  Random beamforming (RBF) is a practically favourable transmission scheme for
multiuser multi-antenna downlink systems since it requires only partial channel
state information (CSI) at the transmitter. Under the conventional single-cell
setup, RBF is known to achieve the optimal sum-capacity scaling law as the
number of users goes to infinity, thanks to the multiuser diversity enabled
transmission scheduling that virtually eliminates the intra-cell interference.
In this paper, we extend the study of RBF to a more practical multi-cell
downlink system with single-antenna receivers subject to the additional
inter-cell interference (ICI). First, we consider the case of finite
signal-to-noise ratio (SNR) at each receiver. We derive a closed-form
expression of the achievable sum-rate with the multi-cell RBF, based upon which
we show an asymptotic sum-rate scaling law as the number of users goes to
infinity. Next, we consider the high-SNR regime and for 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 achievable degrees of
freedom (DoF) for the single-cell case with RBF. Then we extend the analysis to
the multi-cell RBF case by characterizing the DoF region. It is shown that the
DoF region characterization provides useful guideline on how to design a
cooperative multi-cell RBF system to achieve optimal throughput tradeoffs among
different cells. Furthermore, our results reveal that the multi-cell RBF scheme
achieves the "interference-free DoF" region upper bound for the multi-cell
system, provided that the per-cell number of users has a sufficiently large
scaling order with the SNR. Our result thus confirms the optimality of
multi-cell RBF in this regime even without the complete CSI at the transmitter,
as compared to other full-CSI requiring transmission schemes such as
interference alignment.
