On the Condition Number Distribution of Complex Wishart Matrices


Autoria(s): Matthaiou, Michail; McKay, Matthew R.; Smith, Peter J.; Nossek, Josef A.
Data(s)

01/06/2010

Resumo

This paper investigates the distribution of the condition number of complex Wishart matrices. Two closely related measures are considered: the standard condition number (SCN) and the Demmel condition number (DCN), both of which have important applications in the context of multiple-input multipleoutput (MIMO) communication systems, as well as in various branches of mathematics. We first present a novel generic framework for the SCN distribution which accounts for both central and non-central Wishart matrices of arbitrary dimension. This result is a simple unified expression which involves only a single scalar integral, and therefore allows for fast and efficient computation. For the case of dual Wishart matrices, we derive new exact polynomial expressions for both the SCN and DCN distributions. We also formulate a new closed-form expression for the tail SCN distribution which applies for correlated central Wishart matrices of arbitrary dimension and demonstrates an interesting connection to the maximum eigenvalue moments of Wishart matrices of smaller dimension. Based on our analytical results, we gain valuable insights into the statistical behavior of the channel conditioning for various MIMO fading scenarios, such as uncorrelated/semi-correlated Rayleigh fading and Ricean fading. © 2010 IEEE.

Identificador

http://pure.qub.ac.uk/portal/en/publications/on-the-condition-number-distribution-of-complex-wishart-matrices(1e0e48ae-1033-4451-9d23-929e61b26af4).html

http://dx.doi.org/10.1109/TCOMM.2010.06.090328

http://www.scopus.com/inward/record.url?eid=2-s2.0-77953175970&partnerID=8YFLogxK

Idioma(s)

eng

Direitos

info:eu-repo/semantics/restrictedAccess

Fonte

Matthaiou , M , McKay , M R , Smith , P J & Nossek , J A 2010 , ' On the Condition Number Distribution of Complex Wishart Matrices ' IEEE Transactions on Communications , vol 58 , no. 6 , pp. 1705-1717 . DOI: 10.1109/TCOMM.2010.06.090328

Tipo

article