Effect of receive spatial diversity on the degrees of freedom region in multi-cell random beamforming

The random beamforming (RBF) scheme, together with multi-user diversity based user scheduling, is able to achieve interference-free downlink transmission with only partial channel state information (CSI) at the transmitter. The impact of receive spatial diversity on RBF, however, is not fully characterized even under a single-cell setup. In this paper, we study a multi-cell multiple-input multiple-output (MIMO) broadcast system with RBF applied at each base station and either the minimum-meansquare-error (MMSE), matched filter (MF), or antenna selection (AS) based spatial receiver applied at each mobile terminal. We investigate the effect of different spatial diversity receivers on the achievable sum-rate of the multi-cell RBF system subject to both the intra- and inter-cell interferences. We focus on the high signal-to-noise ratio (SNR) regime and for a tractable analysis assume that the number of users in each cell scales in a certain order with the per-cell SNR. Under this setup, we characterize the degrees of freedom (DoF) region for the multi-cell RBF system, which constitutes all the achievable sum-rate DoF tuples of all the cells. Our results reveal significant sum-rate DoF gains with the MMSE-based spatial receiver as compared to the case without spatial diversity or with suboptimal spatial receivers (MF or AS). This observation is in sharp contrast to the existing result that spatial diversity only yields marginal sum-rate gains based on the conventional asymptotic analysis in the regime of large number of users but with fixed SNR per cell.