Digital in-service relative time delay estimation for SDM self-homodyne coherent systems

For space division multiplexing self-homodyne coherent systems, we propose a novel digital in-service relative time delay (RTD) estimation method without any additional optoelectronic device. Taking advantage of the frequency-domain periodicity of the colored frequency modulation noise, we manage to find the peak with location reflecting the RTD in its autocorrelation function (ACF). The peak to average ratio is further enhanced by leveraging a low-pass differential finite impulse response filter for robust identification. By simulations, the method is validated to be feasible for various linewidths, formats (16QAM, 32QAM and 64QAM), and links up to 80 km. Particularly, it is proved to be inherently compatible with large-linewidth low-cost lasers for the 10-km link. Also, for a low-complexity implementation, we discuss the way to reduce the number of points used to calculate the ACF while maintaining the same dynamic range. Furthermore, we demonstrate a 50-GBaud 16-QAM experiment to investigate its performances. With received optical power varying from -11 dBm to -17 dBm, 2¹⁶ points are sufficient to provide an estimation accuracy of standard deviation (STD) less than 0.089 ns for the RTD range of [2.6, 491.0 ns]. The STD can be lowered to 0.036 ns by adopting 2¹⁸ points. Especially, at -11-dBm ROP, the highest performance has been achieved with an accuracy smaller than the symbol period (0.018-ns STD) and a RTD range of [1.5, 491.0 ns].