Carrier frequency offset (CFO) between a transmitter and receiver signaling at 2 Mbps data rate with a 11110000 pattern as the preamble period is corrected within one preamble time period using free-running coarse and fine carrier frequency offset estimations. Two estimates for the CFO are computed, coarse and fine. The fine one is computationally accurate but may not be correct because of a potential wrap at ±180° in the computation. The coarse one is not accurate but delivers the approximate CFO value without wrap over. The comparison between the coarse and fine estimates thus may be used to detect a wrap over in the fine estimate and modify the fine estimate accordingly. Thereafter the compensated fine CFO estimation is used for carrier frequency offset (CFO) compensation.