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This paper presents new design formulations that aim at optimizing the performance of an orthogonal frequency-division multiple-access (OFDMA) ad hoc cognitive radio network through joint subcarrier assignment and power allocation. Aside from an important constraint on the tolerable interference induced to primary networks, to efficiently implement spectrum-sharing control within the unlicensed network, the optimization problems considered here strictly enforce upper and lower bounds on the total amount of temporarily available bandwidth that is granted to individual secondary users. These new requirements are of particular relevance in cognitive radio settings, where the spectral activities of primary users are highly dynamic, leaving little opportunity for secondary access. A dual decomposition framework is then developed for two criteria (throughput maximization and power minimization), which gives rise to the realization of distributed solutions. Because the proposed distributed protocols require very limited cooperation among the participating network elements, they are particularly applicable to ad hoc cognitive networks, where centralized processing and control are certainly inaccessible. In this paper, we recommend that the network collaboration is made possible through the implementation of virtual timers at individual secondary users and through the exchange of pertinent information over a common reserved channel. It is shown that not only is the computational complexity of the devised algorithms affordable but that the performance of these algorithms in practical scenarios attains the actual global optimum as well. The potential of the proposed approaches is thoroughly verified by asymptotic complexity analysis and numerical results.