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Robust Precoding Designs of RSMA for Multiuser MIMO Systems

Wentao Zhou, Yijie Mao, Di Zhang, Mérouane Debbah, Inkyu Lee

TL;DR

The paper addresses robust rate-splitting multiple access (RSMA) precoding for multiuser MIMO with imperfect CSIT. It derives a lower bound on ergodic sum rate using generalized mutual information, smooths the non-smooth objective with log-sum-exp, and reformulates the problem into a tractable WMMSE-like form linked to MMSE matrices. An alternating, three-block (P_p, P_c, t) optimization (BCD) yields a low-complexity precoding design that closely matches the performance of the WMMSE-SAA benchmark while significantly reducing computation. Convergence is guaranteed by monotonic reduction of the objective, and simulations demonstrate robustness to CSIT errors with favorable complexity-performance trade-offs, enabling practical RSMA deployment. Overall, the work provides a scalable framework for robust RSMA precoding in MU-MIMO systems with realistic CSIT imperfections.

Abstract

Rate-splitting multiple access (RSMA) has been studied for multiuser multiple-input multiple-output (MUMIMO) systems especially in the presence of imperfect channel state information (CSI) at the transmitter. However, its precoding designs that maximize the sum rate normally have high computational complexity. To implement an efficient RSMA scheme for the MU-MIMO system, in this work, we propose a novel robust precoding design, which can handle imperfect CSI. Specifically, we first adopt the generalized mutual information to construct a lower bound of the objective function in the sum rate maximization problem. Then, we apply a smooth lower bound of the non-smooth sum rate objective function to construct a new optimization problem. By revealing the relationship between the generalized signal-to-interference-plus-noise ratio and the minimum mean square error matrices, we transform the constructed problem into a tractable one. After decomposing the transformed problem into three subproblems, we investigate a new alternating precoding design based on sequential solutions. Simulation results demonstrate that the proposed precoding scheme achieves comparable performance to conventional methods, while significantly reducing the computational complexity.

Robust Precoding Designs of RSMA for Multiuser MIMO Systems

TL;DR

The paper addresses robust rate-splitting multiple access (RSMA) precoding for multiuser MIMO with imperfect CSIT. It derives a lower bound on ergodic sum rate using generalized mutual information, smooths the non-smooth objective with log-sum-exp, and reformulates the problem into a tractable WMMSE-like form linked to MMSE matrices. An alternating, three-block (P_p, P_c, t) optimization (BCD) yields a low-complexity precoding design that closely matches the performance of the WMMSE-SAA benchmark while significantly reducing computation. Convergence is guaranteed by monotonic reduction of the objective, and simulations demonstrate robustness to CSIT errors with favorable complexity-performance trade-offs, enabling practical RSMA deployment. Overall, the work provides a scalable framework for robust RSMA precoding in MU-MIMO systems with realistic CSIT imperfections.

Abstract

Rate-splitting multiple access (RSMA) has been studied for multiuser multiple-input multiple-output (MUMIMO) systems especially in the presence of imperfect channel state information (CSI) at the transmitter. However, its precoding designs that maximize the sum rate normally have high computational complexity. To implement an efficient RSMA scheme for the MU-MIMO system, in this work, we propose a novel robust precoding design, which can handle imperfect CSI. Specifically, we first adopt the generalized mutual information to construct a lower bound of the objective function in the sum rate maximization problem. Then, we apply a smooth lower bound of the non-smooth sum rate objective function to construct a new optimization problem. By revealing the relationship between the generalized signal-to-interference-plus-noise ratio and the minimum mean square error matrices, we transform the constructed problem into a tractable one. After decomposing the transformed problem into three subproblems, we investigate a new alternating precoding design based on sequential solutions. Simulation results demonstrate that the proposed precoding scheme achieves comparable performance to conventional methods, while significantly reducing the computational complexity.

Paper Structure

This paper contains 17 sections, 3 theorems, 61 equations, 8 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. RSMA for MU-MIMO
  4. Imperfect CSIT Model
  5. Channel estimation error model
  6. Channel quantization error model
  7. Problem Formulation
  8. Proposed Low-complexity Robust Precoding Design
  9. Proposed Precoding Design
  10. Solution of (P1)
  11. Solution to (P2)
  12. Solution to (P3)
  13. Convergence Analysis
  14. Computational Complexity Analysis
  15. Simulation Results
  16. ...and 2 more sections

Key Result

Lemma 1

Let us denote ${\mathbf X} \in \mathbb{C}^{M \times M}$ as a fixed matrix and ${\mathbf Y} \in \mathbb{C}^{M \times N}$ as a random matrix. The $\left( m,n \right)$-th element of ${\mathbf Y}$ is i.i.d. with zero mean and variance $\sigma_{mn}^2$. Then, we have where the $\left( n,m \right)$-th element of $\mathbf{\Theta} \in \mathbb{R}^{N \times M}$ equals $\sigma_{mn}^2$. $\blacksquare$

Figures (8)

  • Figure 1: System model of 1-layer RSMA for MU-MIMO systems.
  • Figure 2: Ergodic sum rate of MU-MIMO systems with $M=8$, $N=2$, and $K=4$ under perfect CSIT.
  • Figure 3: Convergence of the proposed precoding designs of RSMA for MU-MIMO systems.
  • Figure 4: Ergodic sum rate of MU-MIMO systems with imperfect CSIT.
  • Figure 5: Ergodic sum rate of MU-MIMO systems with different transmit antennas under SNR = 30 dB.
  • ...and 3 more figures

Theorems & Definitions (3)

  • Lemma 1: RP23
  • Lemma 2
  • Theorem 1