Abstract

Discrete-Fourier transform (DFT) based offset quadrature amplitude modulation (offset-QAM) orthogonal frequency division multiplexing (OFDM) without cyclic prefix (CP) was shown to offer a dispersion tolerance the same as that of conventional OFDM with ~20% CP overhead. In this paper, we analytically study the fundamental mechanism limiting the dispersion tolerance of this conventional scheme. It is found that the signal and the crosstalk from adjacent subcarriers, which are orthogonal with π/2 phase difference at back to back, can be in-phase when the dispersion increases to a certain value. We propose a novel scheme to overcome this limitation and significantly improve the dispersion tolerance to that of one subcarrier. Simulations show that the proposed scheme can support a 224-Gb/s polarization-division-multiplexed offset-4QAM OFDM signal over 160,000 ps/nm without any CP under 128 subcarriers, and this tolerance scales with the square of the number of subcarriers. It is also shown that this scheme exhibits advantages of greatly enhanced spectral efficiency, larger dispersion tolerance, and/or reduced complexity compared to the conventional CP-OFDM and reduced-guard-interval OFDM using frequency domain equalization.

© 2015 Optical Society of America

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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. S. Randel, A. Sierra, X. Liu, S. Chandrasekhar, and P. J. Winzer, “Study of multicarrier offset-QAM for spectrally efficient coherent optical communications,” in Proc. European Conference on Optical Communication (2011), paper Th.11.A.1.
    [Crossref]
  3. F. Horlin, J. Fickers, P. Emplit, A. Bourdoux, and J. Louveaux, “Dual-polarization OFDM-OQAM for communications over optical fibers with coherent detection,” Opt. Express 21(5), 6409–6421 (2013).
    [Crossref] [PubMed]
  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. M. Xiang, S. Fu, M. Tang, H. Tang, P. Shum, and D. Liu, “Nyquist WDM superchannel using offset-16QAM and receiver-side digital spectral shaping,” Opt. Express 22(14), 17448–17457 (2014).
    [PubMed]
  6. J. Zhao, “DFT-based offset-QAM OFDM for optical communications,” Opt. Express 22(1), 1114–1126 (2014).
    [Crossref] [PubMed]
  7. J. Zhao, “Channel estimation in DFT-based offset-QAM OFDM systems,” Opt. Express 22(21), 25651–25662 (2014).
    [Crossref] [PubMed]
  8. B. Liu, L. Zhang, X. Xin, and J. Yu, “None pilot-tones and training sequence assisted OFDM technology based on multiple-differential amplitude phase shift keying,” Opt. Express 20(20), 22878–22885 (2012).
    [Crossref] [PubMed]
  9. B. Inan, S. Adhikari, O. Karakaya, P. Kainzmaier, M. Mocker, H. von Kirchbauer, N. Hanik, and S. L. Jansen, “Real-time 93.8-Gb/s polarization-multiplexed OFDM transmitter with 1024-point IFFT,” Opt. Express 19(26), B64–B68 (2011).
    [Crossref] [PubMed]
  10. R. Schmogrow, S. Ben-Ezra, P. C. Schindler, B. Nebendahl, C. Koos, W. Freude, and J. Leuthold, “Pulse-shaping with digital, electrical and optical filters–a comparsion,” IEEE J. Lightwave Technol. 31(15), 2570–2577 (2013).
    [Crossref]
  11. 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 ORADMs,” IEEE J. Lightwave Technol. 29(4), 483–490 (2011).
    [Crossref]
  12. Q. Zhuge, C. Chen, and D. V. Plant, “Dispersion-enhanced phase noise effects on reduced-guard-interval CO-OFDM transmission,” Opt. Express 19(5), 4472–4484 (2011).
    [Crossref] [PubMed]

2014 (3)

2013 (3)

2012 (1)

2011 (4)

Adhikari, S.

Ben-Ezra, S.

R. Schmogrow, S. Ben-Ezra, P. C. Schindler, B. Nebendahl, C. Koos, W. Freude, and J. Leuthold, “Pulse-shaping with digital, electrical and optical filters–a comparsion,” IEEE J. Lightwave Technol. 31(15), 2570–2577 (2013).
[Crossref]

Bourdoux, A.

Chandrasekhar, S.

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 ORADMs,” IEEE J. Lightwave Technol. 29(4), 483–490 (2011).
[Crossref]

Chen, C.

Ellis, A. D.

Emplit, P.

Fickers, J.

Freude, W.

R. Schmogrow, S. Ben-Ezra, P. C. Schindler, B. Nebendahl, C. Koos, W. Freude, and J. Leuthold, “Pulse-shaping with digital, electrical and optical filters–a comparsion,” IEEE J. Lightwave Technol. 31(15), 2570–2577 (2013).
[Crossref]

Fu, S.

Gnauck, A. H.

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 ORADMs,” IEEE J. Lightwave Technol. 29(4), 483–490 (2011).
[Crossref]

Hanik, N.

Horlin, F.

Hu, R.

Inan, B.

Jansen, S. L.

Jiang, T.

Kainzmaier, P.

Karakaya, O.

Koos, C.

R. Schmogrow, S. Ben-Ezra, P. C. Schindler, B. Nebendahl, C. Koos, W. Freude, and J. Leuthold, “Pulse-shaping with digital, electrical and optical filters–a comparsion,” IEEE J. Lightwave Technol. 31(15), 2570–2577 (2013).
[Crossref]

Leuthold, J.

R. Schmogrow, S. Ben-Ezra, P. C. Schindler, B. Nebendahl, C. Koos, W. Freude, and J. Leuthold, “Pulse-shaping with digital, electrical and optical filters–a comparsion,” IEEE J. Lightwave Technol. 31(15), 2570–2577 (2013).
[Crossref]

Li, C.

Li, H.

Li, Z.

Liu, B.

Liu, D.

Liu, X.

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 ORADMs,” IEEE J. Lightwave Technol. 29(4), 483–490 (2011).
[Crossref]

Louveaux, J.

Luo, M.

Mocker, M.

Nebendahl, B.

R. Schmogrow, S. Ben-Ezra, P. C. Schindler, B. Nebendahl, C. Koos, W. Freude, and J. Leuthold, “Pulse-shaping with digital, electrical and optical filters–a comparsion,” IEEE J. Lightwave Technol. 31(15), 2570–2577 (2013).
[Crossref]

Peckham, D. W.

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 ORADMs,” IEEE J. Lightwave Technol. 29(4), 483–490 (2011).
[Crossref]

Plant, D. V.

Schindler, P. C.

R. Schmogrow, S. Ben-Ezra, P. C. Schindler, B. Nebendahl, C. Koos, W. Freude, and J. Leuthold, “Pulse-shaping with digital, electrical and optical filters–a comparsion,” IEEE J. Lightwave Technol. 31(15), 2570–2577 (2013).
[Crossref]

Schmogrow, R.

R. Schmogrow, S. Ben-Ezra, P. C. Schindler, B. Nebendahl, C. Koos, W. Freude, and J. Leuthold, “Pulse-shaping with digital, electrical and optical filters–a comparsion,” IEEE J. Lightwave Technol. 31(15), 2570–2577 (2013).
[Crossref]

Shum, P.

Tang, H.

Tang, M.

von Kirchbauer, H.

Winzer, P. J.

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 ORADMs,” IEEE J. Lightwave Technol. 29(4), 483–490 (2011).
[Crossref]

Xiang, M.

Xiao, X.

Xin, X.

Yang, Q.

Yu, J.

Yu, S.

Zhang, L.

Zhang, X.

Zhao, J.

Zhu, B.

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 ORADMs,” IEEE J. Lightwave Technol. 29(4), 483–490 (2011).
[Crossref]

Zhuge, Q.

IEEE J. Lightwave Technol. (2)

R. Schmogrow, S. Ben-Ezra, P. C. Schindler, B. Nebendahl, C. Koos, W. Freude, and J. Leuthold, “Pulse-shaping with digital, electrical and optical filters–a comparsion,” IEEE J. Lightwave Technol. 31(15), 2570–2577 (2013).
[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 ORADMs,” IEEE J. Lightwave Technol. 29(4), 483–490 (2011).
[Crossref]

Opt. Express (9)

Q. Zhuge, C. Chen, and D. V. Plant, “Dispersion-enhanced phase noise effects on reduced-guard-interval CO-OFDM transmission,” Opt. Express 19(5), 4472–4484 (2011).
[Crossref] [PubMed]

J. Zhao and A. D. Ellis, “Offset-QAM based coherent WDM for spectral efficiency enhancement,” Opt. Express 19(15), 14617–14631 (2011).
[Crossref] [PubMed]

B. Inan, S. Adhikari, O. Karakaya, P. Kainzmaier, M. Mocker, H. von Kirchbauer, N. Hanik, and S. L. Jansen, “Real-time 93.8-Gb/s polarization-multiplexed OFDM transmitter with 1024-point IFFT,” Opt. Express 19(26), B64–B68 (2011).
[Crossref] [PubMed]

B. Liu, L. Zhang, X. Xin, and J. Yu, “None pilot-tones and training sequence assisted OFDM technology based on multiple-differential amplitude phase shift keying,” Opt. Express 20(20), 22878–22885 (2012).
[Crossref] [PubMed]

F. Horlin, J. Fickers, P. Emplit, A. Bourdoux, and J. Louveaux, “Dual-polarization OFDM-OQAM for communications over optical fibers with coherent detection,” Opt. Express 21(5), 6409–6421 (2013).
[Crossref] [PubMed]

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]

J. Zhao, “DFT-based offset-QAM OFDM for optical communications,” Opt. Express 22(1), 1114–1126 (2014).
[Crossref] [PubMed]

M. Xiang, S. Fu, M. Tang, H. Tang, P. Shum, and D. Liu, “Nyquist WDM superchannel using offset-16QAM and receiver-side digital spectral shaping,” Opt. Express 22(14), 17448–17457 (2014).
[PubMed]

J. Zhao, “Channel estimation in DFT-based offset-QAM OFDM systems,” Opt. Express 22(21), 25651–25662 (2014).
[Crossref] [PubMed]

Other (1)

S. Randel, A. Sierra, X. Liu, S. Chandrasekhar, and P. J. Winzer, “Study of multicarrier offset-QAM for spectrally efficient coherent optical communications,” in Proc. European Conference on Optical Communication (2011), paper Th.11.A.1.
[Crossref]

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Figures (9)

Fig. 1
Fig. 1 Principle of DFT-based implementation for offset-QAM OFDM.
Fig. 2
Fig. 2 (a) Real (dashed) and imaginary (dotted) parts of the dispersion-induced frequency response, as well as the spectral profile of subcarriers (solid) in offset-QAM OFDM. (b) Relationship between the signal and the ICI in the constellation diagram. In (b), the in-phase tributary of a subcarrier in offset-4QAM OFDM is illustrated.
Fig. 3
Fig. 3 Block diagram of the proposed offset-QAM OFDM decoding scheme.
Fig. 4
Fig. 4 An example to illustrate the principle of the proposed scheme (x = 2 and 7 subcarriers).
Fig. 5
Fig. 5 (a) Normalized time index to decode different subcarriers. (b) The index of paths to decode different subcarriers (circles) and the remainder of normalized delays of subcarriers (solid). The number of subcarriers is 128 (that for data modulation is 90). The dispersion is 42,500 ps/nm. The roll-off factor of the SRRC function and x are 0.5 and 4, respectively.
Fig. 6
Fig. 6 (a) Required OSNR at a BER of 10−3 versus dispersion for conventional CP-OFDM (C) and offset-QAM OFDM (O) when CP is not used. (b) Required OSNR at a BER of 10−3 versus the number of paths for the proposed scheme. In (a) and (b), the number of subcarriers is 128. The roll-off factor of the pulse in offset-QAM OFDM is 0.5.
Fig. 7
Fig. 7 (a) Required OSNR at a BER of 10−3 versus dispersion for different pulse roll-off factors and memory lengths of the FIR filters. The cases using the roll-off factor of 0.5 and 1, and the memory length of 80 are similar to those with the memory length of 2, and so are not plot in the figure. (b) Required OSNR at a BER of 10−3 versus the normalized synchronization error. In (a) and (b), the number of subcarriers is 128 and x = 4.
Fig. 8
Fig. 8 (a) Required OSNR at a BER of 10−3 versus dispersion for the proposed scheme with different number of subcarriers. (b) Dispersion tolerance at an OSNR of 20 dB versus the number of subcarriers for CP-OFDM (C) using different lengths of CP and offset-QPSK OFDM (O) without CP. In (a) and (b), the pulse roll-off factor is 0.5 and x = 4.
Fig. 9
Fig. 9 (a) Normalized spectral efficiency versus dispersion for 224-Gb/s PDM QPSK CP-OFDM and the proposed PDM offset-QPSK OFDM with 128 and 256 subcarriers. (b) Required complexity of RGI-OFDM and the proposed scheme. The number of subcarriers and the point size of the FDE are 128 and 2048, respectively.

Equations (21)

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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)exp(2πj(pN+k)n/N) h filter (iN+kpN) + p= + n=N/2+1 N/2 a p,n imag exp(jπ(n+1)/2)exp(2πj(pN+k)n/N) h filter (iN+kN/2pN) k=N/2+1,N/2+2...N/21,N/2
b i,m real = k=N/2+1 N/2 q= + exp(2πjkm/N)r(qN+k) h receiver_filter ((iq)Nk)
r(qN+k)= d= + e=N/2+1 +N/2 s(dN+e) h c (qN+kdNe)
H c ((m+d)/(TN))= H b ((m+d)/(TN))exp(j β 2 L/2 (2π/(TN)) 2 (m+d) 2 ) H b (m/(TN))exp(j(α m 2 +α2md+α d 2 ))
b i,m real = H b (m/(TN))exp(jπm/2+jα m 2 ) (A a i,m real + I i,m real +jexp(jαm) c m+1 real +jexp(jαm) c m1 real +j c m imag +jexp(jαm) c m+1 imag +jexp(jαm) c m1 imag )
b i,m real = H b (m/(TN))exp(jπm/2jα m 2 ) ( a i,m real +j c m+1 real +j c m1 real +j c m imag +j c m+1 imag +j c m1 imag )
S E net =N/( N CP +N)
N CP =| β 2 LΔω |/T
h c (qN+kdNe) = g=MN/2+1 MN/2 H b (g/(MNT))exp(jα (g/M) 2 )exp(2πj(qN+kdNe)g/(MN))
r(qN+k)= p= + n=N/2+1 N/2 ( a p,n real exp(jπn/2) g=MN/2+1 MN/2 H filter (gMn) H b (g/(MNT)) exp(jα (g/M) 2 )exp(2πj((qN+k)g+(Mng)pN)/(MN)) + a p,n imag exp(jπ(n+1)/2) g=MN/2+1 MN/2 H filter (gMn) H b (g/(MNT)) exp(jα (g/M) 2 )exp(2πj((qN+k)g+(Mng)(pN+N/2))/(MN)))
r(qN+k)= p= + n=N/2+1 N/2 ( a p,n real exp(jπn/2) exp(2πjkn/N) H b (n/(NT)) g 1 =M M H filter ( g 1 ) exp(jα (n+ g 1 /M) 2 )exp(2πj((qN+kpN) g 1 )/(MN)) + a p,n imag exp(jπ(n+1)/2))exp(2πjkn/N) H b (n/(NT)) g 1 =M M H filter ( g 1 ) exp(jα (n+ g 1 /M) 2 )exp(2πj((qN+kpNN/2) g 1 )/(MN)))
exp(jα (n+ g 1 /M) 2 )=exp(jα n 2 +2jαn g 1 /M+jα ( g 1 /M) 2 )
r(qN+k)= p= + n=N/2+1 N/2 exp(2πjkn/N) H b (n/(NT)) ( a p,n real exp(jπn/2) exp(jα n 2 ) h filter (qN+kpN+αNn/π) + a p,n imag exp(jπ(n+1)/2)exp(jα n 2 ) h filter (qN+kpN+αNn/πN/2))
b i,m real =exp(jπm/2+jα m 2 ) H b (m/(NT)) k 1 = + p= + ( a p,m real h filter ( k 1 +(ip)N+αNm/π) h filter ( k 1 ) + j a p,m imag h filter ( k 1 +(ip0.5)N+αNm/π) h filter ( k 1 )) +exp(jπ(m+1)/2+jα (m+1) 2 ) H b ((m+1)/(NT)) k 1 = + p= + ( a p,m+1 real h filter ( k 1 +(ip)N+αN(m+1)/π) h filter ( k 1 )exp(2πj k 1 /N) +j a p,m+1 imag h filter ( k 1 +(ip0.5)N+αN(m+1)/π) h filter ( k 1 )exp(2πj k 1 /N)) +exp(jπ(m1)/2+jα (m1) 2 ) H b ((m1)/(NT)) k 1 = + p= + ( a p,m1 real h filter ( k 1 +(ip)N+αN(m1)/π) h filter ( k 1 )exp(2πj k 1 /N) +j a p,m1 imag h filter ( k 1 +(ip0.5)N+αN(m1)/π) h filter ( k 1 )exp(2πj k 1 /N))
exp(jπm/2+jα m 2 ) H b (m/(NT)) k 1 = + p= + a p,m real h filter ( k 1 +(ip)N+αNm/π) h filter ( k 1 ) =exp(jπm/2+jα m 2 ) H b (m/(NT))( a i,m real k 1 = + h filter ( k 1 + αNm/π) h filter ( k 1 ) + k 1 = + pi a p,m real h filter ( k 1 +(ip)N+αNm/π) h filter ( k 1 ) ) =exp(jπm/2+jα m 2 ) H b (m/(NT))(A a i,m real + I i,m real )
exp(jπ(m+1)/2+jα (m+1) 2 ) H b ((m+1)/(NT)) k 1 = + p= + a p,m+1 real h filter ( k 1 +(ip)N+αN(m+1)/π) h filter ( k 1 )exp(2πj k 1 /N) jexp(jπm/2) (1) ip exp(jα (m+1) 2 ) H b (m/(NT))exp(jα(m+1)) k 2 = + p= + a p,m+1 real h filter ( k 2 + (ip)N+αN(m+1)/π 2 ) h filter ( k 2 (ip)N+αN(m+1)/π 2 )exp(2πj k 2 /N) =jexp(jπm/2+jα m 2 ) H b (m/(NT))exp(jαm) c m+1 real
b i,m real = H b (m/(TN))exp(jπm/2+jα m 2 ) (A a i,m real + I i,m real +jexp(jαm) c m+1 real +jexp(jαm) c m1 real +j c m imag +jexp(jαm) c m+1 imag +jexp(jαm) c m1 imag )
b i,m real = k=N/2+1 N/2 q= + exp(2πjkm/N)r(qN+kαNm/π) h filter (qN+kiN)
r(qN+kαNm/π)= p= + n=N/2+1 N/2 exp(2πjkn/N2jαmn) H b (n/(NT)) ( a p,n real exp(jπn/2) exp(jα n 2 ) h filter (qN+kpN+αN(nm)/π) + a p,n imag exp(jπ(n+1)/2)exp(jα n 2 ) h filter (qN+kpN+αN(nm)/πN/2))
b i,m real = n=m1,m,m+1 exp(jπn/2+jα n 2 2jαmn) H b (n/(NT)) k 1 = + p= + ( a p,n real h filter ( k 1 +(ip)N+αN(nm)/π) h filter ( k 1 )exp(2πj k 1 (nm)/N) +j a p,m imag h filter ( k 1 +(ip0.5)N+αN(nm)/π) h filter ( k 1 )exp(2πj k 1 (nm)/N))
b i,m real = H b (m/(TN))exp(jπm/2jα m 2 ) ( a i,m real +j c m+1 real +j c m1 real +j c m imag +j c m+1 imag +j c m1 imag )

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