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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 4 — Feb. 15, 2010
  • pp: 3919–3927
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Data-aided adaptive weighted channel equalizer for coherent optical OFDM

Mohammad E. Mousa-Pasandi and David V. Plant  »View Author Affiliations


Optics Express, Vol. 18, Issue 4, pp. 3919-3927 (2010)
http://dx.doi.org/10.1364/OE.18.003919


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Abstract

We report an adaptive weighted channel equalizer (AWCE) for orthogonal frequency division multiplexing (OFDM) and study its performance for long-haul coherent optical OFDM (CO-OFDM) transmission systems. This equalizer updates the equalization parameters on a symbol-by-symbol basis thus can track slight drifts of the optical channel. This is suitable to combat polarization mode dispersion (PMD) degradation while increasing the periodicity of pilot symbols which can be translated into a significant overhead reduction. Furthermore, AWCE can increase the precision of RF-pilot enabled phase noise estimation in the presence of noise, using data-aided phase noise estimation. Simulation results corroborate the capability of AWCE in both overhead reduction and improving the quality of the phase noise compensation (PNC).

© 2010 OSA

1. Introduction

OFDM was originally designed for wireless transmission, however, recently it has gained a great deal of attention in optical communications considering its ease of equalization and therefore, robustness with respect to the fiber transmission impairments such as chromatic dispersion (CD) and polarization mode dispersion (PMD) [1

1. W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express 16(2), 841–859 (2008). [CrossRef] [PubMed]

,2

2. W. Shieh, X. Yi, Y. Ma, and Q. Yang, “Coherent optical OFDM: has its time come?” J. Opt. Netw. 7(3), 234–255 (2008). [CrossRef]

]. OFDM transmits high-speed serial information through multiple lower-speed sub-channels. This reduction in the baud-rate leads to a reduction in inter-symbol interference (ISI) and therefore a simplification of the equalization process at the receiver.

One of the key features of digital signal processing (DSP) in optical fiber transmission systems is the capability of sending pilot symbols (PSs) which are known to the receiver to provide channel estimation. In optical OFDM, zero forcing estimation (ZFE) method has been often used to extract the channel information and to calculate the equalization parameters [2

2. W. Shieh, X. Yi, Y. Ma, and Q. Yang, “Coherent optical OFDM: has its time come?” J. Opt. Netw. 7(3), 234–255 (2008). [CrossRef]

5

5. S. L. Jansen, I. Morita, T. C. W. Schenk, N. Takeda, and H. Tanaka, “Theoretical and experimental investigations of direct-detected RF-tone assisted optical OFDM systems,” J. Lightwave Technol. 27(10), 1332–1339 (2009). [CrossRef]

]. For that, by comparing the received PS with the transmitted PS whose subcarriers are known, the channel transfer function for each subcarrier can be extracted by a single complex division. The accuracy of this estimation is often limited by the presence of noise and pattern dependent nonlinearities. To increase the accuracy of channel estimation, usually a time domain averaging method is used in which multiple pilot symbols are used to extract the channel transfer function matrices [2

2. W. Shieh, X. Yi, Y. Ma, and Q. Yang, “Coherent optical OFDM: has its time come?” J. Opt. Netw. 7(3), 234–255 (2008). [CrossRef]

,4

4. S. L. Jansen, I. Morita, T. Schenk, N. Takeda, and H. Tankada, “Coherent Optical 25.8-Gb/s OFDM Transmission Over 4160-km SSMF,” J. Lightwave Technol. 26(1), 6–15 (2008). [CrossRef]

,6

6. X. Liu and F. Buchali, “Intra-symbol frequency-domain averaging based channel estimation for coherent optical OFDM,” Opt. Express 16(26), 21944–21957 (2008). [CrossRef] [PubMed]

]. The improvement can also be obtained by averaging in the frequency domain over multiple subcarriers as presented in [6

6. X. Liu and F. Buchali, “Intra-symbol frequency-domain averaging based channel estimation for coherent optical OFDM,” Opt. Express 16(26), 21944–21957 (2008). [CrossRef] [PubMed]

]. To combat dynamic changes in channel characteristics, the PSs are periodically inserted into the OFDM data symbol sequence so that the channel estimation can be performed periodically in order to track the dynamic behavior of the channel. This basically presumes a stationary (non-varying) channel for the block of data symbols between each two consecutive sets of PSs; therefore, PSs should be sent at a speed that is much faster than the speed of significant channel physical changes. In fiber-optic communications, these physical changes are mainly originating from the PMD and the laser phase noise. The PMD varies due to the mechanical and temperature fluctuation on the time scale of a millisecond [6

6. X. Liu and F. Buchali, “Intra-symbol frequency-domain averaging based channel estimation for coherent optical OFDM,” Opt. Express 16(26), 21944–21957 (2008). [CrossRef] [PubMed]

,7

7. M. Karlsson, J. Brentel, and P. A. Andrekson, “Long-term Measurement of PMD and Polarization Drift in Installed Fibers,” J. Lightwave Technol. 18(7), 941–951 (2000). [CrossRef]

] however, there are reports on microsecond PMD changes under severe mechanical stress [8

8. P. Krummrich, and K. Kotten, “Extremely fast (microsecond timescale) polarization changes in high speed long haul WDM transmission systems,” in Optical Fiber Communication Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2004), paper FI3.

]. In [4

4. S. L. Jansen, I. Morita, T. Schenk, N. Takeda, and H. Tankada, “Coherent Optical 25.8-Gb/s OFDM Transmission Over 4160-km SSMF,” J. Lightwave Technol. 26(1), 6–15 (2008). [CrossRef]

], Jansen reported 25.8 Gb/s CO-OFDM by employing 2 pilot symbols for each 25 data symbols resulting in a 4% overhead only due to the PS insertion. Buchali, in [9

9. F. Buchali, R. Dischler, and X. Liu, “Optical OFDM: A Promising High-Speed Optical Transport Technology,” Bell Labs Tech. J. 14(1), 125–148 (2009). [CrossRef]

], reported a PS overhead of 5%. The PS overhead can be alternatively expressed as an increase in the required optical signal-to-noise ratio (OSNR), defined as ΔOSNRPS
ΔOSNRPS(dB)=10×log[(mSYM+mPS)/mSYM]
(1)
where mSYM and mPS are the number of the data symbols and pilot symbols per block, respectively.

The output of a single-frequency laser is not monochromatic and exhibits some phase noise which results in a finite linewidth of laser output, normally ranging from 100 kHz to several megahertz [2

2. W. Shieh, X. Yi, Y. Ma, and Q. Yang, “Coherent optical OFDM: has its time come?” J. Opt. Netw. 7(3), 234–255 (2008). [CrossRef]

]. Therefore, laser phase noise needs to be tracked on a symbol-by-symbol basis. By using the pilot subcarriers that are inserted in every OFDM symbol, such a fast time variation of the channel can be compensated. The pilot subcarriers are equally distributed over the OFDM spectrum and their state of modulation is known at the receiver. Shieh, in [10

10. X. Yi, W. Shieh, and Y. Tang, “Phase Estimation for Coherent Optical OFDM,” IEEE Photon. Technol. Lett. 19(12), 919–921 (2007). [CrossRef]

], studied the number of required pilot subcarriers for CO-OFDM systems. In [4

4. S. L. Jansen, I. Morita, T. Schenk, N. Takeda, and H. Tankada, “Coherent Optical 25.8-Gb/s OFDM Transmission Over 4160-km SSMF,” J. Lightwave Technol. 26(1), 6–15 (2008). [CrossRef]

,11

11. S. L. Jansen, I. Morita, N. Takeda, and H. Tanaka, “20-Gb/s OFDM transmission over 4,160-km SSMF enabled by RF-Pilot tone phase noise compensation,” in Optical Fiber Communication Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper PDP15.

], the authors proposed RF-pilot enabled PNC for CO-OFDM systems while ideally no extra optical bandwidth needs to be allocated. With this technique, PNC is realized by placing an RF-pilot tone in the middle of the OFDM band at the transmitter that is subsequently used at the receiver to revert phase noise impairments. However, there is a trade-off on the RF-pilot power: for low-power RF-pilot, the accumulated spontaneous emission (ASE) noise reduces the degree with which the phase noise can be compensated for, whereas for high-power RF-pilot the OSNR of the OFDM signal becomes too low and the received signal quality degrades [4

4. S. L. Jansen, I. Morita, T. Schenk, N. Takeda, and H. Tankada, “Coherent Optical 25.8-Gb/s OFDM Transmission Over 4160-km SSMF,” J. Lightwave Technol. 26(1), 6–15 (2008). [CrossRef]

,11

11. S. L. Jansen, I. Morita, N. Takeda, and H. Tanaka, “20-Gb/s OFDM transmission over 4,160-km SSMF enabled by RF-Pilot tone phase noise compensation,” in Optical Fiber Communication Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper PDP15.

].

2. Theory of operation

Assume n denotes the index for the received symbol (time index) and k is the index for the OFDM subcarrier (frequency index). The subcarrier-specific received complex value symbol, Rn,k, is equalized by applying a zero-forcing technique based on the previously estimated transfer factor, H˜n1,k, that is taken as a prediction of the current channel transfer factor:
S^n,k=Rn,kH˜n1,kejΔϕpilot,n
(2)
where S^n,k is the subcarrier-specific equalized complex value symbol and the term Δϕpilot,n is to compensate for the laser phase noise and can be extracted by using RF-pilot [4

4. S. L. Jansen, I. Morita, T. Schenk, N. Takeda, and H. Tankada, “Coherent Optical 25.8-Gb/s OFDM Transmission Over 4160-km SSMF,” J. Lightwave Technol. 26(1), 6–15 (2008). [CrossRef]

] or pilot subcarriers [1

1. W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express 16(2), 841–859 (2008). [CrossRef] [PubMed]

,2

2. W. Shieh, X. Yi, Y. Ma, and Q. Yang, “Coherent optical OFDM: has its time come?” J. Opt. Netw. 7(3), 234–255 (2008). [CrossRef]

]; however, in this paper, we focus on the data-aided PNC based on RF-pilot enabled phase noise estimation. S^n,k is then detected by the demodulator to make decision. Presuming that the decision was correct, the received symbol, Rn,k, can be further divided by the detected symbol, S¯n,k, in order to calculate a new channel transfer factor,H^n,k:

H^n,k=Rn,kS¯n,k
(3)

We call this new channel transfer factor as the ideal channel transfer factor since if we knew it before demodulation and could apply it as the denominator in Eq. (1), then a perfect equalization and decision making would be achieved. H^n,k is basically the updated version of H˜n1,k and includes the information of the optical channel drifts in the time interval of the symbol number n. A low-pass filter (LPF) can be applied to H^n,k to suppress the high- frequency detected noise without applying time averaging over several channel transfer functions in each block as presented in [14

14. M. E. Mousa Pasandi, J. Haghighat, and D. V. Plant, “Adaptive weighted channel equalizer for direct-detection optical OFDM transmission systems,” in Proceedings of IEEE Photonics Society Summer Topicals’09, (Institute of Electrical and Electronics Engineers, New York, 2009), pp. 85–86.

]. At this point, a more accurate estimation of laser phase noise can be provided that can subsequently lead into better PNC. For that, one extra step is required in which we average the difference between the phase term of the ideal channel transfer function and the phase term of the previously estimated transfer function over all subcarriers:
ΔϕAWCE,n=(i=1N(arg{H^n,i}arg{H˜n1,i}))/N
(4)
where N is the total number of OFDM subcarriers including all data subcarriers. Equation (4) tries to extract the phase drift of the optical channel in the time interval equal to the duration of one OFDM symbol and assumes that the drift due to the PMD is negligible. This is a good assumption since PMD variations are low-speed (in the range of kHz) in comparison to the typical CO-OFDM symbol rate. Now, Δϕpilot,n in Eq. (2) can be replaced by ΔϕAWCE,n to provide a more accurate PNC and the new resulting S^n,k is again sent to the demodulator for better decision making. As we see in Eq. (4), since ΔϕAWCE,n is calculated by averaging over all OFDM sub-channels, it is capable of suppressing the effect of ASE noise and therefore, providing a more accurate phase noise estimation. However, because the calculation of Eq. (4) is done after the demodulation and is dependent on Eq. (2), a fairly reliable RF-pilot enabled phase noise estimation is necessary to prevent error propagation.

The adaptive weighting parameter, γ, can also be used in a different way: it can be first transformed by a function f and then, applied to the Eq. (5). f can be any non-decreasing function such as a sigmoid nonlinear function as been used for reliability factors of weighted decision feedback equalizers in [15

15. J. Palicot and A. Goupil, “Performance analysis of the weighted decision feedback equalizer,” Signal Process. 88(2), 284–295 (2008). [CrossRef]

]. Regarding the fact that our main focus in this paper is the concept of the data-aided equalizer and for the sake of simplicity, we use the identity function as f.

3. Simulation of AWCE performance in CO-OFDM transmission system

To mimic the continuous time characteristics of the optical channel, 50 different random sets of time-domain realizations of laser phase noise and PMD have been simulated. The laser phase noise is modeled using the well-established model, described in [16

16. R. W. Tkach and A. R. Chraplyvy, “Phase Noise and Linewidth in an InGaAsP DFB Laser,” J. Lightwave Technol. 4(11), 1711–1716 (1986). [CrossRef]

]. This model assumes that the laser phase undergoes a random walk where the steps are individual spontaneous emission events which instantaneously change the phase by a small amount in a random way. We considered a laser linewidth of 100 kHz for both transmitter and receiver sides. The dynamic response of the PMD is simulated using dynamic wave plate model as proposed in [17

17. C. Xie, D. Werner, and H. F. Haunstein, “Dynamic Performance and Speed Requirement of Polarization Mode Dispersion Compensators,” J. Lightwave Technol. 24(11), 3968–3975 (2006). [CrossRef]

]. This model generates a continuous PMD variation and correlation between adjacent time samples. The PMD coefficient of the fiber medium was set to 0.5 ps/√km and 1600 wave plates were taken into account. Other simulation parameters were properly adjusted to emulate a fast PMD speed in the range of microsecond-scale to millisecond-scale.

As discussed in section 2, AWCE is capable of improving the performance of PNC. Figure 4
Fig. 4 The BER performance of the data-aided PNC for two different received OSNR values of 13 and 16 dB.
compares the BER performance of AWCE versus PSR, with and without data-aided PNC for two different received OSNR values of 13 dB and 16 dB. In this simulation, each OFDM block consists of 2 pilot symbols and 62 data symbols (an overhead of 3% due to PS insertion). In both received OSNR cases, for lower values of PSR, data-aided PNC slightly improves the performance however, as PSR increases it significantly increases the precision of phase noise estimation and therefore, better BER results are obtained. This is due to the fact that data-aided PNC relies on the correct decision making and a fairly good RF-pilot enabled phase noise estimation is required to achieve a pronounced improvement. As one can see, to achieve the forward-error-correction (FEC) threshold, the commonly-reported BER value of 10−3, AWCE with data-aided PNC requires 1 and 2.2 dB less RF-pilot power for the received OSNR values of 16 and 13 dB, respectively, showing higher improvement for the noisier scenario.

In Fig. 5
Fig. 5 The comparison between the BER performance of ZFE with the PS overhead of 3% and 0.3% and AWCE with the PS overhead of 0.3%.
, we investigate the capability of AWCE on PS overhead reduction. For that, we fixed the PSR at −10 dB for all simulations. As one can see for the case of ZFE, when we reduce the PS overhead from 3% (blue curve) to 0.3% (red curve), the signal quality degrades. This degradation introduces an OSNR penalty of 1.2 dB at the FEC threshold. However, when we apply AWCE, without data-aided PNC, to the signal with PS overhead of 0.3%, almost the same performance as ZFE with PS overhead of 3% can be achieved (see the black curve in Fig. 5). This demonstrates that AWCE can significantly reduce the PS overhead, here by a factor of 10, while providing the same signal quality. This improvement is due to the fact that AWCE updates the equalization parameters on a symbol-by-symbol basis and can track slight drifts in the optical channel. Moreover, AWCE with data-aided PNC can further improve the signal quality. As seen by the green curve in Fig. 5, to achieve the BER of 10−3, AWCE with data-aided PNC and PS overhead of 0.3% requires 2.9 and 1.8 dB less OSNR than ZFE with PS overhead of 0.3% and 3%, respectively. This is due to the fact that AWCE not only tracks the PMD drifts but also provides enhanced phase noise estimation and consequently more accurate compensation.

Figure 6
Fig. 6 The comparison between the received constellations after 2000 km transmission, equalized by ZFE and AWCE. The PS overhead is 0.3% for both cases.
compares the received constellation of QPSK signal after equalization by ZFE and AWCE with data-aided PNC. The overhead of PS insertion, the received OSNR and the PSR for both cases are set to 0.3%, 16 dB and −10 dB, respectively. It can be clearly observed that AWCE provides better equalization and subsequently separated constellation points.

4. Conclusion

Acknowledgements

The authors would like to thank Dr. Javad Haghighat for his collaboration and Dr. Pegah Seddighian and Prof. Lawrence R. Chen for the fruitful discussions. The authors gratefully acknowledge the financial support from the NSERC/Bell Canada Industrial Research Chair.

References and links

1.

W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express 16(2), 841–859 (2008). [CrossRef] [PubMed]

2.

W. Shieh, X. Yi, Y. Ma, and Q. Yang, “Coherent optical OFDM: has its time come?” J. Opt. Netw. 7(3), 234–255 (2008). [CrossRef]

3.

I. B. Djordjevic and B. Vasic, “Orthogonal frequency division multiplexing for high-speed optical transmission,” Opt. Express 14(9), 3767–3775 (2006). [CrossRef] [PubMed]

4.

S. L. Jansen, I. Morita, T. Schenk, N. Takeda, and H. Tankada, “Coherent Optical 25.8-Gb/s OFDM Transmission Over 4160-km SSMF,” J. Lightwave Technol. 26(1), 6–15 (2008). [CrossRef]

5.

S. L. Jansen, I. Morita, T. C. W. Schenk, N. Takeda, and H. Tanaka, “Theoretical and experimental investigations of direct-detected RF-tone assisted optical OFDM systems,” J. Lightwave Technol. 27(10), 1332–1339 (2009). [CrossRef]

6.

X. Liu and F. Buchali, “Intra-symbol frequency-domain averaging based channel estimation for coherent optical OFDM,” Opt. Express 16(26), 21944–21957 (2008). [CrossRef] [PubMed]

7.

M. Karlsson, J. Brentel, and P. A. Andrekson, “Long-term Measurement of PMD and Polarization Drift in Installed Fibers,” J. Lightwave Technol. 18(7), 941–951 (2000). [CrossRef]

8.

P. Krummrich, and K. Kotten, “Extremely fast (microsecond timescale) polarization changes in high speed long haul WDM transmission systems,” in Optical Fiber Communication Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2004), paper FI3.

9.

F. Buchali, R. Dischler, and X. Liu, “Optical OFDM: A Promising High-Speed Optical Transport Technology,” Bell Labs Tech. J. 14(1), 125–148 (2009). [CrossRef]

10.

X. Yi, W. Shieh, and Y. Tang, “Phase Estimation for Coherent Optical OFDM,” IEEE Photon. Technol. Lett. 19(12), 919–921 (2007). [CrossRef]

11.

S. L. Jansen, I. Morita, N. Takeda, and H. Tanaka, “20-Gb/s OFDM transmission over 4,160-km SSMF enabled by RF-Pilot tone phase noise compensation,” in Optical Fiber Communication Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper PDP15.

12.

M. Rim, “Optimally combining decision-directed and pilot-symbol-aided channel estimation,” Electron. Lett. 39(6), 558–560 (2003). [CrossRef]

13.

J. Ran, R. Grunheid, H. Rohling, E. Bolinth, and R. Kern, “Decision-directed channel estimation method for OFDM systems with high velocities,” in Proceedings of IEEE Vehicular Technology Conference, (Institute of Electrical and Electronics Engineers, New York, 2003), pp. 2358–2361.

14.

M. E. Mousa Pasandi, J. Haghighat, and D. V. Plant, “Adaptive weighted channel equalizer for direct-detection optical OFDM transmission systems,” in Proceedings of IEEE Photonics Society Summer Topicals’09, (Institute of Electrical and Electronics Engineers, New York, 2009), pp. 85–86.

15.

J. Palicot and A. Goupil, “Performance analysis of the weighted decision feedback equalizer,” Signal Process. 88(2), 284–295 (2008). [CrossRef]

16.

R. W. Tkach and A. R. Chraplyvy, “Phase Noise and Linewidth in an InGaAsP DFB Laser,” J. Lightwave Technol. 4(11), 1711–1716 (1986). [CrossRef]

17.

C. Xie, D. Werner, and H. F. Haunstein, “Dynamic Performance and Speed Requirement of Polarization Mode Dispersion Compensators,” J. Lightwave Technol. 24(11), 3968–3975 (2006). [CrossRef]

OCIS Codes
(060.1660) Fiber optics and optical communications : Coherent communications
(060.4080) Fiber optics and optical communications : Modulation

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: November 9, 2009
Revised Manuscript: January 14, 2010
Manuscript Accepted: February 1, 2010
Published: February 12, 2010

Citation
Mohammad E. Mousa-Pasandi and David V. Plant, "Data-aided adaptive weighted channel equalizer for coherent optical OFDM," Opt. Express 18, 3919-3927 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-4-3919


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References

  1. W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express 16(2), 841–859 (2008). [CrossRef] [PubMed]
  2. W. Shieh, X. Yi, Y. Ma, and Q. Yang, “Coherent optical OFDM: has its time come?” J. Opt. Netw. 7(3), 234–255 (2008). [CrossRef]
  3. I. B. Djordjevic and B. Vasic, “Orthogonal frequency division multiplexing for high-speed optical transmission,” Opt. Express 14(9), 3767–3775 (2006). [CrossRef] [PubMed]
  4. S. L. Jansen, I. Morita, T. Schenk, N. Takeda, and H. Tankada, “Coherent Optical 25.8-Gb/s OFDM Transmission Over 4160-km SSMF,” J. Lightwave Technol. 26(1), 6–15 (2008). [CrossRef]
  5. S. L. Jansen, I. Morita, T. C. W. Schenk, N. Takeda, and H. Tanaka, “Theoretical and experimental investigations of direct-detected RF-tone assisted optical OFDM systems,” J. Lightwave Technol. 27(10), 1332–1339 (2009). [CrossRef]
  6. X. Liu and F. Buchali, “Intra-symbol frequency-domain averaging based channel estimation for coherent optical OFDM,” Opt. Express 16(26), 21944–21957 (2008). [CrossRef] [PubMed]
  7. M. Karlsson, J. Brentel, and P. A. Andrekson, “Long-term Measurement of PMD and Polarization Drift in Installed Fibers,” J. Lightwave Technol. 18(7), 941–951 (2000). [CrossRef]
  8. P. Krummrich, and K. Kotten, “Extremely fast (microsecond timescale) polarization changes in high speed long haul WDM transmission systems,” in Optical Fiber Communication Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2004), paper FI3.
  9. F. Buchali, R. Dischler, and X. Liu, “Optical OFDM: A Promising High-Speed Optical Transport Technology,” Bell Labs Tech. J. 14(1), 125–148 (2009). [CrossRef]
  10. X. Yi, W. Shieh, and Y. Tang, “Phase Estimation for Coherent Optical OFDM,” IEEE Photon. Technol. Lett. 19(12), 919–921 (2007). [CrossRef]
  11. S. L. Jansen, I. Morita, N. Takeda, and H. Tanaka, “20-Gb/s OFDM transmission over 4,160-km SSMF enabled by RF-Pilot tone phase noise compensation,” in Optical Fiber Communication Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper PDP15.
  12. M. Rim, “Optimally combining decision-directed and pilot-symbol-aided channel estimation,” Electron. Lett. 39(6), 558–560 (2003). [CrossRef]
  13. J. Ran, R. Grunheid, H. Rohling, E. Bolinth, and R. Kern, “Decision-directed channel estimation method for OFDM systems with high velocities,” in Proceedings of IEEE Vehicular Technology Conference, (Institute of Electrical and Electronics Engineers, New York, 2003), pp. 2358–2361.
  14. M. E. Mousa Pasandi, J. Haghighat, and D. V. Plant, “Adaptive weighted channel equalizer for direct-detection optical OFDM transmission systems,” in Proceedings of IEEE Photonics Society Summer Topicals’09, (Institute of Electrical and Electronics Engineers, New York, 2009), pp. 85–86.
  15. J. Palicot and A. Goupil, “Performance analysis of the weighted decision feedback equalizer,” Signal Process. 88(2), 284–295 (2008). [CrossRef]
  16. R. W. Tkach and A. R. Chraplyvy, “Phase Noise and Linewidth in an InGaAsP DFB Laser,” J. Lightwave Technol. 4(11), 1711–1716 (1986). [CrossRef]
  17. C. Xie, D. Werner, and H. F. Haunstein, “Dynamic Performance and Speed Requirement of Polarization Mode Dispersion Compensators,” J. Lightwave Technol. 24(11), 3968–3975 (2006). [CrossRef]

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