In this paper we formulate the radio resource allocation problem of maximizing throughput in an OFDMA (Orthogonal Frequency Division Multiple Access) downlink where the BS (Base Station) adapts the power allocation according to non-causal (offline) knowledge of the harvested energy and channel state. The offline case is important from a theoretical point of view since it provides a bound on the performance of the online problem (causal). Differently from previous works that consider a continuous mapping between SNR (Signal-to-Noise Ratio) and transmit data rate, we employ a discrete mapping that depends on the required MCSs (Modulation and Coding Schemes). Also, we propose a heuristic algorithm that provides near-optimal results and achieves a good complexity/performance trade-off. In addition, we analyze the online version of the problem, and we propose two novel solutions to solve the problem only with causal information. Furthermore, we reformulate our problem to satisfy QoS (Quality of Service) constraints for each user in a hybrid power system where the BS is powered by a fixed power source from the electric grid and by a stochastic power source from renewable energy sources. Lastly, we present an offline solution to this new problem that also achieves a considerable complexity/performance gain.Index Terms-Resource allocation, rate maximization, energy harvesting, OFDMA, MCS, hybrid power system, QoS. the energy consumption causality constraints that limit the used energy to the quantity available at the moment, despite the knowledge of future energy arrivals in the offline case. Both restrictions are known as energy harvesting constraints, and are present in several works [2]-[5].