Abstract

A semi-analytical simulation method (SASM) is proposed to evaluate the signal-to-noise ratio (SNR) of time stretched signals at the output of photonic analogue-to-digital converter (Ph-ADC) system. Analytical expressions of the signal at Ph-ADC output considering generic electrical signals applied to the electro-optic modulators of the Ph-ADC are derived. The contribution to the total variance of the received signal from the noise introduced by the electrical transmitter and receiver, and by the optical amplifier are derived analytically taking into account the pulsed nature of the optical signal. The proposed SASM shows excellent agreement of SNR estimates with the estimates provided by Monte Carlo simulation. This result is confirmed for variance dominantly imposed by the noise introduced by the electrical transmitter, by the optical amplifier and by the electrical receiver. A simplified approach is also proposed and compared with previous work. It is shown that mean power estimates obtained from this simplified approach are valid while the modulator is operating in the linear region and the signal is not affected by the frequency response of the electrical receiver filter. Additionally, it is concluded that the estimates of the noise variance due to the electrical transmitter are acceptable when a small signal analysis of noise along the Ph-ADC is valid.

© 2011 Optical Society of America

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References

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  1. L. Du, B. Schmidt, and A. Lowery, "Efficient digital backpropagation for PDM-CO-OFDM optical transmission systems," in Optical Fibre Communication Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2010), paper OTuE2.
  2. Y. Han, and B. Jalali, "Photonic time-stretched analogue-to-digital converter: fundamental concepts and practical considerations," J. Lightwave Technol. 21, 3085-3103 (2003).
    [CrossRef]
  3. F. Coppinger, A. Bhushan, and B. Jalali, "Time magnification of electrical signals using chirped optical pulses," Electron. Lett. 34, 399-400 (1998).
    [CrossRef]
  4. T. Clark, J. Kang, and R. Esman, "Performance of a time- and wavelength-interleaved photonic sampler for analog-digital conversion," IEEE Photon. Technol. Lett. 11, 1168-1170 (1999).
    [CrossRef]
  5. J. Stigwall, and S. Galt, "Signal reconstruction by phase retrieval and optical backpropagation in phase-diverse photonic time-stretched systems," J. Lightwave Technol. 25, 3017 (2007).
    [CrossRef]
  6. G. Valley, "Photonic analog-to-digital converters: a tutorial," in Optical Fibre Communication Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2010), paper OMI1.
  7. R. Llorente, A. Cartaxo, B. Uguen, J. Duplicy, J. Romme, J. Puche, D. Schmertz, Y. Lostanlen, R. Banales, and J. Marti, "Management of UWB picocell clusters: UCELLS project approach," in International Conference on Ultra-Wideband, Technical Digest Series (CD), 2008, pp. 139-142.
  8. R. Llorente, M. Morant, J. Puche, J. Romme, and T. Alves, "Sensing ultra-low-power radio signals by photonic analog-to-digital conversion," in European Conference on Optical Communications, Technical Digest Series (CD), 2009, paper 10.5.3.
  9. R. Llorente, M. Morant, N. Amiot, and B. Uguen, "Localisation of ultra-wide band radio signals by time-multiplexed photonic analog-to-digital processing," in European Conference on Optical Communications, Technical Digest Series (CD), 2010, paper 6.19.
    [CrossRef]
  10. G. Agrawal, Lightwave Technology-Telecommunication Systems, (John Wiley & Sons, New Jersey, 2005).
    [CrossRef]
  11. J. Rebola, and A. Cartaxo, "Gaussian approach for performance evaluation of optically preamplified receivers with arbitrary optical and electrical filters," IEE Proc., Optoelectron. 148, 135-142 (2001).
    [CrossRef]
  12. http://www.ict-ucells.org/
  13. High Rate UltraWideband PHY and MAC Standard, 2nd ed. Geneve, Switzerland: ECMA Int. (2007).

2007 (1)

J. Stigwall, and S. Galt, "Signal reconstruction by phase retrieval and optical backpropagation in phase-diverse photonic time-stretched systems," J. Lightwave Technol. 25, 3017 (2007).
[CrossRef]

2003 (1)

Y. Han, and B. Jalali, "Photonic time-stretched analogue-to-digital converter: fundamental concepts and practical considerations," J. Lightwave Technol. 21, 3085-3103 (2003).
[CrossRef]

2001 (1)

J. Rebola, and A. Cartaxo, "Gaussian approach for performance evaluation of optically preamplified receivers with arbitrary optical and electrical filters," IEE Proc., Optoelectron. 148, 135-142 (2001).
[CrossRef]

1999 (1)

T. Clark, J. Kang, and R. Esman, "Performance of a time- and wavelength-interleaved photonic sampler for analog-digital conversion," IEEE Photon. Technol. Lett. 11, 1168-1170 (1999).
[CrossRef]

1998 (1)

F. Coppinger, A. Bhushan, and B. Jalali, "Time magnification of electrical signals using chirped optical pulses," Electron. Lett. 34, 399-400 (1998).
[CrossRef]

Bhushan, A.

F. Coppinger, A. Bhushan, and B. Jalali, "Time magnification of electrical signals using chirped optical pulses," Electron. Lett. 34, 399-400 (1998).
[CrossRef]

Cartaxo, A.

J. Rebola, and A. Cartaxo, "Gaussian approach for performance evaluation of optically preamplified receivers with arbitrary optical and electrical filters," IEE Proc., Optoelectron. 148, 135-142 (2001).
[CrossRef]

Clark, T.

T. Clark, J. Kang, and R. Esman, "Performance of a time- and wavelength-interleaved photonic sampler for analog-digital conversion," IEEE Photon. Technol. Lett. 11, 1168-1170 (1999).
[CrossRef]

Coppinger, F.

F. Coppinger, A. Bhushan, and B. Jalali, "Time magnification of electrical signals using chirped optical pulses," Electron. Lett. 34, 399-400 (1998).
[CrossRef]

Esman, R.

T. Clark, J. Kang, and R. Esman, "Performance of a time- and wavelength-interleaved photonic sampler for analog-digital conversion," IEEE Photon. Technol. Lett. 11, 1168-1170 (1999).
[CrossRef]

Galt, S.

J. Stigwall, and S. Galt, "Signal reconstruction by phase retrieval and optical backpropagation in phase-diverse photonic time-stretched systems," J. Lightwave Technol. 25, 3017 (2007).
[CrossRef]

Han, Y.

Y. Han, and B. Jalali, "Photonic time-stretched analogue-to-digital converter: fundamental concepts and practical considerations," J. Lightwave Technol. 21, 3085-3103 (2003).
[CrossRef]

Jalali, B.

Y. Han, and B. Jalali, "Photonic time-stretched analogue-to-digital converter: fundamental concepts and practical considerations," J. Lightwave Technol. 21, 3085-3103 (2003).
[CrossRef]

F. Coppinger, A. Bhushan, and B. Jalali, "Time magnification of electrical signals using chirped optical pulses," Electron. Lett. 34, 399-400 (1998).
[CrossRef]

Kang, J.

T. Clark, J. Kang, and R. Esman, "Performance of a time- and wavelength-interleaved photonic sampler for analog-digital conversion," IEEE Photon. Technol. Lett. 11, 1168-1170 (1999).
[CrossRef]

Rebola, J.

J. Rebola, and A. Cartaxo, "Gaussian approach for performance evaluation of optically preamplified receivers with arbitrary optical and electrical filters," IEE Proc., Optoelectron. 148, 135-142 (2001).
[CrossRef]

Stigwall, J.

J. Stigwall, and S. Galt, "Signal reconstruction by phase retrieval and optical backpropagation in phase-diverse photonic time-stretched systems," J. Lightwave Technol. 25, 3017 (2007).
[CrossRef]

Electron. Lett. (1)

F. Coppinger, A. Bhushan, and B. Jalali, "Time magnification of electrical signals using chirped optical pulses," Electron. Lett. 34, 399-400 (1998).
[CrossRef]

IEE Proc., Optoelectron. (1)

J. Rebola, and A. Cartaxo, "Gaussian approach for performance evaluation of optically preamplified receivers with arbitrary optical and electrical filters," IEE Proc., Optoelectron. 148, 135-142 (2001).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

T. Clark, J. Kang, and R. Esman, "Performance of a time- and wavelength-interleaved photonic sampler for analog-digital conversion," IEEE Photon. Technol. Lett. 11, 1168-1170 (1999).
[CrossRef]

J. Lightwave Technol. (2)

J. Stigwall, and S. Galt, "Signal reconstruction by phase retrieval and optical backpropagation in phase-diverse photonic time-stretched systems," J. Lightwave Technol. 25, 3017 (2007).
[CrossRef]

Y. Han, and B. Jalali, "Photonic time-stretched analogue-to-digital converter: fundamental concepts and practical considerations," J. Lightwave Technol. 21, 3085-3103 (2003).
[CrossRef]

Other (8)

L. Du, B. Schmidt, and A. Lowery, "Efficient digital backpropagation for PDM-CO-OFDM optical transmission systems," in Optical Fibre Communication Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2010), paper OTuE2.

http://www.ict-ucells.org/

High Rate UltraWideband PHY and MAC Standard, 2nd ed. Geneve, Switzerland: ECMA Int. (2007).

G. Valley, "Photonic analog-to-digital converters: a tutorial," in Optical Fibre Communication Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2010), paper OMI1.

R. Llorente, A. Cartaxo, B. Uguen, J. Duplicy, J. Romme, J. Puche, D. Schmertz, Y. Lostanlen, R. Banales, and J. Marti, "Management of UWB picocell clusters: UCELLS project approach," in International Conference on Ultra-Wideband, Technical Digest Series (CD), 2008, pp. 139-142.

R. Llorente, M. Morant, J. Puche, J. Romme, and T. Alves, "Sensing ultra-low-power radio signals by photonic analog-to-digital conversion," in European Conference on Optical Communications, Technical Digest Series (CD), 2009, paper 10.5.3.

R. Llorente, M. Morant, N. Amiot, and B. Uguen, "Localisation of ultra-wide band radio signals by time-multiplexed photonic analog-to-digital processing," in European Conference on Optical Communications, Technical Digest Series (CD), 2010, paper 6.19.
[CrossRef]

G. Agrawal, Lightwave Technology-Telecommunication Systems, (John Wiley & Sons, New Jersey, 2005).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Block diagram of the TS Ph-ADC system.

Fig. 2
Fig. 2

Signal waveform at different points of the TS Ph-ADC system: a) at the output of the optical source, b) zoom of the signal presented in a), c) one pulse at the input of the EOM, d) applied to the EOM of sensor 1 overlapped with the optical pulses arriving at the EOM input, e) zoom of the signal presented in d) and f) after the BPF of the electrical receiver.

Fig. 3
Fig. 3

Spectra of the signal at different points of the TS Ph-ADC system: a) at the input of the EOM of sensor 1, b) at the PIN output and c) after the BPF of the electrical receiver.

Fig. 4
Fig. 4

Variance at the output of the Ph-ADC system considering: (a) Ge=40 dB, Go=30 dB, Gr=50 dB, (b) Ge=20 dB, Go=40 dB, Gr=50 dB, and (c) Ge=20 dB, Go=20 dB, Gr=70 dB.

Fig. 5
Fig. 5

Mean power at the Ph-ADC output as a function of the number of periods considered. Ge=40 dB, Go=30 dB, Gr=50 dB.

Fig. 6
Fig. 6

Mean power and SNR at the Ph-ADC output along the signal period. In (a), (c) and (e), results obtained by MC (marks) and noiseless simulation (lines). In (b), (d) and (f), results obtained by MC (marks) and Eq. 13 (lines). (a) and (b) Ge=40 dB, Go=30 dB, Gr=50 dB; (c) and (d) Ge=20 dB, Go=40 dB, Gr=50 dB, (e) and (f) Ge=20 dB, Go=20 dB, Gr=70 dB.

Fig. 7
Fig. 7

Mean power along the signal period for a) Ge=70 dB, Go=20 dB, Gr=30 dB and the receiver BPF described in section 6 and b) Ge=40 dB, Go=30 dB, Gr=50 dB, and a receiver BPF modeled by a 6th order filter with −3 dB passband between 932 MHz and 1.4 GHz. Results obtained by numerical simulation (lines) and from Eq. (15) (marks).

Equations (26)

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v ( k ) ( t ) = 1 I E O M ( k ) { b ( k ) + m ( k ) [ v R F ( k ) ( t ) + n e ( k ) ( t ) ] }
e P I N ( t ) = e m u x ( t ) * h 2 ( t ) = k = 1 N { b ( k ) I E O M ( k ) e E O M , i ( k ) ( t T ( k ) ) * h 2 ( t ) + + m ( k ) I E O M ( k ) [ e E O M , i ( k ) ( t T ( k ) ) ( v R F ( k ) ( t T ( k ) ) + n e ( k ) ( t T ( k ) ) ) ] * h 2 ( t ) }
g c ( k ) ( t ) = e E O M , i ( k ) ( t T ( k ) ) * h 2 ( t )
g R F , c ( k ) ( t ) = { e E O M , i ( k ) ( t T ( k ) ) [ v R F ( k ) ( t T ( k ) ) + n e ( k ) ( t T ( k ) ) ] } * h 2 ( t )
i P I N ( t ) = R λ | e P I N ( t ) | 2 = R λ | k = 1 N { b ( k ) I E O M ( k ) g c ( k ) ( t ) + m ( k ) I E O M ( k ) g R F , c ( k ) ( t ) } | 2 = = R λ k = 1 N 1 I E O M ( k ) { ( b ( k ) ) 2 | g c ( k ) ( t ) | 2 + 2 b ( k ) m ( k ) [ g c ( k ) ( t ) g R F , c ( k ) * ( t ) ] + ( m ( k ) ) 2 | g R F , c ( k ) ( t ) | 2 }
i o ( t ) = i P I N ( t ) * h r ( t ) = R λ + { k = 1 N 1 I E O M ( k ) { ( b ( k ) ) 2 | g c ( k ) ( τ ) | 2 + 2 b ( k ) m ( k ) × × [ g c ( k ) ( τ ) g R F , c ( k ) * ( τ ) ] + ( m ( k ) ) 2 | g R F , c ( k ) ( τ ) | 2 } } h r ( t τ ) d τ
σ n e 2 ( t ) = R L { E [ i o 2 ( t ) ] { E [ i o ( t ) ] } 2 }
σ n e 2 ( t ) 2 R L R λ 2 k = 1 N ( b ( k ) m ( k ) I E O M ( k ) ) 2 { + S e ( k ) ( f ) [ w ( k ) ( t , f ) w ( k ) ( t , f ) + | w ( k ) ( t , f ) | 2 ] d f }
σ A S E 2 ( t ) = 2 R L R λ 2 S A S E + | [ e P I N ( χ ) h r ( t χ ) ] * h o ( χ ) | 2 d χ + R L p R λ 2 S A S E 2 + | H r ( f ) | 2 × × [ | H o ( f ) | 2 * | H o ( f ) | 2 ] d f
σ s A S E 2 ( t ) 2 R L R λ 2 S A S E | e P I N ( t ) | 2 | H o ( 0 ) | 2 + | H r ( f ) | 2 d f
σ n r 2 = R L S r + | H B P F , r ( f ) | 2 d f
σ t 2 ( t ) = σ n e 2 ( t ) + σ A S E 2 ( t ) + σ n r 2
S N R ( t ) = p m ( t ) σ t , m 2 ( t ) = 1 N p k = 0 N p 1 p k ( t ) 1 N p k = 0 N p 1 σ k 2 ( t )
{ p k ( t ) = R L | i o ( t ) | 2 for t [ k T p , ( k + 1 ) T p [ σ k 2 ( t ) = σ n e 2 ( t ) + σ A S E 2 ( t ) + σ n r 2 for t [ k T p , ( k + 1 ) T p [
p m , s ( t ) 4 R L 2 ( R λ m g r b ) 2 P P I N 2 ( t ) p P F
p P F = i = 1 N U W B P R F , i cos 2 ( π L 2 D 2 λ f R F , i 2 ν M )
σ n e 2 ( t ) 4 R L M ( R λ m b ) 2 P P I N 2 ( t ) + S e ( M f ) cos 2 ( π L 2 D 2 λ f 2 ν M ) | H r ( f ) | 2 d f
E [ i o ( t ) ] = R λ I E O M + { b 2 | g c ( τ ) | 2 + b m g c ( τ ) E [ g R F , c * ( τ ) ] + b m E [ g R F , c ( τ ) ] g c * ( τ ) + + m 2 E [ | g R F , c ( τ ) | 2 ] } h r ( t τ ) d τ
σ n e 2 ( t ) = R L R λ 2 I E O M 2 + + { b 2 m 2 [ g c ( τ 1 ) g c ( τ 2 ) E [ n * ( τ 1 ) n * ( τ 2 ) ] + g c ( τ 1 ) g c * ( τ 2 ) E [ n * ( τ 1 ) n ( τ 2 ) ] + + g c * ( τ 1 ) g c ( τ 2 ) E [ n ( τ 1 ) n * ( τ 2 ) ] + g c * ( τ 1 ) g c * ( τ 2 ) E [ n ( τ 1 ) n ( τ 2 ) ] ] + + b m 3 { g c ( τ 1 ) [ E [ n * ( τ 1 ) s ( τ 2 ) n * ( τ 2 ) ] + E [ n * ( τ 1 ) n ( τ 2 ) s * ( τ 2 ) ] ] + + g c * ( τ 1 ) [ E [ n ( τ 1 ) s ( τ 2 ) n * ( τ 2 ) ] + E [ n ( τ 1 ) n ( τ 2 ) s * ( τ 2 ) ] ] + g c ( τ 2 ) [ E [ s ( τ 1 ) n * ( τ 1 ) n * ( τ 2 ) ] + + E [ n ( τ 1 ) s * ( τ 1 ) n * ( τ 2 ) ] + g c * ( τ 2 ) [ E [ s ( τ 1 ) n * ( τ 1 ) n ( τ 2 ) ] + E [ n ( τ 1 ) s * ( τ 1 ) n ( τ 2 ) ] ] } + + m 4 [ E [ s ( τ 1 ) n * ( τ 1 ) s ( τ 2 ) n * ( τ 2 ) ] + E [ s ( τ 1 ) n * ( τ 1 ) n ( τ 2 ) s * ( τ 2 ) ] + E [ n ( τ 1 ) s * ( τ 1 ) s ( τ 2 ) n * ( τ 2 ) ] + + E [ n ( τ 1 ) s * ( τ 1 ) n ( τ 2 ) s * ( τ 2 ) ] + E [ n ( τ 1 ) n * ( τ 1 ) n ( τ 2 ) n * ( τ 2 ) ] ] } h r ( t τ 1 ) h r ( t τ 2 ) d τ 1 d τ 2
σ n e 2 ( t ) 2 R L R λ 2 b 2 m 2 I E O M 2 + + [ { g c ( τ 1 ) g c ( τ 2 ) E [ n * ( τ 1 ) n * ( τ 2 ) ] } + { g c ( τ 1 ) g c * ( τ 2 ) × E [ n * ( τ 1 ) n ( τ 2 ) ] } ] h r ( t τ 1 ) h r ( t τ 2 ) d τ 1 d τ 2
σ n e , 1 2 ( t ) = 2 R L R λ 2 b 2 m 2 I E O M 2 + + { g c ( τ 1 ) g c ( τ 2 ) E [ n * ( τ 1 ) n * ( τ 2 ) ] } h r ( t τ 1 ) h r ( t τ 2 ) d τ 1 d τ 2 = = 2 R L R λ 2 b 2 m 2 I E O M 2 { + + g c ( τ 1 ) g c ( τ 2 ) E [ n * ( τ 1 ) n * ( τ 2 ) ] h r ( t τ 1 ) h r ( t τ 2 ) d τ 1 d τ 2 }
σ n e , 1 2 ( t ) = 2 R L R λ 2 b 2 m 2 I E O M 2 { + + + + g c ( τ 1 ) g c ( τ 2 ) h 2 * ( τ 1 τ 3 ) h 2 * ( τ 2 τ 4 ) h r ( t τ 1 ) × × h r ( t τ 2 ) e E O M , i * ( τ 3 ) e E O M , i * ( τ 4 ) R e ( τ 3 τ 4 ) d τ 1 d τ 2 τ 3 d τ 4 }
σ n e , 1 2 ( t ) = 2 R L R λ 2 b 2 m 2 I E O M 2 { + S e ( f ) w ( t , f ) w ( t , f ) d f }
σ n e , 2 2 ( t ) = 2 R L R λ 2 b 2 m 2 I E O M 2 { + S e ( f ) | w ( t , f ) | 2 d f }
σ n e 2 ( t ) 2 R L R λ 2 b 2 m 2 I E O M 2 { + S e ( f ) w ( t , f ) w ( t , f ) d f + + S e ( f ) | w ( t , f ) | 2 d f }
( σ n e ( k ) ) 2 ( t ) 2 R L ( R λ b ( k ) m ( k ) I E O M ( k ) ) 2 { + S e ( k ) ( f ) [ w ( k ) ( t , f ) w ( k ) ( t , f ) + | w ( k ) ( t , f ) | 2 ] d f }

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