Open Access
Add to BibSonomy
Abstract
We experimentally verified the enhanced nonlinear tolerance of probabilistic shaping (PS) 64QAM super symbol (SUP) transmission over both dispersion uncompensated and compensated standard single mode fiber (SSMF) links. PS-64QAM with SUP is found to provide ∼0.51- and ∼1.6-dB gains in OSNR over PS-64QAM with traditional probabilistic amplitude shaping, after ∼1000-km uncompensated and 320-km compensated links, respectively.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
As a major milestone, probabilistic amplitude shaping (PAS) technique has been proposed and deployed widely today to improve the back-to-back (BtB) performance [1–3]. It is well known that PS techniques could gain up to 1.53 dB in SNR in additive white Gaussian noise (AWGN) channels. However, due to constellation expansion and hence the increased peak-to average-power (PAPR), the nonlinear tolerance of PS-QAM modulation formats is unfortunately degraded. Therefore, PS gain after transmission may not be that promising as that in BtB. For the next generation 400-GBaud and 800-GBaud applications, mitigating nonlinear transmission penalty of PS-QAM signals would thus be a challenging topic. Different PS solutions have been explored to enhance fiber nonlinear tolerance [4–6]. For instance, in [4] the authors reported a super-Gaussian distribution to achieve higher nonlinear tolerance than the conventional Maxwell-Boltzman (MB) distribution; in [5] the authors proposed a multi-dimensional PS method that can effectively reduce PS-QAM PAPR and therefore improve its nonlinearity tolerance; and in [6] the authors reviewed several practical nonlinear mitigation schemes with emphasis on a method that can choose and transmit only “nice” data sequences based on their nonlinear characteristic for a particular fiber link.
More recently, higher fiber nonlinear tolerance of PAS that adopted short shaping blocklength has been demonstrated [7–9]. However, PS-QAM with overly short blocklength would lose PS gain in linear region because the probability distribution generated deviates significantly from MB distribution. Therefore, a super-symbol (SUP) method is proposed in [10,11] to enhance the nonlinear tolerance without sacrificing that much linear shaping gain as previous methods (inter-DM/intra DM) [9]. With the SUP method, every shaped block from distribution-matcher (DM) is divided into four equal-sized subblocks which are transmitted in parallel as four tributaries by Xi, Xq, Yi, and Yq. Therefore, in comparison to inter-DM (intra-DM) pairing, the SUP method can improve its nonlinear tolerance to that of shaping with only 25% (50%) blocklength while keeping a linear shaping gain of the 100% blocklength. However, the superior nonlinear benefit of SUP is only proved and analyzed conceptually by numerical simulations in [10,11]. Then a substantial verification supported by experimental results would be necessarily required.
In this paper, we experimentally verify SUP gain in both the dispersion unmanaged and dispersion managed links. The transmission results with 22.5-GBaud, PS-64QAM SUP over 245-km, 490-km, 735-km and 980-km dispersion uncompensated links, which are the more common scenarios of coherent transmission today, exhibit ∼0.17- to 0.51-dB nonlinear benefit over the tradition PS-64QAM, where a DM output block is temporally broken up and mixed with symbols from other DM blocks by a symbol inter-leaver that is typically present and used to reduce the post-FEC bit error rate (BER) in the presence of burst errors. Furthermore, an even larger nonlinear benefit, ∼1.6 dB, is observed over 320-km dispersion compensated link with 45-GBaud PS-64QAM SUP. Such superior nonlinear tolerance demonstrates the potential of SUP method in other applications, such as submarine system.
This paper is organized as follows. In section 2 we describe the experimental setup and digital signal processing (DSP) algorithms for performance evaluations; in section 3 we present and discuss the measurement results; and in section 4 we conclude this paper.
2. Experimental setup and DSP algorithm
The generation and detection of PS-64QAM signal are very similar for both uncompensated and compensated links, between which the main difference lies within configuration of fiber spans and inline optical amplifiers. We will describe the system configuration of uncompensated link first.
As discussed in [12], lower baud rate, hence less dispersion induced waveform distortion helps to keep the characteristics of SUP over transmission, which results in better nonlinear tolerance. Therefore, a low baud rate at 22.5GBaud is chosen for our verification in dispersion uncompensated link. Simulations [11] show that 22.5-GBaud PS-64QAM SUP on 25-GHz grid has 0.6-dB gain over traditional PAS in a 960-km uncompensated SSMF link. Due to availability of optical components in the lab., the experimental evaluation will base on 17 × 22.5-GBaud PS-64QAM over 50-GHz grid, instead of 26 × 22.5-GBaud PS-64QAM over 25-GHz grid. The justification of lab verification on 50-GHz grid is further discussed in section 3.
The PS-64QAM are generated using shell mapping method [13]. The fixed-to-fixed length DM takes 69 information bits {0,1} as input and produces a block of 40 real-valued symbols {1, 3, 5, 7} as output. The sign of the real-valued symbol is determined by a sign bit with {0} and {1} of equal probability. The 4-level probability distribution is [0.4270, 0.3218, 0.1800, 0.0712]. To form super symbols, the block of 40 real-valued symbols is further divided into 4 subblocks of length 10 that are assigned to Xi, Xq, Yi, and Yq for parallel transmission. This SUP signal is referred to as SUP40 hereafter. 11% overhead FEC with pre-FEC BER threshold at 2.1e-2 is assumed, and thus each 22.5-GBaud channel carries a net data rate of 214.6 Gb/s after removing ∼2% pilot symbol. The PS-64QAM signal generated with traditional PAS, denoted by RND40, is measured under the same condition as SUP40 for comparison. Noted that the data patterns of RND40 in this paper are produced the same way as “TRA” in [11,12]. In traditional PAS, the output blocks from the same DM are temporally broken up and mixed with symbols from other blocks by a symbol inter-leaver, which is emulated with a random permutation routine (randperm) in Matlab.
As illustrated in Fig. 1, the nine odd channels and eight even channels are generated using two different set of components and carry independent random data. We use TX DSP to generate Nyquist-shaped (root-raised cosine, RRC with 0.1 roll-off factor) and bandwidth pre-compensated 22.5-GBaud PS-64QAM digital signals, which are subsequently converted to analog signals with four 85-GS/s Fujitsu digital-to-analog converters (DACs) and a Keysight AWG (M8196A, 93.4GS/s, with 4 ports) respectively for the odd and even channels. Inphi drivers, and dual-polarization Mach-Zehnder (DP-MZM) IQ-modulator are employed for electro-to-optical (EO) conversion to generate the nine odd channels. A NeoPhotonics high-bandwidth coherent driver modulator (HB-CDM) with >40GHz combined EO bandwidth is used for EO conversion of the eight even channels. The even channels are amplified and then pass through a 50-GHz optical inter-leaver (ITL) to filter out amplified spontaneous emission (ASE) noise before being combined with the odd channels via a 3dB optic coupler to form seventeen 22.5-GBaud PS-64QAM channels with 50GHz spacing. Only the central channel at 1543.33 nm is evaluated.
The fiber recirculating loop consists of 6 SSMF spans each with length between 40∼43 km. The length per loop is 245 km. Since all EDFAs in the loop have fixed flat gain and fixed total output power at ∼14 dBm, a variable optical attenuator (VOA) is placed at every EDFA output to adjust per-channel launch power into SSMF to about -2.5dBm. Two more EDFAs are added in the loop to compensate losses from dynamic gain equalizer (DGE), acoustic optical modulator (AOM2), and optical coupler. The DGE placed at the end of the loop is used to compensate the gain ripple, tilt, and suppress out of band noise.
At the receiving end, a Finisar wave shaper is used as optical deMux filter to select the test channel. Coherent front-end consists of a local oscillator (external cavity laser, ECL, PPCL200, with < 100-kHz linewidth), an Optoplex optical hybrid and 4 Finisar photodiodes (BPDV3120RQ, 70-GHz BW). After the photodiodes, a Tektronix DSO (DPO77002SX, 70GHz BW, and 200 GS/s) is applied to capture ∼2 million samples for offline processing. After re-sample to 2 samples per symbol, chromatic dispersion (CD) is compensated using a frequency domain equalizer (FDE). Since high-order QAMs are very sensitive to residual I/Q skews, we used a 4 × 4 real multi-input-multi-output (MIMO) with 21 taps to equalize dual-polarization 22.5-GBaud PS-64QAM signal [14]. The 4 × 4 real MIMO equalizer can effectively mitigate Tx I/Q skew and quadrature error of DP-MZM bias control. CPE is based on pilot-assisted decision-directed phase locked loop (DD-PLL). The pilot is a 16-symbol sequence inserted every 884 data symbols to form a 900-symbol frame. Through the 16-pilot symbols, we can obtain more reliable phase estimation at the beginning of every frame, which is then used to reset the estimated phase of DD-PLL in order to correct the possible cycle slips. For the following 884 data symbols regular DD-PLL [15] is applied. At a given baud rate, the DD-PLL bandwidth is optimized to minimize BER by adjusting loop gain. Direct error counting is used for bit error rate (BER) calculation after MIMO convergence.
Next, we describe the system configuration of compensated link as shown in Fig. 2. As discussed in [11], the characteristic of SUP could be better preserved in a dispersion compensated link (with smaller amount of accumulated CD), therefore larger gain is expected with a higher baud rate. Therefore, in this dispersion-compensated transmission we will consider 45-GBaud for demonstration. The 25-channel 45-GBaud PS-64QAM on 50-GHz WDM grid are generated in the same way as we explained in the system configuration of uncompensated link. Instead of using fiber recirculating loop, we choose a traditional dispersion compensated 4 × 80km SSMF link without any pre-compensation at Tx side. Four 31dB-gain EDFAs with middle stage access (MSA) to accommodate dispersion compensation module (DCM) are used as inline amplifier to compensate span loss, which is ∼19 dB on average. The DCM inserted at MSA is Lucent (OFS) WBDK-80, which compensates fully the CD of each 80-km SSMF span. The inset shows measured optical spectrum after 4 × 80km transmission. The central channel at 1544.13nm is the test channel. The coherent receiver and DSP algorithm are the same as described in the system configuration of uncompensated link.
Fig. 2. Experimental setup for dispersion compensated 4 × 80km SSMF link. The inset is the measured optical spectrum after 4 × 80km transmission.
3. Experimental results and discussion
For the dispersion-uncompensated transmission, Fig. 3 shows the measured BER vs. OSNR results in BtB and after transmission over different number of loops for both SUP40 and RND40. The inset on right presents respective constellation diagrams after 4 loop transmission without ASE noise loading. It is clearly observed that constellation of SUP40 is much more consolidated than RND40. The BER versus OSNR (BO) curves are measured by loading ASE noise at Rx. The solid and dash lines are for BO of SUP40 and RND40, respectively. The required OSNR (rOSNR) at the 11% FEC threshold (2.1e-2) can be readily calculated from the measured BO curves, and the results are summarized in Table 1. The BtB rOSNR are 19.60 and 19.67 dB for SUP40 and RND40, respectively. Since SUP40 and RND40 have the same level distribution, it is reasonable to see comparable BtB performance between them. After transmission, rOSNR gain of SUP40 over RND40 increases with number of loops from ∼0.17dB for 1-loop (245 km) to ∼0.51 dB for 4-loop (980 km) transmission. However, the SUP40 gain as percentage of nonlinear penalty continues drop with increasing number of loops. This indicates SUP40 gain is higher in a few head spans where the accumulated CD is smaller and the characteristic of SUP40, i.e., the spectral dip at around the direct-current (DC) frequency of intensity waveform spectrum [11], is better preserved. With further transmission that effectively enhances the amount of accumulated CD, the absolute SUP gain continuously increases while the relative SUP40 gain is found to drop. This observation agrees well with the physical explanation of spectral model [11].
Fig. 3. Measured back-to-back and loop transmission results of dispersion uncompensated link. BER versus OSNR of SUP40 is plotted using solid line while that of RND40 is plotted with dashed line. The inset on right presents the respective constellation diagrams after 4 loop transmission without ASE noise loading.
Table 1. Measured rOSNR of SUP40 and RND40 at BER=2.1e-2 versus number of loops and reach for dispersion uncompensated link. SUP40 gain is rOSNRRND40-rOSNRSUP40. SUP40 gain over penalty is SUP40 gain measured as percentage of fiber nonlinear penalty of RND40.
In order to compare measured SUP gain directly with simulations, the same link configuration and launch power as described in lab experiment have been used in our simulation, and SSMF fiber parameters are as follows: fiber loss = 0.2 dB/km, fiber dispersion parameter D = 16.9 ps/(km.nm), and nonlinearity coefficient = 1.31 (1/W/km). Simulation results, in terms of OSNR penalty at BER = 2.1e-2, are shown in Fig. 4 by dashed lines. For comparison, the measured results are also plotted by solid lines. The measured penalties are found slightly higher than the simulated ones. This minor misalignment would be caused by the limited accuracy of launch power in the experiments, as well as other linear distortions, such as polarization dependent loss, ignored in the simulations. But in terms of absolute SUP40 gain over RND40, ∼0.51-dB gain measured in lab agrees well with 0.58 dB in simulation.
Fig. 4. Measured and simulated loop transmission penalty at BER=2.1e-2 of dispersion uncompensated link. Solid line for experiment; dashed line for simulation. The difference between simulation and measurement would be caused by the limited accuracy of launch power in the experiment, as well as other linear distortions, such as polarization dependent loss, ignored in the simulations.
For dispersion compensated link, the rOSNR at FEC threshold are measured similarly as described above for dispersion uncompensated link and results are summarized in Table 2. The BtB rOSNR is 22.5dB for both SUP40 and RND40. After 4 × 80km transmission, rOSNR gain of SUP40 over RND40 increases from ∼0.6 to ∼2.2dB for launch power from -3 to -1dBm. Figure 5 shows the measured transmission penalties vs. launch power for both RND40 and SUP40. It is shown that channels with SUP40 method can launch nearly 1.8-dB higher power at 1.5-dB penalty over RND40, which is converted into about 1.6-dB gain in OSNR margin, as shown in Fig. 6. The OSNR margin is defined as the difference between measured OSNR after transmission without ASE noise loading at Rx and the rOSNR measured at 11% FEC threshold (2.1e-2).
Fig. 5. Lab measured 25-channel 45Gbaud PS-64QAM transmission penalty at BER=2.1e-2 over 4 × 80 km dispersion compensated link versus per channel launch powers.
Fig. 6. Lab measured OSNR margin of 25-channel 45Gbaud PS-64QAM at BER=2.1e-2 over 4 × 80km dispersion compensated link versus per channel launch powers.
Table 2. Measured rOSNR of SUP40 and RND40 at BER=2.1e-2 versus per channel launch power for dispersion compensated link. SUP40 gain is rOSNRRND40-rOSNRSUP40.
Compared to the 0.51-dB gain in the dispersion uncompensated link, the 1.6-dB SUP gain here, over the dispersion-compensated link, is found much larger. This is because fiber dispersion induces waveform distortion and as a result, the characteristic of SUP would vanish gradually with the increasing amount of accumulated CD in dispersion uncompensated links. For the dispersion compensated system, however, CD is fully compensated after transmission over every fiber span. Hence, the characteristic of SUP is (almost) fully restored at the beginning of each fiber span, and thus the system can receive more SUP benefit than that in a dispersion-uncompensated link. Therefore, larger SUP gain is measured in dispersion compensated link. Note that this 1.6-dB gain is found with no CD pre-compensation and 100% inline dispersion compensation. For real deployed systems with certain amount of CD pre-compensation and residual CD in each span (due to fiber span length variation), a slightly lower SUP gain is expected. The superior nonlinear transmission performance of SUP is important for the capacity upgrade of deployed system and networks, especially for submarine cable system.
Before conclusion, several questions regarding system configuration and measurement criteria warrant further discussion and explanation.
First, for dispersion uncompensated loop transmission, the verification is on 50-GHz grid instead of the desired 25-GHz grid due to limitation of available components. To evaluate the performance difference of SUP40 and RND40 on 25-GHz and 50-GHz grids, 17-channel WDM transmissions over 24 × 40km SSMF (i.e., 4 loops) are simulated. At 1.5dB transmission penalty, as shown in Fig. 7, the per-channel launch power of SUP40 is 0.66 and 0.61dB higher than that of RND40 on 25-GHz and 50-GHz grid, respectively. The different channel spacing does not alter much the relative benefit of SUP over tradition PAS. Therefore, as a preliminary verification, the presented results with 50-GHz spacing should still serve as a strong evidence of SUP gain.
Fig. 7. Simulated transmission penalty at 2.1e-2 over 24 × 40km dispersion uncompensated SSMF link. 17 WDM channels at 22.5GBaud on 25GHz and 50GHz grids, respectively.
Second, as pointed out in [11], nonlinear gain of SUP comes from its unique spectral dip near DC frequency. As shown in [12], the dip width decreases with the increase of distance (i.e., accumulated CD); therefore, the associated nonlinear gain decreases as well. A different baud rate may suffer different extent of CD distortion, and therefore would have different SUP gain behaviors at a certain transmission distance. The readers can find more related discussions on the effect of baud rates in [12].
Third, 11% FEC is not part of industrial standard as far as we know. However, we believe that 11% FEC with BER threshold at 2.1e-2 is achievable with current industrial capability. Consequently, 2.1e-2 is used throughout the manuscript. Even if the achievable BER threshold of 11% FEC is lower than 2.1e-2, assuming any value between 1.6e-2 and 2.1e-2, it will not alter our conclusion. We show in Fig. 8 our measured BER vs OSNR curves zoomed in on expected FEC threshold. The rOSNR gain with SUP method measured at 1.6e-2 FEC threshold is comparable to that measured at 2.1e-2.
Fig. 8. Measured loop transmission results of dispersion uncompensated link zoomed in on expected FEC threshold. BER versus OSNR of SUP40 is plotted using solid line while that of RND40 is plotted with dashed line.
Fourth, it is noted from the inset of Fig. 2 that the spectra of 45-GBaud even channels, which pass through 50-GHz ITL, are narrower than that of odd channels. To evaluate the impact of ITL bandwidth on SUP40 gain over RND40, the same configuration as lab verification is used in simulation. Table 3 summarizes simulation results of rOSNR and SUP40 gain over RND40 versus ITL bandwidth. A super Gaussian filter of eighth order is assumed. The SUP40 gain variation is less than 0.1dB over a broad range of ITL 3-dB bandwidth between 30-GHz and 50-GHz. Therefore, the influence of ITL bandwidth on SUP40 gain measurement is minimal.
Table 3. Simulated rOSNR of SUP40 and RND40 at BER=2.1e-2 versus ITL bandwidth for dispersion compensated link. Per channel launch power is -2dBm. SUP40 gain is defined as rOSNRRND40-rOSNRSUP40.
4. Conclusions
We experimentally verified the enhanced fiber nonlinear tolerance of super symbol (SUP) method over both dispersion uncompensated and dispersion compensated links. After 980 km transmission over dispersion uncompensated SSMF link, SUP40, that is produced using the super symbol method, offers ∼0.51dB gain in rOSNR over RND40, that is generated with TRA method. While in the dispersion compensated 4 × 80km link, the SUP40 gain is further boosted to ∼1.6dB. These results demonstrate the superior nonlinear tolerance of SUP method. We believe that SUP method will be the next milestone to improve the reaches of coherent transmission, especially for the next generation 400 G and 800 G coherent solutions.
Disclosures
The authors declare no conflicts of interest.
References
1. F. Buchali, G. Bocherer, W. Idler, L. Schmalen, P. Schulte, and F. Steiner, “Experimental demonstration of capacity increase and rate-adaptation by probabilistically shaped 64-QAM,” Proc. European Conference on Optical Communication (ECOC), Valencia, Spain, Sept. 27-Oct.1, 2015, Paper PDP.3.4.
2. Y. Zhu, A. Li, W.-R. Peng, C. Kan, Z. Li, S. Chowdhury, Y. Cui, and Y. Bai, “Spectrally-efficient single-carrier 400G transmission enabled by probabilistic shaping,” in Optical Fiber Communication Conference (OFC) 2017, OSA Technical Digest (Optical Society of America, 2019), Paper M3C1.
3. J. Li, A. Zhang, C. Zhang, X. Huo, Q. Yang, J. Wang, J. Wang, W. Qu, Y. Wang, J. Zhang, M. Si, Z. Zhang, and X. Liu, “Field trial of probabilistic-shaping-programmable real-time 200-Gb/s coherent transceivers in an intelligent core optical network,” Proc. Asia Commun. Photon. Conf., Hangzhou, China, Oct. 2018, Paper Su2C1.
4. M. N. Tehrani, M. Torbatian, H. Sun, P. Mertz, and K. Wu, “A novel nonlinearity tolerant super-Gaussian distribution for probabilistically shaped modulation,” Proc. European Conference on Optical Communication (ECOC), Rome, 2018, pp. 1–3, DOI: 10.1109/ECOC.2018.8535379.
5. Q. Guo, W.-R. Peng, Y. Cui, and Y. Bai, “Multi-dimensional probabilistic shaping for higher fiber nonlinearity tolerance,” Proc. European Conference on Optical Communication (ECOC), 2019, DOI: 10.1049/cp.2019.1104.
6. K. Roberts, M. O’Sullivan, M. Reimer, and M. Hubbard, “Nonlinear mitigation enabling next generation high speed optical transport beyond 100G,” in Optical Fiber Communication Conference (OFC) 2019, OSA Technical Digest (Optical Society of America, 2019), paper M3J.1.
7. A. Amari, S. Goossens, Y. C. Gultekin, O. Vassilieva, I. Kim, T. Ikeuchi, C. Okonkwo, F. M. J. Willems, and A. Alvarado, “Introducing enumerative sphere shaping for optical communication systems with short blocklengths,” J. Lightwave Technol. 37(23), 5926–5936 (2019). [CrossRef]
8. T. Fehenberger, H. Griesser, and J. Elbers, “Mitigating fiber nonlinearities by short-length probabilistic shaping,” in Optical Fiber Communication Conference (OFC) 2020, OSA Technical Digest (Optical Society of America, 2020), paper Th1I.2.
9. T. Fehenberger, D. S. Millar, T. Koike-Akino, K. Kojima, K. Parsons, and H. Griesser, “Analysis of nonlinear fiber interactions for finite-length constant-composition sequences,” J. Lightwave Technol. 38(2), 457–465 (2020). [CrossRef]
10. W.-R Peng, Y. Cui, and Y. Bai, “Super-symbol signaling for optical communication,” filed for IP application, Oct. 2019.
11. W.-R. Peng, A. Li, Q. Guo, Y. Cui, and Y. Bai, “Transmission method of improved fiber nonlinearity tolerance for probabilistic amplitude shaping,” Opt. Express 28(20), 29430–29441 (2020). [CrossRef]
12. W.-R. Peng, A. Li, Q. Guo, Y. Cui, and Y. Bai, “Baud rate and shaping blocklength effects on the nonlinear performance of super-symbol transmission”, Opt. Express (to be published).
13. R. Laroia, N. Farvardin, and S. A. Tretter, “On optimal shaping of multidimensional constellations,” IEEE Trans. Inform. Theory 40(4), 1044–1056 (1994). [CrossRef]
14. A. Li, Y. Zhu, W.-R Peng, Y. Cui, and Y. Bai, “103-GBd PDM-16QAM Coherent Detection Highly Tolerant to Transmitter IQ Impairments Enabled by Real-Valued 4 × 4 MIMO Equalizer,” Proc. European Conference on Optical Communication (ECOC), Dublin, Ireland, 2019, DOI: 10.1049/cp.2019.1139
15. M. Simon and J. Smith, “Carrier synchronization and detection of QASK signal sets,” IEEE Trans. Commun. 22(2), 98–106 (1974). [CrossRef]
