of the doubly correlated Wishart matrices. We obtain an approximation for the spectral distribution of the SCM obtained from windowed data. We also determine a condition on the coefficients of the window, under which the fragmentation of the support of noise eigenvalues can be avoided, in the noise-only data case. For the commonly used exponential window, we derive an explicit expression for the l.s.d of the noise-only data. In addition, we present a method to...

#### Spectral distribution of the exponentially windowed sample covariance matrix

, Article ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, 25 March 2012 through 30 March 2012, Kyoto ; 2012 , Pages 3529-3532 ; 15206149 (ISSN) ; 9781467300469 (ISBN) ; Bastani, M. H ; Gazor, S ; Sharif University of Technology
IEEE
2012

Abstract

In this paper, we investigate the effect of applying an exponential window on the limiting spectral distribution (l.s.d.) of the exponentially windowed sample covariance matrix (SCM) of complex array data. We use recent advances in random matrix theory which describe the distribution of eigenvalues of the doubly correlated Wishart matrices. We derive an explicit expression for the l.s.d. of the noise-only data. Simulations are performed to support our theoretical claims

#### 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...

#### Source enumeration in large arrays based on moments of eigenvalues in sample starved conditions

, Article IEEE Workshop on Signal Processing Systems, SiPS: Design and Implementation, 17 October 2012 through 19 October 2012, Quebec ; October , 2012 , Pages 79-84 ; 15206130 (ISSN) ; 9780769548562 (ISBN) ; Bastani, M. H ; Gazor, S ; Sharif University of Technology
2012

Abstract

This paper presents a scheme to enumerate the incident waves impinging on a high dimensional uniform linear array using relatively few samples. The approach is based on Minimum Description Length (MDL) criteria and statistical properties of eigenvalues of the Sample Covariance Matrix (SCM). We assume that several models, with each model representing a certain number of sources, will compete and MDL criterion will select the best model with the minimum model complexity and maximum model decision. Statistics of noise eigenvalue of SCM can be approximated by the distributional properties of the eigenvalues given by Marcenko-Pastur distribution in the signal-free SCM. In this paper we use random...

#### Effect of unitary transformation on Bayesian information criterion for source numbering in array processing

, Article IET Signal Processing ; Volume 13, Issue 7 , 2019 , Pages 670-678 ; 17519675 (ISSN) ; Aref, M. R ; Razzazi, F ; Sharif University of Technology
Institution of Engineering and Technology
2019

Abstract

An approach based on unitary transformation for the problem of estimating the number of signals is proposed in this study. Among the information theoretic criteria, the authors focus on the conventional Bayesian information criterion (BIC) in the presence of a uniform linear array. The sample covariance matrix of this array is transformed into the real symmetric one by using a unitary transformation. This real symmetric matrix has real eigenvalues and eigenvectors. Therefore its eigenvalue decomposition needs only real computations. Since the eigenvalues of this real symmetric matrix are equal to the eigenvalues of the sample covariance matrix, by replacing them in BIC formula, the term...

#### Source enumeration in large arrays using moments of eigenvalues and relatively few samples

, Article IET Signal Processing ; Volume 6, Issue 7 , 2012 , Pages 689-696 ; 17519675 (ISSN) ; Gazor, S ; Bastani, H ; Sharif University of Technology
IET
2012

Abstract

This study presents a method based on minimum description length criterion to enumerate the incident waves impinging on a large array using a relatively small number of samples. The proposed scheme exploits the statistical properties of eigenvalues of the sample covariance matrix (SCM) of Gaussian processes. The authors use a number of moments of noise eigenvalues of the SCM in order to separate noise and signal subspaces more accurately. In particular, the authors assume a Marcenko-Pastur probability density function (pdf) for the eigenvalues of SCM associated with the noise subspace. We also use an enhanced noise variance estimator to reduce the bias leakage between the subspaces....