The dependence of propagation performance on the signal baud-rate is investigated by simulations for WDM PDM-16QAM systems operating at a spectral efficiency of 4 b/s/Hz. We take into account the case of transmission over uncompensated links, both for standard single-mode fiber and non-zero dispersion-shifted fiber. Three baud-rates are tested: 16.25, 32.5 and 65 Gbaud, including overhead for soft-decision FEC. Hence, we compare the performance limited by the nonlinear impairments in case of 100, 200 and 400 Gb/s data rate transmission, respectively. We demonstrate that the trade-off between higher OSNR margin and nonlinear transmission penalty favors transmission at lower baud-rate (16.25 Gbaud) and narrower channel spacing (25 GHz), among the three different simulated baud-rates.
© 2011 OSA
To allow capacity scaling of wavelength-division multiplexed (WDM) optical networks, the increase of the spectral efficiency (SE) appears necessary. Polarization-division multiplexing (PDM) and multilevel modulation formats are key techniques to achieve this goal, preferably in combination with coherent detection . Exploitation of quadrature phase-shift keying (QPSK) and PDM combined with coherent detection has already allowed to demonstrate the capabilities of optical systems operating at 100 Gb/s within a 50-GHz WDM grid, achieving 2 b/s/Hz SE. Impressive experimental results have been shown for this 100-Gb/s solution [2,3] and coherent systems are already deployed. Coherent detection allows for demodulating complex constellations and a promising candidate format appears 16QAM (quadrature amplitude modulation), where the in-phase I and quadrature Q components are modulated by four bits per symbols. It is known that PDM-16QAM theoretically pays an optical signal-to-noise ratio (OSNR) penalty of 7 dB with respect to PDM-QPSK at the same baud-rate , because of the reduction of the distance between symbols and the doubling of bit-rate at the same WDM grid (hence doubling the SE).
For PDM-16QAM just few simulative  and experimental [6–8] works have been presented. To assess the capabilities of complex optical systems based on PDM-16QAM, it is fundamental to understand their performance dependence on the channel baud-rate. Besides the technological challenges inherent to the transmitters (TXs) and receivers (RXs) implementation, increasing the baud-rate per channel affects not only the theoretical OSNR required at the RX to assure the target bit-error rate (BER), but also the fiber propagation through nonlinear effects. In particular, for coherent systems and in case of uncompensated links without in-line fiber chromatic dispersion (CD) compensation, which have been shown to be the best map for this kind of detection , it is unclear what is the optimum baud-rate and channel spacing for a target SE. Recently, the works [10,11] has analyzed this dependence for various modulation formats.
In this Letter, we investigate by means of simulations the behaviour of PDM-16QAM coherent systems at three different baud-rates: 16.25, 32.5 and 65 Gbaud. Assuming the use of high redundancy soft-decision forward-error correction (FEC) codes , these baud-rates take into account a large overhead for protocol and FEC of 30%. Hence, the behaviours of PDM-16QAM systems operating at 100, 200 and 400 Gb/s data rates, respectively is compared at the same net SE (4 b/s/Hz). The 16QAM signal is generated simulating an optimized Nyquist-like pulse. We address the problem by evaluating the limitations induced by fiber nonlinearities over long-haul uncompensated links, considering both standard single-mode fiber (SSMF) and nonzero dispersion-shifted fiber (NZDSF), taking into account in our analysis newly deployed fiber infrastructures.
2. Simulation setup
We simulate the system setup shown in Fig. 1 . At the TX the laser has a linewidth of 300 kHz and a RIN of 140 dB/Hz, in order to simulate the specifications of commercial ECL sources. The PDM-16QAM signal is generated by two nested Mach-Zehnder modulators (MZMs), followed by a polarization beam combiner (PBC) for polarization multiplexing. Each MZM electrode driving signal is suitable generated by digital-to-analog converters (DACs)  with quantization and holding functionalities. Before DACs, the constellation is pulse shaped by a digital FIR filter (square-root raised cosine) in order to achieve Nyquist-like shaping after detection and to compact the modulated channel spectrum. The exploitation of Nyquist-like pulses allows to considerably increase the signal baud-rate (maintaining the same WDM channel spacing), in order to take into account larger overhead due to soft-decision FEC codes. The generation of the compact spectrum may be also achieved by means of electrical analog filters  or optical filtering. Before DAC, the signal pulse is also predistorted to compensate driver and MZM nonlinear behaviour. A further pre-emphasis filter is also employed after the nonlinear compensation.
Three different WDM system configurations are tested to address the performance at 100, 200, and 400-Gb/s data rates, considering in all simulations 17 copropagating WDM channels with random states of polarization. Each channel is independently modulated by employing eight uncorrelated pseudorandom binary sequences (PRBS) of length 215, corresponding to 32768 symbols (262144 bits). By taking into account first-generation 100-Gb/s systems, implemented by exploiting PDM-QPSK with 50-GHz spacing (2-b/s/Hz SE), we vary the channel spacing of the WDM grid and the baud-rate to double the SE. The tested baud-rates are: 16.25 Gbaud with WDM frequency spacing Δf = 25 GHz (line rate of 130 Gb/s for a 100-Gb/s data rate), 32.5 Gbaud with Δf = 50 GHz (line rate of 260 Gb/s for a 200-Gb/s data rate), and 65 Gbaud with Δf = 100 GHz (line rate of 520 Gb/s for a 400-Gb/s data rate), achieving a SE equal to 4 b/s/Hz in all the configurations.
The link is constituted by uncompensated spans with span loss of 22 dB (corresponding to 100-km span length) without in-line CD fiber compensation. The loss of each span is recovered by means of the erbium-doped fiber amplifier (EDFA) gain with noise-figure NF = 5 dB. To speed up the simulations, the amplified spontaneous emission (ASE) noise is loaded at the end of the link before the RX, considering that  demonstrated no appreciable penalties occur adopting this simplification. We analyze two possible propagation fibers: SSMF (with dispersion coefficient D = 17 ps/nm/km, slope 0.06 ps/nm2/km and effective area 80 μm2) and NZDSF (with D = 4 ps/nm/km, slope 0.11 ps/nm2/km and effective area 72 μm2). Polarization-mode dispersion (PMD) and polarization-dependent loss (PDL) have been both neglected in our simulations.
At the output, the central channel corresponding to 1545 nm is demodulated by a standard coherent RX, which includes polarization-diversity 90° optical hybrids, combining the input signal with the local oscillator (LO) with the same characteristics of the employed laser source. In our simulation the frequency alignment between the LO and the channel under test is considered ideal. The received signal is detected by four balanced photodetectors (BPDs) and suitably filtered by low-pass electrical filters. The four filtered components are then sampled by four analog-to-digital converters (ADCs). Both for DACs at the TX and for ADCs at the RX we have chosen to operate at two samples per symbol (the optimization of the sampling rate is not a relevant aspect of this paper) and with 6-bit quantization, leading to negligible quantization penalties. After quantization, the sampled signals are sent to the digital signal processing (DSP) stage. Chromatic dispersion (CD) is compensated by means of frequency-domain equalization, while adaptive equalization based on the multi-modulus algorithm (MMA) with 15 taps  is employed for polarisation separation. Timing recovery is obtained by means of Gardner algorithm  and for carrier phase recovery we exploit the feed-forward Viterbi&Viterbi partitioning algorithm suited for 16QAM .
In the case of 200-Gb/s transmission at 32.5-Gbaud, the 3-dB bandwidths chosen for the DAC, for the electrical driver and for the nested MZM at the TX are 20 GHz, 30 GHz and 22.5 GHz, respectively. Two optical second-order super-Gaussian filters with 42.5-GHz full bandwidth at half maximum are inserted to simulate the WDM multiplexing/demultiplexing. At the RX the electrical filter and the ADC have 3-dB bandwidth of 22.5 GHz, and 20 GHz, respectively. In the case of 100-Gb/s transmission at 16.25-Gbaud all electrical and optical bandwidths at the TX and RX are halved, while for 400-Gb/s transmission at 65-Gbaud they are doubled.
In order to check the transmission performance we employ a suitable simulator based on split-step Fourier method to solve the nonlinear Schrödinger equations describing signal propagation in fiber. The BER is obtained by error counting over 262144 simulated bits. The BER and the corresponding Q-factor are evaluated as a function of the launched power per channel assuming differential decoding for the three system configurations under test for different SSMF and NZDSF propagation lengths. The large signal overhead chosen for our simulations allows to target a pre-FEC BER of 3·10−2, exploiting soft-decision FEC [12, 17]. Fixing the corresponding Q-factor threshold (5.5 dB) and 3-dB margin threshold (8.5 dB) it is possible to discuss the achievable reach.
3. Simulation results
Figure 2 shows the simulation results related to uncompensated propagation over SSMF links of 600, 800 and 1000 km, respectively, for the three baud-rates taken into accountand a Nyquist roll-off factor equal to 0.6, which gives the best performance in our simulation setup. As shown, for low launch power per channel PTX, transmission is linear and Q-factor increases with the launch power PTX. As PTX is further increased, nonlinear impairments occur and thus the Q-factor decreases. We define the fiber launch power corresponding to the maximum Q-factor as the optimum launch power (OLP) of the system.
In case of 32.5 Gbaud (red curves) the OLP is about 1 dBm, and appears nearly the same independently from the maximum reach. As expected, for lower baud-rate the OLP decreases: about 3-dB penalty in OLP is visible for 16.25 Gbaud (green curves), while for 65 Gbaud (orange curves) the OLP grows about of 3-dB, demonstrating that systems at higher baud-rates are more robust to nonlinear penalty . Performance in case of 1000 km propagation (open circles) are within the FEC threshold (corresponding to a Q-factor of 5.5 dB) for all the three simulated baud-rates, assuring a maximum reach longer than 1000 km, while taking into account 3-dB margin, the reach is limited to 800-km. Hence, the maximum achievable reach appears slightly longer for lower baud-rates with narrower WDM frequency spacing.
In Fig. 3 the simulation results related to uncompensated propagation over NZDSF links are reported. For the three considered baud-rates, the OLP shows about 2-dB penalty with respect to the SSMF propagation. Moreover, the maximum reach is reduced owing to the stronger interchannel nonlinear impairments, due to the lower NZDSF dispersion. Taking into account 3-dB margin, transmission at 16.25 Gbaud allows for 600-km maximum reach.
In this paper we have investigated the performance dependence on the channel baud-rate in case of PDM-16QAM systems for transmission with constant SE equal to 4 b/s/Hz. In the baud-rate range taken into account in our analysis, systems at lower baud-rates with narrower WDM frequency spacing are less tolerant to nonlinear impairments, but the higher OSNR margins associated with the lower baud-rate still allow for the longest reach. For PDM-16QAM this trend is more evident with respect to PDM-QPSK systems, as shown in the simulations of  and confirm the results reported in .
The exploitation of TXs and RXs operating at lower baud-rate can be a feasible solution to implement in the near future systems operating with high spectral efficiency. Obviously, more WDM channels are necessary in order to maintain the same total transmitted capacity leading to an increased number of TXs and RXs interfaces.
References and links
1. S. J. Savory, G. Gavioli, R. I. Killey, and P. Bayvel, “Electronic compensation of chromatic dispersion using a digital coherent receiver,” Opt. Express 15(5), 2120–2126 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-5-2120. [CrossRef] [PubMed]
2. G. Charlet, J. Renaudier, H. Mardoyan, P. Tran, O. B. Pardo, F. Verluise, M. Achouche, A. Boutin, F. Blache, J.-Y. Dupuy, and S. Bigo, “Transmission of 16.4 Tbit/s capacity over 2,550 km using PDM QPSK modulation format and coherent receiver,” J. Lightwave Technol. 27(3), 153–157 (2009). [CrossRef]
3. M. Salsi, H. Mardoyan, P. Tran, C. Koebele, E. Dutisseuil, G. Charlet, and S. Bigo, “155x100 Gbit/s coherent PDM-QPSK transmission over 7,200 km,” in Proceeding ECOC 2009, postdeadline paper PD2.5, Wien (2009).
4. R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. 28(4), 662–701 (2010). [CrossRef]
5. V. Curri, P. Poggiolini, A. Carena, and F. Forghieri, “Performance analysis of coherent 222-Gb/s NRZ PM-16QAM WDM systems over long-haul links,” IEEE Photon. Technol. Lett. 22(5), 266–268 (2010). [CrossRef]
6. P. J. Winzer, A. H. Gnauck, C. R. Doerr, M. Magarini, and L. L. Buhl, “Spectrally efficient long-haul optical networking using 112-Gb/s polarization-multiplexed 16-QAM,” J. Lightwave Technol. 28(4), 547–556 (2010). [CrossRef]
7. S. Makovejs, D. S. Millar, V. Mikhailov, G. Gavioli, R. I. Killey, S. J. Savory, and P. Bayvel, “Experimental investigation of PDM-QAM16 transmission at 112 Gbit/s over 2400km,” in Proceeding OFC/NFOEC 2010, paper OMJ6, San Diego, CA, USA (2010).
8. P. J. Winzer, A. H. Gnauck, S. Chandrasekhar, S. Draving, J. Evangelista, and B. Zhu, “Generation and 1,200-km transmission of 448-Gb/s ETDM 56-Gbaud PDM 16-QAM using a single I/Q modulator,” in Proceedings ECOC 2010, postdeadline paper PD2.2, Torino, Italy (2010).
9. G. Gavioli, E. Torrengo, G. Bosco, A. Carena, V. Curri, V. Miot, P. Poggiolini, F. Forghieri, S. J. Savory, L. Molle, and R. Freund, “NRZ-PM-QPSK 16x100 Gb/s transmission over installed fiber with different dispersion maps,” IEEE Photon. Technol. Lett. 22(6), 371–373 (2010). [CrossRef]
10. P. Poggiolini, G. Bosco, A. Carena, V. Curri, V. Miot, and F. Forghieri, “Performance dependence on channel baud-rate of PM-QPSK systems over uncompensated links,” IEEE Photon. Technol. Lett. 23(1), 15–17 (2011). [CrossRef]
11. C. Behrens, R. I. Killey, S. J. Savory, M. Chen, and P. Bayvel, “Nonlinear transmission performance of higher-order modulation formats,” IEEE Photon. Technol. Lett. 23(6), 377–379 (2011). [CrossRef]
12. K. Onohara, T. Sugihara, Y. Konishi, Y. Miyata, T. Inoue, S. Kametani, K. Sugihara, K. Kubo, H. Yoshida, and T. Mizuochi, “Soft-decision-based forward error correction for 100 Gb/s transport systems,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1258–1267 (2010). [CrossRef]
13. D. McGhan, C. Laperle, A. Savchenko, C. Li, G. Mak, and M. O'Sullivan, “5120-km RZ-DPSK transmission over G.652 fiber at 10 Gb/s without optical dispersion compensation,” IEEE Photon. Technol. Lett. 18(2), 400–402 (2006). [CrossRef]
14. H. Louchet, K. Kuzmin, and A. Richter, Improved DSP algorithms for coherent 16-QAM transmission,” in Proceeding ECOC 2008, paper Tu.1.E.6, Brussels, Belgium (2008).
15. N. A. D’Andrea and M. Luise, “Design and analysis of a jitter-free clock recovery scheme for QAM systems,” IEEE Trans. Commun. 41(9), 1296–1299 (1993). [CrossRef]
16. I. Fatadin, D. Ives, and S. J. Savory, “Laser linewidth tolerance for 16-QAM coherent optical systems using QPSK partitioning,” IEEE Photon. Technol. Lett. 22(9), 631–633 (2010). [CrossRef]
17. I. B. Djordjevic, O. Milenkovic, and B. Vasic, “Generalized low-density parity-check codes for optical communications systems,” J. Lightwave Technol. 23(5), 1939–1946 (2005). [CrossRef]
18. A. Bononi, P. Serena, N. Rossi, and D. Sperti, “Which is the dominant nonlineariy in long-haul PDM-QPSK coherent transmission?” in Proceeding ECOC 2010, paper Th10E1, Torino, Italy (2010).