In this paper, the problem of downlink radio resource allocation for a power‐domain nonorthogonal multiple‐access–based heterogeneous cellular network is investigated. We propose two scenarios: (1) resource allocation with exclusive subcarrier allocation and (2) resource allocation considering intercell interference. The aim of this paper is to obtain joint subcarrier and power allocation for the two considered system models by addressing the maximization of the users' sum rate subject to the bit error rate constraint, the successive interference cancellation constraint, subcarrier constraints, and the transmit power restriction of each base station. To solve the corresponding optimization problems, an alternating method is applied by decoupling the proposed problems into two subproblems, namely, subcarrier allocation problem and power allocation problem, where they are solved by using the mesh adaptive direct search algorithm and different successive convex approximation methods, respectively. Moreover, to evaluate the optimality gap of the alternating method, the proposed problems are solved using an optimal method, namely, monotonic optimization with high complexity as a benchmark. As the results show, with the bit error rate constraint, the link‐level performance, at the cost of a decreasing system sum rate, is improved.