Linearly Precoded Rate Splitting: Optimality and Non-Optimality for MIMO Broadcast Channels

In this paper, we consider a general K-user multiple-input multiple-output (MIMO) broadcast channel (BC). We assume that the channel state is deterministic and known to all the nodes. While the capacity region is well known to be achievable with dirty paper coding (DPC), we are interested in the simpler linearly precoded transmission schemes. First, using a simple two-user example, we show that any linear precoding scheme with only private streams can have an unbounded gap to the sum capacity of the channel. Second, we propose a rate-splitting (RS) scheme with minimum mean square error (MMSE) precoding, and demonstrate that the proposed scheme achieves the whole capacity region to within a constant gap in the two-user case. Third, we prove that the proposed scheme does not enjoy the same optimality in the three-user case, which shows the non-optimality of the proposed RS scheme in general. Through a simple pathological example, our study reveals a fundamental gap between the transmitter-side and the receiver-side interference mitigation.