The Experts below are selected from a list of 6060 Experts worldwide ranked by ideXlab platform

Claudio Ferreira Dias - One of the best experts on this subject based on the ideXlab platform.

  • On the Exact and Approximate Eigenvalue Distribution for Sum of Wishart Matrices
    IEEE Transactions on Vehicular Technology, 2017
    Co-Authors: Gabriel Fernando Pivaro, Gustavo Fraidenraich, Santosh Kumar, Claudio Ferreira Dias
    Abstract:

    The sum of Wishart matrices has an important role in multiple-input multiple-output (MIMO) multiple access channel (MAC) and MIMO relay channel. In this paper, we present a new closed-form expression for the marginal density of one of the unordered Eigenvalues of a sum of K complex central Wishart matrices having covariance matrices proportional to the identity matrix. The expression is general and allows for any set of linear coefficients. The derived expression is used to obtain the ergodic sum-rate capacity for the MIMO-MAC and MIMO relay cases, both as closed-form expressions. We also present a very simple expression to Approximate the sum of Wishart matrices by one equivalent Wishart matrix. The agreement between the exact Eigenvalue distribution and numerical simulations is perfect, whereas for the Approximate solution the difference is indistinguishable.

  • on the exact and Approximate Eigenvalue distribution for sum of wishart matrices
    arXiv: Information Theory, 2015
    Co-Authors: Santosh Kumar, Gabriel Fernando Pivaro, Gustavo Fraidenraich, Claudio Ferreira Dias
    Abstract:

    The sum of Wishart matrices has an important role in multiuser communication employing multiantenna elements, such as multiple-input multiple-output (MIMO) multiple access channel (MAC), MIMO Relay channel, and other multiuser channels where the mathematical model is best described using random matrices. In this paper, the distribution of linear combination of complex Wishart distributed matrices has been studied. We present a new closed form expression for the marginal distribution of the Eigenvalues of a weighted sum of K complex central Wishart matrices having covariance matrices proportional to the identity matrix. The expression is general and allows for any set of linear coefficients. As an application example, we have used the marginal distribution expression to obtain the ergodic sum-rate capacity for the MIMO-MAC network, and the cut-set upper bound for the MIMO-Relay case, both as closed form expressions. We also present a very simple expression to Approximate the sum of Wishart matrices by one equivalent Wishart matrix. All of our results are validated by means of Monte Carlo simulations. As expected, the agreement between the exact Eigenvalue distribution and simulations is perfect, whereas for the Approximate solution the difference is indistinguishable.

Gabriel Fernando Pivaro - One of the best experts on this subject based on the ideXlab platform.

  • On the Exact and Approximate Eigenvalue Distribution for Sum of Wishart Matrices
    IEEE Transactions on Vehicular Technology, 2017
    Co-Authors: Gabriel Fernando Pivaro, Gustavo Fraidenraich, Santosh Kumar, Claudio Ferreira Dias
    Abstract:

    The sum of Wishart matrices has an important role in multiple-input multiple-output (MIMO) multiple access channel (MAC) and MIMO relay channel. In this paper, we present a new closed-form expression for the marginal density of one of the unordered Eigenvalues of a sum of K complex central Wishart matrices having covariance matrices proportional to the identity matrix. The expression is general and allows for any set of linear coefficients. The derived expression is used to obtain the ergodic sum-rate capacity for the MIMO-MAC and MIMO relay cases, both as closed-form expressions. We also present a very simple expression to Approximate the sum of Wishart matrices by one equivalent Wishart matrix. The agreement between the exact Eigenvalue distribution and numerical simulations is perfect, whereas for the Approximate solution the difference is indistinguishable.

  • on the exact and Approximate Eigenvalue distribution for sum of wishart matrices
    arXiv: Information Theory, 2015
    Co-Authors: Santosh Kumar, Gabriel Fernando Pivaro, Gustavo Fraidenraich, Claudio Ferreira Dias
    Abstract:

    The sum of Wishart matrices has an important role in multiuser communication employing multiantenna elements, such as multiple-input multiple-output (MIMO) multiple access channel (MAC), MIMO Relay channel, and other multiuser channels where the mathematical model is best described using random matrices. In this paper, the distribution of linear combination of complex Wishart distributed matrices has been studied. We present a new closed form expression for the marginal distribution of the Eigenvalues of a weighted sum of K complex central Wishart matrices having covariance matrices proportional to the identity matrix. The expression is general and allows for any set of linear coefficients. As an application example, we have used the marginal distribution expression to obtain the ergodic sum-rate capacity for the MIMO-MAC network, and the cut-set upper bound for the MIMO-Relay case, both as closed form expressions. We also present a very simple expression to Approximate the sum of Wishart matrices by one equivalent Wishart matrix. All of our results are validated by means of Monte Carlo simulations. As expected, the agreement between the exact Eigenvalue distribution and simulations is perfect, whereas for the Approximate solution the difference is indistinguishable.

John R Buck - One of the best experts on this subject based on the ideXlab platform.

  • Approximate Eigenvalue distribution of a cylindrically isotropic noise sample covariance matrix
    arXiv: Systems and Control, 2016
    Co-Authors: Saurav R Tuladhar, John R Buck
    Abstract:

    The statistical behavior of the Eigenvalues of the sample covariance matrix (SCM) plays a key role in determining the performance of adaptive beamformers (ABF) in presence of noise. This paper presents a method to compute the Approximate Eigenvalue density function (EDF) for the SCM of a \cin{} field when only a finite number of shapshots are available. The EDF of the ensemble covariance matrix (ECM) is modeled as an atomic density with many fewer atoms than the SCM size. The model results in substantial computational savings over more direct methods of computing the EDF. The Approximate EDF obtained from this method agrees closely with histograms of Eigenvalues obtained from simulation.

  • Approximate Eigenvalue distribution of a cylindrically isotropic noise sample covariance matrix
    IEEE Signal Processing Workshop on Statistical Signal Processing, 2012
    Co-Authors: Saurav R Tuladhar, John R Buck, Kathleen E Wage
    Abstract:

    The statistical behavior of the Eigenvalues of the sample covariance matrix (SCM) plays a key role in determining the performance of adaptive beamformers (ABF) in presence of noise. This paper presents a method to compute the Approximate Eigenvalue density function (EDF) for the SCM of a cylindrically isotropic noise field when only a finite number of shapshots are available. The EDF of the ensemble covariance matrix (ECM) is modeled as an atomic density with many fewer atoms than the SCM size. The model results in substantial computational savings over more direct methods of computing the EDF. The Approximate EDF obtained from this method agrees closely with histograms of Eigenvalues obtained from simulation.

Saurav R Tuladhar - One of the best experts on this subject based on the ideXlab platform.

  • Approximate Eigenvalue distribution of a cylindrically isotropic noise sample covariance matrix
    arXiv: Systems and Control, 2016
    Co-Authors: Saurav R Tuladhar, John R Buck
    Abstract:

    The statistical behavior of the Eigenvalues of the sample covariance matrix (SCM) plays a key role in determining the performance of adaptive beamformers (ABF) in presence of noise. This paper presents a method to compute the Approximate Eigenvalue density function (EDF) for the SCM of a \cin{} field when only a finite number of shapshots are available. The EDF of the ensemble covariance matrix (ECM) is modeled as an atomic density with many fewer atoms than the SCM size. The model results in substantial computational savings over more direct methods of computing the EDF. The Approximate EDF obtained from this method agrees closely with histograms of Eigenvalues obtained from simulation.

  • Approximate Eigenvalue distribution of a cylindrically isotropic noise sample covariance matrix
    IEEE Signal Processing Workshop on Statistical Signal Processing, 2012
    Co-Authors: Saurav R Tuladhar, John R Buck, Kathleen E Wage
    Abstract:

    The statistical behavior of the Eigenvalues of the sample covariance matrix (SCM) plays a key role in determining the performance of adaptive beamformers (ABF) in presence of noise. This paper presents a method to compute the Approximate Eigenvalue density function (EDF) for the SCM of a cylindrically isotropic noise field when only a finite number of shapshots are available. The EDF of the ensemble covariance matrix (ECM) is modeled as an atomic density with many fewer atoms than the SCM size. The model results in substantial computational savings over more direct methods of computing the EDF. The Approximate EDF obtained from this method agrees closely with histograms of Eigenvalues obtained from simulation.

Santosh Kumar - One of the best experts on this subject based on the ideXlab platform.

  • On the Exact and Approximate Eigenvalue Distribution for Sum of Wishart Matrices
    IEEE Transactions on Vehicular Technology, 2017
    Co-Authors: Gabriel Fernando Pivaro, Gustavo Fraidenraich, Santosh Kumar, Claudio Ferreira Dias
    Abstract:

    The sum of Wishart matrices has an important role in multiple-input multiple-output (MIMO) multiple access channel (MAC) and MIMO relay channel. In this paper, we present a new closed-form expression for the marginal density of one of the unordered Eigenvalues of a sum of K complex central Wishart matrices having covariance matrices proportional to the identity matrix. The expression is general and allows for any set of linear coefficients. The derived expression is used to obtain the ergodic sum-rate capacity for the MIMO-MAC and MIMO relay cases, both as closed-form expressions. We also present a very simple expression to Approximate the sum of Wishart matrices by one equivalent Wishart matrix. The agreement between the exact Eigenvalue distribution and numerical simulations is perfect, whereas for the Approximate solution the difference is indistinguishable.

  • on the exact and Approximate Eigenvalue distribution for sum of wishart matrices
    arXiv: Information Theory, 2015
    Co-Authors: Santosh Kumar, Gabriel Fernando Pivaro, Gustavo Fraidenraich, Claudio Ferreira Dias
    Abstract:

    The sum of Wishart matrices has an important role in multiuser communication employing multiantenna elements, such as multiple-input multiple-output (MIMO) multiple access channel (MAC), MIMO Relay channel, and other multiuser channels where the mathematical model is best described using random matrices. In this paper, the distribution of linear combination of complex Wishart distributed matrices has been studied. We present a new closed form expression for the marginal distribution of the Eigenvalues of a weighted sum of K complex central Wishart matrices having covariance matrices proportional to the identity matrix. The expression is general and allows for any set of linear coefficients. As an application example, we have used the marginal distribution expression to obtain the ergodic sum-rate capacity for the MIMO-MAC network, and the cut-set upper bound for the MIMO-Relay case, both as closed form expressions. We also present a very simple expression to Approximate the sum of Wishart matrices by one equivalent Wishart matrix. All of our results are validated by means of Monte Carlo simulations. As expected, the agreement between the exact Eigenvalue distribution and simulations is perfect, whereas for the Approximate solution the difference is indistinguishable.