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We evaluate the dependence of system performance on the roll-off factor, α, of a Nyquist pulse in a single-channel 1.28 Tbit/s-525 km transmission both experimentally and analytically. Low α values are preferable in terms of spectral efficiency and tolerance to chromatic dispersion and polarization-mode dispersion, while a strong overlap with neighboring symbols results in larger nonlinear impairments. On the other hand, a Nyquist pulse with high α values also suffers from nonlinearity due to higher peak power. As a result, we found experimentally that the optimum α value is 0.4~0.6, which agrees well with the analysis.
© 2016 Optical Society of America
1. Introduction
The single-channel transmission capacity at 1 Tbit/s and beyond has been a major research subject since the development of faster network interfaces such as 100 G and 400 G Ethernet. A single-channel bit rate approaching 1 Tbit/s has recently been reported with electrical time division multiplexing (ETDM) and multi-level modulation, for example 856 Gbit/s with polarization-division multiplexed quadrature phase-shift keying (PDM-QPSK) at 107 Gbaud [1] and 1.08 Tbit/s with PDM-64 quadrature amplitude modulation (QAM) at 90 Gbaud [2]. To overcome the fundamental limitations related to ETDM such as the sampling rate and bandwidth of digital-to-analog (DA) and analog-to-digital (AD) converters, optical time division multiplexing (OTDM) has been adopted to achieve a bit rate in the Tbit/s regime [3–5]. However, the ultrashort return-to-zero (RZ) pulses required for ultrahigh-speed OTDM are problematic in terms of spectral efficiency and tolerance to chromatic dispersion (CD) and polarization-mode dispersion (PMD) due to the large bandwidth.
To achieve an ultrahigh-speed and spectrally efficient transmission, we have proposed a novel OTDM scheme using an optical Nyquist pulse (Nyquist OTDM) [6]. A Nyquist pulse is characterized by a parameter called a roll-off factor α (0 ≤ α ≤ 1), which determines the bandwidth of the Nyquist pulse, and has a sinc-function (α = 0) or quasi sinc-function (0 < α ≤ 1) waveform. Regardless of the α value, it features an oscillating tail that crosses zero periodically. As a result, Nyquist pulses can be bit-interleaved to a higher symbol rate given by the period of the zero crossing without being affected by intersymbol interference (ISI) despite the large overlap between neighboring pulses. This feature enables the signal bandwidth to be greatly reduced compared with conventional RZ pulses. Nyquist pulses can be used both as non-coherent pulses for on-off keying (OOK) or differential quadrature phase shift keying (DQPSK) with direct detection, and as coherent pulses for QPSK or QAM with coherent detection. Using this scheme, we have demonstrated a single-channel 2.56 Tbit/s (640 Gbaud)-525 km PDM-DQPSK transmission and 1.92 Tbit/s (160 Gbaud)-150 km PDM-64 QAM transmission, by using non-coherent and coherent Nyquist pulses, respectively [7,8]. It has also been demonstrated that the Nyquist OTDM signals can be scaled to a higher baud rate such as 1.28 Tbaud [9, 10], and their advantages in high-speed elastic networking have also been demonstrated [11].
In general, lower α values are considered to be beneficial because of the narrower spectral width, and are therefore particularly advantageous in terms of spectral efficiency and CD/PMD tolerance. However, the dependence of the transmission performance on the roll-off factor in a long distance transmission has not been investigated in detail, especially when taking nonlinear optical impairments into account. In this paper, we present a detailed comparison of the transmission performance with different α values in a single-channel 1.28 Tbit/s-525 km transmission using Nyquist pulses, and determine the optimum α value while taking account of linear and nonlinear impairments both experimentally and analytically.
2. Experimental setup for 1.28 Tbit/s/ch transmission over 525 km
Figure 1 shows our experimental setup for a 1.28 Tbit/s (640 Gbaud) DQPSK transmission using non-coherent Nyquist pulses. As an optical pulse source, we used a 40 GHz mode-locked fiber laser (MLFL) emitting a 1.5 ps Gaussian pulse at 1541 nm, whose spectrum was externally broadened with a highly nonlinear dispersion-flattened fiber (HNL-DFF). A Nyquist pulse was generated by manipulating the spectrum using an LCoS programmable optical filter. Here, the zero-crossing period of the Nyquist pulse was set at 1.56 ps, which corresponds to an OTDM symbol rate of 640 Gbaud. A Nyquist pulse with a different α value was obtained with a properly designed filter profile. In this experiment, we generated Nyquist pulses with α = 0, 0.2, 0.5, 0.7, and 1. Figure 2 shows the pulse waveforms and optical spectra of the Nyquist pulses generated with α = 0, 0.5, and 1. They fit an ideal profile with high accuracy both in the time and frequency domains as shown by the black curves. The generated Nyquist pulses were all transform-limited. In a Nyquist pulse transmission, it is very important to maintain a flat-top spectral shape during transmission, and therefore we must compensate for imperfect spectral flatness of the in-line EDFA (erbium-doped fiber amplifier) gain profile and other optical components. Here we applied pre-emphasis to the intensity profile at the filter so that the spectrum of an ideal Nyquist pulse could be obtained after a 525 km transmission. The Nyquist pulse after the spectral pre-emphasis was modulated with a 40 Gbaud DQPSK signal using an IQ modulator, and then bit-interleaved to 640 Gbaud using a delay-line multiplexer.
Fig. 2 Nyquist pulse waveform (left) and spectrum (right) with α = 0 (a), 0.5 (b), and 1 (c). Black curves are the ideal Nyquist profile.
The 1.28 Tbit/s Nyquist OTDM signal was launched into a 525 km dispersion-managed transmission link. Each span of the link consisted of a 50 km single-mode fiber (SMF) with an anomalous dispersion of + 20 ps/nm/km and a 25 km inverse dispersion fiber (IDF) with a normal dispersion of − 40 ps/nm/km. The loss of each span was compensated for by using an erbium-doped fiber amplifier (EDFA). The first-order PMD was mitigated with polarization controllers (PC) so that the signal was coupled to the principal state of polarization (PSP) of the fiber link. PSP coupling was realized by maximizing the degree of polarization of the OTDM signal after a 525 km transmission. The bandwidth of the in-line optical filter was 10 nm for α = 0, 0.2 and 15 nm for α = 0.5, 0.7 and 1.
After a 525 km transmission, the Nyquist OTDM signal was first passed through a programmable optical filter, whose amplitude profile equalized the imperfect gain flatness of the EDFA in the receiver, and the phase profile compensated for the residual CD and dispersion slope in the transmission link. We evaluated the waveform and spectrum of the transmitted signal by propagating a Nyquist pulse without OTDM and found that an ideal Nyquist profile with periodic zero crossing at a 1.56 ps interval was precisely recovered after the post-processing [7]. This confirms that the ISI-free property is maintained in the Nyquist OTDM signal after transmission.
After that, the Nyquist OTDM signal was demultiplexed from 640 to 40 Gbaud by using a nonlinear optical loop mirror (NOLM), which was used as an ultrafast optical sampler to extract the ISI-free region of the signal. A 40 GHz MLFL at a wavelength of 1563 nm was used as a control pulse, which was phase-locked loop (PLL)-operated with a 40 GHz clock recovered from the transmitted OTDM signal. The sampling gate width was optimized at 1.0 ps taking account of the trade-off between the OSNR (optical signal-to-noise ratio) decrease after demultiplexing with a shorter gate width and distortion due to ISI with a broader gate width. Finally, the demultiplexed 40 Gbaud DQPSK signal was demodulated with a one-bit delay interferometer (DI) and received with a balanced photo-detector (PD).
3. Experimental results for α dependence of transmission performance
Figure 3 shows the bit error rate (BER) performance for α = 0, 0.5, and 1 in a 1.28 Tbit/s-525 km transmission. The transmission power is set at the optimum value depending on α as we describe belowE. The BER performance was almost the same for all α values under back-to-back conditions. A Nyquist pulse with α = 1 performs slightly better than the other two cases, because an α = 1waveform is much closer to that of a standard RZ pulse. After a 525 km transmission, an error floor was seen in the BER curves, which was caused by OSNR degradation. However, the minimum BER was sufficiently below the forward error correction (FEC) threshold of 2x10−3 with a 7% overhead and can be made error-free by adopting FEC. With α = 0.5, the OSNRs before and after transmission were 35 and 26 dB, respectively. The result in Fig. 3 indicates that a Nyquist pulse with α = 0.5 exhibited the best transmission performance, while the BER was worse with α = 1 and further degraded with α = 0 by more than one order of magnitude compared with α = 0.5. The reason will be described in detail based on the analysis in Section 4 below. Figure 4 shows the waveforms of transmitted and demultiplexed 40 Gbaud signals received with a balanced PD for α = 0 (a), 0.5 (b) and 1 (c), which were obtained at a received power of − 20 dBm. It can also be seen that the waveform is degraded for α = 0 (a) and 1 (c) compared with α = 0.5 (b).
Fig. 3 BER vs. received power (a) and OSNR (b) for different α values in a 1.28 Tbit/s-525 km transmission.
Fig. 4 Output waveforms from a balanced PD at a received power of −20 dBm for α = 0 (a), 0.5 (b) and 1 (c).
Figure 5(a) shows the relationship between the launch power and BER for α = 0, 0.2, 0.5, 0.7 and 1 after a 525 km transmission, which was measured with a received power of −15 dBm. The optimum launch power was 11 dBm for α = 1 and 10 dBm for other α values. The relationship between α and the minimum BER obtained at the optimum launch power is plotted in Fig. 5(b). The lowest BER was obtained when α = 0.5, and the BER increased for both lower and higher α values, as also expected from Fig. 3. Although a Nyquist pulse with small α values should be most beneficial in principle in terms of higher CD and PMD tolerance due to the narrower spectral width, these results indicate that the optimum roll-off factor exists at α =0.4~0.6.
Fig. 5 BER vs. launch power for different α values (a) and the minimum BER vs. α (b) in a 1.28 Tbit/s-525 km transmission.
4. Analysis of α dependence including nonlinear pulse interactions
To explain the α dependence described in the previous section, here we analytically evaluate the influence of nonlinearity in a Nyquist pulse transmission. We apply an analytic model for nonlinear interactions between bit-interleaved pulses developed in [12] to a Nyquist OTDM transmission. Since the Kerr effect is a third-order nonlinear effect, a nonlinear interaction term is generally represented by ul um un*, i.e. the interaction between three pulses, where uk is a Nyquist pulse centered at t = kT (T: symbol interval and k = l + m − n). Hereafter we focus on the nonlinear impairment that occurs for a pulse at t = 0, which corresponds to the condition n = l + m. Depending on the combination (l, m), the term ul um un* can represent self-phase modulation (SPM) when l = m = 0 (|u0|2u0), intra-channel cross-phase modulation (XPM) when l = 0, m ≠ 0 (|ul|2u0) or l ≠ 0, m = 0 (|um|2u0), and intra-channel four-wave mixing (FWM) when l = m ≠ 0 (ul2u2l*) or l ≠ m ≠ 0 (ulumul + m*), respectively.
The influence of the nonlinear interaction on the Nyquist pulse propagation is generally described as
where Δu(z, t) is a perturbation of the linear propagation, β2 is the CD coefficient, γ is the nonlinear coefficient, and a2(z) = exp(−Γz) (Γ: loss coefficient) represents the intensity variation along the length associated with the loss and gain profiles. Following the result in [12], the nonlinear impairment arising from the nonlinear interaction between three pulses, ul um un* can be regarded as a noise, whose power is given byThe noise power, σ2NL, is proportional to the cube of the transmission power, Pav3, with the coefficient given by where η corresponds to either ηSPM, ηXPM, or ηFWM, depending on the combination of (l, m) described earlier. Here, ŝ(f) is the spectrum of a Nyquist pulse, Pp is the peak power of each pulse, N is the number of pulses under consideration, ak is a random data pattern at t = kT, and H(f) is the transfer function of optical filters.We computed the XPM and FWM coefficients, ηXPM and ηFWM, respectively, for various α values using Eqs. (2) and (3). Figure 6(a) shows ηXPM and ηFWM plotted as a function of α. It can be seen that both ηXPM and ηFWM decrease as α increases from 0, but they begin to increase for α > ~0.6. This feature is in good agreement with Fig. 5(b). This result can be explained by the fact that the overlap between neighboring pulses decreases as α increases, but at the same time, the peak power of a Nyquist pulse also increases under a fixed average power (i.e., the increase in Pp/Pav in Eq. (3)a)). The Pp/Pav value as a function of α is plotted in Fig. 6(b). It can be seen that, when α increases to 1, Pp/Pav increases to 1.33 times that of α = 0. Thus, as a universal result, the optimum roll-off factor for the Nyquist pulse transmission is approximately 0.4~0.6.
5. Conclusion
We compared the transmission performance for different roll-off factors of a Nyquist pulse in a single-channel 1.28 Tbit/s-525 km transmission experimentally and analytically. Low α values are preferable in terms of greater CD and PMD tolerance, but the analysis showed that a strong overlap between neighboring symbols results in large impairments due to XPM and FWM. On the other hand, large α values lead to a higher peak power and again increase the nonlinearity. As a result, the optimum roll-off factor was α = 0.4~0.6, which showed good agreement between experiment and analysis.
Funding
JSPS Grant-in-Aid for Specially Promoted Research (26000009).
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