A Novel Method with Martingale Theory for Phase Noise Analysis in Coherent Optical Communication

Chengle Sui, Qiangmin Wang, Shilin Xiao, Pingqing Li

School of Information Security Engineering Shanghai Jiao Tong University, Shanghai, China.
State Key Lab of Advanced Optical Communication System and Networks, Shanghai Jiao Tong University, Shanghai, China.

DOI: 10.4236/opj.2013.32B041                

Abstract

Phase noise has a great influence on the performance of coherent optical communication. In this paper, martingale theory is introduced to analyze the phase noise effect for the first time as far as we know. Through Fubini’s Theory and martingale representation theory, we proved that , which denotes the phase noise effect, is a predictable martingale. Then Ito’s formula for solution to stochastic differential equation is utilized for the analysis of phase noise effect. Using our method, a nonrecursive formula for the moments of phase noise is derived and signal-noise-ratio (SNR) degradation in coherent optical OFDM due to phase noise is calculated with our method.

Keywords

Martingale; Brownian Motion; Ito Itegral; Derivation of Moments; Phase Noise

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	K. Kikuchi, “Characterization of Semiconductor-Laser Phase Noise and Estimation of Bit-Error Rate Performance with Low-Speed Offline Digital Coherent Receivers,” Optics Express, Vol.20, 2012, pp. 5291-5302. doi:10.1364/OE.20.005291
[2]	S. Jansen, D. van den Borne and M. Kuschnerov, “Advances in Modulation Formats for Fiber-Optic Transmission Systems,” in CLEO:2011 Laser Applications to Photonic Applications, OSA Technical Digest (CD) (Optical Society of America, 2011), paper CWJ1.
[3]	M. Nazarathy, X. Liu, L. Christen, Y. Lize and A. Willner, “Self-Coherent Multisymbol Detection of Optical Differential Phase-Shift Keying,” Journal of Lightwave Technology, Vol. 26, 2008, pp. 1921-1934. doi:10.1109/JLT.2007.912055
[4]	G. L. Pierobon and L. Tomba, “Moment Characterization of Phase Noise in Coherent Optical Systems,” Journal of Lightwave Technology, Vol. 9, No. 8, 1991, pp. 996-1005. doi:10.1109/50.84166
[5]	G. J. Foschini and G. Vannucci, “Characterizing Filtered Light Waves Corrupted by Phase Noise,” IEEE Transactions on Information Theory, Vol. 34, No. 6, 1988, pp. 1437-1448. doi:10.1109/18.21283
[6]	C. P. Kaiser, M. Shafi and P. J. Smith, “Analysis Methods for Optical Heterodyne DPSK Receivers Corrupted by Laser Phase Noise,” Journal of Lightwave Technology, Vol. 11, 1993, pp. 1820-1830. doi:10.1109/50.251180
[7]	Y. Atzmon and M. Nazarathy, “Laser Phase Noise in Coherent and Differential Optical Transmission Revisited in the Polar Domain,” Journal of Lightwave Technology, Vol. 27, 2009, pp. 19-29. doi:10.1109/JLT.2008.925036
[8]	A. Etheridge, “A Course in Financial Calculus,” Cambirdge University Press, Cambridge, 2002. doi:10.1017/CBO9780511810107
[9]	I. T. Monroy and G. Hooghiemstra, “On A Recursive Formula for the Moments of Phase Noise,” IEEE Transactions on Communications, Vol. 48, No. 6, 2000, pp.917-920. doi:10.1109/26.848548
[10]	T. Pollet, M. V. Blade and M. Moeneclaey, “BER Sensitivity of OFDM Systems to Carrier Frequency Offset and Wiener Phase Noise” IEEE Transactions on Communications, Vol. 43, No.2, pp. 191-193,
[11]	L. Tomba, “On the Effect of Wiener Phase Noise in OFDM Systems,” IEEE Transactions on Communications, Vol. 46, No. 5, 1998, pp. 580-583. doi:10.1109/26.668721
[12]	K. L. Chung and R. Williams, “Introduction to Stochastic Integration,” 2nd Edition, Birkhauser Press, Berlin, 1990. doi:10.1007/978-1-4612-4480-6
[13]	D. Revuz and M. Yor, “Continuous Martingales and Brownian Motion,” Springer Press, Berlin, 2004.