A Simplified Implementation Method of $M$ th-Power for Frequency Offset Estimation

A simplified implementation method of Mth-power is investigated in this letter. Before frequency offset estimation (FOE), the Mth-power operation is required to remove the modulated data phase. One disadvantage of Mth-power operation is its large computational complexity, especially for high-order modulation systems. In this letter, we propose a low complexity method to approximately implement the Mth-power. In the proposed method, we apply the absolute operation of real number to the real and imaginary parts of received symbols to remove their modulated data phases. In the simulation, the proposed method is compared with the Mth-power operation in the 20-GBd quadrature phase-shift keying (PSK), 8 PSK, and square-16QAM systems for FOEs. The results show that the proposed method can approximately reach the same performance as the Mth-power operation, but the complexity is reduced effectively and no multiplier is required.