Capacity for MIMO systems at low SNR

The paper introduces an asymptotic series expansion for the mutual information of Multiple-Input Multiple-Output (MIMO) channels. For low signal to noise ratio (SNR) the first term of expansion approaches mutual information from below. Using the low SNR approximation a new water filling power allocation at the transmitter is derived when the receiver and the transmitter have perfect channel state information (CSITR). The low SNR approximation is related to existing approximation while the new water filling policy is related to minimum mean square decoding subject to power constraint. Finally, an upper bound for the outage probability at low SNR is presented.