This paper proposes a generalized carrier frequency offset (CFO) estimator for the uplink of orthogonal frequency division multiple access (OFDMA) wireless systems. Using the maximum likelihood criterion, the estimator estimates CFOs using the phase shift between two observation windows at distance less than the length of OFDMA symbol. The scheme offers the possibility to shorten the OFDMA preamble used in synchronization, and thus reduce overhead in packet-based wireless communications.