Antenna Scaling of Multi-Antenna Gaussian Broadcast Channels

We study the gain of dirty paper coding (DPC) by investigating the sum rate as the number of antennas at the transmitter grows in a multi-user MISO broadcast channel. We show a comparative sum rate gain of DPC over the zero forcing (ZF) scheme. The sum rate gap between DPC and ZF is analyzed assuming asymptotically high signal-to-noise ratio (SNR) in the case when the number of users is the same as the number of antennas at the transmitter. As a result, we find the sum rate gap is linearly increased as the number of transmit antennas is increased. Also, numerical results of DPC and ZF are shown in a M-by-1 MISO, M-user Rayleigh fading channel, where M=2, 4, 8, 16. We conclude that the more the number of transmit antennas is, the more attractive DPC becomes with respect to the sum rate.