On the condition number distribution of complex wishart matrices

Abstract—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 intere...

• Type: Journal
• Year: 2010
• Where: TCOM
• Authors: Michail Matthaiou, Matthew R. McKay, Peter J. Smith, Josef A. Nossek
• Keywords: Condition Number, SCN Distribution, TCOM 2010, Wishart Matrices