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

TL;DR

GRAM-DIFF introduces a novel diffusion-based MIMO channel estimation method that leverages second-order structural information via Gram matrix guidance, resulting in significant NMSE improvements over existing baselines.

Contribution

It integrates a Gram-matrix guidance mechanism with diffusion priors for semi-blind MIMO channel estimation, enhancing accuracy by exploiting channel subspace structure.

Findings

Achieves 4-6 dB SNR gain at NMSE 0.1 over baselines.

Demonstrates robustness under coherence-time constraints.

Provides consistent NMSE improvements across channel models.

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.