Exact Demmel Condition Number Distribution of Complex Wishart Matrices via the Mellin Transform

In this letter we study the distribution of the Demmel condition number of complex Wishart matrices, which has various applications in the performance analysis of communication systems. New exact expressions are derived for the probability density function and cumulative distribution function, which are very simple and valid for any matrix dimensions. These results are obtained by taking advantage of properties of the Mellin transform for products of independent random variables.