Abstract

We show that the orthogonality between signal and intrinsic imaginary interference (IMI) in offset quadrature amplitude modulation (offset-QAM) orthogonal frequency division multiplexing (OFDM) can still be maintained under a certain condition even when the timing slots of different subcarriers are misaligned. We show that the phase and velocity differences over subcarriers induced by fiber dispersion satisfy this condition. Based on this, we propose a fast channel estimation and equalization scheme without prior channel information including coarse dispersion. We investigate the proposed scheme in a 40-Gbit/s offset-16QAM OFDM experiment and 240-Gbit/s polarization-division-multiplexed offset-16QAM OFDM simulations, both over 1200-km single-mode fiber. It is shown that the proposed scheme gives better performance, reduced overhead for the training sequence, and/or lower complexity than other schemes. We also compare offset-QAM OFDM with the proposed scheme and conventional OFDM, and show that in addition to the elimination of cyclic prefix overhead, offset-QAM OFDM gives better performance and longer transmission reach for a moderate/small number of subcarriers.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. J. Zhao and A. D. Ellis, “Offset-QAM based coherent WDM for spectral efficiency enhancement,” Opt. Express 19(15), 14617–14631 (2011).
    [Crossref] [PubMed]
  2. A. Saljoghei, F. A. Gutierrez, P. Perry, D. Venkitesh, R. D. Koipillai, and L. P. Barry, “Experimental comparison of FBMC and OFDM for multiple access uplink PON,” J. Lightwave Technol. 35(9), 1595–1604 (2017).
    [Crossref]
  3. J. Fickers, A. Ghazisaeidi, M. Salsi, G. Charlet, P. Emplit, and F. Horlin, “Multicarrier offset-QAM for long-haul coherent optical communications,” J. Lightwave Technol. 32(24), 4069–4076 (2014).
    [Crossref]
  4. Z. Li, T. Jiang, H. Li, X. Zhang, C. Li, C. Li, R. Hu, M. Luo, X. Zhang, X. Xiao, Q. Yang, and S. Yu, “Experimental demonstration of 110-Gb/s unsynchronized band-multiplexed superchannel coherent optical OFDM/OQAM system,” Opt. Express 21(19), 21924–21931 (2013).
    [Crossref] [PubMed]
  5. J. Zhao and C. K. Chan, “Adaptively loaded SP-offset-QAM OFDM for IM/DD communication systems,” Opt. Express 25(18), 21603–21618 (2017).
    [Crossref] [PubMed]
  6. M. Xu, J. Zhang, F. Lu, J. Wang, L. Cheng, M. I. Khalil, D. Guidotti, and G. K. Chang, “Orthogonal multiband CAP modulation based on offset-QAM and advanced filter design in spectral efficient MMW RoF systems,” J. Lightwave Technol. 35(4), 997–1005 (2017).
    [Crossref]
  7. J. Zhao, “Channel estimation in DFT-based offset-QAM OFDM systems,” Opt. Express 22(21), 25651–25662 (2014).
    [Crossref] [PubMed]
  8. N.-Q. Nhan, P. Morel, S. Azou, M. Morvan, P. Gravey, and E. Pincemin, “Sparse preamble design for polarization division multiplexed CO-OFDM/OQAM channel estimation,” J. Lightwave Technol. 36(13), 2737–2745 (2018).
    [Crossref]
  9. X. Fang, Y. Xu, Z. Chen, and F. Zhang, “Frequency-domain channel estimation for polarization-division multiplexed CO-OFDM/OQAM systems,” J. Lightwave Technol. 33(13), 2743–2750 (2015).
    [Crossref]
  10. X. Fang, Y. Xu, Z. Chen, and F. Zhang, “Time-domain least square channel estimation for polarization-division multiplexed CO-OFDM/OQAM sysems,” J. Lightwave Technol. 34(3), 891–900 (2016).
    [Crossref]
  11. Y. Yu, P. D. Townsend, and J. Zhao, “Equalization of dispersion-induced crosstalk in optical offset-QAM OFDM systems,” IEEE Photonics Technol. Lett. 28(7), 782–785 (2016).
    [Crossref]
  12. J. Zhao and P. D. Townsend, “Dispersion tolerance enhancement using an improved offset-QAM OFDM scheme,” Opt. Express 23(13), 17638–17652 (2015).
    [Crossref] [PubMed]
  13. F. Rottenberg, T.H. Nguyen, S.P. Gorza, F. Horlin, and J. Louveaux, “Advanced chromatic dispersion compensation in optical fiber FBMC-OQAM systems,” IEEE Photon. J. 9(6) 7204710 (2017).
  14. T.-H. Nguyen, F. Rottenberg, S.-P. Gorza, J. Louveaux, and F. Horlin, “Efficient chromatic dispersion compensation and carrier phase tracking for optical fiber FBMC/OQAM systems,” J. Lightwave Technol. 35(14), 2909–2916 (2017).
    [Crossref]
  15. Z. Zheng, F. Frey, P. W. Berenguer, and J. K. Fischer, “Low-complexity equalization scheme for multicarrier offet-QAM systems,” IEEE Photonics Technol. Lett. 29(23), 2075–2078 (2017).
    [Crossref]
  16. D. Wang, L. Yuan, J. Lei, G. Wu, S. Li, R. Ding, and D. Wang, “Joint channel/frequency offset estimation and correction for coherent optical FBMC/OQAM system,” Opt. Fiber Technol. 39, 87–94 (2017).
    [Crossref]
  17. H. Tang, S. Fu, H. Liu, M. Tang, P. Shum, and D. Liu, “Low-complexity carrier phase recovery based on constellation classification for M-ary offset-QAM signal,” J. Lightwave Technol. 34(4), 1133–1140 (2016).
    [Crossref]
  18. T. H. Nguyen and C. Peucheret, “Kalman filtering for carrier phase recovery in optical offset-QAM Nyquist WDM systems,” IEEE Photonics Technol. Lett. 29(12), 1019–1022 (2017).
    [Crossref]

2018 (1)

2017 (8)

A. Saljoghei, F. A. Gutierrez, P. Perry, D. Venkitesh, R. D. Koipillai, and L. P. Barry, “Experimental comparison of FBMC and OFDM for multiple access uplink PON,” J. Lightwave Technol. 35(9), 1595–1604 (2017).
[Crossref]

J. Zhao and C. K. Chan, “Adaptively loaded SP-offset-QAM OFDM for IM/DD communication systems,” Opt. Express 25(18), 21603–21618 (2017).
[Crossref] [PubMed]

M. Xu, J. Zhang, F. Lu, J. Wang, L. Cheng, M. I. Khalil, D. Guidotti, and G. K. Chang, “Orthogonal multiband CAP modulation based on offset-QAM and advanced filter design in spectral efficient MMW RoF systems,” J. Lightwave Technol. 35(4), 997–1005 (2017).
[Crossref]

F. Rottenberg, T.H. Nguyen, S.P. Gorza, F. Horlin, and J. Louveaux, “Advanced chromatic dispersion compensation in optical fiber FBMC-OQAM systems,” IEEE Photon. J. 9(6) 7204710 (2017).

T.-H. Nguyen, F. Rottenberg, S.-P. Gorza, J. Louveaux, and F. Horlin, “Efficient chromatic dispersion compensation and carrier phase tracking for optical fiber FBMC/OQAM systems,” J. Lightwave Technol. 35(14), 2909–2916 (2017).
[Crossref]

Z. Zheng, F. Frey, P. W. Berenguer, and J. K. Fischer, “Low-complexity equalization scheme for multicarrier offet-QAM systems,” IEEE Photonics Technol. Lett. 29(23), 2075–2078 (2017).
[Crossref]

D. Wang, L. Yuan, J. Lei, G. Wu, S. Li, R. Ding, and D. Wang, “Joint channel/frequency offset estimation and correction for coherent optical FBMC/OQAM system,” Opt. Fiber Technol. 39, 87–94 (2017).
[Crossref]

T. H. Nguyen and C. Peucheret, “Kalman filtering for carrier phase recovery in optical offset-QAM Nyquist WDM systems,” IEEE Photonics Technol. Lett. 29(12), 1019–1022 (2017).
[Crossref]

2016 (3)

2015 (2)

2014 (2)

2013 (1)

2011 (1)

Azou, S.

Barry, L. P.

Berenguer, P. W.

Z. Zheng, F. Frey, P. W. Berenguer, and J. K. Fischer, “Low-complexity equalization scheme for multicarrier offet-QAM systems,” IEEE Photonics Technol. Lett. 29(23), 2075–2078 (2017).
[Crossref]

Chan, C. K.

Chang, G. K.

Charlet, G.

Chen, Z.

Cheng, L.

Ding, R.

D. Wang, L. Yuan, J. Lei, G. Wu, S. Li, R. Ding, and D. Wang, “Joint channel/frequency offset estimation and correction for coherent optical FBMC/OQAM system,” Opt. Fiber Technol. 39, 87–94 (2017).
[Crossref]

Ellis, A. D.

Emplit, P.

Fang, X.

Fickers, J.

Fischer, J. K.

Z. Zheng, F. Frey, P. W. Berenguer, and J. K. Fischer, “Low-complexity equalization scheme for multicarrier offet-QAM systems,” IEEE Photonics Technol. Lett. 29(23), 2075–2078 (2017).
[Crossref]

Frey, F.

Z. Zheng, F. Frey, P. W. Berenguer, and J. K. Fischer, “Low-complexity equalization scheme for multicarrier offet-QAM systems,” IEEE Photonics Technol. Lett. 29(23), 2075–2078 (2017).
[Crossref]

Fu, S.

Ghazisaeidi, A.

Gorza, S.P.

F. Rottenberg, T.H. Nguyen, S.P. Gorza, F. Horlin, and J. Louveaux, “Advanced chromatic dispersion compensation in optical fiber FBMC-OQAM systems,” IEEE Photon. J. 9(6) 7204710 (2017).

Gorza, S.-P.

Gravey, P.

Guidotti, D.

Gutierrez, F. A.

Horlin, F.

Hu, R.

Jiang, T.

Khalil, M. I.

Koipillai, R. D.

Lei, J.

D. Wang, L. Yuan, J. Lei, G. Wu, S. Li, R. Ding, and D. Wang, “Joint channel/frequency offset estimation and correction for coherent optical FBMC/OQAM system,” Opt. Fiber Technol. 39, 87–94 (2017).
[Crossref]

Li, C.

Li, H.

Li, S.

D. Wang, L. Yuan, J. Lei, G. Wu, S. Li, R. Ding, and D. Wang, “Joint channel/frequency offset estimation and correction for coherent optical FBMC/OQAM system,” Opt. Fiber Technol. 39, 87–94 (2017).
[Crossref]

Li, Z.

Liu, D.

Liu, H.

Louveaux, J.

T.-H. Nguyen, F. Rottenberg, S.-P. Gorza, J. Louveaux, and F. Horlin, “Efficient chromatic dispersion compensation and carrier phase tracking for optical fiber FBMC/OQAM systems,” J. Lightwave Technol. 35(14), 2909–2916 (2017).
[Crossref]

F. Rottenberg, T.H. Nguyen, S.P. Gorza, F. Horlin, and J. Louveaux, “Advanced chromatic dispersion compensation in optical fiber FBMC-OQAM systems,” IEEE Photon. J. 9(6) 7204710 (2017).

Lu, F.

Luo, M.

Morel, P.

Morvan, M.

Nguyen, T. H.

T. H. Nguyen and C. Peucheret, “Kalman filtering for carrier phase recovery in optical offset-QAM Nyquist WDM systems,” IEEE Photonics Technol. Lett. 29(12), 1019–1022 (2017).
[Crossref]

Nguyen, T.H.

F. Rottenberg, T.H. Nguyen, S.P. Gorza, F. Horlin, and J. Louveaux, “Advanced chromatic dispersion compensation in optical fiber FBMC-OQAM systems,” IEEE Photon. J. 9(6) 7204710 (2017).

Nguyen, T.-H.

Nhan, N.-Q.

Perry, P.

Peucheret, C.

T. H. Nguyen and C. Peucheret, “Kalman filtering for carrier phase recovery in optical offset-QAM Nyquist WDM systems,” IEEE Photonics Technol. Lett. 29(12), 1019–1022 (2017).
[Crossref]

Pincemin, E.

Rottenberg, F.

F. Rottenberg, T.H. Nguyen, S.P. Gorza, F. Horlin, and J. Louveaux, “Advanced chromatic dispersion compensation in optical fiber FBMC-OQAM systems,” IEEE Photon. J. 9(6) 7204710 (2017).

T.-H. Nguyen, F. Rottenberg, S.-P. Gorza, J. Louveaux, and F. Horlin, “Efficient chromatic dispersion compensation and carrier phase tracking for optical fiber FBMC/OQAM systems,” J. Lightwave Technol. 35(14), 2909–2916 (2017).
[Crossref]

Saljoghei, A.

Salsi, M.

Shum, P.

Tang, H.

Tang, M.

Townsend, P. D.

Y. Yu, P. D. Townsend, and J. Zhao, “Equalization of dispersion-induced crosstalk in optical offset-QAM OFDM systems,” IEEE Photonics Technol. Lett. 28(7), 782–785 (2016).
[Crossref]

J. Zhao and P. D. Townsend, “Dispersion tolerance enhancement using an improved offset-QAM OFDM scheme,” Opt. Express 23(13), 17638–17652 (2015).
[Crossref] [PubMed]

Venkitesh, D.

Wang, D.

D. Wang, L. Yuan, J. Lei, G. Wu, S. Li, R. Ding, and D. Wang, “Joint channel/frequency offset estimation and correction for coherent optical FBMC/OQAM system,” Opt. Fiber Technol. 39, 87–94 (2017).
[Crossref]

D. Wang, L. Yuan, J. Lei, G. Wu, S. Li, R. Ding, and D. Wang, “Joint channel/frequency offset estimation and correction for coherent optical FBMC/OQAM system,” Opt. Fiber Technol. 39, 87–94 (2017).
[Crossref]

Wang, J.

Wu, G.

D. Wang, L. Yuan, J. Lei, G. Wu, S. Li, R. Ding, and D. Wang, “Joint channel/frequency offset estimation and correction for coherent optical FBMC/OQAM system,” Opt. Fiber Technol. 39, 87–94 (2017).
[Crossref]

Xiao, X.

Xu, M.

Xu, Y.

Yang, Q.

Yu, S.

Yu, Y.

Y. Yu, P. D. Townsend, and J. Zhao, “Equalization of dispersion-induced crosstalk in optical offset-QAM OFDM systems,” IEEE Photonics Technol. Lett. 28(7), 782–785 (2016).
[Crossref]

Yuan, L.

D. Wang, L. Yuan, J. Lei, G. Wu, S. Li, R. Ding, and D. Wang, “Joint channel/frequency offset estimation and correction for coherent optical FBMC/OQAM system,” Opt. Fiber Technol. 39, 87–94 (2017).
[Crossref]

Zhang, F.

Zhang, J.

Zhang, X.

Zhao, J.

Zheng, Z.

Z. Zheng, F. Frey, P. W. Berenguer, and J. K. Fischer, “Low-complexity equalization scheme for multicarrier offet-QAM systems,” IEEE Photonics Technol. Lett. 29(23), 2075–2078 (2017).
[Crossref]

IEEE Photon. J. (1)

F. Rottenberg, T.H. Nguyen, S.P. Gorza, F. Horlin, and J. Louveaux, “Advanced chromatic dispersion compensation in optical fiber FBMC-OQAM systems,” IEEE Photon. J. 9(6) 7204710 (2017).

IEEE Photonics Technol. Lett. (3)

Y. Yu, P. D. Townsend, and J. Zhao, “Equalization of dispersion-induced crosstalk in optical offset-QAM OFDM systems,” IEEE Photonics Technol. Lett. 28(7), 782–785 (2016).
[Crossref]

Z. Zheng, F. Frey, P. W. Berenguer, and J. K. Fischer, “Low-complexity equalization scheme for multicarrier offet-QAM systems,” IEEE Photonics Technol. Lett. 29(23), 2075–2078 (2017).
[Crossref]

T. H. Nguyen and C. Peucheret, “Kalman filtering for carrier phase recovery in optical offset-QAM Nyquist WDM systems,” IEEE Photonics Technol. Lett. 29(12), 1019–1022 (2017).
[Crossref]

J. Lightwave Technol. (8)

H. Tang, S. Fu, H. Liu, M. Tang, P. Shum, and D. Liu, “Low-complexity carrier phase recovery based on constellation classification for M-ary offset-QAM signal,” J. Lightwave Technol. 34(4), 1133–1140 (2016).
[Crossref]

T.-H. Nguyen, F. Rottenberg, S.-P. Gorza, J. Louveaux, and F. Horlin, “Efficient chromatic dispersion compensation and carrier phase tracking for optical fiber FBMC/OQAM systems,” J. Lightwave Technol. 35(14), 2909–2916 (2017).
[Crossref]

A. Saljoghei, F. A. Gutierrez, P. Perry, D. Venkitesh, R. D. Koipillai, and L. P. Barry, “Experimental comparison of FBMC and OFDM for multiple access uplink PON,” J. Lightwave Technol. 35(9), 1595–1604 (2017).
[Crossref]

J. Fickers, A. Ghazisaeidi, M. Salsi, G. Charlet, P. Emplit, and F. Horlin, “Multicarrier offset-QAM for long-haul coherent optical communications,” J. Lightwave Technol. 32(24), 4069–4076 (2014).
[Crossref]

M. Xu, J. Zhang, F. Lu, J. Wang, L. Cheng, M. I. Khalil, D. Guidotti, and G. K. Chang, “Orthogonal multiband CAP modulation based on offset-QAM and advanced filter design in spectral efficient MMW RoF systems,” J. Lightwave Technol. 35(4), 997–1005 (2017).
[Crossref]

N.-Q. Nhan, P. Morel, S. Azou, M. Morvan, P. Gravey, and E. Pincemin, “Sparse preamble design for polarization division multiplexed CO-OFDM/OQAM channel estimation,” J. Lightwave Technol. 36(13), 2737–2745 (2018).
[Crossref]

X. Fang, Y. Xu, Z. Chen, and F. Zhang, “Frequency-domain channel estimation for polarization-division multiplexed CO-OFDM/OQAM systems,” J. Lightwave Technol. 33(13), 2743–2750 (2015).
[Crossref]

X. Fang, Y. Xu, Z. Chen, and F. Zhang, “Time-domain least square channel estimation for polarization-division multiplexed CO-OFDM/OQAM sysems,” J. Lightwave Technol. 34(3), 891–900 (2016).
[Crossref]

Opt. Express (5)

Opt. Fiber Technol. (1)

D. Wang, L. Yuan, J. Lei, G. Wu, S. Li, R. Ding, and D. Wang, “Joint channel/frequency offset estimation and correction for coherent optical FBMC/OQAM system,” Opt. Fiber Technol. 39, 87–94 (2017).
[Crossref]

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Figures (12)

Fig. 1
Fig. 1 Principle of offset-QAM OFDM with timing misalignment between subcarriers. Ts is the OFDM symbol period and is equal to TN. In the conventional system, τn = 0 and φn = 0.
Fig. 2
Fig. 2 An example to illustrate the crosstalk from the (m + 1)th subcarrier to the mth subcarrier. In this example, the delay between the in-phase (or quadrature) tributary of the (m + 1)th subcarrier and the in-phase tributary of the mth subcarrier is 3Ts/8 (or 7Ts/8).
Fig. 3
Fig. 3 An example to illustrate the condition to get zero crosstalk from the (a) in-phase and (b) quadrature tributaries of the (m + 1)th subcarrier, when there is a timing misalignment between subcarriers. The carrier phase in the figure should be controlled so that it is odd symmetric with respect to (τm + τm+1)/2, where τm = 0 and τm+1 = 3Ts/8 or 7Ts/8 in (a) and (b), respectively.
Fig. 4
Fig. 4 Principle of the proposed channel estimation and equalization scheme.
Fig. 5
Fig. 5 Experimental setup
Fig. 6
Fig. 6 (a) BER versus fiber length for conventional OFDM, conventional offset-QAM OFDM, and offset-QAM OFDM with the proposed scheme. (b) BER versus fiber length for offset-QAM OFDM with different equalization schemes. The numbers of training symbols for MTE, SSE, MFB, and the proposed scheme are 160, 64, 64, and 32, respectively.
Fig. 7
Fig. 7 (a) BER versus the number of training symbols for different equalization schemes at 1200 km. (b) Estimated τm/T and τm,improved/T for the proposed scheme at 1200 km.
Fig. 8
Fig. 8 (a) BER versus the delay between DFTs in the MFB scheme at 1200 km. (b) BER versus fiber length for the MFB scheme with different numbers of DFTs.
Fig. 9
Fig. 9 (a) BER versus fiber length for different equalization schemes. The number of DFTs in the MFB scheme is 8. (b) BER versus fiber length for the MFB scheme with different number of DFTs. In both figures, fiber nonlinearity is not included and the OSNR is 22 dB.
Fig. 10
Fig. 10 (a) BER versus fiber length for the MFB (dashed) and the proposed (solid) schemes under different number of subcarriers. The number of DFTs in the MFB scheme is 8. (b) BER versus fiber length for the proposed scheme without (dashed) and with (solid) updated pulse shaping filter. In both figures, fiber nonlinearity is not included and the OSNR is 22 dB.
Fig. 11
Fig. 11 (a) Estimation error versus actual fiber dispersion when the sampling clock of the ADC has a timing delay of 0 (circles) and 6.25 ps (triangles). (b) BER versus the sampling phase of the ADC under different timing jitters. Fiber length is 1200 km. In both figures, the number of subcarriers is 32 and the OSNR is 22 dB.
Fig. 12
Fig. 12 (a) BER versus the CP length for conventional OFDM at 1200 km and 22-dB OSNR. (b) BER versus signal launch power for conventional OFDM (dashed) and offset-QAM OFDM with the proposed scheme (solid) at 1200 km. Fiber nonlinearity is included and the CP length for conventional OFDM is 224.

Equations (15)

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

s(iN+k)= s real (iN+k)+j s imag (iN+k) = p= + n=N/2+1 N/2 a p,n real exp(jπn/2+j φ n )exp(2πjkn/N) h filter (iN+kpN τ n /T) + p= + n=N/2+1 N/2 a p,n imag exp(jπ(n+1)/2+j φ n )exp(2πjkn/N) h filter (iN+kN/2pN τ n /T)
b i,m real =real{exp(jπm/2j φ m ) k=N/2+1 N/2 q= + exp(2πjkm/N)s(qN+k) h receiver_filter ((iq)Nk+ τ m /T) }
φ m+1 φ m =iπ π( τ m+1 + τ m ) NT
b i,m real = a i,m real k=N/2+1 N/2 q= + h filter 2 (qN+kiN τ m /T)
φ m+1 φ m =iπ 2π NT ( τ m+1 + τ m ) 2 =iπ π( τ m+1 + τ m ) NT
H c ((m+d)/(TN))= H p H b ((m+d)/(TN))exp(j β 2 L/2 (2π/(TN)) 2 (m+d) 2 ) = H p H b ((m+d)/(TN))exp(jα d 2 ) effects with a short memeory length exp(j(2αmd+α m 2 )) effects with a long memory length
α (m+1) 2 α m 2 =α(2m+1)= π(α(m+1)NT/παmNT/π) NT
τ m /T=N(Angle( R training,m (N1))Angle( R training,m (1)))/(4π)
R training,m (n)= F k,n { i= N t /2+1 N t /2 | r training,m (iN+k) | 2 }        k= N/2+1N/2
h receiver_filter (k)= h filter_d * (k)
h filter_d (k)= h filter (k) F n,k 1 {exp(jα n 2 )}
b i,m real = a i,m real k=N/2+1 N/2 q= + h filter 2 (qN+kiN τ m /T) +real{ p= + k=N/2+1 N/2 q= + a p,m+1 real exp(j(2πk/N+π/2+ φ m+1 φ m )) h filter (qN+kpN τ m+1 /T) h filter (qN+kiN τ m /T)} +real{ p= + k=N/2+1 N/2 q= + a p,m+1 imag exp(j(2πk/N+π+ φ m+1 φ m )) h filter (qN+kN/2pN τ m+1 /T) h filter (qN+kiN τ m /T)} +real{ p= + k=N/2+1 N/2 q= + a p,m1 real exp(j(2πk/Nπ/2+ φ m1 φ m )) h filter (qN+kpN τ m1 / T filter (qN+kiN τ m /T)} +real{ p= + k=N/2+1 N/2 q= + a p,m1 imag exp(j(2πk/N+ φ m1 φ m )) h filter (qN+kN/2pN τ m1 /T) h filter (qN+kiN τ m /T)}
r training,m (iN+k)= p= + a training,p,m h(iN+kpN τ m /T)
E{ | r training,m (iN+k) | 2 } p= + | h(iN+kpN τ m /T) | 2
R training,m (n)=exp(j 2πn N τ m T ) F k,n { p= + | h(iN+kpN) | 2 }