Simultaneous wireless information and power transfer（SWIPT） is studied in this paper for the wireless powered downlink（DL） and multiuser information uplink（UL） systems. The objective is to maximize the energy efficiency defined as the ratio of the achieved throughput over the energy cost by optimizing the time allocation for the DL and multi-user UL traffics and its goal is to obtain the analytical expression to the optimal time allocation yet the resulting difficulty comes from the sum throughput of the multiuser in UL as well as the corresponding power consumption. To tackle this, the Jensen inequality is applied to approximating the exact expression of the sum throughput for the UL multi-users, leading to an upper-bound of the counterpart.The final closed form is exact in the single-user scenario yet approximate in the multi-user scenario. Numerical simulations verify the tightness of this approximation and the performances of the proposed analytical scheme.
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