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

Neural Calibration for Scalable Beamforming in FDD Massive MIMO with Implicit Channel Estimation