Degrees of freedom region in multi-cell random beamforming

Random beamforming (RBF) is a practically favorable transmission scheme for multiuser multi-antenna downlink systems. This paper studies the asymptotic rates achievable with RBF in a multi-cell system subject to the inter-cell interference, by assuming that the number of users in each cell scales in a given order with the signal-to-noise ratio (SNR). In particular, we investigate the achievable degrees of freedom (DoF) for the sum-rate in each cell when the SNR goes to infinity, and characterize the achievable DoF region for all the cells. Our results show that to achieve the DoF-optimal transmission in a multi-cell system with RBF, the numbers of transmit beams in all the cells need to be assigned in a collaborative manner based on the user densities.