On Linearly Precoded Rate Splitting for Gaussian MIMO Broadcast Channels

In this paper, we consider a general K-user Gaussian multiple-input multiple-output (MIMO) broadcast channel (BC). We assume that the state is deterministic and known to all nodes. While private-message capacity region well be achievable with dirty paper coding (DPC), are interested in simpler linearly precoded transmission schemes. particular, focus on linear precoding schemes combined rate-splitting (RS). First, derive an rate minimum mean square error (MMSE) at transmitter joint decoding of sub-messages receivers. Then, study sum scheme obtain two findings: 1) analytically tractable upper bound shown numerically close approximation, 2) how reduce number active streams - crucial overall complexity while preserving within constant loss. The latter results practical algorithms: stream elimination algorithm ordering algorithm. Finally, investigate constant-gap optimality RS respect capacity. Our result reveals that, alone can arbitrarily far from capacity, introduction help achieve gap two-user case. Nevertheless, prove scheme's does not extend three-user Specifically, show, through pathological example, between unbounded.