Mutual Information Expansion for MIMO Systems and Capacity Formulae at Low SNR

The paper introduces a new asymptotic series expansion for the mutual information of multiple-input multiple-output (MIMO) channels. The expansion approaches mutual information from below, and for low signal to noise ratio (SNR) first and second order terms give a tight lower bound. The low SNR approximation is used to derive a new water-filling power allocation at the transmitter for the case when the receiver and the transmitter have perfect channel state information. The low SNR approximation is also compared against existing approximations, while the new water-filling policy is related to minimum mean square decoding subject to power constraint.