Novel Closed-Form Expressions for Ergodic Capacity of MIMO Ad-Hoc Networks

Abstract

In this letter, we study the ergodic capacity of MIMO Ad-Hoc networks under imperfect channel state information (CSI). Evaluating MIMO capacity under imperfect CSI is still an open problem, and only approximate results for it can be obtained in asymptotic regions so far. In this letter, different from the previous method, we apply the exact probability density function (PDF) of the ratio of two Wishart matrices to evaluate the ergodic capacity of MIMO Ad-Hoc networks. For utilizing the most cutting-edge PDF to solve our problem, we first derive an equivalent Wishart matrix for the sum of interference covariance matrices. And then, based on the equivalent matrix, we obtain an expression for the ergodic capacity by directly applying the PDF of the ratio of two Wishart matrices, which requires M-fold (M is the number of receive antennas) multiple integrals. To avoid the time-consuming M-fold multiple integral, based on Laplace transform, we provide an alternative method which only involves several single integrals.