We demonstrate a real-time coherent optical receiver based on a single field programmable gate array (FPGA) chip. To strike the balance between the performance and hardware resources, we use a clock recovery scheme using the optimal interpolation (OI). The performance and complexity of the OI-based scheme and the traditional schemes are compared and discussed via offline digital signal processing. And a real-time 15GBaud single-polarization 16QAM transmission experiment under different received optical power using the FPGA-based receiver is carried out to demonstrate the overall performance of different clock recovery and equalization schemes. The result proves that, compared to the traditional scheme with a cubic interpolator and a 7-tap equalizer, the optimal interpolator significantly lowers the utilization of LUT, CARRY8, and DSP48 by 35%, 50%, and 11%, respectively, and can work properly under a received optical power of -40dBm.