## MAP detection for impairment compensation in coherent WDM systems

Optics Express, Vol. 17, Issue 16, pp. 13395-13401 (2009)

http://dx.doi.org/10.1364/OE.17.013395

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### Abstract

We propose a novel recursive-algorithm based maximum a posteriori probability (MAP) detector in spectrally-efficient coherent wavelength division multiplexing (CoWDM) systems, and investigate its performance in a 1-bit/s/Hz on-off keyed (OOK) system limited by optical-signal-to-noise ratio. The proposed method decodes each sub-channel using the signal levels not only of the particular sub-channel but also of its adjacent sub-channels, and therefore can effectively compensate deterministic inter-sub-channel crosstalk as well as inter-symbol interference arising from narrow-band filtering and chromatic dispersion (CD). Numerical simulation of a five-channel OOK-based CoWDM system with 10Gbit/s per channel using either direct or coherent detection shows that the MAP decoder can eliminate the need for phase control of each optical carrier (which is necessarily required in a conventional CoWDM system), and greatly relaxes the spectral design of the demultiplexing filter at the receiver. It also significantly improves back-to-back sensitivity and CD tolerance of the system.

© 2009 OSA

## 1. Introduction

1. W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express **16**(2), 841–859 (2008). [CrossRef] [PubMed]

4. F. C. G. Gunning, T. Healy, and A. D. Ellis, “Dispersion tolerance of coherent WDM,” IEEE Photon. Technol. Lett. **18**(12), 1338–1340 (2006). [CrossRef]

1. W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express **16**(2), 841–859 (2008). [CrossRef] [PubMed]

4. F. C. G. Gunning, T. Healy, and A. D. Ellis, “Dispersion tolerance of coherent WDM,” IEEE Photon. Technol. Lett. **18**(12), 1338–1340 (2006). [CrossRef]

4. F. C. G. Gunning, T. Healy, and A. D. Ellis, “Dispersion tolerance of coherent WDM,” IEEE Photon. Technol. Lett. **18**(12), 1338–1340 (2006). [CrossRef]

## 2. Principle and simulation model

*a*

_{i,k},

*b*

_{i,k}, and

*r*

_{i,k}as the

*k*

^{th}logical data, estimated data, and received signal amplitude for channel

*i*respectively, a posteriori probability can be mathematically written as:

*R*

_{i,k}={

*r*

_{p,q}},

*p*∈{

*i*-1

*i*i+1},

*q*∈{1, …,

*k*+1} represents the received samples, and argmax

*f*represents the value of the argument

*x*for which the expression

*f*attains its maximum value. The memory length used in Eq. (1) is 2 and can be easily extended to larger values at the expense of more computation complexity. Note that Eq. (1) estimates ai,k based on the observation of all previously received signal samples Ri,k, which give more information compared to those used in our previous MAP detector [5]. From Eq. (1), we can derive:

*S*={

_{i,k}*a*

^{p,q}},

*p*∈{

*i*-1

*i i*+1},

*q*∈{1, …,

*k*+ 2} represents the transmitted signal. To establish the recursive algorithm for CoWDM MAP detection, we derive the following equation based on Eq. (2):

*A*

_{i,k}={

*a*

_{p,q}},

*p*∈{

*i*-1

*i i*+1},

*q*∈{

*k k*+1

*k*+2}. The summation of

*P*

_{i,k-1}on the right-hand side of Eq. (4) can be obtained during the estimation of the previous bit

*a*

_{i,k-1}. The joint conditional probability

*P*(

*r*

_{i-1,k}+1,

*r*

_{i,k+1},

*r*

_{i+1,k+1}|

*A*

_{i,k}) is further simplified to the multiplication of individual probabilities which are obtained from a lookup table. The lookup table can be established using non-parametric histogram method. Note that direct detection is assumed in Eq. (4). In coherent detection where both in-phase and quadrature components are available, Eq. (4) is modified to:

*r*and

^{o}_{i,k}*r*are the in-phase and quadrature components of the received signal and assumed to be statistically independent in this paper.

^{q}_{i,k}*N*. Note that the overall complexity of FFT/IFFT in the OFDM technique is also approximately proportional to N. However, the MAP detector performs parallel processing of each sub-channel, whereas OFDM requires joint signal processing of all sub-channels with associated synchronization, serial/parallel conversion etc, so that the total capacity is limited by the speed of the electronic circuitry. Therefore, CoWDM based on MAP processing would be a promising solution for ultra high-capacity spectrally-efficient optical transmission. Also note that joint MLSE, proposed to mitigate impairments for two tributaries of multi-level modulation formats [7,8

8. J. Zhao, L. K. Chen, and C. K. Chan, “Joint maximum likelihood sequence estimation for chromatic dispersion compensation in ASK-DPSK modulation format,” IEEE Photon. Technol. Lett. **19**(1), 73–75 (2007). [CrossRef]

*N*.

^{1/2}. After optical-to-electrical conversion, the signals were electrically amplified, filtered by 7GHz 4th-order Bessel electrical filters (EFs), sampled at one sample per bit, and analogue-to-digital converted with 4-bit resolution.

^{-4}by direct error counting. The normalized OSNR was defined by:

## 3. Results and discussions

*ϕ*=

*π*/2 and

*π*respectively, assuming that at the transmitter, the five channels have fixed relative phases of (0

*ϕ*0

*ϕ*0). It can be clearly seen from the figure that the detected signal was degraded by residual inter sub-channel crosstalk from imperfect system response at 10GHz sub-channel spacing, and its performance depended on the phases of adjacent channels. Therefore, in practice, it is essential to optimize the phases to minimize the residual crosstalk at the eye center (sampling point) [3,4

**18**(12), 1338–1340 (2006). [CrossRef]

*±*π/2 [3]. This result was further verified by the dotted lines in Fig. 4, which shows the required normalized OSNR versus phase

*ϕ*for Ch 1–3 (Ch 1: circles; Ch 2: triangles; Ch 3: squares) when the relative phases of the channels are: (a) (0

*ϕ*0

*ϕ*0); (b) (0

*ϕ*2

*ϕ*3

*ϕ*4

*ϕ*). Dotted, dashed, and solid lines represent the cases using conventional hard-decision, DD-based MAP, and coherent-detection based MAP respectively. The 3dB bandwidth of the AWG was 12.8GHz. As expected, the performance variations of Ch 4 and 5 were approximately the same as those of Ch 2 and 1, and were neglected in the figures. Figure 4 shows that when using hard decision, the performance was optimal when the phase difference between adjacent channels was

*±*π/2 where the crosstalk was outside the eye as shown in Fig. 3(b). When the crosstalk was at the center of the eye (Fig. 3(c)), an additional 3~4dB OSNR penalty was induced. However, for a static interference pattern of arbitrary phase, MAP detection canceled the inter sub-channel crosstalk. Consequently, the required OSNR was significantly reduced, and the fluctuations as a function of the phase were less than 0.8dB. Coherent-detection based MAP detector, compared to that using DD, exhibited an additional 0.5~1dB performance improvement by using the recovered phase information.

9. A. D. Ellis and F. C. G. Gunning, “Spectral density enhancement using coherent WDM,” IEEE Photon. Technol. Lett. **17**(2), 504–506 (2005). [CrossRef]

*π*/2

*π*3π/2 2

*π*). It can be seen that a CoWDM system using hard decision was particularly sensitive to narrow-band filtering, with 4~10dB OSNR penalty for a 3dB bandwidth of 10GHz. The MAP detector greatly reduced such sensitivity, and the OSNR penalty caused by narrow-band filtering was limited to less than 1.5dB for a filter bandwidth as small as 8GHz. We attribute this benefit to the inherent ISI mitigation capability of MAP detection. Consequently, the design of AWG was greatly relaxed.

*π*/2

*π*3

*π*/2 2

*π*) for all data in the figure. The AWGs had 3dB bandwidth of 12.8GHz. From the figure, it is seen that by using hard decision, Ch 2 and Ch 3 exhibited poorer back-to-back sensitivity and less CD tolerance than Ch 1 due to larger inter sub-channel interference. At an OSNR of 15dB, the transmission distance was limited to between 40 and 60km (Ch 3 and Ch 1, respectively). By using DD-based MAP, knowledge of the adjacent sub-channels allowed for the compensation of deterministic inter sub-channel crosstalk, which led to 1.5~2.5dB back-to-back sensitivity improvement and a significant enhancement of the CD tolerance to give an optically-uncompensated transmission distance exceeding 125km at 15dB OSNR for all sub-channels. Such performance was further improved using coherent-detection based MAP making use of the recovered phase information, with an additional 0.6dB back-to-back sensitivity improvement and transmission reach extended to 300km at 15dB OSNR. Note that in the presence of CD, optimal performance using hard-decision CoWDM should be obtained by adjusting sub-channel phase relationship for each transmission distance [4

**18**(12), 1338–1340 (2006). [CrossRef]

## 4. Conclusions

## Acknowledgements:

## References and links

1. | W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express |

2. | A. Lowery and J. Armstrong, “Adaptation of orthogonal frequency division multiplexing to compensate impairments in optical transmission systems,” European Conference on Optical Communication, paper 4.2.1 (2008). |

3. | F. C. G. Gunning, T. Healy, X. Yang, and A. D. Ellis, “0.6Tbit/s capacity and 2bit/s/Hz spectral efficiency at 42.6Gsymbol/s using a single DFB laser with NRZ coherent WDM and polarization multiplexing,” European Conference on Lasers and Electro-Optics (E-CLEO), paper C18-5-FRI (2007). |

4. | F. C. G. Gunning, T. Healy, and A. D. Ellis, “Dispersion tolerance of coherent WDM,” IEEE Photon. Technol. Lett. |

5. | J. Zhao and A. D. Ellis, “Performance improvement using a novel MAP detector in coherent WDM systems,” European Conference on Optical Communication (2008), paper Tu.1.D.2. |

6. | J. Proakis, |

7. | M. Cavallari, C. R. S. Fludger, and P. J. Anslow, “Electronic signal processing for differential phase modulation formats,” in Proc. Optical Fiber Communication Conference (2004), paper TuG2. |

8. | J. Zhao, L. K. Chen, and C. K. Chan, “Joint maximum likelihood sequence estimation for chromatic dispersion compensation in ASK-DPSK modulation format,” IEEE Photon. Technol. Lett. |

9. | A. D. Ellis and F. C. G. Gunning, “Spectral density enhancement using coherent WDM,” IEEE Photon. Technol. Lett. |

**OCIS Codes**

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

(060.4080) Fiber optics and optical communications : Modulation

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: March 6, 2009

Revised Manuscript: May 27, 2009

Manuscript Accepted: June 2, 2009

Published: July 20, 2009

**Citation**

J. Zhao and A. D. Ellis, "MAP detection for impairment compensation in coherent WDM systems," Opt. Express **17**, 13395-13401 (2009)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-16-13395

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### References

- W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express 16(2), 841–859 (2008). [CrossRef] [PubMed]
- A. Lowery, and J. Armstrong, “Adaptation of orthogonal frequency division multiplexing to compensate impairments in optical transmission systems,” European Conference on Optical Communication, paper 4.2.1 (2008).
- F. C. G. Gunning, T. Healy, X. Yang, and A. D. Ellis, “0.6Tbit/s capacity and 2bit/s/Hz spectral efficiency at 42.6Gsymbol/s using a single DFB laser with NRZ coherent WDM and polarization multiplexing,” European Conference on Lasers and Electro-Optics (E-CLEO), paper C18–5-FRI (2007).
- F. C. G. Gunning, T. Healy, and A. D. Ellis, “Dispersion tolerance of coherent WDM,” IEEE Photon. Technol. Lett. 18(12), 1338–1340 (2006). [CrossRef]
- J. Zhao, and A. D. Ellis, “Performance improvement using a novel MAP detector in coherent WDM systems,” European Conference on Optical Communication (2008), paper Tu.1.D.2.
- J. Proakis, Digital Communication, 4th Edition, McGraw-Hill, 2001.
- M. Cavallari, C. R. S. Fludger, and P. J. Anslow, “Electronic signal processing for differential phase modulation formats,” in Proc. Optical Fiber Communication Conference (2004), paper TuG2.
- J. Zhao, L. K. Chen, and C. K. Chan, “Joint maximum likelihood sequence estimation for chromatic dispersion compensation in ASK-DPSK modulation format,” IEEE Photon. Technol. Lett. 19(1), 73–75 (2007). [CrossRef]
- A. D. Ellis and F. C. G. Gunning, “Spectral density enhancement using coherent WDM,” IEEE Photon. Technol. Lett. 17(2), 504–506 (2005). [CrossRef]

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