Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A manifold learning-based CSI feedback framework for FDD massive MIMO

Yandi Cao, Haifan Yin, Ziao Qin, Weidong Li, Weimin Wu, Mérouane Debbah

TL;DR

This work tackles the CSI feedback overhead in FDD massive MIMO by proposing a manifold learning-based framework (MLCF) that preserves local CSI geometry through landmark-based dictionaries. It introduces a landmark selection algorithm with an alternating optimization, proving convergence and deriving an error bound, while enabling an incremental compression/reconstruction pipeline that maintains performance with low complexity. Offline learning of high-/low-dimensional landmark dictionaries at the BS and online embedding at the UE/BS enables efficient dimensionality reduction and reconstruction, outperforming several DL-based methods on 3GPP CDL channels, especially at high compression (e.g., $\gamma=\frac{1}{4}$). The approach yields NMSE gains, robustness to noise/quantization, and spectral-efficiency benefits, highlighting the practical impact of leveraging manifold structures for CSI feedback in massive MIMO systems.

Abstract

Massive multi-input multi-output (MIMO) in Frequency Division Duplex (FDD) mode suffers from heavy feedback overhead for Channel State Information (CSI). In this paper, a novel manifold learning-based CSI feedback framework (MLCF) is proposed to reduce the feedback and improve the spectral efficiency for FDD massive MIMO. Manifold learning (ML) is an effective method for dimensionality reduction. However, most ML algorithms focus only on data compression, and lack the corresponding recovery methods. Moreover, the computational complexity is high when dealing with incremental data. Considering to utilize the intrinsic manifold structure where the CSI samples reside, we propose a landmark selection algorithm to describe the topological skeleton of this manifold. Based on the learned skeleton, the local patch of the incremental CSI on the manifold can be easily determined by its nearest landmarks. This motivates us to propose an incremental CSI compression and reconstruction scheme by keeping the local geometric relationships with landmarks invariant. We theoretically prove the convergence of the proposed landmark selection algorithm. Meanwhile, the upper bound on the error of approximating CSI with landmarks is derived. Simulation results under an industrial channel model of 3GPP demonstrate that the proposed MLCF outperforms existing deep learning based algorithms.

A manifold learning-based CSI feedback framework for FDD massive MIMO

TL;DR

This work tackles the CSI feedback overhead in FDD massive MIMO by proposing a manifold learning-based framework (MLCF) that preserves local CSI geometry through landmark-based dictionaries. It introduces a landmark selection algorithm with an alternating optimization, proving convergence and deriving an error bound, while enabling an incremental compression/reconstruction pipeline that maintains performance with low complexity. Offline learning of high-/low-dimensional landmark dictionaries at the BS and online embedding at the UE/BS enables efficient dimensionality reduction and reconstruction, outperforming several DL-based methods on 3GPP CDL channels, especially at high compression (e.g., ). The approach yields NMSE gains, robustness to noise/quantization, and spectral-efficiency benefits, highlighting the practical impact of leveraging manifold structures for CSI feedback in massive MIMO systems.

Abstract

Massive multi-input multi-output (MIMO) in Frequency Division Duplex (FDD) mode suffers from heavy feedback overhead for Channel State Information (CSI). In this paper, a novel manifold learning-based CSI feedback framework (MLCF) is proposed to reduce the feedback and improve the spectral efficiency for FDD massive MIMO. Manifold learning (ML) is an effective method for dimensionality reduction. However, most ML algorithms focus only on data compression, and lack the corresponding recovery methods. Moreover, the computational complexity is high when dealing with incremental data. Considering to utilize the intrinsic manifold structure where the CSI samples reside, we propose a landmark selection algorithm to describe the topological skeleton of this manifold. Based on the learned skeleton, the local patch of the incremental CSI on the manifold can be easily determined by its nearest landmarks. This motivates us to propose an incremental CSI compression and reconstruction scheme by keeping the local geometric relationships with landmarks invariant. We theoretically prove the convergence of the proposed landmark selection algorithm. Meanwhile, the upper bound on the error of approximating CSI with landmarks is derived. Simulation results under an industrial channel model of 3GPP demonstrate that the proposed MLCF outperforms existing deep learning based algorithms.
Paper Structure (15 sections, 6 theorems, 56 equations, 7 figures, 2 tables, 1 algorithm)

This paper contains 15 sections, 6 theorems, 56 equations, 7 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Proposed Landmark Selection Method for Manifold Learning
  4. Manifold structure of CSI
  5. Landmark selection
  6. Proposed alternating iterative optimization algorithm
  7. Convergence analysis for the proposed algorithm
  8. MLCF-based CSI Feedback
  9. Dimensionality reduction for the incremental CSI
  10. Reconstruction for the incremental CSI
  11. Numerical Results
  12. Conclusion
  13. Proof of Proposition \ref{['prop1']}
  14. Proof of Theorem \ref{['thm1']}
  15. Proof of Theorem \ref{['thm2']}

Key Result

Proposition 1

The linear approximation error satisfies where $\xi = \max {\{ {w_{ji}}\} }_j$ is the largest entry in ${{\mathbf{w}}_i}$, $\xi_1 = \sqrt{\frac{N_f}{2} }\xi$, ${\mathbf{J}_g}({{\mathbf{y}}_i})$ is the Jacobi matrix of $g$ at ${{\mathbf{y}}_i}$, ${{\mathbf{b}}_j} = f({\mathbf{d}}_j)$ is the low-dimensional embedding of ${\mathbf{d}}_j$, and among which ${\mathbf{\Psi}_{g_l}}({{\mathbf{y}}_i})$ is

Figures (7)

  • Figure 1: An illustration of the high-dimensional manifold (a) and the corresponding low-dimensional embedding (b). The CSI data ${{\mathbf{x}}_i}$ (the solid circle) is sampled from the surface in (a). ${{\rm span}}({\mathbf{J}}_g({{\mathbf{y}}_i}))$ is the tangent space at ${{\mathbf{x}}_i}$. The hollow circles are the landmarks selected by our proposed Algorithm \ref{['alg1']}. The local geometric relationship between ${{\mathbf{x}}_i}$ and its nearest landmarks remains unchanged before and after dimensionality reduction.
  • Figure 2: The normalized mean square error vs. the size of data set ${\mathbf{X}}$.
  • Figure 3: The normalized mean square error vs. the number of neighbors $k$.
  • Figure 4: The loss of the objective function Eq. \ref{['final objective function']} vs. the number of iterations.
  • Figure 5: The normalized mean square error vs. the algorithms with quantization and non-quantization.
  • ...and 2 more figures

Theorems & Definitions (6)

  • Proposition 1
  • Lemma 1
  • Theorem 1
  • Theorem 2
  • Lemma 2
  • Theorem 3