OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 10 — May. 20, 2013
  • pp: 12351–12362
« Show journal navigation

Study of EEPN mitigation using modified RF pilot and Viterbi-Viterbi based phase noise compensation

Gunnar Jacobsen, Tianhua Xu, Sergei Popov, and Sergey Sergeyev  »View Author Affiliations


Optics Express, Vol. 21, Issue 10, pp. 12351-12362 (2013)
http://dx.doi.org/10.1364/OE.21.012351


View Full Text Article

Acrobat PDF (1909 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We propose – as a modification of the optical (RF) pilot scheme - a balanced phase modulation between two polarizations of the optical signal in order to generate correlated equalization enhanced phase noise (EEPN) contributions in the two polarizations. The method is applicable for n-level PSK system. The EEPN can be compensated, the carrier phase extracted and the nPSK signal regenerated by complex conjugation and multiplication in the receiver. The method is tested by system simulations in a single channel QPSK system at 56 Gb/s system rate. It is found that the conjugation and multiplication scheme in the Rx can mitigate the EEPN to within ½ orders of magnitude. Results are compared to using the Viterbi-Viterbi algorithm to mitigate the EEPN. The latter method improves the sensitivity more than two orders of magnitude. Important novel insight into the statistical properties of EEPN is identified and discussed in the paper.

© 2013 OSA

1. Introduction

Chromatic dispersion (CD) and laser phase noise severely impact the performance of high speed optical fiber transmission systems [1

1. P. S. Henry, “Lightwave primer,” IEEE J. Quantum Electron. 21(12), 1862–1879 (1985). [CrossRef]

,2

2. G. P. Agrawal, Fiber-optic communication systems 3rd Edition (John Wiley & Sons, Inc., 2002), Chap. 2.

]. Digital coherent receivers allow complete equalization of chromatic dispersion in the electrical domain by using discrete signal processing (DSP) techniques [3

3. J. G. Proakis, Digital Communications 5th Edition (McGraw-Hill Companies, Inc., 2008), Chap. 10.

7

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

]. Several discrete (digital) filters have been applied to compensate the chromatic dispersion in the time and frequency domain [4

4. M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett. 16(2), 674–676 (2004). [CrossRef]

12

12. T. Xu, G. Jacobsen, S. Popov, J. Li, E. Vanin, K. Wang, A. T. Friberg, and Y. Zhang, “Chromatic dispersion compensation in coherent transmission system using digital filters,” Opt. Express 18(15), 16243–16257 (2010). [CrossRef] [PubMed]

]. These include the maximum likelihood sequence estimation (MLSE) method [5

5. A. Färbert, S. Langenbach, N. Stojanovic, C. Dorschky, T. Kupfer, C. Schulien, J. P. Elbers, H. Wernz, H. Griesser, and C. Glingener, “Performance of a 10.7 Gb/s Receiver with digital equaliser using maximum likelihood sequence estimation,” in Proceeding of IEEE European Conference on Optical Communication (Stockholm, Sweden, 2004), paper Th4.1.5.

], a time domain fiber dispersion finite impulse response (FD-FIR) filter [7

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

,8

8. S. J. Savory, “Compensation of fibre impairments in digital coherent systems,” in Proceeding of IEEE European Conference on Optical Communication (Brussels, Belgium, 2008), paper Mo.3.D.1.

,12

12. T. Xu, G. Jacobsen, S. Popov, J. Li, E. Vanin, K. Wang, A. T. Friberg, and Y. Zhang, “Chromatic dispersion compensation in coherent transmission system using digital filters,” Opt. Express 18(15), 16243–16257 (2010). [CrossRef] [PubMed]

], or a frequency domain equalizer (FDE) [9

9. K. Ishihara, T. Kobayashi, R. Kudo, Y. Takatori, A. Sano, E. Yamada, H. Masuda, and Y. Miyamoto, “Coherent optical transmission with frequency-domain equalization,” in Proceeding of IEEE European Conference on Optical Communication (Brussels, Belgium, 2008), paper We.2.E.3.

12

12. T. Xu, G. Jacobsen, S. Popov, J. Li, E. Vanin, K. Wang, A. T. Friberg, and Y. Zhang, “Chromatic dispersion compensation in coherent transmission system using digital filters,” Opt. Express 18(15), 16243–16257 (2010). [CrossRef] [PubMed]

]. It is important to note that there is a complicated interplay between the discrete chromatic dispersion compensation and the laser phase noise. This interplay leads to a combination of equalization enhanced phase noise (EEPN), amplitude noise and time jitter [13

13. W. Shieh and K. P. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Express 16(20), 15718–15727 (2008). [CrossRef] [PubMed]

21

21. S. Oda, C. Ohshima, T. Tanaka, T. Tanimura, H. Nakashima, N. Koizumi, T. Hoshida, H. Zhang, Z. Tao, and J. C. Rasmussen, “Interplay between Local oscillator phase noise and electrical chromatic dispersion compensation in digital coherent transmission system,” in Proceeding of IEEE European Conference on Optical Communication (Torino, Italy, 2010), paper Mo.1.C.2. [CrossRef]

].

A traditional coherent receiver (Rx) utilizes a zero-forcing equalizer [13

13. W. Shieh and K. P. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Express 16(20), 15718–15727 (2008). [CrossRef] [PubMed]

] which does not depend on the data (data pattern) or signal parameters (additive optical and electrical noise) and phase noise (laser linewidths). The derivation in [13

13. W. Shieh and K. P. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Express 16(20), 15718–15727 (2008). [CrossRef] [PubMed]

] leads to an analytical form – with a simple physical interpretation - of the EEPN generation which results from the digital dispersion compensation. The zero-forcing equalizer is not optimal for minimizing EEPN generation in the electronic dispersion compensation stage of the Rx. It is possible to optimize a linear minimum mean square (MMSE) equalizer for specific laser phase noise influence by including laser linewidths in the equalizer description [14

14. A. P. T. Lau, T. S. R. Shen, W. Shieh, and K.-P. Ho, “Equalization-enhanced phase noise for 100 Gb/s transmission and beyond with coherent detection,” Opt. Express 18(16), 17239–17251 (2010). [CrossRef] [PubMed]

]. Reference [14

14. A. P. T. Lau, T. S. R. Shen, W. Shieh, and K.-P. Ho, “Equalization-enhanced phase noise for 100 Gb/s transmission and beyond with coherent detection,” Opt. Express 18(16), 17239–17251 (2010). [CrossRef] [PubMed]

] shows that this more optimal equalizer and the resulting EEPN is not given in closed form and that the optimization leads to very marginal influence on the EEPN generation. It is concluded that it is difficult to mitigate EEPN using simple DSP algorithms [14

14. A. P. T. Lau, T. S. R. Shen, W. Shieh, and K.-P. Ho, “Equalization-enhanced phase noise for 100 Gb/s transmission and beyond with coherent detection,” Opt. Express 18(16), 17239–17251 (2010). [CrossRef] [PubMed]

]. It should however be noted that the EEPN influence can be reduced significantly using a DSP implementation of the Viterbi-Viterbi algorithm [15

15. R. Farhoudi, A. Ghazisaeidi, and L. A. Rusch, “Performance of carrier phase recovery for electronically dispersion compensated coherent systems,” Opt. Express 20(24), 26568–26582 (2012). [CrossRef] [PubMed]

]. In [15

15. R. Farhoudi, A. Ghazisaeidi, and L. A. Rusch, “Performance of carrier phase recovery for electronically dispersion compensated coherent systems,” Opt. Express 20(24), 26568–26582 (2012). [CrossRef] [PubMed]

], the carrier phase is extracted using an optical (RF) pilot tone in the orthogonal polarization relative to the QPSK modulated signal and the Viterbi-Viterbi algorithm is applied for reducing EEPN influence. In the current paper we will – in order to simplify the discussion without sacrificing accuracy in any significant way - use the EEPN model in [13

13. W. Shieh and K. P. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Express 16(20), 15718–15727 (2008). [CrossRef] [PubMed]

]. Based upon a leading order Taylor expansion of the laser phase noise it is possible to associate the EEPN effect with an effective laser linewidth [13

13. W. Shieh and K. P. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Express 16(20), 15718–15727 (2008). [CrossRef] [PubMed]

,22

22. T. Xu, G. Jacobsen, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Analytical estimation of phase noise influence in coherent transmission system with digital dispersion equalization,” Opt. Express 19(8), 7756–7768 (2011). [CrossRef] [PubMed]

,23

23. G. Jacobsen, T. Xu, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Receiver implemented RF pilot tone phase noise mitigation in coherent optical nPSK and nQAM systems,” Opt. Express 19(15), 14487–14494 (2011). [CrossRef] [PubMed]

]. It has been verified in brute force simulation results for the Bit-Error-Rate (BER) that this linewidth predicts resulting BER floors for differential QPSK systems well even when the EEPN influence is dominating [22

22. T. Xu, G. Jacobsen, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Analytical estimation of phase noise influence in coherent transmission system with digital dispersion equalization,” Opt. Express 19(8), 7756–7768 (2011). [CrossRef] [PubMed]

,23

23. G. Jacobsen, T. Xu, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Receiver implemented RF pilot tone phase noise mitigation in coherent optical nPSK and nQAM systems,” Opt. Express 19(15), 14487–14494 (2011). [CrossRef] [PubMed]

]. The detailed effect is dependent on which type of discrete chromatic dispersion compensation is implemented in the receiver (Rx) or in the transmitter (Tx), using either post-CD compensation [23

23. G. Jacobsen, T. Xu, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Receiver implemented RF pilot tone phase noise mitigation in coherent optical nPSK and nQAM systems,” Opt. Express 19(15), 14487–14494 (2011). [CrossRef] [PubMed]

] or pre-CD compensation [24

24. G. Jacobsen, M. S. Lidón, T. Xu, S. Popov, A. T. Friberg, and Y. Zhang, “Influence of pre- and post-compensation of CD on EEPN in coherent multilevel systems,” J. Opt. Commun. 32, 257–261 (2012).

].

In this paper, we investigate - for the first time to our knowledge - how the resulting EEPN behavior can be mitigated by introducing modulation of the optical (RF) pilot phase which is correlated with the phase modulation of the QPSK signal. In the Rx, complex conjugation regenerates the deterministic (QPSK) signal, extracts the carrier phase (equivalent to the method used in [15

15. R. Farhoudi, A. Ghazisaeidi, and L. A. Rusch, “Performance of carrier phase recovery for electronically dispersion compensated coherent systems,” Opt. Express 20(24), 26568–26582 (2012). [CrossRef] [PubMed]

]) and mitigates the influence of EEPN as much as possible. We include Viterbi-Viterbi algorithm into our results for the mitigation of EEPN. Our study provides significant new insight into the EEPN effect and the validation of the description via the effective linewidth [13

13. W. Shieh and K. P. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Express 16(20), 15718–15727 (2008). [CrossRef] [PubMed]

,22

22. T. Xu, G. Jacobsen, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Analytical estimation of phase noise influence in coherent transmission system with digital dispersion equalization,” Opt. Express 19(8), 7756–7768 (2011). [CrossRef] [PubMed]

]. The results of the study are presented on a BER basis using the VPI simulation platform [25].

The principle of an optical (RF) pilot tone with phase modulation is presented in section 2 of this paper. Section 3 reports simulation results, i.e. demonstrates benefit and problem areas. Section 4 gives conclusive remarks.

2. Theory

2.1 Principle and structure for Rx using optical (RF) pilot tone or distributed phase modulation in combination with CD equalization

A complete single channel coherent system is schematically shown in Fig. 1
Fig. 1 Block diagram for single channel nPSK system. Figure insert a) is the transmitter Tx) unit for the dual polarization distributed nPSK modulation case. Figure insert b) is for nPSK modulation in one polarization and using the orthogonal polarization signal for an optical (RF) pilot tone. In both cases carrier phase estimation is done in the conjugate multiplication in the Rx. The Viterbi-Viterbi algorithm may be used to filter the phase noise. N(t) shows the added optical noise which is used to measure the Bit-Error-Rate (BER) as a function of optical signal-to-noise ratio (OSNR). Figure abbreviations: Tx – transmitter; PBS – polarizing beam splitter; PBC – polarizing beam combiner; PRBS – pseudo random bit sequence ; LO – local oscillator; ADC – analogue to digital conversion; CD – chromatic dispersion.
including distributed phase modulation in two orthogonal polarizations (insert a)) or including the use of an optical (RF) pilot tone for eliminating the phase noise (insert b)) [26

26. M. Nakamura, Y. Kamio, and T. Miyazaki, “Pilot-carrier based linewidth-tolerant 8PSK self-homodyne using only one modulator,” in Proceeding of IEEE European Conference on Optical Communication (Berlin, Germany, 2007), paper 8.3.6. [CrossRef]

,27

27. M. Nakamura, Y. Kamio, and T. Miyazaki, “Linewidth-tolerant 10-Gbit/s 16-QAM transmission using a pilot-carrier based phase-noise cancelling technique,” Opt. Express 16(14), 10611–10616 (2008). [CrossRef] [PubMed]

]. In the case of distributed phase modulation the system is a modified version of the classical system using an optical (RF) pilot tone since the pilot tone now includes part of the modulated signal. Two polarization states are used to transmit the modulated optical signal; one polarization has a total four level phase modulation amplitude of 2πα (0 ≤ α ≤ 1) and the other a modulation amplitude of 2π(α-1). Negative amplitude means that the phase modulation is reversed. With this Tx configuration we will attempt to generate a correlated EEPN contribution in both polarization states. In order for the correlation to be best possible, the modulation in the two polarizations must be identical i.e. the capacity is the same as for a system with full modulation in a single polarization. The complex conjugation and multiplication in the Rx will cancel the intrinsic phase noise from the Tx and LO laser as well as the EEPN contribution in the best possible way and will extract the carrier phase. With the selected distributed and balanced modulation the complex conjugation and multiplication will furthermore recover a normal QPSK modulated deterministic signal.

In the case of using one polarization state for the modulated nPSK signal and the other polarization for the optical (RF) pilot tone the conjugation and multiplication in the Rx will cancel the intrinsic phase noise from the Tx and LO lasers and recover the carrier phase.

We note that the distributed modulation case is equal to the case with full modulation in one polarization and an optical (RF) pilot tone in the other when α equals 0 or 1.

We will consider an FDE filter for the chromatic dispersion compensation. We note that in this configuration the FDE and the FD-FIR filters give the same Bit-Error-Rate (BER) performance [12

12. T. Xu, G. Jacobsen, S. Popov, J. Li, E. Vanin, K. Wang, A. T. Friberg, and Y. Zhang, “Chromatic dispersion compensation in coherent transmission system using digital filters,” Opt. Express 18(15), 16243–16257 (2010). [CrossRef] [PubMed]

]. The FDE, rather than the FD-FIR filter, is selected as commonly used in most practical system demonstrations at this time. Some earlier works for PSK/QAM systems have considered an optical (RF) pilot tone transmitted in the orthogonal polarization relative to the signal [26

26. M. Nakamura, Y. Kamio, and T. Miyazaki, “Pilot-carrier based linewidth-tolerant 8PSK self-homodyne using only one modulator,” in Proceeding of IEEE European Conference on Optical Communication (Berlin, Germany, 2007), paper 8.3.6. [CrossRef]

,27

27. M. Nakamura, Y. Kamio, and T. Miyazaki, “Linewidth-tolerant 10-Gbit/s 16-QAM transmission using a pilot-carrier based phase-noise cancelling technique,” Opt. Express 16(14), 10611–10616 (2008). [CrossRef] [PubMed]

]. This represents a limiting (best possible) situation for the elimination of phase noise and it is equivalent to the implementations of the optical (RF) pilot tone - and of the distributed nPSK modulation in two polarizations - considered in this paper.

We note that for OFDM systems it is more natural to have the optical (RF) pilot tone as one tone in the center of the OFDM signal grid since each OFDM tone is demodulated separately [28

28. S. L. Jansen, I. Morita, N. Takeda, and H. Tanaka, “20-Gb/s OFDM transmission over 4,160-km SSFM enabled by RF-pilot tone for phase noise compensation”, in Proceeding of Conference on Optical Fiber Communications, (Anaheim, California, 2007), paper PDP 15.

]. The OFDM signal and the optical (RF) pilot tone are in the same polarization state.

The principle of phase noise cancellation and carrier phase extraction by an optical (RF) pilot tone is simple. Let the detected coherent signal field be represented as (in the ideal case where the EEPN is seen as noise on the optical phase):
Es(t)=Aexp(j(φs+φTx(t)+φLO(t)+φEEPN(t)+m(t)))
(1)
where n-level PSK modulation is considered, i.e. A is the modulated (real-valued) amplitude, φSis the carrier phase of the signal (the difference of carrier phase contributions from the transmitter (Tx) and local oscillator (LO) lasers), φTx(t)is the phase noise from the transmitter, φLO(t)is the phase noise from the local oscillator, φEEPN(t)is the noise from EEPN, and m(t) represents the phase modulation. The optical (RF) pilot tone is a CW optical signal from the same optical signal source as the modulated signal (i.e. it has the same phase noise but possibly a different carrier phase φRF). Then in the ideal case the field is given as:
ERF(t)=Bexp((j(φRF+φTx(t)+φLO(t))))
(2)
where B is an arbitrary constant amplitude. The conjugated signal operation that eliminates the intrinsic laser phase noise is given (within the arbitrary amplitude constant, B) as:
Es(t)ERF*(t)=BAexp(j(φSφRF+φEEPN(t)+m(t)))
(3)
where ‘*’ denotes complex conjugation. In Eq. (3) φSφRF is the extracted carrier phase and it appears that the influence of EEPN is not cancelled by the conjugated signal operation.

It is clear that if we can introduce an EEPN on the optical (RF) pilot which is fully correlated with (identical in this particular case) the EEPN on the signal then the conjugated signal operation in the Rx will eliminate the EEPN as well as the intrinsic laser phase noise. We investigate one way of doing this by distributed n-PSK modulation in two polarization states. If the generation of EEPN in the two polarizations is not fully correlated we can specify the effective correlation between the EEPN of the two polarization states through the parameter ρ (−1 ≤ ρ ≤ 1) which is specified through σEff2 = (1-ρ)2σEEPN2, where σEff2 corresponds to the BER-floor position (see Eq. (7) in the following section). Then the conjugation and multiplication operation of the Rx will only partly mitigate the EEPN influence and Eq. (3) is modified to read:
E1(t)E2*(t)=BAexp(j(φ1φ2+(1ρ)φEEPN(t)+m(t)))
(4)
where the carrier phase φ1φ2 is the difference in initial phase between the optical signals in the two polarization states for the system.

2.2 Phase noise analysis

It is relevant to discuss the total phase noise influence in the system. We will use a FDE filter for CD equalization. In this configuration the EEPN scales linearly with the accumulated chromatic dispersion and the linewidth of the LO laser [13

13. W. Shieh and K. P. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Express 16(20), 15718–15727 (2008). [CrossRef] [PubMed]

]. The LO laser that contributes to the generation of EEPN in the digital CD compensation process described via the variance
σEEPN2=πλ22cDLΔfLOTS2πΔfEETs
(5)
where λ is the central wavelength of the transmitted optical carrier wave, c is the light speed in vacuum, D is the chromatic dispersion coefficient of the transmission fiber, L is the transmission fiber length, ΔfLO is the 3-dB linewidth of the LO laser, ΔfEE is the 3 dB linewidth associated with EEPN and Ts is the symbol period of the transmission system. The effective phase noise variance specified in Eq. (5) has 2/3 contribution from the phase noise of EEPN and 1/3 from the amplitude noise [13

13. W. Shieh and K. P. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Express 16(20), 15718–15727 (2008). [CrossRef] [PubMed]

] showing that EEPN is not a pure phase noise and in this way differs from intrinsic laser phase noise. Equation (5) enables a definition of the effective intermediate frequency (IF) linewidth [22

22. T. Xu, G. Jacobsen, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Analytical estimation of phase noise influence in coherent transmission system with digital dispersion equalization,” Opt. Express 19(8), 7756–7768 (2011). [CrossRef] [PubMed]

] - which defines the phase noise influence in the receiver:
ΔfEffσTx2+σLO2+σEEPN22πTSσEff22πTs=ΔfTx+ΔfLO+ΔfEE
(6)
where ΔfTx is the 3-dB transmitter laser linewidth, σTx2=2πΔfTxTS is the transmitter laser phase noise variance, ΔfLO is the 3-dB local oscillator laser linewidth and σLO2=2πΔfLOTS is the LO laser phase noise variance. Equation (6) implies that correlation between the LO and EEPN phase noise contributions can be neglected which is a valid approximation for a normal transmission fiber for very short (few km) or longer distances (above the order of 80 km) [22

22. T. Xu, G. Jacobsen, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Analytical estimation of phase noise influence in coherent transmission system with digital dispersion equalization,” Opt. Express 19(8), 7756–7768 (2011). [CrossRef] [PubMed]

]. The BER-floor position which is defined from the phase noise influence using the optical (RF) pilot tone or the single tap normalized lease mean square (NLMS) filter to determine the carrier phase [29

29. Y. Mori, C. Zhang, K. Igarashi, K. Katoh, and K. Kikuchi, “Unrepeated 200-km transmission of 40-Gbit/s 16-QAM signals using digital coherent receiver,” Opt. Express 17(3), 1435–1441 (2009). [CrossRef] [PubMed]

] is specified as (for an nPSK Rx) [22

22. T. Xu, G. Jacobsen, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Analytical estimation of phase noise influence in coherent transmission system with digital dispersion equalization,” Opt. Express 19(8), 7756–7768 (2011). [CrossRef] [PubMed]

,30

30. G. Jacobsen, “Laser phase noise induced error rate floors in differential n-level phase-shift-keying coherent receivers,” Electron. Lett. 46(10), 698–700 (2010). [CrossRef]

]:

BERfloorNLMS1log2nerfc(πn2σEff)
(7)

Numerical examples will be considered in Section 3 of this paper.

In this paper we focus on n-level PSK systems which effectively utilize two polarizations to transmit the capacity of a normal one polarization system. The same total capacity can be implemented by using both polarizations for transmission with a capacity per polarization which is halved. Then the symbol time Ts is doubled and Eq. (5)Eq. (7) show that the BER floor position is moved down. If the floor position system with high single channel capacity is BERHC then the floor for the system with low capacity is in the order of BERLC ≈(BERHC)2. Thus the dual polarization system can very much eliminate the EEPN influence. For dual polarization operation the carrier phase extraction cannot be done using the optical (RF) pilot scheme as used in this paper, a single tap NLMS filter or the Viterbi-Viterbi algorithm has to be applied [31

31. T. Xu, G. Jacobsen, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Comparison of carrier phase estimation methods in coherent optical transmission systems influenced by equalization enhanced phase noise,” Opt. Commun. 293, 54–60 (2013). [CrossRef]

]. It is to be noted that the BER-floor approximation in Eq. (7) becomes poor (too optimistic by one order of magnitude or more) for dual polarization QPSK systems when the EEPN is significant and the carrier phase is estimated using the single tap NLMS filter or using the Viterbi-Viterbi algorithm (see e.g [31

31. T. Xu, G. Jacobsen, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Comparison of carrier phase estimation methods in coherent optical transmission systems influenced by equalization enhanced phase noise,” Opt. Commun. 293, 54–60 (2013). [CrossRef]

].). Thus a detailed comparison between dual polarization systems and single polarization systems using the optical (RF) principle to extract the carrier phase requires further studies. The results of the current paper show that Eq. (7) is an accurate approximation for large EEPN when the carrier phase is extracted using the optical (RF) principle as presented in section 2.1.

3. Simulation method, results and discussion

3.1 Use of distributed QPSK modulation

In the simulations, we consider a QPSK system with a symbol frequency of 28 GS/s, i.e. the single channel system capacity using In-phase and Quadrature modulation is 56 Gb/s.

We consider a normal single mode transmission fiber with dispersion coefficient D = 16 ps/nm/km and zero dispersion slope. The transmission distance L is 2000 km. We consider an intrinsic intermediate frequency 3 dB linewidth of ΔfLO = ΔfTx = 5 MHz. This gives an effective linewidth of ΔfEE = 206 MHz (see Eq. (6)). We utilize the software tool from VPI [25] for the system simulations, and we evaluate the Bit-Error-Rate versus optical signal-to-noise ratio (OSNR). In the Rx we apply optical (RF) pilot tone principle (see section 2.1) for carrier phase extraction.

Figure 2
Fig. 2 BER for single channel QPSK coherent system of Fig. 1 for transmitter and Local Oscillator linewidths equal to 5 MHz. Results are for transmission distance of 2000 km. Three curves with markers are simulation results for different phase modulation balance as indicated by the α-value. The PRBS length is 216-1. Analytically specified BER-floors (Eq. (7)) are shown by dashed lines with specified ρ-values. Figure abbreviations: OSNR - optical signal-to-noise ratio.
shows BER results. As a reference, we consider the case of α = 1 where the phase modulation is in one polarization only and an optical (RF) pilot tone is transmitted in the orthogonal polarization (Fig. 1 insert b)). In this case the EEPN is not cancelled by the optical (RF) pilot tone and the resulting BER-floor - given by Eq. (7) - of 4.9·10−4 – see dashed blue line. When the cases of α = 0.6/0.5 are considered, part of the EEPN is cancelled resulting in a BER-floor of 1.7·10−4 in the best case (α = 0.5).

We can observe that the implementation of the balanced phase modulation in two polarizations creates a partly correlated EEPN, and this is weakly dependent on the balancing (there is a very small difference in the EEPN cancellation effect between α of 0.6 and 0.5) with the strongest correlation for full balancing (α = 0.5). The EEPN cancellation improves the BER-floor position by about ½ order of magnitude, and thus it has a partial effect. This will be discussed more in section 3.2.

It may be of interest to describe the EEPN cancellation by fitting a BER-floor into the results for α = 0.5 we can specify the effective correlation between the EEPN of the two polarization states through the parameter ρ (−1 ≤ ρ ≤ 1) which is specified through σEff2 = (1-ρ)2σEEPN2 - where σEff2 corresponds to the BER-floor position – Eq. (7). In our case we find ρ = 0.0807 where a value of 1 corresponds to full correlation i.e. complete EEPN mitigation.

3.2 Using the Viterbi-Viterbi algorithm

We will now use the Viterbi-Viterbi algorithm in the Rx considering the transmission cases of Fig. 2. First we look at the effect of this on constellation diagrams for OSNR = 35 dB i.e. when EEPN generates a phase noise error-rate-floor. Figure 3
Fig. 3 Constellation diagrams for single channel QPSK coherent system of Fig. 1 for transmitter and Local Oscillator linewidths equal to 5 MHz. Results are for transmission distance of 2000 km and OSNR of 35 dB. Subfigures (a) and (d) are for α = 1 (classical QPSK system) with optical (RF) pilot tone carrier phase extraction (CPE) (a) and in addition using the Viterbi-Viterbi algorithm (d). Subfigures (b) and (e) are for distributed modulation QPSK (α = 0.5) with optical (RF) pilot tone CPE (b) and using in addition the Viterbi-Viterbi algorithm (e). Subfigures (c) and (f) are for classical QPSK with no optical (RF) pilot tone (using NLMS CPE) with Wiener phase noise and back-to-back transmission (Tx and LO linwidths of 103 MHz) (c) and using in addition the Viterbi-Viterbi algorithm (f).
shows the constellation diagrams for the single polarization QPSK system including an optical (RF) pilot tone in the orthogonal polarization state (α = 1). Results are given without using (Fig. 3(a)) and using (Fig. 3(d)) the Viterbi-Viterbi algorithm. Here we observe in Fig. 3(a) that the constellation symbols are influenced partly by phase noise (the noise cloud is partly banana-shaped) and partly by amplitude noise (the cloud center is circular) in agreement with the nature of EEPN discussed in section 2. The use of the Viterbi-Viterbi algorithm removes the part of the noise cloud which is due to phase noise and a large improvement in the BER is seen (to be quantified later).

Figure 3(b) and 3(e) show diagrams for the QPSK system with distributed phase modulation in two polarizations (α = 0.5). It appears that the modulation generates EEPN which is correlated with the QPSK symbols where the two upper symbols are dominated by phase noise whereas the lower symbols are dominated by additive noise. Also, the Viterbi-Viterbi algorithm does not improve the BER in this particular case. The reason for this is tentatively explained as follows: The Viterbi-Viterbi algorithm [32

32. A. J. Viterbi and A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory 29(4), 543–551 (1983). [CrossRef]

] is in the normal implementation for coherent optical QPSK systems (as used here [31

31. T. Xu, G. Jacobsen, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Comparison of carrier phase estimation methods in coherent optical transmission systems influenced by equalization enhanced phase noise,” Opt. Commun. 293, 54–60 (2013). [CrossRef]

]) raising the complex signal to power 4 in the QPSK case in order to eliminate the signal modulation. For this particular constellation (Fig. 3(b)) the noise is modulation dependent. Thus the Viterbi-Viterbi algorithm does not fully remove the modulation dependence and this is suggested to be the reason why it does not in an effective way mitigate the EEPN. Further theoretical investigation is needed in order to explain the simulation results in all details.

In Fig. 4
Fig. 4 BER for single channel QPSK coherent systems of Fig. 1. Curves are referred to the figure insert. Curves with α = 0.5 are for the distributed PSK modulation in two polarizations. Curves with α = 1 are for the full PSK modulation in one polarization and including an optical (RF) pilot tone in the orthogonal polarization state. Transmission distances are either back-to-back or 2000 km as indicated. Tx and LO laser have equal linwidths as specified in figure inserts. In the reference case with linewidths of 103 MHz and back-to-back transmission no optical (RF) pilot tone is included in the system and the carrier phase estimation is performed using a single tap NLMS filter (also indicated in the insert). Systems are compared using the Viterbi-Viterbi (VV) algorithm or not using it as indicated. The PRBS length for all cases is 216-1. Figure abbreviations: OSNR - optical signal-to-noise ratio; VV – Viterbi-Viterbi; PN – phase noise; NLMS – normalized least mean square.
we show how the phase noise sensitivity is dependent on the use of the Viterbi-Viterbi carrier phase extraction for the three QPSK implementations considered already in Fig. 3. It is observed that the improvement is very significant for the classical QPSK system with an optical (RF) pilot tone which is influenced by EEPN (as may be expected from Figs. 3(a) and 3(d)). An improvement of the BER-floor of more than two orders of magnitude is seen. The use of the Viterbi-Viterbi algorithm does not improve the situation for the distributed QPSK modulation case. We have shown in the figure also the classical QPSK case influenced by pure (Wiener) laser phase noise (Tx and LO linewidths of 103 MHz) using no optical (RF) pilot tone and using NLMS single tap carrier phase extraction. This gives a strong influence of the phase noise and using Viterbi-Viterbi for carrier phase extraction gives only a marginal improvement. Including an optical (RF) pilot tone for phase noise cancellation and carrier phase extraction provides complete phase noise cancellation in the pure phase noise case, and the resulting BER performance is given by the back-to-back results in Fig. 4 for linewidths of 5 MHz. These back-to-back results apply both for the QPSK system with distributed phase modulation between the orthogonal polarizations (α = 0.5) and to the QPSK system with full phase modulation in one polarization and an optical (RF) pilot tone in the orthogonal one (α = 1). The results are the same regardless of the use of the Viterbi-Viterbi algorithm as should be expected since no EEPN has been generated and the Wiener phase noise is small.

From Fig. 4 we conclude that the Viterbi-Viterbi algorithm is a “lucky punch” case particularly for classical QPSK systems influenced by EEPN. The algorithm is expected to work equally well for n-level PSK systems with n > 4.

We have extended our transmission range to 3000 km in order to compare in detail to BER-results of [15

15. R. Farhoudi, A. Ghazisaeidi, and L. A. Rusch, “Performance of carrier phase recovery for electronically dispersion compensated coherent systems,” Opt. Express 20(24), 26568–26582 (2012). [CrossRef] [PubMed]

] for QPSK systems with and without using the Viterbi-Viterbi algorithm and have found excellent agreement.

3.3 Comparison of shared modulation and Viterbi-Viterbi EEPN mitigation techniques for practical systems

The results presented here show that the use of the Viterbi-Viterbi algorithm to improve EEPN sensitivity for classical QPSK systems gives by far the best performance reducing the BER-floor induced by EEPN by more than two orders of magnitude. Furthermore, this implementation allows dual polarization operation of the system and thus it is capacity effective. A disadvantage is that the method is computational demanding as can be seen from the comparison in Table 1

Table 1. Complexity of carrier phase estimation (CPE) methods

table-icon
View This Table
between using the Viterbi-Viterbi algorithm (both to eliminate EEPN and/or to extract the carrier phase), using the optical (RF) pilot tone principle, or using a single tap NLMS filter. (The table is derived from considerations analogous to those for different dispersion compensation implementations in [12

12. T. Xu, G. Jacobsen, S. Popov, J. Li, E. Vanin, K. Wang, A. T. Friberg, and Y. Zhang, “Chromatic dispersion compensation in coherent transmission system using digital filters,” Opt. Express 18(15), 16243–16257 (2010). [CrossRef] [PubMed]

].) This is especially the case when using many cells NVV in the Viterbi-Viterbi algorithm. This is required when dealing with EEPN dominated noise (in the order of Nvv 35 in our case). This may especially be a problem when transmitting real time services that do not allow buffering in the receiver or services requiring low latency. Also the Viterbi-Viterbi method (as implemented as in [31

31. T. Xu, G. Jacobsen, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Comparison of carrier phase estimation methods in coherent optical transmission systems influenced by equalization enhanced phase noise,” Opt. Commun. 293, 54–60 (2013). [CrossRef]

]) does work for n-level PSK modulation but not for classical n-level QAM modulation (with non-circular constellations) where the single tap NLMS carrier phase extraction or the classical (unmodulated) optical (RF) pilot tone implementation works well.

Pilot-tone EEPN mitigation (with distributed QPSK modulation) works for n-level PSK modulated systems. It does not allow dual polarization operation. It gives less improvement of the EEPN sensitivity – about ½ order of magnitude for BER-floor position. However, it is computational effective and suited for real time system operation with low latency.

4. Conclusions

In this paper we propose a balanced phase modulation between two orthogonal polarizations of the optical signal in order to generate correlated equalization enhanced phase noise (EEPN) contributions in the two polarizations. The method is applicable for n-level PSK systems with coherent detection in the receiver. Then the EEPN can be in principle compensated by complex conjugation multiplication in the receiver, and the full phase modulated nPSK signal is regenerated. The proposed method is tested by system simulations in a single channel QPSK system at 56 Gb/s system rate. It is found that the conjugation and multiplication scheme cannot fully mitigate the EEPN. An improvement of about ½ order of magnitude in Bit-Error-Rate (BER) floor position is observed.

Results are compared to using the Viterbi-Viterbi algorithm to mitigate the EEPN in a classical QPSK system with an optical (RF) pilot tone in the orthogonal polarization relative to the signal. The Viterbi-Viterbi method improves the sensitivity by more than two orders of magnitude. We note that the Viterbi-Viterbi algorithm is equally effective in mitigating EEPN for dual polarization QPSK implementations (where the carrier phase is extracted e.g. from the Viterbi-Viterbi algorithm or using single tap NLMS filtering [31

31. T. Xu, G. Jacobsen, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Comparison of carrier phase estimation methods in coherent optical transmission systems influenced by equalization enhanced phase noise,” Opt. Commun. 293, 54–60 (2013). [CrossRef]

]).

It is seen that the use of the Viterbi-Viterbi algorithm does not improve the EEPN sensitivity any further for the system with distributed QPSK modulation in two orthogonal polarization states. For this system implementation, the receiver statistics is clearly symbol dependent and this seems to be the reason why the Viterbi-Viterbi method has problems. The Viterbi-Viterbi algorithm is found to be only marginally efficient for improving the sensitivity for Wiener laser phase noise rather than EEPN in the classical QPSK case. Thus, important novel insight into the statistical properties of EEPN is identified and discussed in this paper presenting subjects which need further investigation.

In this paper we show results for n-level PSK systems which effectively utilize two polarizations to transmit the capacity of a normal one polarization system. The same total capacity can be implemented by using both polarizations for transmission with a capacity per polarization which is halved. Then the symbol time Ts is doubled and Eq. (5)Eq. (7) shows that the BER floor position is moved down. If the floor position system with high single channel capacity is BERHC then the floor for the system with low capacity is about BERLC (BERHC)2. Thus the dual polarization system design can significantly eliminate the EEPN influence and the influence is mitigated further using the Viterbi-Viterbi algorithm. For dual polarization operation the carrier phase extraction cannot be done using the optical (RF) pilot scheme as used in this paper, a single tap NLMS filter or the Viterbi-Viterbi algorithm has to be applied. It is to be noted that the BER-floor approximation in Eq. (7) (without using the Viterbi-Viterbi algorithm) becomes poor (too optimistic by one order of magnitude or more) for dual polarization QPSK systems when the EEPN is significant and the carrier phase is estimated using the single tap NLMS filter or using the Viterbi-Viterbi algorithm (see e.g [31

31. T. Xu, G. Jacobsen, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Comparison of carrier phase estimation methods in coherent optical transmission systems influenced by equalization enhanced phase noise,” Opt. Commun. 293, 54–60 (2013). [CrossRef]

].). Thus a detailed comparison between dual polarization systems and single polarization systems using the optical (RF) principle to extract the carrier phase requires further studies. The results of the current paper show that Eq. (7) is an accurate approximation for large EEPN when the carrier phase is extracted using the optical (RF) principle as presented in section 2.1.

It is of practical interest to consider implications that can be derived from the study in this paper – which is focused on n-level PSK systems - to n-level QAM systems. For practical coherent n-level QAM systems, the use of optical (RF) pilot tone phase noise compensation using distributed modulation does not seem to be feasible. Nor does the Viterbi-Viterbi algorithm (in its current implementation [31

31. T. Xu, G. Jacobsen, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Comparison of carrier phase estimation methods in coherent optical transmission systems influenced by equalization enhanced phase noise,” Opt. Commun. 293, 54–60 (2013). [CrossRef]

]) work for classical QAM systems. For QAM systems it is advisable to select a dual polarization design using a LO-laser with little phase noise in order to eliminate EEPN effects as much as possible or to use hardware based chromatic dispersion compensation implementations. Such are the use of Dispersion Compensating Fibers (DCFs) (rather than digital dispersion compensation in the electronic domain) or the implementation of local oscillator phase noise cancellation by digital coherence enhancement [33

33. G. Colavolpe, T. Foggi, E. Forestieri, and M. Secondini, “Impact of phase noise and compensation techniques in coherent optical systems,” J. Lightwave Technol. 29(18), 2790–2800 (2011). [CrossRef]

]. The use of DCFs require a DSP implementation of an adaptive (few taps) NLMS dispersion compensation in the receiver [12

12. T. Xu, G. Jacobsen, S. Popov, J. Li, E. Vanin, K. Wang, A. T. Friberg, and Y. Zhang, “Chromatic dispersion compensation in coherent transmission system using digital filters,” Opt. Express 18(15), 16243–16257 (2010). [CrossRef] [PubMed]

] in order to admit fluctuations in the dispersion (e.g. due to temperature drafts). The DCF is commercially realized and simple to implement, whereas the LO phase noise cancellation is under research investigation and currently requires rather complex hardware implementation [33

33. G. Colavolpe, T. Foggi, E. Forestieri, and M. Secondini, “Impact of phase noise and compensation techniques in coherent optical systems,” J. Lightwave Technol. 29(18), 2790–2800 (2011). [CrossRef]

].

Acknowledgment

Support of the Engineering and Physical Sciences Research Council (EPSRC) project UNLOC, EP/J017582/1 and FP7-PEOPLE-2012-IAPP (project GRIFFON, No 324391) is acknowledged. We acknowledge constructive comments from two anonymous reviewers. The comments have helped to improve the presentation of the paper.

References and links

1.

P. S. Henry, “Lightwave primer,” IEEE J. Quantum Electron. 21(12), 1862–1879 (1985). [CrossRef]

2.

G. P. Agrawal, Fiber-optic communication systems 3rd Edition (John Wiley & Sons, Inc., 2002), Chap. 2.

3.

J. G. Proakis, Digital Communications 5th Edition (McGraw-Hill Companies, Inc., 2008), Chap. 10.

4.

M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett. 16(2), 674–676 (2004). [CrossRef]

5.

A. Färbert, S. Langenbach, N. Stojanovic, C. Dorschky, T. Kupfer, C. Schulien, J. P. Elbers, H. Wernz, H. Griesser, and C. Glingener, “Performance of a 10.7 Gb/s Receiver with digital equaliser using maximum likelihood sequence estimation,” in Proceeding of IEEE European Conference on Optical Communication (Stockholm, Sweden, 2004), paper Th4.1.5.

6.

S. J. Savory, G. Gavioli, R. I. Killey, and P. Bayvel, “Electronic compensation of chromatic dispersion using a digital coherent receiver,” Opt. Express 15(5), 2120–2126 (2007). [CrossRef] [PubMed]

7.

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

8.

S. J. Savory, “Compensation of fibre impairments in digital coherent systems,” in Proceeding of IEEE European Conference on Optical Communication (Brussels, Belgium, 2008), paper Mo.3.D.1.

9.

K. Ishihara, T. Kobayashi, R. Kudo, Y. Takatori, A. Sano, E. Yamada, H. Masuda, and Y. Miyamoto, “Coherent optical transmission with frequency-domain equalization,” in Proceeding of IEEE European Conference on Optical Communication (Brussels, Belgium, 2008), paper We.2.E.3.

10.

M. Kuschnerov, F. N. Hauske, K. Piyawanno, B. Spinnler, A. Napoli, and B. Lankl, “Adaptive chromatic dispersion equalization for non-dispersion managed coherent systems,” in Proceeding of IEEE Conference on Optical Fiber Communication (San Diego, California, 2009), paper OMT1. [CrossRef]

11.

R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, E. Yamada, H. Masuda, Y. Miyamoto, and M. Mizoguchi, “Two-stage overlap frequency domain equalization for long-haul optical systems,” in Proceeding of IEEE Conference on Optical Fiber Communication (San Diego, California, 2009), paper OMT3. [CrossRef]

12.

T. Xu, G. Jacobsen, S. Popov, J. Li, E. Vanin, K. Wang, A. T. Friberg, and Y. Zhang, “Chromatic dispersion compensation in coherent transmission system using digital filters,” Opt. Express 18(15), 16243–16257 (2010). [CrossRef] [PubMed]

13.

W. Shieh and K. P. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Express 16(20), 15718–15727 (2008). [CrossRef] [PubMed]

14.

A. P. T. Lau, T. S. R. Shen, W. Shieh, and K.-P. Ho, “Equalization-enhanced phase noise for 100 Gb/s transmission and beyond with coherent detection,” Opt. Express 18(16), 17239–17251 (2010). [CrossRef] [PubMed]

15.

R. Farhoudi, A. Ghazisaeidi, and L. A. Rusch, “Performance of carrier phase recovery for electronically dispersion compensated coherent systems,” Opt. Express 20(24), 26568–26582 (2012). [CrossRef] [PubMed]

16.

A. P. T. Lau, W. Shieh, and K. P. Ho, “Equalization-enhanced phase noise for 100Gb/s transmission with coherent detection,” in Proceedings of OptoElectronics and Communications Conference (Hong Kong, 2009), paper FQ3.

17.

K. P. Ho, A. P. T. Lau, and W. Shieh, “Equalization-enhanced phase noise induced timing jitter,” Opt. Lett. 36(4), 585–587 (2011). [CrossRef] [PubMed]

18.

C. Xie, “Local oscillator phase noise induced penalties in optical coherent detection systems using electronic chromatic dispersion compensation,” in Proceeding of IEEE Conference on Optical Fiber Communication (San Diego, California, 2009), paper OMT4. [CrossRef]

19.

C. Xie, “WDM coherent PDM-QPSK systems with and without inline optical dispersion compensation,” Opt. Express 17(6), 4815–4823 (2009). [CrossRef] [PubMed]

20.

I. Fatadin and S. J. Savory, “Impact of phase to amplitude noise conversion in coherent optical systems with digital dispersion compensation,” Opt. Express 18(15), 16273–16278 (2010). [CrossRef] [PubMed]

21.

S. Oda, C. Ohshima, T. Tanaka, T. Tanimura, H. Nakashima, N. Koizumi, T. Hoshida, H. Zhang, Z. Tao, and J. C. Rasmussen, “Interplay between Local oscillator phase noise and electrical chromatic dispersion compensation in digital coherent transmission system,” in Proceeding of IEEE European Conference on Optical Communication (Torino, Italy, 2010), paper Mo.1.C.2. [CrossRef]

22.

T. Xu, G. Jacobsen, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Analytical estimation of phase noise influence in coherent transmission system with digital dispersion equalization,” Opt. Express 19(8), 7756–7768 (2011). [CrossRef] [PubMed]

23.

G. Jacobsen, T. Xu, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Receiver implemented RF pilot tone phase noise mitigation in coherent optical nPSK and nQAM systems,” Opt. Express 19(15), 14487–14494 (2011). [CrossRef] [PubMed]

24.

G. Jacobsen, M. S. Lidón, T. Xu, S. Popov, A. T. Friberg, and Y. Zhang, “Influence of pre- and post-compensation of CD on EEPN in coherent multilevel systems,” J. Opt. Commun. 32, 257–261 (2012).

25.

www.vpiphotonics.com

26.

M. Nakamura, Y. Kamio, and T. Miyazaki, “Pilot-carrier based linewidth-tolerant 8PSK self-homodyne using only one modulator,” in Proceeding of IEEE European Conference on Optical Communication (Berlin, Germany, 2007), paper 8.3.6. [CrossRef]

27.

M. Nakamura, Y. Kamio, and T. Miyazaki, “Linewidth-tolerant 10-Gbit/s 16-QAM transmission using a pilot-carrier based phase-noise cancelling technique,” Opt. Express 16(14), 10611–10616 (2008). [CrossRef] [PubMed]

28.

S. L. Jansen, I. Morita, N. Takeda, and H. Tanaka, “20-Gb/s OFDM transmission over 4,160-km SSFM enabled by RF-pilot tone for phase noise compensation”, in Proceeding of Conference on Optical Fiber Communications, (Anaheim, California, 2007), paper PDP 15.

29.

Y. Mori, C. Zhang, K. Igarashi, K. Katoh, and K. Kikuchi, “Unrepeated 200-km transmission of 40-Gbit/s 16-QAM signals using digital coherent receiver,” Opt. Express 17(3), 1435–1441 (2009). [CrossRef] [PubMed]

30.

G. Jacobsen, “Laser phase noise induced error rate floors in differential n-level phase-shift-keying coherent receivers,” Electron. Lett. 46(10), 698–700 (2010). [CrossRef]

31.

T. Xu, G. Jacobsen, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Comparison of carrier phase estimation methods in coherent optical transmission systems influenced by equalization enhanced phase noise,” Opt. Commun. 293, 54–60 (2013). [CrossRef]

32.

A. J. Viterbi and A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory 29(4), 543–551 (1983). [CrossRef]

33.

G. Colavolpe, T. Foggi, E. Forestieri, and M. Secondini, “Impact of phase noise and compensation techniques in coherent optical systems,” J. Lightwave Technol. 29(18), 2790–2800 (2011). [CrossRef]

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

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: February 27, 2013
Revised Manuscript: April 5, 2013
Manuscript Accepted: May 8, 2013
Published: May 13, 2013

Citation
Gunnar Jacobsen, Tianhua Xu, Sergei Popov, and Sergey Sergeyev, "Study of EEPN mitigation using modified RF pilot and Viterbi-Viterbi based phase noise compensation," Opt. Express 21, 12351-12362 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-10-12351


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. P. S. Henry, “Lightwave primer,” IEEE J. Quantum Electron.21(12), 1862–1879 (1985). [CrossRef]
  2. G. P. Agrawal, Fiber-optic communication systems 3rd Edition (John Wiley & Sons, Inc., 2002), Chap. 2.
  3. J. G. Proakis, Digital Communications 5th Edition (McGraw-Hill Companies, Inc., 2008), Chap. 10.
  4. M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett.16(2), 674–676 (2004). [CrossRef]
  5. A. Färbert, S. Langenbach, N. Stojanovic, C. Dorschky, T. Kupfer, C. Schulien, J. P. Elbers, H. Wernz, H. Griesser, and C. Glingener, “Performance of a 10.7 Gb/s Receiver with digital equaliser using maximum likelihood sequence estimation,” in Proceeding of IEEE European Conference on Optical Communication (Stockholm, Sweden, 2004), paper Th4.1.5.
  6. S. J. Savory, G. Gavioli, R. I. Killey, and P. Bayvel, “Electronic compensation of chromatic dispersion using a digital coherent receiver,” Opt. Express15(5), 2120–2126 (2007). [CrossRef] [PubMed]
  7. S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express16(2), 804–817 (2008). [CrossRef] [PubMed]
  8. S. J. Savory, “Compensation of fibre impairments in digital coherent systems,” in Proceeding of IEEE European Conference on Optical Communication (Brussels, Belgium, 2008), paper Mo.3.D.1.
  9. K. Ishihara, T. Kobayashi, R. Kudo, Y. Takatori, A. Sano, E. Yamada, H. Masuda, and Y. Miyamoto, “Coherent optical transmission with frequency-domain equalization,” in Proceeding of IEEE European Conference on Optical Communication (Brussels, Belgium, 2008), paper We.2.E.3.
  10. M. Kuschnerov, F. N. Hauske, K. Piyawanno, B. Spinnler, A. Napoli, and B. Lankl, “Adaptive chromatic dispersion equalization for non-dispersion managed coherent systems,” in Proceeding of IEEE Conference on Optical Fiber Communication (San Diego, California, 2009), paper OMT1. [CrossRef]
  11. R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, E. Yamada, H. Masuda, Y. Miyamoto, and M. Mizoguchi, “Two-stage overlap frequency domain equalization for long-haul optical systems,” in Proceeding of IEEE Conference on Optical Fiber Communication (San Diego, California, 2009), paper OMT3. [CrossRef]
  12. T. Xu, G. Jacobsen, S. Popov, J. Li, E. Vanin, K. Wang, A. T. Friberg, and Y. Zhang, “Chromatic dispersion compensation in coherent transmission system using digital filters,” Opt. Express18(15), 16243–16257 (2010). [CrossRef] [PubMed]
  13. W. Shieh and K. P. Ho, “Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing,” Opt. Express16(20), 15718–15727 (2008). [CrossRef] [PubMed]
  14. A. P. T. Lau, T. S. R. Shen, W. Shieh, and K.-P. Ho, “Equalization-enhanced phase noise for 100 Gb/s transmission and beyond with coherent detection,” Opt. Express18(16), 17239–17251 (2010). [CrossRef] [PubMed]
  15. R. Farhoudi, A. Ghazisaeidi, and L. A. Rusch, “Performance of carrier phase recovery for electronically dispersion compensated coherent systems,” Opt. Express20(24), 26568–26582 (2012). [CrossRef] [PubMed]
  16. A. P. T. Lau, W. Shieh, and K. P. Ho, “Equalization-enhanced phase noise for 100Gb/s transmission with coherent detection,” in Proceedings of OptoElectronics and Communications Conference (Hong Kong, 2009), paper FQ3.
  17. K. P. Ho, A. P. T. Lau, and W. Shieh, “Equalization-enhanced phase noise induced timing jitter,” Opt. Lett.36(4), 585–587 (2011). [CrossRef] [PubMed]
  18. C. Xie, “Local oscillator phase noise induced penalties in optical coherent detection systems using electronic chromatic dispersion compensation,” in Proceeding of IEEE Conference on Optical Fiber Communication (San Diego, California, 2009), paper OMT4. [CrossRef]
  19. C. Xie, “WDM coherent PDM-QPSK systems with and without inline optical dispersion compensation,” Opt. Express17(6), 4815–4823 (2009). [CrossRef] [PubMed]
  20. I. Fatadin and S. J. Savory, “Impact of phase to amplitude noise conversion in coherent optical systems with digital dispersion compensation,” Opt. Express18(15), 16273–16278 (2010). [CrossRef] [PubMed]
  21. S. Oda, C. Ohshima, T. Tanaka, T. Tanimura, H. Nakashima, N. Koizumi, T. Hoshida, H. Zhang, Z. Tao, and J. C. Rasmussen, “Interplay between Local oscillator phase noise and electrical chromatic dispersion compensation in digital coherent transmission system,” in Proceeding of IEEE European Conference on Optical Communication (Torino, Italy, 2010), paper Mo.1.C.2. [CrossRef]
  22. T. Xu, G. Jacobsen, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Analytical estimation of phase noise influence in coherent transmission system with digital dispersion equalization,” Opt. Express19(8), 7756–7768 (2011). [CrossRef] [PubMed]
  23. G. Jacobsen, T. Xu, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Receiver implemented RF pilot tone phase noise mitigation in coherent optical nPSK and nQAM systems,” Opt. Express19(15), 14487–14494 (2011). [CrossRef] [PubMed]
  24. G. Jacobsen, M. S. Lidón, T. Xu, S. Popov, A. T. Friberg, and Y. Zhang, “Influence of pre- and post-compensation of CD on EEPN in coherent multilevel systems,” J. Opt. Commun.32, 257–261 (2012).
  25. www.vpiphotonics.com
  26. M. Nakamura, Y. Kamio, and T. Miyazaki, “Pilot-carrier based linewidth-tolerant 8PSK self-homodyne using only one modulator,” in Proceeding of IEEE European Conference on Optical Communication (Berlin, Germany, 2007), . [CrossRef]
  27. M. Nakamura, Y. Kamio, and T. Miyazaki, “Linewidth-tolerant 10-Gbit/s 16-QAM transmission using a pilot-carrier based phase-noise cancelling technique,” Opt. Express16(14), 10611–10616 (2008). [CrossRef] [PubMed]
  28. S. L. Jansen, I. Morita, N. Takeda, and H. Tanaka, “20-Gb/s OFDM transmission over 4,160-km SSFM enabled by RF-pilot tone for phase noise compensation”, in Proceeding of Conference on Optical Fiber Communications, (Anaheim, California, 2007), paper PDP 15.
  29. Y. Mori, C. Zhang, K. Igarashi, K. Katoh, and K. Kikuchi, “Unrepeated 200-km transmission of 40-Gbit/s 16-QAM signals using digital coherent receiver,” Opt. Express17(3), 1435–1441 (2009). [CrossRef] [PubMed]
  30. G. Jacobsen, “Laser phase noise induced error rate floors in differential n-level phase-shift-keying coherent receivers,” Electron. Lett.46(10), 698–700 (2010). [CrossRef]
  31. T. Xu, G. Jacobsen, S. Popov, J. Li, A. T. Friberg, and Y. Zhang, “Comparison of carrier phase estimation methods in coherent optical transmission systems influenced by equalization enhanced phase noise,” Opt. Commun.293, 54–60 (2013). [CrossRef]
  32. A. J. Viterbi and A. M. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory29(4), 543–551 (1983). [CrossRef]
  33. G. Colavolpe, T. Foggi, E. Forestieri, and M. Secondini, “Impact of phase noise and compensation techniques in coherent optical systems,” J. Lightwave Technol.29(18), 2790–2800 (2011). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited