Here our focus is on the downlink radio resource allocation in underlay spectrum sharing based on OFDMA technology. Both continuous and discrete rate strategies are investigated. We consider the practical case in which for the wireless channel between the secondary base station and secondary users only partial channel state information (CSI) is available at the secondary base station. We formulate the resource allocation problem in the secondary network as an optimization problem in which the objective is to maximize the secondary users weighted sum rate. Two main constraints at the secondary base station are the maximum total transmission power, and the primary service collision probabilities. The only available a priori information is the channel distribution information (CDI) for the channel between the secondary base station and the primary receivers. Since the optimal radio resource allocation is non convex we utilize dual optimization method to obtain suboptimal solutions. The computational complexity due to the constraints in the original radio resource allocation is then reduced by exploiting system specifications and substituting the original constraints with the equivalent constraints on the transmission power and rate. Simulations studies are conducted to investigate the impact of the different system parameters. We also compare the proposed algorithm with the conventional radio resource allocation and show that by the proposed algorithm we are able to enforce the collision probability constraint in the primary service which in return results in a slight decreasing in the sum rate of the secondary system. Furthermore, we show that the proposed schemes are able to keep the outage probability imposed by imperfect CSI below a given threshold.