On the Condition Number Distribution of Complex Wishart Matrices (2010)
Type of ContentJournal Articles
PublisherUniversity of Canterbury. Electrical and Computer Engineering
University of Canterbury. Mathematics and Statistics
AuthorsMatthaiou, M., McKay, M.R., Smith, P.J., Nossek, J.A.show all
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 multiple-output (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.
CitationMatthaiou, M., McKay, M.R., Smith, P.J., Nossek, J.A. (2010) On the Condition Number Distribution of Complex Wishart Matrices. IEEE Transactions on Communications, 58(6), pp. 1705-1717.
This citation is automatically generated and may be unreliable. Use as a guide only.
KeywordsMIMO systems; complex Wishart matrices; condition number; joint eigenvalue distribution
ANZSRC Fields of Research10 - Technology::1005 - Communications Technologies::100510 - Wireless Communications
01 - Mathematical Sciences::0101 - Pure Mathematics::010101 - Algebra and Number Theory