This paper investigates a wireless powered sensorudnetwork (WPSN), where multiple sensor nodes are deployed toudmonitor a certain external environment. A multi-antenna powerudstation (PS) provides the power to these sensor nodes duringudwireless energy transfer (WET) phase, and consequently theudsensor nodes employ the harvested energy to transmit their ownudmonitoring information to a fusion center (FC) during wirelessudinformation transfer (WIT) phase. The goal is to maximizeudthe system sum throughput of the sensor network, where twouddifferent scenarios are considered, i.e., PS and the sensor nodesudbelong to the same or different service operator(s). For theudfirst scenario, we propose a global optimal solution to jointlyuddesign the energy beamforming and time allocation. We furtheruddevelop a closed-form solution for the proposed sum throughputudmaximization. For the second scenario in which the PS andudthe sensor nodes belong to different service operators, energyudincentives are required for the PS to assist the sensor network.udSpecifically, the sensor network needs to pay in order to purchaseudthe energy services released from the PS to support WIT. Inudthis case, the paper exploits this hierarchical energy interaction,udwhich is known as energy trading. We propose a quadraticudenergy trading based Stackelberg game, linear energy trading basedudStackelberg game, and social welfare scheme, in which we deriveudthe Stackelberg equilibrium for the formulated games, and theudoptimal solution for the social welfare scheme. Finally, numericaludresults are provided to validate the performance of our proposedudschemes.
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