Approximation to the condition number distribution of almost square matrices

The condition number distribution of random matrices is crucial to understand for statistical characterization of various communication systems. In this paper, we propose a general approximation methodology for the condition number distribution of finite dimensional Wishart matrices. This approximation leads to a computable expression for condition number distributions. The proposed method can be applied to both uncorrelated and correlated central Wishart matrices. This approximation is shown to be most accurate when the multivariate sample matrix is close to a square matrix and when there is correlation in the smaller of the dimensions of the sample matrix. The accuracy of the proposed approximation formula is validated by comparing with simulation results, with the achieved accuracy being remarkably good.