In this paper, we study fairness and sum rate performance issues in uplink non-orthogonal multiple access (NOMA) communication system by allocation of subbands and power to users. In a NOMA system, each subband can be shared by L users simultaneously, which leads to higher spectral efficiency than the Orthogonal Multiple Access (OMA) system. It has been studied that, without proper allocation of target data rate for each uplink NOMA user, a user can always be in outage. In this work, we constrain the number of subbands Ns that each user could use to prevent starvation of poor users. We have also analyzed the sum rate performance with different combination of L and Ns in the system. An algorithm to allocate the subbands and power to users is developed to maximize sum rate with proper fairness. The work tries to find the optimal combination of L and Ns to achieve the maximum sum rate for given K users in the system. The system performance of sum rate, fairness, and BER are simulated. The fairness of the proposed scheme is compared with prior NOMA algorithms. Though simple, the proposed fixed Ns scheme improves the fairness significantly.