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GRAM-DIFF: Gram Matrix Guided Diffusion for MIMO Channel Estimation

Xinyuan Wang, Krishna Narayanan

TL;DR

The proposed GRAM-DIFF framework exhibits graceful degradation under coherence-time constraints, smoothly reverting to likelihood-guided diffusion when data-based Gram estimates become unreliable.

Abstract

We propose GRAM-DIFF, a Gram-matrix-guided diffusion framework for semi-blind multiple input multiple output (MIMO) channel estimation. Recent diffusion-based estimators leverage learned generative priors to improve pilot-based channel estimation; but they do not exploit second-order structural information estimated from data symbols. In practical systems, the channel Gram matrix can be estimated from received symbols and it provides realization-level information about channel subspace structure. The proposed method integrates a pre-trained angular-domain diffusion prior with two complementary guidance mechanisms: a novel Gram-matrix guidance term that enforces second-order consistency during the reverse diffusion process, and likelihood guidance from pilot observations. Signal-to-noise ratio (SNR)-matched initialization and adaptive guidance scaling ensure stability and low inference latency. Simulations on 3GPP and QuaDRiGa channel models demonstrate consistent normalized mean-squared error (NMSE) improvements over deterministic diffusion baselines, achieving 4 to 6 dB SNR gains at an NMSE of 0.1 over the baseline in Fest et al. (2024). The framework exhibits graceful degradation under coherence-time constraints, smoothly reverting to likelihood-guided diffusion when data-based Gram estimates become unreliable.

GRAM-DIFF: Gram Matrix Guided Diffusion for MIMO Channel Estimation

TL;DR

The proposed GRAM-DIFF framework exhibits graceful degradation under coherence-time constraints, smoothly reverting to likelihood-guided diffusion when data-based Gram estimates become unreliable.

Abstract

We propose GRAM-DIFF, a Gram-matrix-guided diffusion framework for semi-blind multiple input multiple output (MIMO) channel estimation. Recent diffusion-based estimators leverage learned generative priors to improve pilot-based channel estimation; but they do not exploit second-order structural information estimated from data symbols. In practical systems, the channel Gram matrix can be estimated from received symbols and it provides realization-level information about channel subspace structure. The proposed method integrates a pre-trained angular-domain diffusion prior with two complementary guidance mechanisms: a novel Gram-matrix guidance term that enforces second-order consistency during the reverse diffusion process, and likelihood guidance from pilot observations. Signal-to-noise ratio (SNR)-matched initialization and adaptive guidance scaling ensure stability and low inference latency. Simulations on 3GPP and QuaDRiGa channel models demonstrate consistent normalized mean-squared error (NMSE) improvements over deterministic diffusion baselines, achieving 4 to 6 dB SNR gains at an NMSE of 0.1 over the baseline in Fest et al. (2024). The framework exhibits graceful degradation under coherence-time constraints, smoothly reverting to likelihood-guided diffusion when data-based Gram estimates become unreliable.
Paper Structure (26 sections, 36 equations, 4 figures, 1 table, 1 algorithm)

This paper contains 26 sections, 36 equations, 4 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. Preliminaries and Notation
  4. Related Prior Work
  5. Proposed Algorithm
  6. Training
  7. Pilot-based Preprocessing
  8. SNR-adaptive Reverse Process
  9. Likelihood Guidance
  10. Gram Matrix Guided Diffusion
  11. Simulation Results
  12. Channel Models, Baselines, and Evaluation Setup
  13. Structural differences of the induced channel statistics.
  14. Estimators and baselines.
  15. Evaluation setup.
  16. ...and 11 more sections

Figures (4)

  • Figure 1: 3GPP: NMSE vs. SNR.
  • Figure 2: QuaDRiGa: NMSE vs. SNR.
  • Figure 3: 3GPP: NMSE versus SNR under coherence-time limited Gram estimation.
  • Figure 4: NMSE versus SNR under extreme coherence-time constraints (3GPP channel). We compare the diffusion prior baseline (DM), the DM+likelihood reference, and GRAM-DIFF with very small data block lengths ($N_d=5,10,20$).