  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.
