  In this paper, by exploiting the powerful ability of deep learning, we devote
to designing a well-performing and pilot-saving neural network for the channel
estimation in underwater acoustic (UWA) orthogonal frequency division
multiplexing (OFDM) communications. By considering the channel estimation
problem as a matrix completion problem, we interestingly find it mathematically
equivalent to the image super-resolution problem arising in the field of image
processing. Hence, we attempt to make use of the very deep super-resolution
neural network (VDSR), one of the most typical neural networks to solve the
image super-resolution problem, to handle our problem. However, there still
exist significant differences between these two problems, we thus elegantly
modify the basic framework of the VDSR to design our channel estimation neural
network, referred to as the channel super-resolution neural network (CSRNet).
Moreover, instead of training an individual network for each considered
signal-to-noise ratio (SNR), we obtain an unified network that works well for
all SNRs with the help of transfer learning, thus substantially increasing the
practicality of the CSRNet. Simulation results validate the superiority of the
CSRNet against the existing least square (LS) and deep neural network (DNN)
based algorithms in terms of the mean square error (MSE) and the bit error rate
(BER). Specifically, compared with the LS algorithm, the CSRNet can reduce the
BER by 44.74% even using 50% fewer pilots.
