In this study, the authors propose a novel channel and queue aware algorithm for allocating power and subcarrier to users in orthogonal frequency division multiple access (OFDMA) networks. The proposed algorithm utilises a utility function to simultaneously balance and improve the efficiency and fairness of radio resource allocation. In contrast to the conventional approaches in the literature, in which it is assumed that the OFDMA system is able to support a continuous set of bit rates, here, in the system model the authors consider the fact that in practical OFDMA systems only a limited set of bit rates are supported. Furthermore, the authors do not consider the full buffer assumption and note that in practice a user scheduled for transmission might not always have data to transmit. By formulating the radio resource allocation the authors then show optimal bit loading results in a greedy algorithm that employs both bit removal and bit filling procedures. The solutions are developed in the framework of a matroid theory. The authors then analyse the average system throughput and investigate the performance of the proposed algorithm through simulations. Comparisons to similar approaches are also conducted which indicates significant performance improvement.