# Hybrid Far- and Near-Field Channel Estimation for THz Ultra-Massive MIMO via Fixed Point Networks

arXiv: https://arxiv.org/abs/2205.04944 · HTML: https://mlsanity.com/paper/2205.04944/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 22 references that are in the map.
- First posted on arXiv 10 May 2022.

## Builds on (most cited first, 13 of 13)

- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018)
- [Edge Artificial Intelligence for 6G: Vision, Enabling Technologies, and Applications](https://mlsanity.com/paper/2111.12444/) (2021)
- [Model-Driven Deep Learning for Physical Layer Communications](https://mlsanity.com/paper/1809.06059/) (2018)
- [Feasibility-based Fixed Point Networks](https://mlsanity.com/paper/2104.14090/) (2021)
- [TeraHertz Band Communication: An Old Problem Revisited and Research Directions for the Next Decade](https://mlsanity.com/paper/2112.13187/) (2021)
- [An Overview of Signal Processing Techniques for Terahertz Communications](https://mlsanity.com/paper/2005.13176/) (2020)
- [Channel Estimation and Hybrid Combining for Wideband Terahertz Massive MIMO Systems](https://mlsanity.com/paper/2102.06772/) (2021)
- [Channel Estimation for Extremely Large-Scale Massive MIMO Systems](https://mlsanity.com/paper/1910.05432/) (2019)
- [Channel Estimation for Extremely Large-Scale Massive MIMO: Far-Field, Near-Field, or Hybrid-Field?](https://mlsanity.com/paper/2109.07883/) (2021)
- [Learn to Communicate with Neural Calibration: Scalability and Generalization](https://mlsanity.com/paper/2110.00272/) (2021)
- [Hybrid Beamforming for 5G and Beyond Millimeter-Wave Systems: A Holistic View](https://mlsanity.com/paper/1911.02853/) (2019)
- [A Unified 3D Beam Training and Tracking Procedure for Terahertz Communication](https://mlsanity.com/paper/2110.01066/) (2021)

## Built on by (most cited first, 2 of 2)

- [Lightweight and Flexible Deep Equilibrium Learning for CSI Feedback in FDD Massive MIMO](https://mlsanity.com/paper/2211.15079/) (2022)
- [Recurrent Transformer-Based Near- and Far-Field THz Wideband Channel Estimation for UM-MIMO](https://mlsanity.com/paper/2605.12578/) (2026)

## Abstract (arXiv)

Terahertz ultra-massive multiple-input multiple-output (THz UM-MIMO) is envisioned as one of the key enablers of 6G wireless systems. Due to the joint effect of its array aperture and small wavelength, the near-field region of THz UM-MIMO is greatly enlarged. The high-dimensional channel of such systems thus consists of a stochastic mixture of far and near fields, which renders channel estimation extremely challenging. Previous works based on uni-field assumptions cannot capture the hybrid far- and near-field features, thus suffering significant performance loss. This motivates us to consider hybrid-field channel estimation. We draw inspirations from fixed point theory to develop an efficient deep learning based channel estimator with adaptive complexity and linear convergence guarantee. Built upon classic orthogonal approximate message passing, we transform each iteration into a contractive mapping, comprising a closed-form linear estimator and a neural network based non-linear estimator. A major algorithmic innovation involves applying fixed point iteration to compute the channel estimate while modeling neural networks with arbitrary depth and adapting to the hybrid-field channel conditions. Simulation results verify our theoretical analysis and show significant performance gains over state-of-the-art approaches in the estimation accuracy and convergence rate.