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Summary We consider a radio frequency energy harvesting cognitive radio network in which a secondary user (SU) can opportunistically access channel to transmit packets or harvest radio frequency energy when the channel is idle or occupied by a primary user. The channel occupancy state and the channel fading state are both modeled as finite state Markov chains. At the beginning of each time slot, the SU should determine whether to harvest energy for future use or sense the primary channel to acquire the current channel occupancy state. It then needs to select an appropriate transmission power to execute the packet transmission or harvest energy if the channel is detected to be idle or busy, respectively. This sequential decision‐making, done to maximize the SU's expected throughput, requires to design a joint spectrum sensing and transmission power control policy based on the amount of stored energy, the retransmission index, and the belief on the channel state. We formulate this as a partially observable Markov decision process and use a computationally tractable point‐based value iteration algorithm. Section 5 illustrate the significant outperformance of the proposed optimal policy compared with the optimal fixed‐power policy and the greedy fixed‐power policy.

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