In this article, radio resource allocation in underlay spectrum sharing based on the orthogonal frequency-division multiple access is studied. A cellular-based secondary service is considered in which the licensed spectrum is opportunistically accessed provided that the imposed interference at the primary service receivers because of secondary service transmissions stays below an interference threshold constraint. The main objective here is to maximise the sum capacity of the secondary service and to find the optimal allocated power, subcarrier and rate across all subcarriers and different secondary users. Three different scenarios are considered based on the availability of the channel state information (CSI) between the secondary service base station and primary receivers. The optimal resource allocation for the case of accurate CSI between the secondary base station and the primary receivers is obtained. To manage more practical situations, in the second considered scenario the authors assume that only the channel distribution information information between the secondary base station and the primary receivers is available at the secondary service base station. In the third scenario the authors further propose a novel algorithm, which controls the collision incidences caused by secondary transmissions owing to lack of CSI in secondary base station. Simulation analyses are also conducted in order to investigate the system performance based on the proposed resource allocation algorithms.