We propose a three-message superposition coding scheme in a cognitive radio relay network exploiting active cooperation between primary and secondary users. The primary user is motivated to cooperate by substantial benefits it can reap from this access scenario. Specifically, the time resource is split into three transmission phases: The first two phases are dedicated to primary communication, while the third phase is for the secondary's transmission. We formulate two throughput maximization

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... blems for the secondary network subject to primary user rate constraints and per-node power constraints with respect to the time durations of primary transmission and the transmit power of the primary and the secondary users. The first throughput maximization problem assumes a partial power constraint such that the secondary power dedicated to primary cooperation, i.e. for the first two communication phases, is fixed apriori. In the second throughput maximization problem, a total power constraint is assumed over the three phases of communication. The two problems are difficult to solve analytically when the relaying channel gains are strictly greater than each other and strictly greater than the direct link channel gain. However, mathematically tractable lowerbound and upperbound solutions can be attained for the two problems. For both problems, by only using the lowerbound solution, we demonstrate significant throughput gains for both the primary and the secondary users through this active cooperation scheme. We find that most of the throughput gains come from minimizing the second phase transmission time since the secondary nodes assist the primary communication during this phase. Finally, we demonstrate the superiority of our proposed scheme compared to a number of reference schemes that include best relay selection, dual-hop routing, and an interference channel model.