Mutual Information Bounds for MIMO Gaussian Channels

The mutual information between modulation- constrained input and its output through Gaussian channels has been studied for various purposes such as physical layer abstraction. While the capacity of multiple-input and multiple-output (MIMO) Gaussian channels is well understood and its simple formula exists, this modulation- constrained mutual information for MIMO Gaussian channels has only been computed numerically and its expression for online computation has not been found. To tackle this challenge, this paper proposes several new bounds on the mutual information for MIMO Gaussian channels, which can be used for approximation. The proposed bounds are expressed in the forms that can be computed online. Moreover, these bounds are improved by taking a minimum of upper bounds and a maximum of lower bounds. The proposed bounds are compared with the mutual information obtained through simulation.