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Terahertz ultra-massive multiple-input multiple-output (THz UM-MIMO) isenvisioned as one of the key enablers of 6G wireless systems. Due to the jointeffect of its array aperture and small wavelength, the near-field region of THzUM-MIMO is greatly enlarged. The high-dimensional channel of such systems thusconsists of a stochastic mixture of far and near fields, which renders channelestimation extremely challenging. Previous works based on uni-field assumptionscannot capture the hybrid far- and near-field features, thus sufferingsignificant performance loss. This motivates us to consider hybrid-fieldchannel estimation. We draw inspirations from fixed point theory to develop anefficient deep learning based channel estimator with adaptive complexity andlinear convergence guarantee. Built upon classic orthogonal approximate messagepassing, we transform each iteration into a contractive mapping, comprising aclosed-form linear estimator and a neural network based non-linear estimator. Amajor algorithmic innovation involves applying fixed point iteration to computethe channel estimate while modeling neural networks with arbitrary depth andadapting to the hybrid-field channel conditions. Simulation results verify ourtheoretical analysis and show significant performance gains overstate-of-the-art approaches in the estimation accuracy and convergence rate.

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