Distribution of the Demmel Condition Number of Complex Wishart Matrices

In this paper, we study the statistical distribution of the Demmel condition number of complex Wishart matrices, a quantity which has found numerous applications to wireless communications, such as adaptive switching, link adaptation, and spectrum sensing. 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).