Message Passing Based Two-Timescale Bayesian Learning for Joint Channel and Memory Hardware Impairments Tracking

2026-07-01

AI Summary

This work addresses the degradation of channel estimation performance in massive MIMO receivers caused by hardware impairments, which induce inter-symbol memory and inter-antenna coupling. To tackle this challenge, the authors propose a dual-timescale Bayesian deep learning framework that jointly tracks fast-varying sparse channels and slow-varying hardware impairments by modeling their interaction across multiple time slots as a factor graph. The framework enables online joint calibration through iterative extrinsic information exchange between a Turbo-OAMP module and a customized deep approximate message passing (DAMP) module. By integrating Gaussian–Markov priors with residual recurrent gated units, the proposed method significantly outperforms conventional “compensate-then-estimate” approaches across diverse impairment scenarios and signal-to-noise ratios, achieving substantial reductions in channel estimation error.

Abstract

Hardware impairments in massive multiple-input multiple-output (MIMO) receivers introduce inter-symbol memory and inter-element coupling, severely degrading channel estimation. This paper employs a residual recurrent gated unit (RGRU) to model the intra-slot memory of the hardware impairments and proposes a message-passing-based two-timescale Bayesian deep learning (MP-TTBDL) framework for joint channel and impairment tracking. Owing to small-scale fading, the wireless channel varies rapidly across slots, whereas hardware impairments drift slowly due to hardware aging and environmental variations. To capture these distinct physical timescales, a fastvarying Markov prior and a slow-varying Gaussian Markov prior are assigned to the sparse channel and the network parameters, respectively. Based on a multi-slot factor graph formulation, a message-passing algorithm is developed. Specifically, the inter-slot messages admit closed-form updates, while the intra-slot factor graph, due to its complex recurrent structure, is partitioned into a channel tracking module and an impairments calibration module. The channel tracking module performs sparse channel estimation via turbo orthogonal approximate message passing (Turbo-OAMP), and the impairments calibration module updates the impairment parameters via a specially designed deep approximate message passing (DAMP) procedure, with the two modules iteratively exchanging extrinsic information through expectation propagation (EP) until convergence. Simulation results show that the proposed framework robustly achieves lower channel estimation error than conventional compensators followed by channel estimation across different online impairment scenarios and signal-to-noise ratio (SNR) conditions.

Problem

• hardware impairments
• channel estimation
• massive MIMO
• inter-symbol memory
• inter-element coupling

Innovation

• message passing
• two-timescale Bayesian learning
• hardware impairments tracking
• deep approximate message passing
• massive MIMO