  Channel estimation and beamforming play critical roles in frequency-division
duplexing (FDD) massive multiple-input multiple-output (MIMO) systems. However,
these two modules have been treated as two stand-alone components, which makes
it difficult to achieve a global system optimality. In this paper, we propose a
deep learning-based approach that directly optimizes the beamformers at the
base station according to the received uplink pilots, thereby, bypassing the
explicit channel estimation. Different from the existing fully data-driven
approach where all the modules are replaced by deep neural networks (DNNs), a
neural calibration method is proposed to improve the scalability of the
end-to-end design. In particular, the backbone of conventional time-efficient
algorithms, i.e., the least-squares (LS) channel estimator and the zero-forcing
(ZF) beamformer, is preserved and DNNs are leveraged to calibrate their inputs
for better performance. The permutation equivariance property of the formulated
resource allocation problem is then identified to design a low-complexity
neural network architecture. Simulation results will show the superiority of
the proposed neural calibration method over benchmark schemes in terms of both
the spectral efficiency and scalability in large-scale wireless networks.
