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.
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