  Using Gaussian inputs and treating interference as noise at the receivers has
recently been shown to be sum capacity achieving for the two-user single-input
single-output (SISO) Gaussian interference channel in a low interference
regime, where the interference levels are below certain thresholds. In this
paper, such a low interference regime is characterized for multiple-input
multiple-output (MIMO) Gaussian interference channels. Conditions are provided
on the direct and cross channel gain matrices under which using Gaussian inputs
and treating interference as noise at the receivers is sum capacity achieving.
For the special cases of the symmetric multiple-input single-output (MISO) and
single-input multiple-output (SIMO) Gaussian interference channels, more
explicit expressions for the low interference regime are derived. In
particular, the threshold on the interference levels that characterize low
interference regime is related to the input SNR and the angle between the
direct and cross channel gain vectors. It is shown that the low interference
regime can be quite significant for MIMO interference channels, with the low
interference threshold being at least as large as the sine of the angle between
the direct and cross channel gain vectors for the MISO and SIMO cases.
