The Experts below are selected from a list of 1053 Experts worldwide ranked by ideXlab platform
Andrea Goldsmith - One of the best experts on this subject based on the ideXlab platform.
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1Eigenvalue Dynamics of a Central Wishart Matrix with Application to MIMO Systems
2016Co-Authors: Javier F. Lopez-martinez, Jose F Paris, Eduardo Martos-naya, Andrea GoldsmithAbstract:Abstract—We investigate the dynamic behavior of the sta-tionary random process defined by a central complex Wishart (CW) matrix W(t) as it varies along a certain dimension t. We characterize the second-order Joint Cdf of the largest eigenvalue, and the second-order Joint Cdf of the smallest eigenvalue of this matrix. We show that both Cdfs can be expressed in exact closed-form in terms of a finite number of well-known special functions in the context of communication theory. As a direct application, we investigate the dynamic behavior of the parallel channels associated with multiple-input multiple-output (MIMO) systems in the presence of Rayleigh fading. Studying the complex random matrix that defines the MIMO channel, we characterize the second-order Joint Cdf of the signal-to-noise ratio (SNR) for the best and worst channels. We use these results to study the rate of change of MIMO parallel channels, using different performance metrics. For a given value of the MIMO channel correlation coefficient, we observe how the SNR associated with the best parallel channel changes slower than the SNR of the worst channel. This different dynamic behavior is much more appreciable when the number of transmit (NT) and receive (NR) antennas is similar. However, as NT is increased while keeping NR fixed, we see how the best and worst channels tend to have a similar rate of change
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eigenvalue dynamics of a central wishart matrix with application to mimo systems
IEEE Transactions on Information Theory, 2015Co-Authors: Javier F Lopezmartinez, Eduardo Martosnaya, Jose F Paris, Andrea GoldsmithAbstract:We investigate the dynamic behavior of the stationary random process defined by a central complex Wishart matrix ${\rm {W}}(t)$ as it varies along a certain dimension $t$ . We characterize the second-order Joint cumulative distribution function (Cdf) of the largest eigenvalue, and the second-order Joint Cdf of the smallest eigenvalue of this matrix. We show that both Cdfs can be expressed in exact closed-form in terms of a finite number of well-known special functions in the context of communication theory. As a direct application, we investigate the dynamic behavior of the parallel channels associated with multiple-input multiple-output (MIMO) systems in the presence of Rayleigh fading. Studying the complex random matrix that defines the MIMO channel, we characterize the second-order Joint Cdf of the signal-to-noise ratio (SNR) for the best and worst channels. We use these results to study the rate of change of MIMO parallel channels, using different performance metrics. For a given value of the MIMO channel correlation coefficient, we observe how the SNR associated with the best parallel channel changes slower than the SNR of the worst channel. This different dynamic behavior is much more appreciable when the number of transmit ( $N_{T}$ ) and receive ( $N_{R}$ ) antennas is similar. However, as $N_{T}$ is increased while keeping $N_{R}$ fixed, we see how the best and worst channels tend to have a similar rate of change.
Liu Du - One of the best experts on this subject based on the ideXlab platform.
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reliability based design optimization of problems with correlated input variables using a gaussian copula
Structural and Multidisciplinary Optimization, 2009Co-Authors: Kyung K. Choi, Liu DuAbstract:The reliability-based design optimization (RBDO) using performance measure approach for problems with correlated input variables requires a transformation from the correlated input random variables into independent standard normal variables. For the transformation with correlated input variables, the two most representative transformations, the Rosenblatt and Nataf transformations, are investigated. The Rosenblatt transformation requires a Joint cumulative distribution function (Cdf). Thus, the Rosenblatt transformation can be used only if the Joint Cdf is given or input variables are independent. In the Nataf transformation, the Joint Cdf is approximated using the Gaussian copula, marginal Cdfs, and covariance of the input correlated variables. Using the generated Cdf, the correlated input variables are transformed into correlated normal variables and then the correlated normal variables are transformed into independent standard normal variables through a linear transformation. Thus, the Nataf transformation can accurately estimates Joint normal and some lognormal Cdfs of the input variable that cover broad engineering applications. This paper develops a PMA-based RBDO method for problems with correlated random input variables using the Gaussian copula. Several numerical examples show that the correlated random input variables significantly affect RBDO results.
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Selection of Copula to Generate Input Joint Cdf for RBDO
Volume 1: 34th Design Automation Conference Parts A and B, 2008Co-Authors: Kyung K. Choi, Liu DuAbstract:For RBDO problems with correlated input variables, it is necessary to obtain the input Joint distribution (Cdf, cumulative distribution function). Then Rosenblatt transformation is used to transform the correlated input variables into the independent standard normal variables for the purpose of inverse reliability analysis. However, in practical industry RBDO problems, often only the marginal Cdfs and paired samples are available from limited experimental data. In this paper, a copula, which is a link between a Joint Cdf and marginal Cdfs, is proposed to generate an input Joint Cdf from these marginal Cdfs and paired samples. To identify the right copula from limited data, Bayesian method is proposed to use in this paper. Using Bayesian method, the number of samples required to properly identify the right copula is investigated for different types of copulas and for different correlation coefficients. A real industry problem is used to show how a copula can be identified from the limited experimental data.Copyright © 2008 by ASME
Javier F Lopezmartinez - One of the best experts on this subject based on the ideXlab platform.
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eigenvalue dynamics of a central wishart matrix with application to mimo systems
IEEE Transactions on Information Theory, 2015Co-Authors: Javier F Lopezmartinez, Eduardo Martosnaya, Jose F Paris, Andrea GoldsmithAbstract:We investigate the dynamic behavior of the stationary random process defined by a central complex Wishart matrix ${\rm {W}}(t)$ as it varies along a certain dimension $t$ . We characterize the second-order Joint cumulative distribution function (Cdf) of the largest eigenvalue, and the second-order Joint Cdf of the smallest eigenvalue of this matrix. We show that both Cdfs can be expressed in exact closed-form in terms of a finite number of well-known special functions in the context of communication theory. As a direct application, we investigate the dynamic behavior of the parallel channels associated with multiple-input multiple-output (MIMO) systems in the presence of Rayleigh fading. Studying the complex random matrix that defines the MIMO channel, we characterize the second-order Joint Cdf of the signal-to-noise ratio (SNR) for the best and worst channels. We use these results to study the rate of change of MIMO parallel channels, using different performance metrics. For a given value of the MIMO channel correlation coefficient, we observe how the SNR associated with the best parallel channel changes slower than the SNR of the worst channel. This different dynamic behavior is much more appreciable when the number of transmit ( $N_{T}$ ) and receive ( $N_{R}$ ) antennas is similar. However, as $N_{T}$ is increased while keeping $N_{R}$ fixed, we see how the best and worst channels tend to have a similar rate of change.
Jose F Paris - One of the best experts on this subject based on the ideXlab platform.
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1Eigenvalue Dynamics of a Central Wishart Matrix with Application to MIMO Systems
2016Co-Authors: Javier F. Lopez-martinez, Jose F Paris, Eduardo Martos-naya, Andrea GoldsmithAbstract:Abstract—We investigate the dynamic behavior of the sta-tionary random process defined by a central complex Wishart (CW) matrix W(t) as it varies along a certain dimension t. We characterize the second-order Joint Cdf of the largest eigenvalue, and the second-order Joint Cdf of the smallest eigenvalue of this matrix. We show that both Cdfs can be expressed in exact closed-form in terms of a finite number of well-known special functions in the context of communication theory. As a direct application, we investigate the dynamic behavior of the parallel channels associated with multiple-input multiple-output (MIMO) systems in the presence of Rayleigh fading. Studying the complex random matrix that defines the MIMO channel, we characterize the second-order Joint Cdf of the signal-to-noise ratio (SNR) for the best and worst channels. We use these results to study the rate of change of MIMO parallel channels, using different performance metrics. For a given value of the MIMO channel correlation coefficient, we observe how the SNR associated with the best parallel channel changes slower than the SNR of the worst channel. This different dynamic behavior is much more appreciable when the number of transmit (NT) and receive (NR) antennas is similar. However, as NT is increased while keeping NR fixed, we see how the best and worst channels tend to have a similar rate of change
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eigenvalue dynamics of a central wishart matrix with application to mimo systems
IEEE Transactions on Information Theory, 2015Co-Authors: Javier F Lopezmartinez, Eduardo Martosnaya, Jose F Paris, Andrea GoldsmithAbstract:We investigate the dynamic behavior of the stationary random process defined by a central complex Wishart matrix ${\rm {W}}(t)$ as it varies along a certain dimension $t$ . We characterize the second-order Joint cumulative distribution function (Cdf) of the largest eigenvalue, and the second-order Joint Cdf of the smallest eigenvalue of this matrix. We show that both Cdfs can be expressed in exact closed-form in terms of a finite number of well-known special functions in the context of communication theory. As a direct application, we investigate the dynamic behavior of the parallel channels associated with multiple-input multiple-output (MIMO) systems in the presence of Rayleigh fading. Studying the complex random matrix that defines the MIMO channel, we characterize the second-order Joint Cdf of the signal-to-noise ratio (SNR) for the best and worst channels. We use these results to study the rate of change of MIMO parallel channels, using different performance metrics. For a given value of the MIMO channel correlation coefficient, we observe how the SNR associated with the best parallel channel changes slower than the SNR of the worst channel. This different dynamic behavior is much more appreciable when the number of transmit ( $N_{T}$ ) and receive ( $N_{R}$ ) antennas is similar. However, as $N_{T}$ is increased while keeping $N_{R}$ fixed, we see how the best and worst channels tend to have a similar rate of change.
Kyung K. Choi - One of the best experts on this subject based on the ideXlab platform.
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reliability based design optimization of problems with correlated input variables using a gaussian copula
Structural and Multidisciplinary Optimization, 2009Co-Authors: Kyung K. Choi, Liu DuAbstract:The reliability-based design optimization (RBDO) using performance measure approach for problems with correlated input variables requires a transformation from the correlated input random variables into independent standard normal variables. For the transformation with correlated input variables, the two most representative transformations, the Rosenblatt and Nataf transformations, are investigated. The Rosenblatt transformation requires a Joint cumulative distribution function (Cdf). Thus, the Rosenblatt transformation can be used only if the Joint Cdf is given or input variables are independent. In the Nataf transformation, the Joint Cdf is approximated using the Gaussian copula, marginal Cdfs, and covariance of the input correlated variables. Using the generated Cdf, the correlated input variables are transformed into correlated normal variables and then the correlated normal variables are transformed into independent standard normal variables through a linear transformation. Thus, the Nataf transformation can accurately estimates Joint normal and some lognormal Cdfs of the input variable that cover broad engineering applications. This paper develops a PMA-based RBDO method for problems with correlated random input variables using the Gaussian copula. Several numerical examples show that the correlated random input variables significantly affect RBDO results.
-
Selection of Copula to Generate Input Joint Cdf for RBDO
Volume 1: 34th Design Automation Conference Parts A and B, 2008Co-Authors: Kyung K. Choi, Liu DuAbstract:For RBDO problems with correlated input variables, it is necessary to obtain the input Joint distribution (Cdf, cumulative distribution function). Then Rosenblatt transformation is used to transform the correlated input variables into the independent standard normal variables for the purpose of inverse reliability analysis. However, in practical industry RBDO problems, often only the marginal Cdfs and paired samples are available from limited experimental data. In this paper, a copula, which is a link between a Joint Cdf and marginal Cdfs, is proposed to generate an input Joint Cdf from these marginal Cdfs and paired samples. To identify the right copula from limited data, Bayesian method is proposed to use in this paper. Using Bayesian method, the number of samples required to properly identify the right copula is investigated for different types of copulas and for different correlation coefficients. A real industry problem is used to show how a copula can be identified from the limited experimental data.Copyright © 2008 by ASME
