## Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing

Optics Express, Vol. 16, Issue 20, pp. 15718-15727 (2008)

http://dx.doi.org/10.1364/OE.16.015718

Acrobat PDF (188 KB)

### Abstract

In coherent optical systems employing electronic digital signal processing, the fiber chromatic dispersion can be gracefully compensated in electronic domain without resorting to optical techniques. Unlike optical dispersion compensator, the electronic equalizer enhances the impairments from the laser phase noise. This equalization-enhanced phase noise (EEPN) imposes a tighter constraint on the receive laser phase noise for transmission systems with high symbol rate and large electronically-compensated chromatic dispersion.

© 2008 Optical Society of America

## 1. Introduction

1. D. S. Ly-Gagnon, S. Tsukarnoto, K. Katoh, and K. Kikuchi, “Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation,” J. of Lightwave Technol. **24**,12–21 (2006). [CrossRef]

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

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

6. L. G. Kazovsky, “Performance analysis and laser linewidth requirements for optical PSK heterodyne communication systems,” J. Lightwave Technol. **4**, 415–425 (1986). [CrossRef]

1. D. S. Ly-Gagnon, S. Tsukarnoto, K. Katoh, and K. Kikuchi, “Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation,” J. of Lightwave Technol. **24**,12–21 (2006). [CrossRef]

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

9. H. Bulow, F. Buchali, and A. Klekamp, “Electronic dispersion compensation,” J. of Lightwave Technol. **26**, 158–167 (2007). [CrossRef]

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

12. X. Chen, C. Kim, G. Li, and B. Zhou, “Numerical study of lumped dispersion compensation for 40-Gb/s return-to-zero differential phase-shift keying transmission,” IEEE Photon. Technol. Lett. **19**, 568–570 (2007). [CrossRef]

1. D. S. Ly-Gagnon, S. Tsukarnoto, K. Katoh, and K. Kikuchi, “Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation,” J. of Lightwave Technol. **24**,12–21 (2006). [CrossRef]

3. R. Noé, “Phase noise tolerant synchronous QPSK/BPSK baseband type intradyne receiver concept with feedforward carrier recovery,” J. Lightwave Technol. **23**, 802–808 (2005). [CrossRef]

6. L. G. Kazovsky, “Performance analysis and laser linewidth requirements for optical PSK heterodyne communication systems,” J. Lightwave Technol. **4**, 415–425 (1986). [CrossRef]

## 2. Channel model including the phase noise at both transmit and receive ends

**24**,12–21 (2006). [CrossRef]

**24**,12–21 (2006). [CrossRef]

3. R. Noé, “Phase noise tolerant synchronous QPSK/BPSK baseband type intradyne receiver concept with feedforward carrier recovery,” J. Lightwave Technol. **23**, 802–808 (2005). [CrossRef]

6. L. G. Kazovsky, “Performance analysis and laser linewidth requirements for optical PSK heterodyne communication systems,” J. Lightwave Technol. **4**, 415–425 (1986). [CrossRef]

*k*th information symbol

*c*is bandwidth limited by a pulse shape function

_{k}*h*(

_{ps}*t*). The detail of

*h*(

_{ps}*t*) does not affect the conclusion of the paper. The signal is then impaired by a phase noise at the electrical-to-optical up-conversion, originated from the transmit laser phase noise that provides a phase rotation of

*h*(

_{f}*t*), and the amplifier noise of

*N*(

*t*)is also introduced. In practice, the amplifier noise of

*N*(

*t*) is added distributively along the fiber link span-by-span. The amplifier noise from different spans experiences different chromatic dispersion and

*N*(

*t*) may be a colored noise.

*h*(

_{e}*t*) is used to reverse the channel dispersion effect, and the signal is then passed into another filter

*h*(

_{m}*t*) to match the pulse shaping function

*h*(

_{ps}*t*) for optimal performance. The combined responses of

*h*(

_{e}*t*) and

*h*(

_{m}*t*) are commonly adjusted with an adaptive algorithm.

*c*(

*t*) is sampled periodically at the symbol rate

*T*, which gives the received signal

_{s}*c*′

*. For this analysis, the convolution of*

_{k}*h*(

_{ps}*t*) and

*h*(

_{m}*t*) are assumed as the raised cosine response. The channel model can be altered by moving digital sampling immediately after the optical-to-electrical down-conversion and the subsequent filtering function

*h*(

_{e}*t*) and

*h*(

_{m}*t*) can be performed digitally. This alternation does not change the performance of the system and will not affect our ensuing analysis.

*r*(

*t*) is the received baseband signal given by

*N*′(

*t*)is given by

*h*(

_{f}*t*) and

*h*(

_{e}*t*) are Dirac-delta function

*δ*(

*t*), the signal of (1) is thus simplified as

*h*′

*(*

_{ps}*t*)=

*h*⊗

_{ps}*h*is the overall pulse shaping function, and for this analysis is assumed raised cosine function. The phase noise

_{m}

_{m}*h*(

*t*) because of the short-duration of the pulse shaping function.

*c*′

*of*

_{k}*ϕ*(

_{t}*kT*)+

_{s}*ϕ*(

_{r}*kT*) [1

_{s}**24**,12–21 (2006). [CrossRef]

*ϕ*(

_{t}*kT*)+

_{s}*ϕ*(

_{r}*kT*) is

_{s}*ϕ*̂(

*kT*). The carrier phase compensation (CPC) is performed to recover the estimated transmitted symbol as

_{s}*ϕ*̂(

*kT*) and

_{s}*ϕ*(

_{t}*kT*)+

_{s}*ϕ*(

_{r}*kT*) is beyond the scope of this paper, and can be found in [1

_{s}**24**,12–21 (2006). [CrossRef]

^{-4}[2

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

^{-3}. This suggests that for the 40 and 100 Gb/s polarization-multiplexed systems, the maximum allowed laser linewidth is about 1.3 and 3.25 MHz that seems to be compatible with the conventional distributed-feedback (DFB) laser linewidth specification.

*t*=0 with

*k*=0 and

*c*=1 is considered. We obtain from (1)

_{k}*h*(

_{f}*t*) can be approximated with a set of discrete summation of many taps given by

*T*′

*should be smaller than the symbol period and is often set to half of the symbol period. Substituting (8) into (7), we arrive at*

_{s}*(*

_{i}*t*)≡

*ϕ*(

_{r}*t*)-

*ϕ*(

_{r}*t*-

*iT*′

*). The expression (9) shows that by moving the receive phase noise into the transmit end, the effective channel response can be considered as similar to yet different from*

_{s}*h*(

_{f}*t*), with each tap varying by an additional factor

*(*

_{i}*t*) t is very small and can be assumed to be zero. However, when the channel is very dispersive, Δ

*(*

_{i}*t*) can be no longer approximated to be zero. A thorough analysis is required to understand the impact of the dispersion on the phase noise impairment. The expression (9) is further rearranged by Taylor expansion in Δ

*(*

_{i}*t*) and we have

*h*(

_{f}*t*). It is noted that the transmit laser phase noise

*ϕ*(

_{t}*t*) does not generate any additional impairment because it passes through both fiber channel of

*h*(

_{f}*t*) and equalizer of

*h*(

_{e}*t*) that perfectly cancels the terms due to commuting. The second term of (10) is difficult to evaluate in the time-domain. Analysis of this noise impairment can be developed in the frequency-domain.

*t*=0 with

*k*=0 and

*c*=1 is considered. The transmit phase noise is also omitted as it does not contribute to EEPN. In Fig. 2, the receive response function

_{k}*h*⊗

_{e}*h*is modeled with a set of discrete summation of many taps given by

_{m}*t*of 0, and removing the common phase of

*ϕ*(0), the estimated transmit symbol is given by

_{r}*(*

_{i}*t*)≡

*ϕ*(

_{r}*t*)-

*ϕ*(

_{r}*t*-

*iT*′

*). From (12) and (13), in additional to the original transmit symbol of 1, an additional noise term*

_{s}

_{E}*n*arises from the receive phase noise. From Fig. 2, the output signal

*c*(

*t*) is a summation of multiple copies of the signal with varying delay. The existence of the receive phase noise de-correlates the summing components of

*c*(

*t*) and subsequently contributes the additional noise.

## 3. Analytical results of the equalization-enhanced phase noise (EEPN)

*k*=0 and

*c*=1 is rewritten as

_{k}*ϕ*(0), the carrier phase compensated signal become

_{r}*c*′(

*t*)due to the EEPN is given by

*E*{} stands for statistical average. Using a simplified notation of

*υ*(

*t*) is [6]

*S*(

*f*) is the spectral density of

*υ*(

*t*).

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

**4**, 415–425 (1986). [CrossRef]

16. A. Demir, A. Mehrotra, and J. Roychowdhury, “Phase noise in oscillators: A unifying theory and numerical methods for characterization,” IEEE Trans. Circuits Syst. I **47**, 655–674 (2000). [CrossRef]

17. T. H. Lee and A. Hajimiri, “Oscillator phase noise: A tutorial,” IEEE J. Solid-State Circuits **35**, 326–336 (2000). [CrossRef]

*S*(

*f*)is of Lorentzian line shape given by [6

**4**, 415–425 (1986). [CrossRef]

*f*

_{3dB}is the 3-dB laser linewidth.

*H*

_{1}(

*f*) and

*H*

_{2}(

*f*) are the frequency responses corresponding to the impulse responses of

*h*

_{1}(

*t*) and

*h*

_{2}(

*t*), respectively.

*E*{|

*c*′(

*t*)|

^{2}}, and the result is given by

*t*of zero (or sampled at

*t*of zero) give the complete formulation of the EEPN noise evaluation. Once the frequency-domain transfer functions are specified, expressions of (23) and (24) can be readily computed, and subsequently the noise variance can be obtained using (16).

*c*of 1. The combination of (16), (27) and (28) evaluated at

_{k}*t*of zero gives the complete formulation of the EEPN noise for a continuous signal with arbitrary number of symbols.

## 4. Numerical results of EEPN impairment

*B*is the signal symbol rate.

*f*

_{0}is the laser center frequency,

*c*is the speed of light,

*D*is the accumulated chromatic dispersion. Noting that

_{t}*H*

_{2}(

*f*)=

*H*(

_{e}*f*)

*H*(

_{m}*f*) and

*H*

_{2}(

*f*)=

*H*(

_{e}*f*)

*H*(

_{m}*f*), by substituting (30) and (31) into (23) and (24), we arrive at

*α*≡

*πc*(2

*f*

^{2}

_{0})-1

*D*Bf

_{t}_{3dB}. The expressions of (32) and (33) are derived with the normalization to 1 for |

*E*{

*c*′(0)}| and

*E*{|

*c*′(0)|

^{2}} at zero dispersion. Using the Taylor expansion of (32) and (33), and keeping the first-order of

*α*, we have

*η*defined in (35) is the normalized received signal power. Combing (35), and (36), and (16), we have

*α*, (ii) it induces an intra-symbol interference equal to

*α*/3, and (iii) it also induces an inter-symbol interference, the magnitude of which is to be discussed in the following paragraph.

*η*) for each symbol or is

*α*from (35). This implies that the inter-symbol interference contributes two-third of the total noise. To be specific, the noise variances can be summarized as follows:

*σ*

^{2}

*,*

_{T}*σ*

^{2}

*, and*

_{Inter}*σ*

^{2}

*stand for total interference, intra-symbol interference, and inter-symbol interference, respectively. These interferences are proportional to dispersion, bit rate, and linewidth, which is in contrast to the phase noise impairment without dispersion where the phase noise induced degradation is reduced with the increase of the bit rate.*

_{Inter}*P*, and the amplifier noise power

*n*

_{0}, the total effective SNR under influence of EEPN is

*γ*=

*P*/

*n*

_{0}is the SNR, and

*γ*

_{0}is the effective system SNR with EEPN. The increase of the required SNR, Δ

*P*due to the EEPN can be characterized as

*P*is often expressed in (dB) given by

**16**, 753–791 (2008). [CrossRef] [PubMed]

^{-3}due to the EEPN interference. As the symbol rate increases, the linewidth requirement becomes more stringent, in sharp contrast with the FFCS requirement. The FFCS 1 dB penalty linewidth requirement is also shown for comparison in Fig. 4. The intercept of the FFCS and EEPN curves signifies the boundary for the two symbol rate regimes in which one of two effects is dominant. For instance, for 10,000-km transmission system, the EEPN and FFCS curve intercepts at the symbol rate of 10 Gbaud/s. Below 10 Gbaud/s, the FFCS residual noise will dominate. However, beyond the symbol rate of 10 Gbaud/s, the EEPN is the primary noise source. Although FFCS predicates that the lessening of the laser linewidth requirement beyond 10 Gbaud/s, due to the EEPN interference, as a matter of fact, the increase of the symbol rate will further tighten the requirement of laser linewidth. For instance, FFCS alone permits a laser linewidth of 12 MHz at the symbol rate of 100 Gbaud/s, but this will be preempted by the requirement of EEPN that requires the laser linewidth of 100 kHz, which is about 100 times more stringent. EEPN interference only becomes significant when the dispersion is large and the symbol rate is high. Nevertheless, the coherent systems that support symbol rate of 100 Gb/s and 10,000 km could be a reality for undersea systems with proper span engineering and powerful silicon digital signal processing.

## 5. Conclusion

## References and links

1. | D. S. Ly-Gagnon, S. Tsukarnoto, K. Katoh, and K. Kikuchi, “Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation,” J. of Lightwave Technol. |

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

3. | R. Noé, “Phase noise tolerant synchronous QPSK/BPSK baseband type intradyne receiver concept with feedforward carrier recovery,” J. Lightwave Technol. |

4. | H. Sun, K. -T. Wu, and K. Roberts, “Real-time measurements of a 40 Gb/s coherent system,” Opt. Express |

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

6. | L. G. Kazovsky, “Performance analysis and laser linewidth requirements for optical PSK heterodyne communication systems,” J. Lightwave Technol. |

7. | S. Norimatsu and K. Iwashita, “Linewidth requirements for optical synchronous detection systems with nonnegligible loop delay time,” J. Lightwave Technol. |

8. | K.-P. Ho, |

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

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

11. | S. Tsukamoto, K. Katoh, and K. Kikuchi, “Unrepeated transmission of 20-Gb/s optical quadrature phase-shift-keying signal over 200-km standard single-mode fiber based on digital processing of homodynedetected signal for group-velocity dispersion compensation,” IEEE Photon. Technol. Lett. |

12. | X. Chen, C. Kim, G. Li, and B. Zhou, “Numerical study of lumped dispersion compensation for 40-Gb/s return-to-zero differential phase-shift keying transmission,” IEEE Photon. Technol. Lett. |

13. | E. Ip and J. M. Kahn, “Compensation of dispersion and nonlinear effects using digital back-propagation,” to be published in J. Lightwave Technol.. |

14. | F. M. Gardner, |

15. | H. Meyr, M. Moeneclaey, and S. A. Fechtel, |

16. | A. Demir, A. Mehrotra, and J. Roychowdhury, “Phase noise in oscillators: A unifying theory and numerical methods for characterization,” IEEE Trans. Circuits Syst. I |

17. | T. H. Lee and A. Hajimiri, “Oscillator phase noise: A tutorial,” IEEE J. Solid-State Circuits |

**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: August 7, 2008

Revised Manuscript: September 3, 2008

Manuscript Accepted: September 15, 2008

Published: September 19, 2008

**Citation**

William Shieh and Keang-Po Ho, "Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing," Opt. Express **16**, 15718-15727 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-20-15718

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### References

- D. S. Ly-Gagnon, S. Tsukarnoto, K. Katoh, and K. Kikuchi, "Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation," J. Lightwave Technol. 24, 12-21 (2006). [CrossRef]
- E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, "Coherent detection in optical fiber systems," Opt. Express 16, 753-791 (2008). [CrossRef] [PubMed]
- R. Noé, "Phase noise tolerant synchronous QPSK/BPSK baseband type intradyne receiver concept with feedforward carrier recovery," J. Lightwave Technol. 23, 802-808 (2005). [CrossRef]
- H. Sun, K. -T. Wu, and K. Roberts, "Real-time measurements of a 40 Gb/s coherent system," Opt. Express 16, 873-879 (2008). [CrossRef] [PubMed]
- S. J. Savory, G. Gavioli, R. I. Killey, and P. Bayvel, "Electronic compensation of chromatic dispersion using a digital coherent receiver," Opt. Express 15, 2120-2126 (2007). [CrossRef] [PubMed]
- L. G. Kazovsky, "Performance analysis and laser linewidth requirements for optical PSK heterodyne communication systems," J. Lightwave Technol. 4, 415-425 (1986). [CrossRef]
- S. Norimatsu and K. Iwashita, "Linewidth requirements for optical synchronous detection systems with nonnegligible loop delay time," J. Lightwave Technol. 10, 341-349 (1992). [CrossRef]
- K.-P. Ho, Phase-modulated Optical Communication Systems, (Springer, 2005), ch. 4.
- H. Bulow, F. Buchali, and A. Klekamp, "Electronic dispersion compensation," J. Lightwave Technol. 26, 158 - 167 (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, 674-676 (2004). [CrossRef]
- S. Tsukamoto, K. Katoh, and K. Kikuchi, "Unrepeated transmission of 20-Gb/s optical quadrature phase-shift-keying signal over 200-km standard single-mode fiber based on digital processing of homodyne-detected signal for group-velocity dispersion compensation," IEEE Photon. Technol. Lett. 18, 1016-1018 (2006). [CrossRef]
- X. Chen, C. Kim, G. Li, and B. Zhou, "Numerical study of lumped dispersion compensation for 40-Gb/s return-to-zero differential phase-shift keying transmission," IEEE Photon. Technol. Lett. 19, 568-570 (2007). [CrossRef]
- E. Ip and J. M. Kahn, "Compensation of dispersion and nonlinear effects using digital back-propagation," to be published in J. Lightwave Technol..
- F. M. Gardner, Phaselock Techniques, (2nd Ed., New York: John Wiley, 1979).
- H. Meyr, M. Moeneclaey, and S. A. Fechtel, Digital Communication Receivers: Synchronization, Channel Estimation, and Signal Processing, (New York: John Wiley, 1997).
- A. Demir, A. Mehrotra, and J. Roychowdhury, "Phase noise in oscillators: A unifying theory and numerical methods for characterization," IEEE Trans. Circuits Syst. I 47, 655-674 (2000). [CrossRef]
- T. H. Lee and A. Hajimiri, "Oscillator phase noise: A tutorial," IEEE J. Solid-State Circuits 35, 326-336 (2000). [CrossRef]

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