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This study presents a blind carrier frequency offset (CFO) tracking algorithm for orthogonal frequency division multiplexing systems with constant modulus signalling. Both single-input single-output and multiple-input multiple-output (MIMO) systems are considered. Based on the assumption that the channel frequency response (CFR) has been estimated by training symbols and keeps constant over one frame duration, we discover that the CFO can be estimated via minimising the power difference between the received signals and the CFR. The polynomial rooting method is exploited to derive a low complexity solution. The expectation and mean-square error of the proposed method are derived mathematically. Besides, the effect of channel estimation error on the performance of CFO tracking is addressed and it is shown that the proposed algorithm is robust to this error. At last, this blind scheme can be applied to a MIMO system with the aid of space time block codes.