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In this letter, we analyze an energy-harvesting-based cognitive radio (CR) system. The CR system harvests energy from the radio frequency (RF) signal of primary user (PU) during sensing time as well as the transmission time of a detection cycle if PU is present. The CR accesses the spectrum band of PU opportunistically using the energy harvested over the frames with PU present, while maintaining a quality of service (QoS) constraint on PU in terms of a collision probability. An optimal sensing time is found, which maximizes the harvested energy. The performance is investigated in terms of harvested energy, outage probability, and throughput of the network. Novel analytical expressions for average harvested energy and average throughput are developed under such a scenario, which are validated by simulation.