  This paper investigates the downlink communications of intelligent reflecting
surface (IRS) assisted non-orthogonal multiple access (NOMA) systems. To
maximize the system throughput, we formulate a joint optimization problem over
the channel assignment, decoding order of NOMA users, power allocation, and
reflection coefficients. The formulated problem is proved to be NP-hard. To
tackle this problem, a three-step novel resource allocation algorithm is
proposed. Firstly, the channel assignment problem is solved by a many-to-one
matching algorithm. Secondly, by considering the IRS reflection coefficients
design, a low-complexity decoding order optimization algorithm is proposed.
Thirdly, given a channel assignment and decoding order, a joint optimization
algorithm is proposed for solving the joint power allocation and reflection
coefficient design problem. Numerical results illustrate that: i) with the aid
of IRS, the proposed IRS-NOMA system outperforms the conventional NOMA system
without the IRS in terms of system throughput; ii) the proposed IRS-NOMA system
achieves higher system throughput than the IRS assisted orthogonal multiple
access (IRS-OMA) systems; iii) simulation results show that the performance
gains of the IRS-NOMA and the IRS-OMA systems can be enhanced via carefully
choosing the location of the IRS.
