The traditional orthogonal multiple access (OMA) is unable to satisfy the needs of large number of smart devices. To increase the transmission rate in the limited spectrum resource, implementation of both non-orthogonal multiple access (NOMA) and successive interference cancelation (SIC) is essential. In this paper, an optimal resource allocation algorithm in NOMA is proposed to maximize the total system rate in a multi-sector multi-subcarrier relay-assisted communication network. Since the original problem is a non-convex problem with mixed integer programming which is non-deterministic polynomial-time (NP)-hard, a three-step solution is proposed to solve the primal problem. Firstly, we determine the optimal power allocation of the outer users by using the approach of monotonic discrimination, and then the optimal user pairing is determined. Secondly, the successive convex approximation (SCA) method is introduced to transform the non-convex problem involving central users into convex one, and the Lagrangian dual method is used to determine the optimal solution. Finally, the standard Hungarian algorithm is utilized to determine the optimal subcarrier matching. The simulation results show that resource allocation algorithm is able to meet the user performance requirements with NOMA, and the total system rate is improved compared to the existing algorithms.