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Simultaneous wireless information and power transfer (SWIPT) enables the transmission of information symbols and energy simultaneously. In this paper, we study the multiple-input-multiple-output SWIPT systems with limited RF chains at the base station. We focus on the scenario where there is one information decoder with a target signal-to-interference-plus-noise-ratio and several separate energy-harvesting receivers with harvested energy thresholds. To motivate our energy-efficient hybrid analog&#x2013;digital beamforming strategy, the fully digital power minimization problem is first analyzed, where we mathematically show that the optimal beamformer consists of only the information beamformer, and derive closed-form beamformers for a number of special cases. Based on this result, we further consider hybrid beamforming and propose an iterative scheme where the analog and digital beamformers are alternately updated. For the proposed scheme, in each iteration we design the analog beamformer by minimizing the difference between the fully digital beamformer and the hybrid beamformer. Based on our above-mentioned analysis for fully digital case, the optimal solution for the analog beamformer can be obtained via a geometrical interpretation. We further design the robust beamformers for the proposed schemes, when only imperfect channel state information is available. The numerical results show that the proposed iterative designs achieve a close-to-optimal performance with significant gains in the total power consumption over fully digital SWIPT.

Energy-Efficient SWIPT: From Fully Digital to Hybrid Analog–Digital Beamforming