## Direct-detection optical differential 8-level phase-shift keying (OD8PSK) for spectrally efficient transmission

Optics Express, Vol. 12, Issue 15, pp. 3415-3421 (2004)

http://dx.doi.org/10.1364/OPEX.12.003415

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### Abstract

An implementation of optical differential 8-level phase-shift keying (OD8PSK) is proposed for spectrally efficient high capacity long-haul optical fiber transmission systems. Interferometric demodulation and direct detection at the receiver yield three output binary sequences identical to the three input binary sequences. This is accomplished by proper design of electrical encoding and optical encoding at the transmitter. Three optical encoding schemes are proposed with corresponding differential electrical encoding schemes. Numerical simulations are performed for a single channel transmission to evaluate the transmission performances of OD8PSK systems.

© 2004 Optical Society of America

## 1. Introduction

2. H. Kim and R.-J. Essiambre, “Transmission of 8×20 Gb/s DQPSK signals over 310-km SMF with 0.8-b/s/Hz spectral efficiency,” IEEE Photon. Technol. Lett. **15**, 769–771 (2003). [CrossRef]

3. P. S. Cho, V. S. Grigoryan, Y. A. Godin, A. Salamon, and Y. Achiam, “Transmission of 25-Gb/s RZ-DQPSK signals with 25-GHz channel spacing over 1000 km of SMF-28 fiber,” IEEE Photon. Technol. Lett. **15**, 473–475 (2003). [CrossRef]

## 2. OD8PSK Transmission System

*π*/4,

*π*/2, 3

*π*/4,

*π*, 5

*π*/4, 3

*π*/2, or 7

*π*/4. Each encoded symbol carries three bits of information and the symbol rate is one third of the total bit rate. A schematic diagram for OD8PSK transmission systems is shown in Fig. 1. It consists of an electrical encoder and an optical encoder at the transmitter, and optical demodulators and balanced detectors at the receiver. The electrical encoder maps three independent data channels,

*a, b*, and,

*c*, into three differentially-encoded data sequences,

*I, Q*, and,

*D*. Gray code is implemented in the electrical encoding schemes so that when a symbol error occurs, it is more likely that only one bit error occurs in one of three output channels [7]. In the optical encoder, the encoded data sequences drive optical modulators to generate differentially-encoded optical signal at a symbol rate equal to the bit rate of each input data channel. After transmission through optical fiber, the differentially encoded optical signal is demodulated optically and the original data,

*a, b*, and,

*c*, are recovered by the receivers with direct detection.

### 2.1 Optical demodulator and receivers

*π*/8, 3

*π*/8, -

*π*/8, or -3

*π*/8 between two arms of the interferometer. A balanced detector is used after each optical demodulator to detect the demodulated signal. The demodulators are arranged so that the original input data are recovered directly from the output signals of the receivers. Two input data channels,

*a*and

*b*, are recovered directly while the third input data channel,

*c*, is recovered from two balanced detectors,

*c*and

_{1}*c*, through an XOR gate, as shown in Fig. 2.

_{2}### 2.2 OD8PSK electrical and optical encoders

*π*/4 is required. In this section, we present three different optical encoding schemes and the corresponding electrical encoders to generate OD8PSK encoded optical signals. An obvious method to encode eight different phases is to use three cascaded optical modulators as shown in Fig. 3(a). The modulator after the source laser is for RZ pulse carving for RZ OD8PSK. Without this modulator, non-return-to-zero (NRZ) OD8PSK can be encoded. The first modulator is a Mach-Zehnder (MZ) modulator biased at transmission null and driven by one (

*I*) of the three encoded outputs of the electrical encoder with a peak-to-peak voltage of 2V

_{π}so that the encoded phase difference is 0 or

*π*. The second and third modulators are optical phase modulators with the encoded phase differences of 0 or

*π*/2 and 0 or

*π*/4, respectively. To exactly recover the three original binary input data sequences with the optical encoding and demodulation schemes defined above, the relationships between the input and output of the electrical encoder are found to be

*I, Q*, and,

*D*are the output bits of the electrical encoder for a given set of input bits,

*a, b*, and

*c*, and

*i, q*, and

*d*are the output bits of the electrical encoder in the previous time slot (i.e.,

*i*=

_{k}*I*

_{k-1},

*q*=

_{k}*Q*

_{k-1}, and

*d*=

_{k}*D*

_{k-1}). These logical relationships have been verified by numerical simulations.

*π*/4 is to use a QPSK modulator consisting of two MZ modulators, and a phase modulator as shown in Fig. 3(b). The QPSK modulator driven by

*I*and

*Q*generates a differential phase between successive bits of 0,

*π*/2,

*π*, or 3

*π*/2 [1]. The phase modulator driven by

*D*provides a phase change of 0 or

*π*/4. The logical equations of the electrical encoder for this optical encoding method are given by

*π*/2 between two arms. The first MZ modulators in the upper and lower arms are biased at V

_{π}/2 and driven by

*D*and

*D̂*, respectively, with a peak-to-peak voltage of V

*/2 so that the peak power ratio between the outputs from the two modulators is sin(*

_{π}*π*/8)/cos(

*π*/8) or cos(

*π*/8)/sin(

*π*/8). The second MZ modulators in the upper and lower arms are biased at transmission null and driven by

*I*and

*Q*, respectively, of three encoded outputs of the electrical encoder with a peak-to-peak voltage of 2V

_{π}. The logical equations of the electrical encoder for this optical encoding method are given by

## 3. Numerical simulations of transmission of RZ OD8PSK encoded signals

8. X. Wei, X. Liu, and C. Xu, “Numerical simulation of the SPM penalty in a 10-Gb/s RZ-DPSK system,” IEEE Photon. Technol. Lett. **15**, 1636–1638 (2003). [CrossRef]

^{-4}) showed that results using these two methods agree very well, corresponding to a difference of less than 0.1 dB in the Q factor. We shall use the differential phase Q factor method for the remainder of this paper. When symbol errors are caused by mistaking symbols for adjacent symbols, each symbol error causes a single bit error in one of the three channels due to Gray code implementation. Since the likelihood that symbols are mistaken for other than adjacent symbols is relatively remote, the bit error ratio (BER) of the system is about one-third of SER.

^{-9}is approximately 800km. We also investigated the effect of laser linewidth in the transmitter on the system performance. Figure 6(b) plots the differential phase Q factor as a function of the laser linewidth after 8 spans of transmission. To limit the degradation of performance to 0.5 dB in differential phase Q factor due to finite laser linewidth, the laser linewidth has to be smaller then 2 MHz.

## 4. Conclusions

^{-9}without post-transmission nonlinear phase compensation.

## Acknowledgments

## References and links

1. | R. A. Griffin and A. C. Carter, “Optical differential quadrature phase-shift key (oDQPSK) for high capacity optical transmission,” in |

2. | H. Kim and R.-J. Essiambre, “Transmission of 8×20 Gb/s DQPSK signals over 310-km SMF with 0.8-b/s/Hz spectral efficiency,” IEEE Photon. Technol. Lett. |

3. | P. S. Cho, V. S. Grigoryan, Y. A. Godin, A. Salamon, and Y. Achiam, “Transmission of 25-Gb/s RZ-DQPSK signals with 25-GHz channel spacing over 1000 km of SMF-28 fiber,” IEEE Photon. Technol. Lett. |

4. | S. Hayase, N. Kikuchi, K. Sekein, and S. Sasaki, “Proposal of 8-state per symbol (binary ASK and QPSK) 30-Gbit/s optical modulation/demodulation scheme,” in |

5. | J. Hansryd, J. van Howe, and C. Xu, “Nonlinear crosstalk and compensation in quaternary differential-phase amplitude-shift-keying transmission,” in |

6. | X. Liu, “Nonlinear effect in phase shift keyed transmission,” in |

7. | B. Sklar, |

8. | X. Wei, X. Liu, and C. Xu, “Numerical simulation of the SPM penalty in a 10-Gb/s RZ-DPSK system,” IEEE Photon. Technol. Lett. |

9. | 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. |

10. | C. Xu and X. Liu, “Postnonlinearity compensation with data-driven phase modulators in phase-shift keying transmission,” Opt. Lett. |

**OCIS Codes**

(060.0060) Fiber optics and optical communications : Fiber optics and optical communications

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

(060.4080) Fiber optics and optical communications : Modulation

(060.5060) Fiber optics and optical communications : Phase modulation

**ToC Category:**

Research Papers

**History**

Original Manuscript: June 25, 2004

Revised Manuscript: July 12, 2004

Published: July 26, 2004

**Citation**

Cheolhwan Kim and Guifang Li, "Direct-detection optical differential 8-level phase-shift keying (OD8PSK) for spectrally efficient transmission," Opt. Express **12**, 3415-3421 (2004)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-15-3415

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### References

- R. A. Griffin and A. C. Carter, �??Optical differential quadrature phase-shift key (oDQPSK) for high capacity optical transmission,�?? in Optical Fiber Communications Conference (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2002), Paper WX6.
- H. Kim and R.-J. Essiambre, �??Transmission of 8 �? 20 Gb/s DQPSK signals over 310-km SMF with 0.8-b/s/Hz spectral efficiency,�?? IEEE Photon. Technol. Lett. 15, 769-771 (2003). [CrossRef]
- P. S. Cho, V. S. Grigoryan, Y. A. Godin, A. Salamon, and Y. Achiam, �??Transmission of 25-Gb/s RZ-DQPSK signals with 25-GHz channel spacing over 1000 km of SMF-28 fiber,�?? IEEE Photon. Technol. Lett. 15, 473-475 (2003). [CrossRef]
- S. Hayase, N. Kikuchi, K. Sekein, and S. Sasaki, �??Proposal of 8-state per symbol (binary ASK and QPSK) 30-Gbit/s optical modulation/demodulation scheme,�?? in European Conference on Optical Communication (The Institute of Electrical Engineers, London, United Kingdom, 2003), Paper TH2.6.4.
- J. Hansryd, J. van Howe, and C. Xu, �??Nonlinear crosstalk and compensation in quaternary differential-phase amplitude-shift-keying transmission,�?? in Optical Fiber Communications Conference (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2004), Paper MF64.
- X. Liu, �??Nonlinear effect in phase shift keyed transmission,�?? in Optical Fiber Communications Conference (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 2004), Paper ThM4.
- B. Sklar, Digital Communications: Fundamentals and Applications (Prentice Hall PTR, Upper Saddle River, 2001).
- X. Wei, X. Liu, and C. Xu, �??Numerical simulation of the SPM penalty in a 10-Gb/s RZ-DPSK system,�?? IEEE Photon. Technol. Lett. 15, 1636-1638 (2003). [CrossRef]
- 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. 15, 1616-1618 (2004).
- C. Xu and X. Liu, �??Postnonlinearity compensation with data-driven phase modulators in phase-shift keying transmission,�?? Opt. Lett. 15, 1619-1621 (2004).

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