  In this letter, we address the problem of millimeter-Wave channel estimation
in massive MIMO communication systems. Leveraging the sparsity of the mmWave
channel in the beamspace, we formulate the estimation problem as a sparse
signal recovery problem. To this end, we propose a deep learning based
trainable proximal gradient descent network (TPGD-Net). The TPGD-Net unfolds
the iterative proximal gradient descent (PGD) algorithm into a layer-wise
network, with the gradient descent step size set as a trainable parameter.
Additionally, we replace the proximal operator in the PGD algorithm with a
neural network that exploits data-driven prior channel information to perform
the proximal operation implicitly. To further enhance the transfer of feature
information across layers, we introduce the cross-layer feature attention
fusion module into the TPGD-Net. Our simulation results on the Saleh-Valenzuela
channel model and the DeepMIMO dataset demonstrate the superior performance of
TPGD-Net compared to state-of-the-art mmWave channel estimators.
