We address the symbol-level precoding design problem for the downlink of a multiuser millimeter wave (mmWave) multiple-input multiple-output (MIMO) wireless system where the transmitter is equipped with a large-scale antenna array. The high cost and power consumption associated with the massive use of radio frequency (RF) chains prohibit fully-digital implementation of the precoder, and therefore, we consider a hybrid analog-digital architecture where a small-sized baseband precoder is followed

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... by two successive networks of analog on-off switches and variable phase shifters according to a fully-connected structure. We jointly optimize the digital baseband precoder and the states of the switching network on a symbol-level basis, i.e., by exploiting both the channel state information (CSI) and the instantaneous data symbols, whereas the phase-shifting network is designed only based on the CSI due to practical considerations. Our approach to this joint optimization is to minimize the Euclidean distance between the optimal fully-digital and the hybrid symbol-level precoders. Remarkably, the use of a switching network allows for power-savings in the analog precoder by switching some of the phase shifters off according to the instantaneously optimized states of the switches. Our numerical results indicate that, on average, up to 50 percent of the phase shifters can be switched off. We provide an analysis of energy efficiency by adopting appropriate power dissipation models for the analog precoder, where it is shown that the energy efficiency of precoding can substantially be improved thanks to the phase shifter selection approach, compared to the fully-digital and the state-of-the-art hybrid symbol-level schemes. Index Terms-Energy efficiency, hybrid analog-digital precoding, massive multiuser MIMO, mmWave communications, phase shifter selection, symbol-level precoding.