Abstract

In this paper, we propose a wideband dynamic behavioral model for a bulk reflective semiconductor optical amplifier (RSOA) used as a modulator in colorless radio over fiber (RoF) systems using a tapped-delay multilayer perceptron (TDMLP). 64 quadrature amplitude modulation (QAM) signals with 20 Msymbol/s were used to train, validate and test the model. Nonlinear distortion and dynamic effects induced by the RSOA modulator are demonstrated. The parameters of the model such as the number of nodes in the hidden layer and memory depth were optimized to ensure the generality and accuracy. The normalized mean square error (NMSE) is used as a figure of merit. The NMSE was up to −44.33 dB when the number of nodes in the hidden layer and memory depth were set to 20 and 3, respectively. The TDMLP model can accurately approximate to the dynamic characteristics of the RSOA modulator. The dynamic AM-AM and dynamic AM-PM distortions of the RSOA modulator are drawn. The results show that the single hidden layer TDMLP can provide accurate approximation for behaviors of the RSOA modulator.

© 2013 OSA

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  1. J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics1(6), 319–330 (2007).
    [CrossRef]
  2. A. J. Seeds, “Microwave Photonics,” IEEE Trans. Microw. Theory Tech.50(3), 877–887 (2002).
    [CrossRef]
  3. D. Wake, A. Nkansah, and N. J. Gomes, “Radio over fiber link design for next generation wireless systems,” J. Lightwave Technol.28(16), 2456–2464 (2010).
    [CrossRef]
  4. D. Wake, A. Nkansah, N. J. Gomes, G. de Valicourt, R. Brenot, M. Violas, Z. Liu, F. Ferreira, and S. Pato, “A comparison of radio over fiber link types for the support of wideband radio channels,” J. Lightwave Technol.28(16), 2416–2422 (2010).
    [CrossRef]
  5. T. Durhuus, B. Mikkelsen, C. Joergensen, S. Lykke Danielsen, and K. E. Stubkjaer, “All-optical wavelength conversion by semiconductor optical amplifiers,” J. Lightwave Technol.14(6), 942–954 (1996).
    [CrossRef]
  6. M. J. Connelly, “Wide-band steady-state numerical model and parameter extraction of a tensile-strained bulk semiconductor optical amplifier,” IEEE J. Quantum Electron.43(1), 47–56 (2007).
    [CrossRef]
  7. M. J. Connelly, “Reflective semiconductor optical amplifier pulse propagation model,” IEEE Photon. Technol. Lett.24(2), 95–97 (2012).
    [CrossRef]
  8. N. Nadarajah, K. L. Lee, and A. Nirmalathas, “Upstream access and local area networking in passive optical networks using self-seeded reflective semiconductor optical amplifier,” IEEE Photon. Technol. Lett.19(19), 1559–1561 (2007).
    [CrossRef]
  9. Z. Liu, M. Sadeghi, G. de Valicourt, R. Brenot, and M. Violas, “Experimental validation of a reflective semiconductor optical amplifier model used as a modulator in radio over fiber systems,” IEEE Photon. Technol. Lett.23(9), 576–578 (2011).
    [CrossRef]
  10. Y. Cao and Q. J. Zhang, “A new training approach for robust recurrent neural-network modeling of nonlinear circuits,” IEEE Trans. Microw. Theory Tech.57(6), 1539–1553 (2009).
    [CrossRef]
  11. F. Mkadem and S. Boumaiza, “Physically inspired neural network model for RF power amplifier behavioral modeling and digital predistortion,” IEEE Trans. Microw. Theory Tech.59(4), 913–923 (2011).
    [CrossRef]
  12. N. Vijayakumar and S. N. George, “Design optimization of erbium-doped fiber amplifiers using artificial neural networks,” Opt. Eng.47(8), 085008 (2008).
    [CrossRef]
  13. J. I. Ababneh and O. Qasaimeh, “Simple model for quantum-dot semiconductor optical amplifiers using artificial neural networks,” IEEE Trans. Electron. Dev.53(7), 1543–1550 (2006).
    [CrossRef]
  14. K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximators,” Neural Netw.2(5), 359–366 (1989).
    [CrossRef]
  15. E. B. Baum and D. Haussler, “What size net gives valid generalization?” Neural Comput.1(1), 151–160 (1989).
    [CrossRef]
  16. S. Haykin, Neural Networks: A Comprehensive Foundation (Prentice-Hall, 1999).
  17. M. T. Hagan and M. B. Menhaj, “Training feedforward networks with the Marquardt Algorithm,” IEEE Trans. Neural Netw.5(6), 989–993 (1994).
    [CrossRef] [PubMed]

2012 (1)

M. J. Connelly, “Reflective semiconductor optical amplifier pulse propagation model,” IEEE Photon. Technol. Lett.24(2), 95–97 (2012).
[CrossRef]

2011 (2)

F. Mkadem and S. Boumaiza, “Physically inspired neural network model for RF power amplifier behavioral modeling and digital predistortion,” IEEE Trans. Microw. Theory Tech.59(4), 913–923 (2011).
[CrossRef]

Z. Liu, M. Sadeghi, G. de Valicourt, R. Brenot, and M. Violas, “Experimental validation of a reflective semiconductor optical amplifier model used as a modulator in radio over fiber systems,” IEEE Photon. Technol. Lett.23(9), 576–578 (2011).
[CrossRef]

2010 (2)

2009 (1)

Y. Cao and Q. J. Zhang, “A new training approach for robust recurrent neural-network modeling of nonlinear circuits,” IEEE Trans. Microw. Theory Tech.57(6), 1539–1553 (2009).
[CrossRef]

2008 (1)

N. Vijayakumar and S. N. George, “Design optimization of erbium-doped fiber amplifiers using artificial neural networks,” Opt. Eng.47(8), 085008 (2008).
[CrossRef]

2007 (3)

N. Nadarajah, K. L. Lee, and A. Nirmalathas, “Upstream access and local area networking in passive optical networks using self-seeded reflective semiconductor optical amplifier,” IEEE Photon. Technol. Lett.19(19), 1559–1561 (2007).
[CrossRef]

M. J. Connelly, “Wide-band steady-state numerical model and parameter extraction of a tensile-strained bulk semiconductor optical amplifier,” IEEE J. Quantum Electron.43(1), 47–56 (2007).
[CrossRef]

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics1(6), 319–330 (2007).
[CrossRef]

2006 (1)

J. I. Ababneh and O. Qasaimeh, “Simple model for quantum-dot semiconductor optical amplifiers using artificial neural networks,” IEEE Trans. Electron. Dev.53(7), 1543–1550 (2006).
[CrossRef]

2002 (1)

A. J. Seeds, “Microwave Photonics,” IEEE Trans. Microw. Theory Tech.50(3), 877–887 (2002).
[CrossRef]

1996 (1)

T. Durhuus, B. Mikkelsen, C. Joergensen, S. Lykke Danielsen, and K. E. Stubkjaer, “All-optical wavelength conversion by semiconductor optical amplifiers,” J. Lightwave Technol.14(6), 942–954 (1996).
[CrossRef]

1994 (1)

M. T. Hagan and M. B. Menhaj, “Training feedforward networks with the Marquardt Algorithm,” IEEE Trans. Neural Netw.5(6), 989–993 (1994).
[CrossRef] [PubMed]

1989 (2)

K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximators,” Neural Netw.2(5), 359–366 (1989).
[CrossRef]

E. B. Baum and D. Haussler, “What size net gives valid generalization?” Neural Comput.1(1), 151–160 (1989).
[CrossRef]

Ababneh, J. I.

J. I. Ababneh and O. Qasaimeh, “Simple model for quantum-dot semiconductor optical amplifiers using artificial neural networks,” IEEE Trans. Electron. Dev.53(7), 1543–1550 (2006).
[CrossRef]

Baum, E. B.

E. B. Baum and D. Haussler, “What size net gives valid generalization?” Neural Comput.1(1), 151–160 (1989).
[CrossRef]

Boumaiza, S.

F. Mkadem and S. Boumaiza, “Physically inspired neural network model for RF power amplifier behavioral modeling and digital predistortion,” IEEE Trans. Microw. Theory Tech.59(4), 913–923 (2011).
[CrossRef]

Brenot, R.

Z. Liu, M. Sadeghi, G. de Valicourt, R. Brenot, and M. Violas, “Experimental validation of a reflective semiconductor optical amplifier model used as a modulator in radio over fiber systems,” IEEE Photon. Technol. Lett.23(9), 576–578 (2011).
[CrossRef]

D. Wake, A. Nkansah, N. J. Gomes, G. de Valicourt, R. Brenot, M. Violas, Z. Liu, F. Ferreira, and S. Pato, “A comparison of radio over fiber link types for the support of wideband radio channels,” J. Lightwave Technol.28(16), 2416–2422 (2010).
[CrossRef]

Cao, Y.

Y. Cao and Q. J. Zhang, “A new training approach for robust recurrent neural-network modeling of nonlinear circuits,” IEEE Trans. Microw. Theory Tech.57(6), 1539–1553 (2009).
[CrossRef]

Capmany, J.

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics1(6), 319–330 (2007).
[CrossRef]

Connelly, M. J.

M. J. Connelly, “Reflective semiconductor optical amplifier pulse propagation model,” IEEE Photon. Technol. Lett.24(2), 95–97 (2012).
[CrossRef]

M. J. Connelly, “Wide-band steady-state numerical model and parameter extraction of a tensile-strained bulk semiconductor optical amplifier,” IEEE J. Quantum Electron.43(1), 47–56 (2007).
[CrossRef]

de Valicourt, G.

Z. Liu, M. Sadeghi, G. de Valicourt, R. Brenot, and M. Violas, “Experimental validation of a reflective semiconductor optical amplifier model used as a modulator in radio over fiber systems,” IEEE Photon. Technol. Lett.23(9), 576–578 (2011).
[CrossRef]

D. Wake, A. Nkansah, N. J. Gomes, G. de Valicourt, R. Brenot, M. Violas, Z. Liu, F. Ferreira, and S. Pato, “A comparison of radio over fiber link types for the support of wideband radio channels,” J. Lightwave Technol.28(16), 2416–2422 (2010).
[CrossRef]

Durhuus, T.

T. Durhuus, B. Mikkelsen, C. Joergensen, S. Lykke Danielsen, and K. E. Stubkjaer, “All-optical wavelength conversion by semiconductor optical amplifiers,” J. Lightwave Technol.14(6), 942–954 (1996).
[CrossRef]

Ferreira, F.

George, S. N.

N. Vijayakumar and S. N. George, “Design optimization of erbium-doped fiber amplifiers using artificial neural networks,” Opt. Eng.47(8), 085008 (2008).
[CrossRef]

Gomes, N. J.

Hagan, M. T.

M. T. Hagan and M. B. Menhaj, “Training feedforward networks with the Marquardt Algorithm,” IEEE Trans. Neural Netw.5(6), 989–993 (1994).
[CrossRef] [PubMed]

Haussler, D.

E. B. Baum and D. Haussler, “What size net gives valid generalization?” Neural Comput.1(1), 151–160 (1989).
[CrossRef]

Hornik, K.

K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximators,” Neural Netw.2(5), 359–366 (1989).
[CrossRef]

Joergensen, C.

T. Durhuus, B. Mikkelsen, C. Joergensen, S. Lykke Danielsen, and K. E. Stubkjaer, “All-optical wavelength conversion by semiconductor optical amplifiers,” J. Lightwave Technol.14(6), 942–954 (1996).
[CrossRef]

Lee, K. L.

N. Nadarajah, K. L. Lee, and A. Nirmalathas, “Upstream access and local area networking in passive optical networks using self-seeded reflective semiconductor optical amplifier,” IEEE Photon. Technol. Lett.19(19), 1559–1561 (2007).
[CrossRef]

Liu, Z.

Z. Liu, M. Sadeghi, G. de Valicourt, R. Brenot, and M. Violas, “Experimental validation of a reflective semiconductor optical amplifier model used as a modulator in radio over fiber systems,” IEEE Photon. Technol. Lett.23(9), 576–578 (2011).
[CrossRef]

D. Wake, A. Nkansah, N. J. Gomes, G. de Valicourt, R. Brenot, M. Violas, Z. Liu, F. Ferreira, and S. Pato, “A comparison of radio over fiber link types for the support of wideband radio channels,” J. Lightwave Technol.28(16), 2416–2422 (2010).
[CrossRef]

Lykke Danielsen, S.

T. Durhuus, B. Mikkelsen, C. Joergensen, S. Lykke Danielsen, and K. E. Stubkjaer, “All-optical wavelength conversion by semiconductor optical amplifiers,” J. Lightwave Technol.14(6), 942–954 (1996).
[CrossRef]

Menhaj, M. B.

M. T. Hagan and M. B. Menhaj, “Training feedforward networks with the Marquardt Algorithm,” IEEE Trans. Neural Netw.5(6), 989–993 (1994).
[CrossRef] [PubMed]

Mikkelsen, B.

T. Durhuus, B. Mikkelsen, C. Joergensen, S. Lykke Danielsen, and K. E. Stubkjaer, “All-optical wavelength conversion by semiconductor optical amplifiers,” J. Lightwave Technol.14(6), 942–954 (1996).
[CrossRef]

Mkadem, F.

F. Mkadem and S. Boumaiza, “Physically inspired neural network model for RF power amplifier behavioral modeling and digital predistortion,” IEEE Trans. Microw. Theory Tech.59(4), 913–923 (2011).
[CrossRef]

Nadarajah, N.

N. Nadarajah, K. L. Lee, and A. Nirmalathas, “Upstream access and local area networking in passive optical networks using self-seeded reflective semiconductor optical amplifier,” IEEE Photon. Technol. Lett.19(19), 1559–1561 (2007).
[CrossRef]

Nirmalathas, A.

N. Nadarajah, K. L. Lee, and A. Nirmalathas, “Upstream access and local area networking in passive optical networks using self-seeded reflective semiconductor optical amplifier,” IEEE Photon. Technol. Lett.19(19), 1559–1561 (2007).
[CrossRef]

Nkansah, A.

Novak, D.

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics1(6), 319–330 (2007).
[CrossRef]

Pato, S.

Qasaimeh, O.

J. I. Ababneh and O. Qasaimeh, “Simple model for quantum-dot semiconductor optical amplifiers using artificial neural networks,” IEEE Trans. Electron. Dev.53(7), 1543–1550 (2006).
[CrossRef]

Sadeghi, M.

Z. Liu, M. Sadeghi, G. de Valicourt, R. Brenot, and M. Violas, “Experimental validation of a reflective semiconductor optical amplifier model used as a modulator in radio over fiber systems,” IEEE Photon. Technol. Lett.23(9), 576–578 (2011).
[CrossRef]

Seeds, A. J.

A. J. Seeds, “Microwave Photonics,” IEEE Trans. Microw. Theory Tech.50(3), 877–887 (2002).
[CrossRef]

Stinchcombe, M.

K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximators,” Neural Netw.2(5), 359–366 (1989).
[CrossRef]

Stubkjaer, K. E.

T. Durhuus, B. Mikkelsen, C. Joergensen, S. Lykke Danielsen, and K. E. Stubkjaer, “All-optical wavelength conversion by semiconductor optical amplifiers,” J. Lightwave Technol.14(6), 942–954 (1996).
[CrossRef]

Vijayakumar, N.

N. Vijayakumar and S. N. George, “Design optimization of erbium-doped fiber amplifiers using artificial neural networks,” Opt. Eng.47(8), 085008 (2008).
[CrossRef]

Violas, M.

Z. Liu, M. Sadeghi, G. de Valicourt, R. Brenot, and M. Violas, “Experimental validation of a reflective semiconductor optical amplifier model used as a modulator in radio over fiber systems,” IEEE Photon. Technol. Lett.23(9), 576–578 (2011).
[CrossRef]

D. Wake, A. Nkansah, N. J. Gomes, G. de Valicourt, R. Brenot, M. Violas, Z. Liu, F. Ferreira, and S. Pato, “A comparison of radio over fiber link types for the support of wideband radio channels,” J. Lightwave Technol.28(16), 2416–2422 (2010).
[CrossRef]

Wake, D.

White, H.

K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximators,” Neural Netw.2(5), 359–366 (1989).
[CrossRef]

Zhang, Q. J.

Y. Cao and Q. J. Zhang, “A new training approach for robust recurrent neural-network modeling of nonlinear circuits,” IEEE Trans. Microw. Theory Tech.57(6), 1539–1553 (2009).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. J. Connelly, “Wide-band steady-state numerical model and parameter extraction of a tensile-strained bulk semiconductor optical amplifier,” IEEE J. Quantum Electron.43(1), 47–56 (2007).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

M. J. Connelly, “Reflective semiconductor optical amplifier pulse propagation model,” IEEE Photon. Technol. Lett.24(2), 95–97 (2012).
[CrossRef]

N. Nadarajah, K. L. Lee, and A. Nirmalathas, “Upstream access and local area networking in passive optical networks using self-seeded reflective semiconductor optical amplifier,” IEEE Photon. Technol. Lett.19(19), 1559–1561 (2007).
[CrossRef]

Z. Liu, M. Sadeghi, G. de Valicourt, R. Brenot, and M. Violas, “Experimental validation of a reflective semiconductor optical amplifier model used as a modulator in radio over fiber systems,” IEEE Photon. Technol. Lett.23(9), 576–578 (2011).
[CrossRef]

IEEE Trans. Electron. Dev. (1)

J. I. Ababneh and O. Qasaimeh, “Simple model for quantum-dot semiconductor optical amplifiers using artificial neural networks,” IEEE Trans. Electron. Dev.53(7), 1543–1550 (2006).
[CrossRef]

IEEE Trans. Microw. Theory Tech. (3)

Y. Cao and Q. J. Zhang, “A new training approach for robust recurrent neural-network modeling of nonlinear circuits,” IEEE Trans. Microw. Theory Tech.57(6), 1539–1553 (2009).
[CrossRef]

F. Mkadem and S. Boumaiza, “Physically inspired neural network model for RF power amplifier behavioral modeling and digital predistortion,” IEEE Trans. Microw. Theory Tech.59(4), 913–923 (2011).
[CrossRef]

A. J. Seeds, “Microwave Photonics,” IEEE Trans. Microw. Theory Tech.50(3), 877–887 (2002).
[CrossRef]

IEEE Trans. Neural Netw. (1)

M. T. Hagan and M. B. Menhaj, “Training feedforward networks with the Marquardt Algorithm,” IEEE Trans. Neural Netw.5(6), 989–993 (1994).
[CrossRef] [PubMed]

J. Lightwave Technol. (3)

Nat. Photonics (1)

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics1(6), 319–330 (2007).
[CrossRef]

Neural Comput. (1)

E. B. Baum and D. Haussler, “What size net gives valid generalization?” Neural Comput.1(1), 151–160 (1989).
[CrossRef]

Neural Netw. (1)

K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximators,” Neural Netw.2(5), 359–366 (1989).
[CrossRef]

Opt. Eng. (1)

N. Vijayakumar and S. N. George, “Design optimization of erbium-doped fiber amplifiers using artificial neural networks,” Opt. Eng.47(8), 085008 (2008).
[CrossRef]

Other (1)

S. Haykin, Neural Networks: A Comprehensive Foundation (Prentice-Hall, 1999).

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Figures (7)

Fig. 1
Fig. 1

TDMLP based model with 2 × (m + 1) input nodes, m is the number of memory depth, z−1 is for unit delay operation, M hidden nodes and two output nodes.

Fig. 2
Fig. 2

The experimental test bench.

Fig. 3
Fig. 3

The training performance of the TDMLP based model for the RSOA modulator with memory depth of 3 and hidden nodes of 20.

Fig. 4
Fig. 4

Measured and modeled outputs in-phase and quadrature parts in time domain.

Fig. 5
Fig. 5

Normalized power spectral density of measured and modeled outputs.

Fig. 6
Fig. 6

Normalized constellation (red ‘ + ’ for the transmitted symbol, blue ‘·’ for the measured output, and green ‘x’ for the TDMLP model output).

Fig. 7
Fig. 7

Dynamic AM-AM and AM-PM characteristics of the RSOA modulator.

Tables (1)

Tables Icon

Table 1 TDMLP model performance versus memory depth and the number of hidden nodes

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

u j (n)=f( i=0 m ω i,j x(ni) + b h,j )
y k (n)= j=1 M ω j,k u j (n) + b o,k
f(x)=tanh(x)= e x e x e x + e x
V(ω)= 1 2P p=1 P i=1 N [ t i p (ω) y i p (ω) ] 2 = 1 2P p=1 P i=1 N [ e i p (ω) ] 2
ω n+1 = ω n [ J T J+μI ] 1 J T e
NMSE=10 log 10 { n=1 N ( [ t I (n) y I (n)] 2 + [ t Q (n) y Q (n)] 2 ) n=1 N ( [ t I (n)] 2 + [ t Q (n)] 2 ) }
EVM= n=1 N | s(n)r(n) | 2 n=1 N | r(n) | 2

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