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We consider a two-hop underlay cognitive relay network with an energy harvesting (EH) relay. A simple improved time-switching protocol is proposed in which energy is transmitted in subslots until the relay node is sufficiently charged. The number of charging energy subslots required is fed back to the source by the relay node after the first energy subslot. We demonstrate that the proposed EH transmission scheme can yield better secondary throughput performance as compared to that achieved by an optimal EH transmission protocol using a fixed charging duration, while at the same time eliminating the need for feedback of channel estimates. We first analyze throughput when the source does not possess first-hop channel knowledge, but the relay possesses second hop channel knowledge. We then analyze throughput performance in the important case when the second hop channel estimate is in error, or the …