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In this paper, we proposed a joint user pairing (UP) and power allocation (PA) algorithm in the non-orthogonal multiple access uplink communication systems, aiming at improving the proportional fairness of the users. We first solve the optimization problem in a basic scenario, where the users are distributed in only one base station (BS), which is broadly used in many papers. Subsequently, the algorithm is further extended into a complex scenario that the interfering users are allocated randomly outside the BS by spatial homogeneous Poisson point process (HPPP). The joint UP and PA is an NP-hard problem in both scenarios. To solve the problem efficiently, we decouple the UP and PA part. In the PA part of the basic scenario, according to our analysis, the user pair can be divided into three kinds according to the different relationship between the channel condition and the signal to noise and interference constraint. The different kind of user pair's near optimal PA solution is found in different ways. In the UP part of the basic scenario, a probability-based Tabu search user-pairing algorithm is provided to find the near optimal user pairing solution. While, in the PA part of the complex scenario, the optimization problem is extended into a stochastic programming problem aiming at enhancing proportional fairness in users with the outage rate constraint. We derive the closed form expression of outage rate and average data rate for each possible user pairs according to HPPP. Then, a prediction-based particle swarm optimization algorithm is proposed to solve the stochastic programming problem. The simulation results show that the proposed algorithm provides better proportional fairness comparing to previous algorithms.

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