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Using numerical simulations, we study and compare the performance of 42.8-Gb/s and 112-Gb/s intradyne coherent polarization-division-multiplexed quadrature-phase-shift-keying (PDM-QPSK) systems in wavelength-division-multiplexed (WDM) transmission with inline dispersion compensation fiber (DCF) and that with fully electronic dispersion compensation. Two effects are considered in the studies. One is fiber nonlinearities and the other is the local oscillator (LO) phase noise to amplitude noise conversion induced by electronic dispersion compensation. Results of 1000-km transmission employing standard single-mode fiber (SSMF) show that, for non-return-to-zero (NRZ) PDM-QPSK, both the 42.8-Gb/s and 112-Gb/s WDM systems with DCF have less tolerance to fiber nonlinearities than those with electronic dispersion compensation due to nonlinear polarization scattering. However, by using time-interleaved return-to-zero (RZ) PDM-QPSK, which can significantly suppress nonlinear polarization scattering in a system with inline DCF, the 42.8-Gb/s system with DCF can achieve better performance than that with electronic dispersion compensation, and comparable performance can be obtained for the 112-Gb/s system with DCF and that with electronic dispersion compensation. We find that the LO phase noise to amplitude noise conversion can cause significant penalties in the 112-Gb/s system with only electronic dispersion compensation if distributed feedback lasers are used.
©2009 Optical Society of America
1. Introduction
Optical coherent detection combined with digital signal processing (DSP) is considered a promising technique for next generation optical networks [1–4]. With the full optical field information accessible after coherent detection, optical coherent systems have the potential to increase the spectral efficiency and the ability to perform transmission impairment compensation and polarization demultiplexing for polarization-division-multiplexed (PDM) signals in the electrical domain by high-speed DSP. PDM quadrature-phase-shift-keying (PDM-QPSK) with intradyne coherent detection is considered as a possible solution to upgrade existing 10-Gb/s dense wavelength-division-multiplexed (WDM) networks with 50-GHz channel spacing to 40-Gb/s or 100-Gb/s.
With powerful DSP, coherent receivers have the ability to entirely compensate chromatic dispersion in the electrical domain, thus completely eliminating optical dispersion compensation modules (DCMs) in the systems. It is well known that lumped dispersion compensation at the transmitter or receiver is suboptimal for nonlinear transmission in a WDM system compared with dispersion management, which distributes DCMs along a transmission link, with dispersion pre-compensation and post-compensation at the transmitter and receiver [5–7]. Dispersion management was developed based on single-polarization (SP) signals with direct detection. It can effectively reduce intra-channel and inter-channel nonlinear impairments in such systems.
However, it was shown recently by both experiments and simulations that a WDM coherent PDM-QPSK system with dispersion management may perform worse than that without dispersion management [8, 9]. We found that the main reason why dispersion management performed worse in these cases was nonlinear polarization scattering in PDM-QPSK systems, which was more severe in a dispersion-managed system than in a system without any inline DCMs [10]. We also showed that by using time-interleaved return-to-zero (RZ) PDM-QPSK, where the RZ symbols on the two polarizations are shifted by half a symbol in time, a 42.8-Gb/s WDM coherent PDM-QPSK system in a 1000-km non-zero dispersion-shifted fiber (NZDSF) link with dispersion management could achieve better performance than that with electronic dispersion compensation entirely at the receiver [10].
In this paper, we study and compare the performance of 42.8-Gb/s and 112-Gb/s WDM coherent PDM-QPSK systems in a 1000-km standard single-mode fiber (SSMF) transmission link with inline dispersion compensation fiber (DCF) and that with electronic dispersion compensation entirely at the receiver. Both NRZ-PDM-QPSK and time-interleaved RZ-PDM-QPSK are studied. In addition to fiber nonlinearities, the local oscillator (LO) phase noise to amplitude noise conversion induced by electronic dispersion compensation is also considered [11, 12].
Alternatively, inter-channel XPM and nonlinear polarization scattering can be suppressed by using periodic-group-delay (PGD) chromatic dispersion compensators in a dispersion-managed system [13]. Combination of the PGD chromatic dispersion compensators and time-interleaved RZ-PDM-QPSK could further improve the coherent system tolerance to nonlinearities. These will be discussed in a separate paper.
2. Impact of nonlinear polarization scattering and LO phase noise on PDM-QPSK coherent systems
There are two fiber nonlinear effects in a fiber-optic WDM transmission system: intra-channel nonlinearities and inter-channel nonlinearities. Intra-channel nonlinearities come from self-phase modulation (SPM), which generates intra-channel four-wave mixing (FWM) and intra-channel cross-phase modulation (XPM) in pseudo-linear transmission systems. It has been shown that intra-channel nonlinearities can be significantly reduced by dispersion management [5]. Inter-channel nonlinearities originate from inter-channel XPM between channels in a WDM system. Inter-channel XPM induces timing jitter and nonlinear phase noise, which can also be minimized by using dispersion management [7]. In addition to those, inter-channel XPM also causes nonlinear polarization rotation, which in general can be neglected in a system using SP signals but will have a significant impact on a system using PDM signals [14, 15].
Nonlinear polarization rotation of channel A caused by channel B in a WDM system can be described as [14, 16]
where S⃗a and S⃗b are Stokes vectors for the SOPs of channels A and B, Pb is the power of channel B, γ is the Kerr nonlinearity coefficient. The evolution of S⃗b can be obtained by exchanging the subscripts in Eq. (1). If different symbols of a channel experience different nonlinear polarization rotations, nonlinear polarization scattering occurs, which causes crosstalk between two polarizations in a PDM system and significantly degrades the system performance. It is hard to compensate nonlinear polarization scattering using either optical or electrical methods as the SOP of the signal having nonlinear polarization scattering changes as fast as the symbol rate.
The SOPs of a PDM signal at different times are usually data dependent, and the data dependent SOPs in general cause large nonlinear polarization scattering in WDM transmission. For a NRZ-PDM-QPSK or synchronized RZ-PDM-DQPSK signal, the SOPs at different symbols change among four points on the Poincaré sphere, depending on data on each polarization, as shown in Figs. 1(a) and 1(b). In a dispersion-managed system with inline DCF, the pulses suffer minimally from chromatic dispersion accumulation, and the SOP of the PDM-QPSK signal remains nearly fixed to these four points. The few data dependent SOPs and small walk off between channels increase the nonlinear polarization scattering. For a system without DCF, the pulses are rapidly broadened by chromatic dispersion and the SOPs of the signal at different times spread over the whole Poincaré Sphere. The averaging effect of rapid SOP spread and large walk off between channels reduce the nonlinear polarization scattering effect in a system without DCF.
Fig. 1. (a) Waveform of NRZ-PDM-QPSK (dashed lines) and synchronized RZ-PDM-DQPSK (solid lines), (b) SOP of the PDM-QPSK signal in (a) on the Poincaré sphere, (c) Waveform of time-interleaved RZ-PDM-QPSK, (d) SOP of the time-interleaved RZ-PDM-DQPSK signal on the Poincaré sphere. Ts: symbol period.
One technique to suppress nonlinear polarization scattering in a dispersion-managed PDM system is to use RZ signals and time interleave the two polarizations by half a symbol period, as shown in Fig. 1(c) [10, 15]. The time-interleaved RZ-PDM signal has three features that help reduce nonlinear polarization scattering in a dispersion-managed system: 1) the SOP at each symbol alternates between S1 and -S1 on the Poincaré sphere, independent of the data, as shown in Fig. 1(d); 2) the SOP at S1 and -S1 causes opposite nonlinear polarization rotation according to Eq. (1); and 3) the time interleaving reduces the signal peak power [17]. Please note that using time-interleaved RZ-PDM signal in a system without inline DCMs does not provide much improvement, as pulses broaden rapidly in the propagation. Time-interleaving NRZ-PDM-QPSK does not get any benefit either, as none of the above features for time-interleaved RZ-PDM-QPSK can be obtained for time-interleaved NRZ-PDM-QPSK.
Another effect that needs to be considered when comparing a coherent system with and without optical DCMs is LO phase noise [11, 12]. Laser phase noise is expected to be converted to amplitude noise by chromatic dispersion in an optical communication system. In a coherent system without electronic dispersion compensation at the transmitter, as the net dispersion experienced by transmitter phase noise is close to zero, transmitter phase noise to amplitude noise conversion is negligible. However, as LO phase noise only goes through electronic chromatic dispersion compensator at the receiver, which has large chromatic dispersion in a system without optical DCMs, LO phase noise could significantly degrade the performance of a high-speed coherent system with only electronic chromatic dispersion compensation at the receiver through phase noise to amplitude noise conversion (chromatic dispersion causes little phase spread changes but large amplitude fluctuations, as shown in [11]). Since the amplitude noise at the receiver is proportional to the signal bandwidth, the LO phase noise to amplitude noise conversion induced penalty increases with the symbol rate [11, 12]. For a system with DCMs, the LO phase noise to amplitude noise conversion is negligible as chromatic dispersion provided by electronic dispersion compensator at the receiver is small.
3. System model
The system model is shown in Fig. 2. There are seven channels with 50-GHz channel spacing. In the transmitter, CW light is modulated with a nested Mach-Zehnder QPSK modulator by 211 De Bruijn bit sequence at 21.4 Gb/s or 56-Gb/s. For RZ-QPSK signal, a 50% duty cycle RZ pulse carver is used after the QPSK modulator. The QPSK signal splits into two parts, and the two parts are shifted relatively by about 511 symbols and combined with a polarization beam combiner (PBC) to form a 42.8-Gb/s or 112-Gb/s PDM-QPSK signal, as shown in Fig. 1(b). The QPSK signal is differentially encoded to avid phase ambiguity [1]. The transmission line consists of 10 spans of SSMF with chromatic dispersion coefficient of 17.0 ps/(nm.km), nonlinear coefficient of 1.17 (km.W)-1 and loss coefficient of 0.21 dB/km. The span length is 100 km and lumped amplification is provided by erbium-doped fiber amplifiers (EDFAs). For the system with DCF, the dispersion map consists of -400 ps/nm dispersion pre-compensation, and 30 ps/nm residual dispersion per span.
The block diagram of the PDM-QPSK coherent receiver is depicted in Fig. 2(c). After passing through a polarization beam splitter (PBS), each polarization of the demultiplexed signal is combined with a LO in a 90° hybrid. Three LO linewidths are studied, which are 0, 2 MHz and 4 MHz. After the hybrids, the four tributaries of the signal are detected by four balanced detectors and sampled at two samples per symbol. The DSP is comprised of four steps: 1) chromatic dispersion compensation with two finite impulse response (FIR) filters (the numbers of taps are 101 and 335 for the 42.8-Gb/s and 112-Gb/s systems without DCF, respectively, and 35 for the system with DCF); 2) polarization demultiplexing with four 7-tap FIR filters employing the Constant Modulus Algorithm (CMA) [2, 18]; 3) carrier phase estimation using the block Mth-power scheme [1]. Block length of 10 is used in the carrier phase estimation; and 4) symbol identification. The bit error rate (BER) is evaluated by counting errors.
Fig. 2. System model. (a) transmission line, (b) block diagram of the PDM-QPSK transmitter, (c) block diagram of the coherent receiver. The DCF shown are removed for systems without DCF. Tx: transmitter, Rx: receiver, BD: balanced detector, CD: chromatic dispersion.
In the simulations, the signal of 1024 symbols first propagates in the transmission line. The bit sequence length is sufficient to catch the nonlinear interaction for the system studied here [19]. Then amplified spontaneous emission (ASE) noise is loaded at the receiver side. 204,800 symbols with 200 different ASE noise and LO phase noise realizations are used to calculate BER.
4. Results and discussions
4.1 42.8-Gb/s PDM-QPSK Systems
The transmission performance of the 42.8-Gb/s synchronized NRZ-PDM-QPSK and time-interleaved RZ-PDM-QPSK are given in Fig. 3, which shows the required OSNR at BER of 10-3 after 1000 km transmission for the system with and without DCF at three LO line widths: 0, 2 MHz and 4 MHz. It shows that, using synchronized NRZ-PDM-QPSK, the system with DCF is less tolerant to fiber nonlinearities than that without DCF. The allowed launch power at 1-dB penalty is about 2-dB lower for the system with DCF compared to the system without DCF. However, when the time-interleaved RZ-PDM-QPSK is used, the nonlinear tolerance of the system with DCF is significantly increased. The allowed launch power at 1-dB penalty for the system with DCF is about 4-dB higher than that without DCF. It also shows that the penalty caused by LO phase noise is similar for the system with and without DCF, about 0.2 dB and 0.4 dB for the line widths of 2 MHz and 4 MHz respectively, which indicates that the chromatic dispersion induced phase noise to amplitude noise conversion is small at this symbol rate and distance [11] and the penalty is caused by LO phase noise itself [20].
To estimate the level of the nonlinear polarization scattering, we calculate the degree of polarization (DOP) of a 21.4-Gb/s SP-QPSK channel surrounded by six 42.8-Gb/s PDM-QPSK channels with 50-GHz channel spacing, as shown in Fig. 4. For the synchronous NRZ-PDM-QPSK system with inline DCF, DOP decreases rapidly with the launch power, indicating that the nonlinear polarization scattering significantly depolarizes the signal on each polarization for the PDM signal and induces a large crosstalk between the two polarizations. When time-interleaved RZ-PDM-QPSK is used, the nonlinear polarization scattering is greatly suppressed and DOP reduction is much smaller. For the system without DCF, the nonlinear polarization scattering is small and the system penalties mainly come from inter-channel XPM and intra-channel nonlinearities.
Fig. 3. Required OSNR at BER of 10-3 after 1000-km transmission versus launch power per channel for the 42.8-Gb/s synchronized NRZ-PDM-QPSK coherent system (a), and time-interleaved RZ-PDM-QPSK coherent system (b). The solid, dash and dotted lines are for LO linewidths of 0, 2 MHz and 4 MHz respectively.
Fig. 4. DOP of the 21.4-Gb/s SP-QPSK reference channel after 1000 km transmission versus launch power per channel for the synchronized NRZ-PDM-QPSK and time-interleaved RZ-PDM-QPSK system. Solid lines: surrounding channels are 42.8-Gb/s synchronized NRZ-PDM-QPSK, dashed lines: surrounding channels are 42.8-Gb/s time-interleaved RZ-PDM-QPSK.
Figure 5 depicts the received signal constellation diagrams of one polarization after equalization and carrier phase estimation for a 42.8-Gb/s synchronized NRZ-PDM-QPSK channel after 1000-km WDM transmission. The results of different system configurations are given: with and without DCF, and with SP-QPSK and PDM-QPSK surrounding channels. The same launch power per channel (4 dBm) is used for all the configurations. It shows that when the synchronized NRZ-PDM-QPSK channel is surrounded by 21.4-Gb/s NRZ-SP-QPSK channels, the system with DCF can achieve better performance than that without DCF, as shown in Figs. 5(a) and 5(b). However, when the surrounding channels are 42.8-Gb/s NRZ-PDM-QPSK signals, the system with DCF performs much worse than that without DCF, as shown in Figs. 5(c) and 5(d). Results in Figs. 4 and 5 clearly indicate that it is the nonlinear polarization scattering caused by the other PDM-QPSK channels that make the NRZ-PDM-QPSK system with DCF perform worse than the system without DCF. We note that Fig. 5(d) has a clearer constellation than Fig. 5(b). This is due to the reduced peak power for a PDM-QPSK signal compared with a SP-QPSK signal for a given average power.
Fig. 5. Signal constellation diagrams of X polarization of a 42.8-Gb/s synchronized NRZ-PDM-QPSK channel after 1000-km WDM transmission at OSNR = 16 dB. (a) and (b): surrounding channels are 21.4-Gb/s NRZ-SP-QPSK, (c) and (d): surrounding channels are 42.8-Gb/s NRZ-PDM-QPSK. (a) and (c) for the system with DCF and (b) and (d) without DCF. The launch power per channel is 4 dBm. LO linewidth is zero.
Fig. 6. Required OSNR after 1000-km transmission versus launch power per channel for the 112-Gb/s synchronized NRZ-PDM-QPSK coherent system (a), and time-interleaved RZ-PDM-QPSK coherent system (b). The solid, dash and dotted lines are for LO linewidths of 0, 2 MHz and 4 MHz respectively.
4.2 112-Gb/s PDM-QPSK Systems
The performance of the 112-Gb/s synchronized NRZ-PDM-QPSK and time-interleaved RZ-PDM-QPSK coherent system with and without DCF are shown in Fig. 6. The results of three LO linewidths, 0, 2 MHz and 4 MHz, are given. Similar to the 42.8-Gb/s systems, when the synchronized NRZ-PDM-QPSK is used, the system with DCF can tolerate less fiber nonlinearities than that without DCF. The launch power at 1-dB penalty is about 2-dB lower for the system with DCF compared to the system without DCF if the LO phase noise effect is not considered. By using the time-interleaved RZ-PDM-QPSK, the nonlinear tolerance of the system with DCF is increased and comparable with the system without DCF. The performance difference of the synchronized NRZ-PDM-QPSK and the time-interleaved RZ-PDM-QPSK for the 112-Gb/s system with DCF is reduced compared with that for the 42.8-Gb/s system. We attribute this to two reasons. One is that with the increase of symbol rate, nonlinear polarization scattering and other inter-channel nonlinear effects become smaller due to the averaging effect (same walk off time covers more symbols) [16]. The other reason is that when symbol rate is higher, the pulses are more broadened during propagation, and the SOPs of the symbols cannot be always maintained in a system with DCF as that shown in Fig. 1(d).
With the increase of symbol rate, the penalty caused by laser phase noise itself is reduced [11, 20]. For the system with DCF, the LO phase noise to amplitude noise conversion is negligible as the chromatic dispersion experienced by LO phase noise is small. Therefore, for the 112-Gb/s coherent PDM-QPSK system with DCF, there is little performance difference among 0, 2 MHz and 4 MHz LO linewidths, as shown in Fig. 6. However, for the 112-Gb/s coherent PDM-QPSK system without DCF, the penalty caused by the LO phase noise to amplitude noise conversion cannot be neglected anymore, which is about 0.4 and 0.8 dB for 2-MHz and 4-MHz linewidths, respectively. Fig. 6 shows that with 4-MHz LO linewidth, at 1-dB penalty the system with DCF has similar performance as that without DCF if the synchronized NRZ-PDM-QPSK is used, whereas if the time-interleaved RZ-PDM-QPSK is used, the system with DCF is about 1.5 dB better than that without DCF.
Fig. 7. DOP of the 56-Gb/s SP-QPSK reference channel after 1000 km transmission versus launch power per channel for the synchronized NRZ-PDM-QPSK and time-interleaved RZ-PDM-QPSK system. Solid lines: surrounding channels are 112-Gb/s synchronized NRZ-PDM-QPSK, dashed lines: surrounding channels are 112-Gb/s time-interleaved RZ-PDM-QPSK.
Figure 7 depicts the depolarization caused by the nonlinear polarization scattering in the 112-Gb/s PDM-QPSK systems. The DOP of a 56-Gb/s SP-QPSK channel surrounded by six 112-Gb/s PDM-QPSK channels with 50-GHz channel spacing is calculated. Similar to the 42.8-Gb/s systems, the time-interleaved RZ-PDM-QPSK has smaller nonlinear polarization scattering than the synchronized NRZ-PDM-QPSK in the system with DCF. In the system without DCF, the nonlinear polarization scattering is small, and the system penalties mainly come from inter-channel XPM and intra-channel nonlinearities. Fig. 7 also shows that the decrease of the DOP in the 112-Gb/s synchronized NRZ-PDM-QPSK system with DCF is slower than that in the 42.8-Gb/s system, and the DOP difference between the synchronized NRZ-PDM-QPSK system and the time-interleaved RZ-PDM-QPSK system with DCF for the 112-Gb/s bit rate is smaller than that for the 42.8-Gb/s bit rate, consistent with the results in Fig. 6.
Note that we used a typical dispersion map for a SP on-off-keying system. The performance of the time-interleaved RZ-PDM-QPSK system could be further improved by optimizing dispersion maps. The benefits of the timing interleaving could be reduced by PMD. Those issues are subject to further investigation.
5. Conclusions
We have studied and compared the performance of the 42.8-Gb/s and 112-Gb/s PDM-QPSK intradyne coherent systems with and without inline DCF in a 1000-km SSMF transmission. Two effects are considered in the studies. One is the fiber nonlinearities and the other is the LO phase noise to amplitude noise conversion induced by electronic dispersion compensation. We found that nonlinear polarization scattering could severely degrade the performance of a PDM-QPSK system with dispersion management, but can be significantly suppressed by using time-interleaved RZ-PDM signals. Using time-interleaved RZ-PDM-QPSK, the 42.8-Gb/s system with DCF can achieve better tolerance to fiber nonlinearities than that with electronic dispersion compensation, and comparable performance can be obtained for the 112-Gb/s system with DCF and that with electronic dispersion compensation. We showed that the LO phase noise to amplitude noise conversion can not be neglected for the 112-Gb/s system with electronic dispersion compensation if distributed feedback lasers are used.
Acknowledgment
The author is grateful to acknowledge valuable discussions with R. W. Tkach and R. -J. Essiambre.
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