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The problem of wireless resource management in broadband cognitive OFDMA networks is addressed. The objective is to maximise the multiple cognitive users' weighted rate sum by jointly adjusting their rate, frequency and power resource, under the constraints of multiple primary users' interference temperatures. First, based on two interpretations of the interference temperatures, the problem studied is formulated as two nonlinear and non-convex optimisation problems. Secondly, these two problems are analysed, and a centralised greedy algorithm is proposed to solve one problem, as well as a centralised algorithm based on Lagrangian duality theory for the other. The two centralised algorithms are shown to be optimal and both have polynomial time complexities. Finally, it is shown that the two centralized algorithms can be distributively implemented by introducing the idea of virtual clock. And the distributed algorithms can be interpreted as an interesting distributed negotiated secondary market approach. It is believed that the work will provide a good reference for the emerging cognitive network protocol design.