Attention-Aided MMSE with Ridge Denoising: How to Train under Noisy Channel Samples

Abstract

Deep neural channel estimators are typically trained with clean channel state information (CSI), which is unavailable in practical orthogonal frequency-division multiplexing (OFDM) systems. In pilot-based OFDM, naive noisy-target training is structurally biased because the pilot input and noisy full-grid target share the same noise realization, driving the estimator toward identity copying. To address this for Attention-aided MMSE (A-MMSE), we propose a ridge-regularized objective that penalizes the generated filter directly. In a stylized fixed-filter model, this penalty induces scalar shrinkage and recovers the scalar MMSE gain at an explicit penalty value. We further construct surrogate training targets by estimating the channel covariance via eigenvalue clipping of the noisy empirical second-moment matrix, without requiring clean CSI labels. On COST 2100 channels, the proposed Ridge-A-MMSE consistently outperforms the Noise2Noise (N2N) baselines considered in this paper, and the combination of ridge regularization and covariance shrinkage approaches the same network trained with clean CSI labels at high signal-to-noise ratios (SNRs).