On the Asymptotic Geometric Mean of MIMO Channel Eigenvalues

The geometric mean of the eigenvalues of multiple-input multiple-output (MIMO) channels is a parameter occurring in a variety of instances, including MIMO transceiver design based on the so-called geometric mean decomposition (GMD), and MIMO mutual information at high SNR. In this paper, we derive the asymptotic geometric mean of MIMO channel eigenvalues in the case where the entries of the channel matrix are independent and identically distributed. We demonstrate that the result can be easily extended to channels with an exponential correlation model. As an application of the result, we provide an analytical expression for the asymptotic system capacity of GMD-based transceivers.