# Learning MMSE Filters for OFDM Channel Estimation: Attention Transformer Gains at Linear Inference

arXiv: https://arxiv.org/abs/2506.00452 · HTML: https://mlsanity.com/paper/2506.00452/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 42 references that are in the map.
- First posted on arXiv 31 May 2025.

## Builds on (most cited first, 16 of 16)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [On the Relationship between Self-Attention and Convolutional Layers](https://mlsanity.com/paper/1911.03584/) (2019)
- [Model-Based Deep Learning](https://mlsanity.com/paper/2012.08405/) (2020)
- [KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics](https://mlsanity.com/paper/2107.10043/) (2021)
- [Deep Learning-Based Channel Estimation](https://mlsanity.com/paper/1810.05893/) (2018)
- [High Dimensional Channel Estimation Using Deep Generative Networks](https://mlsanity.com/paper/2006.13494/) (2020)
- [Adaptive Neural Signal Detection for Massive MIMO](https://mlsanity.com/paper/1906.04610/) (2019)
- [Channelformer: Attention based Neural Solution for Wireless Channel Estimation and Effective Online Training](https://mlsanity.com/paper/2302.04368/) (2023)
- [Low Complexity Channel estimation with Neural Network Solutions](https://mlsanity.com/paper/2201.09934/) (2022)
- [Optimization or Architecture: How to Hack Kalman Filtering](https://mlsanity.com/paper/2310.00675/) (2023)
- [Leveraging Deep Neural Networks for Massive MIMO Data Detection](https://mlsanity.com/paper/2204.05350/) (2022)
- [Splitting Messages in the Dark- Rate-Splitting Multiple Access for FDD Massive MIMO Without CSI Feedback](https://mlsanity.com/paper/2405.00979/) (2024)
- [Power Measurement Based Channel Estimation for IRS-Enhanced Wireless Coverage](https://mlsanity.com/paper/2405.12432/) (2024)

## Abstract (arXiv)

In orthogonal frequency division multiplexing (OFDM), accurate channel estimation is crucial. Classical signal processing-based approaches, such as linear minimum mean-squared error (LMMSE) estimation, often require second-order statistics that are difficult to obtain in practice. Recent deep neural network (DNN)-based methods have been introduced to address this, but they often suffer from high inference complexity. This paper proposes an Attention-aided MMSE (A-MMSE), a model-based DNN framework that learns the linear MMSE filter via the Attention Transformer. Once trained, the A-MMSE performs channel estimation through a single linear operation, eliminating nonlinear activations during inference and thus reducing computational complexity. To improve the learning efficiency of the A-MMSE, we develop a two-stage Attention encoder that captures the frequency and temporal correlation structure of OFDM channels. We also introduce a rank-adaptive extension that adjusts the filter rank at deployment time, enabling efficient operation under resource-constrained receivers. Numerical simulations show that A-MMSE consistently outperforms baseline methods across a wide range of signal-to-noise ratio (SNR) conditions. In particular, the A-MMSE and its rank-adaptive extension provide an improved performance-complexity trade-off.