Non-orthogonal multiple access (NOMA) has attracted a lot of attention recently due to its superior spectral efficiency and could play a vital role in improving the capacity of future networks. In this paper, a resource allocation scheme is developed for a downlink multi-user NOMA system. An optimization problem is formulated to maximize the sum rate under the total power and proportional rate constraints. Due to the complexity of computing the optimal solution, we develop a low complexity sub-optimal solution for two-user scenario and then extend it to the multi-user case by proposing a user-pairing approach as well as a number of power allocation techniques that facilitate dealing with a large number of users in NOMA system. Simulation results support the effectiveness of the proposed approaches and show the close performance to the optimal one. In addition, we propose a new hybrid multiple access technique that combines the properties of NOMA and the orthogonal frequency division multiple access (OFDMA). Simulation results show that the proposed hybrid method provides better performance than NOMA in terms of the overall achievable sum rate and the coverage probability