The Experts below are selected from a list of 30924 Experts worldwide ranked by ideXlab platform

Kefei Liu - One of the best experts on this subject based on the ideXlab platform.

  • an eigenvalue moment ratio approach to blind spectrum sensing for cognitive radio under sample starving environment
    IEEE Transactions on Vehicular Technology, 2015
    Co-Authors: Lei Huang, Jun Fang, Kefei Liu
    Abstract:

    Eigenvalue-based methods have been widely investigated for multiantenna blind spectrum sensing in cognitive radio (CR). However, most of them are formulated in the framework of maximum likelihood (ML) estimation, which is optimal only when the number of samples is much larger than the number of antennas. In relatively small-sample scenarios where the number of antennas is comparable in magnitude to the number of samples, their optimality cannot be guaranteed. Based on the random Matrix theory (RMT), an eigenvalue moment ratio (EMR) approach is proposed for spectrum sensing. As the distribution of the EMR statistic in the absence of signals can be precisely determined by the RMT, this approach is able to reliably predict the theoretical threshold. Moreover, as the EMR detector is developed from the RMT perspective and utilizes all the signal eigenvalues for detection, it can be superior to state-of-the-art detection algorithms, particularly for relatively small samples. Furthermore, we derive the asymptotic distribution of the EMR statistic in the presence of signals and analyze the theoretical detection probability of the EMR approach. Additionally, the EMR statistic is calculated via the Frobenius inner product and Matrix Trace operations instead of the eigenvalue decomposition (EVD), which offers computational efficiency. Simulation results are presented to illustrate the superiority of the EMR approach and confirm our theoretical calculation.

Fulvio Gini - One of the best experts on this subject based on the ideXlab platform.

  • cramer rao lower bounds on covariance Matrix estimation for complex elliptically symmetric distributions
    IEEE Transactions on Signal Processing, 2013
    Co-Authors: Maria Greco, Fulvio Gini
    Abstract:

    This paper introduces the Cramer-Rao Lower Bounds (CRLBs) for the scatter Matrix of Complex Elliptically Symmetric distributions and compares them to the performance of the (constrained-)ML estimators in the particular cases of complex Gaussian, Generalized Gaussian (GG) and t-distributed observation vectors. Numerical results confirm the goodness of the ML estimators and the advantage of taking into proper account a constraint on the Matrix Trace for small data size. The work is completed with the comparison with the performance of Tyler's Matrix estimator that shows a very robust behavior in almost all the analyzed cases and with the CRLBs for the Complex Angular Elliptical distributions, whose Tyler's estimator is the ML one.

Fumio Hiai - One of the best experts on this subject based on the ideXlab platform.

  • concavity of certain Matrix Trace and norm functions ii
    Linear Algebra and its Applications, 2013
    Co-Authors: Fumio Hiai
    Abstract:

    Abstract We refine Epstein's method to prove joint concavity/convexity of Matrix Trace functions of Lieb type Tr f ( Φ ( A p ) 1 / 2 Ψ ( B q ) Φ ( A p ) 1 / 2 ) and symmetric (anti-) norm functions of the form ‖ f ( Φ ( A p ) σ Ψ ( B q ) ) ‖ , where Φ and Ψ are positive linear maps, σ is an operator mean, and f ( x γ ) with a certain power γ is an operator monotone function on ( 0 , ∞ ) . Moreover, the variational method of Carlen, Frank and Lieb is extended to general non-decreasing convex/concave functions on ( 0 , ∞ ) so that we prove joint concavity/convexity of more Trace functions of Lieb type.

  • concavity of certain Matrix Trace and norm functions ii
    arXiv: Functional Analysis, 2012
    Co-Authors: Fumio Hiai
    Abstract:

    We refine Epstein's method to prove joint concavity/convexity of Matrix Trace functions of the extended Lieb type $Tr{\Phi(A^p)^{1/2}\Psi(B^q)\Phi(A^p)^{1/2}}^s$, where $\Phi$ and $\Psi$ are positive linear maps. By the same method combined with majorization technique, similar properties are proved for symmetric (anti-) norm functions of the form $||{\Phi(A^p)\sigma\Psi(B^q)}^s||$ involving an operator mean $\sigma$. Carlen and Lieb's variational method is also used to improve the convexity property of norm functions $||\Phi(A^p)^s||$.

Lei Huang - One of the best experts on this subject based on the ideXlab platform.

  • an eigenvalue moment ratio approach to blind spectrum sensing for cognitive radio under sample starving environment
    IEEE Transactions on Vehicular Technology, 2015
    Co-Authors: Lei Huang, Jun Fang, Kefei Liu
    Abstract:

    Eigenvalue-based methods have been widely investigated for multiantenna blind spectrum sensing in cognitive radio (CR). However, most of them are formulated in the framework of maximum likelihood (ML) estimation, which is optimal only when the number of samples is much larger than the number of antennas. In relatively small-sample scenarios where the number of antennas is comparable in magnitude to the number of samples, their optimality cannot be guaranteed. Based on the random Matrix theory (RMT), an eigenvalue moment ratio (EMR) approach is proposed for spectrum sensing. As the distribution of the EMR statistic in the absence of signals can be precisely determined by the RMT, this approach is able to reliably predict the theoretical threshold. Moreover, as the EMR detector is developed from the RMT perspective and utilizes all the signal eigenvalues for detection, it can be superior to state-of-the-art detection algorithms, particularly for relatively small samples. Furthermore, we derive the asymptotic distribution of the EMR statistic in the presence of signals and analyze the theoretical detection probability of the EMR approach. Additionally, the EMR statistic is calculated via the Frobenius inner product and Matrix Trace operations instead of the eigenvalue decomposition (EVD), which offers computational efficiency. Simulation results are presented to illustrate the superiority of the EMR approach and confirm our theoretical calculation.

Uri Ascher - One of the best experts on this subject based on the ideXlab platform.

  • Improved Bounds on Sample Size for Implicit Matrix Trace Estimators
    Foundations of Computational Mathematics, 2015
    Co-Authors: Farbod Roosta-khorasani, Uri Ascher
    Abstract:

    This article is concerned with Monte Carlo methods for the estimation of the Trace of an implicitly given Matrix $$A$$ A whose information is only available through Matrix-vector products. Such a method approximates the Trace by an average of $$N$$ N expressions of the form $$ \mathbf{w} ^t (A \mathbf{w} )$$ w t ( A w ) , with random vectors $$ \mathbf{w} $$ w drawn from an appropriate distribution. We prove, discuss and experiment with bounds on the number of realizations $$N$$ N required to guarantee a probabilistic bound on the relative error of the Trace estimation upon employing Rademacher (Hutchinson), Gaussian and uniform unit vector (with and without replacement) probability distributions. In total, one necessary bound and six sufficient bounds are proved, improving upon and extending similar estimates obtained in the seminal work of Avron and Toledo (JACM 58(2). Article 8, 2011 ) in several dimensions. We first improve their bound on $$N$$ N for the Hutchinson method, dropping a term that relates to $$\mathrm{rank}(A)$$ rank ( A ) and making the bound comparable with that for the Gaussian estimator. We further prove new sufficient bounds for the Hutchinson, Gaussian and unit vector estimators, as well as a necessary bound for the Gaussian estimator, which depend more specifically on properties of Matrix  $$A$$ A . As such, they may suggest the type of Matrix for which one distribution or another provides a particularly effective or relatively ineffective stochastic estimation method.