In the sixth-generation (6G) networks, massive low-power devices are expected to sense environment and deliver tremendous data. To enhance the radio resource efficiency, the integrated sensing and communication (ISAC) technique exploits the sensing and communication functionalities of signals, while the simultaneous wireless information and power transfer (SWIPT) techniques utilizes the same signals as the carriers for both information and power delivery. The further combination of ISAC and SWIPT leads to the advanced technology namely integrated sensing, communication, and power transfer (ISCPT). In this paper, a multi-user multiple-input multiple-output (MIMO) ISCPT system is considered, where a base station equipped with multiple antennas transmits messages to multiple information receivers (IRs), transfers power to multiple energy receivers (ERs), and senses a target simultaneously. The sensing target can be regarded as a point or an extended surface. When the locations of IRs and ERs are separated, the MIMO beamforming designs are optimized to improve the sensing performance while meeting the communication and power transfer requirements. The resultant non-convex optimization problems are solved based on a series of techniques including Schur complement transformation and rank reduction. Moreover, when the IRs and ERs are co-located, the power splitting factors are jointly optimized together with the beamformers to balance the performance of communication and power transfer. To better understand the performance of ISCPT, the target positioning problem is further investigated. Simulations are conducted to verify the effectiveness of our proposed designs, which also reveal a performance tradeoff among sensing, communication, and power transfer.
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