To improve the radio throughput, novel radio access techniques need to be designed. With exploiting the multiuser diversity at power domain, nonorthogonal multiple access (NOMA) is one promising candidate technique for sixth-generation (6G). In this article, a downlink joint device assignment and power allocation problem is investigated in multihoming heterogeneous multicarrier NOMA networks. The joint device assignment and power allocation problem maximizes the network throughput with total power constraint at each base station, required minimum transmission rate for each device, and maximum number of accessed devices at each subchannel. Since the joint device assignment and power allocation problem is a mixed-integer nonlinear problem, the original optimization problem is divided into a device assignment subproblem and a power allocation subproblem. Then, the greedy method is applied to propose a device assignment algorithm, and successive convex approximation theory is adopted to design a power allocation algorithm. Finally, an iterative joint device assignment and power allocation algorithm is proposed. Numerical simulation results demonstrate that the proposed algorithm can improve the throughput and the average satisfactory of devices compared with other algorithms significantly.