Abstract

A novel joint symbol timing and carrier frequency offset (CFO) estimation algorithm is proposed for reduced-guard-interval coherent optical orthogonal frequency-division multiplexing (RGI-CO-OFDM) systems. The proposed algorithm is based on a constant amplitude zero autocorrelation (CAZAC) sequence weighted by a pseudo-random noise (PN) sequence. The symbol timing is accomplished by using only one training symbol of two identical halves, with the weighting applied to the second half. The special structure of the training symbol is also utilized in estimating the CFO. The performance of the proposed algorithm is demonstrated by means of numerical simulations in a 115.8-Gb/s 16-QAM RGI-CO-OFDM system.

© 2015 Optical Society of America

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References

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  1. W. Shieh, H. Bao, and Y. Tang, “Coherent optical OFDM: theory and design,” Opt. Express 16(2), 841–859 (2008).
    [Crossref] [PubMed]
  2. A. J. Lowery, L. Diu, and J. Armstrong, “Orthogonal frequency division multiplexing for adaptive dispersion compensation in long haul WDM systems,” in Proc. Optical Fiber Commun. Conf. (OFC) 2006, paper PDP39.
    [Crossref]
  3. I. B. Djordjevic and B. Vasic, “Orthogonal frequency division multiplexing for high-speed optical transmission,” Opt. Express 14(9), 3767–3775 (2006).
    [Crossref] [PubMed]
  4. S. L. Jansen, I. Morita, T. C. Schenk, and H. Tanaka, “Long-haul transmission of 16×52.5 Gbits/s polarization-division-multiplexed OFDM enabled by MIMO processing (Invited),” J. Opt. Netw. 7(2), 173–182 (2008).
    [Crossref]
  5. P. Poggiolini, A. Carena, V. Curri, and F. Forghieri, “Evaluation of the computational effort for chromatic dispersion compensation in coherent optical PM-OFDM and PM-QAM systems,” Opt. Express 17(3), 1385–1403 (2009).
    [Crossref] [PubMed]
  6. D. R. Goff and K. S. Hansen, Fiber Optic Reference Guide: A Practical Guide to Communications Technology (Focal, 2002).
  7. X. Liu, S. Chandrasekhar, B. Zhu, P. J. Winzer, A. H. Gnauck, and D. W. Peckham, “448-Gb/s reduced-guard-interval CO-OFDM transmission over 2000 km of ultra-large-area fiber and five 80-GHz-grid ROADMS,” J. Lightwave Technol. 29(4), 483–490 (2011).
    [Crossref]
  8. 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(2/3/4), 191–193 (1995).
    [Crossref]
  9. T. M. Schmidl and D. C. Cox, “Robust frequency and timing synchronization for OFDM,” IEEE Trans. Commun. 45(12), 1613–1621 (1997).
    [Crossref]
  10. H. Minn, M. Zeng, and V. K. Bhargava, “On timing offset estimation for OFDM systems,” IEEE Commun. Lett. 4(7), 242–244 (2000).
    [Crossref]
  11. B. Park, H. Cheon, C. Kang, and D. Hong, “A novel timing estimation method for OFDM systems,” IEEE Commun. Lett. 7(5), 239–241 (2003).
    [Crossref]
  12. 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]
  13. X. Zhou, X. Yang, R. Li, and K. Long, “Efficient joint carrier frequency offset and phase noise compensation scheme for high-speed coherent optical OFDM systems,” J. Lightwave Technol. 31(11), 1755–1761 (2013).
    [Crossref]
  14. Y. Huang, X. Zhang, and L. Xi, “Modified synchronization scheme for coherent optical OFDM systems,” J. Opt. Commun. Netw. 5(6), 584–592 (2013).
    [Crossref]
  15. X. Zhou, K. Long, R. Li, X. Yang, and Z. Zhang, “A simple and efficient frequency offset estimation algorithm for high-speed coherent optical OFDM systems,” Opt. Express 20(7), 7350–7361 (2012).
    [Crossref] [PubMed]
  16. X. Zhou, X. Chen, and K. Long, “Wide-range frequency offset estimation algorithm for optical coherent systems using training sequence,” IEEE Photon. Technol. Lett. 24(1), 82–84 (2012).
    [Crossref]
  17. Optical Internetworking Forum, “Integrable Tunable Laser Assembly MSA,” OIF-ITLA-MSA-01.1 (Nov. 22, 2005).
  18. R. Frank, S. Zadoff, and R. Heimiller, “Phase shift pulse codes with good periodic correlation properties,” IRE Trans. Inf. Theory 8(6), 381–382 (1962).
    [Crossref]
  19. D. C. Chu, “Polyphase codes with good periodic correlation properties,” IEEE Trans. Inf. Theory 18(4), 531–532 (1972).
    [Crossref]
  20. A. Milewski, “Periodic sequences with optimal properties for channel estimation and fast start-up equalization,” IBM J. Res. Develop. 27(5), 426–431 (1983).
    [Crossref]
  21. Z. Yang, L. Dai, J. Wang, J. Wang, and Z. Wang, “Transmit diversity for TDS-OFDM broadcasting over doubly selective fading channels,” IEEE Trans. Broadcast 57(1), 135–142 (2011).
    [Crossref]
  22. G. Ren, Y. Chang, H. Zhang, and H. Zhang, “Synchronization method based on a new constant envelop preamble for OFDM systems,” IEEE Trans. Broadcast 51(1), 139–143 (2005).
    [Crossref]
  23. H. Wang, L. Zhu, Y. Shi, T. Xing, and Y. Wang, “A novel synchronization algorithm for OFDM systems with weighted CAZAC sequence,” J. Comput. Inf. Syst. 8(6), 2275–2283 (2012).
  24. C. E. M. Silva, F. J. Harris, and G. J. Dolecek, “Synchronization algorithms based on weighted CAZAC preambles for OFDM systems,” in Proc. IEEE International Symposium Commun. Inf. Technol. (ISCIT) 2013.
    [Crossref]
  25. S. L. Jansen, I. Morita, T. C. W. Schenk, N. Takeda, and H. Tanaka, “Coherent optical 25.8-Gb/s OFDM transmission over 4160-km SSMF,” J. Lightwave Technol. 26(1), 6–15 (2008).
    [Crossref]
  26. R. Kudo, T. Kobayashi, K. Ishihara, Y. Takatori, A. Sano, and Y. Miyamoto, “Coherent optical single carrier transmission using overlap frequency domain equalization for long-haul optical systems,” J. Lightwave Technol. 27(16), 3721–3728 (2009).
    [Crossref]

2013 (2)

2012 (3)

X. Zhou, K. Long, R. Li, X. Yang, and Z. Zhang, “A simple and efficient frequency offset estimation algorithm for high-speed coherent optical OFDM systems,” Opt. Express 20(7), 7350–7361 (2012).
[Crossref] [PubMed]

X. Zhou, X. Chen, and K. Long, “Wide-range frequency offset estimation algorithm for optical coherent systems using training sequence,” IEEE Photon. Technol. Lett. 24(1), 82–84 (2012).
[Crossref]

H. Wang, L. Zhu, Y. Shi, T. Xing, and Y. Wang, “A novel synchronization algorithm for OFDM systems with weighted CAZAC sequence,” J. Comput. Inf. Syst. 8(6), 2275–2283 (2012).

2011 (2)

Z. Yang, L. Dai, J. Wang, J. Wang, and Z. Wang, “Transmit diversity for TDS-OFDM broadcasting over doubly selective fading channels,” IEEE Trans. Broadcast 57(1), 135–142 (2011).
[Crossref]

X. Liu, S. Chandrasekhar, B. Zhu, P. J. Winzer, A. H. Gnauck, and D. W. Peckham, “448-Gb/s reduced-guard-interval CO-OFDM transmission over 2000 km of ultra-large-area fiber and five 80-GHz-grid ROADMS,” J. Lightwave Technol. 29(4), 483–490 (2011).
[Crossref]

2009 (2)

2008 (3)

2006 (1)

2005 (1)

G. Ren, Y. Chang, H. Zhang, and H. Zhang, “Synchronization method based on a new constant envelop preamble for OFDM systems,” IEEE Trans. Broadcast 51(1), 139–143 (2005).
[Crossref]

2003 (1)

B. Park, H. Cheon, C. Kang, and D. Hong, “A novel timing estimation method for OFDM systems,” IEEE Commun. Lett. 7(5), 239–241 (2003).
[Crossref]

2000 (1)

H. Minn, M. Zeng, and V. K. Bhargava, “On timing offset estimation for OFDM systems,” IEEE Commun. Lett. 4(7), 242–244 (2000).
[Crossref]

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. 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(2/3/4), 191–193 (1995).
[Crossref]

1983 (1)

A. Milewski, “Periodic sequences with optimal properties for channel estimation and fast start-up equalization,” IBM J. Res. Develop. 27(5), 426–431 (1983).
[Crossref]

1972 (1)

D. C. Chu, “Polyphase codes with good periodic correlation properties,” IEEE Trans. Inf. Theory 18(4), 531–532 (1972).
[Crossref]

1962 (1)

R. Frank, S. Zadoff, and R. Heimiller, “Phase shift pulse codes with good periodic correlation properties,” IRE Trans. Inf. Theory 8(6), 381–382 (1962).
[Crossref]

Bao, H.

Bhargava, V. K.

H. Minn, M. Zeng, and V. K. Bhargava, “On timing offset estimation for OFDM systems,” IEEE Commun. Lett. 4(7), 242–244 (2000).
[Crossref]

Borjesson, P. O.

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]

Carena, A.

Chandrasekhar, S.

Chang, Y.

G. Ren, Y. Chang, H. Zhang, and H. Zhang, “Synchronization method based on a new constant envelop preamble for OFDM systems,” IEEE Trans. Broadcast 51(1), 139–143 (2005).
[Crossref]

Chen, X.

X. Zhou, X. Chen, and K. Long, “Wide-range frequency offset estimation algorithm for optical coherent systems using training sequence,” IEEE Photon. Technol. Lett. 24(1), 82–84 (2012).
[Crossref]

Cheon, H.

B. Park, H. Cheon, C. Kang, and D. Hong, “A novel timing estimation method for OFDM systems,” IEEE Commun. Lett. 7(5), 239–241 (2003).
[Crossref]

Chu, D. C.

D. C. Chu, “Polyphase codes with good periodic correlation properties,” IEEE Trans. Inf. Theory 18(4), 531–532 (1972).
[Crossref]

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]

Curri, V.

Dai, L.

Z. Yang, L. Dai, J. Wang, J. Wang, and Z. Wang, “Transmit diversity for TDS-OFDM broadcasting over doubly selective fading channels,” IEEE Trans. Broadcast 57(1), 135–142 (2011).
[Crossref]

Djordjevic, I. B.

Forghieri, F.

Frank, R.

R. Frank, S. Zadoff, and R. Heimiller, “Phase shift pulse codes with good periodic correlation properties,” IRE Trans. Inf. Theory 8(6), 381–382 (1962).
[Crossref]

Gnauck, A. H.

Heimiller, R.

R. Frank, S. Zadoff, and R. Heimiller, “Phase shift pulse codes with good periodic correlation properties,” IRE Trans. Inf. Theory 8(6), 381–382 (1962).
[Crossref]

Hong, D.

B. Park, H. Cheon, C. Kang, and D. Hong, “A novel timing estimation method for OFDM systems,” IEEE Commun. Lett. 7(5), 239–241 (2003).
[Crossref]

Huang, Y.

Ishihara, K.

Jansen, S. L.

Kang, C.

B. Park, H. Cheon, C. Kang, and D. Hong, “A novel timing estimation method for OFDM systems,” IEEE Commun. Lett. 7(5), 239–241 (2003).
[Crossref]

Kobayashi, T.

Kudo, R.

Li, R.

Liu, X.

Long, K.

Milewski, A.

A. Milewski, “Periodic sequences with optimal properties for channel estimation and fast start-up equalization,” IBM J. Res. Develop. 27(5), 426–431 (1983).
[Crossref]

Minn, H.

H. Minn, M. Zeng, and V. K. Bhargava, “On timing offset estimation for OFDM systems,” IEEE Commun. Lett. 4(7), 242–244 (2000).
[Crossref]

Miyamoto, Y.

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(2/3/4), 191–193 (1995).
[Crossref]

Morita, I.

Park, B.

B. Park, H. Cheon, C. Kang, and D. Hong, “A novel timing estimation method for OFDM systems,” IEEE Commun. Lett. 7(5), 239–241 (2003).
[Crossref]

Peckham, D. W.

Poggiolini, P.

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(2/3/4), 191–193 (1995).
[Crossref]

Ren, G.

G. Ren, Y. Chang, H. Zhang, and H. Zhang, “Synchronization method based on a new constant envelop preamble for OFDM systems,” IEEE Trans. Broadcast 51(1), 139–143 (2005).
[Crossref]

Sandell, M.

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]

Sano, A.

Schenk, T. C.

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]

Shi, Y.

H. Wang, L. Zhu, Y. Shi, T. Xing, and Y. Wang, “A novel synchronization algorithm for OFDM systems with weighted CAZAC sequence,” J. Comput. Inf. Syst. 8(6), 2275–2283 (2012).

Shieh, W.

Takatori, Y.

Takeda, N.

Tanaka, H.

Tang, Y.

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(2/3/4), 191–193 (1995).
[Crossref]

van de Beek, J. J.

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]

Vasic, B.

Wang, H.

H. Wang, L. Zhu, Y. Shi, T. Xing, and Y. Wang, “A novel synchronization algorithm for OFDM systems with weighted CAZAC sequence,” J. Comput. Inf. Syst. 8(6), 2275–2283 (2012).

Wang, J.

Z. Yang, L. Dai, J. Wang, J. Wang, and Z. Wang, “Transmit diversity for TDS-OFDM broadcasting over doubly selective fading channels,” IEEE Trans. Broadcast 57(1), 135–142 (2011).
[Crossref]

Z. Yang, L. Dai, J. Wang, J. Wang, and Z. Wang, “Transmit diversity for TDS-OFDM broadcasting over doubly selective fading channels,” IEEE Trans. Broadcast 57(1), 135–142 (2011).
[Crossref]

Wang, Y.

H. Wang, L. Zhu, Y. Shi, T. Xing, and Y. Wang, “A novel synchronization algorithm for OFDM systems with weighted CAZAC sequence,” J. Comput. Inf. Syst. 8(6), 2275–2283 (2012).

Wang, Z.

Z. Yang, L. Dai, J. Wang, J. Wang, and Z. Wang, “Transmit diversity for TDS-OFDM broadcasting over doubly selective fading channels,” IEEE Trans. Broadcast 57(1), 135–142 (2011).
[Crossref]

Winzer, P. J.

Xi, L.

Xing, T.

H. Wang, L. Zhu, Y. Shi, T. Xing, and Y. Wang, “A novel synchronization algorithm for OFDM systems with weighted CAZAC sequence,” J. Comput. Inf. Syst. 8(6), 2275–2283 (2012).

Yang, X.

Yang, Z.

Z. Yang, L. Dai, J. Wang, J. Wang, and Z. Wang, “Transmit diversity for TDS-OFDM broadcasting over doubly selective fading channels,” IEEE Trans. Broadcast 57(1), 135–142 (2011).
[Crossref]

Zadoff, S.

R. Frank, S. Zadoff, and R. Heimiller, “Phase shift pulse codes with good periodic correlation properties,” IRE Trans. Inf. Theory 8(6), 381–382 (1962).
[Crossref]

Zeng, M.

H. Minn, M. Zeng, and V. K. Bhargava, “On timing offset estimation for OFDM systems,” IEEE Commun. Lett. 4(7), 242–244 (2000).
[Crossref]

Zhang, H.

G. Ren, Y. Chang, H. Zhang, and H. Zhang, “Synchronization method based on a new constant envelop preamble for OFDM systems,” IEEE Trans. Broadcast 51(1), 139–143 (2005).
[Crossref]

G. Ren, Y. Chang, H. Zhang, and H. Zhang, “Synchronization method based on a new constant envelop preamble for OFDM systems,” IEEE Trans. Broadcast 51(1), 139–143 (2005).
[Crossref]

Zhang, X.

Zhang, Z.

Zhou, X.

Zhu, B.

Zhu, L.

H. Wang, L. Zhu, Y. Shi, T. Xing, and Y. Wang, “A novel synchronization algorithm for OFDM systems with weighted CAZAC sequence,” J. Comput. Inf. Syst. 8(6), 2275–2283 (2012).

IBM J. Res. Develop. (1)

A. Milewski, “Periodic sequences with optimal properties for channel estimation and fast start-up equalization,” IBM J. Res. Develop. 27(5), 426–431 (1983).
[Crossref]

IEEE Commun. Lett. (2)

H. Minn, M. Zeng, and V. K. Bhargava, “On timing offset estimation for OFDM systems,” IEEE Commun. Lett. 4(7), 242–244 (2000).
[Crossref]

B. Park, H. Cheon, C. Kang, and D. Hong, “A novel timing estimation method for OFDM systems,” IEEE Commun. Lett. 7(5), 239–241 (2003).
[Crossref]

IEEE Photon. Technol. Lett. (1)

X. Zhou, X. Chen, and K. Long, “Wide-range frequency offset estimation algorithm for optical coherent systems using training sequence,” IEEE Photon. Technol. Lett. 24(1), 82–84 (2012).
[Crossref]

IEEE Trans. Broadcast (2)

Z. Yang, L. Dai, J. Wang, J. Wang, and Z. Wang, “Transmit diversity for TDS-OFDM broadcasting over doubly selective fading channels,” IEEE Trans. Broadcast 57(1), 135–142 (2011).
[Crossref]

G. Ren, Y. Chang, H. Zhang, and H. Zhang, “Synchronization method based on a new constant envelop preamble for OFDM systems,” IEEE Trans. Broadcast 51(1), 139–143 (2005).
[Crossref]

IEEE Trans. Commun. (2)

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(2/3/4), 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]

IEEE Trans. Inf. Theory (1)

D. C. Chu, “Polyphase codes with good periodic correlation properties,” IEEE Trans. Inf. Theory 18(4), 531–532 (1972).
[Crossref]

IEEE Trans. Signal Process. (1)

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]

IRE Trans. Inf. Theory (1)

R. Frank, S. Zadoff, and R. Heimiller, “Phase shift pulse codes with good periodic correlation properties,” IRE Trans. Inf. Theory 8(6), 381–382 (1962).
[Crossref]

J. Comput. Inf. Syst. (1)

H. Wang, L. Zhu, Y. Shi, T. Xing, and Y. Wang, “A novel synchronization algorithm for OFDM systems with weighted CAZAC sequence,” J. Comput. Inf. Syst. 8(6), 2275–2283 (2012).

J. Lightwave Technol. (4)

J. Opt. Commun. Netw. (1)

J. Opt. Netw. (1)

Opt. Express (4)

Other (4)

Optical Internetworking Forum, “Integrable Tunable Laser Assembly MSA,” OIF-ITLA-MSA-01.1 (Nov. 22, 2005).

A. J. Lowery, L. Diu, and J. Armstrong, “Orthogonal frequency division multiplexing for adaptive dispersion compensation in long haul WDM systems,” in Proc. Optical Fiber Commun. Conf. (OFC) 2006, paper PDP39.
[Crossref]

D. R. Goff and K. S. Hansen, Fiber Optic Reference Guide: A Practical Guide to Communications Technology (Focal, 2002).

C. E. M. Silva, F. J. Harris, and G. J. Dolecek, “Synchronization algorithms based on weighted CAZAC preambles for OFDM systems,” in Proc. IEEE International Symposium Commun. Inf. Technol. (ISCIT) 2013.
[Crossref]

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Figures (9)

Fig. 1
Fig. 1 (a) Simulation setup of the RGI-CO-OFDM system. (b) OFDM frame structure. S/P: serial-to-parallel conversion. P/S: parallel-to-serial conversion. LPF: low-pass filter. OBPF: optical band-pass filter. SYN: synchronization symbol. DS: data symbol. TS: training symbol.
Fig. 2
Fig. 2 Comparison of timing metric of estimators for 800-km SSMF transmission. (a) without CFO and without optical noise. (b) with a CFO of 5 GHz and without optical noise. (c) with a CFO of 5 GHz and for an OSNR of 6 dB.
Fig. 3
Fig. 3 Timing estimation mean vs. OSNR for 800-km SSMF transmission with a CFO of 5 GHz.
Fig. 4
Fig. 4 Timing estimation variance vs. OSNR for 800-km SSMF transmission with a CFO of 5 GHz (no timing offset variations are observed for the proposed method, hence, the corresponding results are not included in the figure).
Fig. 5
Fig. 5 Mean of estimated CFO vs. actual CFO for 800-km SSMF transmission and an OSNR of 18 dB.
Fig. 6
Fig. 6 Zoomed-in version of Fig. 5, illustrating the CFO estimation range of the Schmidl and Cox’s algorithm when 1 TS is used.
Fig. 7
Fig. 7 MSE of the estimated CFO vs. OSNR for 800-km SSMF transmission and a CFO of 5 GHz.
Fig. 8
Fig. 8 BER vs. CFO for 800-km SSMF transmission.
Fig. 9
Fig. 9 BER vs. OSNR for 800-km SSMF transmission.

Equations (13)

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

c( m )=exp( jπr m 2 L )m=0,1,,L1,
m=0 L1 c( m ) c * ( [ m+τ ] modL ) ={ L,τ=0 0,τ0
TS=[ A M B M ],
M(d)= | P( d ) | 2 R 2 ( d ) ,
P( d )= n=0 M1 r( d+n )p( n ) r * ( d+n+M ) ,
R( d )= 1 2 k=0 N1 | r( d+k ) | 2 ,
d ^ =arg[ max d ( M( d ) ) ].
ρ=α+2β,
r( n+M )=p( n )r( n ) e jπα .
α ^ = 1 π angle( n=0 M1 r( d ^ +n )p( n ) r * ( d ^ +n+M ) ).
Ψ( β )= | k=0 N1 B f * ( k ) R f ( k+2β ) | 2 ( k=0 N1 | B f ( k ) | 2 ) 2 β= M 2 , M 2 +1,, M 2 1.
β ^ =arg[ max β ( Ψ( β ) ) ].
ρ ^ = α ^ +2 β ^ .

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