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Efficient Information Geometry Approach for Massive MIMO-OFDM Channel Estimation

Jiyuan Yang, Yan Chen, Mingrui Fan, An-An Lu, Wen Zhong, Xiqi Gao, Xiaohu You, Xiang-Gen Xia, Dirk Slock

TL;DR

This work addresses scalable channel estimation for massive MIMO-OFDM by refining a Bayesian information-geometry framework. It reveals two key structural properties under constant-magnitude measurement matrices that enable a simplified Efficient Information Geometry (EIGA) method with an FFT-based implementation. EIGA replaces multiple NP’s with a single common NP, provides convergence guarantees via a damping range, and yields an asymptotically MMSE a posteriori mean at the fixed point. Empirical results show EIGA achieves near-optimal NMSE with substantially lower complexity than prior IGA or MMSE, demonstrating practical viability for large-scale systems. Overall, the paper delivers a principled, low-complexity Bayesian estimator for high-dimensional MIMO-OFDM channels with rigorous convergence and asymptotic optimality guarantees.

Abstract

We investigate the channel estimation for massive multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. We revisit the information geometry approach (IGA) for massive MIMO-OFDM channel estimation. By using the constant magnitude property of the entries of the measurement matrix, we find that the second-order natural parameters of the distributions on all the auxiliary manifolds are equivalent to each other, and the first-order natural parameters are asymptotically equivalent to each other at the fixed point. Motivated by these results, we simplify the process of IGA and propose an efficient IGA (EIGA) for massive MIMO-OFDM channel estimation, which allows efficient implementation with fast Fourier transformation (FFT). We then establish a sufficient condition of its convergence and accordingly find a range of the damping factor for the convergence. We show that this range of damping factor is sufficiently wide by using the specific properties of the measurement matrices. Further, we prove that at the fixed point, the a posteriori mean obtained by EIGA is asymptotically optimal. Simulations confirm that EIGA can achieve the optimal performance with low complexity in a limited number of iterations.

Efficient Information Geometry Approach for Massive MIMO-OFDM Channel Estimation

TL;DR

This work addresses scalable channel estimation for massive MIMO-OFDM by refining a Bayesian information-geometry framework. It reveals two key structural properties under constant-magnitude measurement matrices that enable a simplified Efficient Information Geometry (EIGA) method with an FFT-based implementation. EIGA replaces multiple NP’s with a single common NP, provides convergence guarantees via a damping range, and yields an asymptotically MMSE a posteriori mean at the fixed point. Empirical results show EIGA achieves near-optimal NMSE with substantially lower complexity than prior IGA or MMSE, demonstrating practical viability for large-scale systems. Overall, the paper delivers a principled, low-complexity Bayesian estimator for high-dimensional MIMO-OFDM channels with rigorous convergence and asymptotic optimality guarantees.

Abstract

We investigate the channel estimation for massive multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. We revisit the information geometry approach (IGA) for massive MIMO-OFDM channel estimation. By using the constant magnitude property of the entries of the measurement matrix, we find that the second-order natural parameters of the distributions on all the auxiliary manifolds are equivalent to each other, and the first-order natural parameters are asymptotically equivalent to each other at the fixed point. Motivated by these results, we simplify the process of IGA and propose an efficient IGA (EIGA) for massive MIMO-OFDM channel estimation, which allows efficient implementation with fast Fourier transformation (FFT). We then establish a sufficient condition of its convergence and accordingly find a range of the damping factor for the convergence. We show that this range of damping factor is sufficiently wide by using the specific properties of the measurement matrices. Further, we prove that at the fixed point, the a posteriori mean obtained by EIGA is asymptotically optimal. Simulations confirm that EIGA can achieve the optimal performance with low complexity in a limited number of iterations.
Paper Structure (33 sections, 19 theorems, 249 equations, 4 figures, 4 tables, 1 algorithm)

This paper contains 33 sections, 19 theorems, 249 equations, 4 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model and Problem Statement
  3. System Configuration and Channel Model
  4. Problem Statement
  5. Revisiting IGA
  6. IGA
  7. New Results
  8. Efficient IGA
  9. EIGA
  10. Efficient Implementation
  11. Convergence and Fixed point
  12. Convergence
  13. Fixed Point
  14. Simulation Results
  15. Complexity
  16. ...and 18 more sections

Key Result

Theorem 1

If the matrix $\mathbf{A}$ in equ:maMIMO rece signal 4 has constant magnitude entry property, then at each iteration of IGA, the SONPs of both $p_n, n\in\mathcal{Z}_{N}^+$, and its $m$-projection on the OBM are independent of $n$, i.e., when the initializations of the SONPs of $\left\lbrace p_n\right\rbrace_{n=1}^N$ are the same. Furthermore, if the initializations of the SONPs of $p_0$ and $p_n,

Figures (4)

  • Figure 1: NMSE performance of EIGA compared with GAMP, IGA and MMSE.
  • Figure 2: Convergence performance of EIGA compared with GAMP and IGA at SNR = $0$ dB.
  • Figure 3: Convergence performance of EIGA compared with GAMP and IGA at SNR = $10$ dB.
  • Figure 4: Convergence performance of EIGA compared with GAMP and IGA at SNR = $20$ dB.

Theorems & Definitions (38)

  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Theorem 3
  • proof
  • ...and 28 more