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Abstract
We demonstrate the 1,600-km transmission at nearly 1-Tb/s/λ signals with a capacity of 21.5 Tb/s. Probabilistic shaping was newly applied to high-speed coherent optical Nyquist pulse transmission systems to maximize the transmission capacity. Employing a 160-GBd PS-32 QAM format, WDM signals at nearly 1-Tb/s/λ were successfully transmitted over 1,600 km with a capacity of 21.5 Tb/s.
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1. Introduction
Information traffic has been rapidly and continuously growing with the evolution of broadband services such as 5G and beyond 5G mobile services, the internet of things (IoT), and data-driven artificial intelligence (AI). To meet these traffic demands, there is a strong need for high-capacity and long-haul optical transmission systems as a backbone network. If the transmission capacity is to be increased sustainably, it is essential to increase transmission capacity while reducing electrical power consumption. Reducing the number of wavelength channels in dense wavelength division multiplexing (DWDM) systems by using high-speed signals is considered a promising way of mitigating power consumption. Quadrature amplitude modulation (QAM) formats are also needed to increase the total transmission capacity of the high-speed DWDM transmission systems. Recently, 1-Tb/s/λ 100-GBd-class QAM transmission has been actively studied [1–5], in which broadband optical and electrical devices are utilized to modulate continuous wave (CW) light. Figure 1 shows recent reports on 1-Tb/s/λ coherent transmission experiments. For example, 96-GBd 256 QAM signal generation and 41-Tb/s WDM high-capacity transmission have been reported [4]. However, due to the high spectral efficiency but low noise tolerance of such higher order modulated signals, the transmission distance was limited to 100 km. Recently, 35-Tb/s WDM 120-GBd probabilistically shaped (PS) 64 QAM transmission over 800 km has been demonstrated [5], where probabilistic shaping was employed to maximize the transmission capacity at 800 km. As shown in Fig. 1, the maximum transmission distance obtained thus far in high-capacity (≥ 20 Tb/s) transmission experiments using coherent 1-Tb/s/λ signals has been 800 km, and a long-haul and high-capacity 1-Tb/s/λ signal transmission beyond 20 Tb/s over > 1,000 km has yet to be reported.
Optical time division multiplexing (OTDM) using ultrashort optical pulses is another approach for high-speed transmission while avoiding the bandwidth limitation of electronic devices [6–9]. A coherent optical Nyquist pulse [10] is attractive as an optical pulse for OTDM transmission systems, because the time-domain orthogonality of the optical Nyquist pulse enables simultaneous demultiplexing in the optical domain and homodyne detection [11], thus eliminating the need for an OTDM demultiplexer. In our previous work, we reported a single-channel 15.3 Tb/s, 1.28-TBd 64 QAM signal transmission with coherent optical Nyquist pulses over 150 km [12]. To increase both the transmission distance and transmission capacity while achieving a net rate of 1 Tb/s/λ, a combination of WDM and OTDM technologies [6] is expected to be promising. In addition, the PS-QAM format is also expected to increase the transmission distance in high-speed transmission systems, since it allows a higher noise tolerance than conventional QAM signals [13,14].
In this paper, we report the 1,600-km transmission of 1 Tb/s/λ signals at nearly with a transmission capacity of 21.5 Tb/s using the WDM of OTDM coherent optical Nyquist pulses, where we newly constructed a low-nonlinear dispersion-managed recirculating loop transmission system. A precise group delay compensation technique was introduced into the recirculating loop system to improve the transmission performance. Moreover, a PS-32 QAM format was also introduced to maximize the transmission capacity. With these techniques, 160-GBd PS-32 QAM signals at nearly 1-Tb/s/λ were transmitted over 1,600 km. We successfully obtained normalized generalized mutual information (NGMI) exceeding the forward error correction (FEC) threshold in all WDM channels, while achieving a total capacity of 21.5 Tb/s. To the best of our knowledge, this is the first long-haul high-capacity signal transmission at nearly 1 Tb/s/λ beyond 20 Tb/s over > 1,000 km.
2. Experimental setup for long-haul WDM coherent Nyquist pulse transmission
Figure 2 shows our experimental setup for a long-haul WDM 1-Tb/s/λ coherent Nyquist pulse transmission. At the transmitter, a 10 GHz optical pulse train was generated by an optical comb generator and an 8-kHz linewidth external cavity laser diode (ECLD) [15]. Figure 3(a) shows the optical spectrum of the 10 GHz optical pulse train from the comb generator with a resolution of 0.02 nm. The optical signal to noise ratio (OSNR) of the comb was 45 dB. One of comb lines was extracted with an optical bandpass filter (BPF), and was used as a pilot tone for injection locking to a local oscillator (LO) at the receiver. The 10 GHz pulse train was fed into a pulse shaper based on spectral manipulation with a liquid crystal on silicon (LCoS) to generate a 10 GHz optical Nyquist pulse train with a roll-off factor α = 0 and a 160-GHz bandwidth. Figures 3(b) and (c), respectively, show an optical spectrum and a waveform obtained after pulse shaping. As shown in Fig. 3(c), the intensity of a 10 GHz optical Nyquist pulse train becomes zero every 6.25 ps, which corresponds to a frequency of 160 GHz. This enables OTDM multiplexing from 10 to 160 GBd without inter-symbol interference [10].
Fig. 2. Experimental setup for long-haul WDM coherent Nyquist pulse transmission at nearly 1-Tb/s/λ.
Fig. 3. (a) Optical spectrum of output signal from a 10 GHz comb generator, (b), (c) optical spectrum and its intensity waveform after pulse shaping with a pulse shaper, respectively.
The 10 GHz optical Nyquist pulse train was modulated with an electrical 10-GBd PS-32 QAM signal generated by an arbitrary waveform generator (AWG) with a sampling rate of 10 GSa/s and a bandwidth of 7.5 GHz. A shaped complex amplitude sequence was generated in the first quadrant, assuming a two-dimensional distribution matcher as proposed in [16]. The amplitude sequence was folded back against the IQ axis according to randomly generated sign bits in the same way as a conventional probabilistic amplitude sequence to obtain a PS-32 QAM sequence. The probability density function (PDF) of the PS-32 QAM signal had a Maxwell Boltzmann distribution, which is given by the following equation,
For WDM transmission, 22-WDM dummy channels with a 180-GHz spacing were prepared as follows. The output from a 10 GHz mode-locked fiber laser (MLFL) [19] was first modulated with a 10-GBd PS-32 QAM signal, and then its spectrum was broadened over a bandwidth of 4 THz covering the entire C-band with a 500 m-long highly nonlinear fiber (HNLF) with a normal dispersion. After ×16 OTDM and polarization multiplexing, the spectrum was flattened by using a pulse shaper while carving a 180 GHz-bandwidth notch into the spectrum to embed the CUT signal and the pilot tone. The CUT signal with the pilot tone, the clock signal, and the WDM dummy channels were combined with a wavelength selective switch (WSS) as shown in Fig. 4. Here, fiber delay lines with different lengths are inserted to eliminate the correlation between WDM dummy channels [6]. The signals were fed into a recirculating loop, where acoustic optical modulators (AOMs) were used to control the recirculation timing.
The recirculating transmission line consists of 60, 60 and 40-km ultra large area fibers (ULAFs). The loss and effective area of the ULAFs were 0.18 dB/km and 153 µm2, respectively. The launch power was optimized at -0.6 dBm/ch, as described in Sec. 3. The loss of the ULAFs was compensated for by distributed Raman amplification. Backward Raman pumping was adopted, and the number of pump lasers per span was 3. The pump powers were 26.5, 24.8, and 25.7 dBm at 1425, 1445, and 1465 nm, respectively, for a 60 km span. For a 40 km span, the pump powers were 24.8, 23.0, and 24.0 dBm at 1425, 1445, and 1465 nm, respectively. The on/off Raman gains were 12 and 8 dB for 60 and 40 km spans, respectively. The amount of gain ripple before the optical equalizer (OEQ) based on LCoS was 4 dB in the short wavelength region, where the OSNR was worst. Polarization controllers (PCs) were installed in each span to mitigate the first-order polarization-mode dispersion (PMD) of the transmission line [12]. After a 160-km transmission, the gain ripple induced by erbium-doped fiber amplifiers (EDFAs) and distributed Raman amplification was compensated for by an OEQ. The optical spectrum after a 1,600 km transmission with the OEQ is shown in Fig. 5. The power fluctuation is suppressed to within ± 1 dB. The chromatic dispersion was roughly compensated for with an accuracy of ${\sim} $ 1.1 ps/nm by using a 20-m long chirped fiber Bragg grating (CFBG) [12]. However, the CFBG has a small group delay fluctuation due to the non-uniformity of the grating period. Therefore, the residual chromatic dispersion and group delay fluctuation attributed to the CFBG were compensated for by using the OEQ as a programmable phase filter. It is important to measure the group delay characteristics precisely prior to transmission experiments.
In our previous work, we proposed a group delay measurement technique with a good accuracy of 1.6 ps by using two sinusoidal modulated signals [20]. However, even a small measurement error in the residual group delay accumulates as the transmission distance increases, and hence the error should be reduced further for long-haul coherent Nyquist pulse transmission. To measure the group delay precisely, we improved our previous method as follows. Figure 6 shows the setup and the principle of the group delay measurement. Reference (λref) and signal (λsig) tones, which were intensity-modulated by a 10-GHz sinusoidal signal, were simultaneously coupled into the recirculating transmission line. For instance, when we measured a group delay around 1550 nm, the wavelengths λref and λsig were 1545 nm and 1549.2∼1549.8 nm (0.1 nm intervals), respectively. After the transmission, the two 10-GHz modulated tones were separated into two paths with an optical coupler and two optical BPFs. They were then detected by two photodetectors (PDs) simultaneously. We can evaluate the group delay between the two wavelengths from the phase difference between these detected sinusoidal waveforms by using a sampling oscilloscope. Here, the accuracy was limited by the bandwidth (70 GHz) of the sampling oscilloscope [20]. To improve the accuracy of the group delay measurement, we received tones after a recirculating loop transmission instead of a straight-line transmission. As the recirculation number increases, a small group delay is magnified, and the accuracy of the group delay measurement is significantly improved. In this work, we measured the group delay after 5 circulations by considering the decrease in measurement accuracy due to the OSNR degradation of the tones. Figure 7 shows the residual group delay after group delay compensation by CBFG and LCoS based on conventional (green) and proposed (blue) group delay measurement methods, respectively. As shown in Fig. 7, the residual group delay was significantly reduced from 1.5 to 0.49 ps. For a 1,600-km transmission achieved by using 10-fold recirculations, this residual group delay is enhanced by a factor of 10, resulting in an accumulated group delay of 5 ps. This value is lower than the pulse period of a 160-GBd signal (i.e., 6.25 ps). Thus, it is shown that the proposed method is effective in suppressing the inter-symbol interference caused by the residual group delay in a long-distance transmission.
Fig. 7. Residual group delay after group delay compensation with CBFG and LCoS based on conventional (green) and proposed (blue) group delay measurement methods, respectively.
We first evaluated the transmission performance after an 800-km transmission with precise compensation for the residual group delay, where a 16 QAM signal was used in a preliminary experiment before introducing the PS-QAM technique. Figure 8(a) and (b), respectively, show the bit error rate (BER) of a 160-GBd 16 QAM signal at 1550 nm before and after the improvement of the group delay measurement. The BER was improved from 4.52 to 2.14 ${\times} $ 10−3 by precise group delay compensation. Precise compensation for the residual group delay can be achieved in all 23 WDM channels simultaneously, because LCoS can modulate the phase independently for each wavelength.
Fig. 8. BER of a 160-GBd 16 QAM signal after an 800-km transmission at 1550 nm (a) before and (b) after the improvement in the group delay measurement.
At the receiver, the CUT is demultiplexed with a bandpass filter, and then X- or Y-pol. signal is extracted with a polarizer in a 90-degree optical hybrid module. Here, we precisely tuned a polarization controller on the receiver by monitoring polarization crosstalk with an optical spectrum analyzer. Although the state of polarization (SOP) of the CUT drifts with time, the rate of change of the SOP is less than 1 Hz and slow enough for it to be tracked. The pilot tone and the 10-GHz clock signal were extracted by using tunable optical BPFs. The pilot tone was 30-GHz phase modulated, then the 3rd harmonic was extracted using a tunable narrow optical filter. As the pilot tone was 90 GHz away from the center frequency of the CUT, the frequency of the 3rd harmonic was the same as the center frequency of the CUT. The pilot tone was fed into a free-running distributed feedback (DFB) LD for injection locking. After injection locking, the phase noise of the DFB-LO was reduced to as low as 0.21 degrees [21]. On the other hand, the 10-GHz clock signal was directly detected with a PD. The 10-GHz clock was recovered by using a phase-locked loop (PLL) circuit consisting of a double balanced mixer (DBM), loop filter and voltage-controlled oscillator (VCO). The 10 GHz clock and the injection-locked DFB-LD were fed into an optical comb generator. The optical comb was spectrally shaped by a pulse shaper to produce a 10 GHz LO Nyquist pulse train with α = 0 to be used for homodyne detection and OTDM demultiplexing. The CUT and LO Nyquist pulse train were detected with a coherent receiver, where an OTDM tributary was selected by adjusting a variable optical delay line (VODL). After the coherent detection, a 10-GBd PS-32 QAM signal was sampled with an 80 GSa/s analog to digital (A/D) converter and processed by an offline digital signal processor (DSP). The bandwidth of the ADC was 33 GHz. Thanks to OTDM demultiplexing in the optical domain, the required ADC bandwidth was narrower than the signal bandwidth of ±80 GHz. The received signal can be demodulated even when the ADC bandwidth is less than 10 GHz. In the DSP, the PS-32 QAM signal was equalized with an adaptive T/2-spaced finite impulse response (FIR) filter based on a training-aided least mean square algorithm followed in a decision directed manner [22]. After the equalization, generalized mutual information (GMI) and NGMI were calculated as a performance metric [23]. The number of demodulated symbols exceeded 16384 symbols. We assumed an FEC code with a coding rate R = 0.668 and an NGMI threshold of 0.75 [24], which is a concatenation code of the inner soft decision FEC and outer hard decision FEC to guarantee a post-FEC BER of zero. In addition, we assumed FEC gain sharing [25] between the OTDM and polarization tributaries. Therefore, we focused on whether the average NGMI over all tributaries rather than the NGMI in each tributary could exceed the NGMI threshold. The net spectral efficiency (SE) of the PS-32 QAM signal with shaping parameter $\nu $ is given by [23],
where $H(\nu )$ is the entropy of the PS-32 QAM signal. For instance, $H(\nu )$ = 4.785 when $\nu $ = 0.05.3. Experimental results for 1-Tb/s/λ coherent Nyquist pulse transmission over 1,600 km
First, we evaluated the back-to-back NGMI performance of a 160 GBd PS-32 QAM signal with $\nu $ = 0.05. Figure 9(a) shows the PDF of an ideal PS-32 QAM signal with $\nu $ = 0.05, and Fig. 9(b) shows the NGMI of a 160 GBd PS-32 QAM signal with $\nu $ = 0.05 as a function of OSNR. OSNR is defined as the ratio of signal power to noise power evaluated by integration over 1.2 nm. The OSNR sensitivity needed to achieve the NGMI threshold of 0.75 was estimated to be 16 dB.
Fig. 9. (a) PDF of a PS-32 QAM signal with $\nu $ = 0.05. (b) NGMI of a 160 GBd PS-32 QAM signal with $\nu $ = 0.05 as a function of the OSNR in a back-to-back configuration.
Next, we optimized the launch power into the transmission link. In this optimization, a 16 QAM signal is used in a preliminary experiment before introducing the PS-QAM technique. Figure 10 shows the BER versus launch power of WDM OTDM 160 GBd 16 QAM signals after an 800-km transmission. The BER was minimized at a launch power of 13 dBm (namely, -0.6 dBm/ch). Therefore, we set the launch power at 13 dBm in subsequent long-haul WDM OTDM transmission experiments. The average optimum launch power should be smaller than that used in non-OTDM coherent transmission experiments since the high peak power of the pulse signal induces a larger nonlinear distortion, which limits the launch power [26].
At an optimized launch power of 13 dBm, we optimized the shaping parameter of a PS-32 QAM signal to maximize GMI. Figure 11 shows the GMI gain of PS-32 QAM against conventional 16 QAM as a function of the shaping parameter. A shaping parameter of zero corresponds to conventional 32 QAM. When the shaping parameter was smaller than 0.05, the GMI gain increased as the shaping parameter increased thanks to the shaping gain of probabilistic shaping. However, when the shaping parameter exceeded 0.05, the GMI gain decreased rapidly. This would be caused by the enhanced modulation format dependent nonlinear interference noise (NLIN) resulting from probabilistic shaping [17]. In PS-QAM formats governed by the Maxwell Boltzmann distribution, the kurtosis increases as the shaping parameter increases since the kurtosis depends on the PDF [17,27]. Since the modulation format dependent NLIN becomes larger as the kurtosis increases, PS-32 QAM signals shaped by too large a shaping parameter suffer from enhanced NLIN. Moreover, the modulation format dependent NLIN is emphasized in dispersion-managed transmission links [28]. Therefore, there is a tradeoff between shaping gain and NLIN penalty as shown in Fig. 11. We optimized the shaping parameter $\nu $ as 0.05 to maximize GMI.
Fig. 11. Shaping parameter optimization of a PS-32 QAM signal at 1547 nm after a 1,600-km transmission.
With the optimized shaping parameter $\nu $ = 0.05, we evaluated GMI as a function of transmission distance. Figure 12(a) and (b), respectively, show the GMI of a 16 QAM and PS-32 QAM signal at 1547 nm versus transmission distance. We confirmed that the PS-32 QAM had a GMI higher than that of the 16 QAM signal regardless of the transmission distance.
Fig. 12. Comparison of GMI of (a) 16 QAM and (b) PS-32 QAM at 1547 nm as a function of transmission distance.
With the optimized launch power and shaping parameter, we evaluated the NGMI of all 16 OTDM tributaries with dual polarizations at 1547 nm after a 1,600-km transmission, and the result is shown in Fig. 13. Although NGMI depends slightly on the OTDM tributary and polarization, the average NGMI over all OTDM tributaries and polarizations was 0.795 and it exceeded the NGMI threshold of 0.75. Using Eq. (2), the net rate per channel was calculated as [{4.785 – (1 - 0.668) × 5} × 160 GBd × 2] = 1.0 Tb/s/λ. Thus, a 1-Tb/s/λ signal was successfully transmitted over 1,600 km.
The NGMI variation depending on the OTDM tributary shown in Fig. 13 would be caused by the imperfection of the OTDM emulator since there is a variation of about ±15% in the intensity of each tributary. Moreover, only the Y-polarization of tributary #7 is specifically degraded, which might result from other factors such as imperfect OTDM demultiplexing at a receiver due to the fluctuation of the timing skew between the OTDM signal and the LO Nyquist pulse. Since a small fluctuation of the group delay caused by temperature drift and random stress along a fiber is magnified in proportion to the recirculation number, it was difficult to precisely match the timing between the OTDM signal and the LO Nyquist pulse by manually adjusting a VODL at the receiver. The NGMI dependency on OTDM tributary can be mitigated by employing timing skew locking [12]. Another approach involves using DSP-based OTDM demultiplexing by employing a broadband coherent receiver to receive all OTDM tributaries simultaneously [29]. In the present experiment, since two polarizations were demultiplexed by using a PC rather than a DSP at the receiver, it was not possible to compensate for the frequency-dependent polarization crosstalk (i.e., 2nd order PMD) [30]. This may also have contributed to the degradation of the NGMI. Thus, the DSP-based demultiplexing of not only OTDM tributaries but also polarizations is a future subject.
To clarify the WDM transmission performance, we measured the OSNR in each WDM channel after a 1,600-km WDM OTDM transmission as shown in Fig. 14. The OSNR at both ends of the WDM channels degraded by the insufficient gain of the EDFAs and Raman amplifiers.
Since OSNR depends on the wavelength as shown in Fig. 14, we optimized the shaping parameters of the PS-32 QAM signals zone-by-zone in wavelength to achieve NGMI above the NGMI threshold for all WDM channels. This allows error-free transmission using the same FEC for all WDM channels, with a slight reduction in SE [31]. Figure 15(a) and (b) show the shaping parameters we adopted and the corresponding entropy over the C band, respectively. We employed three shaping parameters of $\nu $ = 0.05, 0.07 and 0.09, corresponding to entropies of H = 4.785, 4.606 and 4.405 bit/symbol, respectively. At the shorter and longer wavelengths, we used larger shaping parameters (i.e. lower entropies) than around the center wavelengths to keep NGMI above the NGMI threshold. The number of WDM channels assigned to $\nu $ = 0.05, 0.07 and 0.09 was 9, 3 and 11, respectively.
Fig. 15. (a) Shaping parameter and (b) entropy distribution of PS-32 QAM signals over the C band after a 1,600-km transmission.
Finally, we measured the NGMI of all the WDM channels after a 1,600-km transmission. Figure 16 shows the average NGMI over all OTDM tributaries and polarizations in each WDM channel. The NGMI successfully exceeded the NGMI threshold of 0.75 for all WDM channels. Using Eq. (2), the total capacity can be calculated as [{(4.785× 9 + 4.606× 3 + 4.405× 11) – (1–0.668) × 5 × 23} × 160 GBd × 2] = 21.5 Tb/s. Thus, we achieved a 21.5 Tb/s 1,600-km transmission with the maximum net rate of 1 Tb/s/λ.
Fig. 16. Average NGMI over all OTDM tributaries and polarizations in each WDM channel after a 1,600-km transmission.
In the present system, the transmission performance is limited by inaccuracies in manual polarization demultiplexing and LO pulse timing adjustment at the receiver. To overcome these problems, a digital demultiplexing scheme will prove useful, where a CW-LO and a high-speed ADC are used to convert the entire optical signal band into digital signals. Then, OTDM demultiplexing is performed using a digital LO Nyquist pulse in the DSP. With this scheme, dispersion compensation and polarization demultiplexing can be performed in the DSP. This will enable highly accurate polarization demultiplexing and LO pulse timing adjustment, resulting in improved transmission performance. Although we have already reported a DSP method in a back-to-back condition [32], WDM transmission with a digital demultiplexing scheme will constitute our future work.
4. Conclusion
We constructed a low-nonlinear dispersion-managed recirculating loop transmission system for the high-capacity and long-haul transmission of a WDM OTDM coherent Nyquist pulse with signals at nearly 1-Tb/s/λ. The transmission performance was improved by precise group delay measurement and compensation for the group delay ripple. Probabilistic shaping was newly applied to a high-speed coherent optical Nyquist pulse transmission to increase the transmission distance. With these techniques, we successfully demonstrated a 21.5-Tb/s transmission over 1,600 km using 160-GBd PS-32 QAM signals at nearly 1-Tb/s/λ. To the best of our knowledge, this is the first high-capacity and long-haul transmission beyond 20 Tb/s over > 1,000 km using signals at nearly 1-Tb/s/λ.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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