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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 5 — Mar. 1, 2010
  • pp: 4776–4782
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Equalization of nonlinear transmission impairments by maximum-likelihood-sequence estimation in digital coherent receivers

Md. Khairuzzaman, Chao Zhang, Koji Igarashi, Kazuhiro Katoh, and Kazuro Kikuchi  »View Author Affiliations


Optics Express, Vol. 18, Issue 5, pp. 4776-4782 (2010)
http://dx.doi.org/10.1364/OE.18.004776


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Abstract

We describe a successful introduction of maximum-likelihood-sequence estimation (MLSE) into digital coherent receivers together with finite-impulse response (FIR) filters in order to equalize both linear and nonlinear fiber impairments. The MLSE equalizer based on the Viterbi algorithm is implemented in the offline digital signal processing (DSP) core. We transmit 20-Gbit/s quadrature phase-shift keying (QPSK) signals through a 200-km-long standard single-mode fiber. The bit-error rate performance shows that the MLSE equalizer outperforms the conventional adaptive FIR filter, especially when nonlinear impairments are predominant.

© 2010 OSA

1. Introduction

Over the past few years, digital signal processing (DSP) techniques has been drawing much more attention as methods of mitigating optical transmission impairments, which stem from chromatic dispersion (CD) and polarization-mode dispersion (PMD). This is because they can offer the potential for significant cost savings compared to optical approaches. Among all electronic equalization techniques, finite-impulse-response (FIR) filtering and maximum-likelihood sequence estimation (MLSE) have attracted significant attention.

On the other hand, the digital coherent receiver enables more sophisticated electronic signal processing because not only the amplitude but also the phase can be recovered after detection [9

9. T. Okoshi, and K. Kikuchi, Coherent optical fiber communications, KTK Scientific Publishers, Tokyo, Japan (1988).

]. Linear transmission impairments due to CD and PMD have been equalized electrically by using FIR filters [10

10. K. Kikuchi, “Phase-diversity homodyne detection of multilevel optical modulation with digital carrier phase estimation”, IEEE J. Sel. Top. Quantum Electron. 12(4), 563–570 (2006). [CrossRef]

]. Since CD and PMD can be expressed as linear transfer functions operating on the complex amplitude of the modulated optical signal, we can compensate for them by linearly equalizing the homodyne-detected complex amplitude with FIR filters [11

11. S. Tsukamoto, K. Katoh, and K. Kikuchi, “Unrepeated transmission of 20-Gb/s optical quadrature phase-shift-keying signal over 200-km standard single-mode fiber based on digital processing of homodyne-detected signal for group-velocity dispersion compensation,” IEEE Photon. Technol. Lett. 18(9), 1016–1018 (2006). [CrossRef]

,12

12. S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16(2), 804–817 (2008). [CrossRef] [PubMed]

].

In digital coherent receivers, SPM and XPM can hardly be equalized even by FIR filters, because unlike CD and PMD, these cannot be expressed as linear transfer functions. On the other hand, differently from FIR filters, MLSE works well because the maximum likelihood data are determined from training patterns affected by the nonlinear impairments; and hence, it may play a superior role for the equalization of such nonlinear impairments also in the coherent receiver.

In this paper, we demonstrate optical transmission experiments, where we introduce the MLSE equalizer based on the Viterbi algorithm [13

13. G. D. Forney Jr., “Maximum-likelihood sequence estimation of digital sequences in the presence of intersymbol interference,” IEEE Trans. Inf. Theory 18(3), 363–378 (1972). [CrossRef]

,14

14. G. D. Forney Jr., “The Viterbi algorithm,” IEEE Proc. 61(3), 268–278 (1973). [CrossRef]

] together with the FIR filter into digital coherent receivers, aiming at equalization of both linear and nonlinear impairments. This experimental work deals only with SPM in a single-channel transmission system. XPM can usually be mitigated by the large amount of accumulated CD of standard single-mode fibers (SMFs) for transmission, and SPM remains the main origin of nonlinear impairments even for WDM transmission.

With the coherent receiver including the MLSE equalizer, we demonstrate unrepeated transmission of 20-Gbit/s optical quadrature phase-shift keying (QPSK) signals over a 200-km-long SMF. When the launched power is increased up to 10 dBm, SPM begins to deteriorate the bit-error rate (BER) performance, and it cannot be compensated for by adaptive FIR filters; however, the MLSE equalizer can equalizes SPM, improving the power penalty by 2 dB.

This paper is organized is as follows: Sec. 2 provides the experimental setup. In Sec. 3, we describe how we implement MLSE equalizers together with FIR filters into DSP circuits. In Sec. 4, MLSE performances are examined and compared with conventional adaptive FIR filters for both linear and nonlinear cases. In Sec. 5, we discuss effectiveness and limitation of our approach and finally Sec. 6 concludes our paper.

2. Experimental setup

Figure 1
Fig. 1 Experimental setup for 20-Gbit/s QPSK transmission.
shows the experimental setup for measuring QPSK transmission characteristics through 100- and 200-km-long SMFs. The laser for the transmitter was a distributed-feedback laser diode (DFB-LD) and its wavelength was 1552 nm. An arbitrary waveform generator (AWG) was used to generate two 10-Gbit/s data streams, which were pre-coded to be a 29-1 pseudorandom pattern after decoding. An optical QPSK signal was created by a LiNbO3 optical IQ modulator (IQM).

Firstly, the input power launched on the SMF was fixed at 0 dBm to avoid nonlinear effects. Secondly, the input power was fixed to 10 dBm to induce nonlinear effects intentionally. The SPM effect along a fiber of length Lf becomes dominant when Lf is longer than the nonlinearity length LNL defined by γP, where γ is the nonlinear coefficient of the fiber and P the launched power. When P = 0 dBm and 10 dBm, we calculate LNL to be 670 km and 67 km, respectively, by using γ = 1.5/W/km. Since Lf = 100 km and 200 km in our case, the SPM effect may appear significantly when the input power is 10 dBm. On the other hand, we can almost neglect the SPM effect when the input power is 0 dBm. The SMF had the dispersion D = 17 ps/nm/km (β2 = -22 ps2/km). We confirmed that the stimulated Brillouin scattering (SBS) never occurred when the input power was increased up to10 dBm.

At the receiver, the received average power Pin was controlled by a variable optical attenuator (VOA). Then, the signal was pre-amplified by an erbium-doped fiber amplifier (EDFA) and detected by a homodyne phase-diversity receiver. More details on homodyne phase-diversity coherent receivers can be found in [8

8. S. Chandrasekhar and A. H. Gnauck, “Performance of MLSE receiver in a dispersion-managed multispan experiment at 10.7 Gb/s under nonlinear transmission,” IEEE Photon. Technol. Lett. 18(23), 2448–2450 (2006). [CrossRef]

]. Another DFB-LD having the characteristics same as the transmitter DFB-LD was used as a local oscillator (LO). The real and imaginary parts of the beat signal were simultaneously sampled at 20 Gsample/s with 8-bit analog-to-digital converters (ADCs). The sampled data were then processed offline by the digital signal processing (DSP) circuit, whose functions were FIR filtering, clock recovery, phase estimation and MLSE.

In our experiment, we used 15-tap and 21-tap fixed FIR filters to compensate for dispersion values of 1700 ps/nm of the 100-km-long fiber and 3400 ps/nm of the 200-km-long fiber, respectively. Although CD is compensated for to a significant degree by such FIR filters, power penalties still remain which may stem from non-ideal tap coefficients. Then, we used a 200-tap adaptive FIR filter for both lengths of the fibers. To show the effectiveness and performance comparison of MLSE, we replaced this adaptive FIR filter by MLSE which is based on the 16-state Viterbi algorithm.

3. MLSE implementation

If the level of modulation is M and the channel-memory length is L, the number of states in the trellis diagram (TD) is ML and the number of state transitions is ML + 1. In our experiment, we apply the QPSK (M = 4) signal with the channel memory L = 2. In such a case, each of 64 state transitions is given as a six-bit word consisting of a symbol together with a predecessor symbol and a post-cursor symbol.

Before the MLSE equalization starts, we need to prepare a look-up table during the training process, where we receive a known sequence of symbols that has been affected by impairments of the channel. We sort the received symbols surrounded by predecessor and post-cursor symbols according to prescribed state transitions, and calculate the mean complex amplitude p(i) of those sorted symbols, which belong to the i-th state transition. The complex amplitude p(i) thus obtained is stored in the look-up table.

The method of implementing the MLSE equalizer in our experiment is shown in Fig. 2
Fig. 2 MLSE implementation in the DSP circuit.
. The signal complex amplitude from the phase-diversity homodyne receiver is sampled and digitized by ADCs and then it is applied to a fixed FIR filter. After the clock is recovered by using the clock recovery unit, the signal is resampled so that each symbol has one sample. Then, the carrier phase is estimated through the Mth-power feed-forward scheme, and we restore the symbol z(k). Such symbol is now ready for equalization by an MLSE module consisting of the look up table, the BM computation block and the Viterbi algorithm block. The look up table stores p(i) and sends it to the BM computation block.

4. Experimental results

We performed offline measurements of BER from recorded 100-k-symbol data after unrepeated transmission through 100- and 200-km-long SMFs.

We measured BERs of the 20-Gbit/s QPSK signal for the following four cases:
  • 1) The case without any equalizer,
  • 2) The case using only a fixed FIR filter,
  • 3) The case using an adaptive FIR filter along with the fixed FIR filter, and
  • 4) The case using MLSE together with the fixed FIR filter.
Figures 3
Fig. 3 BERs measured as a function for received power after transmission through a 100-km-long SMF.
and 4
Fig. 4 BERs measured as a function for received power after transmission through a 200-km-long SMF.
show BERs measured as a function of the received power in these cases for 100- and 200-km transmission, respectively. We observe the performance of the equalizers in both linear and nonlinear regions. The theoretical limit is the shot-noise limited BER for QPSK signal calculated from(1/2)erfc(γb), where γbis the SNR/bit and erfc(*) represents the complementally error function [15

15. J. G. Proakis, Digital communications, 4th Edition. McGraw-Hill, New York, NY, USA (2001).

].

From BERs for Case 1 and Case 2, we can observe a significant improvement of BER characteristics by the fixed FIR filter, which proves that GVD can be compensated for by such filter in the digital coherent receiver. However, there still remain some penalties due to non-ideal tap coefficients of the filter which can be equalized by adaptive FIR filters especially when the input power is low enough. Case 3 describes the BER improvement owing to such adaptive equalization. Since the performance of adaptive filters depends on the number of taps, we have optimized the number of taps to get the best BER performance.

To examine the MLSE performance, we compare BERs of Case 3 and Case 4 for both fiber lengths. In the linear region, where the input power is 0 dBm, BER curves obtained by using adaptive FIR filters are 1-dB and 2-dB worse than the theoretical limit for 100-km and 200-km transmission, respectively. MLSE gives us small improvement for both fiber lengths in the linear region. However, when the input power is increased up to 10 dBm, BERs obtained with adaptive FIR filters show higher penalties. On the other hand, introducing MLSE instead of adaptive FIR filters, we can achieve significant receiver sensitivity improvement, which is about 1 dB and 2 dB at BER = 10−4 for 100-km and 200-km transmission, respectively.

5. Discussion

Figure 5
Fig. 5 Power penalty analysis for the MLSE receiver. BERs are measured as a function of the received power in the 200-km-long 20-Gbit/s QPSK transmission system.
presents the power-penalty analysis for the MLSE receiver in the 200-km-long system. We measured power penalties at BER = 10−4 with respect to the theoretical limit. Green curves show the BER performance in the linear case. We can see that GVD can be perfectly compensated for by fixed and adaptive FIR filters, and the sensitivity can be improved by very small amount (less than 1 dB) with the MLSE scheme. Although either FIR filters or MLSE can be the perfect solution to mitigate linear inter-symbol interference (ISI), the FIR-filter-based scheme should be implemented in the digital coherent receiver because of its smaller computational complexity.

Blue curves of the Fig. 5, on the other hand, represent the BER performance in the nonlinear region, where the input power is 10 dBm. In such region, the sensitivity of the MLSE receiver is improved by as large as 2 dB compared to the FIR-filter-based receiver, because MLSE can mitigate SPM in our receiver. However, we still have 3.6 dB power penalties from the theoretical limit even with MLSE. This power penalty can further be reduced by using a greater memory length in the MLSE scheme; however, the increase in the memory length results in the exponential-order increase in the computational complexity, making it much more difficult to implement MLSE in real systems.

We thus find that the FIR equalizer in the coherent receiver can compensate for CD nearly perfectly in the linear region, but that the MLSE equalizer is more effective for nonlinearity mitigation. Indeed, the combination of the MLSE equalizer and the fixed FIR filter shows the best BER performance.

6. Conclusion

We have successfully introduced MLSE into digital coherent receivers together with fixed FIR filters in order to equalize both linear and nonlinear fiber impairments. 20-Gbit/s QPSK signals are transmitted through a 200-km-long SMF, and the MLSE receiver can equalize SPM which becomes significant when the launched power is increased up to 10 dBm. The combination of MLSE and fixed FIR filtering in the digital coherent receiver is considered to be the most powerful technique for signal equalization in optical communication systems.

Acknowledgements

The author would like to thank Dr. F. N. Hauske of Universität der Bundeswehr München, Germany for insightful technical discussions and very helpful advices. This work was supported in part by Strategic Information and Communications R&D Promotion Programme of Ministry of Internal Affairs and Communications, Japan.

References

1.

A. Faerbert, S. Langenbach, N. Stojanovic, C. Dorschky, T. Kupfer, C. Schulien, J.-P. Elbers, H. Wernz, H. Griesser, and C. Glingener, “Performance of a 10.7Gb/s receiver with digital equalizer using maximum likelihood sequence estimation”, European Conference on Optical Communication (ECOC 2004), Stockholm, Sweden, Post deadline paper PD Th4.1.5 (2004).

2.

J. M. Gene, P. J. Winzer, S. Chandrasekhar, and H. Kogelnik, “Joint PMD and chromatic dispersion compensation using an MLSE”, European Conference on Optical Communication (ECOC 2006), Cannes, France, Paper We2.5.2 (2006).

3.

N. Alić, G. C. Papen, R. E. Saperstein, L. B. Milstein, and Y. Fainman, “Signal statistics and maximum likelihood sequence estimation in intensity modulated fiber optic links containing a single optical preamplifier,” Opt. Express 13(12), 4568–4579 (2005). [CrossRef] [PubMed]

4.

F. N. Hauske, B. Lankl, C. Xie, and E.-D. Schmidt, “Iterative electronic equalization utilizing low complexity MLSEs for 40 Gbit/s DQPSK modulation”, Optical Fiber Communication Conference (OFC 2007), Anaheim, CA, USA, Paper OMG2 (2007).

5.

G. Agrawal, Fiber-Optic Communication Systems, John Wiley & Sons, New York, NY, USA, (2002).

6.

O. E. Agazzi, and V. Gopinathan, “The impact of nonlinearity on electronic dispersion compensation of optical channels”, Optical Fiber Communication Conference (OFC 2004), Anaheim, CA, USA, Paper TuG6 (2004).

7.

O. E. Agazzi, M. R. Hueda, H. S. Carrer, and D. E. Crivelli, “Maximum-likelihood sequence estimation in dispersive optical channels,” J. Lightwave Technol. 23(2), 749–763 (2005). [CrossRef]

8.

S. Chandrasekhar and A. H. Gnauck, “Performance of MLSE receiver in a dispersion-managed multispan experiment at 10.7 Gb/s under nonlinear transmission,” IEEE Photon. Technol. Lett. 18(23), 2448–2450 (2006). [CrossRef]

9.

T. Okoshi, and K. Kikuchi, Coherent optical fiber communications, KTK Scientific Publishers, Tokyo, Japan (1988).

10.

K. Kikuchi, “Phase-diversity homodyne detection of multilevel optical modulation with digital carrier phase estimation”, IEEE J. Sel. Top. Quantum Electron. 12(4), 563–570 (2006). [CrossRef]

11.

S. Tsukamoto, K. Katoh, and K. Kikuchi, “Unrepeated transmission of 20-Gb/s optical quadrature phase-shift-keying signal over 200-km standard single-mode fiber based on digital processing of homodyne-detected signal for group-velocity dispersion compensation,” IEEE Photon. Technol. Lett. 18(9), 1016–1018 (2006). [CrossRef]

12.

S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16(2), 804–817 (2008). [CrossRef] [PubMed]

13.

G. D. Forney Jr., “Maximum-likelihood sequence estimation of digital sequences in the presence of intersymbol interference,” IEEE Trans. Inf. Theory 18(3), 363–378 (1972). [CrossRef]

14.

G. D. Forney Jr., “The Viterbi algorithm,” IEEE Proc. 61(3), 268–278 (1973). [CrossRef]

15.

J. G. Proakis, Digital communications, 4th Edition. McGraw-Hill, New York, NY, USA (2001).

OCIS Codes
(060.1660) Fiber optics and optical communications : Coherent communications
(060.2330) Fiber optics and optical communications : Fiber optics communications
(060.2920) Fiber optics and optical communications : Homodyning

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: November 18, 2009
Revised Manuscript: February 18, 2010
Manuscript Accepted: February 18, 2010
Published: February 23, 2010

Citation
Md. Khairuzzaman, Chao Zhang, Koji Igarashi, Kazuhiro Katoh, and Kazuro Kikuchi, "Equalization of nonlinear transmission impairments by maximum-likelihood-sequence estimation in digital coherent receivers," Opt. Express 18, 4776-4782 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-5-4776


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References

  1. A. Faerbert, S. Langenbach, N. Stojanovic, C. Dorschky, T. Kupfer, C. Schulien, J.-P. Elbers, H. Wernz, H. Griesser, and C. Glingener, “Performance of a 10.7Gb/s receiver with digital equalizer using maximum likelihood sequence estimation,” European Conference on Optical Communication (ECOC 2004), Stockholm, Sweden, Post deadline paper PD Th4.1.5 (2004).
  2. J. M. Gene, P. J. Winzer, S. Chandrasekhar, and H. Kogelnik, “Joint PMD and chromatic dispersion compensation using an MLSE,” European Conference on Optical Communication (ECOC 2006), Cannes, France, Paper We2.5.2 (2006).
  3. N. Alić, G. C. Papen, R. E. Saperstein, L. B. Milstein, and Y. Fainman, “Signal statistics and maximum likelihood sequence estimation in intensity modulated fiber optic links containing a single optical preamplifier,” Opt. Express 13(12), 4568–4579 (2005). [CrossRef] [PubMed]
  4. F. N. Hauske, B. Lankl, C. Xie, and E.-D. Schmidt, “Iterative electronic equalization utilizing low complexity MLSEs for 40 Gbit/s DQPSK modulation,” Optical Fiber Communication Conference (OFC 2007), Anaheim, CA, USA, Paper OMG2 (2007).
  5. G. Agrawal, Fiber-Optic Communication Systems, (John Wiley & Sons, New York, NY, USA, 2002).
  6. O. E. Agazzi, and V. Gopinathan, “The impact of nonlinearity on electronic dispersion compensation of optical channels,” Optical Fiber Communication Conference (OFC 2004), Anaheim, CA, USA, Paper TuG6 (2004).
  7. O. E. Agazzi, M. R. Hueda, H. S. Carrer, and D. E. Crivelli, “Maximum-likelihood sequence estimation in dispersive optical channels,” J. Lightwave Technol. 23(2), 749–763 (2005). [CrossRef]
  8. S. Chandrasekhar and A. H. Gnauck, “Performance of MLSE receiver in a dispersion-managed multispan experiment at 10.7 Gb/s under nonlinear transmission,” IEEE Photon. Technol. Lett. 18(23), 2448–2450 (2006). [CrossRef]
  9. T. Okoshi, and K. Kikuchi, Coherent optical fiber communications, (KTK Scientific Publishers, Tokyo, Japan, 1988).
  10. K. Kikuchi, “Phase-diversity homodyne detection of multilevel optical modulation with digital carrier phase estimation,” IEEE J. Sel. Top. Quantum Electron. 12(4), 563–570 (2006). [CrossRef]
  11. S. Tsukamoto, K. Katoh, and K. Kikuchi, “Unrepeated transmission of 20-Gb/s optical quadrature phase-shift-keying signal over 200-km standard single-mode fiber based on digital processing of homodyne-detected signal for group-velocity dispersion compensation,” IEEE Photon. Technol. Lett. 18(9), 1016–1018 (2006). [CrossRef]
  12. S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16(2), 804–817 (2008). [CrossRef] [PubMed]
  13. G. D. Forney, “Maximum-likelihood sequence estimation of digital sequences in the presence of intersymbol interference,” IEEE Trans. Inf. Theory 18(3), 363–378 (1972). [CrossRef]
  14. G. D. Forney, “The Viterbi algorithm,” IEEE Proc. 61(3), 268–278 (1973). [CrossRef]
  15. J. G. Proakis, Digital communications, 4th Edition. (McGraw-Hill, New York, NY, USA, 2001).

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