MIMO Broadcast Channel Rate Region With Linear Precoding at High SNR: No Full Multiplexing Case

In this paper, the rate region of the two user MIMO Broadcast Channel (BC) with linear filtering at high Signal-to-Noise Ratio (SNR) is studied when time sharing is not available and the transmitter has fewer antennas than the sum of the receiving antennas. To reach the boundary of the rate region, the sum rate is maximized subject to a rate ratio constraint. Furthermore, the sum rate is approximated as an affine function of the logarithm of the SNR and the two parameters of this approximation, which are the Multiplexing Gain (MG) and the Rate Offset (RO), are derived.