Attention-Aided MMSE for OFDM Channel Estimation: Learning Linear Filters with Attention

TL;DR

The paper tackles OFDM channel estimation by moving beyond covariance-dependent MMSE and end-to-end DNN approaches to a model-based DNN framework called A-MMSE that learns a linear MMSE-like filter via an Attention Transformer. A two-stage Frequency-then-Temporal Attention encoder captures the separable frequency-temporal channel correlations, enabling each pilot observation to be whitened and interpolated through a learned linear filter, with a rank-adaptive extension (RA-A-MMSE) to trade accuracy for computational cost. Empirical results on 3GPP TDL channels show substantial NMSE and BER gains over LS, MMSE, ChannelNet, and Channelformer, while RA-A-MMSE achieves similar performance at dramatically reduced complexity; A-MMSE also demonstrates robustness to SNR mismatch and outperforms sensing-aided approaches in high-mobility scenarios. Overall, the work offers a practical, scalable path for learning-enhanced, low-complexity channel estimation that integrates domain knowledge with data-driven learning. This approach has potential implications for future 5G/6G transceivers by delivering accurate channel state information with reduced hardware demands.

Abstract

In orthogonal frequency division multiplexing (OFDM), accurate channel estimation is crucial. Classical signal processing based approaches, such as minimum mean-squared error (MMSE) estimation, often require second-order statistics that are difficult to obtain in practice. Recent deep neural networks based methods have been introduced to address this; yet they often suffer from high inference complexity. This paper proposes an Attention-aided MMSE (A-MMSE), a novel model-based DNN framework that learns the optimal MMSE filter via the Attention Transformer. Once trained, the A-MMSE estimates the channel through a single linear operation for channel estimation, eliminating nonlinear activations during inference and thus reducing computational complexity. To enhance the learning efficiency of the A-MMSE, we develop a two-stage Attention encoder, designed to effectively capture the channel correlation structure. Additionally, a rank-adaptive extension of the proposed A-MMSE allows flexible trade-offs between complexity and channel estimation accuracy. Extensive simulations with 3GPP TDL channel models demonstrate that the proposed A-MMSE consistently outperforms other baseline methods in terms of normalized MSE across a wide range of signal-to-noise ratio (SNR) conditions. In particular, the A-MMSE and its rank-adaptive extension establish a new frontier in the performance-complexity trade-off, providing a powerful yet highly efficient solution for practical channel estimation

Figures (12)

• Figure 1: Comparison of OFDM channel estimation structure: conventional approaches vs. the proposed A-MMSE approach.
• Figure 2: Architecture and end‑to‑end training pipeline of the proposed A-MMSE network for learning the MMSE filter
• Figure 3: Detailed structure of the proposed two-stage Attention encoder.
• Figure 4: TDL-D: Channel estimation NMSE comparing Huber loss vs. MSE loss
• Figure 5: RA‑A-MMSE architecture: a rank-adaptation module is appended to A-MMSE to flexibly adjust the rank of the learned A-MMSE filter.

Theorems & Definitions (4)

• Remark 1
• Remark 2
• Remark 3
• Remark 4