Approximate Condition Number Distribution of Complex Non-Central Correlated Wishart Matrices

Statistical properties of the channel condition number is important in performance analysis and design of communication systems. In this paper we study the condition number distribution of complex non-central correlated Wishart matrices, relevant for spatially correlated Ricean MIMO channels and detection performance in cognitive radio. We present an approximation framework which is utilized to calculate finite dimensional condition number distributions, valid for arbitrary matrix dimensions. The same framework is applied to obtain asymptotical condition number distributions with low computational complexity for large dimensional matrices. Intensive simulations are conducted to investigate accuracy of the proposed approximations, with the achieved accuracy being remarkably good.