End-to-end Optimization of Constellation Shaping for Wiener Phase Noise Channels with a Differentiable Blind Phase Search

TL;DR

This paper introduces a differentiable blind phase search algorithm integrated into an end-to-end optimization framework for constellation shaping, enhancing spectral efficiency in optical communication systems affected by phase noise.

Contribution

It develops a differentiable version of the blind phase search algorithm and demonstrates improved constellation shaping for phase noise channels.

Findings

Improved spectral efficiency by at least 0.1 bit/symbol over square QAM.

Achieved better performance than previous geometric-only shaping methods.

Enhanced robustness and pilot-free operation in 64-ary systems.

Abstract

As the demand for higher data throughput in coherent optical communication systems increases, we need to find ways to increase capacity in existing and future optical communication links. To address the demand for higher spectral efficiencies, we apply end-to-end optimization for joint geometric and probabilistic constellation shaping in the presence of Wiener phase noise and carrier phase estimation. Our approach follows state-of-the-art bitwise auto-encoders, which require a differentiable implementation of all operations between transmitter and receiver, including the DSP algorithms. In this work, we show how to modify the ubiquitous blind phase search (BPS) algorithm, a popular carrier phase estimation algorithm, to make it differentiable and include it in the end-to-end constellation shaping. By leveraging joint geometric and probabilistic constellation shaping, we are able to obtain a robust and pilot-free modulation scheme improving the performance of 64-ary communication systems by at least 0.1bit/symbol compared to square QAM constellations with neural demappers and by 0.05 bit/symbol compared to previously presented approaches applying only geometric constellation shaping.