The orthogonal frequency division multiple access (OFDMA) system is considered in the downlink wireless communication system with the time division duplex (TDD) mode. Due to the trade-off between the subcarrier allocation gain and transmission overhead, we consider the subcarrier allocation employing only a given number of users forming a subset of total users in the system, rather than total users as in conventional schemes. Considering the transmission overhead, the optimal number of users for the subcarrier allocation is found in the maximum spectral efficiency sense. The proposed scheme can considerably mitigate the transmission overhead, which leads to performance improvement in the spectral efficiency. Although the overall transmit power is increased maximally 5.7% in the proposed scheme, the spectral efficiency is enhanced up to 28% comparing with the conventional one.