We introduce an adaptive subchannel, bit, and power allocation (ASBPA) algorithm to maximize the bandwidth efficiency of the mobile communication system that use orthogonal frequency division multiplexing (OFDM). We propose a suboptimal rate adaptive ASBPA algorithm that guarantees fairness in resource allocation and overcomes inherent co-channel interference (CCI) in the cellular system. Furthermore, we evaluate the maximum possible bandwidth efficiency of the cellular OFDM system achieved by the ASBPA algorithm which is practical to implement. Our simulation results show that the proposed algorithm outperforms the existing ones and achieves the cellular bandwidth efficiency of up to 5 b/s/Hz/cell. We also investigate some of the conditions that govern the bandwidth efficiency of the cellular OFDM system using the proposed ASBPA algorithm.