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

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 pilotfree modulation scheme improving the performance of 64-ary communication systems by at least 0.1 bit/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.

High-Capacity Coherent WDM Networks Empowered by Probabilistic Shaping and End-to-End Deep Learning

“…To optimize data rates in optical communication systems, an effective strategy is used to improve spectral efficiency by employing constellation shaping techniques. A shaping gain is achieved by probabilistic and geometric constellation shaping, compared to conventional QAM constellations [6], offering a noticeable gap in comparison with Shannon capacity [7].…”

Hybrid Constellation Shaping 64QAM Based on Hexagonal Lattice of Constellation Subset

“…For example, Hu et al proposed a hexagonal constellation with a larger min-ED, which combined with rotation coding achieved around 1 dB gain of Q factor than square-16QAM [15]. To obtain a higher shaping gain and better transmission performance, hybrid shaping (HS) technology has become a research subject, which combines GS with PS [21][22][23][24]. Wu et al proposed a PS method based on reduced-exponentiation subset indexing and honeycomb-structured constellation optimization, which compressed the number of signal constellation points and significantly decreased the average signal power [21].…”

“…Wu et al proposed a PS method based on reduced-exponentiation subset indexing and honeycomb-structured constellation optimization, which compressed the number of signal constellation points and significantly decreased the average signal power [21]. Andrej et al proposed a robust and pilot-free modulation scheme by leveraging joint geometric and probabilistic constellation shaping, which achieved a gain of at least 0.1 bit/symbol over square QAM constellations with neural demappers [22]. To the best knowledge of the authors, there has been much less research on HS than that on only PS or only GS over the past few decades.…”