Non-Data-Aided ML Estimation of Timing Offset and Carrier Phase for <i>M</i>-APSK Modulated FSO Systems

This letter presents a non-data-aided maximum likelihood (ML) approach for joint estimation of symbol timing offset (STO) and common phase error (CPE) in coherent optical orthogonal frequency-division multiplexing (CO-OFDM) systems, applicable to both fiber-optic and free space optical (FSO) communications. By utilizing the phase information from received spectrum data, we derive closed-form maximum likelihood (ML) expressions for STO and CPE estimates. Simulation results show that the proposed ML approach achieves mean squared error (MSE) close to the Cramér-Rao lower bound (CRLB), demonstrating superior robustness to noise and laser linewidths.