# Physically constrained unfolded multi-dimensional OMP for large MIMO systems

arXiv: https://arxiv.org/abs/2601.10771 · HTML: https://mlsanity.com/paper/2601.10771/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 20 references that are in the map.
- First posted on arXiv 15 Jan 2026.

## Builds on (most cited first, 9 of 9)

- [An Introduction to Deep Learning for the Physical Layer](https://mlsanity.com/paper/1702.00832/) (2017)
- [Model-Based Deep Learning](https://mlsanity.com/paper/2012.08405/) (2020)
- [mpNet: variable depth unfolded neural network for massive MIMO channel estimation](https://mlsanity.com/paper/2008.04088/) (2020)
- [Learn to Rapidly and Robustly Optimize Hybrid Precoding](https://mlsanity.com/paper/2301.00369/) (2023)
- [Efficient Deep Unfolding for SISO-OFDM Channel Estimation](https://mlsanity.com/paper/2210.06588/) (2022)
- [Physically Parameterized Differentiable MUSIC for DoA Estimation with Uncalibrated Arrays](https://mlsanity.com/paper/2411.15144/) (2024)
- [Multidimensional orthogonal matching pursuit: theory and application to high accuracy joint localization and communication at mmWave](https://mlsanity.com/paper/2208.11600/) (2022)
- [Modeling and Analysis of OFDM-based 5G/6G Localization under Hardware Impairments](https://mlsanity.com/paper/2301.01042/) (2023)
- [Model-based learning for joint channel estimationand hybrid MIMO precoding](https://mlsanity.com/paper/2505.04255/) (2025)

## Abstract (arXiv)

Sparse recovery methods are essential for channel estimation and localization in modern communication systems, but their reliability relies on accurate physical models, which are rarely perfectly known. Their computational complexity also grows rapidly with the dictionary dimensions in large MIMO systems. In this paper, we propose MOMPnet, a novel unfolded sparse recovery framework that addresses both the reliability and complexity challenges of traditional methods. By integrating deep unfolding with data-driven dictionary learning, MOMPnet mitigates hardware impairments while preserving interpretability. Instead of a single large dictionary, multiple smaller, independent dictionaries are employed, enabling a low-complexity multidimensional Orthogonal Matching Pursuit algorithm. The proposed unfolded network is evaluated on realistic channel data against multiple baselines, demonstrating its strong performance and potential.