  Millimeter-wave (mmWave) communications have been one of the promising
technologies for future wireless networks that integrate a wide range of
data-demanding applications. To compensate for the large channel attenuation in
mmWave band and avoid high hardware cost, a lens-based beamspace massive
multiple-input multiple-output (MIMO) system is considered. However, the beam
squint effect in wideband mmWave systems makes channel estimation very
challenging, especially when the receiver is equipped with a limited number of
radio-frequency (RF) chains. Furthermore, the real channel data cannot be
obtained before the mmWave system is used in a new environment, which makes it
impossible to train a deep learning (DL)-based channel estimator using real
data set beforehand. To solve the problem, we propose a model-driven
unsupervised learning network, named learned denoising-based generalized
expectation consistent (LDGEC) signal recovery network. By utilizing the
Stein's unbiased risk estimator loss, the LDGEC network can be trained only
with limited measurements corresponding to the pilot symbols, instead of the
real channel data. Even if designed for unsupervised learning, the LDGEC
network can be supervisingly trained with the real channel via the
denoiser-by-denoiser way. The numerical results demonstrate that the
LDGEC-based channel estimator significantly outperforms state-of-the-art
compressive sensing-based algorithms when the receiver is equipped with a small
number of RF chains and low-resolution ADCs.
