A Linearly Precoded Rate Splitting Approach and Its Optimality for MIMO Broadcast Channels

Previously, the authors have shown that linear precoding with only private streams can have unbounded gap to the sum capacity of the two-user multi-input single-output (MISO) broadcast channel (BC), and that rate-splitting (RS) combined with zero-forcing (ZF) can reduce the gap to a constant number of bits per channel use. In this paper, we extend the investigation to the general K-user multiple-input multiple-output (MIMO) channel. We propose a RS scheme with minimum mean square error (MMSE) precoding. First, we show that the proposed scheme achieves the whole capacity region to within a constant gap in the two-user case. Second, we prove that the proposed scheme does not enjoy the same optimality in the three-user case in general. Third, we provide a simple pathological example showing why RS with linear precoding does not work beyond the two-user case. The current study reveals a fundamental gap between the transmitter-side and the receiver-side interference mitigation.