We show super-Nyquist-WDM transmission technique, where optical signals with duobinary-pulse shaping can be wavelength-multiplexed with frequency spacing of below baudrate. Duobinary-pulse shaping can reduce the signal bandwidth to be a half of baudrate while controlling inter-symbol interference can be compensated by the maximum likelihood sequence estimation in a receiver. First, we experimentally evaluate crosstalk characteristics as a function of channel spacing between the dual-channel DP-QPSK signals with duobinary-pulse shaping. As a result, the crosstalk penalty can be almost negligible as far as the ratio of baudrate to frequency spacing is maintained to be less than 1.20. Next, we demonstrate 140.7-Tbit/s, 7,326-km transmission of 7 × 201-channel 25-GHz-spaced super-Nyquist-WDM 100-Gbit/s optical signals using seven-core fiber and full C-band seven-core EDFAs. To the best of our knowledge, this is one of the first reports of high-capacity transmission experiments with capacity-distance product in excess of 1 Exabit/s·km.
© 2014 Optical Society of America
Researches and developments in optical fiber communication are mainly driven by two crucial challenges, which are enlarging the fiber capacity and extending the transmission distance. Recent development of the digital coherent receiver has opened up ultra-long-haul and ultra-high-capacity transmission with a capacity-distance product of over 100 Pbit/s·km even with single-core single-mode fibers (SMFs) [1–5]. Recently, the record capacity-distance product in the SMF transmission experiments has been achieved to be over 400 Pbit/s·km .
Space division multiplexing (SDM) based on multi-core fibers (MCFs) can increase the capacity-distance product furthermore . For much higher capacity, even in such ultra-long-haul MCF transmission, higher spectral efficiency is strongly required because there is a strict limitation of the number of cores due to crosstalk between cores of MCF. Although the introduction of the higher-order multi-level modulation is one of promising techniques for improving the spectral efficiency, an appropriate format has to be deliberately considered because such modulation formats require higher OSNR and are less tolerant against core-to-core crosstalk and fiber nonlinearity.
Here, we introduce ultra-dense WDM technique with frequency spacing of less than baudrate, which is called super-Nyquist WDM or Faster-than-Nyquist-WDM technique [8,9]. Here, 100-Gbit/s optical signals at 30 Gbaud can be packed with 25-GHz spacing without introducing 16QAM format. In order to reduce the signal bandwidth to below baudrate, we use duobinary-pulse shaping in a transmitter. To mitigate the inter-symbol interference (ISI) due to such limitation of the signal bandwidth, we introduce the maximum likelihood sequence estimation (MLSE) in a receiver. First, we experimentally investigate crosstalk performance of dual-channel dual-polarization quadrature phase shift keying (DP-QPSK) signals with duobinary-pulse shaping. Next, we demonstrate 140.7-Tbit/s 201-channel super-Nyquist-WDM transmission over 7,326-km seven-core fibers with full C-band seven-core EDFAs in the re-circulating loop experiment. This is one of the first reports [10,11] of high capacity transmission with a capacity-distance product in excess of 1 Exabit/s·km.
2. Concept of super-Nyquist-WDM techniques
In the super-Nyquist-WDM systems, the signal would be required to be band-limited in order to suppress the WDM crosstalk from adjacent channels. Here, we introduce the duobinary-pulse shaping, which can control ISI while narrowing the signal bandwidth. Although such ISI degrades a receiver sensitivity, it can be compensated by MLSE with just one memory in a receiver. Ideally, aggregate transfer function of a transmitter, a transmission channel, and a receiver should be designed to be the duobinary-pulse shaping. Since the square-root duobinary-pulse shaping is used in the transmitter, an adaptive filter in the receiver should be controlled so that transfer function of the transmission channel with the receiver is the square-root duobinary-pulse shaping.
In a transmitter, the duobinary-pulse-shaped QPSK signals can be directly generated by optical IQ modulation with digital-analog converter (DAC) following digital signal processing (DSP). The DSP procedure is shown in Fig. 1(a). A binary data sequence is upsampled twice, and then the samples are square-root duobinary-pulse-shaped after the discrete Fourier transform (DFT). The samples after inverse DFT (IDFT) are resampled to sampling rate of DAC, and then they are sent to DAC. Figure 1(b) shows a model of duobinary-pulse shaping. An incoming sequence is summed with itself delayed by one symbol before the Nyquist-pulse shaping with the sinc function. The impulse response of the duobinary-pulse shaping hduo(t) is given asFig. 1(c). It is composed of one-symbol-delayed two impulse responses with the Nyquist-pulse shaping as shown by dashed lines. The transfer function of the impulse response is given by the Fourier transformation of Eq. (1), and it is expressed asFigure 1(d) shows |Hduo(f)|2 of the duobinary-pulse shaped signal. The signal bandwidth after the pulse shaping is reduced to be a half of baudrate at full width at half maximum. In DSP of our transmitter, the signal after DFT and Hduo(f) are multiplexed in the frequency domain.
The binary sequence is converted to the three-level sequence after the duobinary-pulse shaping, resulting in the degradation of a receiver sensitivity. Receiving the duobinary-pulse-shaped signals by decision on the symbol-by-symbol basis gives a 2.1-dB loss in the receiver sensitivity in principle. However, this penalty can be ideally compensated by MLSE with one memory. Figure 2(a) indicates DSP in the receiver. Firstly, two streams corresponding to two polarizations of received optical complex amplitudes are dispersion-compensated (DC) and Nyquist-filtered in the frequency domain. After that, the polarization demultiplexing and linear equalization are done by an adaptive finite impulse response (FIR) filter with the butterfly configuration. The tap coefficients are updated based on the least-mean-square (LMS) algorithm. Using MLSE, the symbols are decoded from the real and imaginary parts of the equalized samples after the adaptive filter. Figure 2(b) shows the trellis for the duobinary signals. Each node at t = k has two incoming paths and two corresponding metrics. One out of two incoming paths is selected as the most probable, based on the metric calculated by the decision error of the path with the metric of the nodes at t = k – 1.
So far, there have been reports on super-Nyquist-WDM transmission using optical filters as duobinary-pulse shaping filters [8,9]. Here, we directly generated duobinary-pulse-shaped DP-QPSK signals using DAC following DSP and the optical IQ modulation. This has advantages of higher accuracy and higher resolution compared with pulse shaping in the optical domain.
3. Crosstalk characteristics of dual-channel DP-QPSK signals with duobinary-pulse shaping
First, we experimentally evaluated the crosstalk characteristics of dual-channel duobinary-pulse-shaped DP-QPSK signals. Here, the baudrate B was set to 18 Gbaud relatively lower in order to minimize the impact of bandwidth limitation by optical and electrical devices used in the experiments. Two continuous wave (CW) lights generated from external-cavity lasers (ECLs) with different wavelengths were independently modulated by two LiNbO3 optical IQ modulators (IQMs). The IQMs were driven by 18-Gbaud electrical signals with square-root duobinalry-pulse shaping which were generated by an arbitrary waveform generator (AWG) with a 24-Gsample/s DAC after DSP as shown in Fig. 1(a). After the polarization multiplexing, we obtained dual-channel duobinary-pulse-shaped DP-QPSK signals. The spectral waveforms are shown in Fig. 3(a). The frequency spacing δf between dual channels was set to 18 GHz, 15 GHz, or 12 GHz, which corresponded to B/δf of 1.00, 1.20, or 1.50, respectively. Here, the frequency fluctuation of the lasers was below 10 MHz, and we adjusted precisely powers of dual channels to be equal. Using a digital coherent receiver, one of channels was detected.
Measured BERs of the single-channel duobinary-pulse-shaped signals without and with MLSE are plotted as a function of optical signal to noise ratio (OSNR) in the back-to-back configuration by dots and closed triangles in Fig. 3(b). Open circles and open triangles are results of the single-channel conventional Nyquist-pulse-shaped signals without and with MLSE, respectively. A dashed line indicates the theoretical curve of Nyquist-pulse-shaped DP-QPSK signals. Although we observed the penalty of >3 dB in the case of the duobinary-pulse shaped signal without MLSE compared with the conventional Nyquist-pulse-shaped signal at the BER of 10−2, the penalty was improved by 1 ~2 dB by using MLSE. On contrary, we cannot find any improvement by MLSE in the case of the Nyquist-pulse-shaped signals. Consequently, the penalty of the duobinary-pulse-shaped signals with MLSE is about 2 dB at the BER of 10−2 compared with Nyquist-pulse-shaped signals.
Figure 3(c) shows measured BERs of dual-channel duobinary-pulse-shaped signals. Dots, open triangles, and closed triangles indicate results when the δf was set to be 18 GHz, 15 GHz, or 12 GHz, respectively. Open circles are results in the single-channel (SC) case. We observed that the penalty due to crosstalk became larger with the smaller frequency spacing. The penalty at δf = 15 GHz was suppressed to be 1 dB, although that at 12-GHz spacing was significantly large. It is shown that the penalty can be suppressed as far as B/δf ≤ 1.20.
When the frequency spacing was fixed to be 15 GHz, we compared duobinary-pulse-shaped DP-QPSK signals with conventional Nyquist-pulse-shaped signals. Dots and closed triangles in Fig. 3(d) indicate measured BERs of the single-channel and dual-channel duobinary-pulse-shaped signals, respectively. Open circles and open triangles are results of Nyquist-pulse-shaped signals in the single-channel and dual-channel cases, respectively. We can see that even though the performance of the duobinary-pulse shaping is about 2 dB worse than that of the conventional Nyquist-pulse shaping in the single channel case, it was significantly better than that of Nyquist-pulse shaping in the 15-GHz spaced WDM case at the BER of 10−2. These results suggest that the duobinary-pulse shaping is effective to suppress the crosstalk between super-Nyquist-WDM channels.
4. Super-Nyquist-WDM transmission experiment over seven-core fibers with full-C-band seven-core EDFAs
Next, we evaluated the transmission performance of the super-Nyquist-WDM DP-QPSK signals with duobinary-pulse shaping. Here, we multiplexed 201-channel 30-Gbaud duobinary-pulse-shaped DP-QPSK signals with frequency spacing of 25 GHz. This corresponds to B/δf = 1.2, and this condition satisfies that duobinary-pulse shaping can efficiently suppress the penalty due to the linear crosstalk as mentioned in Section 3.
4.1 Experimental setup
Figure 4 shows the experimental setup. The transmitter consisted of a three-rail configuration as reported in . The two rails were used for eight even and eight odd channels. The even and odd channels were generated by multiplexing eight ECLs arranged with frequency spacing of 50 GHz, and they were then independently modulated by two IQMs driven by 30-Gbaud electrical duobinary-pulse-shaped binary signals generated from an AWG at sampling rate of 50 Gsample/s. After the modulation, we equalized the power per channel of WDM signals by a polarization-maintained wavelength selective switch (WSS) based on a liquid crystal on silicon (LCOS). The third rail was a loading rail for generating 201 WDM channels in order to maintain not only an OSNR but also nonlinear effects. A total of 101 lasers were combined onto a 50-GHz frequency grid. After they were modulated by a LiNbO3 Mach-Zehnder modulator (MZM) driven by 12.5-GHz electrical clock so that the carrier components were suppressed, we obtained 201 CW tones with a 25-GHz spacing ranging from 191.2625 THz to 196.2875 THz. All 201 channels were then passed through an IQM driven in the same manner as the modulators in other two rails. In the experiment, we disabled 16 consecutive channels on the loading rail, and the measured 16 channels from other two rails were tuned to the corresponding frequencies.
After the modulated WDM signals from three rails were fed into the polarization multiplexing emulators (PMEs), they were combined by WSS. Each channel power of the WDM signals was automatically equalized by the WSS with power monitor. Consequently, we obtained 201-channel 25-GHz-spaced super-Nyquist-WDM 30-Gbaud duobinary-pulse-shaped DP-QPSK signals, resulting in a spectral efficiency of 4 bit/s/Hz assuming a LDPC-based SD-FEC with 20% overhead .
For multi-core fiber (MCF) transmission, the 201-channel WDM signals were launched into a specially configured seven-fold recirculating loop consisting of a span of 45.5-km seven-core fiber, a seven-core EDFA, external gain-flattening filters (GFFs), and optical switches (SWs). The seven loops were synchronously operated as reported in . The seven re-circulating loops shared a common load switch that launched identical copies of the WDM signals into each of the loops through a power splitter with over 75-symbol delay between cores for the signal decorrelation. After amplification by the seven-core EDFA with external GFFs, the signals were launched into the cores of the 45.5-km MCF. The output signals from one core were sent to the re-circulating loop input of the next core, in a cyclic fashion. The core-to-core configuration can average out variations in span loss, dispersion, and other component imperfections . Two WSSs and two single-core EDFAs were inserted at input of the fourth and seventh cores for gain equalization, and the gain flatness was automatically managed by the WSS at input of the seventh core. A polarization scrambler was inserted at the input of the fifth core.
The transmitted signals were received by a digital coherent receiver after pre-amplification and channel selection with an optical band-pass filter (OBPF) with a bandwidth of 1 nm. Electrical signals from the receiver were stored in sets of 1M samples by using a four-channel digital oscilloscope operating at 50 Gsample/s. The stored data were processed offline by DSP as follows: The received signals were re-sampled to two sample/symbol. After square-root duobinalry-pulse shaping and dispersion compensation in the frequency domain, polarization demultiplexing and signal equalization were performed by half-symbol-spaced FIR filters with 80 taps, which were adapted by the decision-directed least-mean square (DD-LMS) algorithm . After MLSE, the symbols were decoded.
4.2 Measured back-to-back performance of super-Nyquist-WDM signals
Figure 5 shows optical spectra of 25-GHz-spaced super-Nyquist-WDM 30-Gbaud Nyquist-pulse-shaped and duobinary-pulse-shaped DP-QPSK signals. We can see the significant spectral overlapping in Nyquist-pulse-shaped WDM signals. On the other hand, by using duobinary-pulse shaping, such spectral overlapped components can be sufficiently suppressed.
Open circles and open triangles in Fig. 6 indicate the measured bit-error rates (BERs) of single-channel (SC) and super-Nyquist-WDM cases of duobinary-pulse-shaped DP-QPSK signals compared with those (indicated by closed circles and closed triangles) of Nyquist-pulse-shaped DP-QPSK signals. Dashed line represents the theoretical curve of the single-channel DP-QPSK signal. The 25-GHz-spaced-WDM Nyquist-pulse-shaped signals are significantly degraded due to the crosstalk form adjacent WDM channels. Adapting duobinary-pulse shaping, the OSNR penalty can be suppressed to below 2 dB compared with the single-channel DP-QPSK signals.
Based on the measured back-to-back performance, we design the OSNR and the launched power into the MCF transmission line required for long-haul transmission over 7,000 km. Using an SD-FEC with a 20% overhead, the error-free operation can be achieved as long as the BER is less than 2.7 × 10−2 corresponding to a Q factor of 5.7 dB . Supposing a margin of about 1.5 dB for the Q factor, we set the target Q factor at 7.2 dB which corresponds to the BER of 1.1 × 10−2. Using our PDM-QPSK transmitter and receiver, the OSNR would be required to be over 13 dB for a BER of less than 1.1 × 10−2, as shown in Fig. 6. Assuming a 2- ~3-dB penalty after transmission, the required OSNR after transmission is estimated to be over 15 ~16 dB. Figure 7 shows the calculated launched power required for an OSNR of 15 ~16 dB as a function of the transmission distance. The launched powers required for 7,000-km transmission are calculated to be −2.6 and −3.6 dBm/ch required for an OSNR of 16 dB and 15 dB, respectively. In our experiment, the launched power per channel was set at −2 dBm/ch corresponding to a total power of all 201 super-Nyquist-WDM channels of 21 dBm.
4.3 Results of transmission experiments
Figure 8 shows the Q factors and OSNRs of the channel at the frequency of 193.4625 THz as a function of the transmission distance with a fiber launched power of −2 dBm/ch as mentioned in Section 4.2. The Q factors are calculated from the measured BERs. The Q penalty is estimated to be 2.2 dB and 2.0 dB by referring to the OSNR at 6,370-km and 7,326-km transmission, respectively. Therefore, the significant performance degradation due to core-to-core crosstalk and fiber nonlinearity could not be observed even in ultra-long-haul transmission. Note that since the crosstalk of the optical switch in each loop input was relatively larger, the penalty caused by the crosstalk of the input optical switch was included in this Q factor penalty in particular for the shorter transmission distance.
The optical spectra before and after 7,326-km transmission are shown in Fig. 9. After transmission, the power differences of all channels were maintained to be less than 2 dB thanks to precise gain equalization. The measured Q factors after 7,326 km transmission are shown in Fig. 10. The inset shows the typical constellation of the received signal before MLSE. The Q factors of all 201 channels for seven cores of MCF were confirmed to be over 6.0 dB, which exceeds the limit of the 20%-overhead LDPC-based SD-FEC with the maximum number of iterations of 12, namely 5.7 dB .
We showed super-Nyquist-WDM techniques based on the duobinary-pulse shaping in the transmitter and MLSE in the receiver. First, we evaluated crosstalk performance of dual-channel DP-QPSK signals with duobinary-pulse shaping. The penalty can be suppressed as far as the ratio of baudrate to frequency spacing is maintained to be less than 1.20. Next, we demonstrated 140.7-Tbit/s super-Nyquist-WDM transmission using 30-Gbaud duobinary-pulse-shaped DP-QPSK signals over 7,326 km seven-core fibers with seven-core EDFAs. We achieved a record capacity distance product of 1 Exabit/s·km.
The authors would like to thank Mr. Kawakami of Tektronix for providing AWG. A part of this work was supported by NICT, Japan.
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