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Accurate integer frequency offset (IFO) estimation is crucial for orthogonal frequency-division multiplexing (OFDM) systems, particularly in the presence of frequency-selective fading and residual timing offset (RTO). For existing algorithms, however, it is still a challenge to obtain a good tradeoff among the estimation performance, complexity, and spectrum overhead. In this paper, we propose a novel cross ambiguity function (CAF)-based IFO estimator using only one training sequence. By designing the training sequence, which has only a single sharp peak on its ambiguity function surface, a highly accurate and full acquisition range estimation of the IFO can be obtained in the presence of frequency-selective fading and RTO. Moreover, the adoption of the CAF expression in terms of time-domain signals ensures that the complexity of the proposed algorithm is relatively low. Simulation results verify its superior accuracy in frequency-selective fading channels and in the presence of RTO.