Abstract

In this paper, we propose new closed-form approximations to the probability-density function (pdf) of the received signal in intensity-modulation/direct-detection (IM/DD) optical channels. These approximations greatly simplify the problem of channel estimation. This is an important problem in the implementation of maximum-likelihood sequence-estimation (MLSE) receivers for electronic dispersion compensation (EDC) of optical fibers, which has been a topic of great interest in recent years. The approximations proposed here are also useful in the analysis of the error rate of these receivers. It is well known that noise in IM/DD optical channels is strongly non-Gaussian and signal dependent. Except in the simplest situations, the pdf of the signal corrupted by noise does not have a closed-form expression. This leads to difficulties in the calculation of the probability of error on these channels and, more importantly, in the implementation of receivers that exploit knowledge of the signal pdf to minimize the error rate, for example, those based on MLSE techniques. To limit the complexity of channel estimation (an important requirement in real-time adaptive EDC receivers), it is important that the functional form assumed for the pdf be as simple as possible, while providing a good match with the actual statistical properties of the channel. In this paper, we introduce a new generic functional form for the pdf that accurately models the behavior of the received signal. Based on this expression, we introduce a channel-estimation approach that dramatically simplifies the analysis and design of MLSE receivers for IM/DD channels. Simulations show an excellent agreement between the results based on the approximations proposed here and the exact expressions for the pdf.

© 2007 IEEE

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2006 (3)

G. Bosco, P. Poggiolini, "Long-distance effectiveness of MLSE IMDD receivers," IEEE Photon. Technol. Lett. 18, 1037-1039 (2006).

T. Freckmann, J. Speidel, "Viterbi equalizer with analytically calculated branch metrics for optical ASK and DBPSK ," IEEE Photon. Technol. Lett. 18, 277-279 (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).

2005 (4)

H. S. Carrer, D. E. Crivelli, M. R. Hueda, "Reduced complexity maximum likelihood sequence estimator for high-speed fiber optic communication systems," Lat. Amer. Appl. Res. 35, 99-104 (2005) http://lcd.efn.uncor.edu.

N. Alić, "Signal statistics and maximum likelihood sequence estimation in intensity modulated fiber optic links containing a single optical preamplifier," Opt. Express 13, 4568-4579 (2005).

T. Nielsen, S. Chandrasekhar, "OFC 2004 workshop on optical and electronic mitigation of impairments," J. Lightw. Technol. 23, 131-142 (2005).

O. E. Agazzi, M. R. Hueda, H. S. Carrer, D. E. Crivelli, "Maximum likelihood sequence estimation in dispersive optical channels," J. Lightw. Technol. 23, 749-763 (2005).

2004 (2)

H. F. Haunstein, W. Sauer-Greff, A. Dittrich, K. Sticht, R. Urbansky, "Principles for electronic equalization for polarization-mode dispersion," J. Lightw. Technol. 22, 1169-1182 (2004).

F. Buchali, H. Bulow, "Adaptive PMD compensation by electrical and optical techniques," J. Lightw. Technol. 22, 1116-1126 (2004).

2003 (2)

A. J. Weiss, "On the performance of electrical equalization in optical fiber transmission systems ," IEEE Photon. Technol. Lett. 15, 1225-1227 (2003).

G. Bosco, G. Montorsi, S. Benedetto, "Soft decoding in optical systems," IEEE Trans. Commun. 51, 1258-1265 (2003).

2000 (2)

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).

A. Kavcic, J. Moura, "The Viterbi algorithm and Markov noise memory," IEEE Trans. Inf. Theory 46, 291-301 (2000).

1996 (1)

B. Widrow, I. Kollár, M. Liu, "Statistical theory of quantization," IEEE Trans. Instrum. Meas. 45, 353-361 (1996).

1995 (1)

W. F. Wong, E. Goto, "Fast evaluation of the elementary functions in single precision," IEEE Trans. Comput. 44, 453-457 (1995).

1991 (1)

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).

1990 (1)

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

IEEE Photon. Technol. Lett. (3)

G. Bosco, P. Poggiolini, "Long-distance effectiveness of MLSE IMDD receivers," IEEE Photon. Technol. Lett. 18, 1037-1039 (2006).

A. J. Weiss, "On the performance of electrical equalization in optical fiber transmission systems ," IEEE Photon. Technol. Lett. 15, 1225-1227 (2003).

T. Freckmann, J. Speidel, "Viterbi equalizer with analytically calculated branch metrics for optical ASK and DBPSK ," IEEE Photon. Technol. Lett. 18, 277-279 (2006).

IEEE Trans. Commun. (1)

G. Bosco, G. Montorsi, S. Benedetto, "Soft decoding in optical systems," IEEE Trans. Commun. 51, 1258-1265 (2003).

IEEE Trans. Comput. (1)

W. F. Wong, E. Goto, "Fast evaluation of the elementary functions in single precision," IEEE Trans. Comput. 44, 453-457 (1995).

IEEE Trans. Inf. Theory (1)

A. Kavcic, J. Moura, "The Viterbi algorithm and Markov noise memory," IEEE Trans. Inf. Theory 46, 291-301 (2000).

IEEE Trans. Instrum. Meas. (1)

B. Widrow, I. Kollár, M. Liu, "Statistical theory of quantization," IEEE Trans. Instrum. Meas. 45, 353-361 (1996).

J. Lightw. Technol. (8)

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

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).

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).

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).

T. Nielsen, S. Chandrasekhar, "OFC 2004 workshop on optical and electronic mitigation of impairments," J. Lightw. Technol. 23, 131-142 (2005).

F. Buchali, H. Bulow, "Adaptive PMD compensation by electrical and optical techniques," J. Lightw. Technol. 22, 1116-1126 (2004).

O. E. Agazzi, M. R. Hueda, H. S. Carrer, D. E. Crivelli, "Maximum likelihood sequence estimation in dispersive optical channels," J. Lightw. Technol. 23, 749-763 (2005).

H. F. Haunstein, W. Sauer-Greff, A. Dittrich, K. Sticht, R. Urbansky, "Principles for electronic equalization for polarization-mode dispersion," J. Lightw. Technol. 22, 1169-1182 (2004).

Lat. Amer. Appl. Res. (1)

H. S. Carrer, D. E. Crivelli, M. R. Hueda, "Reduced complexity maximum likelihood sequence estimator for high-speed fiber optic communication systems," Lat. Amer. Appl. Res. 35, 99-104 (2005) http://lcd.efn.uncor.edu.

Opt. Express (1)

Other (22)

C. Xie, P. P. Mai, F. Hauske, B. Lankl, E. Schmidt, "BER estimation of a MLSE using the union bound," Proc. IEE Semin. Opt. Fibre Commun. and Electron. Signal Process. (2005) pp. 9/1-9/4.

D. E. Crivelli, H. S. Carrer, M. R. Hueda, "On the performance of reduced-state Viterbi receivers in IM/DD optical transmission systems ," Eur. Conf. Optical Commun. StockholmSweden (2004) Paper We4.P.083.

T. M. Cover, J. A. Thomas, Telecommunications (Wiley, 1991).

E. A. Lee, D. G. Messerschmitt, Digital Communications (KAP, 1988).

H. F. Haunstein, K. Sticht, A. Dittrich, W. Sauer-Greff, R. Urbansky, "Design of near optimum electrical equalizers for optical transmission in the presence of PMD ," Proc. OFC (2001) pp. 558-560.

H. Bulow, "Measurement of the maximum speed of PMD fluctuation in installed field fiber," Proc. OFC (1999) pp. 83-85.

MIPS Technologies, Inc. Mountain ViewCA (2006) www.mips.comMountain ViewCA.

S. Benedetto, E. Biglieri, Principles of Digital Transmission (Kluwer, 1999).

D. G. Zill, Calculus with Analytic Geometry (PWS, 1987).

F. Buchali, H. Bulow, "Correlation sensitive Viterbi equalization of 10 Gb/s signals in bandwidth limited receivers ," Proc. OFC (2005).

A. Faerber, "Performance of a 10.7 Gb/s receiver with digital equalizer using maximum likelihood sequence estimation," Eur. Conf. Optical Commun. StockholmSweden (2004) Paper Th4.1.5.

O. E. Agazzi, V. Gopinathan, "The impact of nonlinearity on electronic dispersion compensation of optical channels ," Proc. OFC (2004).

J. Weem, P. Kirkpatrick, J. Verdiell, "Electronic dispersion compensation for 10 gigabit communication links over FDDI legacy multimode fiber," Proc. OFC (2005) pp. 306-308.

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

W. Xi, T. Adali, Y. Cai, "Probability distribution estimation for an integrated coding and equalization scheme in optical communications systems," Proc. IEEE ICASSP (2005) pp. 961-964.

W. Xi, T. Adali, J. Zweck, "Electrical estimation of conditional probability for maximum-likelihood based PMD mitigation [polarization mode dispersion]," Proc. OFC (2005).

J. G. Proakis, Digital Communications (McGraw-Hill, 1995).

M. R. Hueda, D. E. Crivelli, H. S. Carrer, "Analysis of SISO front-end decoders in IM/DD optical channels with application to turbo code decoding," Proc. IEEE ICCS (2004) pp. 552-558.

International Telecommunications Union ITU-T Recommendation G.652Characteristics of Single-Mode Optical Fibre and Cable (2003).

R. Ramaswami, K. Sivarajan, Optical Networks: A Practical Perspective (Morgan Kaufmann, 2002).

W. van Etten, J. van der Plaats, Fundamentals of Optical Fiber Communications (Prentice-Hall, 1991).

A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, 1991).

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