## Adaptive frequency-domain equalization in digital coherent optical receivers |

Optics Express, Vol. 19, Issue 13, pp. 12789-12798 (2011)

http://dx.doi.org/10.1364/OE.19.012789

Acrobat PDF (1082 KB)

### Abstract

We propose a novel frequency-domain adaptive equalizer in digital coherent optical receivers, which can reduce computational complexity of the conventional time-domain adaptive equalizer based on finite-impulse-response (FIR) filters. The proposed equalizer can operate on the input sequence sampled by free-running analog-to-digital converters (ADCs) at the rate of two samples per symbol; therefore, the arbitrary initial sampling phase of ADCs can be adjusted so that the best symbol-spaced sequence is produced. The equalizer can also be configured in the butterfly structure, which enables demultiplexing of polarization tributaries apart from equalization of linear transmission impairments. The performance of the proposed equalization scheme is verified by 40-Gbits/s dual-polarization quadrature phase-shift keying (QPSK) transmission experiments.

© 2011 OSA

## 1. Introduction

1. K. Kikuchi, “Phase-diversity homodyne detection of multilevel optical modulation with digital carrier phase estimation,” IEEE J. Sel. Top. Quantum Electron. **12**(4), 563–570 (2006). [CrossRef]

3. C. R. S. Fludger, T. Duthel, D. van den Borne, C. Schulien, E.-D. Schmidt, T. Wuth, J. Geyer, E. De Man, Khoe Giok-Djan, and H. de Waardt, “Coherent equalization and POLMUX-RZ-DQPSK for robust 100-GE transmission,” J. Lightwave Technol. **26**(1), 64–72 (2008). [CrossRef]

4. S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express **16**(2), 804–817 (2008). [CrossRef] [PubMed]

*i.e.*, twofold oversampling). Such oversampling significantly reduces the aliasing effect. Next, we use time-domain finite-impulse-response (FIR) filters in the butterfly structure, where filter-tap weights are adapted every two samples through the constant-modulus algorithm (CMA). With such a time-domain equalizer (TDE), we can achieve the following three functions simultaneously: (1) Linear impairments stemming from GVD and tight optical/electrical filtering are adaptively equalized. (2) We can demultiplex polarization tributaries and compensate for PMD. (3) The initial sampling phase, which has been decided by free-running ADC, is adjusted optimally during the filter-tap adaptation process, as far as clock frequencies are synchronized between the transmitter and the receiver. This is because the sampled waveform is continuously time-shifted so that sampling instance for the symbol-spaced sequence comes to the best positions in symbol duration. Such function is essentially clock recovery, and details of clock-recovery characteristics by adaptive FIR filters can be found in [5

5. K. Kikuchi, “Clock recovering characteristics of adaptive finite-impulse-response filters in digital coherent optical receivers,” Opt. Express **19**(6), 5611–5619 (2011). [CrossRef] [PubMed]

6. K. Roberts, M. O’Sullivan, Kuang-Tsan Wu, A. Han Sun, D. J. Awadalla, Krause, and C. Laperle, “Performance of dual-polarization QPSK for optical transport system,” J. Lightwave Technol. **27**(16), 3546–3559 (2009). [CrossRef]

7. B. Spinnler, “Equalizer design and complexity for digital coherent receivers,” IEEE J. Sel. Top. Quantum Electron. **16**(5), 1180–1192 (2010). [CrossRef]

**O**

_{L}is a column vector with

*L*zeros; superscripts (

**•**)

*and (*

^{e}**•**)

*correspond to even and odd sub-equalizer parameters, respectively; and conj(*

^{o}**•**) is the conjugate operator.

## 2. Proposal of a novel frequency-domain equalizer

### 2.1 Equivalence of the half-symbol-spaced FIR filter with even and odd sub-equalizers

*x*and

*y*ports, whereas their output ports as

*X*and

*Y*ports. The symbol duration is

*T,*the delay spacing is

*T*/2, and the delay-tap length of each filter is

*N.*When

*n*-th input sequences for

*x*and

*y*ports, respectively, which are twofold oversampled, the output from the

*X*port can be expressed as

*m*such that

*m*= 0, 1, 2, ···); and then, the down-sampled output from the

*X*port can be written as

*N*is even so that

*T*/2. Thus, Eq. (2) can be rewritten asand similarly, the output from the

*Y*port can be written aswhere

*p*and

*q*are either

*x*or

*y*. Thus, we may split the equalizer into even and odd sub-equalizers with tap coefficients taken from even and odd filter-tap indices. Correspondingly, the input sequences for the sub-equalizers are taken from even and odd samples of twofold-oversampled sequences. Eventually, instead of updating tap coefficients of conventional

*T*/2-spaced FIR filters every two samples, we can use even and odd sub-equalizers, where tap updating is done every symbol without down-sampling output sequences.

15. J. J. Shynk, “Frequency-domain and multirate adaptive filtering,” IEEE Signal Process. Mag. **9**(1), 14–37 (1992). [CrossRef]

### 2.2 Configuration of the proposed frequency-domain equalizer

*L*. Then,

*L*for the

*k*-th block.

15. J. J. Shynk, “Frequency-domain and multirate adaptive filtering,” IEEE Signal Process. Mag. **9**(1), 14–37 (1992). [CrossRef]

*L*samples from the current block and

*L*samples from the previous block and can be written aswhere DFT is performed by fast Fourier transform (FFT). Then,

*L*tap weights of the sub-equalizers are padded with the equal number of zeros and

*2L-*point FFT is executed. Let

*L*is given aswhere

**V**

*(*

_{x}*k*) and

**V**

*(*

_{y}*k*) are given as Eqs. (9) and (10), and the first

*L*elements of IFFT{

*L*is given aswhere the vector

*L*rows and all of its elements are 1. After augmenting

*L*zeros, we convert it to the frequency-domain vector with the column length of

*2L*asApplying the overlap-save method, we calculate the gradient vector

*L*zeros.

## 3. Computational complexity analysis

*T/2*and the tap length is

*N.*To obtain one output symbol from the

*X*port and one output symbol from the

*Y*port of the TDE, we need 8

*N*multiplications for output calculations, 4

*N*multiplications for tap updating by CMA, and additional 4 multiplications for error-value calculations. By putting these together, the computational complexity

*C*

_{TDE}of the adaptive TDE can be expressed aswhere

*M*is the number of constellation points on the signal constellation.

*N*/2 output symbols from the

*X*port and

*N*/2 output symbols from the

*Y*port through processing of one block in our proposed FDE, we need

*4N*multiplications for output calculations of one block,

*4N*multiplications for tap updating by CMA,

*2N*multiplications for error-value calculations, and

*N*complex numbers [7

7. B. Spinnler, “Equalizer design and complexity for digital coherent receivers,” IEEE J. Sel. Top. Quantum Electron. **16**(5), 1180–1192 (2010). [CrossRef]

*C*

_{FDE}of the proposed FDE can be expressed as

*M*= 4). From Table 1, it is clear that the proposed adaptive FDE provides much lower complexity than the adaptive TDE when

*N*is 16 or more. This benefit enhances significantly with the increased number of

*N*.

## 4. Experimental verification of the principle of operation of our scheme

_{3}optical IQ modulator (IQM) from two streams of precoded data from an arbitrary waveform generator (AWG) with 2

^{9}-1 pseudo-random binary sequences (PRBS). A 40-Gbit/s dual-polarization signal was then produced with a combination of a polarization-beam splitter (PBS), a fiber delay for pattern decorrelation, and a polarization-beam combiner (PBC). PDL was generated by attenuating one polarization component using a variable optical attenuator (VOA). Then, the signal passed through a commercial PMD emulator (PMDE) and a 100-km-long standard single-mode fiber (SMF). In front of the receiver, a VOA was used to control the received average power. After that, the signal was pre-amplified by an erbium-doped fiber amplifier (EDFA) and detected by a phase-and-polarization diversity coherent optical receiver having a local oscillator (LO) whose characteristics are the same as those of the transmitting laser. The frequency mismatch between the transmitting laser and LO was set below 10 MHz. Outputs from the receiver were sampled at 20 Gsample/s with ADCs, and digitized signals

^{5}samples were stored for offline DSP.

*N*= 32 and the block length of each sub-equalizer for the FDE was

*N*/2 = 16. The step-size parameter was 2

^{−10}. Then, the carrier recovery was done by the 4-th power algorithm [18

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

^{5}symbols per polarization.

*T*/2-spaced FIR filters [5

5. K. Kikuchi, “Clock recovering characteristics of adaptive finite-impulse-response filters in digital coherent optical receivers,” Opt. Express **19**(6), 5611–5619 (2011). [CrossRef] [PubMed]

## 5. Conclusion

## Acknowledgments

## References and links

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

2. | K. Kikuchi, “Coherent optical communications: historical perspectives and future directions,” in |

3. | C. R. S. Fludger, T. Duthel, D. van den Borne, C. Schulien, E.-D. Schmidt, T. Wuth, J. Geyer, E. De Man, Khoe Giok-Djan, and H. de Waardt, “Coherent equalization and POLMUX-RZ-DQPSK for robust 100-GE transmission,” J. Lightwave Technol. |

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

5. | K. Kikuchi, “Clock recovering characteristics of adaptive finite-impulse-response filters in digital coherent optical receivers,” Opt. Express |

6. | K. Roberts, M. O’Sullivan, Kuang-Tsan Wu, A. Han Sun, D. J. Awadalla, Krause, and C. Laperle, “Performance of dual-polarization QPSK for optical transport system,” J. Lightwave Technol. |

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

8. | J. Leibrich and W. Rosenkranz, “Frequency domain equalization with minimum complexity in coherent optical transmission systems,” in |

9. | M. Selmi, P. Ciblat, Y. Jaouen, and C. Gosset, “Block versus adaptive MIMO equalization for coherent PolMux QAM transmission system,” in |

10. | J. C. Geyer, C. R. S. Fludger, T. Duthel, C. Schulien, and B. Schmauss, “Efficient frequency domain chromatic dispersion compensation in a coherent polmux QPSK-receiver,” in |

11. | R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, and Y. Miyamoto, “Coherent optical single carrier transmission using overlap frequency domain equalization for long-haul optical systems,” J. Lightwave Technol. |

12. | 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 |

13. | R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, E. Yamada, H. Masuda, and Y. Miyamoto, “PMD compensation in optical coherent single carrier transmission using frequency-domain equalization,” Electron. Lett. |

14. | K. Ishihara, T. Kobayashi, R. Kudo, Y. Takatori, A. Sano, and Y. Miyamoto, “Frequency-domain equalization for coherent optical single-carrier transmission systems,” IEICE Trans. Commun. |

15. | J. J. Shynk, “Frequency-domain and multirate adaptive filtering,” IEEE Signal Process. Mag. |

16. | S. Haykin, |

17. | Md. S. Faruk, Y. Mori, C. Zhang, and K. Kikuchi, “Proper polarization demultiplexing in coherent optical receiver using constant modulus algorithm with training mode,” in |

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

**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: April 11, 2011

Revised Manuscript: May 20, 2011

Manuscript Accepted: June 10, 2011

Published: June 17, 2011

**Citation**

Md. Saifuddin Faruk and Kazuro Kikuchi, "Adaptive frequency-domain equalization in digital coherent optical receivers," Opt. Express **19**, 12789-12798 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-13-12789

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### References

- K. Kikuchi, “Phase-diversity homodyne detection of multilevel optical modulation with digital carrier phase estimation,” IEEE J. Sel. Top. Quantum Electron. 12(4), 563–570 (2006). [CrossRef]
- K. Kikuchi, “Coherent optical communications: historical perspectives and future directions,” in High Spectral Density Optical Communication Technology, M. Nakazawa, K. Kikuchi, and T. Miyazaki, eds (Springer, 2010), Chap. 2.
- C. R. S. Fludger, T. Duthel, D. van den Borne, C. Schulien, E.-D. Schmidt, T. Wuth, J. Geyer, E. De Man, Khoe Giok-Djan, and H. de Waardt, “Coherent equalization and POLMUX-RZ-DQPSK for robust 100-GE transmission,” J. Lightwave Technol. 26(1), 64–72 (2008). [CrossRef]
- S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16(2), 804–817 (2008). [CrossRef] [PubMed]
- K. Kikuchi, “Clock recovering characteristics of adaptive finite-impulse-response filters in digital coherent optical receivers,” Opt. Express 19(6), 5611–5619 (2011). [CrossRef] [PubMed]
- K. Roberts, M. O’Sullivan, Kuang-Tsan Wu, A. Han Sun, D. J. Awadalla, Krause, and C. Laperle, “Performance of dual-polarization QPSK for optical transport system,” J. Lightwave Technol. 27(16), 3546–3559 (2009). [CrossRef]
- B. Spinnler, “Equalizer design and complexity for digital coherent receivers,” IEEE J. Sel. Top. Quantum Electron. 16(5), 1180–1192 (2010). [CrossRef]
- J. Leibrich and W. Rosenkranz, “Frequency domain equalization with minimum complexity in coherent optical transmission systems,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2010), paper OWV1.
- M. Selmi, P. Ciblat, Y. Jaouen, and C. Gosset, “Block versus adaptive MIMO equalization for coherent PolMux QAM transmission system,” in Proceedings of European Conference on Optical Communication (2010), paper Th.9.A.5.
- J. C. Geyer, C. R. S. Fludger, T. Duthel, C. Schulien, and B. Schmauss, “Efficient frequency domain chromatic dispersion compensation in a coherent polmux QPSK-receiver,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2010), paper OWV5.
- R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, and Y. Miyamoto, “Coherent optical single carrier transmission using overlap frequency domain equalization for long-haul optical systems,” J. Lightwave Technol. 27(16), 3721–3728 (2009). [CrossRef]
- 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 (Optical Society of America, 2009), paper OMT1.
- R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, E. Yamada, H. Masuda, and Y. Miyamoto, “PMD compensation in optical coherent single carrier transmission using frequency-domain equalization,” Electron. Lett. 45(2), 124–125 (2009). [CrossRef]
- K. Ishihara, T. Kobayashi, R. Kudo, Y. Takatori, A. Sano, and Y. Miyamoto, “Frequency-domain equalization for coherent optical single-carrier transmission systems,” IEICE Trans. Commun. E92-B(12), 3736–3743 (2009). [CrossRef]
- J. J. Shynk, “Frequency-domain and multirate adaptive filtering,” IEEE Signal Process. Mag. 9(1), 14–37 (1992). [CrossRef]
- S. Haykin, Adaptive Filter Theory, 3rd ed., (Prentice Hall, 2001).
- Md. S. Faruk, Y. Mori, C. Zhang, and K. Kikuchi, “Proper polarization demultiplexing in coherent optical receiver using constant modulus algorithm with training mode,” in Proceedings of Optoelectronics and Communication Conference (2010), paper 9B3–3.
- D.-S. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, “Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation,” J. Lightwave Technol. 24(1), 12–21 (2006). [CrossRef]

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