Orthogonal Frequency Division Multiple Access (OFDMA) techniques are investigated in this paper. Five subchannel allocation algorithms are analysed and their performance in a multicellular environment is evaluated with simulations. Four schemes of lower complexity, suitable for the early deployment of wireless systems, are compared with a more computationally demanding scheme with respect to their blocking probability, loading factor, and offered bit rate. The channel condition of each carrier is calculated and its knowledge is used for power controlled adaptive modulation, as an essential feature of the OFDMA technique. The results show that a wireless system in its early deployment phase (up to 15%-30% blocking probability) can employ simple OFDMA techniques capable of achieving high throughput.