Abstract

We carry out a comprehensive analysis to examine the performance of our recently proposed correlation-based and pilot-tone-assisted frequency offset compensation method in coherent optical OFDM system. The frequency offset is divided into two parts: fraction part and integer part relative to the channel spacing. Our frequency offset scheme includes the correlation-based Schmidl algorithm for fraction part estimation as well as pilot-tone-assisted method for integer part estimation. In this paper, we analytically derive the error variance of fraction part estimation methods in the presence of laser phase noise using different correlation-based algorithms: Schmidl, Cox and Cyclic Prefix based. This analytical expression is given for the first time in the literature. Furthermore, we give a full derivation for the pilot-tone-assisted integer part estimation method using the OFDM model.

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References

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  1. T. Pollet, M. Van Bladel, and M. Moeneclaey, “BER sensitivity of OFDM systems to carrier frequency offset and wiener phase noise,” IEEE Trans. Commun.43(2), 191–193 (1995).
    [CrossRef]
  2. T. M. Schmidl and D. C. Cox, “Robust frequency and timing synchronization for OFDM,” IEEE Trans. Commun.45(12), 1613–1621 (1997).
    [CrossRef]
  3. P. H. Moose, “A technique for orthogonal frequency division multiplexing frequency offset correction,” IEEE Trans. Commun.42(10), 2908–2914 (1994).
    [CrossRef]
  4. J. van de Beek, M. Sandell, and P. O. Borjesson, “ML estimation of time and frequency offset in OFDM systems,” IEEE Trans. Signal Process.45(7), 1800–1805 (1997).
    [CrossRef]
  5. F. Buchali, R. Dischler, M. Mayrock, X. Xiao, and Y. Tang, “Improved frequency offset correction in coherent optical OFDM systems,” in IEEE Proc. ECOC 2008, paper Mo.4.D.4.
  6. S. Fan, J. Yu, D. Qian, and G.-K. Chang, “A fast and efficient frequency offset correction technique for coherent optical orthogonal frequency division multiplexing,” J. Lightwave Technol.29(13), 1997–2004 (2011).
    [CrossRef]
  7. S. L. Jansen, I. Morita, T. C. W. Schenk, N. Takeda, and H. Tanaka, “Coherent Optical 25.8-Gb/s OFDM Transmission over 4,160-km SSMF,” J. Lightwave Technol.26(1), 6–15 (2008).
    [CrossRef]
  8. S. Cao, S. Zhang, C. Yu, and P.-Y. Kam, “Full-range pilot-assisted frequency offset estimation for OFDM systems,” in Proceedings of OFC/NFOEC 2013, paper JW2A.53.

2011 (1)

2008 (1)

1997 (2)

T. M. Schmidl and D. C. Cox, “Robust frequency and timing synchronization for OFDM,” IEEE Trans. Commun.45(12), 1613–1621 (1997).
[CrossRef]

J. van de Beek, M. Sandell, and P. O. Borjesson, “ML estimation of time and frequency offset in OFDM systems,” IEEE Trans. Signal Process.45(7), 1800–1805 (1997).
[CrossRef]

1995 (1)

T. Pollet, M. Van Bladel, and M. Moeneclaey, “BER sensitivity of OFDM systems to carrier frequency offset and wiener phase noise,” IEEE Trans. Commun.43(2), 191–193 (1995).
[CrossRef]

1994 (1)

P. H. Moose, “A technique for orthogonal frequency division multiplexing frequency offset correction,” IEEE Trans. Commun.42(10), 2908–2914 (1994).
[CrossRef]

Borjesson, P. O.

J. van de Beek, M. Sandell, and P. O. Borjesson, “ML estimation of time and frequency offset in OFDM systems,” IEEE Trans. Signal Process.45(7), 1800–1805 (1997).
[CrossRef]

Chang, G.-K.

Cox, D. C.

T. M. Schmidl and D. C. Cox, “Robust frequency and timing synchronization for OFDM,” IEEE Trans. Commun.45(12), 1613–1621 (1997).
[CrossRef]

Fan, S.

Jansen, S. L.

Moeneclaey, M.

T. Pollet, M. Van Bladel, and M. Moeneclaey, “BER sensitivity of OFDM systems to carrier frequency offset and wiener phase noise,” IEEE Trans. Commun.43(2), 191–193 (1995).
[CrossRef]

Moose, P. H.

P. H. Moose, “A technique for orthogonal frequency division multiplexing frequency offset correction,” IEEE Trans. Commun.42(10), 2908–2914 (1994).
[CrossRef]

Morita, I.

Pollet, T.

T. Pollet, M. Van Bladel, and M. Moeneclaey, “BER sensitivity of OFDM systems to carrier frequency offset and wiener phase noise,” IEEE Trans. Commun.43(2), 191–193 (1995).
[CrossRef]

Qian, D.

Sandell, M.

J. van de Beek, M. Sandell, and P. O. Borjesson, “ML estimation of time and frequency offset in OFDM systems,” IEEE Trans. Signal Process.45(7), 1800–1805 (1997).
[CrossRef]

Schenk, T. C. W.

Schmidl, T. M.

T. M. Schmidl and D. C. Cox, “Robust frequency and timing synchronization for OFDM,” IEEE Trans. Commun.45(12), 1613–1621 (1997).
[CrossRef]

Takeda, N.

Tanaka, H.

Van Bladel, M.

T. Pollet, M. Van Bladel, and M. Moeneclaey, “BER sensitivity of OFDM systems to carrier frequency offset and wiener phase noise,” IEEE Trans. Commun.43(2), 191–193 (1995).
[CrossRef]

van de Beek, J.

J. van de Beek, M. Sandell, and P. O. Borjesson, “ML estimation of time and frequency offset in OFDM systems,” IEEE Trans. Signal Process.45(7), 1800–1805 (1997).
[CrossRef]

Yu, J.

IEEE Trans. Commun. (3)

T. Pollet, M. Van Bladel, and M. Moeneclaey, “BER sensitivity of OFDM systems to carrier frequency offset and wiener phase noise,” IEEE Trans. Commun.43(2), 191–193 (1995).
[CrossRef]

T. M. Schmidl and D. C. Cox, “Robust frequency and timing synchronization for OFDM,” IEEE Trans. Commun.45(12), 1613–1621 (1997).
[CrossRef]

P. H. Moose, “A technique for orthogonal frequency division multiplexing frequency offset correction,” IEEE Trans. Commun.42(10), 2908–2914 (1994).
[CrossRef]

IEEE Trans. Signal Process. (1)

J. van de Beek, M. Sandell, and P. O. Borjesson, “ML estimation of time and frequency offset in OFDM systems,” IEEE Trans. Signal Process.45(7), 1800–1805 (1997).
[CrossRef]

J. Lightwave Technol. (2)

Other (2)

F. Buchali, R. Dischler, M. Mayrock, X. Xiao, and Y. Tang, “Improved frequency offset correction in coherent optical OFDM systems,” in IEEE Proc. ECOC 2008, paper Mo.4.D.4.

S. Cao, S. Zhang, C. Yu, and P.-Y. Kam, “Full-range pilot-assisted frequency offset estimation for OFDM systems,” in Proceedings of OFC/NFOEC 2013, paper JW2A.53.

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Figures (5)

Fig. 1
Fig. 1

The schematic of CO-OFDM system (Mod: modulation, Demod: demodulation, S/P: serial to parallel, P/S: parallel to serial, DAC: digital to analog converter, ADC: analog to digital converter)

Fig. 2
Fig. 2

Analytical and simulation curves of estimation variance versus SNR for v = 0,1,100 kHz, using Schmidl, Moose and CP estimator.

Fig. 3
Fig. 3

(a) Analytical and simulation curves for estimation variance versus laser linewidth (v) at SNR = 15 dB, using Schmidl, Moose and CP estimator; (b) Estimation variance versus relative frequency offset for v = 0, 1, 10, 100 kHz, using Schmidl, Moose and CP estimator.

Fig. 4
Fig. 4

Simulation curves for estimation variance versus SNR under various dispersion values (0, 1700ps/nm, 17000ps/nm) using: (a)Schmidl/Moose; (b) CP.

Fig. 5
Fig. 5

Probability of correct detection versus pilot to average signal power ratio: (a) for different DFT size, SNR, f0, εi and dispersion; (b) for different SNR and laser phase noise.

Equations (18)

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x Ni+n =( 1/N ) k=0 N1 X ki e j2πkn/N ,
y N*i+n = e j2π(N*i+n)ε/N+j ϕ N*i+n l=0 L1 h l x N*i+nl + w N*i+n ,
Y k,i = l=0 N1 Ψ kl,i H l X l,i + W k,i , Ψ m,i = 1 N n=0 N1 e j2π(N*i+n)ε/N+j ϕ N*i+n e j2πmn/N ,
ε ^ Schmidl = { n=0 N-1 y N+n y n * } / 2π , ε ^ Moose = { n=0 N-1 Y k1 Y k0 * } / 2π ,
ε ^ CP = { d=0 D1 n=0 CP1 y (N+CP)*d+n+N y ( N+CP )*d+n * } / 2π .
y n = r n + w n , y N+n = r n e j2πε+j( ϕ N+n - ϕ n ) + w N+n ,
tan[2π( ε ^ - Schmidl ε)]= ( n=0 N1 Im[ y N+n y n * e 2πjε ] ) / ( n=0 N1 Re[ y N+n y n * e 2πjε ] ) ,
ε ^ - Schmidl ε 1 2π ( n=0 N1 Im[ X ] ) / ( n=0 N1 Re[ X ] ) ,X=( r n e j( ϕ N+n - ϕ n ) + w N+n e 2πjε )( r n * + w n * )
ε ^ - Schmidl ε Δ ϕ Schmidl 2π + n=0 N1 Im( w N+n r n * e j2πε + r n w n * ) 2π n=0 N1 | r n | 2
Var[ ε ^ Schmidl ]= ( 1/ 2π ) 2 [ σ Schmidl 2 + N 0 / ( N E s ) ]
Var[ ε ^ CP ]= ( 1/ 2π ) 2 [ σ CP 2 + N 0 / ( N E s ) ]
Δ ϕ CP = d=0 D1 n=0 CP1 [ ϕ (N+CP)*d+n+N ϕ (N+CP)*d+n ] / (D*CP)
σ CP 2 = [ (1C P 2 ) / (3CP) +N+2 ] /D
Ψ m = 1 N sin(π(m+ ε i )) sin(π(m+ ε i )/N) e (jπ(m+ε)(1 1 N )) ,
Y k = H k+ ε i X k+ ε i + W k
ε ^ i ={ I,( 0IN/21 ) IN,(N/2IN1) ,
P c = k=1 N1 P( | X p + W p | 2 > | X k + W k | 2 )
P c = P N1 ( | X p + W p | 2 > | X s + W s | 2 )

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