Title :
Exact Minimum Eigenvalue Distribution of a Correlated Complex Non-Central Wishart Matrix
Author :
Dharmawansa, Prathapasinghe ; McKay, Matthew R.
Author_Institution :
Dept. of Electron. & Comput. Eng., Hong Kong Univ. of Sci. & Technol., Kowloon
Abstract :
We derive the exact cumulative distribution function (c.d.f.) of the minimum eigenvalue of a correlated complex non-central Wishart matrix. This result is in the form of a simple infinite series with fast convergence, and applies for the important case where the non-centrality matrix has rank one. Simplified asymptotic expressions for the c.d.f. are given for large matrix dimensions, as well as first-order expansions around the origin. The eigenvalue distributions in this paper have various important applications to multiple-input multiple-output (MIMO) communication systems, as well other scientific areas such as econometrics and multivariate statistics.
Keywords :
convergence; eigenvalues and eigenfunctions; higher order statistics; matrix algebra; series (mathematics); statistical distributions; MIMO communication system; asymptotic expression; correlated complex noncentral Wishart matrix; cumulative distribution function; econometrics; infinite series convergence; minimum eigenvalue distribution; multiple-input multiple-output communication system; multivariate statistics; Computer vision; Distributed computing; Distribution functions; Econometrics; Eigenvalues and eigenfunctions; Information technology; MIMO; Performance analysis; Symmetric matrices; Wireless communication;
Conference_Titel :
Global Telecommunications Conference, 2008. IEEE GLOBECOM 2008. IEEE
Conference_Location :
New Orleans, LO
Print_ISBN :
978-1-4244-2324-8
DOI :
10.1109/GLOCOM.2008.ECP.212
