Abstract

An analytical method based on the moment generating function (MGF) is proposed for assessing the performance of direct-detection (DD) orthogonal frequency division multiplexing (OFDM) optical receivers with radio-frequency (RF) demodulation. The MGF-based method is a generalization of the method previously reported in the literature for DD baseband OFDM optical receivers. The proposed method relies on the analytical derivation of equivalent filters that describe the combined effect of electrical filtering + RF demodulation + FFT operation + the equalizer of the OFDM receiver for the real and imaginary parts of the signal at the equalizer output. The method takes into account imperfections of the RF demodulator, namely, power and phase imbalance between the RF demodulator arms and different electrical filtering on its arms. Numerical results show excellent agreement between the bit error probability estimates provided by the proposed method and estimates obtained from Monte Carlo simulation, in the absence and presence of receiver imperfections.

© 2014 Optical Society of America

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References

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  1. W. Shieh and I. Djordjevic, Orthogonal Frequency Division Multiplexing for Optical Communications. San Diego: Academic, 2010, chs. 1, 2, and 7.
  2. B. Schmidt, A. Lowery, and J. Armstrong, “Experimental demonstrations of electronic dispersion compensation for long-haul transmission using direct-detection optical OFDM,” J. Lightwave Technol., vol.  26, no. 1, pp. 196–203, Jan. 2008.
    [CrossRef]
  3. W. Peng, I. Morita, H. Takahashi, and T. Tsuritani, “Transmission of high-speed (>100  Gb/s) direct-detection optical OFDM superchannel,” J. Lightwave Technol., vol.  30, no. 12, pp. 2025–2034, June 2012.
    [CrossRef]
  4. X. Chen, A. Li, D. Che, Q. Hu, Y. Wang, J. He, and W. Shieh, “Block-wise phase switching for double-sideband direct detected optical OFDM signals,” Opt. Express, vol.  21, no. 11, pp. 13436–13441, May 2013.
    [CrossRef]
  5. I. Cano, M. Santos, and J. Prat, “Optimum carrier to signal power ratio for remote heterodyne DD-OFDM in PONs,” IEEE Photon. Technol. Lett., vol.  25, no. 13, pp. 1242–1245, July 2013.
    [CrossRef]
  6. N. Cvijetic, “OFDM for next-generation optical access networks,” J. Lightwave Technol., vol.  30, no. 4, pp. 384–398, Feb. 2012.
    [CrossRef]
  7. X. Jin, J. Groenewald, E. Salas, R. Gidding, and J. Tang, “Upstream power budgets of IMDD optical OFDMA PONs incorporating RSOA intensity modulator-based colorless ONUs,” J. Lightwave Technol., vol.  31, no. 12, pp. 1914–1920, June 2013.
    [CrossRef]
  8. E. Vanin, “Performance evaluation of intensity modulated optical OFDM systems with digital baseband distortion,” Opt. Express, vol.  19, no. 5, pp. 4280–4293, Feb. 2011.
    [CrossRef]
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    [CrossRef]
  10. T. Alves and A. Cartaxo, “Semi-analytical approach for performance evaluation of direct-detection OFDM optical communication systems,” Opt. Express, vol.  17, no. 21, pp. 18714–18729, Oct. 2009.
    [CrossRef]
  11. J. Rebola and A. Cartaxo, “Moment generating function for the rigorous performance assessment of direct-detection baseband OFDM communication systems,” J. Lightwave Technol., vol.  30, no. 23, pp. 3617–3626, Dec. 2012.
    [CrossRef]
  12. A. Lowery, L. Du, and J. Armstrong, “Performance of optical OFDM in ultralong-haul WDM lightwave systems,” J. Lightwave Technol., vol.  25, no. 1, pp. 131–138, Jan. 2007.
    [CrossRef]
  13. W. Peng, B. Zhang, K. Feng, X. Wu, A. Willner, and S. Chi, “Spectrally efficient direct-detected OFDM transmission incorporating a tunable frequency gap and an iterative detection techniques,” J. Lightwave Technol., vol.  27, no. 24, pp. 5723–5735, Dec. 2009.
    [CrossRef]
  14. L. Yang, K. Panta, and J. Armstrong, “Impact of timing jitter and I/Q imbalance in OFDM systems,” IEEE Commun. Lett., vol.  17, no. 2, pp. 253–256, Feb. 2013.
    [CrossRef]
  15. A. Amin, S. Jansen, H. Takahashi, I. Morita, and H. Tanaka, “A hybrid IQ imbalance compensation method for optical OFDM transmission,” Opt. Express, vol.  18, no. 5, pp. 4859–4866, Mar. 2010.
    [CrossRef]
  16. E. Forestieri, “Evaluating the error probability in lightwave systems with chromatic dispersion, arbitrary pulse shape and pre- and postdetection filtering,” J. Lightwave Technol., vol.  18, no. 11, pp. 1493–1503, Nov. 2000.
    [CrossRef]
  17. B. Schmidt, A. Lowery, and L. Du, “Low sample rate transmitter for direct-detection optical OFDM,” in Proc. 10th Optical Fiber Communication Conf. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), San Diego, 2009, paper OWM4.
  18. W. Peng, X. Wu, V. Arbab, K. Feng, B. Shamee, L. Christen, J. Yang, A. Willner, and S. Chi, “Theoretical and experimental investigations of direct-detected RF-tone-assisted optical OFDM systems,” J. Lightwave Technol., vol.  27, no. 10, pp. 1332–1339, May 2009.
    [CrossRef]
  19. G. Agrawal, “Optical signal generation,” in Lightwave Technology Communication Systems. Wiley, 2005, ch. 2, pp. 37–38.
  20. X. Zhou, “Enabling technologies and challenges for transmission of 400  Gb/s signals in 50  GHz channel grid,” Front. Optoelectron., vol.  6, no. 1, pp. 30–45, Mar. 2013.
  21. A. Lowery, “Amplified-spontaneous noise limit of optical OFDM lightwave systems,” Opt. Express, vol.  16, no. 2, pp. 860–865, Jan. 2008.
    [CrossRef]

2013

I. Cano, M. Santos, and J. Prat, “Optimum carrier to signal power ratio for remote heterodyne DD-OFDM in PONs,” IEEE Photon. Technol. Lett., vol.  25, no. 13, pp. 1242–1245, July 2013.
[CrossRef]

L. Yang, K. Panta, and J. Armstrong, “Impact of timing jitter and I/Q imbalance in OFDM systems,” IEEE Commun. Lett., vol.  17, no. 2, pp. 253–256, Feb. 2013.
[CrossRef]

X. Zhou, “Enabling technologies and challenges for transmission of 400  Gb/s signals in 50  GHz channel grid,” Front. Optoelectron., vol.  6, no. 1, pp. 30–45, Mar. 2013.

X. Jin, J. Groenewald, E. Salas, R. Gidding, and J. Tang, “Upstream power budgets of IMDD optical OFDMA PONs incorporating RSOA intensity modulator-based colorless ONUs,” J. Lightwave Technol., vol.  31, no. 12, pp. 1914–1920, June 2013.
[CrossRef]

X. Chen, A. Li, D. Che, Q. Hu, Y. Wang, J. He, and W. Shieh, “Block-wise phase switching for double-sideband direct detected optical OFDM signals,” Opt. Express, vol.  21, no. 11, pp. 13436–13441, May 2013.
[CrossRef]

2012

2011

2010

2009

2008

2007

2000

Agrawal, G.

G. Agrawal, “Optical signal generation,” in Lightwave Technology Communication Systems. Wiley, 2005, ch. 2, pp. 37–38.

Alves, T.

Amin, A.

Arbab, V.

Armstrong, J.

Cano, I.

I. Cano, M. Santos, and J. Prat, “Optimum carrier to signal power ratio for remote heterodyne DD-OFDM in PONs,” IEEE Photon. Technol. Lett., vol.  25, no. 13, pp. 1242–1245, July 2013.
[CrossRef]

Cartaxo, A.

Che, D.

Chen, X.

Chi, S.

Christen, L.

Cvijetic, N.

Djordjevic, I.

W. Shieh and I. Djordjevic, Orthogonal Frequency Division Multiplexing for Optical Communications. San Diego: Academic, 2010, chs. 1, 2, and 7.

Du, L.

A. Lowery, L. Du, and J. Armstrong, “Performance of optical OFDM in ultralong-haul WDM lightwave systems,” J. Lightwave Technol., vol.  25, no. 1, pp. 131–138, Jan. 2007.
[CrossRef]

B. Schmidt, A. Lowery, and L. Du, “Low sample rate transmitter for direct-detection optical OFDM,” in Proc. 10th Optical Fiber Communication Conf. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), San Diego, 2009, paper OWM4.

Feng, K.

Forestieri, E.

Gidding, R.

Groenewald, J.

He, J.

Hu, Q.

Jansen, S.

Jin, X.

Li, A.

Lowery, A.

Morita, I.

Panta, K.

L. Yang, K. Panta, and J. Armstrong, “Impact of timing jitter and I/Q imbalance in OFDM systems,” IEEE Commun. Lett., vol.  17, no. 2, pp. 253–256, Feb. 2013.
[CrossRef]

Peng, W.

Prat, J.

I. Cano, M. Santos, and J. Prat, “Optimum carrier to signal power ratio for remote heterodyne DD-OFDM in PONs,” IEEE Photon. Technol. Lett., vol.  25, no. 13, pp. 1242–1245, July 2013.
[CrossRef]

Rebola, J.

Salas, E.

Santos, M.

I. Cano, M. Santos, and J. Prat, “Optimum carrier to signal power ratio for remote heterodyne DD-OFDM in PONs,” IEEE Photon. Technol. Lett., vol.  25, no. 13, pp. 1242–1245, July 2013.
[CrossRef]

Schmidt, B.

B. Schmidt, A. Lowery, and J. Armstrong, “Experimental demonstrations of electronic dispersion compensation for long-haul transmission using direct-detection optical OFDM,” J. Lightwave Technol., vol.  26, no. 1, pp. 196–203, Jan. 2008.
[CrossRef]

B. Schmidt, A. Lowery, and L. Du, “Low sample rate transmitter for direct-detection optical OFDM,” in Proc. 10th Optical Fiber Communication Conf. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), San Diego, 2009, paper OWM4.

Shamee, B.

Shieh, W.

Takahashi, H.

Tanaka, H.

Tang, J.

Tsuritani, T.

Vanin, E.

Wang, Y.

Willner, A.

Wu, X.

Yang, J.

Yang, L.

L. Yang, K. Panta, and J. Armstrong, “Impact of timing jitter and I/Q imbalance in OFDM systems,” IEEE Commun. Lett., vol.  17, no. 2, pp. 253–256, Feb. 2013.
[CrossRef]

Zhang, B.

Zhou, X.

X. Zhou, “Enabling technologies and challenges for transmission of 400  Gb/s signals in 50  GHz channel grid,” Front. Optoelectron., vol.  6, no. 1, pp. 30–45, Mar. 2013.

Front. Optoelectron.

X. Zhou, “Enabling technologies and challenges for transmission of 400  Gb/s signals in 50  GHz channel grid,” Front. Optoelectron., vol.  6, no. 1, pp. 30–45, Mar. 2013.

IEEE Commun. Lett.

L. Yang, K. Panta, and J. Armstrong, “Impact of timing jitter and I/Q imbalance in OFDM systems,” IEEE Commun. Lett., vol.  17, no. 2, pp. 253–256, Feb. 2013.
[CrossRef]

IEEE Photon. Technol. Lett.

I. Cano, M. Santos, and J. Prat, “Optimum carrier to signal power ratio for remote heterodyne DD-OFDM in PONs,” IEEE Photon. Technol. Lett., vol.  25, no. 13, pp. 1242–1245, July 2013.
[CrossRef]

J. Lightwave Technol.

E. Forestieri, “Evaluating the error probability in lightwave systems with chromatic dispersion, arbitrary pulse shape and pre- and postdetection filtering,” J. Lightwave Technol., vol.  18, no. 11, pp. 1493–1503, Nov. 2000.
[CrossRef]

A. Lowery, L. Du, and J. Armstrong, “Performance of optical OFDM in ultralong-haul WDM lightwave systems,” J. Lightwave Technol., vol.  25, no. 1, pp. 131–138, Jan. 2007.
[CrossRef]

B. Schmidt, A. Lowery, and J. Armstrong, “Experimental demonstrations of electronic dispersion compensation for long-haul transmission using direct-detection optical OFDM,” J. Lightwave Technol., vol.  26, no. 1, pp. 196–203, Jan. 2008.
[CrossRef]

W. Peng, X. Wu, V. Arbab, K. Feng, B. Shamee, L. Christen, J. Yang, A. Willner, and S. Chi, “Theoretical and experimental investigations of direct-detected RF-tone-assisted optical OFDM systems,” J. Lightwave Technol., vol.  27, no. 10, pp. 1332–1339, May 2009.
[CrossRef]

W. Peng, K. Feng, A. Willner, and S. Chi, “Estimation of the bit error rate for direct-detected OFDM signals with optically preamplified receivers,” J. Lightwave Technol., vol.  27, no. 10, pp. 1340–1346, May 2009.
[CrossRef]

N. Cvijetic, “OFDM for next-generation optical access networks,” J. Lightwave Technol., vol.  30, no. 4, pp. 384–398, Feb. 2012.
[CrossRef]

W. Peng, I. Morita, H. Takahashi, and T. Tsuritani, “Transmission of high-speed (>100  Gb/s) direct-detection optical OFDM superchannel,” J. Lightwave Technol., vol.  30, no. 12, pp. 2025–2034, June 2012.
[CrossRef]

J. Rebola and A. Cartaxo, “Moment generating function for the rigorous performance assessment of direct-detection baseband OFDM communication systems,” J. Lightwave Technol., vol.  30, no. 23, pp. 3617–3626, Dec. 2012.
[CrossRef]

X. Jin, J. Groenewald, E. Salas, R. Gidding, and J. Tang, “Upstream power budgets of IMDD optical OFDMA PONs incorporating RSOA intensity modulator-based colorless ONUs,” J. Lightwave Technol., vol.  31, no. 12, pp. 1914–1920, June 2013.
[CrossRef]

W. Peng, B. Zhang, K. Feng, X. Wu, A. Willner, and S. Chi, “Spectrally efficient direct-detected OFDM transmission incorporating a tunable frequency gap and an iterative detection techniques,” J. Lightwave Technol., vol.  27, no. 24, pp. 5723–5735, Dec. 2009.
[CrossRef]

Opt. Express

Other

W. Shieh and I. Djordjevic, Orthogonal Frequency Division Multiplexing for Optical Communications. San Diego: Academic, 2010, chs. 1, 2, and 7.

B. Schmidt, A. Lowery, and L. Du, “Low sample rate transmitter for direct-detection optical OFDM,” in Proc. 10th Optical Fiber Communication Conf. and the Nat. Fiber Optic Engineers Conf. (OFC/NFOEC), San Diego, 2009, paper OWM4.

G. Agrawal, “Optical signal generation,” in Lightwave Technology Communication Systems. Wiley, 2005, ch. 2, pp. 37–38.

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Figures (11)

Fig. 1.
Fig. 1.

Block diagram of the DD optical receiver followed by the OFDM electrical receiver with I/Q RF demodulation.

Fig. 2.
Fig. 2.

BEP as a function of the RF carrier frequency fRF for a sixth-order Butterworth electrical filter (B6) and a fifth-order Bessel electrical filter (B5) with 3dB bandwidth of 1.5 B, for N=32 and N=64. Lines: MC; symbols: MGF.

Fig. 3.
Fig. 3.

BEP as a function of the electrical filter 3dB bandwidth (normalized to the OFDM signal bandwidth) for a sixth-order Butterworth electrical filter (B6) and a fifth-order Bessel electrical filter (B5), for a RF carrier frequency of fRF=7.5GHz and subcarrier numbers of N=32 and N=64. Lines, MC; symbols, MGF.

Fig. 4.
Fig. 4.

BEP as a function of the optical filter 3dB bandwidth (normalized to the OFDM signal bandwidth) for a second-order super-Gaussian optical filter and a Gaussian optical filter, for a RF carrier frequency of fRF=7.5GHz, a sixth-order Butterworth electrical filter with 3dB bandwidth of 1.5B, and a subcarrier number of N=32. Lines, MC; symbols, MGF.

Fig. 5.
Fig. 5.

BEP as a function of the RF carrier frequency fRF for a sixth-order Butterworth electrical filter with 3dB bandwidth of 1.5B and N=32, for several values of the parameter μ and η=0.6. Line, MC; symbols, MGF.

Fig. 6.
Fig. 6.

BEP as a function of the RF carrier frequency fRF for a sixth-order Butterworth electrical filter with 3dB bandwidth of 1.5B and N=32, for several values of the parameter η and μ=1.1. Line, MC; symbols, MGF.

Fig. 7.
Fig. 7.

BEP as a function of the number of realizations of the OFDM signal, for a sixth-order Butterworth electrical filter with 3dB bandwidth of 1.5B, N=32, η=0.6, and μ=1.1, for RF carrier frequencies fRF=3.5, 5, and 7.5 GHz. The BEP is estimated from the MGF.

Fig. 8.
Fig. 8.

BEP as a function of ξ, for the subcarrier numbers N=32 and N=64. Lines, MC; symbols, MGF.

Fig. 9.
Fig. 9.

BEP as a function of ϕ1, for the subcarrier numbers N=32 and N=64. Lines, MC; symbols, MGF.

Fig. 10.
Fig. 10.

BEP as a function of the optical filter detuning (relative to the optical carrier frequency) for the subcarrier numbers N=32 and different optical filter 3dB bandwidths of 20, 25, and 30 GHz. Lines, MC; symbols, MGF.

Fig. 11.
Fig. 11.

BEP as a function of the modulation index of the modulator for N=32 subcarriers and DSB and SSB optical OFDM signaling. Lines, MC; symbols, MGF.

Equations (21)

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id(t)=|(Gx(t)+n(t))*ho(t)|2*hel(t).
w(t)=[ξid(t)cos(2πfRFt+ϕ1)]*h1(t)j[(1ξ)id(t)sin(2πfRFt+ϕ2)]*h2(t).
Heq(n)=ρn·exp(jθn).
Zγ(n)=k=1Nw(tk(γ))·ej2π(k1)(n1)NHeq(n),with{n=1,,Nγ=1,,Ns.
WR,γ,n(f)=Hel(f)·ρn2·k=1N[ej2π(f+fRF)tk(γ)[an,kH1(f+fRF)+bn,kH2(f+fRF)]+ej2π(ffRF)tk(γ)[an,k*H1(ffRF)+bn,k*H2(ffRF)]],
WI,γ,n(f)=Hel(f)·ρn2·k=1N[ej2π(f+fRF)tk(γ)[cn,kH1(f+fRF)+dn,kH2(f+fRF)]+ej2π(ffRF)tk(γ)[cn,k*H1(ffRF)+dn,k*H2(ffRF)],
WR,γ,n(f)=Hel(f)·ρn4·k=1N[ej2π(f+fRF)tk(γ)H(f+fRF)·ej(φn,k+ϕ)+ej2π(ffRF)tk(γ)H(ffRF)·ej(φn,k+ϕ)],
WI,γ,n(f)=jHel(f)·ρn4·k=1N[ej2π(f+fRF)tk(γ)H(f+fRF)·ej(φn,k+ϕ)ej2π(ffRF)tk(γ)H(ffRF)·ej(φn,k+ϕ)].
WR,γ,n(f)=Hel(f)ρn4[R1,n(f+fRF)[ξejϕ1H1(f+fRF)+(1ξ)ejϕ2H2(f+fRF)]+R2,n(f+fRF)[ξejϕ1H1(f+fRF)(1ξ)ejϕ2H2(f+fRF)]+R1,n(ffRF)[ξejϕ1H1(ffRF)(1ξ)ejϕ2H2(ffRF)]+R2,n(ffRF)[ξejϕ1H1(ffRF)+(1ξ)ejϕ2H2(ffRF)]],
WI,γ,n(f)=jHel(f)ρn4[R1,n(f+fRF)[ξejϕ1H1(f+fRF)+(1ξ)ejϕ2H2(f+fRF)]R2,n(f+fRF)[ξejϕ1H1(f+fRF)(1ξ)ejϕ2H2(f+fRF)]+R1,n(ffRF)[ξejϕ1H1(ffRF)(1ξ)ejϕ2H2(ffRF)]R2,n(ffRF)[ξejϕ1H1(ffRF)+(1ξ)ejϕ2H2(ffRF)]],
R1,n(f)=ej2πfto(γ)[1ej2πfNTc]·ejθn1ej[2πfTc+2π(n1)/N],
R2,n(f)=ej2πfto(γ)[1ej2πfNTc]·ejθn1ej[2πfTc2π(n1)/N].
ψRe[Zγ(n)](s)=exp(dns)·i=12M+11(1λi,nSeq/Tos)p·exp(Seq/To·|bi,n|2s21λi,nSeq/To·s)
BEP=γ=1Nsn=1Ni1[1SEP{Re[Zγ(n)]}][1SEP{Im[Zγ(n)]}]NsNilog2M,
hFFT,n(t)=ρnk=1Nδ(t+tk(γ))·ejφn,k,
Zγ(n)=[w(t)*hFFT,n(t)]|t=0,
Zγ(n)=ρn[k=1Nξid(τ2)cos(2πfRFτ2+ϕ1)cosφn.k·δ(tτ1+tk(γ))h1(τ1τ2)dτ1dτ2k=1N(1ξ)id(τ2)·sin(2πfRFτ2+ϕ2)sinφn.kδ(tτ1+tk(γ))h2(τ1τ2)dτ1dτ2j[k=1Nξid(τ2)cos(2πfRFτ2+ϕ1)sinφn.kδ(tτ1+tk(γ))h1(τ1τ2)dτ1dτ2+k=1N(1ξ)id(τ2)sin(2πfRFτ2+ϕ2)cosφn.kδ(tτ1+tk(γ))h2(τ1τ2)dτ1dτ2]]|t=0.
id(τ2)=l=LLm=LLGxlxm*Ho(lTw)Hel(lmTw)Ho*(mTw)ej2π(lm)τ2/Tw+l=LLm=MMGxlnm*Ho(lTw)Hel(lTwmTo)Ho*(mTo)ej2πlτ2/Tw+l=LLm=MMGxl*nmHo*(lTw)Hel*(lTwmTo)Ho(mTo)ej2πlτ2/Tw+l=MMm=MMnlnm*Ho(lTo)Hel(lmTo)Ho*(mTo),
v(τ)δ(ttdτ)dτ=v(ttd),
ej2πfoτ·h(tτ)dτ=ej2πfotH(fo),
Re[Zγ(n)]=l=LLm=LLGxlxm*Ho(lTw)WR,γ,n(lmTw)Ho*(mTw)+l=LLm=MMGxlnm*Ho(lTw)WR,γ,n(lTwmTo)Ho*(mTo)+l=LLm=MMGxl*nmHo*(lTw)WR,γ,n*(lTwmTo)Ho(mTo)+l=MMm=MMnlnm*Ho(lTo)WR,γ,n(lmTo)Ho*(mTo)