A Constant-Gap Result on the Multi-Antenna Broadcast Channels with Linearly Precoded Rate Splitting

In this paper, we consider a simple downlink channel with a multi-antenna base station and two single-antenna receivers. We assume that the channel is deterministic and known to all the nodes. Our contribution is two-fold. First, we show that linear precoding with private streams can have unbounded gap to the capacity of the channel. Second, we show that using rate-splitting with a simple power allocation one can achieve the sum capacity to within a constant gap for any channel realization.