Abstract

There is a great need for easy-to-fabricate and versatile fiber optic signal processing systems in which optical fibers are used for the delay and storage of wideband guided lightwave signals. We describe the design of the least-mean-square algorithm-based fiber optic adaptive filters for processing guided lightwave signals in real time. Fiber optic adaptive filters can learn to change their parameters or to process a set of characteristics of the input signal. In our realization we employ as few electronic devices as possible and use optical computation to utilize the advantages of optics in the processing speed, parallelism, and interconnection. Many schemes for optical adaptive filtering of electronic signals are available in the literature. The new optical adaptive filters described in this paper are for optical processing of guided lightwave signals, not electronic signals. We analyzed the convergence or learning characteristics of the adaptive filtering process as a function of the filter parameters and the fiber optic hardware errors. From this analysis we found that the effects of the optical round-off errors and noise can be reduced, and the learning speed can be comparatively increased in our design through an optimal selection of the filter parameters. A general knowledge of the fiber optic hardware, the statistics of the lightwave signal, and the desired goal of the adaptive processing are enough for this optimum selection of the parameters. Detailed computer simulations validate the theoretical results of performance optimization.

© 1991 Optical Society of America

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References

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  1. K. Jackson et al., “Optical Fiber Delay-Line Signal Processing,” IEEE Trans. Microwave Theory Tech. MTT-33, 193–210 (1985).
    [CrossRef]
  2. H. Taylor, “Application of Guided-Wave Optics in Signal Processing and Sensing,” Proc. IEEE 75, 1524–1535 (1987).
    [CrossRef]
  3. B. Widrow, S. D. Stearns, Adaptive Signal Processing (Prentice-Hall, Englewood Cliffs, NJ, 1985).
  4. S. T. Alexander, Adaptive Signal Processing (Springer-Verlag, New York, 1986).
    [CrossRef]
  5. B. Widrow, R. Winter, “Neural Nets for Adaptive Filtering and Adaptive Pattern Recognition,” IEEE Comput. Mag. 21, 25–39 (1988).
    [CrossRef]
  6. D. G. Feitelson, Optical Computing (MIT Press, Cambridge, 1988).
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  8. A. Vander Lugt, “Adaptive Optical Processor,” Appl. Opt. 21, 4005–4011 (1982).
    [CrossRef]
  9. W. A. Penn, “Acousto-Optic Signal Canceller,” in ICALEO Conference Proceedings, Vol. 34, Laser and Electro-optics, 9 (Laser Institute of America, 1982).
  10. J. F. Rhodes, “Adaptive Filter with a Time-Domain Implementation Using Correlation Cancellation Loops,” Appl. Opt. 22, 282–287 (1983).
    [CrossRef] [PubMed]
  11. D. Psaltis, J. Hong, “Adaptive Acoustooptic Filter,” Appl. Opt. 23, 3475–3481 (1984).
    [CrossRef] [PubMed]
  12. J. D. Cohen, “Optical Adaptive Linear Predictors,” Appl. Opt. 24, 4247–4259 (1985).
    [CrossRef] [PubMed]
  13. J. N. Lee, A. VanderLugt, “Acoustooptic Signal Processing and Computing,” Proc. IEEE 77, 1528–1557 (1989).
    [CrossRef]
  14. A. M. Bardos, W. R. Beaudet, A. VanderLugt, “Stability Considerations for Adaptive Optical Filtering,” Appl. Opt. 25, 2314–2325 (1986).
    [CrossRef] [PubMed]
  15. P. Paparao, A. Ghosh, “Performance Optimization of Fiber Optic Adaptive Filters,” in Conference Record, 1990 International Topical Meeting on Optical Computing, Kobe, Japan (SPIE, Bellingham, WA, 1990), p. 311.
  16. A. Ghosh, “Design of Fiber Optic Adaptive Filters and Neural Networks,” OSA Annual Meeting, 1989 Technical Digest Series, Vol. 18, (Optical Society of America, Washington, DC, 1989), p. 129.
  17. A. Ghosh, S. Lisle, S. D. Allen, “Guidelines for the Design of Fiber Optic Transversal Filters,” OSA Annual Meeting, 1989 Technical Digest Series, Vol. 18 (Optical Society of America, Washington, DC, 1989), p. 64.
  18. A. Ghosh, S. D. Allen, P. Paparao, “Arithmetic Fourier-Transform Calculation Using Fiber-Optical Parallel Processors,” J. Opt. Soc. Am. A 7, 701–707 (1990).
    [CrossRef]
  19. K. Imen, C. Lee, Y. Y. Yang, S. D. Allen, A. Ghosh, “Laser Fabricated Fiber Optical Taps for Interconnects and Optical Data Processing Devices,” Opt. Lett. 15, 950–952 (1990).
    [CrossRef] [PubMed]
  20. B. Nyman, P. Prucnal, “Passive Waveguide Structures for Integrated Optical Signal Processing,” Opt. Eng. 28, 982–989 (1989).
  21. S. Pappert, “Ultra-Wideband Direction Finding Using a Fiber Optic Beamforming Processor,” Proc. Soc. Photo-Opt. Instrum. Eng. 886, 239–246 (1988); see also D. M. Gookin, M. H. Berry, “Finite Impulse Response Filter with Large Dynamic Range and High Sampling Rate,” Appl. Opt. 29, 1061–1062 (1990).
    [CrossRef] [PubMed]
  22. A. Goutzoulis, D. Davies, “High Speed Programmable Fiber Optic Binary Data Generator,” Opt. Eng. 28, 35–41 (1989).
  23. C. Lee, R. R. Atkins, H. Taylor, “Reflectively Tapped Optical Fiber Transversal Filters,” Electron. Lett. 23, 596–598 (1987).
    [CrossRef]
  24. W. W. Morey, G. Meltz, W. H. Glenn, “Holographically Generated Gratings in Optical Fibers,” Opt. Photon. News 1, No. 7, 14–16 (1990).
    [CrossRef]
  25. D. S. Shenk, L. G. Cohen, “Fiber-Optic Tapping Via Induced Scattering,” IEEE/OSA J. Lightwave Technol. LT-7, 1556–1558 (1989).
    [CrossRef]
  26. D. Du Toit, H. Roberts, “A Single Fiber Linear Bus LAN Topology,” Proc. Soc. Photo-Opt. Instrum. Eng. 991, 170–178 (1988).
  27. W. Beck, “Tapping Hard-Clad Silica Optical Fiber: A New Tool for Short-Haul Systems Designers,” Laser Focus 23, 138–143 (Nov.1987).
  28. D. B. Sarrazin, H. F. Jordan, V. P. Heuring, “Fiber Optic Delay Line Memory,” Appl. Opt. 29, 627–637 (1990).
    [CrossRef] [PubMed]
  29. F. Ito, K. Kitayama, “Optical Implementation of the Hopfield Neural Network Using Multiple Fiber Nets,” Appl. Opt. 28, 4176–4181 (1989).
    [CrossRef] [PubMed]
  30. B. S. Agrawalla, B. T. Dai, S. D. Allen, “Laser Ablative Chemical Etching of SiO2,” J. Vac. Sci. Technol. B 5, 601–605 (1987).
    [CrossRef]
  31. D. Casasent, A. Ghosh, “Direct and Implicit Optical Matrix–Vector Algorithms,” Appl. Opt. 22, 3572–3578 (1983).
    [CrossRef] [PubMed]
  32. C. Caraiscos, B. Liu, “A Roundoff Error Analysis of the LMS Adaptive Algorithm,” IEEE Trans. Acoust. Speech Signal Process. ASSP-32, 34–41 (1984).
    [CrossRef]
  33. D. Casasent, A. Ghosh, “Optical Linear Algebra Processors: Noise and Error-Source Modeling,” Opt. Lett. 10, 252–254 (1985).
    [CrossRef] [PubMed]
  34. M. Tur, B. Moslehi, J. Goodman, “Theory of Laser Phase Noise in Recirculating Fiber Optics Delay Line,” IEEE/OSA J. Lightwave Technol. LT-3, 20–31 (1985).
    [CrossRef]
  35. S. Ardalan, “Floating-Point Error Analysis of Recursive Least Squares and Least-Mean-Squares Adaptive Filters,” IEEE Trans. Circuits Syst. CAS-23, 1192–1208 (1986).
    [CrossRef]
  36. B. Kuo, Automatic Control Systems (Prentice-Hall, Englewood Cliffs, NJ, 1987).
  37. S. S. Narayan, A. M. Peterson, M. J. Narasimha, “Transform Domain LMS Algorithm,” IEEE Trans. Acoust. Speech Signal Process. ASSP-31, 609–615 (1983).
    [CrossRef]
  38. D. F. Marshall, W. K. Jenkins, J. J. Murphy, “The Use of Orthogonal Transforms for Improving Performance of Adaptive Filters,” IEEE Trans. Circuits Syst. 36, 474–483 (1989).
    [CrossRef]
  39. A. Ghosh, P. Paparao, “Performance Analysis of Matrix Preconditioning Algorithms on Parallel Optical Processors,” J. Opt. Soc. Am. A 5, 39–48 (1988).
    [CrossRef]
  40. D. K. Faddeev, V. N. Faddeeva, Computational Methods of Linear Algebra (Freeman, San Francisco, 1963).

1990 (4)

1989 (6)

F. Ito, K. Kitayama, “Optical Implementation of the Hopfield Neural Network Using Multiple Fiber Nets,” Appl. Opt. 28, 4176–4181 (1989).
[CrossRef] [PubMed]

A. Goutzoulis, D. Davies, “High Speed Programmable Fiber Optic Binary Data Generator,” Opt. Eng. 28, 35–41 (1989).

D. F. Marshall, W. K. Jenkins, J. J. Murphy, “The Use of Orthogonal Transforms for Improving Performance of Adaptive Filters,” IEEE Trans. Circuits Syst. 36, 474–483 (1989).
[CrossRef]

D. S. Shenk, L. G. Cohen, “Fiber-Optic Tapping Via Induced Scattering,” IEEE/OSA J. Lightwave Technol. LT-7, 1556–1558 (1989).
[CrossRef]

B. Nyman, P. Prucnal, “Passive Waveguide Structures for Integrated Optical Signal Processing,” Opt. Eng. 28, 982–989 (1989).

J. N. Lee, A. VanderLugt, “Acoustooptic Signal Processing and Computing,” Proc. IEEE 77, 1528–1557 (1989).
[CrossRef]

1988 (4)

B. Widrow, R. Winter, “Neural Nets for Adaptive Filtering and Adaptive Pattern Recognition,” IEEE Comput. Mag. 21, 25–39 (1988).
[CrossRef]

S. Pappert, “Ultra-Wideband Direction Finding Using a Fiber Optic Beamforming Processor,” Proc. Soc. Photo-Opt. Instrum. Eng. 886, 239–246 (1988); see also D. M. Gookin, M. H. Berry, “Finite Impulse Response Filter with Large Dynamic Range and High Sampling Rate,” Appl. Opt. 29, 1061–1062 (1990).
[CrossRef] [PubMed]

D. Du Toit, H. Roberts, “A Single Fiber Linear Bus LAN Topology,” Proc. Soc. Photo-Opt. Instrum. Eng. 991, 170–178 (1988).

A. Ghosh, P. Paparao, “Performance Analysis of Matrix Preconditioning Algorithms on Parallel Optical Processors,” J. Opt. Soc. Am. A 5, 39–48 (1988).
[CrossRef]

1987 (4)

C. Lee, R. R. Atkins, H. Taylor, “Reflectively Tapped Optical Fiber Transversal Filters,” Electron. Lett. 23, 596–598 (1987).
[CrossRef]

B. S. Agrawalla, B. T. Dai, S. D. Allen, “Laser Ablative Chemical Etching of SiO2,” J. Vac. Sci. Technol. B 5, 601–605 (1987).
[CrossRef]

W. Beck, “Tapping Hard-Clad Silica Optical Fiber: A New Tool for Short-Haul Systems Designers,” Laser Focus 23, 138–143 (Nov.1987).

H. Taylor, “Application of Guided-Wave Optics in Signal Processing and Sensing,” Proc. IEEE 75, 1524–1535 (1987).
[CrossRef]

1986 (2)

A. M. Bardos, W. R. Beaudet, A. VanderLugt, “Stability Considerations for Adaptive Optical Filtering,” Appl. Opt. 25, 2314–2325 (1986).
[CrossRef] [PubMed]

S. Ardalan, “Floating-Point Error Analysis of Recursive Least Squares and Least-Mean-Squares Adaptive Filters,” IEEE Trans. Circuits Syst. CAS-23, 1192–1208 (1986).
[CrossRef]

1985 (4)

D. Casasent, A. Ghosh, “Optical Linear Algebra Processors: Noise and Error-Source Modeling,” Opt. Lett. 10, 252–254 (1985).
[CrossRef] [PubMed]

M. Tur, B. Moslehi, J. Goodman, “Theory of Laser Phase Noise in Recirculating Fiber Optics Delay Line,” IEEE/OSA J. Lightwave Technol. LT-3, 20–31 (1985).
[CrossRef]

J. D. Cohen, “Optical Adaptive Linear Predictors,” Appl. Opt. 24, 4247–4259 (1985).
[CrossRef] [PubMed]

K. Jackson et al., “Optical Fiber Delay-Line Signal Processing,” IEEE Trans. Microwave Theory Tech. MTT-33, 193–210 (1985).
[CrossRef]

1984 (2)

D. Psaltis, J. Hong, “Adaptive Acoustooptic Filter,” Appl. Opt. 23, 3475–3481 (1984).
[CrossRef] [PubMed]

C. Caraiscos, B. Liu, “A Roundoff Error Analysis of the LMS Adaptive Algorithm,” IEEE Trans. Acoust. Speech Signal Process. ASSP-32, 34–41 (1984).
[CrossRef]

1983 (3)

1982 (1)

Agrawalla, B. S.

B. S. Agrawalla, B. T. Dai, S. D. Allen, “Laser Ablative Chemical Etching of SiO2,” J. Vac. Sci. Technol. B 5, 601–605 (1987).
[CrossRef]

Alexander, S. T.

S. T. Alexander, Adaptive Signal Processing (Springer-Verlag, New York, 1986).
[CrossRef]

Allen, S. D.

A. Ghosh, S. D. Allen, P. Paparao, “Arithmetic Fourier-Transform Calculation Using Fiber-Optical Parallel Processors,” J. Opt. Soc. Am. A 7, 701–707 (1990).
[CrossRef]

K. Imen, C. Lee, Y. Y. Yang, S. D. Allen, A. Ghosh, “Laser Fabricated Fiber Optical Taps for Interconnects and Optical Data Processing Devices,” Opt. Lett. 15, 950–952 (1990).
[CrossRef] [PubMed]

B. S. Agrawalla, B. T. Dai, S. D. Allen, “Laser Ablative Chemical Etching of SiO2,” J. Vac. Sci. Technol. B 5, 601–605 (1987).
[CrossRef]

A. Ghosh, S. Lisle, S. D. Allen, “Guidelines for the Design of Fiber Optic Transversal Filters,” OSA Annual Meeting, 1989 Technical Digest Series, Vol. 18 (Optical Society of America, Washington, DC, 1989), p. 64.

Ardalan, S.

S. Ardalan, “Floating-Point Error Analysis of Recursive Least Squares and Least-Mean-Squares Adaptive Filters,” IEEE Trans. Circuits Syst. CAS-23, 1192–1208 (1986).
[CrossRef]

Atkins, R. R.

C. Lee, R. R. Atkins, H. Taylor, “Reflectively Tapped Optical Fiber Transversal Filters,” Electron. Lett. 23, 596–598 (1987).
[CrossRef]

Bardos, A. M.

Beaudet, W. R.

Beck, W.

W. Beck, “Tapping Hard-Clad Silica Optical Fiber: A New Tool for Short-Haul Systems Designers,” Laser Focus 23, 138–143 (Nov.1987).

Caraiscos, C.

C. Caraiscos, B. Liu, “A Roundoff Error Analysis of the LMS Adaptive Algorithm,” IEEE Trans. Acoust. Speech Signal Process. ASSP-32, 34–41 (1984).
[CrossRef]

Casasent, D.

Cohen, J. D.

Cohen, L. G.

D. S. Shenk, L. G. Cohen, “Fiber-Optic Tapping Via Induced Scattering,” IEEE/OSA J. Lightwave Technol. LT-7, 1556–1558 (1989).
[CrossRef]

Dai, B. T.

B. S. Agrawalla, B. T. Dai, S. D. Allen, “Laser Ablative Chemical Etching of SiO2,” J. Vac. Sci. Technol. B 5, 601–605 (1987).
[CrossRef]

Davies, D.

A. Goutzoulis, D. Davies, “High Speed Programmable Fiber Optic Binary Data Generator,” Opt. Eng. 28, 35–41 (1989).

Du Toit, D.

D. Du Toit, H. Roberts, “A Single Fiber Linear Bus LAN Topology,” Proc. Soc. Photo-Opt. Instrum. Eng. 991, 170–178 (1988).

Faddeev, D. K.

D. K. Faddeev, V. N. Faddeeva, Computational Methods of Linear Algebra (Freeman, San Francisco, 1963).

Faddeeva, V. N.

D. K. Faddeev, V. N. Faddeeva, Computational Methods of Linear Algebra (Freeman, San Francisco, 1963).

Feitelson, D. G.

D. G. Feitelson, Optical Computing (MIT Press, Cambridge, 1988).

Ghosh, A.

A. Ghosh, S. D. Allen, P. Paparao, “Arithmetic Fourier-Transform Calculation Using Fiber-Optical Parallel Processors,” J. Opt. Soc. Am. A 7, 701–707 (1990).
[CrossRef]

K. Imen, C. Lee, Y. Y. Yang, S. D. Allen, A. Ghosh, “Laser Fabricated Fiber Optical Taps for Interconnects and Optical Data Processing Devices,” Opt. Lett. 15, 950–952 (1990).
[CrossRef] [PubMed]

A. Ghosh, P. Paparao, “Performance Analysis of Matrix Preconditioning Algorithms on Parallel Optical Processors,” J. Opt. Soc. Am. A 5, 39–48 (1988).
[CrossRef]

D. Casasent, A. Ghosh, “Optical Linear Algebra Processors: Noise and Error-Source Modeling,” Opt. Lett. 10, 252–254 (1985).
[CrossRef] [PubMed]

D. Casasent, A. Ghosh, “Direct and Implicit Optical Matrix–Vector Algorithms,” Appl. Opt. 22, 3572–3578 (1983).
[CrossRef] [PubMed]

P. Paparao, A. Ghosh, “Performance Optimization of Fiber Optic Adaptive Filters,” in Conference Record, 1990 International Topical Meeting on Optical Computing, Kobe, Japan (SPIE, Bellingham, WA, 1990), p. 311.

A. Ghosh, “Design of Fiber Optic Adaptive Filters and Neural Networks,” OSA Annual Meeting, 1989 Technical Digest Series, Vol. 18, (Optical Society of America, Washington, DC, 1989), p. 129.

A. Ghosh, S. Lisle, S. D. Allen, “Guidelines for the Design of Fiber Optic Transversal Filters,” OSA Annual Meeting, 1989 Technical Digest Series, Vol. 18 (Optical Society of America, Washington, DC, 1989), p. 64.

Glenn, W. H.

W. W. Morey, G. Meltz, W. H. Glenn, “Holographically Generated Gratings in Optical Fibers,” Opt. Photon. News 1, No. 7, 14–16 (1990).
[CrossRef]

Goodman, J.

M. Tur, B. Moslehi, J. Goodman, “Theory of Laser Phase Noise in Recirculating Fiber Optics Delay Line,” IEEE/OSA J. Lightwave Technol. LT-3, 20–31 (1985).
[CrossRef]

Goutzoulis, A.

A. Goutzoulis, D. Davies, “High Speed Programmable Fiber Optic Binary Data Generator,” Opt. Eng. 28, 35–41 (1989).

Heuring, V. P.

Hong, J.

Imen, K.

Ito, F.

Jackson, K.

K. Jackson et al., “Optical Fiber Delay-Line Signal Processing,” IEEE Trans. Microwave Theory Tech. MTT-33, 193–210 (1985).
[CrossRef]

Jenkins, W. K.

D. F. Marshall, W. K. Jenkins, J. J. Murphy, “The Use of Orthogonal Transforms for Improving Performance of Adaptive Filters,” IEEE Trans. Circuits Syst. 36, 474–483 (1989).
[CrossRef]

Jordan, H. F.

Kitayama, K.

Kuo, B.

B. Kuo, Automatic Control Systems (Prentice-Hall, Englewood Cliffs, NJ, 1987).

Lee, C.

Lee, J. N.

J. N. Lee, A. VanderLugt, “Acoustooptic Signal Processing and Computing,” Proc. IEEE 77, 1528–1557 (1989).
[CrossRef]

Lisle, S.

A. Ghosh, S. Lisle, S. D. Allen, “Guidelines for the Design of Fiber Optic Transversal Filters,” OSA Annual Meeting, 1989 Technical Digest Series, Vol. 18 (Optical Society of America, Washington, DC, 1989), p. 64.

Liu, B.

C. Caraiscos, B. Liu, “A Roundoff Error Analysis of the LMS Adaptive Algorithm,” IEEE Trans. Acoust. Speech Signal Process. ASSP-32, 34–41 (1984).
[CrossRef]

Marshall, D. F.

D. F. Marshall, W. K. Jenkins, J. J. Murphy, “The Use of Orthogonal Transforms for Improving Performance of Adaptive Filters,” IEEE Trans. Circuits Syst. 36, 474–483 (1989).
[CrossRef]

Meltz, G.

W. W. Morey, G. Meltz, W. H. Glenn, “Holographically Generated Gratings in Optical Fibers,” Opt. Photon. News 1, No. 7, 14–16 (1990).
[CrossRef]

Morey, W. W.

W. W. Morey, G. Meltz, W. H. Glenn, “Holographically Generated Gratings in Optical Fibers,” Opt. Photon. News 1, No. 7, 14–16 (1990).
[CrossRef]

Moslehi, B.

M. Tur, B. Moslehi, J. Goodman, “Theory of Laser Phase Noise in Recirculating Fiber Optics Delay Line,” IEEE/OSA J. Lightwave Technol. LT-3, 20–31 (1985).
[CrossRef]

Murphy, J. J.

D. F. Marshall, W. K. Jenkins, J. J. Murphy, “The Use of Orthogonal Transforms for Improving Performance of Adaptive Filters,” IEEE Trans. Circuits Syst. 36, 474–483 (1989).
[CrossRef]

Narasimha, M. J.

S. S. Narayan, A. M. Peterson, M. J. Narasimha, “Transform Domain LMS Algorithm,” IEEE Trans. Acoust. Speech Signal Process. ASSP-31, 609–615 (1983).
[CrossRef]

Narayan, S. S.

S. S. Narayan, A. M. Peterson, M. J. Narasimha, “Transform Domain LMS Algorithm,” IEEE Trans. Acoust. Speech Signal Process. ASSP-31, 609–615 (1983).
[CrossRef]

Nyman, B.

B. Nyman, P. Prucnal, “Passive Waveguide Structures for Integrated Optical Signal Processing,” Opt. Eng. 28, 982–989 (1989).

Paparao, P.

Pappert, S.

S. Pappert, “Ultra-Wideband Direction Finding Using a Fiber Optic Beamforming Processor,” Proc. Soc. Photo-Opt. Instrum. Eng. 886, 239–246 (1988); see also D. M. Gookin, M. H. Berry, “Finite Impulse Response Filter with Large Dynamic Range and High Sampling Rate,” Appl. Opt. 29, 1061–1062 (1990).
[CrossRef] [PubMed]

Penn, W. A.

W. A. Penn, “Acousto-Optic Signal Canceller,” in ICALEO Conference Proceedings, Vol. 34, Laser and Electro-optics, 9 (Laser Institute of America, 1982).

Peterson, A. M.

S. S. Narayan, A. M. Peterson, M. J. Narasimha, “Transform Domain LMS Algorithm,” IEEE Trans. Acoust. Speech Signal Process. ASSP-31, 609–615 (1983).
[CrossRef]

Prucnal, P.

B. Nyman, P. Prucnal, “Passive Waveguide Structures for Integrated Optical Signal Processing,” Opt. Eng. 28, 982–989 (1989).

Psaltis, D.

Rhodes, J. F.

Roberts, H.

D. Du Toit, H. Roberts, “A Single Fiber Linear Bus LAN Topology,” Proc. Soc. Photo-Opt. Instrum. Eng. 991, 170–178 (1988).

Sarrazin, D. B.

Shenk, D. S.

D. S. Shenk, L. G. Cohen, “Fiber-Optic Tapping Via Induced Scattering,” IEEE/OSA J. Lightwave Technol. LT-7, 1556–1558 (1989).
[CrossRef]

Stearns, S. D.

B. Widrow, S. D. Stearns, Adaptive Signal Processing (Prentice-Hall, Englewood Cliffs, NJ, 1985).

Taylor, H.

H. Taylor, “Application of Guided-Wave Optics in Signal Processing and Sensing,” Proc. IEEE 75, 1524–1535 (1987).
[CrossRef]

C. Lee, R. R. Atkins, H. Taylor, “Reflectively Tapped Optical Fiber Transversal Filters,” Electron. Lett. 23, 596–598 (1987).
[CrossRef]

Tur, M.

M. Tur, B. Moslehi, J. Goodman, “Theory of Laser Phase Noise in Recirculating Fiber Optics Delay Line,” IEEE/OSA J. Lightwave Technol. LT-3, 20–31 (1985).
[CrossRef]

Vander Lugt, A.

VanderLugt, A.

J. N. Lee, A. VanderLugt, “Acoustooptic Signal Processing and Computing,” Proc. IEEE 77, 1528–1557 (1989).
[CrossRef]

A. M. Bardos, W. R. Beaudet, A. VanderLugt, “Stability Considerations for Adaptive Optical Filtering,” Appl. Opt. 25, 2314–2325 (1986).
[CrossRef] [PubMed]

Widrow, B.

B. Widrow, R. Winter, “Neural Nets for Adaptive Filtering and Adaptive Pattern Recognition,” IEEE Comput. Mag. 21, 25–39 (1988).
[CrossRef]

B. Widrow, S. D. Stearns, Adaptive Signal Processing (Prentice-Hall, Englewood Cliffs, NJ, 1985).

Winter, R.

B. Widrow, R. Winter, “Neural Nets for Adaptive Filtering and Adaptive Pattern Recognition,” IEEE Comput. Mag. 21, 25–39 (1988).
[CrossRef]

Yang, Y. Y.

Appl. Opt. (8)

Electron. Lett. (1)

C. Lee, R. R. Atkins, H. Taylor, “Reflectively Tapped Optical Fiber Transversal Filters,” Electron. Lett. 23, 596–598 (1987).
[CrossRef]

IEEE Comput. Mag. (1)

B. Widrow, R. Winter, “Neural Nets for Adaptive Filtering and Adaptive Pattern Recognition,” IEEE Comput. Mag. 21, 25–39 (1988).
[CrossRef]

IEEE Trans. Acoust. Speech Signal Process. (2)

C. Caraiscos, B. Liu, “A Roundoff Error Analysis of the LMS Adaptive Algorithm,” IEEE Trans. Acoust. Speech Signal Process. ASSP-32, 34–41 (1984).
[CrossRef]

S. S. Narayan, A. M. Peterson, M. J. Narasimha, “Transform Domain LMS Algorithm,” IEEE Trans. Acoust. Speech Signal Process. ASSP-31, 609–615 (1983).
[CrossRef]

IEEE Trans. Circuits Syst. (2)

D. F. Marshall, W. K. Jenkins, J. J. Murphy, “The Use of Orthogonal Transforms for Improving Performance of Adaptive Filters,” IEEE Trans. Circuits Syst. 36, 474–483 (1989).
[CrossRef]

S. Ardalan, “Floating-Point Error Analysis of Recursive Least Squares and Least-Mean-Squares Adaptive Filters,” IEEE Trans. Circuits Syst. CAS-23, 1192–1208 (1986).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

K. Jackson et al., “Optical Fiber Delay-Line Signal Processing,” IEEE Trans. Microwave Theory Tech. MTT-33, 193–210 (1985).
[CrossRef]

IEEE/OSA J. Lightwave Technol. (2)

D. S. Shenk, L. G. Cohen, “Fiber-Optic Tapping Via Induced Scattering,” IEEE/OSA J. Lightwave Technol. LT-7, 1556–1558 (1989).
[CrossRef]

M. Tur, B. Moslehi, J. Goodman, “Theory of Laser Phase Noise in Recirculating Fiber Optics Delay Line,” IEEE/OSA J. Lightwave Technol. LT-3, 20–31 (1985).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Vac. Sci. Technol. B (1)

B. S. Agrawalla, B. T. Dai, S. D. Allen, “Laser Ablative Chemical Etching of SiO2,” J. Vac. Sci. Technol. B 5, 601–605 (1987).
[CrossRef]

Laser Focus (1)

W. Beck, “Tapping Hard-Clad Silica Optical Fiber: A New Tool for Short-Haul Systems Designers,” Laser Focus 23, 138–143 (Nov.1987).

Opt. Eng. (2)

A. Goutzoulis, D. Davies, “High Speed Programmable Fiber Optic Binary Data Generator,” Opt. Eng. 28, 35–41 (1989).

B. Nyman, P. Prucnal, “Passive Waveguide Structures for Integrated Optical Signal Processing,” Opt. Eng. 28, 982–989 (1989).

Opt. Lett. (2)

Opt. Photon. News (1)

W. W. Morey, G. Meltz, W. H. Glenn, “Holographically Generated Gratings in Optical Fibers,” Opt. Photon. News 1, No. 7, 14–16 (1990).
[CrossRef]

Proc. IEEE (2)

H. Taylor, “Application of Guided-Wave Optics in Signal Processing and Sensing,” Proc. IEEE 75, 1524–1535 (1987).
[CrossRef]

J. N. Lee, A. VanderLugt, “Acoustooptic Signal Processing and Computing,” Proc. IEEE 77, 1528–1557 (1989).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

D. Du Toit, H. Roberts, “A Single Fiber Linear Bus LAN Topology,” Proc. Soc. Photo-Opt. Instrum. Eng. 991, 170–178 (1988).

S. Pappert, “Ultra-Wideband Direction Finding Using a Fiber Optic Beamforming Processor,” Proc. Soc. Photo-Opt. Instrum. Eng. 886, 239–246 (1988); see also D. M. Gookin, M. H. Berry, “Finite Impulse Response Filter with Large Dynamic Range and High Sampling Rate,” Appl. Opt. 29, 1061–1062 (1990).
[CrossRef] [PubMed]

Other (10)

B. Kuo, Automatic Control Systems (Prentice-Hall, Englewood Cliffs, NJ, 1987).

P. Paparao, A. Ghosh, “Performance Optimization of Fiber Optic Adaptive Filters,” in Conference Record, 1990 International Topical Meeting on Optical Computing, Kobe, Japan (SPIE, Bellingham, WA, 1990), p. 311.

A. Ghosh, “Design of Fiber Optic Adaptive Filters and Neural Networks,” OSA Annual Meeting, 1989 Technical Digest Series, Vol. 18, (Optical Society of America, Washington, DC, 1989), p. 129.

A. Ghosh, S. Lisle, S. D. Allen, “Guidelines for the Design of Fiber Optic Transversal Filters,” OSA Annual Meeting, 1989 Technical Digest Series, Vol. 18 (Optical Society of America, Washington, DC, 1989), p. 64.

B. Widrow, S. D. Stearns, Adaptive Signal Processing (Prentice-Hall, Englewood Cliffs, NJ, 1985).

S. T. Alexander, Adaptive Signal Processing (Springer-Verlag, New York, 1986).
[CrossRef]

D. G. Feitelson, Optical Computing (MIT Press, Cambridge, 1988).

J. L. Horner, Ed., Optical Signal Processing (Academic, San Diego, 1987).

W. A. Penn, “Acousto-Optic Signal Canceller,” in ICALEO Conference Proceedings, Vol. 34, Laser and Electro-optics, 9 (Laser Institute of America, 1982).

D. K. Faddeev, V. N. Faddeeva, Computational Methods of Linear Algebra (Freeman, San Francisco, 1963).

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Figures (13)

Fig. 1
Fig. 1

Block diagram of tapped delay line adaptive filter.

Fig. 2
Fig. 2

Block diagram illustrating the configuration for system identification.

Fig. 3
Fig. 3

(a) Fiber bundle type tapped delay line; (b) longitudinal tapped delay line.

Fig. 4
Fig. 4

Radiation pattern from a laser fabricated tap on the cladding of a multimode fiber.19

Fig. 5
Fig. 5

Fiber optic adaptive filter using a fiber bundle type FOTDL.

Fig. 6
Fig. 6

Fiber optic adaptive filter using a LACE processed FOTDL.

Fig. 7
Fig. 7

Schematic diagram of the fiber optic LMS adaptive filter with dominant error sources.

Fig. 8
Fig. 8

Learning curve for the ideal LMS adaptive filter. The dotted line is the theoretically calculated steady state mean squared error (number of taps = 2, μ = 0.29, σ 0 2 = 0 , D = 1.0, and variance of input signal = 0.0625).

Fig. 9
Fig. 9

Learning curves for the fiber optic LMS adaptive filter for two different values of adaptive gain μ. Dotted lines are the theoretically calculated steady state mean squared error (number of taps = 2, σ 0 2 = 10 - 4 , D = 1.0, and variance of input signal = 0.0625).

Fig. 10
Fig. 10

Learning curves for the fiber optic LMS adaptive filter for two different optical error levels σ 0 2 . Dotted lines are the theoretically calculated steady state mean squared error (number of taps = 2, μ = 0.29, D = 1.0, and variance of input signal = 0.0625).

Fig. 11
Fig. 11

Variation of steady state mean squared error ξ (theoretically calculated) with the adaptive gain μ for different levels of optical errors (number of taps = 5, D = 1.0, and variance of input signal = 0.0625).

Fig. 12
Fig. 12

Variation of steady state mean squared error ξ (theoretically calculated) with the adaptive gain μ for different number of taps ( σ 0 2 = 10 - 4 , D = 1.0, and variance of input signal = 0.0625).

Fig. 13
Fig. 13

Learning time vs the adaptive gain μ (number of taps = 5, D = 1, and variance of input signal = 0.0625).

Equations (52)

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x n = [ x n x n - 1 , , x n - ( N - 1 ) ] T ,
w n = [ w n 0 w n 1 , , w n ( N - 1 ) ] T ,
y n = x n T w n = w n T x n .
e n = d n - y n .
w n + 1 = w n + μ e n x n ,
E [ w n + 1 ] = ( I - μ R ) E [ w n ] + μ p ,
R = E [ x n x n T ]
p = E [ d n x n ]
w * = R - 1 p .
0 < μ < 2 / λ max ,
0 < μ < 2 / tr [ R ] .
ξ min = E [ d n 2 ] - p T R - 1 p .
ξ s s = ξ min + μ ξ min tr [ R ] / ( 2 - μ tr [ R ] ) .
x n = F ( x n + δ x n ) ,
w n = w n + Δ w n ,
y n = ( w n + δ w n ) T x n + β n ,
y n = w n T x n + Δ w n T x n + δ w n T x n + w n T x n + β n .
e n = d n - y n = e n - ( Δ w n T x n + δ w n T x n + w n T δ x n + β n ) e n + Δ e n ,
ξ = E [ e n 2 ] = E [ e n 2 ] + E [ Δ e n 2 ] ,
E [ Δ e n 2 ] = E [ ( Δ w n T x n ) 2 ] + E [ ( δ w n T x n ) 2 ] + E [ ( w n T δ x n ) 2 ] + E [ β n 2 ] .
E [ ( w n T δ x n ) 2 ] = E [ w n T w n ] σ δ x 2 = ( w * 2 + μ ξ min N / 2 ) σ δ x 2 .
E [ ( δ w n T x n ) 2 ] = tr [ E ( δ w n δ w n T ) R ] = σ w 2 tr [ R ] .
w n + 1 = w n + μ x n e n + γ n = w n + μ x n e n + μ x n Δ e n + μ e n δ x n + γ n ,
Δ w n + 1 = G n Δ w n + b n ,             n = 0 , 1 , 2 , ,
G n = I - μ x n x n T ,
b n = - μ x n δ w n T x n - μ x n w n T δ x n - μ x n β n + μ e n δ x n + γ n .
P n + 1 = E [ G n P n G n ] + Q n = P n - μ ( R P n + P n R ) + μ 2 E [ x n x n T P n x n x n T ] + Q n
- μ ( R P n + P n R ) + Q n = 0.
tr [ R P n ] = tr [ Q n ] 2 μ .
Q n = E [ b n b n T ] = μ 2 E [ x n x n T x n x n T ] σ w 2 + μ 2 σ δ x 2 w * 2 R + μ 2 σ β 2 R + ( μ 2 ξ min σ δ x 2 + σ γ 2 ) I .
x n = u n + D g ,
ξ = ξ min + μ ξ min tr [ R ] 2 - μ tr [ R ] + ( 1 + μ tr [ R ] / 2 ) σ β 2 + N σ γ 2 2 μ + ( μ w * 2 tr [ R ] + 2 μ N ξ min + 2 w * 2 ) σ δ x 2 / 2 + ( μ tr [ R 2 ] + μ tr 2 [ R ] / 2 - μ N 2 D 4 + tr [ R ] ) σ w 2 .
ξ / μ = c 4 μ 4 + c 3 μ 3 + c 2 μ 2 + c 1 μ + c 0 = 0 ,
c 4 = tr 3 [ R ] σ β 2 + ( tr [ R ] w * 2 + 2 N ξ min ) tr 2 [ R ] σ δ x 2 + ( 2 tr [ R 2 ] + tr 2 [ R ] - 2 N 2 D 4 ) tr 2 [ R ] σ w 2 , c 3 = - 4 tr 2 [ R ] σ β 2 - 4 ( tr [ R ] w * 2 + 2 N ξ min ) tr [ R ] σ δ x 2 + 4 ( 2 N 2 D 4 - tr 2 [ R ] - 2 tr [ R 2 ] ) tr [ R ] σ w 2 , c 2 = 4 ξ min tr [ R ] - N tr 2 [ R ] σ γ 2 + 4 tr [ R ] σ β 2 + 4 ( w * 2 tr [ R ] + 2 N ξ min ) σ δ x 2 + 4 ( 2 tr [ R 2 ] + tr 2 [ R ] - 2 N 2 D 4 ) σ w 2 , c 1 = 4 N tr [ R ] σ γ 2 , c 0 = - 4 N σ γ 2 .
x = u + D g ,
E [ x ] = D g 0.
R u = E [ u u T ] ,
R = E [ x x T ] = R u + D 2 g g T ,
Z = E [ x x T Axx T ] ,
Z = E [ u u T Auu T ] + D 2 R u Agg T + D 2 E [ u g T Aug T ] + D 2 E [ u g T Agu T ] + D 2 E [ g u T Aug T ] + D 2 E [ g u T Agu T ] + D 2 g g T A R u + D 4 g g T Agg T .
E [ u u T Auu T ] = 2 R u A R u + R u tr [ A R u ] .
Z = 2 RAR + R tr [ AR ] - 2 D 4 g g T Agg T .
E [ x x T x x T ] = 2 R 2 + R tr [ R ] - 2 N D 4 g g T ,
x n = [ x n x n - 1 ] T ,
d n = a 1 x n + a 2 x n - 1 + a 3 x n - 2 ,
w * = [ a 1 a 2 ] T ,
R = σ u 2 I + D 2 g g T .
ξ min = E [ d n 2 ] - p T R - 1 p .
E [ d n 2 ] = w * T R w * + a 3 2 ( σ u 2 + D 2 ) + 2 a 3 D 2 ( g T w * ) ,
p = E [ d n x n ] = R w * + D 2 a 3 g .
R - 1 = 1 σ u 2 I - D 2 σ u 4 + N D 2 σ u 2 g g T .
ξ min = [ σ u 2 + ( N + 1 ) D 2 σ u 2 + N D 2 ] a 3 2 σ u 2 .

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