In this paper, cooperative cognitive radio networks are considered, in which a primary user (PU) and an off-the-grid secondary user (SU) co-exist by exploiting simultaneous wireless information and power transfer. Based on a two-phase relaying model, adaptive power splitting is performed at the SU for information decoding while collecting the energy remaining in the first phase. The energy harvested is then used to forward the decoded primary signal, with the secondary signal superimposed in the second phase. To enhance the utilization of both the spectrum and energy, an energy-aware retransmission approach is proposed for enabling successful decoding at the SU while collecting a reasonable amount of energy for relaying. The outage probability and throughput are theoretically analyzed for both the PU and the SU. To provide more analytical insights, tight performance upper and lower bounds are obtained in closed forms. Our results demonstrate that a mutually beneficial relationship can be built between the PU and the SU under proper parameter configurations. Furthermore, a performance tradeoff with respect to the number of retransmissions is demonstrated, where additional performance gains can be achieved by the proposed retransmission approach under unfavorable conditions of high rate, low power, and weak channels.INDEX TERMS Cooperative cognitive radio networks, simultaneous wireless information and power transfer, adaptive power splitting, decode-and-forward, energy-aware retransmission.