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Interference Cancellation Information Geometry Approach for Massive MIMO Channel Estimation

An-An Lu, Bingyan Liu, Xiqi Gao

TL;DR

The paper tackles the high computational burden of MMSE-based channel estimation in massive MIMO by developing an information-geometry framework that yields low-complexity approximations. It introduces two algorithms, IC-IGA and IC-SIGA, built on modified MMSE forms and auxiliary manifolds to approximate the MMSE posterior mean with reduced time and space complexity. The authors prove that at equilibrium the estimators converge to the MMSE mean and provide complexity analyses showing substantial savings over MMSE and prior IGA, including FFT-based implementations and BSCM/ZC pilot considerations. Numerical experiments with QuaDRiGa-based 3GPP channels demonstrate near-MMSE performance and faster convergence, highlighting practical relevance for real-time massive MIMO channel estimation.

Abstract

In this paper, the interference cancellation information geometry approaches (IC-IGAs) for massive MIMO channel estimation are proposed. The proposed algorithms are low-complexity approximations of the minimum mean square error (MMSE) estimation. To illustrate the proposed algorithms, a unified framework of the information geometry approach for channel estimation and its geometric explanation are described first. Then, a modified form that has the same mean as the MMSE estimation is constructed. Based on this, the IC-IGA algorithm and the interference cancellation simplified information geometry approach (IC-SIGA) are derived by applying the information geometry framework. The a posteriori means on the equilibrium of the proposed algorithms are proved to be equal to the mean of MMSE estimation, and the complexity of the IC-SIGA algorithm in practical massive MIMO systems is further reduced by considering the beam-based statistical channel model (BSCM) and fast Fourier transform (FFT). Simulation results show that the proposed methods achieve similar performance as the existing information geometry approach (IGA) with lower complexity.

Interference Cancellation Information Geometry Approach for Massive MIMO Channel Estimation

TL;DR

The paper tackles the high computational burden of MMSE-based channel estimation in massive MIMO by developing an information-geometry framework that yields low-complexity approximations. It introduces two algorithms, IC-IGA and IC-SIGA, built on modified MMSE forms and auxiliary manifolds to approximate the MMSE posterior mean with reduced time and space complexity. The authors prove that at equilibrium the estimators converge to the MMSE mean and provide complexity analyses showing substantial savings over MMSE and prior IGA, including FFT-based implementations and BSCM/ZC pilot considerations. Numerical experiments with QuaDRiGa-based 3GPP channels demonstrate near-MMSE performance and faster convergence, highlighting practical relevance for real-time massive MIMO channel estimation.

Abstract

In this paper, the interference cancellation information geometry approaches (IC-IGAs) for massive MIMO channel estimation are proposed. The proposed algorithms are low-complexity approximations of the minimum mean square error (MMSE) estimation. To illustrate the proposed algorithms, a unified framework of the information geometry approach for channel estimation and its geometric explanation are described first. Then, a modified form that has the same mean as the MMSE estimation is constructed. Based on this, the IC-IGA algorithm and the interference cancellation simplified information geometry approach (IC-SIGA) are derived by applying the information geometry framework. The a posteriori means on the equilibrium of the proposed algorithms are proved to be equal to the mean of MMSE estimation, and the complexity of the IC-SIGA algorithm in practical massive MIMO systems is further reduced by considering the beam-based statistical channel model (BSCM) and fast Fourier transform (FFT). Simulation results show that the proposed methods achieve similar performance as the existing information geometry approach (IGA) with lower complexity.
Paper Structure (25 sections, 4 theorems, 20 equations, 9 figures, 2 tables, 2 algorithms)

This paper contains 25 sections, 4 theorems, 20 equations, 9 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Affine and Dual Affine Coordinate Systems
  4. $e$-flat Submanifold and $m$-Projection
  5. Information Geometry Framework for Massive MIMO Channel Estimation
  6. Problem Formulation
  7. Information Geometry Framework
  8. Split of Natural Parameter and the $e$-Condition
  9. The $m$-Condition and General Algorithm
  10. Geometrical Explanation
  11. IC-IGA for Massive MIMO Channel Estimation
  12. Definition of Auxiliary Manifolds with Modified MMSE Form
  13. Derivation of IC-IGA
  14. Equilibrium and Complexity Analysis
  15. IC-SIGA for Massive MIMO Channel Estimation with BSCM and ZC Sequences
  16. ...and 10 more sections

Key Result

Theorem 1

Let the matrices $\mathbf T$ and $\bm\Upsilon$ be defined as $\mathbf T = \sigma_z^{-2}\mathbf A^H\mathbf A - \mathbf I \odot (\sigma_z^{-2}\mathbf A^H\mathbf A)$ and $\bm\Upsilon = \left(\mathbf I \odot (\sigma_z^{-2}\mathbf A^H\mathbf A) + \mathbf D^{-1}\right)^{-1}$. The estimator is equivalent to the MMSE estimator.

Figures (9)

  • Figure 1: $e$-condition
  • Figure 2: $m$-condition
  • Figure 3: The layout of the massive MIMO-OFDM system.
  • Figure 4: Time Complexity.
  • Figure 5: Space Complexity.
  • ...and 4 more figures

Theorems & Definitions (8)

  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Theorem 3
  • proof
  • Theorem 4
  • proof