Prathapasinghe Dharmawansa — Page 3

arXiv2012

On the Exact Distribution of the Scaled Largest Eigenvalue

In this paper we study the distribution of the scaled largest eigenvalue of complexWishart matrices, which has diverse applications both in statistics and wireless communications. Exact expressions, valid for any matrix dimensions, have been derived for the probability density function and the cumulative distribution function. The derived results involve only finite sums of polynomials. These results are obtained by taking advantage of properties of the Mellin transform for products of independent random variables.

cs.IT↗

arXiv2011

Extreme Eigenvalue Distributions of Some Complex Correlated Non-Central Wishart and Gamma-Wishart Random Matrices

Let $\mathbf{W}$ be a correlated complex non-central Wishart matrix defined through $\mathbf{W}=\mathbf{X}^H\mathbf{X}$, where $\mathbf{X}$ is $n\times m \, (n\geq m)$ complex Gaussian with non-zero mean $\boldsymbolΥ$ and non-trivial covariance $\boldsymbolΣ$. We derive exact expressions for the cumulative distribution functions (c.d.f.s) of the extreme eigenvalues (i.e., maximum and minimum) of $\mathbf{W}$ for some particular cases. These results are quite simple, involving rapidly converging infinite series, and apply for the practically important case where $\boldsymbolΥ$ has rank one. We also derive analogous results for a certain class of gamma-Wishart random matrices, for which $\boldsymbolΥ^H\boldsymbolΥ$ follows a matrix-variate gamma distribution. The eigenvalue distributions in this paper have various applications to wireless communication systems, and arise in other fields such as econometrics, statistical physics, and multivariate statistics.

math.ST↗