On Linearly Precoded Rate Splitting for MIMO Broadcast Channels

Zheng Li (1, 2) , Sheng Yang (1) , Shlomo Shamai (3)

1 L2S - Laboratoire des signaux et systèmes
2 Orange Labs Networks
3 EE-Technion - Department of Electrical Engineering - Technion [Haïfa]

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. Then, we show that applying rate-splitting (RS) with minimum mean square error (MMSE) precoding, one can achieve the entire capacity region to within a constant gap in the two-user case. Remarkably, such constant-gap optimality of the RS scheme does not extend to the three-user case. Specifically, we derive the constant-gap sum rate of the three-user RS scheme and show that its gap to the sum capacity can be unbounded through a pathological example. For the general K-user RS scheme with arbitrary K, we derive a constant-gap sum rate upper bound that is shown numerically to be tight. Finally, we propose a practical stream elimination algorithm that can reduce the total number of active streams while preserving the constant-gap rate, i.e., with only a finite sum rate loss. Based on the same idea, we propose a second algorithm to order the 2^K-1 streams.

Domaines: Théorie de l'information [cs.IT]

Zheng Li, Sheng Yang, Shlomo Shamai. On Linearly Precoded Rate Splitting for MIMO Broadcast Channels. IEEE Transactions on Information Theory, 2020, ⟨10.1109/TIT.2021.3076888⟩. ⟨hal-02157818⟩