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Journal of Lightwave Technology

Journal of Lightwave Technology


  • Vol. 26, Iss. 22 — Nov. 15, 2008
  • pp: 3677–3693

Optically Amplified Direct Detection With Pre- and Postfiltering: A Volterra Series Approach

Moshe Nazarathy, Betty Livshitz, Yuval Atzmon, Marco Secondini, and Enrico Forestieri

Journal of Lightwave Technology, Vol. 26, Issue 22, pp. 3677-3693 (2008)

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We present yet another quasi-analytic model for an optically amplified receiver, comprising an optical preamplifier, an optical prefilter, a photodetector, and an electrical postfilter. Due to the square-law nonlinearity and its interaction with the linear pre- and postfilters, the understanding of this seemingly simple structure has been elusive, gradually evolving over a succession of studies, culminating in the models by Lee and Shim and Forestieri. Here we adopt a new approach to this old problem, applying Volterra nonlinear theory to obtain fresh insight deriving a simplified model streamlining the pseudoanalytic simulations. Volterra series is a powerful mathematical tool for simulating nonlinear systems, applied here to quadratic optical detection in an unconventional way, by deriving a mixed frequency-time representation, leading to a simple and compact quadratic form in the combined signal-plus-noise signal spectra, albeit not computationally efficient. Next, Forestieri's results, which used distinct bases for the signal and noise, are rederived using the insightful Volterra formalism. Finally, we reformulate the model using an expansion of both signal and noise in a common harmonic basis over a sliding window of duration equal to the ISI system memory. This final version of the optically amplified receiver model is most computationally efficient, provides the most compact description, and lends itself to intuitive interpretation. Applications of the new method include accurate determination of the bit error ratio of amplitude-shift keying, frequency-shift keying, and differential phase-shift keying transmission systems in the linear optical link propagation regime, including the effects of dispersion and fully accounting for intersymbol interference. The theory developed here is naturally extensible to advanced optical equalization techniques, involving Volterra nonlinear optoelectronic equalizers.

© 2008 IEEE

Moshe Nazarathy, Betty Livshitz, Yuval Atzmon, Marco Secondini, and Enrico Forestieri, "Optically Amplified Direct Detection With Pre- and Postfiltering: A Volterra Series Approach," J. Lightwave Technol. 26, 3677-3693 (2008)

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  1. M. Shetzen, The Volterra and Wiener Theories of Nonlinear Systems (Krieger, 1980).
  2. W. J. Ruch, Nonlinear System Theory: The Volterra/Wiener Approach (Johns Hopkins Univ. Press, 1981).
  3. T. K. Biswas, W. F. McGee, "Volterra series analysis of semiconductor laser diode," IEEE Photon. Technol. Lett. 3, 706-708 (1991).
  4. L. Hassine, Z. Toffano, F. Lamnabhi-Lagarrigue, A. Destrez, I. Joindot, "Volterra functional series expansions for noise in semiconductor lasers," IEEE J. Quantum Electron. 30, 2534-2546 (1994).
  5. J. C. Froidure, C. Lebrun, P. Megret, E. Jaunart, P. Goerg, T. Tasia, M. Lamquin, M. Blondel, "Theoretical and experimental study of second-order distortions in CATV DFB laser diodes," IEEE Photon. Technol. Lett. 7, 266-268 (1995).
  6. L. Agarossi, S. Bellini, F. Bregoli, P. Migliorati, "Equalization of non-linear optical channels," Proc. ICC '98 (1998) pp. 662-667.
  7. X. Chunmin, R. Werner, "Nonlinear electrical equalization for different modulation formats with optical filtering," J. Lightw. Technol. 25, 996-1001 (2007).
  8. K. V. Peddanarappagari, M. Brandt-Pearce, "Volterra series transfer function of single-mode fibers," J. Lightw. Technol. 15, 2232-2241 (1997).
  9. P. S. Henry, "Error-rate performance of optical amplifiers," Tech. Dig. OFC'89 (1989).
  10. N. A. Olsson, "Lightwave systems with optical amplifiers," J. Lightw. Technol. 7, 1071-1082 (1989).
  11. D. Marcuse, "Derivation of analytical expressions for the bit-error probability in lightwave systems with optical amplifiers," J. Lightw. Technol. 8, 1816-1823 (1990).
  12. O. K. Tonguz, L. G. Kazovsky, "Theory of direct-detection lightwave receivers using optical amplifiers," J. Lightw. Technol. 9, 174-181 (1991).
  13. D. Marcuse, "Calculation of bit-error probability for a lightwave system with optical amplifiers and post-detection Gaussian noise," J. Lightw. Technol. 9, 505-513 (1991).
  14. P. A. Humblet, M. Azizoglu, "On the bit error rate of lightwave systems with optical amplifiers," J. Lightw. Technol. 9, 1576-1582 (1991).
  15. 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).
  16. N. G. Jensen, E. Bodtker, G. Jacobsen, J. Strandberg, "Performance of preamplified direct detection systems under influence of receiver noise," IEEE Photon. Technol. Lett. 6, 1488-1490 (1994).
  17. L. F. B. Ribeiro, J. R. F. Da Rocha, J. L. Pinto, "Performance evaluation of EDFA preamplified receivers taking into account intersymbol interference," J. Lightw. Technol. 13, 225-232 (1995).
  18. S. L. Danielsen, B. Mikkelesen, T. Durhuus, C. Joergensen, K. E. Stubkjaer, "Detailed noise statistics for an optically preamplified direct detection receiver," J. Lightw. Technol. 13, 977-981 (1995).
  19. C. Lawetz, J. C. Cartledge, "Performance of optically preamplified receivers with Fabry-Perot optical filters," J. Lightw. Technol. 14, 2467-2474 (1996).
  20. 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).
  21. E. Forestieri, "Evaluating the error probability in lightwave systems with chromatic dispersion, arbitrary pulse shape and pre- and postdetection filtering," J. Lightw. Technol. 18, 1493-1503 (2000).
  22. P. J. Winzer, K. Hoon, "Degradations in balanced DPSK receivers," IEEE Photon. Technol. Lett. 15, 1282-1284 (2003).
  23. W. Jin, J. M. Kahn, "Conventional DPSK versus symmetrical DPSK: Comparison of dispersion tolerances," IEEE Photon. Technol. Lett. 16, 1585-1587 (2004).
  24. M. Nazarathy, W. V. Sorin, D. M. Baney, S. A. Newton, "Spectral analysis of optical mixing measurements," J. Lightw. Technol. 7, 1083-1096 (1989).
  25. C. W. Helstrom, "Distribution of the filtered output of a quadratic rectifier computed by numerical contour integration," IEEE Trans. Inf. Theory IT-32, 450-463 (1986).
  26. F. Yuan, A. Opal, "Distortion analysis of periodically switched nonlinear circuits using time-varying Volterra series," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 48, 726-738 (2001).
  27. T. Ching-Hsiang, "A mixed-domain method for identification of quadratically nonlinear systems," IEEE Trans. Signal Process. 45, 1013-1024 (1997).
  28. W. B. Davenport, W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, 1958).
  29. M. Nazarathy, "Accurate evaluation of bit error rates of optical communication systems using the Gram-Charlier series," IEEE Trans. Commun. 54, 295-301 (2006).
  30. S. Blinnikov, G. Moessner, "Expansions for nearly Gaussian distributions," Astron. Astrophys. Suppl. Ser. 193-205 (1998).
  31. R. Holzlohner, W. L. Kath, C. R. Menyuk, V. S. Grigoryan, "Efficient and accurate computation of eye diagrams and bit-error rates in a single-channel CRZ system," IEEE Photon. Technol. Lett. 14, 1079-1081 (2002).
  32. J. Wang, J. M. Kahn, "Impact of chromatic and polarization-mode dispersion on DPSK systems using interferometric demodulation and direct detection," J. Lightw. Technol 22, 362-371 (2004).
  33. M. K. Ng, Iterative Methods for Toeplitz Systems (Oxford Science, 2004).
  34. E. Forestieri, M. Secondini, "On the error probability evaluation in lightwave systems with optical amplification," J. Lightw. Technol. .

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