On Linearly Precoded Rate Splitting for Gaussian MIMO Broadcast Channels

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.

Rate Splitting in MIMO RIS-Assisted Systems With Hardware Impairments and Improper Signaling

“…Now we discuss the complexity of solving the surrogate optimization problem in each iteration, which is provided in (14). Since (14) includes the most general optimization problem, we consider the MWRM problem in (17), which has a specific structure. Note that it is straightforward to extend to the computational complexity analysis to other optimization problems.…”

“…Unlike NOMA, RSMA does not need any user ordering and has been shown to be robust against imperfect CSI [20], [21]. The performance of RSMA in MIMO systems has to be developed further, but the existing literature shows that RSMA may improve the spectral efficiency of 2user MIMO IC and/or BC [17], [22]. To summarize, RSMA can be adapted to the interference level and is robust against imperfect CSI.…”

Rate-Splitting Multiple Access: Fundamentals, Survey, and Future Research Trends

“…The authors of [62], [91] characterized the entire GDoF region of the two-user underloaded MISO BC with imperfect CSIT, and the GDoF optimal achievable scheme is built upon RS. Capacity region: Besides the DoF metrics, RS has been shown to achieve the sum capacity [63] and further the entire capacity region [64], [65] within a constant gap for the two- user MIMO BC with perfect CSIT. The reviewed informationtheoretic works on RSMA are summarized in Table IV.…”

“…The authors of [90] further establish the achievable sum-DoF of RSMA in the K-user symmetric MIMO BC with M transmit antennas, Q receive antennas at each user, and an arbitrary number of common streams in the range of [1, min(M, Q)]. In [65], RSMA was shown to achieve the capacity region of the two-user MIMO BC with perfect CSIT within a constant gap, but such constantgap optimality does not extend to the three-user case.…”

Deep Learning-Based Signal Detection for Rate-Splitting Multiple Access Under Generalized Gaussian Noise

“…Although the most popular receiver is SIC-based, several other receiver architectures have also been proposed in the literature. A turbo decoding receiver and a joint decoding receiver have been proposed in [43], [51], [52]. However, these designs largely rely on the channel, noise and interference models and associated assumptions, which could be highly application-specific [21].…”