Many carrier frequency offset estimation algorithms for multicarrier communication systems utilize autocorrelation of repeating sequences. Limited frequency acquisition range due high temporal distance between the repeating parts do not allow to use these algorithms in communication systems with unique word prefixed block-wise transmission. This contribution is addressed to solve fine carrier frequency offset estimation problem in such communication systems by proposing simple algorithms that employ cross-correlation between training sequence and received time domain samples. Numerous computer simulations and theoretical analysis confirm applicability of the proposed methods to the multicarrier communication systems.