## Experimental demonstration of adaptive digital monitoring and compensation of chromatic dispersion for coherent DP-QPSK receiver |

Optics Express, Vol. 19, Issue 26, pp. B728-B735 (2011)

http://dx.doi.org/10.1364/OE.19.00B728

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### Abstract

We experimentally demonstrate a digital signal processing (DSP)-based optical performance monitoring (OPM) algorithm for in-service monitoring of chromatic dispersion (CD) in coherent transport networks. Dispersion accumulated in 40 Gbit/s QPSK signal after 80 km of fiber transmission is successfully monitored and automatically compensated without prior knowledge of fiber dispersion coefficient. Four different metrics for assessing CD mitigation are implemented and simultaneously verified proving to have high estimation accuracy. No observable penalty is measured when the monitoring module drives an adaptive digital CD equalizer.

© 2011 OSA

## 1. Introduction

1. S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express **16**, 804–817 (2008). [CrossRef] [PubMed]

2. F. Hauske, J. Geyer, M. Kuschnerov, K. Piyawanno, T. Duthel, C. Fludger, D. van den Borne, E. Schmidt, B. Spinnler, H. de Waardt, and B. Lankl, “Optical performance monitoring from FIR filter coefficients in coherent receivers,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OThW2.

5. D. Wang, C. Lu, A.P.T Lau, and S. He, “Adaptive chromatic dispersion compensation for coherent communication systems using delay-tap sampling technique,” IEEE Photon. Technol. Lett. **14**, 1016–1018 (2011). [CrossRef]

## 2. Blind chromatic dispersion monitoring for digital coherent receivers

### 2.1. Generic scanning algorithm

*p*[

*k*] representing received complex optical field is first divided into blocks of length

*N*, indexed consecutively with

*k*= 0...

*N*– 1, and transformed to frequency domain. The resulting signal is then multiplied with the

*H*digital filter where

_{CD}*f*is the clock frequency,

*λ*the signal wavelength,

*c*the speed of light and

*CD*the value of CD. The rationale behind using an FDE is the number of required complex multiplications as compared to time domain approach [6

6. B. Spinnler, “Equalizer design and complexity for digital coherent receivers,” IEEE J. Sel. Topics Quantum Electron. **5**, 1180–1192 (2010). [CrossRef]

*Q*[

*k*] obtained after multiplication is transformed back to time domain as

*q*[

*k*] and constitutes the output of the equalizer. Signals

*p*and

*q*(or

*Q*, depending on particular method) are fed to a CD DSP OPM module which computes the metric

*J*. Since the value of CD present in the channel is unknown, the transfer function

*H*may not be computed. However, due to the fact that

_{CD}*H*has only one degree of freedom, adaptation can be performed by sweeping over a range of

_{CD}*CD*parameter, every time updating

*H*, until an optimal operating point is found. An interest range of CD values shall be specified, which in general will be different for each optical network and may depend on the topology and traffic characteristic. The

_{CD}*CD*parameter can be initialized as to coincide with the most probable CD value of the received signal in order to increase the convergence speed. The space of

*CD*parameter is then gradually searched with a given resolution and the metric

*J*[

*CD*] is computed for every value of CD under test.

*CD*parameter that should be used to recalculate

*H*to mitigate the CD ISI.

_{CD}### 2.2. Dispersion metrics

#### 2.2.1. CMA metric

7. M. Kuschnerov, F. N. Hauske, K. Piyawanno, B. Spinnler, M.S. Alfiad, A. Napoli, and B. Lankl, “DSP for coherent single-carrier receivers,” J. Lightwave Technol. **27**, 3614–3622 (2009). [CrossRef]

*R*

_{2}is the error function (metric). Since the received signal is sampled at twice the symbol rate, another normalization constant

*R*

_{1}has to be used. Both

*R*

_{1}and

*R*

_{2}have to be constantly estimated from the power of odd and even samples of the received signal. The metric

*J*is then computed The required normalization constants

*R*

_{1}and

*R*

_{2}are determined for each block. First, the mean power of odd and even samples,

*q̄*

_{1}and

*q̄*

_{2}, is calculated Based on the ratio of

*q̄*

_{2}to

*q̄*

_{1},

*R*

_{1}and

*R*

_{2}normalization constants are determined as follows: with proposed empirically adjusted parameters

*ξ*= 1.25,

*R*= 0.6,

_{a}*R*= 1.5 and

_{b}*R*= 2 for the received complex signal power normalized to 1.

_{c}*N*= 256 samples.

#### 2.2.2. Mean signal power

*q*at the output of the CD equalizer is given by Next,

*J*metric is found according to and the estimated value of

*CD*parameter is indicated by the maximum of the metric.

*N*= 2048.

#### 2.2.3. Eigenvalue spread

*χ*of the autocorrelation matrix

**R**is a quantitative measure of signal distortion. Specifically,

**R**is the following Toeplitz matrix of size

*L*×

*L*where

*r*is the autocorrelation of the signal

*q*calculated as and

^{*}denotes complex conjugate. The eigenvalue spread of the autocorrelation matrix and the CD metric itself is then defined as where

*λ*

_{max}and

*λ*

_{min}are eigenvalues of

**R**with the largest and the smallest magnitudes respectively. If the dispersion was correctly compensated, the autocorrelation matrix is well-conditioned and the spread of eigenvalues approaches the theoretical minimum at 1. Otherwise, the matrix is ill-conditioned and the spread is significantly larger than that. This approach allows for construction of a minimum-search metric.

*CD*parameter (expressed in ps/nm) in the range of interest are used (units neglected). It should be noted that eigenvalues computation is an expensive task in terms of required processing power and, therefore, practical use of this metric might be limited.

#### 2.2.4. Frequency spectrum autocorrelation

*Q*, which is the frequency domain representation of the CD equalizer output after multiplication with the filtering function

*H*as presented in Fig. 1. First, a discrete circular autocorrelation is computed where 〇

_{CD}*(*

_{m}*Q*) is a circular shift operator that circularly shifts vector

*Q*by

*m*positions (

*m*∈

*N*) and csgn is a complex extension of the sign function sgn, defined as csgn(

*x*) = sgn[ℜ (

*x*)] +

*ι*sgn[ℑ (

*x*)], with ℜ and ℑ denoting, respectively, real and imaginary part of a complex number. It is not necessary for

*m*to cover all possible shifts and thus

*m*ranging from

*J*[

*CD*] for a single CD value under test is then calculated as where summation over

*m*covers all applied circular shifts.

*Q*of size

*N*= 256 samples as to smoothen the obtained curve.

## 3. Experimental setup

## 4. Experimental results

*Preset*is a reference line showing performance of the receiver when CD filter is manually set with an a priori known CD value of either 0 ps/nm (Fig. 4a) or 1280 ps/nm (Fig. 4b). Remaining lines show the performance of the receiver for different CD metrics as OSNR is varied for both transmission distances. It may be observed that regardless of the CD distortion present in the channel, lines depart only to a very small extent from the reference

*Preset*line. This shows that both: each metric and the CD DSP monitor itself are reliable enough as not to introduce any penalty when compared to a CD filter with a fixed CD value. The FIR filter used for polarization demultiplexing is too short to compensate CD after 80 km of fiber transmission; effectively only residual CD is mitigated via the FIR filter, while bulk of the dispersion is removed by the FDE CD equalizer driven by the monitoring module. It is necessary to point out that this proof-of-concept works satisfactory with single polarization QPSK signal and it should be scalable to PDM-QPSK as CD affects both polarizations equally.

## 5. Conclusions

## References and links

1. | S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express |

2. | F. Hauske, J. Geyer, M. Kuschnerov, K. Piyawanno, T. Duthel, C. Fludger, D. van den Borne, E. Schmidt, B. Spinnler, H. de Waardt, and B. Lankl, “Optical performance monitoring from FIR filter coefficients in coherent receivers,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OThW2. |

3. | M. Kuschnerov, F. N. Hauske, K. Piyawanno, B. Spinnler, A. Napoli, and B. Lankl, “Adaptive chromatic dispersion equalization for non-dispersion managed coherent systems,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper OMT1. |

4. | F. N. Hauske, C. Xie, Z. P. Zhang, C. Li, L. Li, and Q. Xiong, “Frequency domain chromatic dispersion estimation,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper JThA11. |

5. | D. Wang, C. Lu, A.P.T Lau, and S. He, “Adaptive chromatic dispersion compensation for coherent communication systems using delay-tap sampling technique,” IEEE Photon. Technol. Lett. |

6. | B. Spinnler, “Equalizer design and complexity for digital coherent receivers,” IEEE J. Sel. Topics Quantum Electron. |

7. | M. Kuschnerov, F. N. Hauske, K. Piyawanno, B. Spinnler, M.S. Alfiad, A. Napoli, and B. Lankl, “DSP for coherent single-carrier receivers,” J. Lightwave Technol. |

8. | S. Haykin, |

**OCIS Codes**

(060.1660) Fiber optics and optical communications : Coherent communications

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

**ToC Category:**

Backbone and Core Networks

**History**

Original Manuscript: October 3, 2011

Revised Manuscript: November 25, 2011

Manuscript Accepted: November 26, 2011

Published: December 6, 2011

**Virtual Issues**

European Conference on Optical Communication 2011 (2011) *Optics Express*

**Citation**

Robert Borkowski, Xu Zhang, Darko Zibar, Richard Younce, and Idelfonso Tafur Monroy, "Experimental demonstration of adaptive digital monitoring and compensation of chromatic dispersion for coherent DP-QPSK receiver," Opt. Express **19**, B728-B735 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-26-B728

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### References

- S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express16, 804–817 (2008). [CrossRef] [PubMed]
- F. Hauske, J. Geyer, M. Kuschnerov, K. Piyawanno, T. Duthel, C. Fludger, D. van den Borne, E. Schmidt, B. Spinnler, H. de Waardt, and B. Lankl, “Optical performance monitoring from FIR filter coefficients in coherent receivers,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OThW2.
- M. Kuschnerov, F. N. Hauske, K. Piyawanno, B. Spinnler, A. Napoli, and B. Lankl, “Adaptive chromatic dispersion equalization for non-dispersion managed coherent systems,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper OMT1.
- F. N. Hauske, C. Xie, Z. P. Zhang, C. Li, L. Li, and Q. Xiong, “Frequency domain chromatic dispersion estimation,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper JThA11.
- D. Wang, C. Lu, A.P.T Lau, and S. He, “Adaptive chromatic dispersion compensation for coherent communication systems using delay-tap sampling technique,” IEEE Photon. Technol. Lett.14, 1016–1018 (2011). [CrossRef]
- B. Spinnler, “Equalizer design and complexity for digital coherent receivers,” IEEE J. Sel. Topics Quantum Electron.5, 1180–1192 (2010). [CrossRef]
- M. Kuschnerov, F. N. Hauske, K. Piyawanno, B. Spinnler, M.S. Alfiad, A. Napoli, and B. Lankl, “DSP for coherent single-carrier receivers,” J. Lightwave Technol.27, 3614–3622 (2009). [CrossRef]
- S. Haykin, Adaptive filter theory (Prentice-Hall, 2002).

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