Sharif Digital Repository

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... 

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  

The effective resistance or two-point resistance between two nodes of a resistor network is the potential difference that appears across them when a unit current source is applied between the nodes as terminals. This concept arises in problems which deal with graphs as electrical networks including random walks, distributed detection and estimation, sensor networks, distributed clock synchronization, collaborative filtering, clustering algorithms and etc. In the previous paper (Jafarizadeh et al. in J. Math. Phys. 50:023302, 2009) a recursive formula for evaluation of effective resistances on the so-called distance-regular networks was given based on the Christoffel-Darboux identity. In this... 

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...