In this thesis, we address resource allocation optimization to achieve preferable performance for the downlink of generic non-orthogonal multiple access (NOMA)-assisted single-input single-output (SISO) Gaussian broadcast channels (BCs). In particular, we obtain the closed-form of optimal power allocation to maximize users' sum-rate as well as minimize transmitter’s power consumption. Our results are then extended to downlink multi-cell NOMA with single-cell processing, i.e., treating interference as noise (TIN) between the cells. In this system, power control among the interfering cells may affect the optimal successive interference cancellation (SIC) decoding order among NOMA users. The impact of dynamic/static SIC decoding order, and various successful SIC conditions (enabling NOMA) and their performances are also analyzed and numerically evaluated. We also address resource allocation optimization for downlink multi-cell NOMA with joint processing, where the information of a user is available at multiple transmitters. In this case, these transmitters simultaneously send the same message to that user, called joint transmission (JT)-coordinated multi-point (CoMP). We also address resource allocation optimization for downlink multicarrier NOMA (MC-NOMA) systems. For the sum-rate and energy efficiency maximization problems, we show that MC-NOMA can be equivalently transformed to a virtual OMA system, where the effective channel gain of each virtual OMA user is obtained in closed-form. Then, the sum-rate and energy efficiency maximization problems are solved by using fast (super-linear) water-filling and Dinkelbach algorithms, respectively.