A Peaceman-Rachford Splitting Approach with Deep Equilibrium Network for Channel Estimation

TL;DR

This paper introduces a novel MIMO channel estimation method combining Peaceman-Rachford splitting with a deep equilibrium network, offering low training complexity and proven convergence.

Contribution

It develops a fixed-point equation-based approach integrated into a DEQ model for MIMO channel estimation, with theoretical convergence guarantees.

Findings

Achieves accurate channel estimation in MIMO systems.

Demonstrates low training complexity of the proposed method.

Shows favorable results in hybrid far- and near-field channel simulations.

Abstract

Multiple-input multiple-output (MIMO) is pivotal for wireless systems, yet its high-dimensional, stochastic channel poses significant challenges for accurate estimation, highlighting the critical need for robust estimation techniques. In this paper, we introduce a novel channel estimation method for the MIMO system. The main idea is to construct a fixed-point equation for channel estimation, which can be implemented into the deep equilibrium (DEQ) model with a fixed network. Specifically, the Peaceman-Rachford (PR) splitting method is applied to the dual form of the regularized minimization problem to construct fixed-point equation with non-expansive property. Then, the fixed-point equation is implemented into the DEQ model with a fixed layer, leveraging its advantage of the low training complexity. Moreover, we provide a rigorous theoretical analysis, demonstrating the convergence and optimality of our approach. Additionally, simulations of hybrid far- and near-field channels demonstrate that our approach yields favorable results, indicating its ability to advance channel estimation in MIMO system.