# Structure-Informed Estimation for Pilot-Limited MIMO Channels via Tensor Decomposition

arXiv: https://arxiv.org/abs/2602.04083 · HTML: https://mlsanity.com/paper/2602.04083/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 55 references that are in the map.
- First posted on arXiv 3 Feb 2026.

## Builds on (most cited first, 22 of 22)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
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- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Tensor Decomposition for Signal Processing and Machine Learning](https://mlsanity.com/paper/1607.01668/) (2016)
- [DeepMIMO: A Generic Deep Learning Dataset for Millimeter Wave and Massive MIMO Applications](https://mlsanity.com/paper/1902.06435/) (2019)
- [Integrated Sensing and Communications: Towards Dual-functional Wireless Networks for 6G and Beyond](https://mlsanity.com/paper/2108.07165/) (2021)
- [Deep Learning-Based Channel Estimation](https://mlsanity.com/paper/1810.05893/) (2018)
- [Model-Driven Deep Learning for Physical Layer Communications](https://mlsanity.com/paper/1809.06059/) (2018)
- [Nonconvex Low-Rank Tensor Completion from Noisy Data](https://mlsanity.com/paper/1911.04436/) (2019)
- [A Tutorial on Extremely Large-Scale MIMO for 6G: Fundamentals, Signal Processing, and Applications](https://mlsanity.com/paper/2307.07340/) (2023)
- [Massive MIMO is a Reality -- What is Next? Five Promising Research Directions for Antenna Arrays](https://mlsanity.com/paper/1902.07678/) (2019)
- [Pruning the Pilots: Deep Learning-Based Pilot Design and Channel Estimation for MIMO-OFDM Systems](https://mlsanity.com/paper/2006.11796/) (2020)
- [Deep Plug-and-play Prior for Low-rank Tensor Completion](https://mlsanity.com/paper/1905.04449/) (2019)
- [Integrated Sensing and Communication with Massive MIMO: A Unified Tensor Approach for Channel and Target Parameter Estimation](https://mlsanity.com/paper/2401.01738/) (2024)
- [Deep Learning for Joint Channel Estimation and Feedback in Massive MIMO Systems](https://mlsanity.com/paper/2011.07242/) (2020)
- [Channel Estimation for Intelligent Reflecting Surface Assisted MIMO Systems: A Tensor Modeling Approach](https://mlsanity.com/paper/2008.04766/) (2020)
- [Physics-Informed Generative Modeling of Wireless Channels](https://mlsanity.com/paper/2502.10137/) (2025)
- [Deep Learning for Massive MIMO Channel State Acquisition and Feedback](https://mlsanity.com/paper/2002.06945/) (2020)
- [Deep Learning based Channel Estimation for Massive MIMO with Hybrid Transceivers](https://mlsanity.com/paper/2202.03220/) (2022)
- [Deep-Learning-Aided Alternating Least Squares for Tensor CP Decomposition and Its Application to Massive MIMO Channel Estimation](https://mlsanity.com/paper/2305.13947/) (2023)

## Abstract (arXiv)

Accurate channel state information in wideband MIMO systems is constrained by pilot overhead, a challenge intensifying as bandwidths scale toward 6G. This paper proposes a structure-informed hybrid estimator formulating pilot-limited MIMO channel estimation as low-rank tensor completion from sparse pilot observations---an underdetermined inverse problem that prior approaches avoid by assuming fully observed tensors. Canonical polyadic~(CP) and Tucker decompositions are compared: CP excels for specular channels matching its rank-one parameterization exactly, while Tucker provides numerical stability at extreme pilot scarcity where CP exhibits heavy-tail divergence. A lightweight 3D U-Net learns residual components beyond the low-rank structure, compensating for diffuse scattering and hardware non-idealities. On synthetic specular channels, Tucker completion improves normalized mean-squared error (NMSE) by 10.88~dB over least squares and 7.83~dB over orthogonal matching pursuit at 10% pilot density (ρ); CP outperforms Tucker by 13.11~dB at SNR=20~dB. On DeepMIMO channels, the hybrid Tensor--NN estimator has two regimes: Tensor--NN(Tucker) remains stable at ρ=2% where CP diverges, while a CP-guided variant becomes best from ρ≥ 4%, reaching -16.44~dB at ρ=8% and -20.34~dB at ρ=20%. The Tucker-guided variant outperforms unconstrained deep learning across the full pilot range; the CP-guided variant widens this gap once stable. Empirical analysis confirms sample complexity scales with intrinsic channel dimensionality (dominant paths) rather than ambient tensor size.