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

Ehsan Yazdian1*, Saeed Gazor2 and Mohammad Hasan Bastani3

Author Affiliations

1 Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan, Iran

2 Department of Electrical and Computer Engineering, Queens University, Kingston, ON, Canada

3 Electrical Engineering Department, Sharif University of Technology, Tehran, Iran

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EURASIP Journal on Advances in Signal Processing 2013, 2013:42  doi:10.1186/1687-6180-2013-42

Published: 6 March 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 identify the support of eigenvalues in the general case of signal-plus-noise. Simulations are performed to support our theoretical claims. The results of this article can be directly employed in many applications working with windowed array data such as source enumeration and subspace tracking algorithms.