High SNR analysis of MIMO broadcast channels

The behavior of the multiple antenna broadcast channel at high SNR is investigated. The multiple antenna broadcast channel achieves the same multiplexing gain as the system in which all receivers are allowed to perfectly cooperate (i.e. transforming the system into a point-to-point MIMO system). However, the multiplexing gain alone is not sufficient to accurately characterize the behavior of sum rate capacity at high SNR. An affine approximation to capacity which incorporates the multiplexing gain as well as a power offset (i.e. a zero-order term) is a more accurate representation of high SNR behavior. The power offset of the sum rate capacity is shown to equal the power offset of the cooperative MIMO system when there are less receivers than transmit antennas. In addition, the power offset of using the sub-optimal strategy of beamforming is calculated. These calculations show that beamforming can perform quite well when the number of antennas is sufficiently larger than the number of receivers, but performs very poorly when there are nearly as many receivers as transmit antennas