In this paper, the problem of maximizing the wireless users’ sum-rate for uplink rate splitting multiple access (RSMA) communications is studied. In the considered model, the message intended for a single user is split into two sub-messages with separate transmit power and the base station (BS) uses a successive decoding technique to decode the received messages. To maximize each user’s transmission rate, the users must adjust their transmit power and the BS must determine the decoding order of the messages transmitted from the users to the BS. This problem is formulated as a sum-rate maximization problem with proportional rate constraints by adjusting the users’ transmit power and the BS’s decoding order. However, since the decoding order variable in the optimization problem is discrete, the original maximization problem with transmit power and decoding order variables can be transformed into a problem with only the rate splitting variable. Then, the optimal rate splitting of each user is determined. Given the optimal rate splitting of each user and a decoding order, the optimal transmit power of each user is calculated. Next, the optimal decoding order is determined by an exhaustive search method. To further reduce the complexity of the optimization algorithm used for sum-rate maximization in RSMA, a user pairing based algorithm is introduced, which enables two users to use RSMA in each pair and also enables the users in different pairs to be allocated with orthogonal frequency. For comparisons, the optimal sum-rate maximizing solutions with proportional rate constraints are obtained for non-orthogonal multiple access (NOMA), frequency division multiple access (FDMA), and time division multiple access (TDMA). Simulation results show that RSMA can achieve up to 10.0, 22.2, and 81.2 percent gains in terms of sum-rate compared to NOMA, FDMA, and TDMA.