Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Robust Precoding Designs for Multiuser MIMO Systems with Limited Feedback

Wentao Zhou, Di Zhang, Merouane Debbah, Inkyu Lee

TL;DR

This work tackles the rate loss in downlink MU-MIMO caused by limited feedback quantization. It introduces a tight second-order-statistics approximation and a channel-decomposition model to enable robust precoding, including non-iterative RMMSE and iterative RWMMSE schemes that compensate for CSI quantization errors. The proposed methods yield substantial rate improvements over conventional precoding (MRT, BD, MMSE, WMMSE), especially at finite feedback and high SNR, and offer a practical trade-off between performance and complexity. Overall, the paper provides a principled framework for robust precoding under correlated quantization errors, with demonstrated gains in simulated scenarios relevant to limited-feedback systems.

Abstract

It has been well known that the achievable rate of multiuser multiple-input multiple-output systems with limited feedback is severely degraded by quantization errors when the number of feedback bits is not sufficient. To overcome such a rate degradation, we propose new robust precoding designs which can compensate for the quantization errors. In this paper, we first analyze the achievable rate of traditional precoding designs for limited feedback systems. Then, we obtain an approximation of the second-order statistics of quantized channel state information. With the aid of the derived approximation, we propose robust precoding designs in terms of the mean square error (MSE) with conditional expectation in non-iterative and iterative fashions. For the non-iterative precoding design, we study a robust minimum MSE (MMSE) precoding algorithm by extending a new channel decomposition. Also, in the case of iterative precoding, we investigate a robust weighted MMSE (WMMSE) precoding to further improve the achievable rate. Simulation results show that the proposed precoding schemes yield significant improvements over traditional precoding designs.

Robust Precoding Designs for Multiuser MIMO Systems with Limited Feedback

TL;DR

This work tackles the rate loss in downlink MU-MIMO caused by limited feedback quantization. It introduces a tight second-order-statistics approximation and a channel-decomposition model to enable robust precoding, including non-iterative RMMSE and iterative RWMMSE schemes that compensate for CSI quantization errors. The proposed methods yield substantial rate improvements over conventional precoding (MRT, BD, MMSE, WMMSE), especially at finite feedback and high SNR, and offer a practical trade-off between performance and complexity. Overall, the paper provides a principled framework for robust precoding under correlated quantization errors, with demonstrated gains in simulated scenarios relevant to limited-feedback systems.

Abstract

It has been well known that the achievable rate of multiuser multiple-input multiple-output systems with limited feedback is severely degraded by quantization errors when the number of feedback bits is not sufficient. To overcome such a rate degradation, we propose new robust precoding designs which can compensate for the quantization errors. In this paper, we first analyze the achievable rate of traditional precoding designs for limited feedback systems. Then, we obtain an approximation of the second-order statistics of quantized channel state information. With the aid of the derived approximation, we propose robust precoding designs in terms of the mean square error (MSE) with conditional expectation in non-iterative and iterative fashions. For the non-iterative precoding design, we study a robust minimum MSE (MMSE) precoding algorithm by extending a new channel decomposition. Also, in the case of iterative precoding, we investigate a robust weighted MMSE (WMMSE) precoding to further improve the achievable rate. Simulation results show that the proposed precoding schemes yield significant improvements over traditional precoding designs.
Paper Structure (16 sections, 6 theorems, 60 equations, 7 figures, 1 algorithm)

This paper contains 16 sections, 6 theorems, 60 equations, 7 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model and Preliminaries
  3. Limited Feedback Model
  4. Channel Decomposition
  5. Problem Formulation
  6. Robust Precoding Designs
  7. Robust Non-iterative Precoding Design
  8. Robust Iterative Precoding Design
  9. Computational Complexity Analysis
  10. Simulation Results
  11. Conclusion
  12. Proof of Theorem \ref{['theorem_achierate']}
  13. Proof of Lemma \ref{['lemma_equality']}
  14. Proof of Theorem \ref{['theorem_Rk']}
  15. Proof of Lemma \ref{['lemma_chandecomp']}
  16. ...and 1 more sections

Key Result

Lemma 1

For positive definite matrices ${\mathbf X}$, ${\mathbf Y}_1$, $\cdots$, ${\mathbf Y}_J$, we have an approximation as where ${\mathbf Y} = \sum_{j=1}^J {\mathbf Y}_j$. The above approximation becomes tight when $J$ increases.

Figures (7)

  • Figure 1: Achievable rate of the MRT precoding and the BD precoding with their bounds under $B=10$.
  • Figure 2: Normalized gap between ${\mathbf R}_k$ and ${\mathbf R}_k^o$ with respect to the number of feedback bits.
  • Figure 3: Achievable rate of MU-MIMO systems with perfect CSI.
  • Figure 4: Convergence behavior of the proposed iterative precoding design.
  • Figure 5: Achievable rate of limited-feedback MU-MIMO systems with $B=10$.
  • ...and 2 more figures

Theorems & Definitions (7)

  • Lemma 1
  • Theorem 1
  • Lemma 2
  • Theorem 2
  • Lemma 3
  • Lemma 4
  • Remark 1