  In this paper, we propose a data-driven deep learning (DL) approach to
jointly design the pilot signals and channel estimator for wideband massive
multiple-input multiple-output (MIMO) systems. By exploiting the angular-domain
compressibility of massive MIMO channels, the conceived DL framework can
reliably reconstruct the high-dimensional channels from the under-determined
measurements. Specifically, we design an end-to-end deep neural network (DNN)
architecture composed of dimensionality reduction network and reconstruction
network to respectively mimic the pilot signals and channel estimator, which
can be acquired by data-driven deep learning. For the dimensionality reduction
network, we design a fully-connected layer by compressing the high-dimensional
massive MIMO channel vector as input to low-dimensional received measurements,
where the weights are regarded as the pilot signals. For the reconstruction
network, we design a fully-connected layer followed by multiple cascaded
convolutional layers, which will reconstruct the high-dimensional channel as
the output. By defining the mean square error between input and output as loss
function, we leverage Adam algorithm to train the end-to-end DNN aforementioned
with extensive channel samples. In this way, both the pilot signals and channel
estimator can be simultaneously obtained. The simulation results demonstrate
that the superiority of the proposed solution over state-of-the-art compressive
sensing approaches.
