On Linearly Precoded Rate Splitting for Gaussian MIMO Broadcast Channels

TL;DR

This paper explores linear precoding combined with rate-splitting for Gaussian MIMO broadcast channels, providing new achievable rate regions, practical algorithms for stream management, and insights into the scheme's near-optimality and limitations.

Contribution

It introduces a tractable achievable rate region with MMSE precoding, practical algorithms for stream reduction, and analyzes the constant-gap optimality of rate-splitting in multi-user MIMO channels.

Findings

Derived an achievable rate region with MMSE precoding and joint decoding.

Provided an upper bound on sum rate close to actual performance.

Showed rate-splitting achieves near-capacity in two-user case but not in three-user case.

Abstract

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