Laser Phase Noise Tolerance of Uniform and Probabilistically Shaped QAM Signals for High Spectral Efficiency Systems

Abstract

We numerically and experimentally investigate the laser phase noise tolerance of probabilistically shaped (PS) and uniformly shaped (US) quadrature amplitude modulation (QAM) signals. In the simulations, we compare PS-64QAM to US-16QAM, PS-256QAM to US-64QAM, and PS-1024QAM to US-256QAM under the same information rate (IR). We confirm that a sufficient shaping gain is observed with narrow linewidth lasers, whereas degradation of the shaping gain is clearly observed when large phase noise and high order modulation formats are assumed. In our experiments, we compare polarization-division-multiplexed (PDM) 16-GBd PS-1024QAM and US-256QAM under the same IR using lasers with 0.1-kHz and 40-kHz linewidths. For carrier phase recovery (CPR), we employ a pilot-assisted digital phase locked loop. Results reveal that PS-1024QAM achieves high performance with the 0.1 kHz-laser or > 5% pilot ratio, whereas US-256QAM outperforms PS-1024QAM when lasers with 40-kHz linewidth and < 5% pilot ratio are used. We also evaluate the pilot ratio dependency of the required optical signal-to-noise ratio at the forward error correction limit and the achievable information rate. Additionally, we compare the performance of two types of CPR updating schemes: updating phase estimation at only the pilot symbol or at all symbols.

Simple Closed-Form Approximations for Achievable Information Rates of Coded Modulation Systems

“…Note a particularly good agreement for QPSK, 16-QAM and 64-QAM in [7], and 64-QAM in [20]. We attribute this to the fact that the approximation C M−QAM in (17) underestimates the ideal AIR C M in (3) while the experimental B2B or E2E rates are also below the ideal AIR by about 0.5-2 [b/sym.] (due to finite blocklength/complexity codes with non-zero overhead and non-zero guard bands, in addition to other imperfections of practical systems [21]) Hence, the proposed approximations are more accurate than the ideal AIR C M with respect to the rates of real-world systems.…”

“…[28]) can be used to solve them. The main contributions of this paper are the approximations of the modulation-constrained achievable information rates of M -PAM and M -QAM constellations in (11), (17), and (19), from which the minimum number of constellation points to approach closely the channel capacity (without significant rate loss due to limited M ) can be found as in (12) and (18).…”

Digital Longitudinal Monitoring of Optical Fiber Communication Link

“…One is for signal preprocessing to restore the dispersion and reshape the demodulated vectors, and the other is for transmitted signal reconstruction for gradient descent. The latter path consists of carrier phase recovery (CPR) [36], symbol decision, transmitted signal reconstruction, the same Nyquist filtering as on the transmitter side, and reloading of the phase noise estimated in CPR. Regarding the channel emulator, the length per DBP step (distance granularity) z is a constant 2 km and the mini-batch size is 100.…”

Probabilistic shaping: a step closer to the Shannon limit in channel capacity for optical communications

“…Therefore, PS signals are more sensitive to laser linewidth as their phase margin is smaller. In [6 ], the authors investigated the phase noise tolerance of both PS and conventional signals. The normalized generalized mutual information (NGMI) is selected as the evaluation metric as it can predict the post forward error correction (post‐FEC) performance accurately [3 ].…”