Achievable throughput approximation for RBD precoding at high SNRS

In this paper, we study the achievable throughput for regularized block diagonalization (RBD) precoding in multi-user MIMO broadcast channels at high SNRs. By applying an analytical framework for a high SNR affine approximation to capacity, we derive the multiplexing gains and the power offsets for RBD in two cases separately. In the first case, we assume that the aggregate number of receive antennas is less than or equal to the number of transmit antennas. It is found that RBD can maintain the same multiplexing gain as dirty paper coding (DPC) and block diagonalization (BD) precoding at high SNRs and has a smaller power offset than BD. The sum rate differences relative to DPC and BD are analyzed and bounded as simple functions of the system parameters. In the second case, we assume that the aggregate number of receive antennas is larger than the number of transmit antennas. Although RBD can still be performed, the achievable throughput is degraded with an increasing number of receive antennas. The benefit of spatial multiplexing is completely lost due to a unit spatial multiplexing gain at high SNRs.