Influence of self-and cross-phase modulation on 40 Gbaud dual polarization DQPSK / D 8 PSK signals in 10 Gbit / s OOK WDM systems

This paper, for the first time, investigates the nonlinear degradation of 40 Gbaud singleand dual polarization RZ-DQPSK/D8PSK signals caused by SPM and XPM-induced crosstalk from neighboring 10 Gbit/s NRZ-OOK channels in an WDM upgrade scenario. The investigations were numerically and experimentally conducted over a 320 km transmission link with three different wavelength configurations to address the impact of the walk-off length. The paper also presents the first numerical analysis of the XPM dependence on the relative state of polarization of the D8PSK with respect to the neighbors. ©2010 Optical Society of America OCIS codes: (060.2330) Fiber optics communications; (060.4080) Modulation. References and links 1. P. J. Winzer, and R. J. Essiambre, “Advanced Optical Modulation Formats,” Proc. IEEE 94(5), 952–985 (2006). 2. P. Govind, Agrawal, Nonlinear Fiber Optics (Academic Press, 1995), Chap. 7. 3. M. Lefrancois, F. Houndonougbo, T. Fauconnier, G. Charlet, and S. Bigo, “Cross comparison of the nonlinear impairments caused by 10Gbit/s neighboring channels on a 40Gbit/s channel modulated with various formats, and over various fiber types,” in Optical Fiber Communications Conference. paper JThA44 (2007) 4. X. Liu, and S. Chandrasekhar, “Suppression of XPM Penalty on 40-Gb/s DQPSK Resulting from 10-Gb/s OOK Channels by Dispersion Management,” in Optical Fiber Communications Conference, paper OMQ6 (2008) 5. M. S. Alfiad, D. van den Borne, T. Wuth, M. Kuschnerov, B. Lankl, C. Weiske, E. de Man, A. Napoli, and H. de Waardt, “111-Gb/s POLMUX-RZ-DQPSK Transmission over 1140 km of SSMF with 10.7-Gb/s NRZ-OOK neighbours,” in European Conference on Optical Communications, paper Mo.4.E.2 (2008) 6. E. Tipsuwannakul, M. Sköld, M. Karlsson, and P. Andrekson, “Transmission of 240 Gb/s PM-RZ-D8PSK over 320 km in 10 Gb/s NRZ-OOK WDM System,” in Optical Fiber Communications Conference, paper OMJ2 (2010) 7. C. Kim, and G. Li, “Direct-detection optical differential 8-level phase-shift keying (OD8PSK) for spectrally efficient transmission,” Opt. Express 12(15), 3415–3421 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-15-3415. 8. H. Wernz, S. Bayer, B. E. Olsson, M. Camera, H. Griesser, and C. Fürst, “112Gb/s PolMux RZ-DQPSK with Fast Polarization Tracking Based on Interference Control,” in Optical Fiber Communications Conference, paper OTuN4 (2009) 9. R. F. Pawula, S. O. Rice, and J. H. Roberts, “Distribution of the Phase Angle Between Two Vectors Perturbed by Gaussian Noise,” IEEE Trans. Commun. 30, 1828–1841 (1982) 10. X. Liu, S. Chandrasekhar, A. Gnauck, and X. Wei, “OSNR Margin Assessment for Optical Transmissions in the Nonlinear Regime with Forward Error Correction,” in Optical Fiber Communications Conference, paper ThN2 (2003) 11. M. Shtaif, and M. Eiselt, “Analysis of intensity interference caused by cross-phase modulation in dispersive optical fibers,” IEEE Photon. Technol. Lett. 10(7), 979–981 (1998). 12. J. Renaudier, O. Bertran-Pardo, G. Charlet, M. Salsi, M. Bertolini, P. Tran, H. Mardoyan, and S. Bigo, “On the Required Number of WDM Channels When Assessing Performance of 100Gb/s Coherent PDM-QPSK Overlaying Legacy Systems,” in European Conference on Optical Communications, paper 3.4.5 (2009) 13. M. Karlsson, and H. Sunnerud, “Effects of Nonlinearities on PMD-Induced System Impairments,” J. Lightwave Technol. 24, 4127–4137 (2006). #135171 $15.00 USD Received 15 Sep 2010; revised 22 Oct 2010; accepted 22 Oct 2010; published 3 Nov 2010 (C) 2010 OSA 8 November 2010 / Vol. 18, No. 23 / OPTICS EXPRESS 24178 14. D. Rafique, M. Forzati, and J. Mårtensson, “Impact of Nonlinear Fibre Impairments in 112 Gb/s PM-QPSK Transmission with 43 Gb/s and 10.7 Gb/s Neighbours,” in Proceedings of the International Conference on Transparent Optical Networks, paper We.D1.6. (2010) 15. O. Vassilieva, T. Hoshida, X. Wang, J. Rasmussen, H. Miyata, and T. Naito, “Impact of Polarization Dependent Loss and Cross-Phase Modulation on Polarization Multiplexed DQPSK Signals”, in Optical Fiber Communications Conference. paper OThU6 (2008).


Introduction
Over the past years, much attention has been devoted to identifying schemes capable of increasing the optical network capacities to meet the ever-growing bandwidth demands.One possible approach is to upgrade an existing on/off keying (OOK) channel in wavelength division multiplexing (WDM) systems with more sophisticated modulation formats.Differential phase shift keying (DPSK) formats have been suggested as potential candidates for such hybrid systems.This is due to not only their high spectral efficiency and robustness towards fiber nonlinearities [1], but also their good sensitivity and relatively simple receiver structures that provide cost-efficient systems, which can be very attractive for near-term commercialization.
XPM-induced phase shift coupling among co-propagating channels is, however, a major constraint of transmitting DSPK signals in the OOK WDM systems.This nonlinear process, always accompanied by self-phase modulation (SPM), is polarization dependent and dependent not only to the power of the probed signal but also to that of co-propagating channels [2].The process, hence, transfers the power variation of the temporally overlapping OOK signals into phase noise and leads to nonlinear degradation of the phase-modulated signal.As a result, the impact of XPM on DPSK formats in the OOK WDM systems has been extensively investigated to quantify system limitations [3][4][5][6].However, most of these studies focus on the quadrature DPSK (DQPSK) format.
In this paper, we report transmission of 40 Gbaud single polarization (SP) and dual polarization (DP) Return-to-Zero (RZ) 8-level DPSK (D8PSK) signals over a 320 km link in a 10 Gbit/s NRZ-OOK WDM environment.This, together with [6], is the first demonstration of D8PSK transmission at 40 Gbaud.We, furthermore, investigate the nonlinear degradation of the phase-modulated signal caused by SPM and XPM-induced coupling among the copropagating channels.The study is carried out in three different channel-spacing scenarios to quantify the impact of the walk-off length.Moreover, we analyze the XPM dependence on the state of polarization (SOP) of the phase-modulated signal relative to that of the neighboring OOK channels.The numerical and experimental results in this work are presented as a direct comparison with those of SP-and DP-RZ-DQPSK signals at the same baud-rate.Lastly, given the transmission distance and the channel spacing considered, the systems demonstrated here are highly relevant to an upgrade scenario as, for example, in metro-networks.

Numerical and experimental setups
This section describes the system implementation in both numerical and experimental setups.
The simulated system was modeled in VPItransmissionMaker®, according to that implemented in the experiment.An overview of the investigated system is illustrated in Fig. 1.
As can be seen, the system can be separated into four main parts: a DP-RZ-D8PSK transmitter, a 320 km transmission link, a DP-RZ-D8PSK receiver, and an NRZ-OOK WDM transmitter.The D8PSK signal and the OOK channels were multiplexed together into the transmission link via a 3-dB coupler.A filter (77 GHz 3-dB bandwidth flat top filter) was used to demultiplex the phase modulated signal in the receiver.The phase modulated transmitter and receiver, together with the transmission link is described in more detail below.

DP-RZ-D8PSK transmitter
As depicted in Fig. 2, the 40 Gbaud DP-RZ-D8PSK transmitter consists of a distributed feedback (DFB) laser with 1 MHz linewidth, a 30 GHz I/Q modulator, a 35 GHz phase modulator, and a Mach-Zehner (MZ) modulator for 50% duty cycle pulse carving.The I/Q modulator was driven by two of 40 Gbit/s binary data streams (D1 and D2), providing the 40 Gbaud DQPSK signal at the output.The phase modulator was driven by the third 40 Gbit/s binary data stream (D3), creating a π/4 phase shift to generate the D8PSK signal.Polarization multiplexing was realized by a 3-dB coupler, a variable optical delay, two polarization controllers (PCs), and a polarization beam combiner (PBC).
In the numerical setup, we emulated the modulator bandwidth by low-pass filtering the driving signals (D1, D2, and D3) with the bandwidth similar to those of the modulators.The differential encoder was also implemented in the way that original binary sequences (A, B, and C) could be obtained directly from the receiver [7].The original sequences used in the numerical setup were decorrelated De-Bruin bit sequences (DBBSs) with the length of 2 11 .In  the experimental setup, however, the modulators were directly driven by three decorrelated 2 11 -1 pseudo random bit sequences (PRBSs) due to the lack of an actual D8PSK encoder.Figure 3 illustrates the numerical (left) and experimental (right) constellations of 40 Gbaud SP-RZ-DQPSK and SP-RZ-D8PSK signals generated by the setups described above.Note that the constellations were captured with EXFO PSO-200 optical modulation analyzer.

Transmission link
The 320 km transmission link, which is shown in Fig. 4, was realized by four spans of 80 km standard single mode fiber (SSMF) and double-stage Erbium-doped fiber amplifiers (EDFAs) with a 12 km dispersion compensation fiber (DCF) in between.The average loss of the SSMFs and DCFs in each span were measured to be 18 and 12 dB, respectively.The chromatic dispersion (CD) at an operating wavelength of the DCFs is found to be approximately 110 ps/nm-km, yielding the accumulated CD of ~-1320 ps/nm.A variable optical attenuator (VOA) and the EDFA located after the four spans were used to vary OSNR into the receiver.In the numerical setup, however, we modeled the optical amplifiers as ideal noise-free EDFAs and all optical noise was added at the receiver.

DP-RZ-D8PSK receiver
Figure 5 shows a block diagram of the DP-RZ-D8PSK receiver.First, the SOP of the input signal to the receiver was manually adjusted via the PC.Then, the signal was polarization demultiplexed by a polarization beam splitter (PBS) and was uniformly distributed into four delay line interferometers (DLIs) with a free spectral range (FSR) of 43 GHz for differential demodulation.The demodulated signal from each DLI was later detected by balanced detectors.Since the encoder is implemented in the numerical setup, the original binary sequences (A, B) were obtained directly from the branches with + 3π/8 and -π/8 phase shifts applied in the DLIs while the last sequence (C) was retrieved from an exclusive-OR operation between the outputs of the two branches with + π/8 and 3π/8 phase shifts.In the experimental setup, however, we utilized a single DLI and the balanced detector and performed the bit-error-rate (BER) measurements by applying four different phase shifts into the DLI individually.The output from the balanced receiver was then fed into an error detector, which was programmed with expected differentially demodulated bit patterns.It should be noted that the SOP rotation of the input signal to the receiver is a vital issue in the differential detection system as it gives rise to the polarization crosstalk.This issue, however, can be solved by using, for instance, a polarization tracking device [8].

NRZ-OOK WDM transmitter
The four 10 Gbit/s NRZ-OOK WDM channels were realized by four tunable laser sources (TLSs) followed by a MZ modulator as shown in Fig. 1.These channels were later combined with the phase-modulated signal via a 3-dB coupler.In the experimental setup, we used PRBS sequences with a length of 2 31 -1 as a driving signal to the modulator.In the numerical setup, however, De Bruijn binary sequence (DBBS) with the length of 2 11 was used instead.Since, in the experiment, the four OOK channels were generated by the same modulator, the signals were co-polarized and correlated, yielding maximum nonlinear degradation of the probed signal.
For the XPM study, we investigate 3 different scenarios: (a) a single-wavelength system, 100 GHz-spaced WDM systems with (b) 200 GHz, and (c) 100 GHz separation to the nearest neighbors.The transmitted signal spectra of the three scenarios are also depicted in Fig. 7.

Single-wavelength back-to-back performance
The numerical back-to-back BER performances of 40 Gbaud SP-and DP-RZ-DQPSK/D8PSK as a function of signal OSNR are plotted in Fig. 7(a).The curves illustrate 6.5 dB OSNR difference between DQPSK and D8PSK signals for BER = 10 3 , which is in good agreement with the theoretical value (6.4 dB) reported in [9].The plot also depicts an expected 3 dB OSNR difference between SP and DP systems for both DQPSK and D8PSK signals.Note that such predetermined BER threshold can achieve the corrected BER = 10 15 , providing the forward error correction (FEC) overhead with enhanced Reed-Solomon (RS) with concatenation (e-FEC) is applied [10].Similar to Fig. 7(a), Fig. 7(b) shows the experimental back-to-back BER performance of the four modulation formats as a function of signal OSNR.The dashed lines represent the measured error rates corresponding to binary decision thresholds of all tributaries for the four modulation formats.Each tributary was measured individually by applying phase offsets to one arm of the DLI ( ± π/4 for DQPSK, and ± π/8, ± 3π/8 for D8PSK) on the orthogonal polarizations, corresponding to 4 and 8 curves for the DP system, respectively.By assuming that Gray coding is implemented and symbol errors only occur between nearest neighbors, BER (solid lines) of the system is the average of the dashed lines for the DQPSK signal but the average multiplied by 4/3 for the D8PSK signal [7].
Table 1 summarizes the required OSNR of the four formats for BER = 10 3 .As can be seen, the numerical sensitivities are comparable to the experimental results in the case of SP and DP-RZ-DQPSK signals.However, the experimental sensitivities of D8PSK signals are 2.0 to 2.5 dB worse than the numerical results.These excess penalties are likely caused by the extra phase modulator, which linearly transfers the electrical driving signal imperfections such as overshoots and ripples into the optical domain.

SPM and XPM-induced coupling among co-propagating channels
In this section, we study the 3 different scenarios depicted in Fig. 6.In (a), SPM is exclusively evaluated for the four modulation formats while in (b) and (c) the XPM-induced coupling among the co-propagating channels and the effect of the walk-off length are investigated.The input powers into DCFs were also kept 5 dB lower than those into SSMFs, which is a compromise between OSNR and fiber nonlinearities.Lastly, the power per WDM channel per polarization was kept equal.Note that the BER performances plotted in these figures are computed from all tributaries simulated/measured according to the preceding sections.In Fig. 8, we plot the (a) numerical and (b) experimental results of required OSNR for BER = 10 3 as a function of launched power per channel per polarization for the four modulation formats.From the figures, we observe that the results from the simulations are   consistent with those obtained from the experiments and both illustrate OSNR penalty caused by nonlinear impairments at high launch powers.In Fig. 9, we compare the nonlinear threshold (NLT) between the numerical and experimental results for all the cases.The NLT here is defined as the launch power, for which the required OSNR is increased by 1 dB compared to those at low launch powers, at which the impact of fiber nonlinearities are negligible.The plot shows that the NLT decreases with channel spacing, which can be understood from the fact that the XPM grows with the walk-off length [11], i.e. with the inverse channel spacing.Moreover, it shows less robustness towards fiber nonlinearities in the case of the SP-and DP-RZ-D8PSK signals (compared to DQPSK) due to narrower angular distances between symbols.One may also see in Fig. 9 the tradeoff between the bit-rate on the DPSK channel and the nonlinear tolerance.Such an increased nonlinear tolerance can in principle be translated in to extra SNR and longer transmission distance.For example, DP-DQPSK seems to be a better alternative than SP-D8PSK, offering both higher data rate and higher nonlinear threshold.On the other hand in future systems that may allow for adaptive bit-rates and modulation formats, this plot shows the tradeoff between transmission distance (i.e.nonlinear threshold), bit-rate and format.Note that several tens of neighboring channels are needed to accurately examine the XPM-induced degradation [12].In this work, the number of neighboring channels was, however, limited to four due to the hardware availability.Hence, an excess OSNR penalty can be expected when increasing the number neighboring channels.

Impact of relative SOP on XPM-induced nonlinearity
The following discussion will analyze the dependence of the XPM-induced penalty on the SOP of the DP-DxPSK signals relative to their neighbors.We report here the case of DP-DQPSK transmission with 200 GHz spacing from the nearest neighbors (similar results are observed for the other four cases).Figure 10, shows the required OSNR for BER = 10 3 versus launch power per channel per polarization, with the neighboring NRZ-OOK channels have linear horizontal polarization (LHP) (red curve), and linear + 45° polarization (black solid curve).For both cases the SOP of the two (x and y) polarization components of the DP-DQPSK/D8PSK channel at the transmitter is LHP and linear vertical polarization (LVP), respectively.At the transmitter, the SOP of the DP-DQPSK signal is 45°, + 45°, RHP and LHP, depending on the relative phase of x and y polarization components.In the presence of neighboring channels, however, according to the Manakov model, the SOP will rotate around the vector sum of all the wavelength's Stokes vectors at that instance of time [13].In the cases we study, this sum vector will be almost aligned with the Stokes vector of LHP and + 45° respectively.This sum vector is shown by the blue dots in Fig. 11, when ones are transmitted in the OOK neighbors.This polarization rotation will have a different impact in the two cases.When the OOK channels are LHP (Fig. 11a), the SOP of the DP-DQPSK channel will rotate roughly along the meridian through ± 45° (around one of the four blue dots in Fig. 11a) by an angle Φ p , which is proportional to the launch power, or more specifically, related to the XPM-induced nonlinear phase shift.This is equivalent to changing the relative phase of the data-carrying x and y polarization components.In other words, the polarization of the individual x and y polarization components will not change but, according to the Manakov model, the component that is parallel with the OOK neighbors will acquire a phase shift that is twice as large as the orthogonal component.
When the OOK channels are + 45° (Fig. 11b) the SOP of the DP-DQPSK channel will rotate roughly along the meridian through LHP and LVP (around one of the three blue dots in Fig. 11b and Fig. 11c).This is equivalent to introducing an ellipticity in the SOP of the datacarrying x and y components.The PBS at the receiver splits the DP DQPSK signal into LHP and LVP which are then a linear combination of data-carrying x and y components therefore introducing errors.
In order to avoid this mixing of x and y components on the output ports of the PBS, we should therefore rotate the SOP of the DP-DQPSK signal on the Poincaré sphere by -Φ p (this is done by default in the lab experiment because the SOP of the received signal is random, and a polarization controller is needed anyway).Numerically we do that through a wave plate (Fig. 11c), the bit error rate is reduced considerably.The required OSNR for BER = 10 3 versus launch power per channel per polarization is shown by the dashed curve in Fig. 10.For each launch power, an optimum SOP rotation angle, Φ p , is obtained by BER minimization.Figure 12 shows Φ p versus launch power per channel per polarization.As can be expected from theory [13] this grows with the nonlinear phase shift, i.e. linearly with the power.
As can be observed in Fig. 10, however, the SOP rotation by -Φ p still leaves a considerable residual penalty.The data-dependent non-linearity (giving higher induced phase shift when many 1's are being transmitted in the neighboring OOK channels, and less when many 0's are being transmitted) will translate into a phase variation when the OOK channels are LHP and into a residual amplitude variation and polarization crosstalk when the OOK channels are + 45°.For the current system setup the latter case results in higher penalty, which is in disagreement with some observations in other publications [14,15].In [14], no significant dependence on the relative polarization was observed for the case of coherent detection.This difference might be explained by the fact that differential detection is more tolerant to phase noise than e.g.coherent detection.In [15], however, the opposite dependence on relative polarization was observed in the case of differential detection, i.e. lower penalty was observed when the OOK neighbors were + 45°.One possible explanation is that in that case the bit rate of the DP-DQPSK channel was different.These issues have to be analyzed further.Last but not least, in Fig. 13 we plot the numerical and experimental OSNR penalty of the DP-RZ-D8PSK signal for BER = 10 3 with respect to launch powers.The plot shows that the experimental results lie in between those from the simulations due to the fact that, in the experiment, the SOP of the OOK channels relative to the phase modulated signal is uncontrolled at the transmitter and it gets further randomized during transmission.As a consequence, an intermediate situation between the two numerical cases can be expected.

Summary and conclusion
We numerically and experimentally investigate the impact of SPM and XPM on 40 Gbaud SP-and DP-RZ-DQPSK/D8PSK signals in 10 Gbit/s NRZ-OOK WDM systems over a 320 km transmission link.We find that, for the dual polarization system, D8PSK requires 7.5 dB higher OSNR and has roughly 2 dB lower NLT than DQPSK at the same baud-rate, which we attribute partly to the reduced distance between the levels in signal space, and partly to the less optimized D8PSK transmitter.We also observe an approximately 1-dB increased NLT when the nearest neighbors are placed 200 GHz away (compared to a 100 GHz case) from the phase-modulated signal due to a larger walk-off effect.Lastly, we found that in this system XPM induced Polarization crosstalk dominates XPM induced phase noise.SOP between the phase-modulated signal and the OOK neighbors.In the paper we analyze this in terms of SOP rotation, using the Manakov model.All in all, both the numerical and the experimental results we obtained are highly consistent.

Fig. 1 .
Fig. 1.An overview of the investigated system.OSA denotes an optical spectrum analyzer.

Fig. 6 .
Fig. 6.The transmitted signal spectra of 40 Gbaud DP-RZ-D8PSK signal in (a) a single wavelength system, 100 GHz-spaced WDM systems with (b) 200 GHz, and (c) 100 GHz separation to the nearest channels obtained from the numerical (left column) and experimental (right column) setups.

Fig. 8 .
Fig. 8. (a) numerical and (b) experimental signal OSNR required for BER = 10 3 of the four modulation formats as a function of launch power per channel per polarization over 320 km in three different scenarios: the single wavelength system (squares), 100 GHz-spaced WDM systems with 200 GHz (circles), and 100 GHz (diamonds) to the nearest channels.

Fig. 9 .
Fig. 9. Nonlinear Threshold of the four modulation formats in three different scenarios: the single wavelength system (squares), 100 GHz-spaced WDM systems with 200 GHz (circles), and 100 GHz (diamonds) to the nearest channels from both simulation (filled) and experiment (open).

Fig. 10 .
Fig. 10.Required OSNR for BER = 10 3 versus launch power per channel per polarization for a DP DQPSK channel co-propagating with four NRZ-OOK channels with 200 GHz between the central channel and the closest neighbors, with different SOP.

Fig. 11 .
Fig. 11.SOP of DP-DQPSK signal as measured in the middle of each symbol slot (red dots), after transmission at different launch powers, when the SOP of the NRZ OOK neighboring channels is LHP (a), + 45° (b); in (c) the signal shown in (b) passed through a wave plate; the blue dots are the vector sum of the Stokes vectors of all the wavelength channels at the transmitter.