  Non-orthogonal multiple access (NOMA) has been considered as a promising
solution for improving the spectrum efficiency of next-generation wireless
networks. In this paper, the performance of a p-persistent slotted ALOHA system
in support of NOMA transmissions is investigated. Specifically, wireless users
can choose to use high or low power for data transmissions with certain
probabilities. To achieve the maximum network throughput, an analytical
framework is developed to analyze the successful transmission probability of
NOMA and long term average throughput of users involved in the non-orthogonal
transmissions. The feasible region of the maximum number of concurrent users
using high and low power to ensure successful NOMA transmissions are
quantified. Based on the analysis, an algorithm is proposed to find the optimal
transmission probabilities for users to choose high and low power to achieve
the maximum system throughput. In addition, the impact of power settings on the
network performance is further investigated. Simulations are conducted to
validate the analysis.
