## Equalization-enhanced phase noise for 100Gb/s transmission and beyond with coherent detection |

Optics Express, Vol. 18, Issue 16, pp. 17239-17251 (2010)

http://dx.doi.org/10.1364/OE.18.017239

Acrobat PDF (9702 KB)

### Abstract

The probability density function and impact of equalization-enhanced phase noise (EEPN) is analytically investigated and simulated for 100 Gb/s coherent systems using electronic dispersion compensation. EEPN impairment induces both phase noise and amplitude noise with the former twice as much as the latter. The effects of transmitter phase noise on EEPN are negligible for links with residual dispersion in excess of 700 ps/nm. Optimal linear equalizer in the presence of EEPN is derived but show only marginal performance improvement, indicating that EEPN is difficult to mitigate using simple DSP techniques. In addition, the effects of EEPN on carrier recovery techniques and corresponding cycle slip probabilities are studied.

© 2010 Optical Society of America

## 1.Introduction

1. E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, “Coherent detection in optical fiber systems,” Opt. Express **16**(1), 753–791 (2008). [CrossRef] [PubMed]

2. E. Ip and J. M. Kahn, “Digital equalization of Chromatic Dispersion and Polarization Mode Dispersion,” IEEE/OSA J. Lightwave Technol. **25**(8), 2033–2043 (2007). [CrossRef]

6. F. Buchali and H. Bulow, “Adaptive PMD Compensation by Elecgtrical and Optical Techniques,” IEEE/OSA J. Lightwave Technol. **22**(4), 1116–1126 (2004). [CrossRef]

5. K. Roberts, C. Li, L. Strawczyski, M. O. Sullivan, and I. Hardcastle, “Electronic precompensation of optical nonlinearity,” IEEE Photon. Technol. Lett.18(13), 403–405 (2006). [CrossRef]

9. H. Bulow, F. Buchali, and A. Klekamp, “Electronic dispersion compensation,” IEEE/OSA J. Lightwave Technol. **26**(1), 158–167 (2008). [CrossRef]

14. E. Ip and J. M. Kahn, “Feedforward carrier recovery for coherent optical communications,” IEEE/OSA J. Lightwave Technol. **25**(9), 2675–2692 (2007). [CrossRef]

17. 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]

18. G. Charlet, M. Salsi, P. Tran, M. Bertolini, H. Mardoyan, J. Renaudier, O. Bertran-Pardo, and S. Bigo, “72×100 Gb/s transmission over transoceanic distance, using large effective area fiber, hybrid Raman-Erbium amplification and coherent detection,” in *Proceedings OFC/NFOEC*, San Diego, CA, 2009, Paper PDPB6.

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

## 2.Equalization-Enhanced Phase Noise

### A. Theoretical model and system impact

*x*denotes independent identically distributed (i.i.d.) information symbols with a symbol rate

_{n}*R*of 27.59 GSym/s and normalized average power

*E*[∣

*x*∣

_{n}^{2}]=1. With polarization-multiplexing (PM) and a 7 % Forward Error Correction (FEC) overhead, such symbol rate corresponds to 100 Gb/s and 200 Gb/s per channel transmission using Quadrature Phase-Shift Keying (QPSK) and 16-Quadrature Amplitude Modulation (QAM) modulation formats respectively. Fiber nonlinearity and polarization effects are neglected for simplicity.

*b*(

*t*) to form the transmitted signal

*T*

_{0}is the symbol period. Optical amplifiers located along the link introduce amplified spontaneous emission (ASE) noise collectively modeled as

*n*(

*t*) =

*n*(

_{re}*t*) +

*jn*(

_{im}*t*). The noise in each quadrature

*n*(

_{re}*t*) and

*n*(

_{im}*t*) are independent additive white Gaussian noise (AWGN) process with power spectral density

*N*

_{0}/2. In the absence of phase noises from lasers, the transmitted signal is mixed with a local oscillator at the receiver and the output is given by

*q*(

*t*) =

*p*(

*t*)*

*g*(

*t*) =

*p*(

*t*)*

*h*(

*t*)*

*b*(

*t*) and

*ν*(

*t*) =

*p*(

*t*)*

*n*(

*t*).In this formulation, ‘*’ denotes convolution, and

*h*(

*t*) and

*p*(

*t*) respectively denote the impulse response characterizing a channel with chromatic dispersion and electrical low pass filter after photo-detection respectively. The received signal is then sampled to form

*y*=

_{m}*y*(

*mT*) where

*T*is the sampling period and

*S*=

*T*/

_{0}*T*is the over-sampling rate. To compensate for CD and demodulate the

*k*transmitted symbol

^{th}*x*, a vector of received samples

_{k}*N*=

*2L*+

*1*is formed and passed through a equalizer, or, a linear finite impulse response (FIR) filter,

**w**. In absence of laser phase noise, the estimate of the transmitted symbol

*x̂*is simply given by

_{k}**w**

_{lin}is derived as

**A**and

*α*are given by [2

2. E. Ip and J. M. Kahn, “Digital equalization of Chromatic Dispersion and Polarization Mode Dispersion,” IEEE/OSA J. Lightwave Technol. **25**(8), 2033–2043 (2007). [CrossRef]

*ε*=

*x̂*−

_{n}*x*and the phase error as

_{n}*θ*= arg(

*x̂*) −arg(

_{n}*x*), the corresponding mean-squared error becomes

_{n}*σ*

^{2}

_{θ}is given by

*ϕ*(

_{r}*t*), the spectrum of a laser

*υ*in which

*ϕ*(

_{r}*t*) can be modeled as a Wiener process in which

*ϕ*(

_{r}*t*

_{2})−

*ϕ*(

_{r}*t*

_{1}) is Gaussian distributed with zero mean and variance

*σ*

^{2}

_{p}= 2

*π*Δ

*υ*∣

*t*

_{1}−

*t*

_{2}∣. In presence of receiver (Rx) or LO phase noise and uncompensated CD, the received signal becomes

*x*is given by

_{k}**X**= […

*x*

_{k−2},

*x*

_{k−1},

*x*

_{k+1},

*x*

_{k+2}…],

*C*is the set {1, −1} for BPSK and {1, −1,

*j*, −

*j*} for QPSK formats etc. Figure 2 (a)–(c) illustrate the pdf of EEPN for various laser linewidths and transmission distance for QPSK systems with electronic dispersion compensation. The EEPN induces more phase noise on

*x̂*than amplitude noise, resulting in the pdf being elliptical in nature. In presence of ASE noise, the pdf is more circular-like as shown in Figure 2 (d), indicating the relative significance of complex circularly symmetric ASE noise compared with EEPN.

_{k}*D*=17 ps/(nm-km) and fiber attenuation coefficient

*α*= 0.25 dB/km. The amplifiers are assumed to be Erbium-doped fiber amplifiers (EDFA) with a noise figure of 4.5 dB. The gain of each EDFA exactly compensates for the loss of the fiber in each span. For the rest of the paper, such configurations will be assumed for each span of propagation unless otherwise stated. The carrier recovery is performed after CD compensation [17

_{fiber}17. 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]

^{−3}is also shown for reference. From the figure, it can be seen that EEPN induces a non-negligible OSNR penalty for typical DFB lasers with linewidths of several MHz. In addition, for any LO linewidth, the overall phase noise variance converges to a value corresponding to the system impact due to EEPN alone. The system tolerance to EEPN decreases dramatically for higher-order modulation formats such as 16-QAM or 64-QAM, as depicted in Figure 5 for a transmission length of 1600 km. In this case, even lasers with sub-MHz linewidth such as external-cavity lasers will induce a non-negligible OSNR penalty due to EEPN.

### B. EEPN Induced Phase and Amplitude Noise

*x̂*∣) as well as phase noise

_{k}*σ*

^{2}

_{θ}induced by EEPN for a QPSK system and simulation results are shown in Figure 6. From the figure, it can be seen that the interaction between Rx phase noise and electronic CD compensation induces more phase noise than amplitude noise even at high OSNR, in contrast to systems corrupted by AWGN alone. For various values of OSNR and uncompensated CD, the EEPN induced phase noise variance is approximately twice the amplitude noise variance, indicating that EEPN induced phase noise rather than amplitude noise is a more dominant transmission impairment for systems using electronic CD compensation.

### C. EEPN from transmitter laser

**w**

_{lin}for CD compensation for various laser linewidths and propagation distance for a QPSK system. The dispersion coefficient is 17 ps/nm-km. ASE noise from optical amplifiers is not included to highlight the contribution of the overall phase noise by the Tx and Rx lasers. Two scenarios are studied: ideal Tx laser with Rx phase noise only and systems with both Rx and Tx phase noises. From Figure 6, it can be seen that for 10 km of propagation, the presence of Tx phase noise doubles the overall phase noise variance, indicating that Rx and Tx phase noise contributes equally to overall signal degradation after sampling and electronic CD compensation. On the other hand, for more than 40 km of propagation, Tx phase noise does not increase the overall phase noise variance by much. Therefore, even for a propagation distance of 40 km with an accumulated dispersion of about 700 ps/nm, EEPN from the interaction between Rx phase noise and electronic dispersion compensation already dominates system performance. In a WDM system with periodic optical dispersion compensation, residual dispersion in this range can be present for some channels due to dispersion map design for mitigation of fiber nonlinearity induced impairments or dispersion slope mismatch between the propagating fibers and dispersion compensating fibers. Consequently, the Rx laser linewidth requirement will typically be more stringent than Tx laser for WDM links even with periodic dispersion compensation.

## 3. Optimal Equalization in Presence of EEPN

**w**

_{lin}previously studied for CD compensation is no longer optimal as the derivation of

**w**

_{lin}does not take into account the statistics of the Rx phase noise. In this case, the received signal is given by

*x̂*=

_{n}*α*

^{T}

_{PN}

**A**

^{−1}

_{PN}

**y**=

**w**

^{T}

_{PN}

**y**where

*p*(

*t*) is a low-pass filter that filters out-of-band noise and laser linewidth is at most in the order of MHz for practical optical communication systems, it can be shown (from the Appendix B) that

**w**

_{PN}with a LO linewidth of 3 MHz and

**w**

_{lin}with zero LO linewidth, both for a QPSK system with a transmission distance of 1200 km. One can see that with the received vector

**y**corrupted by EEPN, the exponential decay terms in

*α*

_{PN}

**, A**

^{−1}

_{PN}that capture the LO phase noise statistics result in samples of

**y**further away from the center having bigger ‘weights’. However, as the samples further away from the center are more corrupted by LO phase noise, they became less relevant for the detection of the bit of interest and therefore system performance degrades with EEPN. Note also that in presence of EEPN, the samples with the largest weight are shifted from 98 to 95 samples from the center of the filter.

**w**

_{lin}to compensate CD in presence of EEPN, the mean-squared error will be given by

**w**

_{PN}for CD compensation in presence of EEPN, the corresponding mean-squared error will be given by

**w**

_{PN}does not improve the performance by much. The performance with

**w**

_{PN,opt}corresponds to the case when the approximation in (16) is not used and

*E*[

*x*

_{k}**y**

^{*}] and

*E*[

**y**

^{*}

**y**

^{T}] are numerically obtained from simulations to form

**w**

_{PN,opt}= (

*E*[

**y**

^{*}

**y**

^{T}])

^{−1}

*E*[

*x*

_{k}**y**

^{*}]. From Figure 9, we can see that the mean-squared error using

**w**

_{PN,opt}is very close to that using

**w**

_{PN}and therefore we can safely use the approximations in (17) for further analysis. Unfortunately, the optimal FIR filter

**w**

_{PN}only provides marginal performance improvements for systems with EEPN. Consequently, EEPN is difficult to mitigate by using simple DSP algorithms.

## 4. EEPN Impact on Carrier Phase Recovery

*ϕ*(

*t*) =

*ϕ*(

_{t}*t*) +

*ϕ*(

_{r}*t*) together with the tracked phase for systems with optical or electrical CD compensation for a 1200-km link. To achieve phase tracking, the Viterbi-Viterbi algorithm is performed on the CD-equalized samples and the phases of the resulting output are passed through a Wiener filter described in Eq. (26) of [14

14. E. Ip and J. M. Kahn, “Feedforward carrier recovery for coherent optical communications,” IEEE/OSA J. Lightwave Technol. **25**(9), 2675–2692 (2007). [CrossRef]

*π*/4 =

*π*/2, which is depicted in Figure 11.

**w**

_{PN}in presence of EEPN, the cycle slip probability is indeed lower compared with the case using

**w**

_{lin}. However, the difference maybe too small for practical interest.

## 5. Conclusions

## APPENDIX A: Pdf of EEPN

_{m−m′}=

*ϕ*(

_{r}*mT*) −

*ϕ*(

_{r}*m′T*) and

**w**

_{lin}= [

*w*

_{L}*w*

_{L−1}…

*w*

_{−L+1}

*w*

_{−L}]

^{T}. In this case, the estimation error for the

*k*

^{th}transmitted symbol is given by

*r*=

_{i}*jw*, and Δ

_{i}Q_{Sk+i}_{i}− Δ

_{i±1}are independent Gaussian random variables with zero mean and variance 2

*π*Δ

*υT*. For a given

*x*,

_{k}*r*,

_{−L}*r*

_{−L+1}, ⋯,

*r*

_{L−1},

*r*are functions of the neighboring symbols

_{L}**X**= […

*x*

_{k−2},

*x*

_{k−1},

*x*

_{k+1},

*x*

_{k+2}…]. Therefore, for a given neighboring symbol sequence

**X**,

*ε*will be a complex Gaussian random variable with zero mean and covariance matrix

*π*Δ

*υ*

*T*Λ(

**X**) where

*x*, the pdf of EEPN is given by

_{k}*C*is the set {1, −1} for BPSK and {1, −1,

*j*, −

*j*} for QPSK formats etc. and ∣

*C*∣ denotes the cardinality of

*C*. Note that in presence of ASE noise with variance

*σ*

^{2}per quadrature, Λ(

**X**) can be replaced by Λ(

**X**) +

*σ*

^{2}

**I**.

## APPENDIX B: Proof of (g(t)·ejϕr(t))*p(t)≈q(t)ejϕr(t)

*u*(

*t*) is given by

*U*(

*f*) = (

*G*(

*f*)*Φ(

*f*))·

*P*(

*f*)

*f*) is the Fourier Transform of

*υ*. Since the bandwidth of the low-pass filter

*P*(

*f*) is in the order of 30 GHz for a symbol rate of 27.59 GSym/s and Δ

*υ*is at most several MHz in practice,

*P*(

*f*) with

*υ*,

*H*

^{−1}(

*f*) ≠

*H*

^{−1}(

*f*−

*f*1) for ∣

*f*

_{1}∣ ≤ Δ

*υ*/2 whenever

*β*

_{2}

*L*is large enough and hence (B.2) will not follow and multiplication and convolution will not commute. Therefore, the effect of EEPN will always scale up with accumulated CD independent of laser linewidth.

## Acknowledgements

## References and links

1. | E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, “Coherent detection in optical fiber systems,” Opt. Express |

2. | E. Ip and J. M. Kahn, “Digital equalization of Chromatic Dispersion and Polarization Mode Dispersion,” IEEE/OSA J. Lightwave Technol. |

3. | M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon.Technol. Lett. |

4. | G. Goldfarb and G. Li, “Chromatic dispersion compensation using digital IIR filtering with coherent detection,” IEEE Photon. Technol. Lett. |

5. | K. Roberts, C. Li, L. Strawczyski, M. O. Sullivan, and I. Hardcastle, “Electronic precompensation of optical nonlinearity,” IEEE Photon. Technol. Lett.18(13), 403–405 (2006). [CrossRef] |

6. | F. Buchali and H. Bulow, “Adaptive PMD Compensation by Elecgtrical and Optical Techniques,” IEEE/OSA J. Lightwave Technol. |

7. | D. Schlump, B. Wedding, and H. Bulow, “Electronic equalization of PMD and chromatic dispersion induced distortion after 100 km standard fibre at 10Gb/s,” |

8. | J. M. Gené, P. J. Winzer, S. Chandrasekhar, and H. Kogelnik, “Simultaneous compensation of Polarization Mode Dispersion and chromatic dispersion using electronic signal processing,” IEEE/OSA J. Lightwave Technol. |

9. | H. Bulow, F. Buchali, and A. Klekamp, “Electronic dispersion compensation,” IEEE/OSA J. Lightwave Technol. |

10. | E. Ip and J. M. Kahn, “Compensation of Dispersion and Nonlinear Impairments Using Digital Backpropagation,” IEEE/OSA J. Lightwave Technol. |

11. | X. Li, X. Chen, G. Goldfarb, E. Mateo, I. Kim, F. Yaman, and G. Li, “Electronic post-compensation of WDM transmission impairments using coherent detection and digital signal processing,” Opt. Express |

12. | K. Kikuchi, “Electronic post-compensation for nonlinear phase fluctuations in a 1000-km 20-Gbit/s optical quadrature phase-shift keying transmission system using the digital coherent receiver,” Opt. Express |

13. | A.P.T. Lau and J. M. Kahn, “Signal design and detection in presence of nonlinear phase noise,” IEEE/OSA J. Lightwave Technol.25(10), 3008–3016 (2007). [CrossRef] |

14. | E. Ip and J. M. Kahn, “Feedforward carrier recovery for coherent optical communications,” IEEE/OSA J. Lightwave Technol. |

15. | D. S. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, “Coherent Detection of Optical Quadrature Phase-Shift Keying Signals With Carrier Phase Estimation,” IEEE/OSA J. Lightwave Technol. |

16. | R. Noe, “Phase noise-tolerant synchronous QPSK/BPSK baseband-type intradyne receiver concept with feedforward carrier recovery,” IEEE/OSA J. Lightwave Technol. |

17. | S. J. Savory, G. Gavioli, R. I. Killey, and P. Bayvel, “Electronic compensation of chromatic dispersion using a digital coherent receiver,” Opt. Express |

18. | G. Charlet, M. Salsi, P. Tran, M. Bertolini, H. Mardoyan, J. Renaudier, O. Bertran-Pardo, and S. Bigo, “72×100 Gb/s transmission over transoceanic distance, using large effective area fiber, hybrid Raman-Erbium amplification and coherent detection,” in |

19. | W. Shieh and K.P. Ho, “Equalization-enhanced phase noise for coherent detection systems using electronic digital signal processing,” Opt. Express |

20. | C. Xie, “Local oscillator phase noise induced penalties in optical coherent detection systems using electronic chromatic dispersion compensation,” in |

21. | C. Xie, “WDM coherent PDM-QPSK systems with and without inline optical dispersion compensation,” Optics Express |

**OCIS Codes**

(060.1660) Fiber optics and optical communications : Coherent communications

(060.5060) Fiber optics and optical communications : Phase modulation

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: February 19, 2010

Revised Manuscript: April 5, 2010

Manuscript Accepted: June 29, 2010

Published: July 29, 2010

**Citation**

Alan Pak Tao Lau, Thomas Shun Rong Shen, William Shieh, and Keang-Po Ho, "Equalization-enhanced phase noise for 100Gb/s transmission and beyond with coherent detection," Opt. Express **18**, 17239-17251 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-16-17239

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### References

- E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, "Coherent detection in optical fiber systems,’’Opt. Express 16(1), 753-791 (2008). [CrossRef] [PubMed]
- E. Ip and J. M. Kahn, "Digital equalization of Chromatic Dispersion and Polarization Mode Dispersion," IEEE/OSAJ. Lightwave Technol. 25(8), 2033-2043 (2007). [CrossRef]
- 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]
- G. Goldfarb and G. Li, "Chromatic dispersion compensation using digital IIR filtering with coherent detection," IEEE Photon. Technol. Lett. 19(13), 969-971 (2007). [CrossRef]
- K. Roberts, C. Li, L. Strawczyski, M. O. Sullivan, and I. Hardcastle, "Electronic precompensation of optical nonlinearity," IEEE Photon. Technol. Lett. 18(13), 403-405 (2006). [CrossRef]
- F. Buchali and H. Bulow, "Adaptive PMD Compensation by Elecgtrical and Optical Techniques," IEEE/OSAJ. Lightwave Technol. 22(4), 1116-1126 (2004). [CrossRef]
- D. Schlump, B. Wedding, and H. Bulow, "Electronic equalization of PMD and chromatic dispersion induced distortion after 100 km standard fibre at 10Gb/s," in Proceedings ECOC, Madrid, Spain, 1998, pp. 535-536.
- J. M. Gené, P. J. Winzer, S. Chandrasekhar, and H. Kogelnik, "Simultaneous compensation of Polarization Mode Dispersion and chromatic dispersion using electronic signal processing," IEEE/OSAJ. Lightwave Technol. 26(7), 1735-1741 (2007). [CrossRef]
- H. Bulow, F. Buchali and A. Klekamp, "Electronic dispersion compensation," IEEE/OSAJ. Lightwave Technol. 26(1), 158-167 (2008). [CrossRef]
- E. Ip and J. M. Kahn, "Compensation of Dispersion and Nonlinear Impairments Using Digital Backpropagation," IEEE/OSAJ. Lightwave Technol. 26(20), 3416-3425 (2008). [CrossRef]
- X. Li, X. Chen, G. Goldfarb, E. Mateo, I. Kim, F. Yaman, and G. Li, "Electronic post-compensation of WDM transmission impairments using coherent detection and digital signal processing," Opt. Express 16(2), 880-888 (2008). [CrossRef] [PubMed]
- K. Kikuchi, "Electronic post-compensation for nonlinear phase fluctuations in a 1000-km 20-Gbit/s optical quadrature phase-shift keying transmission system using the digital coherent receiver," Opt. Express 16(1), 889-896 (2008). [CrossRef] [PubMed]
- A.P.T. Lau and J. M. Kahn, "Signal design and detection in presence of nonlinear phase noise," J. Lightwave Technol. 25(10), 3008-3016 (2007). [CrossRef]
- E. Ip and J. M. Kahn, "Feedforward carrier recovery for coherent optical communications," J. Lightwave Technol. 25(9), 2675-2692 (2007). [CrossRef]
- D. S. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, "Coherent Detection of Optical Quadrature Phase-Shift Keying Signals With Carrier Phase Estimation," J. Lightwave Technol. 24(1), 12-21 (2006). [CrossRef]
- R. Noe, "Phase noise-tolerant synchronous QPSK/BPSK baseband-type intradyne receiver concept with feedforward carrier recovery," J. Lightwave Technol. 23(2), 802-808 (2006). [CrossRef]
- 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]
- G. Charlet, M. Salsi, P. Tran, M. Bertolini, H. Mardoyan, J. Renaudier, O. Bertran-Pardo, and S. Bigo, "72x100 Gb/s transmission over transoceanic distance, using large effective area fiber, hybrid Raman-Erbium amplification and coherent detection," in Proceedings OFC/NFOEC, San Diego, CA, 2009, Paper PDPB6.
- 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]
- C. Xie, "Local oscillator phase noise induced penalties in optical coherent detection systems using electronic chromatic dispersion compensation," in Proceedings OFC/NFOEC, San Diego, CA, 2009, Paper OMT4.
- C. Xie, "WDM coherent PDM-QPSK systems with and without inline optical dispersion compensation," Opt. Express 17(6), 4815-4823 (2009). [CrossRef] [PubMed]

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