  Terahertz ultra-massive MIMO (THz UM-MIMO) is envisioned as one of the key
enablers of 6G wireless networks, for which channel estimation is highly
challenging. Traditional analytical estimation methods are no longer effective,
as the enlarged array aperture and the small wavelength result in a mixture of
far-field and near-field paths, constituting a hybrid-field channel. Deep
learning (DL)-based methods, despite the competitive performance, generally
lack theoretical guarantees and scale poorly with the size of the array. In
this paper, we propose a general DL framework for THz UM-MIMO channel
estimation, which leverages existing iterative channel estimators and is with
provable guarantees. Each iteration is implemented by a fixed point network
(FPN), consisting of a closed-form linear estimator and a DL-based non-linear
estimator. The proposed method perfectly matches the THz UM-MIMO channel
estimation due to several unique advantages. First, the complexity is low and
adaptive. It enjoys provable linear convergence with a low per-iteration cost
and monotonically increasing accuracy, which enables an adaptive
accuracy-complexity tradeoff. Second, it is robust to practical distribution
shifts and can directly generalize to a variety of heavily out-of-distribution
scenarios with almost no performance loss, which is suitable for the
complicated THz channel conditions. For practical usage, the proposed framework
is further extended to wideband THz UM-MIMO systems with beam squint effect.
Theoretical analysis and extensive simulation results are provided to
illustrate the advantages over the state-of-the-art methods in estimation
accuracy, convergence rate, complexity, and robustness.
