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. This paper considers resource allocation for a downlink, multi-user (MU) MIMO-NOMA system that aims at maximizing the sum rate with interference alignment (IA) technique. Using singular ecomposition value (SVD) based IA, we propose IA based NOMA system in which a number of users are grouped together while the others are aligned to the null space as interference. The targeted group of users employ NOMA with a low complexity hierarchical power allocation scheme for sum rate maximization. In addition, an optimization problem is formulated to maximize the sum rate under the total power and proportional fairness constraints. A low complexity sub-optimal solution for two-user scenario is obtained and then extended to
the multi-user case by a hierarchical pairing scheme. Another approach is proposed to allocate the transmission power of each user using an iterative subgradient method. Simulation results show that the proposed schemes provide better performance than an existing scheme and perform close to the optimal one. In addition, the simulation scenario considers the case where two
users share the data streams while performing IA as compared to the case where all users are sharing it without IA. Simulation results verify that applying IA with NOMA could improve the achievable sum rate and offers simplicity in terms of successive interference cancellation (SIC) application.