Error probability of DPSK signals with cross-phase modulation induced nonlinear phase noise

The error probability is derived analytically for differential phase-shift keying (DPSK) signals contaminated by both self- and cross-phase modulation (SPM and XPM)-induced nonlinear phase noise. XPM-induced nonlinear phase noise is modeled as Gaussian distributed phase noise. When fiber dispersion is compensated perfectly in each fiber span, XPM-induced nonlinear phase is summed coherently span after span and is the dominant nonlinear phase noise for typical wavelength-division-multiplexed (WDM) DPSK systems. For systems without or with XPM-suppressed dispersion compensation, SPM-induced nonlinear phase noise is usually the dominant nonlinear phase noise. With longer walkoff length, for the same mean nonlinear phase shift, 10-Gb/s systems are more sensitive to XPM-induced nonlinear phase noise than 40-Gb/s systems.

[1]  Keang-Po Ho,et al.  Statistical properties of stimulated Raman crosstalk in WDM systems , 2000, Journal of Lightwave Technology.

[2]  H. Saunders,et al.  Probability, Random Variables and Stochastic Processes (2nd Edition) , 1989 .

[3]  B. Lankl,et al.  High spectral efficiency 1.6-b/s/Hz transmission (8 x 40 Gb/s with a 25-GHz grid) over 200-km SSMF using RZ-DQPSK and polarization multiplexing , 2003, IEEE Photonics Technology Letters.

[4]  N. Kagi,et al.  Cross-phase modulation in dispersive fibers: theoretical and experimental investigation of the impact of modulation frequency , 1994, IEEE Photonics Technology Letters.

[5]  Keang-Po Ho,et al.  Asymptotic probability density of nonlinear phase noise. , 2003, Optics letters.

[6]  Keang-Po Ho,et al.  Compensation improvement of DPSK signal with nonlinear phase noise , 2003 .

[7]  Keang-Po Ho,et al.  Electronic compensation technique to mitigate nonlinear phase noise , 2004, Journal of Lightwave Technology.

[8]  A.H. Gnauck,et al.  6.4-Tb/s (160/spl times/42.7 Gb/s) transmission with 0.8 bit/s/Hz spectral efficiency over 32/spl times/100 km of fiber using CSRZ-DPSK format , 2003, OFC 2003 Optical Fiber Communications Conference, 2003..

[9]  Xiang Liu,et al.  Postnonlinearity compensation with data-driven phase modulators in phase-shift keying transmission. , 2002, Optics letters.

[10]  G. Jacobsen,et al.  Theory for optical heterodyne DPSK receivers with post-detection filtering , 1987 .

[11]  Analysis and measurement of root-mean-squared bandwidth of cross-phase-modulation-induced spectral broadening , 1999, IEEE Photonics Technology Letters.

[12]  Hoon Kim.  Cross-phase-modulation-induced nonlinear phase noise in WDM direct-detection DPSK systems , 2003 .

[13]  Leonid G. Kazovsky,et al.  Cross-phase modulation in fiber links with multiple optical amplifiers and dispersion compensators , 1996 .

[14]  R.M. Jopson,et al.  Resonances in cross-phase modulation impairment in wavelength-division-multiplexed lightwave transmission , 1999, IEEE Photonics Technology Letters.

[15]  Robert A. Griffin,et al.  10 Gb/s optical differential quadrature phase shift key (DQPSK) transmission using GaAs/AlGaAs integration , 2002, Optical Fiber Communication Conference and Exhibit.

[16]  I. S. Gradshteyn,et al.  Table of Integrals, Series, and Products , 1976 .

[17]  Robert A. Griffin,et al.  Optical differential quadrature phase-shift key (oDQPSK) for high capacity optical transmission , 2002, Optical Fiber Communication Conference and Exhibit.

[18]  Keang-Po Ho.  Compensation improvement of DPSK signal with nonlinear phase noise , 2003, IEEE Photonics Technology Letters.

[19]  S. Bigo,et al.  10 x 10 Gb/s cross-phase modulation suppressor for multispan transmissions using WDM narrow-band fiber Bragg gratings , 2000, IEEE Photonics Technology Letters.

[20]  F. Forghieri,et al.  Effect of modulation statistics on Raman crosstalk in WDM systems , 1994, IEEE Photonics Technology Letters.

[21]  Hoon Kim,et al.  Transmission of 8 x 20 Gb/s DQPSK signals over 310-km SMF with 0.8-b/s/Hz spectral efficiency , 2003, IEEE Photonics Technology Letters.

[22]  N. Blachman.  The Effect of Phase Error on DPSK Error Probability , 1981, IEEE Trans. Commun..

[23]  Jin-Xing Cai,et al.  A DWDM demonstration of 3.73 Tb/s over 11,000 km using 373 RZ-DPSK channels at 10 Gb/s , 2003, OFC 2003 Optical Fiber Communications Conference, 2003..

[24]  J. Gordon,et al.  Phase noise in photonic communications systems using linear amplifiers. , 1990, Optics letters.

[25]  Takashi Mizuochi,et al.  A comparative study of DPSK and OOK WDM transmission over transoceanic distances and their performance degradations due to nonlinear phase noise , 2003 .

[26]  S. Ryu,et al.  Signal linewidth broadening due to nonlinear Kerr effect in long-haul coherent systems using cascaded optical amplifiers , 1992 .

[27]  Pravin C. Jain,et al.  Error probabilities in binary angle modulation , 1974, IEEE Trans. Inf. Theory.

[28]  G. Raybon,et al.  25 x 40-Gb/s copolarized DPSK transmission over 12 x 100-km NZDF with 50-GHz channel spacing , 2003, IEEE Photonics Technology Letters.

[29]  S. Norimatsu,et al.  The influence of cross-phase modulation on optical FDM PSK homodyne transmission systems , 1993 .

[30]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

[31]  Keang-Po Ho,et al.  Probability density of nonlinear phase noise , 2003 .

[32]  F. Forghieri,et al.  Chapter 8 – Fiber Nonlinearities and Their Impact on Transmission Systems , 1997 .

[33]  Hoon Kim,et al.  Degradations in balanced DPSK receivers , 2003, IEEE Photonics Technology Letters.

[34]  A. Mecozzi.  Limits to long-haul coherent transmission set by the Kerr nonlinearity and noise of the in-line amplifiers , 1994 .

[35]  Y. Akasaka,et al.  DWDM 40G transmission over trans-pacific distance (10 000 km) using CSRZ-DPSK, enhanced FEC, and all-Raman-amplified 100-km UltraWave fiber spans , 2004, Journal of Lightwave Technology.

[36]  G. Raybon,et al.  2.5 Tb/s (64/spl times/42.7 Gb/s) transmission over 40/spl times/100 km NZDSF using RZ-DPSK format and all-Raman-amplified spans , 2002, Optical Fiber Communication Conference and Exhibit.

[37]  G. Nicholson.  Probability of error for optical heterodyne DPSK system with quantum phase noise , 1984 .

[38]  Hoon Kim,et al.  Experimental investigation of the performance limitation of DPSK systems due to nonlinear phase noise , 2003, IEEE Photonics Technology Letters.

[39]  Xiang Liu,et al.  Comparison of return-to-zero differential phase-shift keying and ON-OFF keying in long-haul dispersion managed transmission , 2003, IEEE Photonics Technology Letters.

[40]  Mamoru Aiki,et al.  System performance of coherent transmission over cascaded in-line fiber amplifiers , 1993 .

[41]  Y. Achiam,et al.  Transmission of 25-Gb/s RZ-DQPSK signals with 25-GHz channel spacing over 1000 km of SMF-28 fiber , 2003, IEEE Photonics Technology Letters.

[42]  R. Slusher,et al.  Improving transmission performance in differential phase-shift-keyed systems by use of lumped nonlinear phase-shift compensation. , 2002, Optics letters.

[43]  C. Wree,et al.  CF-RZ-DPSK for suppression of XPM on dispersion-managed long-haul optical WDM transmission on standard single-mode fiber , 2002, IEEE Photonics Technology Letters.

[44]  S. Bigo,et al.  Cross-phase modulation suppressor for multispan dispersion-managed WDM transmissions , 2000, IEEE Photonics Technology Letters.

[45]  K. Petermann,et al.  Small signal analysis for dispersive optical fiber communication systems , 1992 .

[46]  Peter J. Winzer,et al.  Robustness to laser frequency offset in direct-detection DPSK and DQPSK systems , 2003 .

[47]  Keang-Po Ho.  The effect of interferometer phase error on direct-detection DPSK and DQPSK signals , 2004, IEEE Photonics Technology Letters.

[48]  M. O. Pedersen,et al.  6.4-Tb/s (160×42.7 Gb/s) transmission with 0.8 bit/s/Hz spectral efficiency over 32×100 km of fiber using CSRZ-DPSK format , 2003, OFC 2003.

[49]  Keang-Po Ho,et al.  Performance degradation of phase-modulated systems due to nonlinear phase noise , 2003 .