Joint subcarrier and power allocation with proportional fairness in multicarrier nonorthogonal multiple access systems

In this paper, we investigate joint subcarrier and power allocation in multicarrier nonorthogonal multiple access (MC-NOMA) systems aims to guarantee rate proportional fairness among all users. To this end, we adopt the sum logarithmic rate function as the objective and formulate a resource optimization problem which is a mixed-integer nonlinear programming (MINLP) problem. Based on variable relaxation and replacement, we convert this problem into a convex optimization problem. On this basis, the expressions of joint subcarrier and power allocation solutions are obtained by using convex optimization theory and the Karush-Kuhn-Tucker (KKT) condition. However, power and subcarrier allocation solutions are highly coupled, and it is difficult to derive both solutions simultaneously. Fortunately, when the subcarrier allocation strategy is given, the optimal power allocation solution can be derived by solving the equations. Furthermore, we develop an iterative resource allocation algorithm to implement joint subcarrier and power allocation among users. Numerical results reveal that the proposed algorithm is effective in general multiuser and multicarrier scenarios, and a substantial performance improvement can be achieved by the proposed algorithm in contrast with the traditional orthogonal multiple access (OMA) schemes. In specific, the proposed algorithm achieves 63% and 59% gains in terms of utility and fairness performance, respectively.