Geometric Shaping of 2-D Constellations in the Presence of Laser Phase Noise

Abstract

In this paper, we propose a geometric shaping (GS) strategy to design 8, 16, 32 and 64-ary modulation formats for the optical fibre channel impaired by both additive white Gaussian (AWGN) and phase noise. The constellations were optimised to maximise generalised mutual information (GMI) using a mismatched channel model. The presented formats demonstrate an enhanced signal-to-noise ratio (SNR) tolerance in high phase noise regimes when compared with their quadrature amplitude modulation (QAM) or AWGN-optimised counterparts. By putting the optimisation results in the context of the 400ZR implementation agreement, we show that GS alone can either relax the laser linewidth (LW) or carrier phase estimation (CPE) requirements of 400 Gbit/s transmission links and beyond. Following the GMI validation, the performance of the presented formats was examined in terms of post forward error correction (FEC) biterror-rate (BER) for a soft decision (SD) extended Hamming code (128, 120), implemented as per the 400ZR implementation agreement. We demonstrate gains of up to 1.2 dB when compared to the 64-ary AWGN shaped formats.

The Partially-Coherent AWGN Channel: Transceiver Strategies for Low-Complexity Fibre Links

“…In contrast to our previous work [24], we replaced the Euclidean distance metric in the optimiser with the proposed PCAWGN approximation from the Eq. (4).…”

“…Then, to estimate the BW AIR performance for each of the symbol arrangements, we calculated the 3-dimensional Gauss-Hermite integral (with L = 7 per dimension [35]). As in [24], we modelled the RPN variances (i.e., α values) in the optimiser (via Monte Carlo estimation with 2 19 symbols) to produce approximately the same variance as if the CPE strategy from Sec. V-B was used.…”

“…In our previous work [24], we designed a range of shaped modulation formats for the PCAWGN channel, focusing explicitly on channel parameters originating from the specifications given by the 400ZR implementation agreement [13]. The proposed constellations were shaped via a Monte Carlo approach, in which, we maximised the generalized mutual information (GMI) [25], [26] of each symbol arrangement in the presence of both AWGN and high levels of RPN, assuming a typical, circular Gaussian metric LLR calculation.…”

“…Herein, we look at the low-complexity PCAWGN demapper proposed in [4] and use it to improve on our previous constellation optimisation algorithm in [24]. Then, we maximise the BW AIRs of the GS 8 to 64-ary constellations in the presence of both AWGN and RPN.…”

Generalized Mutual Information Analysis for BICM-8QAM With Residual Phase Noise

“…The existing literature is abundant with works on mutual information analysis for enhanced modulation schemes in a purely AWGN channel [1], [2]. However, there is only limited work on the mutual information analysis with phase noise considered, and most are for constellation design [14]- [16]. For instance, even though RPN is considered in [16], the GMI analysis therein is still based on using a mismatched channel model, i.e., a mismatched Gaussian receiver.…”