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Scalable and Convergent Generalized Power Iteration Precoding for Massive MIMO Systems

Seunghyeong Yoo, Mintaek Oh, Jeonghun Park, Namyoon Lee, Jinseok Choi

TL;DR

A scalable and computationally efficient generalized power iteration precoding (GPIP) framework for massive MIMO systems under both perfect and imperfect channel state information at the transmitter (CSIT) by exploiting the low-dimensional subspace property of optimal precoders.

Abstract

In massive multiple-input multiple-output (MIMO) systems, achieving high spectral efficiency (SE) often requires advanced precoding algorithms whose complexity scales rapidly with the number of antennas, limiting practical deployment. In this paper, we develop a scalable and computationally efficient generalized power iteration precoding (GPIP) framework for massive MIMO systems under both perfect and imperfect channel state information at the transmitter (CSIT). By exploiting the low-dimensional subspace property of optimal precoders, we reformulate the high-dimensional beamforming problem into a lower-dimensional weight optimization that scales with the number of users rather than antennas. We further extend this framework to the imperfect CSIT scenario by showing that stationary solutions reside in a combined subspace spanned by the estimated channel and error covariance matrices, enabling a robust design via low-rank approximation. To reduce computational cost, we leverage the Sherman-Morrison formula to simplify matrix inversions. Moreover, interpreting the GPIP update as a projected preconditioned gradient ascent method, we establish convergence guarantees and develop a stable and monotonic algorithm using a backtracking line search. Numerical results demonstrate that the proposed methods achieve the highest SE performance compared to state-of-the-art linear precoders with significantly reduced complexity and convergence, highlighting their suitability for large-scale MIMO systems.

Scalable and Convergent Generalized Power Iteration Precoding for Massive MIMO Systems

TL;DR

A scalable and computationally efficient generalized power iteration precoding (GPIP) framework for massive MIMO systems under both perfect and imperfect channel state information at the transmitter (CSIT) by exploiting the low-dimensional subspace property of optimal precoders.

Abstract

In massive multiple-input multiple-output (MIMO) systems, achieving high spectral efficiency (SE) often requires advanced precoding algorithms whose complexity scales rapidly with the number of antennas, limiting practical deployment. In this paper, we develop a scalable and computationally efficient generalized power iteration precoding (GPIP) framework for massive MIMO systems under both perfect and imperfect channel state information at the transmitter (CSIT). By exploiting the low-dimensional subspace property of optimal precoders, we reformulate the high-dimensional beamforming problem into a lower-dimensional weight optimization that scales with the number of users rather than antennas. We further extend this framework to the imperfect CSIT scenario by showing that stationary solutions reside in a combined subspace spanned by the estimated channel and error covariance matrices, enabling a robust design via low-rank approximation. To reduce computational cost, we leverage the Sherman-Morrison formula to simplify matrix inversions. Moreover, interpreting the GPIP update as a projected preconditioned gradient ascent method, we establish convergence guarantees and develop a stable and monotonic algorithm using a backtracking line search. Numerical results demonstrate that the proposed methods achieve the highest SE performance compared to state-of-the-art linear precoders with significantly reduced complexity and convergence, highlighting their suitability for large-scale MIMO systems.
Paper Structure (22 sections, 6 theorems, 78 equations, 6 figures, 1 table, 3 algorithms)

This paper contains 22 sections, 6 theorems, 78 equations, 6 figures, 1 table, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Works
  3. Contributions
  4. System Model and Problem Formulation
  5. Proposed Scalable Precoding
  6. Low-dimensional Projection
  7. Reformulation and Algorithm
  8. Complexity Reduction
  9. Scalable Precoding with Imperfect CSIT
  10. Low-dimensional Projection
  11. Reformulation and Algorithm
  12. Complexity Reduction
  13. Convergence
  14. PPGA Interpretation of the GPIP Update Rule
  15. Convergence Analysis and Convergent S-GPIP
  16. ...and 7 more sections

Key Result

Proposition 1

Any nontrivial stationary point ${\bf f}_{k}$ of the problem in problem must lie in the range space of the DL channel ${\bf H}$, i.e., ${\bf f}_{k} = {\bf H} {\bf w}_{k}$, with a unique vector ${\bf w}_{k} \in \hbox{$\mathbb{C}$}^{K}$ for $k \in \{1,...,K\}$.

Figures (6)

  • Figure 1: The sum SE versus the BS maximum transmit power budget $P$ for $N=32$ and $K=4$ under perfect CSIT.
  • Figure 2: (a) The sum SE and (b) computation time versus the BS transmit antennas $N$ for $K=4$ and $P=30\,\mathrm{dBm}$ under perfect CSIT.
  • Figure 3: The sum SE versus the BS maximum transmit power budget $P$ for $N=32$, $K=4$, and $\kappa=0.3$ under imperfect CSIT.
  • Figure 4: (a) The sum SE and (b) computation time versus the BS transmit antennas $N$ for $K=4$, $P=30\,\mathrm{dBm}$, and $\kappa=0.3$ under imperfect CSIT.
  • Figure 5: (a) The sum SE and (b) computation time versus DL users $K$ for $N=32$, $P=30\,\mathrm{dBm}$, and $\kappa=0.3$ under imperfect CSIT.
  • ...and 1 more figures

Theorems & Definitions (13)

  • Proposition 1: zhao2023TSP:R-WMMSE
  • Lemma 1
  • proof
  • Proposition 2
  • proof
  • Remark 1
  • Lemma 2
  • proof
  • Lemma 3: Uniform bounds for $\widetilde{{{\bf B}}}^{-1}(\bar{{\bf w}})$
  • proof
  • ...and 3 more