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Blind maximum-likelihood (ML) carrier-frequency-offset (CFO) estimation is considered to be difficult in interleaved orthogonal frequency-division multiple-access (OFDMA) uplink systems. This is because multiple CFOs have to be simultaneously estimated (each corresponding to a user's carrier), and an exhaustive multidimensional search is required. The computational complexity of the search may be prohibitively high. Methods such as the multiple signal classification and the estimation of signal parameters via the rotational invariance technique have been proposed as alternatives. However, these methods cannot maximize the likelihood function, and the performance is not optimal. In this paper, we propose a new method to solve the problem. With our formulation, the likelihood function can be maximized, and the optimum solution can be obtained by solving a polynomial function. Compared with the exhausted search, the computational complexity can be reduced dramatically. Simulations show that the performance of the proposed method can approach that of the Cramér-Rao lower bound.