In wireless networks, the exponentially increasing demands for wireless services are encountered by the scarcity of the available radio resources. More bandwidth is required for not only accommodating the increasing number of users, but also to meet the requirements of the new services such as TV on demand, wireless gaming, and mobile Internet. Non-orthogonal multiple access (NOMA) has attracted a great attention recently due to its superior spectral efficiency (SE) over orthogonal multiple access and could play a vital role in improving the capacity of future networks. In particular, power based NOMA multiplexes the users in power domain via superposition coding (SC) and allows them to access the whole spectrum simultaneously while using successive interference cancellation (SIC) at the receiver side for signal detection. Since NOMA exploits the power domain for multiple access, power allocation is vital to achieve superior SE with NOMA. Resource allocation and its optimization are general methods used to further improve the NOMA based networks performance. In this thesis, the resource allocation in the downlink NOMA system is considered and optimized for different objective functions such as the sum rate and the energy efficiency (EE). In addition, the combination of NOMA and multiple antenna is considered using linear and non-linear precoders. In all the considered cases, suboptimal power allocation schemes are proposed and compared to the numerically obtained optimal one. Results confirm that NOMA outperforms OFDMA. It also support the effectiveness of the proposed schemes as compared to the existing ones and to the optimal one. The results also reveal that using multiple antennas with NOMA can significantly enhance the overall performance. Furthermore, a NOMA-multicell scenario is considered to test the proposed schemes under the effect of intercell interference (ICI). The results prove that the proposed methods effective as compared to the optimal one at a much lower complexity.