Abstract

We propose a method for covert fiber-optic communication in both frequency and time domains. The power spectral density of the pulse sequence bearing the information is spread in the frequency domain below the noise level by means of sampling. In addition, temporal phase encryption prevents the coherent addition of the various pulses in the frequency domain, further reducing the signal power spectral density. Thus, there is no need to transmit the signal within the bandwidth of a public user in order to spectrally conceal the signal. Temporal spreading of the pulse sequence is achieved by spectral phase encoding, resulting in a stealthy temporal and spectral transmission.

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References

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  1. A. J. Viterbi, “Spread spectrum communications – myths and realities,” IEEE Commun. Mag. 17(3), 11–18 (1979).
    [Crossref]
  2. B. B. Wu and E. E. Narimanov, “A method for secure communications over a public fiber-optical network,” Opt. Express 14(9), 3738–3751 (2006).
    [Crossref] [PubMed]
  3. K. Kravtsov, B. Wu, I. Glysk, P. R. Prucnal, and E. Narimanov, “Stealth transmission over a WDM network with detection based on an all-optical thresholder,” in Proceedings of IEEE Conference on Lasers and Electro-Optics (IEEE, 2007), pp. 480–481.
  4. B. Wu, A. Agarwal, I. Glesk, E. Narimanov, S. Etemad, and P. R. Prucnal, “Steganographic fiber-optic transmission using coherent spectral-phase-encoded optical CDMA,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest (CD) (Optical Society of America, 2008), paper CFF5, http://www.opticsinfobase.org/abstract.cfm?URI=CLEO-2008-CFF5 .
  5. Z. Wang, M. P. Fok, L. Xu, J. Chang, and P. R. Prucnal, “Improving the privacy of optical steganography with temporal phase masks,” Opt. Express 18(6), 6079–6088 (2010).
    [Crossref] [PubMed]
  6. Z. Gao, X. Wang, N. Kataoka, and N. Wada, “Stealth transmission of time-domain spectral phase encoded OCDMA signal over WDM network,” IEEE Photon. Technol. Lett. 22(13), 993–995 (2010).
    [Crossref]
  7. D. Sinefeld, C. R. Doerr, and D. M. Marom, “Photonic spectral processor employing two-dimensional WDM channel separation and a phase LCoS modulator,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper OMP5, http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2010-OMP5 .
  8. D. Sinefeld and D. M. Marom, “Hybrid guided-wave/free-space optics photonic spectral processor based on LCoS phase only modulator,” IEEE Photon. Technol. Lett. 22(7), 510–512 (2010).
    [Crossref]
  9. X. Wang, “Novel time domain spectral phase encoding/decoding technique for OCDMA application,” in International Conference on Transparent Optical Networks (IEEE, S. Miguel (Portugal), 2009), paper Th.A3.4.
  10. X. Wang and N. Wada, “Spectral phase encoding of ultra-short optical pulse in time domain for OCDMA application,” Opt. Express 15(12), 7319–7326 (2007).
    [Crossref] [PubMed]
  11. D. Miyamoto and H. Tsuda, “Spectral phase encoder employing an arrayed-waveguide grating and phase-shifting structure,” IEEE Photon. Technol. Lett. 19(17), 1289–1291 (2007).
    [Crossref]
  12. E. Ip and J. M. Kahn, “Digital equalization of chromatic dispersion and polarization mode dispersion,” J. Lightwave Technol. 25(8), 2033–2043 (2007).
    [Crossref]
  13. J. G. Proakis and M. Salehi, Communication Systems Engineering (Prentice Hall, 1994), Chap. 8.
  14. Y. Frauel, A. Castro, T. J. Naughton, and B. Javidi, “Resistance of the double random phase encryption against various attacks,” Opt. Express 15(16), 10253–10265 (2007).
    [Crossref] [PubMed]

2010 (3)

Z. Wang, M. P. Fok, L. Xu, J. Chang, and P. R. Prucnal, “Improving the privacy of optical steganography with temporal phase masks,” Opt. Express 18(6), 6079–6088 (2010).
[Crossref] [PubMed]

Z. Gao, X. Wang, N. Kataoka, and N. Wada, “Stealth transmission of time-domain spectral phase encoded OCDMA signal over WDM network,” IEEE Photon. Technol. Lett. 22(13), 993–995 (2010).
[Crossref]

D. Sinefeld and D. M. Marom, “Hybrid guided-wave/free-space optics photonic spectral processor based on LCoS phase only modulator,” IEEE Photon. Technol. Lett. 22(7), 510–512 (2010).
[Crossref]

2007 (4)

2006 (1)

1979 (1)

A. J. Viterbi, “Spread spectrum communications – myths and realities,” IEEE Commun. Mag. 17(3), 11–18 (1979).
[Crossref]

Castro, A.

Chang, J.

Fok, M. P.

Frauel, Y.

Gao, Z.

Z. Gao, X. Wang, N. Kataoka, and N. Wada, “Stealth transmission of time-domain spectral phase encoded OCDMA signal over WDM network,” IEEE Photon. Technol. Lett. 22(13), 993–995 (2010).
[Crossref]

Ip, E.

Javidi, B.

Kahn, J. M.

Kataoka, N.

Z. Gao, X. Wang, N. Kataoka, and N. Wada, “Stealth transmission of time-domain spectral phase encoded OCDMA signal over WDM network,” IEEE Photon. Technol. Lett. 22(13), 993–995 (2010).
[Crossref]

Marom, D. M.

D. Sinefeld and D. M. Marom, “Hybrid guided-wave/free-space optics photonic spectral processor based on LCoS phase only modulator,” IEEE Photon. Technol. Lett. 22(7), 510–512 (2010).
[Crossref]

Miyamoto, D.

D. Miyamoto and H. Tsuda, “Spectral phase encoder employing an arrayed-waveguide grating and phase-shifting structure,” IEEE Photon. Technol. Lett. 19(17), 1289–1291 (2007).
[Crossref]

Narimanov, E. E.

Naughton, T. J.

Prucnal, P. R.

Sinefeld, D.

D. Sinefeld and D. M. Marom, “Hybrid guided-wave/free-space optics photonic spectral processor based on LCoS phase only modulator,” IEEE Photon. Technol. Lett. 22(7), 510–512 (2010).
[Crossref]

Tsuda, H.

D. Miyamoto and H. Tsuda, “Spectral phase encoder employing an arrayed-waveguide grating and phase-shifting structure,” IEEE Photon. Technol. Lett. 19(17), 1289–1291 (2007).
[Crossref]

Viterbi, A. J.

A. J. Viterbi, “Spread spectrum communications – myths and realities,” IEEE Commun. Mag. 17(3), 11–18 (1979).
[Crossref]

Wada, N.

Z. Gao, X. Wang, N. Kataoka, and N. Wada, “Stealth transmission of time-domain spectral phase encoded OCDMA signal over WDM network,” IEEE Photon. Technol. Lett. 22(13), 993–995 (2010).
[Crossref]

X. Wang and N. Wada, “Spectral phase encoding of ultra-short optical pulse in time domain for OCDMA application,” Opt. Express 15(12), 7319–7326 (2007).
[Crossref] [PubMed]

Wang, X.

Z. Gao, X. Wang, N. Kataoka, and N. Wada, “Stealth transmission of time-domain spectral phase encoded OCDMA signal over WDM network,” IEEE Photon. Technol. Lett. 22(13), 993–995 (2010).
[Crossref]

X. Wang and N. Wada, “Spectral phase encoding of ultra-short optical pulse in time domain for OCDMA application,” Opt. Express 15(12), 7319–7326 (2007).
[Crossref] [PubMed]

Wang, Z.

Wu, B. B.

Xu, L.

IEEE Commun. Mag. (1)

A. J. Viterbi, “Spread spectrum communications – myths and realities,” IEEE Commun. Mag. 17(3), 11–18 (1979).
[Crossref]

IEEE Photon. Technol. Lett. (3)

Z. Gao, X. Wang, N. Kataoka, and N. Wada, “Stealth transmission of time-domain spectral phase encoded OCDMA signal over WDM network,” IEEE Photon. Technol. Lett. 22(13), 993–995 (2010).
[Crossref]

D. Sinefeld and D. M. Marom, “Hybrid guided-wave/free-space optics photonic spectral processor based on LCoS phase only modulator,” IEEE Photon. Technol. Lett. 22(7), 510–512 (2010).
[Crossref]

D. Miyamoto and H. Tsuda, “Spectral phase encoder employing an arrayed-waveguide grating and phase-shifting structure,” IEEE Photon. Technol. Lett. 19(17), 1289–1291 (2007).
[Crossref]

J. Lightwave Technol. (1)

Opt. Express (4)

Other (5)

K. Kravtsov, B. Wu, I. Glysk, P. R. Prucnal, and E. Narimanov, “Stealth transmission over a WDM network with detection based on an all-optical thresholder,” in Proceedings of IEEE Conference on Lasers and Electro-Optics (IEEE, 2007), pp. 480–481.

B. Wu, A. Agarwal, I. Glesk, E. Narimanov, S. Etemad, and P. R. Prucnal, “Steganographic fiber-optic transmission using coherent spectral-phase-encoded optical CDMA,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest (CD) (Optical Society of America, 2008), paper CFF5, http://www.opticsinfobase.org/abstract.cfm?URI=CLEO-2008-CFF5 .

X. Wang, “Novel time domain spectral phase encoding/decoding technique for OCDMA application,” in International Conference on Transparent Optical Networks (IEEE, S. Miguel (Portugal), 2009), paper Th.A3.4.

D. Sinefeld, C. R. Doerr, and D. M. Marom, “Photonic spectral processor employing two-dimensional WDM channel separation and a phase LCoS modulator,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper OMP5, http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2010-OMP5 .

J. G. Proakis and M. Salehi, Communication Systems Engineering (Prentice Hall, 1994), Chap. 8.

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Figures (5)

Fig. 1
Fig. 1

Digital covert communication system. TPE-Temporal Phase Encoder, FFT- Fast Fourier Transform, SPE-Spectral Phase Encoder, IFFT-Inverse Fast Fourier Transform, D/A-Digital to Analog converter, Mod.-Modulator, EDFA – Erbium Doped Fiber Amplifier, AWGN-Additive White Gaussian Noise, SPD-Spectral Phase Decoder, A/D-Analog to Digital converter, MF-Matched Filter, TPD-Temporal Phase Decoder.

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Fig. 2
Fig. 2

Proposed covert communication system. Mod.-Modulator, TPE-Temporal Phase Encoder, SPE-Spectral Phase Encoder, EDFA-Erbium Doped Fiber Amplifier, AWGN-Additive White Gaussian Noise, SPD-Spectral Phase Decoder, MF-Matched Filter, TPD-Temporal Phase Decoder.

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Fig. 3
Fig. 3

SNR after decoding.

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Fig. 4
Fig. 4

BER after decoding.

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Fig. 5
Fig. 5

Decoded signal, authorized user and eavesdropper. (a) Original noiseless pulse sequence and authorized user noisy decoded pulse sequence. (b) Original noiseless pulse sequence and eavesdropper noisy decoded pulse sequence. (c) Authorized user pulse sequence and noise power spectral density. (d) Eavesdropper pulse sequence and noise power spectral density.

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Equations (57)

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s( t )= ∑ n=1 N a n p( t−nΔt ) e j2π f c t =b( t ) e j2π f c t
b( t )= ∑ n=1 N a n p( t−nΔt )
ρ( t )= ∑ n=1 N Φ n rect( t−nΔt Δt )
s 1 ( t )=s( t ) e jρ( t ) = ∑ n=1 N a n e j Φ n p( t−nΔt ) e j2π f c t = b 1 ( t ) e j2π f c t
b 1 ( t )= ∑ n=1 N a n e j Φ n p( t−nΔt )
S 2 ( f )= 1 M ∑ m=−( M−1 )/2 ( M−1 )/2 S 1 ( f−mΔf ) = 1 M ∑ m=−( M−1 )/2 ( M−1 )/2 B 1 ( f−mΔf− f c )
ψ( f )= ∑ k=−( K−1 )/2 ( K−1 )/2 φ k rect( f−kδf− f c δf )
rect( f )={ 1       |f|≤1/2 0     ​ |f| >1/2
S 3 ( f )= S 2 ( f ) e jψ( f ) = e jψ( f ) M ∑ m=−( M−1 )/2 ( M−1 )/2 S 1 ( f−mΔf )
u( f )={ 1 f≥0 0 f<0
s 4 ( t )= M s 3 ( t )+ n A ( t )
S 4 ( f )= M S 3 ( f )+2u( f )N( f )= e jψ( f ) ∑ m=−( M−1 )/2 ( M−1 )/2 S 1 ( f−mΔf ) +2u( f )N( f )
S 5 ( f )= S 4 ( f )rect( f− f c BW ) e −jψ( f ) = ∑ m=−( M−1 )/2 ( M−1 )/2 S 1 ( f−mΔf ) +2N( f )rect( f− f c BW ) e −jψ( f )
S 6 ( f )= 1 2 S 5 ( f+ f c )= 1 2 [ ∑ m=−( M−1 )/2 ( M−1 )/2 B 1 ( f−mΔf ) +2N( f+ f c )rect( f BW ) e −jψ( f+ f c ) ]
N d ( f )=N( f+ f c )
ψ d ( f )=ψ( f+ f c )
S 6 ( f )= S 5 ( f+ f c )= 1 2 [ ∑ m=−( M−1 )/2 ( M−1 )/2 B 1 ( f−mΔf ) +2 N d ( f )rect( f BW ) e −j ψ d ( f ) ]
S 7 ( f )= S 6 ( f )* 1 M ∑ l=−( M−1 )/2 ( M−1 )/2 δ( f−lΔf ) =               = 1 2 M ∑ l=−( M−1 )/2 ( M−1 )/2 ∑ m=−( M−1 )/2 ( M−1 )/2 B 1 ( f−mΔf−lΔf ) +               + 1 2 M ∑ l=−( M−1 )/2 ( M−1 )/2 2 N d ( f−lΔf )rect( f−lΔf BW ) e −j ψ d ( f−lΔf )
S 8 ( f )= S 7 ( f ) P * ( f )=               = P * ( f ) 2 M ∑ l=−( M−1 )/2 ( M−1 )/2 ∑ m=−( M−1 )/2 ( M−1 )/2 B 1 ( f−mΔf−lΔf )  +              + P * ( f ) 2 M ∑ l=−( M−1 )/2 ( M−1 )/2 2 N d ( f−lΔf )rect( f−lΔf BW ) e −j ψ d ( f−lΔf )
S 8 ( f )= P * ( f ) 2 M   ∑ m=−( M−1 )/2 ( M−1 )/2 B 1 ( f ) +                              + P * ( f ) 2 M ∑ m=−( M−1 )/2 ( M−1 )/2 2 N d ( f−mΔf )rect( f−mΔf BW ) e −j ψ d ( f−mΔf )
S 8 ( f )= P * ( f ) 2 M M B 1 ( f )+                  + P * ( f ) 2 M ∑ m=−( M−1 )/2 ( M−1 )/2 2 N d ( f−mΔf )rect( f−mΔf BW ) e −j ψ d ( f−mΔf )
s 9 ( t )= e −jρ( t ) ∫ −∞ ∞ S 8 ( f ) e j2πft df=             = e −jρ( t ) ∫ −∞ ∞ P * ( f ) 2   M B 1 ( f ) e j2πft df+   e −jρ( t ) ∫ −∞ ∞ P * ( f ) 2 M ⋅             ⋅ ∑ m=−( M−1 )/2 ( M−1 )/2 2 N d ( f−mΔf )rect( f−mΔf BW ) e −j ψ d ( f−mΔf ) e j2πft df 
s ˜ A ( t )= e −jρ( t ) ∫ −∞ ∞ P * ( f ) 2   M B 1 ( f ) e j2πft df
n ˜ A ( t )= e −jρ( t ) ∫ −∞ ∞ P * ( f ) 2 M ⋅ ∑ m=−( M−1 )/2 ( M−1 )/2 2 N d ( f−mΔf )rect( f−mΔf BW ) e −j ψ d ( f−mΔf ) e j2πft df
s ˜ A ( t )= e −jρ( t ) ∫ −∞ ∞ P * ( f ) 2   M B 1 ( f ) e j2πft df = M 2 e −jρ( t ) ∫ −∞ ∞ p * ( τ−t ) ∑ n=1 N a n e j Φ n p( τ−nΔt ) dτ
s ˜ A ( nΔt )= M 2 e −jρ( t ) ∫ −∞ ∞ p * ( τ−nΔt ) ∑ k=1 N a k e j Φ k p( τ−kΔt ) dτ =                  = M 2 ∑ l=1 N e −j Φ l rect( nΔt−lΔt Δt ) ∫ −∞ ∞ p * ( τ−nΔt ) ∑ k=1 N a k e j Φ k p( τ−kΔt ) dτ =                  = M 2 a n E p
E p ≡ ∫ −∞ ∞ | p( t ) | 2 dt
s 10 ( t )={ s 9 ( nΔt )= s ˜ A ( nΔt )+ n ˜ A ( nΔt ) t=nΔt 0 otherwise
SNR= ( s ˜ ( nΔt ) ) 2 E[ ( n ˜ ( nΔt ) ) 2 ]
s ˜ ( t )=Re{ s ˜ A ( t ) }
n ˜ ( t )=Re{ n ˜ A ( t ) }
s ˜ ( nΔt )=Re[ s ˜ A ( nΔt ) ]= M 2 a n E p
s ˜ ( nΔt )= M 2 E p
( s ˜ ( nΔt ) ) 2 = ( M 2 E p ) 2 = M 4 E p 2
E[ ( n ˜ ( t ) ) 2 ]=E[ ( Re{ n ˜ A ( t ) } ) 2 ]=                         =E[ ( 1 2 { n ˜ A ( t )+ n ˜ A * ( t ) } ) 2 ]=                         = 1 4 E[ ( n ˜ A ( t ) ) 2 ]+ 1 2 E[ n ˜ A ( t ) n ˜ A * ( t ) ]+ 1 4 E[ ( n ˜ A * ( t ) ) 2 ]
E[ ( n ˜ ( t ) ) 2 ]= 1 2 E[ n ˜ A ( t ) n ˜ A * ( t ) ]= σ 2 2M ∫ −∞ ∞ ∑ m=−( M−1 )/2 ( M−1 )/2 | P( f ) | 2  df= σ 2 2 E p
SNR= | s ˜ ( nΔt ) | 2 E[ ( n ˜ ( nΔt ) ) 2 ] = M 4 E p 2 σ 2 2 E p =M E p 2 σ 2
E[ n ˜ ( t ) ]= 1 2 E[ n ˜ A ( t )+ n ˜ A * ( t ) ]=0
BER= 1 2 erfc( SNR 2 2 )
BER= 1 2 erfc( SNR 2 2 )= 1 2 erfc( 1 2 2 M E p 2 σ 2 )= 1 2 erfc( 1 4 M E p σ 2 )
G v ( f )= 1 T ˜ | V( f ) | 2
S 4 ( f )= e jψ( f ) ∑ m=−( M−1 )/2 ( M−1 )/2 S 1 ( f−mΔf ) +2u( f )N( f )
S 4 ( f )= e jψ( f ) ∑ m=−( M−1 )/2 ( M−1 )/2 S 1 ( f−mΔf ) +2rect( f− f c BW )N( f )
S 4 ( f )= e jψ( f ) ∑ m=−( M−1 )/2 ( M−1 )/2 S 1 ( f−mΔf ) +               +2rect( f− f c BW ){ N( f )*[ NΔtsinc( f⋅NΔt )exp( −j2πf⋅NΔt/2 ) ] } 
S ⌢ 5 ( f )= 1 2 e jψ( f+ f c ) ∑ m=−( M−1 )/2 ( M−1 )/2 B 1 ( f−mΔf ) +                  +{ rect( f− f c BW )[ N( f )*( NΔtsinc( f⋅NΔt ) e −jπf⋅NΔt ) ] }*δ( f+ f c )
S ⌢ 6 ( f )= S ⌢ 5 ( f )* 1 M ∑ l=−( M−1 )/2 ( M−1 )/2 δ( f−lΔf ) =              = 1 2 M ∑ m=−( M−1 )/2 ( M−1 )/2 ∑ l=−( M−1 )/2 ( M−1 )/2 B 1 ( f−mΔf−lΔf ) e jψ( f+ f c −lΔf ) + NΔt M ∑ l=−( M−1 )/2 ( M−1 )/2 rect( f−lΔf BW ) ⋅                 ⋅ ∫ −∞ ∞ N( f 1 ) sinc( ( f+ f c −lΔf− f 1 )⋅NΔt ) e −jπ( f+ f c −lΔf− f 1 )⋅NΔt d f 1                                                 
S ⌢ 7 ( f )= S ⌢ 6 ( f ) P * ( f )=               = P * ( f ) 2 M ∑ m=−( M−1 )/2 ( M−1 )/2 B 1 ( f ) e jψ( f+ f c −mΔf ) +                  + NΔt P * ( f ) M ∑ l=−( M−1 )/2 ( M−1 )/2 ∫ −∞ ∞ N( f 1 ) sinc( ( f+ f c −lΔf− f 1 )⋅NΔt ) e −jπ( f+ f c −lΔf− f 1 )⋅NΔt d f 1
G s ( f )= 1 NΔt E[ | P * ( f ) 2 M B 1 ( f ) ∑ m=−( M−1 )/2 ( M−1 )/2 e jψ( f+ f c −mΔf ) | 2 ]=                = | P( f ) | 2 4MNΔt | ∑ m=−( M−1 )/2 ( M−1 )/2 e jψ( f+ f c −mΔf ) | 2 ∑ n=1 N ∑ l=1 N E[ a n a l ] e j( Φ n − Φ l ) e j2πf( n−l )Δt =                = | P( f ) | 4 8MNΔt [ ∑ m=−( M−1 )/2 ( M−1 )/2 ∑ l≠m e −j[ ψ( f+ f c −mΔf )−ψ( f+ f c −lΔf ) ] +M ][ ∑ n=1 N ∑ l≠n 1 2 e j( Φ n − Φ l ) e j2πf( n−l )Δt +N ]
G s ( f )≈ 1 8MNΔt | P( f ) | 4 MN= 1 8Δt | P( f ) | 4
G n ( f )= 1 NΔt E( | { rect( f− f c BW )[ N( f )*( NΔtsinc( f⋅NΔt ) e −jπf⋅NΔt ) ] }*δ( f+ f c ) | 2 )=                 = 1 NΔt E [ | NΔt P * ( f ) M ⋅                            ⋅ ∑ l=−( M−1 )/2 ( M−1 )/2 ∫ −∞ ∞ N( f 1 ) sinc( ( f+ f c −lΔf− f 1 )⋅NΔt ) e −jπ( f+ f c −lΔf− f 1 )⋅NΔt d f 1 | 2 ]=                = ( NΔt ) 2 | P( f ) | 2 σ 2 MNΔt ∑ l=−( M−1 )/2 ( M−1 )/2 ∑ m=−( M−1 )/2 ( M−1 )/2 ∫ −∞ ∞ sinc( ( f+ f c −lΔf− f 1 )⋅NΔt ) ⋅                     ⋅sinc( ( f+ f c −mΔf− f 1 )⋅NΔt ) e jπ( l−m )Δf⋅NΔt d f 1
sinc( ( f ˜ −mΔf− f 1 )⋅NΔt )sinc( ( f ˜ −lΔf− f 1 )⋅NΔt )≈sin c 2 [ ( f ˜ −mΔf− f 1 )⋅NΔt ] δ m,l
G n ( f )≈ NΔt | P( f ) | 2 σ 2 M ∑ m=−( M−1 )/2 ( M−1 )/2 1 NΔt = σ 2 | P( f ) | 2
SN R E ( f )= G s ( f ) G n ( f ) ≈ 1 8Δt | P( f ) | 4 σ 2 | P( f ) | 2 = | P( f ) | 2 8 σ 2 Δt
T eav = ( Q f,eav ) N f f SLM
T E = 2 N f / f SLM = 2 125 / 10 6 Hz=1.35⋅ 10 24  years
T E = 2 N f / f SLM = 2 53 / 10 6 Hz=285.6 years
T E = 2 N f / f SLM = 2 30 / 10 6 Hz=3.4⋅ 10 −5  years

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