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Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 11 — Jun. 2, 2014
  • pp: 13454–13459
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Digital coherent superposition of optical OFDM subcarrier pairs with Hermitian symmetry for phase noise mitigation

Xingwen Yi, Xuemei Chen, Dinesh Sharma, Chao Li, Ming Luo, Qi Yang, Zhaohui Li, and Kun Qiu  »View Author Affiliations


Optics Express, Vol. 22, Issue 11, pp. 13454-13459 (2014)
http://dx.doi.org/10.1364/OE.22.013454


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Abstract

Digital coherent superposition (DCS) provides an approach to combat fiber nonlinearities by trading off the spectrum efficiency. In analogy, we extend the concept of DCS to the optical OFDM subcarrier pairs with Hermitian symmetry to combat the linear and nonlinear phase noise. At the transmitter, we simply use a real-valued OFDM signal to drive a Mach-Zehnder (MZ) intensity modulator biased at the null point and the so-generated OFDM signal is Hermitian in the frequency domain. At receiver, after the conventional OFDM signal processing, we conduct DCS of the optical OFDM subcarrier pairs, which requires only conjugation and summation. We show that the inter-carrier-interference (ICI) due to phase noise can be reduced because of the Hermitain symmetry. In a simulation, this method improves the tolerance to the laser phase noise. In a nonlinear WDM transmission experiment, this method also achieves better performance under the influence of cross phase modulation (XPM).

© 2014 Optical Society of America

1. Introduction

Coherent optical OFDM (CO-OFDM) has been demonstrated as a viable solution for high-capacity and long-haul transmissions [1

1. W. Shieh, X. Yi, and Y. Tang, “Transmission experiment of multi-gigabit coherent optical OFDM systems over 1000 km SSMF fiber,” Electron. Lett. 43(3), 183–185 (2007). [CrossRef]

4

4. D. Qian, M. Huang, E. Ip, Y. Huang, Y. Shao, J. Hu, and T. Wang, “101.7-Tb/s (370×294-Gb/s) PDM-128QAM-OFDM transmission over 3×55-km SSMF using pilot-based phase noise mitigation,” in Optical Fiber Commun. Conf., USA (2011), paper PDPB5.

]. However it is well-known that OFDM is sensitive to phase noise leading to inter-carrier interference (ICI) [5

5. S. Wu and Y. Bar-Ness, “OFDM systems in the presence of phase noise: consequences and solutions,” IEEE Trans. Commun. 52(11), 1988–1996 (2004). [CrossRef]

]. It is aggravated in CO-OFDM because of the linear phase noise of laser sources and the nonlinear phase noise due to fiber nonlinearity [6

6. X. Yi, W. Shieh, and Y. Ma, “Phase noise effects on high spectral efficiency coherent optical OFDM transmission,” J. Lightwave Technol. 26(10), 1309–1316 (2008). [CrossRef]

], which limits the capacity of optical fiber transmissions. Some of the existing methods of reducing ICI lower the spectrum efficiency by half to combat phase noise [7

7. J. Armstrong, “Analysis of new and existing methods of reducing intercarrier interference due to carrier frequency offset in OFDM,” IEEE Trans. Commun. 47(3), 365–369 (1999). [CrossRef]

]. This trade-off could be justified in certain scenarios. In fact, it has been proposed in single-carrier systems, namely digital coherent superposition (DCS) [8

8. X. Liu, S. Chandrasekhar, P. J. Winzer, A. R. Chraplyvy, R. W. Tkach, B. Zhu, T. F. Taunay, M. Fishteyn, and D. J. DiGiovanni, “Scrambled coherent superposition for enhanced optical fiber communication in the nonlinear transmission regime,” Opt. Express 20(17), 19088–19095 (2012). [CrossRef] [PubMed]

], where otherwise the DSP-based methods tend to have unpractical computational complexity to combat the fiber nonlinearity. For single-core fiber transmissions, Liu et al. have proposed phase-conjugated twin waves on two polarization tributaries over a record distance in fiber [9

9. X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 7(7), 560–568 (2013). [CrossRef]

]. Tian et al. has demonstrated a conjugated copy via four-wave mixing, which can cancel the phase noise after DCS [10

10. Y. Tian, Y. K. Huang, S. Zhang, P. R. Prucnal, and T. Wang, “Demonstration of digital phase-sensitive boosting to extend signal reach for long-haul WDM systems using optical phase-conjugated copy,” Opt. Express 21(4), 5099–5106 (2013). [CrossRef] [PubMed]

].

2. ICI reduction by DCS of OFDM subcarrier pairs with Hermitian symmetry

Let X(k) denote the transmitted data in subcarrier of an OFDM symbol. The low-pass equivalent output after IDFT with a length of N can be expressed as

s(m)=1Nk=0N1X(k)exp(j2πkm/N),k,m=0,...,N1.
(1)

This output is real-valued if we pair up the OFDM subcarriers with Hermitian symmetry,
X(Nk)=X*(k),
(2)
where * stands for conjugation. For simplicity, we have dropped the index of OFDM symbols in this paper. Equation (2) also means that half of the OFDM subcarriers carry the redundant data, which lowers the spectrum efficiency by half. To up-convert this real signal s(m) with polarity to the optical domain, we use an intensity MZ modulator biased at the null point [13

13. Y. Tang, W. Shieh, X. Yi, and R. Evans, “Optimum design for RF-to-optical up-converter in coherent optical OFDM systems,” IEEE Photon. Technol. Lett. 19(7), 483–485 (2007). [CrossRef]

]. Note this configuration was used in the early demonstration of CO-OFDM, where the redundant OFDM subcarriers were also treated as the effective data for performance evaluation [1

1. W. Shieh, X. Yi, and Y. Tang, “Transmission experiment of multi-gigabit coherent optical OFDM systems over 1000 km SSMF fiber,” Electron. Lett. 43(3), 183–185 (2007). [CrossRef]

]. Here we re-use the redundant OFDM subcarriers by the concept of DCS to combat phase noise.

To focus on the phase noise ϕ(m), we ignore the channel response and the AWGN noise, and the received OFDM signal is

y(m)=s(m)exp[jϕ(m)].
(3)

Assuming a perfect DFT window synchronization, the received OFDM subcarriers with common phase error (CPE) and ICI are [5

5. S. Wu and Y. Bar-Ness, “OFDM systems in the presence of phase noise: consequences and solutions,” IEEE Trans. Commun. 52(11), 1988–1996 (2004). [CrossRef]

]

Yk=XkI(0)+ICI(k),
(4)
ICI(k)=l=0,lkN1X(l)I(kl),
(5)
I(k)=1Nn=0N-1exp[j2πkn/N+jϕ(n)].
(6)

The CPE phase estimation is to calculate ψ=arg[I(0)], i.e., the angle of I(0) [14

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

]. We assume that the CPE phase estimation is accurate, then after the CPE phase compensation, the recovered OFDM subcarriers are

Y^k=Xk|I(0)|+ICI(k)exp(jψ).
(7)

Assuming that the transmitted data are mutually independent with zero mean and variance of Es, and following a similar derivation in [15

15. T. Pollet, M. Van Bladel, and M. Moeneclaey, “BER sensitivity of OFDM systems to carrier frequency offset andWiener phase noise,” IEEE Trans. Commun. 43(2/3/4), 191–193 (1995). [CrossRef]

], the noise variance due to ICI is
|ICI(k)|2=Es(1|I(0)|2),
(8)
where stands for the average operation. The DCS of OFDM subcarrier pairs with Hermitian symmetry can be expressed as

(Y^k+Y^Nk*)/2=Xk|I(0)|+ICI(k)exp(jψ)/2+ICI*(Nk)exp(jψ)/2.
(9)

On the other hand,combining Eqs. (2) and (5) yields

ICI*(Nk)=l=0,lkN1X(l)I*(lk).
(10)

Inserting Eq. (10) to (9) yields

(Y^k+Y^Nk*)/2=Xk|I(0)|+ICIDCS(k),
(11)
ICIDCS(k)=l=0,lkN1X(l)IDCS(kl),
(12)
IDCS(k)=1Nn=0N-1exp(j2πkn/N)cos[ϕ(n)-ψ].
(13)

Comparing Eqs. (6) and (12), in the conventional OFDM, the ICI is from the phase noise exp[jϕ(n)],whereas in DCS-OFDM, the ICI is from cos[ϕ(n)-ψ].

Equation (13) also means that IDCS(k) is the IDFT output of cos[ϕ(n)-ψ] divided by a factor of 1/N and further, the Fourier transform does not change the signal power, denoted as A. We obtain

A=k=0N1|IDCS(k)|2=|cos[ϕ(n)-ψ]|2,
(14)
|ICIDCS(k)|2=Es(A|IDCS(0)|2).
(15)

To compare the values of Eqs. (8) and (15), firstly, from the definition of ψ, we have ϕ(n)-ψ=0 and therefore,

|IDCS(0)|2=|cos[ϕ(n)ψ]|2|exp[jϕ(n)jψ]|2=|exp[jϕ(n)]|2=|I(0)|2.
(16)

Secondly, from Eq. (14), we are certain that A<1. Therefore we conclude that |ICIDCS(k)|2<|ICI(k)|2, which means that the ICI noise power is reduced. It also becomes clear that DCS-OFDM mitigates the ICI by reducing the energy of exp[jϕ(n)] to that of cos[ϕ(n)-ψ].

Note that our derivation above is general and applicable to either laser phase noise or nonlinear phase noise. Our future research will quantify the ICI reduction, which requires the statistical characteristics of phase noise.

3. Simulation of DCS-OFDM under the laser phase noise

We conduct a simple simulation of CO-OFDM with single-polarization to investigate the effect of laser phase noise on DCS-OFDM. We have three cases for comparison:

Case I: A conventional CO-OFDM transmission using an IQ modulator at transmitter. This is the baseline for our comparison.

Case II: At the transmitter, we use a real-valued OFDM signal to drive an MZ intensity modulator biased at the null point. At the receiver, we follow the conventional DSP of CO-OFDM and count the BER for all the OFDM subcarriers, despite that half of them are redundant. This is identical to the configuration in [1

1. W. Shieh, X. Yi, and Y. Tang, “Transmission experiment of multi-gigabit coherent optical OFDM systems over 1000 km SSMF fiber,” Electron. Lett. 43(3), 183–185 (2007). [CrossRef]

], except that we use a direct down-conversion coherent receiver.

Case III: It is very similar to Case II, but we conduct the DSC for the OFDM subcarrier pairs with Hermitian symmetry, i.e., DCS-OFDM.

In Case I, the sampling rate of DAC is 10 GS/S and IDFT length is 128. Both parameters are doubled in Case II and III. In three cases, we intentionally equal the OFDM subcarrier bandwidth, which is the main parameter to investigate the effect of the laser phase [3

3. S. L. Jansen, I. Morita, C. W. Schenk, N. Takeda, and H. Tanaka, “Coherent optical 25.8-Gb/s OFDM transmission over 4160-km SSMF,” J. Lightwave Technol. 26(1), 6–15 (2008). [CrossRef]

]. The cyclic prefix (CP) is 1/8 of IDFT length for all cases. The raw data rates are 17.8 Gb/s, 35.7 Gb/s, and 17.8 Gb/s, respectively.

Figure 1
Fig. 1 BER comparison for three cases with 0-MHz laser linewdith (solid line) and 1-MHz (dash line). The insets on the left are the constellations at the indicated BER points.
shows the BER performance with 0-MHz or 1-MHz linewidth for both transmitter and receiver lasers. Case II has the largest OSNR penalty due to phase noise and the conventional OFDM in Case I has an OSNR penalty of 1.3 dB at BER of 10−3. DCS-OFDM in Case III has the smallest OSNR penalty of 0.5 dB at BER of 10−3, which means a better tolerance to the laser phase noise. With 1-MHz linewidth, from Case II to III, the OSNR is drastically reduced, much more than 3 dB, which follows the derivation in Section 2. The inset constellations in Fig. 1 also demonstrate this significant improvement, which results from the simple operation of Eq. (9).

4. Experiment of DCS-OFDM in a nonlinear WDM transmission

To verify the ICI reduction of DCS-OFDM, we conduct a nonlinear WDM transmission, where the transmitter uses a comb generator to emulate the multiple laser sources. As shown in Fig. 2
Fig. 2 Experimental setup of the emulated WDM transmission. The inset optical spectra are the optical signal before and after the data modulation. ECL: external cavity laser, PM: phase modulator, IM: intensity modulator, IQ: IQ modulator, WSS: wavelength selective switch, ATT: attenuator, BPF: bandpass filter.
, a 25-GHz clock signal drives a phase modulator followed by a wavelength selective switch (WSS) to flatten and select the comb lines. For comparison, all the comb lines pass through either an IM or IQ modulator driven by an arbitrary waveform generator (AWG) operated at 10 GS/s. The transmitted OFDM signal with 4-QAM format is generated off-line by a MATLAB program. The DFT length is 128 and we also use 1/8 of it as cyclic prefix. We use 44 OFDM subcarriers for Case I and 88 OFDM subcarriers for both Case II and III. This OFDM signal is further duplicated into three copies, or a super-channel [16

16. Q. Yang, Y. Tang, Y. Ma, and W. Shieh, “Experimental demonstration and numerical simulation of 107-Gb/s high spectral efficiency coherent optical OFDM,” J. Lightwave Technol. 27(3), 168–176 (2009). [CrossRef]

], by another IM modulator driven at 6.875 GHz. Inside the transmitter, we also use two EDFAs to compensate for the losses. The inset spectra in Fig. 2 are before and after the data modulation, respectively. In short, the transmitter side includes 25 super-channels on 25-GHz WDM grid, covering 5-nm wide spectrum. The raw bit rate of one super-channel is 18.3 Gb/s for Case I and Case III, and 36.7 Gb/s for Case II. The frequency gaps among the super-channels are too narrow (a few GHz wide), and consequently, the spectrum in Fig. 2 measured by an optical spectrum analyzer seems gapless. The launch power per super-channel in the following measurement is obtained by dividing the total power of all channels by the channel number.

Figure 3
Fig. 3 Estimated SNR vs launch power in the nonlinear WDM transmission: (a) without electrical dispersion compensation, (b) with electrical dispersion compensation. The dash lines are the SNR difference between Case III and Case II. (c) Constellations before and after DCS at the maximum SNR improvement.
shows the performance of the three cases in the nonlinear transmission. At the linear transmission regime with the lower launch power, the conventional CO-OFDM of Case I is slightly better, which is due to that its narrower spectrum has a better tolerance to the fiber dispersion. Meanwhile, the SNR difference by DCS between Case II and Case III is 3 dB, which is as expected in the linear regime [8

8. X. Liu, S. Chandrasekhar, P. J. Winzer, A. R. Chraplyvy, R. W. Tkach, B. Zhu, T. F. Taunay, M. Fishteyn, and D. J. DiGiovanni, “Scrambled coherent superposition for enhanced optical fiber communication in the nonlinear transmission regime,” Opt. Express 20(17), 19088–19095 (2012). [CrossRef] [PubMed]

,9

9. X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 7(7), 560–568 (2013). [CrossRef]

]. However, when the launch power is larger than −12 dBm per super-channel, the SNR improvement of Case III is apparently larger than 3 dB. Without electrical dispersion compensation, the maximum SNR improvement is 4.5 dB at the launch power of −7.4 dBm. With dispersion compensation, the estimated SNRs are all slightly improved for the three cases, and the maximum SNR improvement is increased to 4.9 dB. Correspondingly, Fig. 3(c) shows that the constellation spreading is dramatically reduced by DCS. Therefore, the electrical dispersion compensation can further improve the performance of DCS-OFDM in the nonlinear regime. Although it is not explained in Section 2, this similar conclusion was reported in the other experiment [9

9. X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 7(7), 560–568 (2013). [CrossRef]

]. Finally, comparing Case III and Case I around the optimum launch power, we find that the SNRs of DCS-OFDM are apparently larger than that of the conventional CO-OFDM and its optimum launch power is increased by 3.4 dB. Based on the results in Fig. 3, we can conclude that DCS-OFDM trades off the spectrum efficiency for a better performance in the nonlinear WDM transmission, where XPM is dominant.

5. Conclusion

DCS trades off the spectrum efficiency to achieve a better transmission performance. We have extended the concept of DCS to the OFDM subcarrier pairs with Hermitian symmetry. The transmitter is simplified as an MZ intensity modulator driven with real-valued signals. The receiver's DSP only requires one additional conjugation and summation for DCS. We have shown that the ICI due to phase noise can be reduced. In simulation, DCS-OFDM has a better tolerance to laser phase noise. In a nonlinear WDM transmission experiment, DCS-OFDM increases both the optimum launch power and the maximum SNR under the influence of XPM. Further research is under plan to quantify the benefit of DCS-OFDM, both in theory and experiment.

Acknowledgments

This work was supported in part by National High Technology Research and Development Program of China (863 Program) (2013AA010503, 2012AA011302 and 2012AA011304) and NSFC (No. 61107060).

References and links

1.

W. Shieh, X. Yi, and Y. Tang, “Transmission experiment of multi-gigabit coherent optical OFDM systems over 1000 km SSMF fiber,” Electron. Lett. 43(3), 183–185 (2007). [CrossRef]

2.

A. J. Lowery, L. Du, and J. Armstrong, “Orthogonal frequency division multiplexing for adaptive dispersion compensation in long haul WDM systems,” in Optical Fiber Commun. Conf., Anaheim, CA (2006), Paper PDP39. [CrossRef]

3.

S. L. Jansen, I. Morita, C. W. Schenk, N. Takeda, and H. Tanaka, “Coherent optical 25.8-Gb/s OFDM transmission over 4160-km SSMF,” J. Lightwave Technol. 26(1), 6–15 (2008). [CrossRef]

4.

D. Qian, M. Huang, E. Ip, Y. Huang, Y. Shao, J. Hu, and T. Wang, “101.7-Tb/s (370×294-Gb/s) PDM-128QAM-OFDM transmission over 3×55-km SSMF using pilot-based phase noise mitigation,” in Optical Fiber Commun. Conf., USA (2011), paper PDPB5.

5.

S. Wu and Y. Bar-Ness, “OFDM systems in the presence of phase noise: consequences and solutions,” IEEE Trans. Commun. 52(11), 1988–1996 (2004). [CrossRef]

6.

X. Yi, W. Shieh, and Y. Ma, “Phase noise effects on high spectral efficiency coherent optical OFDM transmission,” J. Lightwave Technol. 26(10), 1309–1316 (2008). [CrossRef]

7.

J. Armstrong, “Analysis of new and existing methods of reducing intercarrier interference due to carrier frequency offset in OFDM,” IEEE Trans. Commun. 47(3), 365–369 (1999). [CrossRef]

8.

X. Liu, S. Chandrasekhar, P. J. Winzer, A. R. Chraplyvy, R. W. Tkach, B. Zhu, T. F. Taunay, M. Fishteyn, and D. J. DiGiovanni, “Scrambled coherent superposition for enhanced optical fiber communication in the nonlinear transmission regime,” Opt. Express 20(17), 19088–19095 (2012). [CrossRef] [PubMed]

9.

X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, and S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 7(7), 560–568 (2013). [CrossRef]

10.

Y. Tian, Y. K. Huang, S. Zhang, P. R. Prucnal, and T. Wang, “Demonstration of digital phase-sensitive boosting to extend signal reach for long-haul WDM systems using optical phase-conjugated copy,” Opt. Express 21(4), 5099–5106 (2013). [CrossRef] [PubMed]

11.

X. Yi, X. Chen, C. Li, M. Luo, Q. Yang, Z. Li, and K. Qiu, “Experimental demonstration of digital coherent superposition of optical OFDM subcarrier pairs for mitigation of linear and nonlinear phase noise,” in Optical Fiber Commun. Conf. (2014), Tu3G.6. [CrossRef]

12.

Y. Wu, J. Li, C. Zhao, Y. Zhao, F. Zhang, and Z. Chen, “Coherent optical OFDM scheme with inter-carrier interference self-cancellation and common phase error compensation,” Chin. Opt. Lett. 8, 634–638 (2010). [CrossRef]

13.

Y. Tang, W. Shieh, X. Yi, and R. Evans, “Optimum design for RF-to-optical up-converter in coherent optical OFDM systems,” IEEE Photon. Technol. Lett. 19(7), 483–485 (2007). [CrossRef]

14.

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

15.

T. Pollet, M. Van Bladel, and M. Moeneclaey, “BER sensitivity of OFDM systems to carrier frequency offset andWiener phase noise,” IEEE Trans. Commun. 43(2/3/4), 191–193 (1995). [CrossRef]

16.

Q. Yang, Y. Tang, Y. Ma, and W. Shieh, “Experimental demonstration and numerical simulation of 107-Gb/s high spectral efficiency coherent optical OFDM,” J. Lightwave Technol. 27(3), 168–176 (2009). [CrossRef]

OCIS Codes
(060.0060) Fiber optics and optical communications : Fiber optics and optical communications
(060.4080) Fiber optics and optical communications : Modulation
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers

ToC Category:
Optical Communications

History
Original Manuscript: April 16, 2014
Revised Manuscript: May 19, 2014
Manuscript Accepted: May 20, 2014
Published: May 27, 2014

Citation
Xingwen Yi, Xuemei Chen, Dinesh Sharma, Chao Li, Ming Luo, Qi Yang, Zhaohui Li, and Kun Qiu, "Digital coherent superposition of optical OFDM subcarrier pairs with Hermitian symmetry for phase noise mitigation," Opt. Express 22, 13454-13459 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-11-13454


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References

  1. W. Shieh, X. Yi, Y. Tang, “Transmission experiment of multi-gigabit coherent optical OFDM systems over 1000 km SSMF fiber,” Electron. Lett. 43(3), 183–185 (2007). [CrossRef]
  2. A. J. Lowery, L. Du, and J. Armstrong, “Orthogonal frequency division multiplexing for adaptive dispersion compensation in long haul WDM systems,” in Optical Fiber Commun. Conf., Anaheim, CA (2006), Paper PDP39. [CrossRef]
  3. S. L. Jansen, I. Morita, C. W. Schenk, N. Takeda, H. Tanaka, “Coherent optical 25.8-Gb/s OFDM transmission over 4160-km SSMF,” J. Lightwave Technol. 26(1), 6–15 (2008). [CrossRef]
  4. D. Qian, M. Huang, E. Ip, Y. Huang, Y. Shao, J. Hu, and T. Wang, “101.7-Tb/s (370×294-Gb/s) PDM-128QAM-OFDM transmission over 3×55-km SSMF using pilot-based phase noise mitigation,” in Optical Fiber Commun. Conf., USA (2011), paper PDPB5.
  5. S. Wu, Y. Bar-Ness, “OFDM systems in the presence of phase noise: consequences and solutions,” IEEE Trans. Commun. 52(11), 1988–1996 (2004). [CrossRef]
  6. X. Yi, W. Shieh, Y. Ma, “Phase noise effects on high spectral efficiency coherent optical OFDM transmission,” J. Lightwave Technol. 26(10), 1309–1316 (2008). [CrossRef]
  7. J. Armstrong, “Analysis of new and existing methods of reducing intercarrier interference due to carrier frequency offset in OFDM,” IEEE Trans. Commun. 47(3), 365–369 (1999). [CrossRef]
  8. X. Liu, S. Chandrasekhar, P. J. Winzer, A. R. Chraplyvy, R. W. Tkach, B. Zhu, T. F. Taunay, M. Fishteyn, D. J. DiGiovanni, “Scrambled coherent superposition for enhanced optical fiber communication in the nonlinear transmission regime,” Opt. Express 20(17), 19088–19095 (2012). [CrossRef] [PubMed]
  9. X. Liu, A. R. Chraplyvy, P. J. Winzer, R. W. Tkach, S. Chandrasekhar, “Phase-conjugated twin waves for communication beyond the Kerr nonlinearity limit,” Nat. Photonics 7(7), 560–568 (2013). [CrossRef]
  10. Y. Tian, Y. K. Huang, S. Zhang, P. R. Prucnal, T. Wang, “Demonstration of digital phase-sensitive boosting to extend signal reach for long-haul WDM systems using optical phase-conjugated copy,” Opt. Express 21(4), 5099–5106 (2013). [CrossRef] [PubMed]
  11. X. Yi, X. Chen, C. Li, M. Luo, Q. Yang, Z. Li, and K. Qiu, “Experimental demonstration of digital coherent superposition of optical OFDM subcarrier pairs for mitigation of linear and nonlinear phase noise,” in Optical Fiber Commun. Conf. (2014), Tu3G.6. [CrossRef]
  12. Y. Wu, J. Li, C. Zhao, Y. Zhao, F. Zhang, Z. Chen, “Coherent optical OFDM scheme with inter-carrier interference self-cancellation and common phase error compensation,” Chin. Opt. Lett. 8, 634–638 (2010). [CrossRef]
  13. Y. Tang, W. Shieh, X. Yi, R. Evans, “Optimum design for RF-to-optical up-converter in coherent optical OFDM systems,” IEEE Photon. Technol. Lett. 19(7), 483–485 (2007). [CrossRef]
  14. X. Yi, W. Shieh, Y. Tang, “Phase estimation for coherent optical OFDM,” IEEE Photon. Technol. Lett. 19(12), 919–921 (2007). [CrossRef]
  15. T. Pollet, M. Van Bladel, M. Moeneclaey, “BER sensitivity of OFDM systems to carrier frequency offset andWiener phase noise,” IEEE Trans. Commun. 43(2/3/4), 191–193 (1995). [CrossRef]
  16. Q. Yang, Y. Tang, Y. Ma, W. Shieh, “Experimental demonstration and numerical simulation of 107-Gb/s high spectral efficiency coherent optical OFDM,” J. Lightwave Technol. 27(3), 168–176 (2009). [CrossRef]

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