  Non-orthogonal multiple access (NOMA) is envisioned to be one of the most
beneficial technologies for next generation wireless networks due to its
enhanced performance compared to other conventional radio access techniques.
Although the principle of NOMA allows multiple users to use the same frequency
resource, due to decoding complication, information of users in practical
systems cannot be decoded successfully if many of them use the same channel.
Consequently, assigned spectrum of a system needs to be split into multiple
subchannels in order to multiplex that among many users. Uplink resource
allocation for such systems is more complicated compared to the downlink ones
due to the individual users' power constraints and discrete nature of
subchannel assignment. In this paper, we propose an uplink subchannel and power
allocation scheme for such systems. Due to the NP-hard and non-convex nature of
the problem, the complete solution, that optimizes both subchannel assignment
and power allocation jointly, is intractable. Consequently, we solve the
problem in two steps. First, based on the assumption that the maximal power
level of a user is subdivided equally among its allocated subchannels, we apply
many-to-many matching model to solve the subchannel-user mapping problem. Then,
in order to enhance the performance of the system further, we apply iterative
water-filling and geometric programming two power allocation techniques to
allocate power in each allocated subchannel-user slot optimally. Extensive
simulation has been conducted to verify the effectiveness of the proposed
scheme. The results demonstrate that the proposed scheme always outperforms all
existing works in this context under all possible scenarios.
