On the Exact Distribution of the Scaled Largest Eigenvalue
In this paper, the authors study the distribution of the scaled largest eigenvalue of complex Wishart matrices, which has diverse applications both in statistics and wireless communications. Exact expressions, valid for any matrix dimensions, have been derived for the probability density function and the cumulative distribution function. The derived results involve only finite sums of polynomials. These results are obtained by taking advantage of properties of the Mellin transform for products of independent random variables. Eigenvalue statistics of Wishart matrices play a key role in the performance analysis and design of various communication systems. Among these, the distribution of Scaled Largest Eigenvalue (SLE), defined as the ratio of the largest eigenvalue to the normalized sum of all eigenvalues, has been shown to be an important measure.