Coherent optics are emerging as promising solutions for future passive optical networks. However, upstream burst-mode coherent detection faces challenges due to the need for fast digital signal processing and its susceptibility to laser wavelength drift. To address these issues, we propose an algorithm capable of rapid channel equalization and frequency offset estimation (FOE). The feasibility of the proposed scheme is experimentally verified through 128-Gbits/s 16QAM signal transmission systems. Consequently, integrating a fine FOE tap into the AEQ allows for rapid convergence and accurate frequency offset estimates within approximately ±0.5 times the symbol rate, while maintaining low complexity.