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In this paper, we demonstrate that despite the power constraints on all transmit nodes caused by the interference temperature limit (ITL) imposed by the primary user, power domain cooperative non-orthogonal multiple access (NOMA) can ensure much higher throughput in underlay cognitive radio networks than conventional orthogonal multiple access (OMA), provided the network is adaptive. We use intelligent user-selection and switching between cooperative NOMA, (non-cooperative) NOMA and OMA to ensure high throughput at the selected far-user while ensuring a desired performance at the selected near-user. The suggested user and mode selection scheme is simple and easy to implement, and yet ensures performance comparable to that attained by a scheme using more information. When the ITL is broadcast by the primary receiver in every coherence interval based on the primary channel, we show that …