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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 1 — Jan. 14, 2013
  • pp: 276–288
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Experimental demonstration of a frequency-domain Volterra series nonlinear equalizer in polarization-multiplexed transmission

Fernando P. Guiomar, Jacklyn D. Reis, Andrea Carena, Gabriella Bosco, António L. Teixeira, and Armando N. Pinto  »View Author Affiliations


Optics Express, Vol. 21, Issue 1, pp. 276-288 (2013)
http://dx.doi.org/10.1364/OE.21.000276


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Abstract

Employing 100G polarization-multiplexed quaternary phase-shift keying (PM-QPSK) signals, we experimentally demonstrate a dual-polarization Volterra series nonlinear equalizer (VSNE) applied in frequency-domain, to mitigate intra-channel nonlinearities. The performance of the dual-polarization VSNE is assessed in both single-channel and in wavelength-division multiplexing (WDM) scenarios, providing direct comparisons with its single-polarization version and with the widely studied back-propagation split-step Fourier (SSF) approach. In single-channel transmission, the optimum power has been increased by about 1 dB, relatively to the single-polarization equalizers, and up to 3 dB over linear equalization, with a corresponding bit error rate (BER) reduction of up to 63% and 85%, respectively. Despite of the impact of inter-channel nonlinearities, we show that intra-channel nonlinear equalization is still able to provide approximately 1 dB improvement in the optimum power and a BER reduction of ∼33%, considering a 66 GHz WDM grid. By means of simulation, we demonstrate that the performance of nonlinear equalization can be substantially enhanced if both optical and electrical filtering are optimized, enabling the VSNE technique to outperform its SSF counterpart at high input powers.

© 2013 OSA

1. Introduction

Thanks to coherent detection, digital equalization of linear fiber impairments can nowadays be performed with negligible penalty. The ultimate limits of fiber capacity are then set by nonlinearities and their interaction with noise [1

1. A. N. Pinto and G. P. Agrawal, “Nonlinear interaction between signal and noise in optical fibers,” J. Lightw. Technol. 26, 1847–1853 (2008). [CrossRef]

]. The development of efficient nonlinear compensation algorithms is therefore of utmost importance. The issue of nonlinear compensation has been most commonly approached through digital backward propagation (DBP) employing split-step Fourier (SSF) methods [2

2. E. Ip and J. M. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightwave Technol. 26, 3416–3425 (2008). [CrossRef]

, 3

3. F. Yaman and G. Li, “Nonlinear impairment compensation for polarization-division multiplexed WDM transmission using digital backward propagation,” IEEE Photon. J. 2, 816–832 (2010). [CrossRef]

]. Recently, new algorithms based on Volterra series theory have been reported either in time [4

4. Z. Pan, B. Chatelain, M. Chagnon, and D. V. Plant, “Volterra filtering for nonlinearity impairment mitigation in DP-16QAM and DP-QPSK fiber optic communication systems,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2011), paper JThA040.

] or frequency-domain [5

5. F. P. Guiomar, J. D. Reis, A. L. Teixeira, and A. N. Pinto, “Mitigation of intra-channel nonlinearities using a frequency-domain Volterra series equalizer,” Opt. Express 20, 1360–1369, (2012). [CrossRef] [PubMed]

]. In [5

5. F. P. Guiomar, J. D. Reis, A. L. Teixeira, and A. N. Pinto, “Mitigation of intra-channel nonlinearities using a frequency-domain Volterra series equalizer,” Opt. Express 20, 1360–1369, (2012). [CrossRef] [PubMed]

], an intra-channel Volterra series nonlinear equalizer (VSNE) applied in frequency-domain has been proposed and assessed through numerical simulations. The VSNE algorithm can be beneficial for real-time implementation due to its parallel structure, while maintaining very high equalization performance even at 2 samples per symbol [5

5. F. P. Guiomar, J. D. Reis, A. L. Teixeira, and A. N. Pinto, “Mitigation of intra-channel nonlinearities using a frequency-domain Volterra series equalizer,” Opt. Express 20, 1360–1369, (2012). [CrossRef] [PubMed]

].

Digital compensation of single-polarization inter-channel [6

6. L. Zhu, F. Yaman, and G. Li, “Experimental demonstration of XPM compensation for WDM fibre transmission,” Electron. Lett. 46, 1140–1141 (2010). [CrossRef]

] and dual-polarization intra-channel [7

7. S. J. Savory, G. Gavioli, E. Torrengo, and P. Poggiolini, “Impact of interchannel nonlinearities on a split-step intrachannel nonlinear equalizer,” IEEE Photon. Technol. Lett. 22, 673–675 (2010). [CrossRef]

] effects has been already experimentally demonstrated using SSF approaches. Time-domain Volterra series filtering has been demonstrated in single-polarization QPSK transmission [8

8. F. Zhang, Y. Gao, Y. Luo, J. Li, L. Zhu, L. Li, Z. Chen, and A. Xu, “Experimental demonstration of intra-channel nonlinearity mitigation in coherent QPSK systems with nonlinear electrical equaliser,” Electron. Lett. 46, 353–355 (2010). [CrossRef]

] at 10 Gbaud, using 5 samples per symbol. A recent experimental demonstration of the single-polarization VSNE algorithm has been reported for a 28 Gbaud polarization-multiplexed (PM)-16QAM transmission over 250 km of ultra-large area fiber [9

9. H.-M. Chin, J. Mårtensson, and M. Forzati, “Volterra based nonlinear compensation on 224 Gb/s PolMux-16QAM optical fibre link,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2012), paper JW2A.61.

]. However, these performance assessments of Volterra series equalization are limited by their underlying single-polarization model. Although a dual-polarization nonlinear equalizer based on the regular perturbation method has been recently proposed [10

10. L. Liu, L. Li, Y. Huang, K. Cui, Q. Xiong, F. N. Hauske, C. Xie, and Y. Cai, “Intrachannel nonlinearity compensation by inverse Volterra series transfer function,” J. Lightwave Technol. 30, 310–316 (2012). [CrossRef]

], its performance is only assessed through simulations.

2. Theoretical formulation

The propagation of polarization-multiplexed optical signals can be analytically modeled by the nonlinear Schrödinger (NLS) equation in its vectorial form. However, being a complex and computationally expensive model, the vectorial NLS equation is not adequate for DBP. To overcome this complexity issue, the vectorial model can be replaced by the Manakov equation. This simplified approach is based on the observation that, since the polarization scattering length is much shorter than the typical nonlinear interaction length, the resulting nonlinearities can be determined with small penalty by averaging the fast polarization changes along the fiber. Then, using the Manakov equation we may analytically describe DBP as [3

3. F. Yaman and G. Li, “Nonlinear impairment compensation for polarization-division multiplexed WDM transmission using digital backward propagation,” IEEE Photon. J. 2, 816–832 (2010). [CrossRef]

]
Ax/y(z)=α2Ax/y+iβ222Ax/yt2i8γ9(|Ax|2+|Ay|2)Ax/y,
(1)
where Ax/y is the slowly varying complex field envelope in the x/y states of polarization, z and t are the spatial and temporal coordinates respectively, α is the attenuation coefficient, β2 accounts for chromatic dispersion and γ is the nonlinearity parameter.

Starting from Eq. (1) we may redefine the frequency-domain Volterra series nonlinear equalizer derived in [5

5. F. P. Guiomar, J. D. Reis, A. L. Teixeira, and A. N. Pinto, “Mitigation of intra-channel nonlinearities using a frequency-domain Volterra series equalizer,” Opt. Express 20, 1360–1369, (2012). [CrossRef] [PubMed]

] in order to account for polarization-dependent nonlinear crosstalk,
A˜eqx/y(ωn)=89n2=1NFFTn1=1NFFTK3P(ωn1,ωn2)A˜rxx/y(ωnωn1+ωn2),
(2)
where Ãrxx/y and Ãeqx/y are the Fourier transforms of the received and nonlinearly equalized electrical fields after each fiber span, in both states of polarization, and K3 is an abbreviation of the inverse third-order Volterra kernel, K3(ωn1, ωn2, ωnωn1 + ωn2, z), which is defined as
K3(ωn1,ωn2,ωnωn1+ωn2)=iξγexp(α2Lspaniβ22ωn2Lspan)×1exp(αLspaniβ2(ωn1ωn)(ωn1ωn2)Lspan)α+iβ2(ωn1ωn)(ωn1ωn2),
(3)
where Lspan represents the length of each fiber span and 0 < ξ ≤ 1 is an optimization factor to control the optimum amount of nonlinear compensation, similarly to the SSF method [2

2. E. Ip and J. M. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightwave Technol. 26, 3416–3425 (2008). [CrossRef]

]. The P(ωn1, ωn2) term refers to the coherent cross-polarization power transfer, being given by
P(ωn1,ωn2)=A˜rxx(ωn1)A˜rxx*(ωn2)+A˜rxy(ωn1)A˜rxy*(ωn2).
(4)
Equation (2) is applied span-by-span for each angular frequency, ωn, composing the signal spectrum. By scanning the spectrum of interest with the auxiliary angular frequencies, ωn1 and ωn2, the nonlinear equalizer is evaluated over a memory range of NFFT samples, corresponding to the length of each fast-Fourier transform (FFT) block. Finally, a phase correction can be applied to the output field in order to avoid energy divergence [12

12. B. Xu and M. Brandt-Pearce, “Modified Volterra series transfer function method,” IEEE Photon. Technol. Lett. 14, 47–49 (2002). [CrossRef]

]. Regarding numerical complexity, only an extra NFFT2 complex additions per sample are required, relatively to the single-polarization VSNE.

3. Experimental demonstration

3.1. Experimental setup

In this work, we will consider two distinct major experimental setups, which are summarized in Table 1. A simplified schematic representation of all experimental scenarios is presented in Fig. 1. The differences between scenarios A and B lie on the transmitter side and on the propagation fiber. In experimental setup A, the transmitted signal is a Nyquist-shaped 30 Gbaud PM-QPSK, which is propagated in a recirculating loop consisting of a single 100 km NZDSF spooled span. In turn, setup B is based on a 25 Gbaud PM-QPSK signal recirculated over 63.6 km of installed SSMF (FASTWEB’s Turin Metro Plant). Additionally, within experimental setup A we will consider three different sub-scenarios: A.1, which is a single-channel experiment; A.2, which is based on a 66 GHz-spaced 10-channel WDM experiment; and A.3, which is a 10-channel ultra-dense WDM experiment (33 GHz interchannel spacing). In all scenarios, the central channel is optically generated by an external cavity laser (ECL) with 100 kHz linewidth. In scenarios A.2 and A.3, additional distributed feedback (DFB) lasers are used to generate the WDM signal. A pulse pattern generator (PPG) outputs the digital data, which is modulated onto the optical field by a nested Mach-Zehnder (NMZ) modulator. A WaveShaper™ (WS) is employed in setup A, providing a Nyquist pulse shaping to the transmitted optical signal [13

13. G. Gavioli, E. Torrengo, G. Bosco, A. Carena, S. J. Savory, F. Forghieri, and P. Poggiolini, “Ultra-narrow-spacing 10-channel 1.12 Tb/s D-WDM long-haul transmission over uncompensated SMF and NZDSF,” IEEE Photon. Technol. Lett. 22, 1419–1421 (2010). [CrossRef]

]. The −3 dB bandwidth of the WaveShaper™ filter has been set to 32 GHz, and a ∼2 dB pre-emphasis towards the filter sides has been applied to enhance high frequencies, partially compensating for the receiver bandwidth limitation. In setup A.3, an optical frequency doubler (OFD) is used to halve the inter-channel frequency spacing from 66 GHz down to 33 GHz [14

14. E. Torrengo, R. Cigliutti, G. Bosco, A. Carena, V. Curri, P. Poggiolini, A. Nespola, D. Zeolla, and F. Forghieri, “Experimental validation of an analytical model for nonlinear propagation in uncompensated optical links,” in European Conference and Exhibition on Optical Communication, OSA Technical Digest (Optical Society of America, 2011), paper We.7.B.2.

]. Finally, polarization-multiplexing (PolMux) is emulated by applying an optical delay line. The delay between the two polarization tributaries is of 882 symbols (29.4 ns) for scenario A and 916 symbols (36.64 ns) for scenario B, thus ensuring polarization de-correlation. The transmitted signal is then propagated in a recirculating fiber loop controlled by acousto-optic switches (AOS). Optical power at the fiber input and output is controlled by two pairs of erbium-doped fiber amplifiers (EDFA) cascaded with variable optical attenuators (VOA). A gain flattening filter is employed to equalize power level in all channels, compensating for EDFA unbalancing. After coherent detection, the four resulting electrical signals are finally sampled at 50 Gsample/s in a Tektronix DPO71604 and stored for subsequent offline processing. Given the different symbol rates, the sampling rates provided for the DSP system are 1.67 and 2 samples per symbol (SpS), for scenarios A and B, respectively.

Fig. 1 Experimental setup of the PM-QPSK transmission system. PPG - pulse pattern generator; NMZ - nested Mach-Zehnder; WS - Finisar’s WaveShaper™; OFD - optical frequency doubler; VOA - variable optical attenuator. The dashed blocks indicate optional equipment: the WS filter is only used in setup A; the DFB lasers are employed in the WDM scenarios A.2 and A.3; the OFD is only required in scenario A.3, in order to halve the interchannel spacing from 66 GHz down to 33 GHz.

Table 1. Experimental setup parameters. Δf - inter-channel spacing; Rs - symbol rate.

table-icon
View This Table

3.2. DSP system

A block diagram representing the DSP system is presented in Fig. 2.

Fig. 2 Sequential application of DSP subsystems for offline processing of the received signal samples stored by the Tektronix DPO71604 oscilloscope.

Offline processing for BER evaluation has been carried out on 217 bits. A digital upsampling stage is applied for scenario A, in order to provide 2 SpS for the remaining DSP subsystems. IQ imbalance is kept under control by careful back-to-back calibration and confirmed by analyzing the output constellations. Both chromatic dispersion and intra-channel nonlinearities are equalized within the static equalization block. Frequency-domain equalization is enabled by the overlap-save method, using the minimum FFT block length, NFFT, that captures the long-term memory effects of the signal (mainly due to chromatic dispersion), thus avoiding inter-block interference (32 samples for scenario A and 128 samples for scenario B). Linear equalization is performed by a frequency-domain chromatic dispersion equalizer (CDE). Digital nonlinear equalization is performed using both the single- and dual-polarization versions of the SSF and VSNE methods. The SSF method with N steps per span is denoted as SSFN. Subsequently, frequency estimation is achieved by a common feedforward spectral method [15

15. S. J. Savory, “Digital coherent optical receivers: Algorithms and subsystems,” IEEE J. Sel. Top. Quantum Electron. 16, 1164–1179, 2010. [CrossRef]

]. In the dynamic equalization block, polarization demultiplexing and residual dispersion compensation are performed by a 25 taps adaptive filter driven by the constant modulus algorithm (CMA). After downsampling to 1 SpS, phase estimation is implemented by the Viterbi-Viterbi algorithm (no differential coding) with an optimized block-length. Finally, BER calculation is carried out after symbol decoding.

3.3. Single-channel results

In order to find the best nonlinear compensation provided by the SSF and VSNE methods, we have performed an optimization procedure for each input power, which is based on measuring the nonlinear equalization performance for a set of predefined trial values of the ξ factor in Eq. (3). As a figure of merit for this optimization procedure we use the error vector magnitude (EVM) of the equalized signal, defined as
EVM[dB]=20log10(|AeqAref|2|Aref|2),
(5)
where Aeq is the equalized optical field and Aref is a reference signal, reconstructed from the transmitted pseudo-random bit sequence. In Fig. 3 we show the optimization of both single-and dual-polarization nonlinear equalizers at the optimum power (0.4 dBm for the 16 spans experiment and 0.2 dBm for the 31 spans experiment, as shown in Fig. 4) for scenario A.1, composed of 16 and 31 spans. The ξ parameter has been varied between 0.6 and 1, with a step-size of 0.05.

Fig. 3 Optimization of the SSF and VSNE methods at the optimum power level, as a function of the ξ parameter, for experimental scenario A.1.
Fig. 4 Experimental BER results obtained for a single-channel 120 Gb/s PM-QPSK signal, corresponding to scenario A.1 composed of 16 spans (a)) and 31 spans (b)) of NZDSF.

The obtained results clearly show that the maximum SSF performance, for both the single-and dual-polarization models, has been achieved by applying only 1 step per span. This low DBP spatial resolution stems from the challenging filtering conditions, both at the transmitter and receiver. At the transmitter side, the employed Nyquist pulse shaping imposes an aggressive optical filtering to the signal spectrum, causing some inter-symbol interference that cannot be removed by the nonlinear equalizers. In turn, at the receiver side, the low ADC sampling rate (∼1.67 SpS) and analog bandwidth (∼13 GHz, corresponding to ∼43% of the symbol rate), reduce the available spectrum (before digital interpolation) for nonlinear equalization. Being limited by the same external factors, the VSNE optimization curves are also overlapped with those obtained for the SSF method. It is also worth mentioning that the dual-polarization versions of the SSF and VSNE methods enable to significantly increase the optimum fraction of nonlinear compensation, which is a consequence of taking into account the cross-polarization effects. The same ξ optimization procedure has been carried out for each input power, with similar conclusions.

In Fig. 4 we show the evolution of BER as a function of input power for experimental setup A.1, considering a total propagation distance of 1600 km (Fig. 4(a)) and 3100 km (Fig. 4(b)). Solid/dashed lines are obtained by third-order polynomial fittings of data.

In order to assess the performance of the nonlinear equalizers with less stringent filtering conditions, we will now analyze the alternative experimental setup B, which presents the following advantages: i) absence of tight optical filtering (no WS is used) at the transmitter side; ii) higher sampling rate (2 SpS) and higher ratio between analog ADC bandwidth and signal symbol rate, at the receiver side.

Fig. 5 Experimental results obtained for a single-channel 100 Gb/s PM-QPSK signal, corresponding to scenario B, composed of 50 spans of SSMF. a) ξ optimization at the optimum power (1 dBm); b) BER as a function of input power.

3.4. WDM results

With the aim to study the effectiveness of intra-channel nonlinear equalization in multi-channel signal propagation, we have also analyzed two 10-channel WDM scenarios, with 66 GHz and 33 GHz inter-channel spacing, corresponding to experimental setups A.2 and A.3, respectively. The performance of linear and nonlinear equalization in scenario A.2 is presented in Fig. 6.

Fig. 6 Experimental BER results obtained for a 10-channel 120 Gb/s PM-QPSK signal with 66 GHz channel spacing, corresponding to scenario A.2, composed of 10 spans (a)) and 15 spans (b)) of NZDSF.

As expected, due to the effect of inter-channel nonlinearities, we may observe that the gains achieved by nonlinear equalization in both optimum power and BER are now significantly reduced, relatively to the single-channel scenarios. A direct comparison between Figs. 6(b) and 4(a), which roughly correspond to the same propagation distance (1500/1600 km), reveals a BER degradation of about half an order of magnitude in terms of CDE performance. However, when the same comparison is performed in terms of nonlinear equalization, this BER degradation is now increased to approximately one order of magnitude, revealing the strong impact of uncompensated inter-channel nonlinearities.

To conclude the WDM analysis, we have tested nonlinear equalization in scenario A.3, which is based on a WDM experiment with ultra-narrow spacing of 1.1× the symbol rate. The experimental results presented in Fig. 7 clearly show the ineffectiveness of intra-channel nonlinear compensation in ultra-dense WDM scenarios. For the 5×100 km case (Fig. 7(a)) there is no visible improvement brought by either single- or dual-polarization nonlinear equalizers. Doubling the propagation distance (see Fig. 7(b)), a residual performance gain is still obtained, even though inter-channel effects are now clearly the dominant nonlinear distortions.

Fig. 7 Experimental BER results obtained for a 10-channel 120 Gb/s PM-QPSK signal with 33 GHz channel spacing, corresponding to scenario A.3, composed of 5 spans (a)) and 10 spans (b)) of NZDSF.

4. Simulation results

4.1. Simulation modeling of the experimental conditions

The previously discussed experimental results denote a severe equalization performance limitation due to narrow optical and electrical filtering. With the aim to provide a clearer picture on the impact of filtering on nonlinear equalization under the considered experimental conditions, we have performed a simulation analysis of the experimental results, from which we extrapolate the achievable performance of nonlinear equalization under near-optimum filtering conditions.

The performance of the simulation model obtained for scenario A.1 (16 spans trial) is presented in Fig. 8(a), showing a good agreement with the correspondent experimental results and thus enabling to accurately mimic the experimental conditions in simulation environment. Signal generation and propagation has been performed using VPItransmissionMaker8.6. The experimentally measured WS transfer function, with 3 dB bandwidth of approximately 32 GHz, has also been considered in the simulation setup. A 5 dB noise figure has been estimated for the EDFA and a noise loading stage has been added at the receiver side, in order to account for the equivalent noise figure characterization of the loop, as defined in [14

14. E. Torrengo, R. Cigliutti, G. Bosco, A. Carena, V. Curri, P. Poggiolini, A. Nespola, D. Zeolla, and F. Forghieri, “Experimental validation of an analytical model for nonlinear propagation in uncompensated optical links,” in European Conference and Exhibition on Optical Communication, OSA Technical Digest (Optical Society of America, 2011), paper We.7.B.2.

]. The entire DSP system is then implemented in MATLAB. A fifth-order Butterworth low-pass filter (LPF) with 3 dB cutoff frequency of 13 GHz has been used to model the ADC bandwidth limitation, providing a good agreement between simulated and experimental spectra, as shown in Fig. 8(b).

Fig. 8 Validation of the simulation model by comparison with the experimental results. a) Comparison of the digital equalization performance in terms of EVM; b) Comparison of signal spectra at ∼1 dBm input power and associated optical/electrical filtering.

4.2. The impact of electrical and optical filtering on equalization performance

Making use of the previously obtained simulation model, in this section we intend to extrapolate the achievable performance of nonlinear equalization under near-optimum filtering conditions.

Considering a fixed input power of 1 dBm (the optimum power after nonlinear equalization, in the experimental conditions), we have gradually increased the bandwidth of the LPF from 13 GHz to 30 GHz, in order to remove the electrical filtering limitation at the receiver. The obtained results, presented in Fig. 9, show that both linear and nonlinear equalization approximate their maximum performance for an electrical bandwidth of 16 GHz, which is roughly matched with the equivalent baseband 3 dB cutoff frequency of the WS filter, but represents only approximately 53% of the symbol rate. Although the electrical bandwidth limitations have been removed, the effect of the Nyquist pulse shaping imposed by the WS filter still poses a severe impact on the equalization performance. As a consequence, there is no visible improvement obtained by increasing the sampling rate from 1.67 SpS to 2 SpS. Moreover, the maximum split-step spatial accuracy is still limited to 1 step per span, matching the performance of the VSNE technique. We highlight the impact of the WS filter on the SSF step-size, which can be easily understood by noticing that the WS employed in the experimental setup cuts approximately 65% of the ideal bandwidth of 3× the symbol rate, required by the SSF method [2

2. E. Ip and J. M. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightwave Technol. 26, 3416–3425 (2008). [CrossRef]

]. Due to the lack of spectral information, the nonlinear step is not capable to accurately invert the nonlinear phase-shift. Indeed, the power estimation error caused by aggressive filtering can be higher than that induced by the interplay between dispersion and nonlinearities over a given propagation distance, thereby limiting the maximum achievable spatial resolution. The same analysis has also been performed for higher input powers, from which similar conclusions were drawn.

Fig. 9 EVM as a function of the LPF cutoff frequency for a fixed input power of 1 dBm, obtained by the experimentally validated simulation model.

Fig. 10 Performance of nonlinear equalization as a function of LPF cutoff frequency, without the WS filter. ADC sampling rate is a) 50 Gsample/s, and b) 60 Gsample/s.

Finally, in Fig. 11 we provide a direct comparison between the achievable equalization performance under the different filtering conditions discussed above. The highest EVM reference curves correspond to the performance in the experimental conditions, as depicted in Fig. 8(a). To represent the wide electrical filtering and Nyquist pulse shaping scenario, we have applied an LPF cutoff frequency of 20 GHz, which is shown in Fig. 9 to provide the optimum performance at 1 dBm, with a safe bandwidth margin for higher input powers. An improved setup is obtained without the WS filter and with an LPF cutoff frequency of 24 GHz. We may observe that, although an EVM improvement of approximately 2 dB can be obtained by solely removing the electrical filtering limitations, this leads to a negligible improvement in terms of optimum power. In fact, part of this 2 dB EVM gain is transversal to linear and nonlinear equalization, being obtained as a direct consequence of relaxing the electrical filtering at the receiver, which contributes to reduce the inter-symbol interference. Since optical filtering still affects a significant part of the baseband spectrum, nonlinear equalization performance remains limited, leading to a small gain in optimum power (∼1 dB). A further 2 dB improvement in the maximum performance has been obtained by relaxing the optical filtering at the transmitter. Noticeably, a ∼3 dB increase on the optimum input power is obtained relatively to the experimental conditions. With near-optimum electrical and optical filtering, the full spectrum at 2× over-sampling is available for nonlinear equalization, enabling to more accurately calculate the nonlinear phase-shift up to significantly higher launched powers. In those conditions, it can also be observed that the VSNE advantage over SSF tends to increase with the input power, confirming its robustness to highly nonlinear regimes.

Fig. 11 EVM as a function of the input power under different electrical and optical filtering conditions. Solid lines refer to the simulation setup with the WS filter and an LPF cutoff frequency of 13 GHz (experimental conditions) and 20 GHz. Dashed lines refer to the simulation setup without the WS filter and an LPF cutoff frequency of 24 GHz.

5. Conclusion

Simulation results obtained for less stringent optical and electrical filtering conditions have confirmed that the assessed experimental equalization performance can be substantially optimized. Although the performance of nonlinear equalization can be enhanced by about 2 dB (in terms of EVM) by solely optimizing the electrical receiver bandwidth, we have found a strong impact of the Nyquist pulse shaping on equalization performance. Considering near-optimum optical/electrical filtering, we have shown that the dual-polarization VSNE is able to outperform the back-propagation SSF method in the nonlinear regime, confirming the previously reported advantage of the single-polarization version of the algorithm [5

5. F. P. Guiomar, J. D. Reis, A. L. Teixeira, and A. N. Pinto, “Mitigation of intra-channel nonlinearities using a frequency-domain Volterra series equalizer,” Opt. Express 20, 1360–1369, (2012). [CrossRef] [PubMed]

]. Being intrinsically single-step, the VSNE is most beneficial in terms of computational complexity for scenarios with wide optical and electrical filtering, where the maximum SSF performance is attained at several steps per span. It is worth mentioning that, despite of the VSNE parallel structure, the total number of operations per FFT block depends quadratically on the FFT block-size, requiring very short FFT blocks in order to keep the algorithm in a tolerable region of complexity. Simplification of the algorithm structure and reduction of the overall computational complexity are topics currently under investigation.

Acknowledgments

This work was supported in part by the FCT - Fundação para a Ciência e a Tecnologia, through the Ph.D. Grant SFRH/BD/74049/2010, by EURO-FOS, a Network of Excellence funded by the European Union through the 7th ICT-Framework Programme, by PT Inovação, SA, through the project “AdaptDig” and by the FCT and the Instituto de Telecomunicações, under the PEst-OE/EEI/LA0008/2011 program, project NG-COS.

References and links

1.

A. N. Pinto and G. P. Agrawal, “Nonlinear interaction between signal and noise in optical fibers,” J. Lightw. Technol. 26, 1847–1853 (2008). [CrossRef]

2.

E. Ip and J. M. Kahn, “Compensation of dispersion and nonlinear impairments using digital backpropagation,” J. Lightwave Technol. 26, 3416–3425 (2008). [CrossRef]

3.

F. Yaman and G. Li, “Nonlinear impairment compensation for polarization-division multiplexed WDM transmission using digital backward propagation,” IEEE Photon. J. 2, 816–832 (2010). [CrossRef]

4.

Z. Pan, B. Chatelain, M. Chagnon, and D. V. Plant, “Volterra filtering for nonlinearity impairment mitigation in DP-16QAM and DP-QPSK fiber optic communication systems,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2011), paper JThA040.

5.

F. P. Guiomar, J. D. Reis, A. L. Teixeira, and A. N. Pinto, “Mitigation of intra-channel nonlinearities using a frequency-domain Volterra series equalizer,” Opt. Express 20, 1360–1369, (2012). [CrossRef] [PubMed]

6.

L. Zhu, F. Yaman, and G. Li, “Experimental demonstration of XPM compensation for WDM fibre transmission,” Electron. Lett. 46, 1140–1141 (2010). [CrossRef]

7.

S. J. Savory, G. Gavioli, E. Torrengo, and P. Poggiolini, “Impact of interchannel nonlinearities on a split-step intrachannel nonlinear equalizer,” IEEE Photon. Technol. Lett. 22, 673–675 (2010). [CrossRef]

8.

F. Zhang, Y. Gao, Y. Luo, J. Li, L. Zhu, L. Li, Z. Chen, and A. Xu, “Experimental demonstration of intra-channel nonlinearity mitigation in coherent QPSK systems with nonlinear electrical equaliser,” Electron. Lett. 46, 353–355 (2010). [CrossRef]

9.

H.-M. Chin, J. Mårtensson, and M. Forzati, “Volterra based nonlinear compensation on 224 Gb/s PolMux-16QAM optical fibre link,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2012), paper JW2A.61.

10.

L. Liu, L. Li, Y. Huang, K. Cui, Q. Xiong, F. N. Hauske, C. Xie, and Y. Cai, “Intrachannel nonlinearity compensation by inverse Volterra series transfer function,” J. Lightwave Technol. 30, 310–316 (2012). [CrossRef]

11.

F. P. Guiomar, J. D. Reis, A. Carena, G. Bosco, A. L. Teixeira, and A. N. Pinto, “Experimental demonstration of a frequency-domain Volterra series nonlinear equalizer in polarization-multiplexed transmission,” in European Conference and Exhibition on Optical Communication, OSA Technical Digest (Optical Society of America, 2012), paper Th.1.D.1.

12.

B. Xu and M. Brandt-Pearce, “Modified Volterra series transfer function method,” IEEE Photon. Technol. Lett. 14, 47–49 (2002). [CrossRef]

13.

G. Gavioli, E. Torrengo, G. Bosco, A. Carena, S. J. Savory, F. Forghieri, and P. Poggiolini, “Ultra-narrow-spacing 10-channel 1.12 Tb/s D-WDM long-haul transmission over uncompensated SMF and NZDSF,” IEEE Photon. Technol. Lett. 22, 1419–1421 (2010). [CrossRef]

14.

E. Torrengo, R. Cigliutti, G. Bosco, A. Carena, V. Curri, P. Poggiolini, A. Nespola, D. Zeolla, and F. Forghieri, “Experimental validation of an analytical model for nonlinear propagation in uncompensated optical links,” in European Conference and Exhibition on Optical Communication, OSA Technical Digest (Optical Society of America, 2011), paper We.7.B.2.

15.

S. J. Savory, “Digital coherent optical receivers: Algorithms and subsystems,” IEEE J. Sel. Top. Quantum Electron. 16, 1164–1179, 2010. [CrossRef]

OCIS Codes
(060.1660) Fiber optics and optical communications : Coherent communications
(060.2330) Fiber optics and optical communications : Fiber optics communications

ToC Category:
Transmission Systems and Network Elements

History
Original Manuscript: October 2, 2012
Revised Manuscript: December 1, 2012
Manuscript Accepted: December 2, 2012
Published: January 4, 2013

Virtual Issues
European Conference on Optical Communication 2012 (2012) Optics Express

Citation
Fernando P. Guiomar, Jacklyn D. Reis, Andrea Carena, Gabriella Bosco, António L. Teixeira, and Armando N. Pinto, "Experimental demonstration of a frequency-domain Volterra series nonlinear equalizer in polarization-multiplexed transmission," Opt. Express 21, 276-288 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-1-276


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References

  1. A. N. Pinto and G. P. Agrawal, “Nonlinear interaction between signal and noise in optical fibers,” J. Lightw. Technol.26, 1847–1853 (2008). [CrossRef]
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  3. F. Yaman and G. Li, “Nonlinear impairment compensation for polarization-division multiplexed WDM transmission using digital backward propagation,” IEEE Photon. J.2, 816–832 (2010). [CrossRef]
  4. Z. Pan, B. Chatelain, M. Chagnon, and D. V. Plant, “Volterra filtering for nonlinearity impairment mitigation in DP-16QAM and DP-QPSK fiber optic communication systems,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2011), paper JThA040.
  5. F. P. Guiomar, J. D. Reis, A. L. Teixeira, and A. N. Pinto, “Mitigation of intra-channel nonlinearities using a frequency-domain Volterra series equalizer,” Opt. Express20, 1360–1369, (2012). [CrossRef] [PubMed]
  6. L. Zhu, F. Yaman, and G. Li, “Experimental demonstration of XPM compensation for WDM fibre transmission,” Electron. Lett.46, 1140–1141 (2010). [CrossRef]
  7. S. J. Savory, G. Gavioli, E. Torrengo, and P. Poggiolini, “Impact of interchannel nonlinearities on a split-step intrachannel nonlinear equalizer,” IEEE Photon. Technol. Lett.22, 673–675 (2010). [CrossRef]
  8. F. Zhang, Y. Gao, Y. Luo, J. Li, L. Zhu, L. Li, Z. Chen, and A. Xu, “Experimental demonstration of intra-channel nonlinearity mitigation in coherent QPSK systems with nonlinear electrical equaliser,” Electron. Lett.46, 353–355 (2010). [CrossRef]
  9. H.-M. Chin, J. Mårtensson, and M. Forzati, “Volterra based nonlinear compensation on 224 Gb/s PolMux-16QAM optical fibre link,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2012), paper JW2A.61.
  10. L. Liu, L. Li, Y. Huang, K. Cui, Q. Xiong, F. N. Hauske, C. Xie, and Y. Cai, “Intrachannel nonlinearity compensation by inverse Volterra series transfer function,” J. Lightwave Technol.30, 310–316 (2012). [CrossRef]
  11. F. P. Guiomar, J. D. Reis, A. Carena, G. Bosco, A. L. Teixeira, and A. N. Pinto, “Experimental demonstration of a frequency-domain Volterra series nonlinear equalizer in polarization-multiplexed transmission,” in European Conference and Exhibition on Optical Communication, OSA Technical Digest (Optical Society of America, 2012), paper Th.1.D.1.
  12. B. Xu and M. Brandt-Pearce, “Modified Volterra series transfer function method,” IEEE Photon. Technol. Lett.14, 47–49 (2002). [CrossRef]
  13. G. Gavioli, E. Torrengo, G. Bosco, A. Carena, S. J. Savory, F. Forghieri, and P. Poggiolini, “Ultra-narrow-spacing 10-channel 1.12 Tb/s D-WDM long-haul transmission over uncompensated SMF and NZDSF,” IEEE Photon. Technol. Lett.22, 1419–1421 (2010). [CrossRef]
  14. E. Torrengo, R. Cigliutti, G. Bosco, A. Carena, V. Curri, P. Poggiolini, A. Nespola, D. Zeolla, and F. Forghieri, “Experimental validation of an analytical model for nonlinear propagation in uncompensated optical links,” in European Conference and Exhibition on Optical Communication, OSA Technical Digest (Optical Society of America, 2011), paper We.7.B.2.
  15. S. J. Savory, “Digital coherent optical receivers: Algorithms and subsystems,” IEEE J. Sel. Top. Quantum Electron.16, 1164–1179, 2010. [CrossRef]

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