Format-transparent phase estimation based on KL divergence in coherent optical systems

We propose a novel format-transparent phase estimation method in coherent optical systems by minimizing the Kullback-Leibler (KL) divergence between the signal constellation and the samples for estimation. The proposed metric exhibits the same standard deviation of estimation errors as that in conventional blind phase searching (BPS) with an infinite resolution, while eliminating the pre-decisions in BPS so that phase estimation can be realized using a recursive algorithm. The complexity and the performance of the proposed KL method are compared with previously reported 2-stage BPS, Kalman filtering, principal component analysis (PCA), and the PCA + BPS hybrid method. It is shown that this method is particularly suitable for probabilistically shaped (PS) formats in which the PCA method does not work properly. It exhibits better performance than Kalman filtering and the PCA + BPS hybrid method and has lower complexity than 2-stage BPS. It is also shown that the proposed KL method has a relaxed cycle-slip problem and is less sensitive to the noise due to a smaller number of samples compared to the 2-stage BPS and the PCA + BPS hybrid method. Therefore, the proposed method can be a very promising solution for format-transparent phase estimation in coherent optical systems, particularly using the PS formats.