Orthogonal Frequency Division Multiple Access (OFDMA) allows multiple users to make use of the same bandwidth as the single-user OFDM for data transmission and is a promising candidate to be used for future cellular systems. A key issue at hand is the rate-adaptive resource allocation problem. In this paper, we propose two basic subcarrier allocation schemes with low complexities based on the magnitude of the channel frequency responses. The proposed algorithms ensure a fair resource allocation in terms of the number of subcarriers with affordable bit-rates. Through extensive discussions and Monte Carlo simulations, a comprehensive comparison with previously derived subcarrier allocation schemes is performed which depicts the pros and cons of our proposed algorithms.