Distribution of the Demmel Condition Number of Wishart Matrices


Autoria(s): Zhong, C.J.; McKay, M.R.; Ratnarajah, Tharmalingam; Wong, K.K.
Data(s)

01/05/2011

Resumo

This paper studies the Demmel condition number of Wishart matrices, a quantity which has numerous applications to wireless communications, such as adaptive switching between beamforming and diversity coding, link adaptation, and spectrum sensing. For complex Wishart matrices, we give an exact analytical expression for the probability density function (p.d.f.) of the Demmel condition number, and also derive simplified expressions for the high tail regime. These results indicate that the condition of complex Wishart matrices is dominantly decided by the difference between the matrix dimension and degree of freedom (DoF), i.e., the probability of drawing a highly ill conditioned matrix decreases considerably when the difference between the matrix dimension and DoF increases. We further investigate real Wishart matrices, and derive new expressions for the p.d.f. of the smallest eigenvalue, when the difference between the matrix dimension and DoF is odd. Based on these results, we succeed to obtain an exact p.d.f. expression for the Demmel condition number, and simplified expressions for the high tail regime.

Formato

application/pdf

Identificador

http://pure.qub.ac.uk/portal/en/publications/distribution-of-the-demmel-condition-number-of-wishart-matrices(99392bfa-c4da-49d0-9fe8-2e04a83de904).html

http://dx.doi.org/10.1109/TCOMM.2011.040111.100137

http://pure.qub.ac.uk/ws/files/839292/ratnarajah4.pdf

Idioma(s)

eng

Direitos

info:eu-repo/semantics/restrictedAccess

Fonte

Zhong , C J , McKay , M R , Ratnarajah , T & Wong , K K 2011 , ' Distribution of the Demmel Condition Number of Wishart Matrices ' IEEE Transactions on Communications , vol 59 , no. 5 , 5766671 , pp. 1309-1320 . DOI: 10.1109/TCOMM.2011.040111.100137

Palavras-Chave #/dk/atira/pure/subjectarea/asjc/2200/2208 #Electrical and Electronic Engineering
Tipo

article