## Characterization of semiconductor-laser phase noise and estimation of bit-error rate performance with low-speed offline digital coherent receivers |

Optics Express, Vol. 20, Issue 5, pp. 5291-5302 (2012)

http://dx.doi.org/10.1364/OE.20.005291

Acrobat PDF (1080 KB)

### Abstract

We develop a systematic method for characterizing semiconductor-laser phase noise, using a low-speed offline digital coherent receiver. The field spectrum, the FM-noise spectrum, and the phase-error variance measured with such a receiver can completely describe phase-noise characteristics of lasers under test. The sampling rate of the digital coherent receiver should be much higher than the phase-fluctuation speed. However, 1 GS/s is large enough for most of the single-mode semiconductor lasers. In addition to such phase-noise characterization, interpolating the taken data at 1.25 GS/s to form a data stream at 10 GS/s, we can predict the bit-error rate (BER) performance of multi-level modulated optical signals at 10 Gsymbol/s. The BER degradation due to the phase noise is well explained by the result of the phase-noise measurements.

© 2012 OSA

## 1. Introduction

1. 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]

3. K. Kikuchi, “Digital coherent optical communication systems: Fundamentals and future prospects,” IEICE Electron. Express **8**, 1642–1662 (2011). [CrossRef]

4. A.H. Gnauck, P. J. Winzer, S. Chandrasekhar, X. Liu, B. Zhu, and D. W. Peckham, “10×224-Gb/s WDM transmission of 28-Gbaud PDM 16-QAM on a 50-GHz grid transmission over 1,200 km of fiber,” in *2010 OSA Technical Digest of Optical Fiber Communication Conference* (Optical Society of America, 2010), PDPB8.

6. K. Kikuchi, “Analyses of wavelength- and polarization-division multiplexed transmission characteristics of optical quadrature-amplitude-modulation signals,” Opt. Express **19**, 17985–17995 (2011). [CrossRef] [PubMed]

7. R. Nagarajan, D. Lambert, M. Kato, V. Lal, G. Goldfarb, J. Rahn, M. Kuntz, J. Pleumeekers, A. Dentai, H.-S. Tsai, R. Malendevich, M. Missey, K.-T. Wu, H. Sun, J. McNicol, J. Tang, J. Zhang, T. Butrie, A. Nilsson, M. Reffle, F. Kish, and D. Welch, “10 channel, 100Gbit/s per channel, dual polarization, coherent QPSK, monolithic InP receiver photonic integrated circuit,” in *2011 OSA Technical Digest of Optical Fiber Communication Conference* (Optical Society of America, 2011), OML7.

## 2. Evaluation method of phase-noise characteristics

### 2.1. Functions characterizing the phase noise

*E*(

*t*) of the laser under test, the phase difference Δ

*ϕ*(

_{τ}*t*), the field spectrum

*S*(

*f*), the FM-noise spectrum

*S*(

_{F}*t*), and the phase-error variance

*σ*(

_{ϕ}*τ*)

^{2}. Equations (1)–(6) in Fig. 1, which relate those to each other, are listed in Table 1 [8]. As shown in Fig. 1, we measure

*E*(

*t*) by a digital coherent receiver and calculate the three functions, the field spectrum

*S*(

*f*), the FM-noise spectrum

*S*(

_{F}*f*), and the phase-error variance

*σ*(

*τ*)

^{2}, using Eqs.(1)–(6) in Table 1. These functions are applied to characterizing the phase noise.

*E*(

*t*). The field spectrum

*S*(

*f*) is defined as the power-spectral-density function of

*E*(

*t*) as shown by Eq. (1) in Table 1. Since the AM noise of semiconductor lasers operating well above threshold is negligibly small, the spectral width of

*S*(

*f*) mainly stems from the phase noise and is the most common measure of the phase noise.

*E*(

*t*): The phase difference Δ

*ϕ*(

_{τ}*t*) generated in a time interval

*τ*is given as Eq. (2). Then, the phase-error variance

*σ*(

_{ϕ}*τ*)

^{2}, which is the mean-square value of such phase difference, is obtained from Eq. (3). The slope of the

*τ*-versus-

*σ*(

_{ϕ}*τ*)

^{2}characteristics is another measure of the phase noise. Especially in differentially coherent detection schemes such as differential phase-shift keying (DPSK) and differential quadrature PSK (DQPSK) schemes,

*σ*(

_{ϕ}*T*)

^{2}can directly determine the BER performance where

*T*denotes the symbol duration [9

9. K. Kikuchi, T. Okoshi, M. Nagamatsu, and N. Henmi, “Degradation of bit-error rate in coherent optical communications due to spectral spread of the transmitter and the local oscillator,” J. Lightwave Technol. **2**, 1024–1033 (1984). [CrossRef]

### 2.2. Typical examples of the relation among the field spectrum, the FM-noise spectrum, and the phase-error variance

*σ*(

_{ϕ}*τ*)

^{2}is given from Eq. (5) as Note that the phase-error variance is linearly proportional to

*τ*. Then, Eq. (6) leads to the double-sided field spectrum having the Lorentzian shape as Thus, we find that

*δf*in Eq. (9) represents the 3-dB linewidth of the field spectrum

*S*(

*f*). Figure 2 illustrates (a)

*S*(

_{F}*f*), (b)

*σ*(

_{ϕ}*τ*)

^{2}, and (c)

*S*(

*f*) in the ideal case. Using only one parameter of

*δf*, we can fully describe the phase-noise characteristics. Such ideal case is usually assumed in the coherent system design.

10. K. Kikuchi, “Impact of 1/f-type FM noise on coherent optical communications,” Electron. Lett. **23**, 885–887 (1987). [CrossRef]

*τ*(Fig. 3(b)). Then, the field spectrum is dependent on the measurement time as discussed in what follows: The Lorentzian lineshape determined from the white FM noise is measured only when the measurement time interval is short enough; however, the center frequency of the Lorentzian spectrum drifts because of instantaneous-frequency fluctuations in the low frequency side, as the measurement time becomes longer. Such frequency drift results in a broadened field spectrum as shown in Fig. 3(c). This fact means that the 3-dB linewidth of

*S*(

*f*) is no more a good measure of the phase noise since it is dependent on the measurement time. Therefore, for the coherent system design, we need the information on

*S*(

_{F}*f*).

### 2.3. Experimental setup for phase-noise characterization

11. K. Kikuchi and T. Okoshi, “Measurement of FM noise, AM noise, and field spectra of 1.3*μ*m InGaAsP DFB lasers and determination of the linewidth enhancement factor,” IEEE J. Quantum Electron. **21**, 1814–1818 (1985). [CrossRef]

13. R. Maher and B. Thomsen, “Dynamic linewidth measurement technique using digital intradyne coherent receivers,” Opt. Express **19**, B313–B322 (2011). [CrossRef]

*S*(

*f*),

*σ*(

_{ϕ}*τ*)

^{2}, and

*S*(

_{F}*f*), all at once. In contrast to the receiver for optical communications, our receiver can operate offline for phase-noise analyses.

## 3. Experimental Results

*S*(

*f*), the FM-noise spectrum

*S*(

_{F}*f*), and the phase-error variance

*σ*(

_{ϕ}*τ*)

^{2}of the beat between the two DFB lasers, respectively. The sampling rate was 1/

*τ*= 1.25 GS/s and the number of samples

_{s}*n*= 1.25 × 10

^{5}. Then, the measurement time in this case was

*τ*= 10

_{s}n^{−4}s. The offset frequency of the beat was maintained less than 10 MHz. From Fig. 5(c), we find that the phase-error variance is proportional to the delay time

*τ*, as shown by the red broken line fitted to the experimental result. Noting that the slope of the red broken line is 2

*πδf*in the ideal case (Eq. (10)), we can estimate that

*δf*= 170 kHz, which means that the linewidth of each laser is 85 kHz if linewidths of the two lasers are equal. Then, we can draw a Lorentzian shape with

*δf*= 170 kHz shown by the red curve in Fig. 5(a) (Eq. (11)), which is in perfect agreement with the experimental result over a range of 40 dB. On the other hand, Fig. 5(b) shows that the FM-noise spectrum is approximately white, and the red line represents its spectral density obtained from the linewidth as

*δf*/

*π*(Eq. (9)), which is also in good agreement with the experimental result.

*τ*= 12.5 MS/s and the number of the samples was

_{s}*n*= 1.25 ×10

^{5}. The measurement time

*τ*was extended to 10

_{s}n^{−2}s. The offset frequency of the beat was kept below 1 MHz. Since the spectral width in Fig. 6(a) is still much smaller than the sampling rate, the spectrum folding due to the aliasing effect is not significant. In this case, we clearly find that the phase-noise characteristics deviate from the ideal ones shown in Fig. 2 due to low-frequency FM noise [10

10. K. Kikuchi, “Impact of 1/f-type FM noise on coherent optical communications,” Electron. Lett. **23**, 885–887 (1987). [CrossRef]

^{−2}is divided into ten sections having 10

^{−3}-s time intervals, and the field spectrum in each section is calculated in time order from 1 × 10

^{−3}s to 10 × 10

^{−3}s. Figure 7 shows such time-resolved field spectra. The range of the vertical axis is limited to 15 dB in order to show only the center-frequency fluctuation. We find that the center frequency of the spectrum measured in the shorter time interval of 10

^{−3}s fluctuates significantly, resulting in a broadened spectrum measured in the longer time interval of 10

^{−2}s.

*S*(

*f*), the FM-noise spectrum

*S*(

_{F}*f*), and the phase-error variance

*σ*(

_{ϕ}*τ*)

^{2}of the DBR laser, respectively. The sampling rate was 1/

*τ*= 1.25 GS/s and the number of samples was

_{s}*n*= 1.25 × 10

^{5}. As seen from Figs. 5(b) and 8(b), the low-frequency FM noise of the DBR laser is much larger than that of the DFB laser. The passive phase-control region in the DBR laser most likely generates such low-frequency FM noise, which may be reduced by a current source with lower electrical noise [13

13. R. Maher and B. Thomsen, “Dynamic linewidth measurement technique using digital intradyne coherent receivers,” Opt. Express **19**, B313–B322 (2011). [CrossRef]

## 4. Estimation of bit-error rate performance

^{5}samples are interpolated to form a 10-GS/s data stream with 10

^{6}samples. The 10-GS/s data are differentially encoded in the QPSK and 16-QAM modulation formats at the symbol rate of 10 Gsymbol/s. Gaussian noise is then loaded to change the energy per bit to noise spectral density ratio

*E*/

_{b}*N*

_{0}. Carrier-phase estimation is done by the 4-th power algorithm for QPSK [14

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

*E*/

_{b}*N*

_{0}for the case (1) using two DFB lasers. Figure 9(a) represents the BER calculated from the 1.25-GS/s data through the interpolation process, whereas Fig. 9 (b) shows the BER calculated directly from the 10-GS/s data. Red curves are theoretical BERs which do not include the phase-noise effect. Black, green, and blue curves are obtained when the averaging span for carrier-phase estimation is 11, 101, and 1001 symbols, respectively. Since any difference in the BER performance is not observed between Figs. 9 (a) and (b), we find that the 1.25 GS/s data can predict the BER performance at 10 Gsymbol/s. The optimum averaging span is 101 symbols, but the BER is not so sensitive to the averaging span. In addition, the BER degradation by the phase noise is negligibly small. These facts are owing to the sufficiently small phase noise of DFB lasers having the 3-dB linewidth below 100 kHz [3

3. K. Kikuchi, “Digital coherent optical communication systems: Fundamentals and future prospects,” IEICE Electron. Express **8**, 1642–1662 (2011). [CrossRef]

*E*/

_{b}*N*

_{0}for the case (2) using DBR and DFB lasers. Figure 10(a) represents the BER calculated from the 1.25-GS/s data through the interpolation process. On the other hand, Fig. 10(b) shows the BER calculated directly from the 10-GS/s data. Red curves are theoretical BERs without the phase-noise effect. Black, green, and blue curves are obtained when the averaging span for carrier-phase estimation is 5, 61, and 201 symbols, respectively. Also in this case, the difference between Figs. 10(a) and 9(b) is not so significant, and we find that the 1.25-GS/s data can be used for calculating the BER performance at 10 Gsymbol/s. When the averaging span is 61 symbols, the BER curve is very close to the theoretical limit. The BER performance in such case is determined from the 600-kHz intrinsic linewidth of the Lorentzian spectrum, and the 600-kHz linewidth is small enough for the 10-GSymbol/s QPSK system [3

3. K. Kikuchi, “Digital coherent optical communication systems: Fundamentals and future prospects,” IEICE Electron. Express **8**, 1642–1662 (2011). [CrossRef]

*E*/

_{b}*N*

_{0}for the case (1) using two DFB lasers. Figure 11(a) represents the BER calculated from the 1.25-GS/s data through the interpolation process, whereas Fig. 11 (b) shows the BER calculated directly from the 10-GS/s data. Red curves are BERs when the phase-noise effect is not included. Black, green, and blue curves are obtained when the averaging span for carrier-phase estimation is 11, 51, and 101 symbols, respectively. The difference in the BER performance is not so remarkable between Figs. 11(a) and (b). The optimum averaging span is 51 symbols, and the power penalty at BER=10

^{−4}is about 1 dB from the theoretical limit, which is due to the 170-kHz linewidth of the beat.

*E*/

_{b}*N*

_{0}for the case (2) using DBR and DFB lasers. Figure 12(a) represents the BER calculated from the 1.25-GS/s data through the interpolation process. On the other hand, Fig. 10(b) shows the BER calculated directly from the 10-GS/s data. Red curves represent BERs without the phase-noise effect. Black, green, and blue curves are obtained when the averaging span for carrier-phase estimation is 11, 41, and 101 symbols, respectively. The difference between Figs. 12(a) and 10(b) is not so significant also in this case. When the averaging span is 41 symbols, the power penalty at BER=10

^{−4}is about 2 dB, which stems from the 600-kHz intrinsic linewidth of the Lorentzian spectrum. On the other hand, when the averaging span is 101, the BER degradation becomes remarkable as shown by the blue curves, because the effect of the low-frequency FM noise becomes serious.

## 5. Conclusions

## Acknowledgments

## References and links

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

2. | K. Kikuchi, “Phase-diversity homodyne detection of multi-level optical modulation with digital carrier phase estimation,” IEEE J. Sel. Top. Quantum Electron. |

3. | K. Kikuchi, “Digital coherent optical communication systems: Fundamentals and future prospects,” IEICE Electron. Express |

4. | A.H. Gnauck, P. J. Winzer, S. Chandrasekhar, X. Liu, B. Zhu, and D. W. Peckham, “10×224-Gb/s WDM transmission of 28-Gbaud PDM 16-QAM on a 50-GHz grid transmission over 1,200 km of fiber,” in |

5. | A. Sano, T. Kobayashi, K. Ishihara, H. Masuda, S. Yamamoto, K. Mori, E. Yamazaki, E. Yoshida, Y. Miyamoto, T. Yamada, and H. Yamazaki, “240-Gb/s polarization-multiplexed 64-QAM modulation and blind detection using PLC-LN hybrid integrated modulator and digital coherent receiver,” European Conference on Optical Communication, Sept. 2009, Vienna, Austria, PD2.2. |

6. | K. Kikuchi, “Analyses of wavelength- and polarization-division multiplexed transmission characteristics of optical quadrature-amplitude-modulation signals,” Opt. Express |

7. | R. Nagarajan, D. Lambert, M. Kato, V. Lal, G. Goldfarb, J. Rahn, M. Kuntz, J. Pleumeekers, A. Dentai, H.-S. Tsai, R. Malendevich, M. Missey, K.-T. Wu, H. Sun, J. McNicol, J. Tang, J. Zhang, T. Butrie, A. Nilsson, M. Reffle, F. Kish, and D. Welch, “10 channel, 100Gbit/s per channel, dual polarization, coherent QPSK, monolithic InP receiver photonic integrated circuit,” in |

8. | T. Okoshi and K. Kikuchi, |

9. | K. Kikuchi, T. Okoshi, M. Nagamatsu, and N. Henmi, “Degradation of bit-error rate in coherent optical communications due to spectral spread of the transmitter and the local oscillator,” J. Lightwave Technol. |

10. | K. Kikuchi, “Impact of 1/f-type FM noise on coherent optical communications,” Electron. Lett. |

11. | K. Kikuchi and T. Okoshi, “Measurement of FM noise, AM noise, and field spectra of 1.3 |

12. | K. Kikuchi and K. Igarashi, “Characterization of semiconductor-laser phase noise with digital coherent receivers,” in |

13. | R. Maher and B. Thomsen, “Dynamic linewidth measurement technique using digital intradyne coherent receivers,” Opt. Express |

14. | A. J. Viterbi and A. N. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory |

15. | M. Seimetz, “Laser linewidth limitations for optical systems with high-order modulation employing feed forward digital carrier phase estimation,” in |

**OCIS Codes**

(060.1660) Fiber optics and optical communications : Coherent communications

(060.2330) Fiber optics and optical communications : Fiber optics communications

(060.2920) Fiber optics and optical communications : Homodyning

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: January 3, 2012

Revised Manuscript: February 2, 2012

Manuscript Accepted: February 13, 2012

Published: February 17, 2012

**Citation**

Kazuro Kikuchi, "Characterization of semiconductor-laser phase noise and estimation of bit-error rate performance with low-speed offline digital coherent receivers," Opt. Express **20**, 5291-5302 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-5-5291

Sort: Year | Journal | Reset

### References

- 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]
- K. Kikuchi, “Phase-diversity homodyne detection of multi-level optical modulation with digital carrier phase estimation,” IEEE J. Sel. Top. Quantum Electron.12, 563–570 (2006). [CrossRef]
- K. Kikuchi, “Digital coherent optical communication systems: Fundamentals and future prospects,” IEICE Electron. Express8, 1642–1662 (2011). [CrossRef]
- A.H. Gnauck, P. J. Winzer, S. Chandrasekhar, X. Liu, B. Zhu, and D. W. Peckham, “10×224-Gb/s WDM transmission of 28-Gbaud PDM 16-QAM on a 50-GHz grid transmission over 1,200 km of fiber,” in 2010 OSA Technical Digest of Optical Fiber Communication Conference (Optical Society of America, 2010), PDPB8.
- A. Sano, T. Kobayashi, K. Ishihara, H. Masuda, S. Yamamoto, K. Mori, E. Yamazaki, E. Yoshida, Y. Miyamoto, T. Yamada, and H. Yamazaki, “240-Gb/s polarization-multiplexed 64-QAM modulation and blind detection using PLC-LN hybrid integrated modulator and digital coherent receiver,” European Conference on Optical Communication, Sept. 2009, Vienna, Austria, PD2.2.
- K. Kikuchi, “Analyses of wavelength- and polarization-division multiplexed transmission characteristics of optical quadrature-amplitude-modulation signals,” Opt. Express19, 17985–17995 (2011). [CrossRef] [PubMed]
- R. Nagarajan, D. Lambert, M. Kato, V. Lal, G. Goldfarb, J. Rahn, M. Kuntz, J. Pleumeekers, A. Dentai, H.-S. Tsai, R. Malendevich, M. Missey, K.-T. Wu, H. Sun, J. McNicol, J. Tang, J. Zhang, T. Butrie, A. Nilsson, M. Reffle, F. Kish, and D. Welch, “10 channel, 100Gbit/s per channel, dual polarization, coherent QPSK, monolithic InP receiver photonic integrated circuit,” in 2011 OSA Technical Digest of Optical Fiber Communication Conference (Optical Society of America, 2011), OML7.
- T. Okoshi and K. Kikuchi, Coherent Optical Communication Systems (KTK/Kluwer, 1988), Chap.3.
- K. Kikuchi, T. Okoshi, M. Nagamatsu, and N. Henmi, “Degradation of bit-error rate in coherent optical communications due to spectral spread of the transmitter and the local oscillator,” J. Lightwave Technol.2, 1024–1033 (1984). [CrossRef]
- K. Kikuchi, “Impact of 1/f-type FM noise on coherent optical communications,” Electron. Lett.23, 885–887 (1987). [CrossRef]
- K. Kikuchi and T. Okoshi, “Measurement of FM noise, AM noise, and field spectra of 1.3μm InGaAsP DFB lasers and determination of the linewidth enhancement factor,” IEEE J. Quantum Electron.21, 1814–1818 (1985). [CrossRef]
- K. Kikuchi and K. Igarashi, “Characterization of semiconductor-laser phase noise with digital coherent receivers,” in 2011 OSA Technical Digest of Optical Fiber Communication Conference (Optical Society of America, 2011), OML3.
- R. Maher and B. Thomsen, “Dynamic linewidth measurement technique using digital intradyne coherent receivers,” Opt. Express19, B313–B322 (2011). [CrossRef]
- A. J. Viterbi and A. N. Viterbi, “Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission,” IEEE Trans. Inf. Theory29, 543–551 (1983). [CrossRef]
- M. Seimetz, “Laser linewidth limitations for optical systems with high-order modulation employing feed forward digital carrier phase estimation,” in 2008 OSA Technical Digest of Optical Fiber Communication Conference (Optical Society of America, 2008), NWA4.

## Cited By |
Alert me when this paper is cited |

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

« Previous Article | Next Article »

OSA is a member of CrossRef.