This item from - IEEE Journal - Communication, Networking and Broadcast Technologies - This paper considers radio resource allocation (RRA) in the downlink of an orthogonal frequency division multiple access (OFDM)-based spectrum-sharing network. The objective of RRA is to maximize the average achievable throughput subject to the primary service interference threshold and the secondary service transmit power constraint. RRA is usually implemented based on a time window T over which system parameters are averaged and checked against resource constraints. We use short-term ( T=1 time slot) and long-term ( Tgg 1 slots) averaging as approximations to instantaneous and average constraints, respectively. RRA is also investigated for this system with long-term interference threshold and short-term interference threshold constraints. RRA optimization is a nonconvex optimization problem in which the duality principle is adopted to obtain approximate solutions. The duality gap indicates the degree of approximation in the thus-obtained solution. We prove that the duality gap corresponding to each resource allocation asymptotically decays at least with an exponential rate of T. We further show that OFDMA is, asymptotically, the optimal subcarrier assignment. We also propose a practically implementable online power and subcarrier allocation with on-the-fly channel state information measurement. An extensive simulation study has been conducted to verify the theoretically predicted duality gap behavior and to investigate the impact of different system parameters on the secondary service performance. The developed algorithms are also validated to be robust in practical settings and converge fast to theoretical bounds, and thus practically implementable.