Abstract

We present some analytical methods for Gaussian optical receivers whose impulse responses of optical and electrical filters are Gaussian. We obtain the Gaussian optical receiver's eigenmodes exactly in frequency domain. Their eigenfunctions are Hermite functions multiplied by a common phase factor. Using these eigenmodes, we investigate the probability distribution functions of the electrical filter's output before the decision circuit. We derive a bit-error rate (BER) expression in a closed form using the lowest-order eigenmode. It is valid when the optical filter bandwidth is comparable to the modulation bandwidth as in conventional high capacity optical wavelength-division multiplexing transmission systems. The BER expression can be applied also to non-Gaussian optical receivers.

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  1. Kikuchi, Optical Fiber Telecommunications, V B: Systems and Networks (Academic, 2008).
  2. Y. Tang, W. Shieh, "Coherent optical OFDM transmission up to 1 Tb/s per channel," J. Lightw. Technol. 27, 3511-3517 (2009).
  3. X. Liu, T. H. Wood, R. W. Tkach, S. Chandrasekhar, "Demonstration of record sensitivities in optically preamplified receivers by combining PDM-QPSK and $M$ -ary pulse-position modulation," J. Lightw. Technol. 30, 406-413 (2012).
  4. D. Marcuse, "Derivation of analytical expressions for the bit-error probability in Lightw. systems with optical amplifiers," J. Lightw. Technol. 8, 1816-1823 (1990).
  5. P. A. Humblet, M. Azizoglu, "On the bit error rate of lightwave systems with optical amplifiers," J. Lightw. Technol. 9, 1576-1582 (1991).
  6. G. Einarsson, Principles of Lightwave Communications (Wiley, 1996).
  7. P. J. Winzer, "Receiver noise modeling in presence of optical amplification," Proc. OAA '01 (2001).
  8. Y. Cai, J. M. Morris, T. Adali, C. R. Menyuk, "On turbo code decoder performance in optical-fiber communication systems with dominating ASE noise," J. Lightw. Technol. 21, 727-734 (2003).
  9. M. R. Hueda, D. E. Crivelli, H. S. Carrer, "Performance of MLSE-based receivers in lightwave systems with nonlinear dispersion and amplified spontaneous emission noise," Proc. IEEE GLOBECOM (2004) pp. 299-303.
  10. T. Foggi, E. Forestieri, G. Colavolpe, G. Prati, "Maximum-likelihood sequence detection with closed-form metrics in OOK optical systems impaired by GVD and PMD," J. Lightw. Technol. 24, 3073-3087 (2006).
  11. G. Bosco, P. Poggiolini, M. Visintin, "Performance analysis of MLSE receivers based on the square-root metric," J. Lightw. Technol. 26, 2098-2109 (2008).
  12. M. Rubsamen, P. J. Winzer, R.-J. Essiambre, "MLSE receivers for narrowband optical filtering," Opt. Fiber Commun. Conf. (OFC) AnaheimCA (2006) Session OWB6.
  13. J. D. Downie, J. Hurley, M. Sauer, S. Lobanov, S. Raghavan, "Experimental measurements of the effectiveness of MLSE against narrowband optical filtering distortion," Opt. Fiber Commun. Conf. (OFC/NFOEC) AnaheimCA (2007) Session OMG4.
  14. M. Rubsamen, J. M. Gené, P. J. Winzer, R.-J. Essiambre, "ISI mitigation capability of MLSE direct-detection receivers," IEEE Photon. Technol. Lett. 20, 656-658 (2008).
  15. I. T. Monroy, G. Einarsson, "Bit error evaluation of optically preamplified direct detection receivers with Fabry–Perot optical filters," J. Lightw. Technol. 15, 1546-1553 (1997).
  16. S. R. Chinn, "Error-rate performance of optical amplifiers with Fabry–Perot filters," Electron. Lett. 31, 756-757 (1995).
  17. M. Kac, A. J. F. Siegert, "On the theory of noise in radio receivers with square law detectors," J. Appl. Phys. 18, 383-397 (1947).
  18. J. S. Lee, C. S. Shim, "Bit-error-rate analysis of optically preamplified receivers using an eigenfunction expansion method in optical frequency domain," J. Lightw. Technol. 12, 1224-1229 (1994).
  19. E. Forestieri, M. Secondini, "On the error probability evaluation in lightwave systems with optical amplification," J. Lightw. Technol. 27, 706-717 (2009).
  20. R. Holzlohner, V. S. Grigoryan, C. R. Menyuk, W. L. Kath, "Accurate calculation of eye diagrams and bit error rates in optical transmission systems using linearization," J. Lightw. Technol. 20, 389-400 (2002).
  21. A. Demir, "Nonlinear phase noise in optical-fiber-communication systems," J. Lightw. Technol. 25, 2002-2032 (2007).
  22. P. J. Winzer, R. J. Essiambre, J. Broamge, "Combined impact of double-Rayleigh backscatter and amplified spontaneous emission on receiver noise," Proc. Opt. Fiber Commun. Conf. (OFC) (2002).
  23. J. Bromage, P. J. Winzer, R.-J. Essiambre, Raman Amplifiers and Oscillators in Telecommunications (Springer-Verlag, 2003).
  24. J. S. Lee, "Signal-to-noise ratio of spectrum-sliced incoherent light sources including optical modulation effects," J. Lightw. Technol. 14, 2197-2201 (1996).
  25. G. N. Watson, "Notes on generating functions. II. Hermite polynomials," J. London Math. Soc. 8, 194-199 (1933).
  26. G. Arfken, H. Weber, Mathematical Methods for Physicists (Elsevier, 2005).
  27. S. D. Personick, "Receiver design for digital fiber optic communications systems, I," Bell Syst. Tech. J. 52, 843-874 (1973).
  28. N. S. Bergano, F. W. Kerfoot, C. R. Davidson, "Margin measurements in optical amplifier systems," IEEE Photon. Technol. Lett. 5, 304-306 (1993).
  29. B. Chan, J. Conradi, "On the non-Gaussian noise in Erbium-doped fiber amplifiers," J. Lightw.. Technol. 15, 680-687 (1997).
  30. P. J. Winzer, M. Pfennigbauer, M. M. Strasser, W. R. Leeb, "Optimum filter bandwidths for optically preamplified NRZ and RZ receivers," J. Lightw. Technol. 19, 1263-1273 (2001).

2012

X. Liu, T. H. Wood, R. W. Tkach, S. Chandrasekhar, "Demonstration of record sensitivities in optically preamplified receivers by combining PDM-QPSK and $M$ -ary pulse-position modulation," J. Lightw. Technol. 30, 406-413 (2012).

2009

Y. Tang, W. Shieh, "Coherent optical OFDM transmission up to 1 Tb/s per channel," J. Lightw. Technol. 27, 3511-3517 (2009).

E. Forestieri, M. Secondini, "On the error probability evaluation in lightwave systems with optical amplification," J. Lightw. Technol. 27, 706-717 (2009).

2008

G. Bosco, P. Poggiolini, M. Visintin, "Performance analysis of MLSE receivers based on the square-root metric," J. Lightw. Technol. 26, 2098-2109 (2008).

M. Rubsamen, J. M. Gené, P. J. Winzer, R.-J. Essiambre, "ISI mitigation capability of MLSE direct-detection receivers," IEEE Photon. Technol. Lett. 20, 656-658 (2008).

2007

A. Demir, "Nonlinear phase noise in optical-fiber-communication systems," J. Lightw. Technol. 25, 2002-2032 (2007).

2006

T. Foggi, E. Forestieri, G. Colavolpe, G. Prati, "Maximum-likelihood sequence detection with closed-form metrics in OOK optical systems impaired by GVD and PMD," J. Lightw. Technol. 24, 3073-3087 (2006).

2003

Y. Cai, J. M. Morris, T. Adali, C. R. Menyuk, "On turbo code decoder performance in optical-fiber communication systems with dominating ASE noise," J. Lightw. Technol. 21, 727-734 (2003).

2002

R. Holzlohner, V. S. Grigoryan, C. R. Menyuk, W. L. Kath, "Accurate calculation of eye diagrams and bit error rates in optical transmission systems using linearization," J. Lightw. Technol. 20, 389-400 (2002).

2001

P. J. Winzer, M. Pfennigbauer, M. M. Strasser, W. R. Leeb, "Optimum filter bandwidths for optically preamplified NRZ and RZ receivers," J. Lightw. Technol. 19, 1263-1273 (2001).

1997

B. Chan, J. Conradi, "On the non-Gaussian noise in Erbium-doped fiber amplifiers," J. Lightw.. Technol. 15, 680-687 (1997).

I. T. Monroy, G. Einarsson, "Bit error evaluation of optically preamplified direct detection receivers with Fabry–Perot optical filters," J. Lightw. Technol. 15, 1546-1553 (1997).

1996

J. S. Lee, "Signal-to-noise ratio of spectrum-sliced incoherent light sources including optical modulation effects," J. Lightw. Technol. 14, 2197-2201 (1996).

1995

S. R. Chinn, "Error-rate performance of optical amplifiers with Fabry–Perot filters," Electron. Lett. 31, 756-757 (1995).

1994

J. S. Lee, C. S. Shim, "Bit-error-rate analysis of optically preamplified receivers using an eigenfunction expansion method in optical frequency domain," J. Lightw. Technol. 12, 1224-1229 (1994).

1993

N. S. Bergano, F. W. Kerfoot, C. R. Davidson, "Margin measurements in optical amplifier systems," IEEE Photon. Technol. Lett. 5, 304-306 (1993).

1991

P. A. Humblet, M. Azizoglu, "On the bit error rate of lightwave systems with optical amplifiers," J. Lightw. Technol. 9, 1576-1582 (1991).

1990

D. Marcuse, "Derivation of analytical expressions for the bit-error probability in Lightw. systems with optical amplifiers," J. Lightw. Technol. 8, 1816-1823 (1990).

1973

S. D. Personick, "Receiver design for digital fiber optic communications systems, I," Bell Syst. Tech. J. 52, 843-874 (1973).

1947

M. Kac, A. J. F. Siegert, "On the theory of noise in radio receivers with square law detectors," J. Appl. Phys. 18, 383-397 (1947).

1933

G. N. Watson, "Notes on generating functions. II. Hermite polynomials," J. London Math. Soc. 8, 194-199 (1933).

Bell Syst. Tech. J.

S. D. Personick, "Receiver design for digital fiber optic communications systems, I," Bell Syst. Tech. J. 52, 843-874 (1973).

Electron. Lett.

S. R. Chinn, "Error-rate performance of optical amplifiers with Fabry–Perot filters," Electron. Lett. 31, 756-757 (1995).

IEEE Photon. Technol. Lett.

M. Rubsamen, J. M. Gené, P. J. Winzer, R.-J. Essiambre, "ISI mitigation capability of MLSE direct-detection receivers," IEEE Photon. Technol. Lett. 20, 656-658 (2008).

IEEE Photon. Technol. Lett.

N. S. Bergano, F. W. Kerfoot, C. R. Davidson, "Margin measurements in optical amplifier systems," IEEE Photon. Technol. Lett. 5, 304-306 (1993).

J. Lightw. Technol.

P. J. Winzer, M. Pfennigbauer, M. M. Strasser, W. R. Leeb, "Optimum filter bandwidths for optically preamplified NRZ and RZ receivers," J. Lightw. Technol. 19, 1263-1273 (2001).

G. Bosco, P. Poggiolini, M. Visintin, "Performance analysis of MLSE receivers based on the square-root metric," J. Lightw. Technol. 26, 2098-2109 (2008).

E. Forestieri, M. Secondini, "On the error probability evaluation in lightwave systems with optical amplification," J. Lightw. Technol. 27, 706-717 (2009).

J. Appl. Phys.

M. Kac, A. J. F. Siegert, "On the theory of noise in radio receivers with square law detectors," J. Appl. Phys. 18, 383-397 (1947).

J. Lightw. Technol.

P. A. Humblet, M. Azizoglu, "On the bit error rate of lightwave systems with optical amplifiers," J. Lightw. Technol. 9, 1576-1582 (1991).

Y. Cai, J. M. Morris, T. Adali, C. R. Menyuk, "On turbo code decoder performance in optical-fiber communication systems with dominating ASE noise," J. Lightw. Technol. 21, 727-734 (2003).

J. Lightw. Technol.

T. Foggi, E. Forestieri, G. Colavolpe, G. Prati, "Maximum-likelihood sequence detection with closed-form metrics in OOK optical systems impaired by GVD and PMD," J. Lightw. Technol. 24, 3073-3087 (2006).

Y. Tang, W. Shieh, "Coherent optical OFDM transmission up to 1 Tb/s per channel," J. Lightw. Technol. 27, 3511-3517 (2009).

X. Liu, T. H. Wood, R. W. Tkach, S. Chandrasekhar, "Demonstration of record sensitivities in optically preamplified receivers by combining PDM-QPSK and $M$ -ary pulse-position modulation," J. Lightw. Technol. 30, 406-413 (2012).

D. Marcuse, "Derivation of analytical expressions for the bit-error probability in Lightw. systems with optical amplifiers," J. Lightw. Technol. 8, 1816-1823 (1990).

R. Holzlohner, V. S. Grigoryan, C. R. Menyuk, W. L. Kath, "Accurate calculation of eye diagrams and bit error rates in optical transmission systems using linearization," J. Lightw. Technol. 20, 389-400 (2002).

A. Demir, "Nonlinear phase noise in optical-fiber-communication systems," J. Lightw. Technol. 25, 2002-2032 (2007).

I. T. Monroy, G. Einarsson, "Bit error evaluation of optically preamplified direct detection receivers with Fabry–Perot optical filters," J. Lightw. Technol. 15, 1546-1553 (1997).

J. S. Lee, C. S. Shim, "Bit-error-rate analysis of optically preamplified receivers using an eigenfunction expansion method in optical frequency domain," J. Lightw. Technol. 12, 1224-1229 (1994).

J. S. Lee, "Signal-to-noise ratio of spectrum-sliced incoherent light sources including optical modulation effects," J. Lightw. Technol. 14, 2197-2201 (1996).

J. Lightw.. Technol.

B. Chan, J. Conradi, "On the non-Gaussian noise in Erbium-doped fiber amplifiers," J. Lightw.. Technol. 15, 680-687 (1997).

J. London Math. Soc.

G. N. Watson, "Notes on generating functions. II. Hermite polynomials," J. London Math. Soc. 8, 194-199 (1933).

Other

G. Arfken, H. Weber, Mathematical Methods for Physicists (Elsevier, 2005).

M. Rubsamen, P. J. Winzer, R.-J. Essiambre, "MLSE receivers for narrowband optical filtering," Opt. Fiber Commun. Conf. (OFC) AnaheimCA (2006) Session OWB6.

J. D. Downie, J. Hurley, M. Sauer, S. Lobanov, S. Raghavan, "Experimental measurements of the effectiveness of MLSE against narrowband optical filtering distortion," Opt. Fiber Commun. Conf. (OFC/NFOEC) AnaheimCA (2007) Session OMG4.

P. J. Winzer, R. J. Essiambre, J. Broamge, "Combined impact of double-Rayleigh backscatter and amplified spontaneous emission on receiver noise," Proc. Opt. Fiber Commun. Conf. (OFC) (2002).

J. Bromage, P. J. Winzer, R.-J. Essiambre, Raman Amplifiers and Oscillators in Telecommunications (Springer-Verlag, 2003).

G. Einarsson, Principles of Lightwave Communications (Wiley, 1996).

P. J. Winzer, "Receiver noise modeling in presence of optical amplification," Proc. OAA '01 (2001).

Kikuchi, Optical Fiber Telecommunications, V B: Systems and Networks (Academic, 2008).

M. R. Hueda, D. E. Crivelli, H. S. Carrer, "Performance of MLSE-based receivers in lightwave systems with nonlinear dispersion and amplified spontaneous emission noise," Proc. IEEE GLOBECOM (2004) pp. 299-303.

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