## Electronic post-compensation of WDM transmission impairments using coherent detection and digital signal processing

Optics Express, Vol. 16, Issue 2, pp. 880-888 (2008)

http://dx.doi.org/10.1364/OE.16.000880

Acrobat PDF (208 KB)

### Abstract

A universal post-compensation scheme for fiber impairments in wavelength-division multiplexing (WDM) systems is proposed based on coherent detection and digital signal processing (DSP). Transmission of 10×10 Gbit/s binary-phase-shift-keying (BPSK) signals at a channel spacing of 20 GHz over 800 km dispersion shifted fiber (DSF) has been demonstrated numerically.

© 2008 Optical Society of America

## 1. Introduction

1. A. M. Vengsarkar and W. A. Reed, “Dispersion-compensating single mode fiber: Efficient designs for first- and second-order compensation,” Opt. Lett. **18**, 924–926 (1993). [CrossRef] [PubMed]

2. C. Kurtzke, “Suppression of fiber nonlinearities by appropriate dispersion management,” IEEE Photon. Technol. Lett. **5**, 1250–1253 (1993). [CrossRef]

4. X. Liu, X. Wei, R. E. Slusher, and C. J. Mckinstrie, “Improving transmission performance in differential phase-shift-keyed systems by use of lumped nonlinear phase-shift compensation,” Opt. Lett. **27**, 1616–1618 (2002). [CrossRef]

5. S. Watanabe and M. Shirasaki, “Exact compensation for both chromatic dispersion and Kerr effect in a transmission fiber using optical phase conjugation,” IEEE J. Lightwave Technol. **14**, 243–248 (1996). [CrossRef]

6. R. I. Killey, P. M. Watts, V. Mikhailov, M. Glick, and P. Bayvel, “Electronic dispersion compensation by signal predistortion using digital processing and a dual-drive Mach-Zehnder modulator,” IEEE Photon. Technol. Lett. **17**, 714–716 (2005). [CrossRef]

10. 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]

11. K. Kikuchi “Phase-diversity homodyne detection of multilevel optical modulation with digital carrier phase estimation”, IEEE J. Sel. Topics Quantum Electron.12, 563–570 (2006). [CrossRef]

## 2. Post-compensation based on backward propagation

*C*) and post-compensation of fiber impairments. The schematic of the transmission system is shown in Fig. 1 where post-compensation is performed in the digital domain after coherent detection. The WDM signals are transmitted over multiple amplified fiber spans. After transmission, the received signals are mixed in a 90° optical hybrid with a set of local oscillators (LOs), of which

*C*LOs are aligned at the center of the WDM channels. Additional LOs on the both sides are aligned with other FWM components outside the WDM signal. The in-phase and quadrature components of each WDM channel are obtained by balanced photodetectors. Analog-to-digital (A/D) conversion is followed by DSP to achieve post-compensation and data recovery.

*G*is the optical gain of the linear optical amplifiers in the fiber link,

*A*′(

*t*) and

*A*(

*t*) are the electric fields of the received signal and the compensated signal, respectively. The nonlinear Schrödinger equation (

*NLSE*) governing the backward propagation in each span can be written in the form

*N̂*

^{-1}and

*D̂*

^{-1}are inverse nonlinear and differential operators, respectively, and given by [12]:

*γ*′,

*β*′

_{2},

*β*′

_{3}and

*α*′ are fiber nonlinear, first- and second-order chromatic dispersion, and loss coefficient. When these parameters are chosen to be exactly the negative of the values for transmission fiber, nonlinearity and dispersion could be compensated through backward propagation. The

*NLSE*is most commonly solved using the split-step Fourier method. In this approach, each span of fiber is divided into

*N*sections and

*N̂*

^{-1}and

*D̂*

^{-1}are implemented iteratively. To facilitate real-time implementation, the dispersion or differential operator (

*D̂*

^{-1}) can be realized using a finite impulse response (FIR) filter instead of Fourier transform, which has been shown to achieve acceptable accuracy [13

13. X. Li, X. Chen, and M. Qasmi, “A broad-band digital filtering approach for time-domain simulation of pulse propagation in optical fiber,” IEEE J. Lightwave Technol. **23**, 864–875 (2005). [CrossRef]

## 3. DSP implementation for backward propagation

### 3.1 Signal up-sampling

*F*, a set of

_{s}*N*coherent receivers may cover a total bandwidth of

_{c}*N*·

_{c}*F*. Up-sampling to a bandwidth of

_{s}*M*·

*F*(

_{s}*M*is an integer and

*M*>

*N*) can be achieved in the digital domain using the following generalized formula:

_{c}*s*is the sample at time

_{i, k}*t*=

*k*/

*F*of the

_{s}*i*th frequency band and

*k*(

*n*)=⌊

*n*/

*M*⌋·

*M*/

*F*, where ⌊

_{s}*x*⌋ stands for the nearest integer smaller than or equal to

*x*. The above formula effectively zero-pads the spectrum to obtain up-sampling. Note that each re-sampled data point is calculated independently, making this spectral stitching technique highly compatible with parallel implementation. If the DSP speed is 10 GHz, 32 streams of 10 Gsa/s are required to cover the 320 GHz total spectrum. Recall that sampling is at 20 GHz so two identical sets of resampling modules, operating independently, should be used for up-sampling. To align the outputs from the two up-sampling modules, the output from the first module may be delayed by 50 ps.

### 3.2 Parallel implementation for backward propagation

*N*=

_{s}*L*×

*N*is the total step number in the backward propagation. We assume the processing rate of DSP is

*R*. In our simulation,

_{P}*R*is assumed to be 10 GHz, same as the symbol rate. However, the processing rate can be reduced using time-division DEMUX technique, which requires more processing units but helps the real-time operation at a lower rate [14].

_{P}*N*sampling points are generated in parallel and output simultaneously in

_{b}*N*branches every period

_{b}*T*, where

*N*=

_{b}*M*·

*F*/

_{s}*R*is the number of parallel processing branches, and

_{P}*T*=1/

*R*is the clock cycle in each branch. One-symbol delay latches for some branches are used to obtain additional outputs for the parallel implementation of the following FIR filter. The number of additional outputs is

_{P}*N*-1, where

_{t}*N*is the FIR filter length or tap number.

_{t}*A*is the

_{k,i}*k*th sampling point in the

*i*th symbol and is processed in the

*k*th branch. Sampled data from all the branches are then sent into a number of cascaded modules to realize backward propagation using the split-step FIR method [13

13. X. Li, X. Chen, and M. Qasmi, “A broad-band digital filtering approach for time-domain simulation of pulse propagation in optical fiber,” IEEE J. Lightwave Technol. **23**, 864–875 (2005). [CrossRef]

*N*sub-units to perform backward propagation for each branch respectively.

_{b}*M*is the sub-unit in the

_{k}*k*th branch of each step.

*A*(

_{k,i}*n*) is the output of the

*k*th branch in the

*n*th step and

*i*is the symbol index.

*a*, where

_{i}*i*∊0..

*N*-1. We renamed the inputs and outputs from Fig. 3 to simplify the illustrations. The sub-unit is designed according to the symmetric split-step scheme with two iterations when solving the

_{t}*NLSE*[12]

*N̂*

^{-1}(

*z*+

*h*) by

*N̂*

^{-1}(

*z*), then use (3) to estimate

*A*(

*z*+

*h*,

*T*) which in turn is used to calculate the new value of

*N̂*

^{-1}(

*z*+

*h*). As shown in Fig. 4, three FIR filters are used for dispersion and loss compensation and two inverse nonlinear operators for nonlinearity compensation in a sub-unit. The

*inverse nonlinear operator*1 performs exp{

*hN̂*

^{-1}(

*z*)/2} and the

*inverse nonlinear operator*2 performs exp{

*h*(

*N̂*

^{-1}(

*z*)+

*N̂*

^{-1}(

*z*+

*h*))/2}.

*Y*

_{k, i}is the output of the first stage and

*Z*is the output of the second stage. The FIR filter is implemented in a parallel configuration, which has multiple inputs instead of one input combined with a series of delay latches. Therefore, each unit operates at a speed of

_{k, i}*R*although the overall bandwidth is

_{P}*N*·

_{b}*R*[7

_{P}7. S. L. Woodward, S. Huang, M.D. Feuer, and M. Boroditsky, “Demonstration of an electronic dispersion compensation in a 100-km 10-Gb/s ring network,” IEEE Photon. Technol. Lett. **15**, 867–869 (2003). [CrossRef]

*N*-1 sub-units (from the (

_{t}*N*-

_{b}*N*+2)th to the (

_{t}*N*)th) has two outputs to the next step, while the other sub-units only have one output. The additional outputs in the

_{b}*N*-1 sub-unit are required for the inputs of the FIR filters in the next step. Also, additional interfaces with adjacent branches are needed in these

_{t}*N*-1 sub-units. All the additional outputs and modules required in some sub-units are indicated by the dashed lines in Fig. 3. Since each module processes only signals that are already available, the scheme can be carried out in real time.

_{t}*MAC*) units is

*MAC*s is calculated as follows. Each FIR filter requires 4×

*N*multiplications and 4×

_{t}*N*-2 summations;

_{t}*inverse nonlinear operator*1 requires 7 multiplications and 3 summations;

*inverse nonlinear operator*2 requires 9 multiplications and 5 summations. The latency of the backward propagation scheme is

*x*⌉ stands for the nearest integer greater than or equal to

*x*. A look-up table is used for the calculation of

*e*. The latency is calculated as follows. It is assumed that the look-up table requires one clock cycle (

^{jx}*T*) and each multiplication or summation requires half of clock cycle (

*T*/2). Each FIR filter requires (⌈log

_{2}

*N*⌉+2)×(

_{t}*T*/2);

*inverse nonlinear operator*1 and

*inverse nonlinear operator*2 require 7×(

*T*/2) and 8×(

*T*/2), respectively.

## 4. Simulation results

*F*=20 GHz,

_{s}*N*=12,

_{c}*M*=16,

*N*=32 and

_{b}*T*=100 ps.

^{th}WDM channel is shown in Fig.5 a). The rails on eyes are from linear crosstalk due to small channel spacing. Fig.5 b) and c) show the eye diagrams of the received signals after 500 km transmission over DSF without and with ENLC, respectively. The

*Q*-factor of the eye diagram in Fig. 5 b) is about 6. It is clearly seen that the eye diagram in Fig.5 c) are more open because of nonlinearity compensation. Fig.5 d) shows the eye diagram (

*Q*≈6) after 800 km transmission over DSF with ENLC. Fig.6 shows the dependence of the

*Q*-factor of the 5

^{th}WDM channel on the average launching power. After transmission of 500 km DSF the optimum launching power is increased from -11 dBm to -9 dBm due to nonlinearity compensation. When the launching power is more than -9 dBm, the performance of ENLC is limited by the nondeterministic effect, which is introduced by the amplified spontaneous emitted (ASE) noise from the optical amplifiers along the fiber chain. After transmission of 800 km and with ENLC, the

*Q*-factor is similar to that after 500 km transmission but without ENLC. This implies that the transmission distance with digital nonlinearity compensation is increased by 60%. It is noted that the degradation of the

*Q*-factor in long-haul transmission is also from the numerical errors in the backward propagation calculations. The system performance could be further improved by optimizing the FIR filter used for dispersion compensation.

## 5. Discussion and conclusions

^{6}

*MACs*and 0.78 µs, respectively. The average number of

*MACs*required for each channel is 5.184×10

^{5}. It should be noted that this overall computation and latency is realized using fixed step size. It is expected that employing variable step size [15

15. O. V. Sinkin, R. Holzlöhner, J. Zweck, and C. R. Menyuk, “Optimization of the step-size fourier method in modeling optical-fiber communications systems”, IEEE J. Lightwave Technol.21, 61–68 (2003). [CrossRef]

*MACs*and processing speed per channel to within about one order of magnitude of the state of art field-programmable gate arrays (FPGAs). Block processing of the incoming samples coupled with fast Fourier transform implementation allows dispersion compensation in the frequency domain [16]. This may lead to further decrease in the number of operations and better compensation at longer transmission distances. Furthermore, when high-order modulation formats such as quadrature amplitude modulation (QAM) with multi-bit/symbol spectral efficiency are used, the required

*MACs*per symbol should remain about the same and thus the required

*MACs*per bit should decrease proportionally with spectral efficiency. The channel spacing can be further reduced to be equal to the symbol rate using the orthogonal WDM approach that we have demonstrated recently [17

17. G. Goldfarb, G. Li, and M. G. Taylor, “Orthogonal wavelength-division multiplexing using coherent detection”, submitted to IEEE Photon. Technol. Lett. (2007). [CrossRef]

## References and links

1. | A. M. Vengsarkar and W. A. Reed, “Dispersion-compensating single mode fiber: Efficient designs for first- and second-order compensation,” Opt. Lett. |

2. | C. Kurtzke, “Suppression of fiber nonlinearities by appropriate dispersion management,” IEEE Photon. Technol. Lett. |

3. | K. Nakajima, M. Ohashi, T. Horiguchi, K. Kurokawa, and Y. Miyajha, “Design of dispersion managed fiber and its FWM suppression performance,” in |

4. | X. Liu, X. Wei, R. E. Slusher, and C. J. Mckinstrie, “Improving transmission performance in differential phase-shift-keyed systems by use of lumped nonlinear phase-shift compensation,” Opt. Lett. |

5. | S. Watanabe and M. Shirasaki, “Exact compensation for both chromatic dispersion and Kerr effect in a transmission fiber using optical phase conjugation,” IEEE J. Lightwave Technol. |

6. | R. I. Killey, P. M. Watts, V. Mikhailov, M. Glick, and P. Bayvel, “Electronic dispersion compensation by signal predistortion using digital processing and a dual-drive Mach-Zehnder modulator,” IEEE Photon. Technol. Lett. |

7. | S. L. Woodward, S. Huang, M.D. Feuer, and M. Boroditsky, “Demonstration of an electronic dispersion compensation in a 100-km 10-Gb/s ring network,” IEEE Photon. Technol. Lett. |

8. | K. Roberts, C. Li, L. Strawczynski, M. O’Sullivan, and I. Hardcatle, “Electronic precompensation of optical nonlinearity,” IEEE Photon. Technol. Lett. |

9. | E. Yamazaki, F. Inuzuka, K. Yonenaga, A. Takada, and M. Koga, “Compensation of interchannel crosstalk induced by optical fiber nonlinearity in carrier phase-locked WDM system,” IEEE Photon. Technol. Lett. |

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

11. | K. Kikuchi “Phase-diversity homodyne detection of multilevel optical modulation with digital carrier phase estimation”, IEEE J. Sel. Topics Quantum Electron.12, 563–570 (2006). [CrossRef] |

12. | G. P. Agrawal, |

13. | X. Li, X. Chen, and M. Qasmi, “A broad-band digital filtering approach for time-domain simulation of pulse propagation in optical fiber,” IEEE J. Lightwave Technol. |

14. | R. Noé, “Phase noise tolerant synchronous QPSK receiver concept with digital I&Q baseband processing,” in |

15. | O. V. Sinkin, R. Holzlöhner, J. Zweck, and C. R. Menyuk, “Optimization of the step-size fourier method in modeling optical-fiber communications systems”, IEEE J. Lightwave Technol.21, 61–68 (2003). [CrossRef] |

16. | H. Sari, G. Karam, and I. Jeanclaude, “Frequency domain equalization of mobile radio and terrestrial broadcast channels”, in |

17. | G. Goldfarb, G. Li, and M. G. Taylor, “Orthogonal wavelength-division multiplexing using coherent detection”, submitted to IEEE Photon. Technol. Lett. (2007). [CrossRef] |

**OCIS Codes**

(060.1660) Fiber optics and optical communications : Coherent communications

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

**ToC Category:**

Nonlinearity Compensation

**History**

Original Manuscript: September 6, 2007

Revised Manuscript: November 7, 2007

Manuscript Accepted: November 7, 2007

Published: January 9, 2008

**Virtual Issues**

Coherent Optical Communication (2008) *Optics Express*

**Citation**

Xiaoxu Li, Xin Chen, Gilad Goldfarb, Eduardo Mateo, Inwoong Kim, Fatih Yaman, and Guifang Li, "Electronic post-compensation of WDM transmission impairments using coherent detection and digital signal processing," Opt. Express **16**, 880-888 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-2-880

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### References

- A. M. Vengsarkar and W. A. Reed, "Dispersion-compensating single mode fiber: Efficient designs for first- and second-order compensation," Opt. Lett. 18, 924-926 (1993). [CrossRef] [PubMed]
- C. Kurtzke, "Suppression of fiber nonlinearities by appropriate dispersion management," IEEE Photon. Technol. Lett. 5, 1250-1253 (1993). [CrossRef]
- K. Nakajima, M. Ohashi, T. Horiguchi, K. Kurokawa, and Y. Miyajha, "Design of dispersion managed fiber and its FWM suppression performance," in Optical Fiber Communication Conference, Vol. 3 of 1999 OSA Technical Digest Series (Optical Society of America, 1999), paper ThG3.
- X. Liu, X. Wei, R. E. Slusher, and C. J. Mckinstrie, "Improving transmission performance in differential phase-shift-keyed systems by use of lumped nonlinear phase-shift compensation," Opt. Lett. 27, 1616-1618 (2002). [CrossRef]
- S. Watanabe and M. Shirasaki, "Exact compensation for both chromatic dispersion and Kerr effect in a transmission fiber using optical phase conjugation," IEEE J. Lightwave Technol. 14, 243-248 (1996). [CrossRef]
- R. I. Killey, P. M. Watts, V. Mikhailov, M. Glick, and P. Bayvel, "Electronic dispersion compensation by signal predistortion using digital processing and a dual-drive Mach-Zehnder modulator," IEEE Photon. Technol. Lett. 17, 714-716 (2005). [CrossRef]
- S. L. Woodward, S. Huang, M.D. Feuer, and M. Boroditsky, "Demonstration of an electronic dispersion compensation in a 100-km 10-Gb/s ring network," IEEE Photon. Technol. Lett. 15, 867-869 (2003). [CrossRef]
- K. Roberts, C. Li, L. Strawczynski, M. O’Sullivan, and I. Hardcatle, "Electronic precompensation of optical nonlinearity," IEEE Photon. Technol. Lett. 18, 403-405 (2006). [CrossRef]
- E. Yamazaki, F. Inuzuka, K. Yonenaga, A. Takada, and M. Koga, "Compensation of interchannel crosstalk induced by optical fiber nonlinearity in carrier phase-locked WDM system," IEEE Photon. Technol. Lett. 19, 9-11 (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]
- K. Kikuchi "Phase-diversity homodyne detection of multilevel optical modulation with digital carrier phase estimation", IEEE J. Sel. Topics Quantum Electron., 12, 563-570 (2006). [CrossRef]
- G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).
- X. Li, X. Chen, and M. Qasmi, "A broad-band digital filtering approach for time-domain simulation of pulse propagation in optical fiber," IEEE J. Lightwave Technol. 23, 864-875 (2005). [CrossRef]
- R. Noé, "Phase noise tolerant synchronous QPSK receiver concept with digital I&Q baseband processing," in Proceedings of Opto-Electronics and Communications Conf. (2004), pp.818-819.
- O. V. Sinkin, R. Holzlöhner, J. Zweck, and C. R. Menyuk, "Optimization of the step-size fourier method in modeling optical-fiber communications systems", IEEE J. Lightwave Technol. 21, 61-68 (2003). [CrossRef]
- H. Sari, G. Karam, and I. Jeanclaude, "Frequency domain equalization of mobile radio and terrestrial broadcast channels", in Proceedings of IEEE Global Telecomm. Conf., (IEEE,1994), pp.1-5.
- G. Goldfarb, G. Li, M. G. Taylor, "Orthogonal wavelength-division multiplexing using coherent detection", submitted to IEEE Photon. Technol. Lett. (2007). [CrossRef]

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