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In this paper, we propose a hybrid scheme for the carrier frequency offset (CFO) estimation in OFDM communication systems. The main novelty of the approach is the judicious combination of two methods so as to reduce the bandwidth overhead and computational complexity without compromising the estimation range. The cyclic prefix (CP) associated with the OFDM symbols are used for the fractional frequency offset estimation. The integer frequency offset is estimated by means of a cost function minimization employing a few null subcarriers, which are allocated using a modified Fibonacci series. Performance of the frequency offset estimator is mathematically analyzed by deriving the Cramer-Rao bound (CRB) and is compared with the mean square error performance of the estimator. For moderate SNRs, our algorithm is shown to outperform some existing methods in terms of MSE (and thereby BER) performance, training overhead and receiver complexity.