The estimation of carrier frequency offset (CFO) is a challenging issue in uplink orthogonal frequency division multiple access (OFDMA) systems. Many estimation methods have been proposed in the past. However most existing methods are derived under specified carrier assignment schemes (CAS). In this paper, we propose a new blind algorithm exploiting the virtual carriers or un-used subchannels for the estimation of multiple CFOs. Our method can be applied to general CAS. Only one OFDM block is needed to obtain the CFO estimates. In order to reduce the complexity, we derive a closed form formula when the CFO is small and also develop a two-step algorithm for larger CFO range. The proposed algorithms reduce the computational complexity significantly. Numerical simulations are provided to show the effectiveness of the proposed methods.INDEX TERMS Carrier assignment scheme (CAS), carrier frequency offset (CFO), estimation, multiuser, orthogonal frequency division multiple access (OFDMA).