Recursive Flow: A Generative Framework for MIMO Channel Estimation

TL;DR

This work tackles the ill-posed problem of high-dimensional MIMO channel state information estimation under limited pilots by proposing RC-Flow, a closed-loop, fixed-point generative framework that uses anchored trajectory rectification and a flow-based prior. By combining a pre-trained flow-matching prior with a physics-aware proximal projection and a recursive anchor refinement, RC-Flow achieves global asymptotic stability and robust performance in low-SNR regimes while drastically reducing inference latency compared to diffusion-based methods. The approach is validated on 3GPP CDL channels, showing state-of-the-art NMSE across a range of pilot densities and MIMO scales, with substantial latency reductions suitable for real-time 6G applications. The results suggest RC-Flow as a practical paradigm for constrained inverse problems, enabling high-fidelity, low-latency generative inference in wireless channel estimation and related domains.

Abstract

Channel estimation is a fundamental challenge in massive multiple-input multiple-output systems, where estimation accuracy governs the spectral efficiency and link reliability. In this work, we introduce Recursive Flow (RC-Flow), a novel solver that leverages pre-trained flow matching priors to robustly recover channel state information from noisy, under-determined measurements. Different from conventional open-loop generative models, our approach establishes a closed-loop refinement framework via a serial restart mechanism and anchored trajectory rectification. By synergizing flow-consistent prior directions with data-fidelity proximal projections, the proposed RC-Flow achieves robust channel reconstruction and delivers state-of-the-art performance across diverse noise levels, particularly in noise-dominated scenarios. The framework is further augmented by an adaptive dual-scheduling strategy, offering flexible management of the trade-off between convergence speed and reconstruction accuracy. Theoretically, we analyze the Jacobian spectral radius of the recursive operator to prove its global asymptotic stability. Numerical results demonstrate that RC-Flow reduces inference latency by two orders of magnitude while achieving a 2.7 dB performance gain in low signal-to-noise ratio regimes compared to the score-based baseline.

Figures (14)

• Figure 1: Schematic of the RC-Flow algorithm. The method employs a nested loop structure: the Outer Loop recursively resets the anchor to correct trajectory drift, while the Inner Loop refines the estimate. The Core Component Operators combine a deep flow prior, physics-aware proximal projection, and anchored rectification to achieve robust reconstruction.
• Figure 2: The U-net architecture for flow matching. The yellow block represents the convolutional residual module, the red block represents down-sampling while the blue block represents up-sampling.
• Figure 3: Visual evolution of the channel estimation during an outer loop. The process recovers the channel structure from noise ($t=1$) to the target distribution ($t=0$). GT refers to ground truth channel. Rows display the intermediate outputs of the flow denoising ($\tilde{\mathbf{H}}$), physical projection ($\mathbf{H}_{\text{proj}}$), and anchor interpolation ($\mathbf{H}^{(k, i+1)}$), respectively.
• Figure 4: Performance comparison of various schemes trained on CDL-C channels and evaluated across diverse channel conditions in a $16 \times 64$ mmWave MIMO system when $\alpha=0.6$.
• Figure 5: Visualization of the trade-off between algorithm performance and computational cost. The evaluation is conducted with $\alpha=0.6$ at an SNR of 30 dB. The bubble size represents the scale of model parameters, and the color corresponds to the inference latency. The models were trained on CDL-C and tested on CDL-D.

Theorems & Definitions (4)

• Theorem 1: Existence of Fixed Point
• proof
• Theorem 2: Global Asymptotic Stability in Generalized Metric Space
• proof