In this paper, we propose an ordinal optimization (OO) theory-based four-stage approach to deal with the subcarrier assignment and bit allocation problem of a multiuser orthogonal frequency-division multiplexing (OFDM) system. The four-stage OO approach ensures the quality of the obtained solution, however, at the cost of solving a continuous version of the considered problem in the first stage. To resolve this computational complexity problem, we propose a hardware-implementable dual projected gradient (DPG) method to exploit deep-submicrometer technology. Compared to some existing methods using numerous simulation cases with randomly generated parameters, our approach is excellent in the aspect of power consumption. In the meantime, the estimated computation time of our approach can meet the real-time application requirement. Furthermore, we use extensive simulations to compare our good-enough solutions with the true optimal solutions, and the results show that the objective value obtained by our approach deviates from the optimal objective value around 1% on average.