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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 16 — Aug. 2, 2010
  • pp: 17239–17251
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Equalization-enhanced phase noise for 100Gb/s transmission and beyond with coherent detection

Alan Pak Tao Lau, Thomas Shun Rong Shen, William Shieh, and Keang-Po Ho  »View Author Affiliations


Optics Express, Vol. 18, Issue 16, pp. 17239-17251 (2010)
http://dx.doi.org/10.1364/OE.18.017239


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Abstract

The probability density function and impact of equalization-enhanced phase noise (EEPN) is analytically investigated and simulated for 100 Gb/s coherent systems using electronic dispersion compensation. EEPN impairment induces both phase noise and amplitude noise with the former twice as much as the latter. The effects of transmitter phase noise on EEPN are negligible for links with residual dispersion in excess of 700 ps/nm. Optimal linear equalizer in the presence of EEPN is derived but show only marginal performance improvement, indicating that EEPN is difficult to mitigate using simple DSP techniques. In addition, the effects of EEPN on carrier recovery techniques and corresponding cycle slip probabilities are studied.

© 2010 Optical Society of America

1.Introduction

2.Equalization-Enhanced Phase Noise

A. Theoretical model and system impact

Consider a coherent communication system consisting of multiple spans of propagation without dispersion compensating fibers as shown in Figure 1. In this setup,xn denotes independent identically distributed (i.i.d.) information symbols with a symbol rate R of 27.59 GSym/s and normalized average power E[∣xn2]=1. With polarization-multiplexing (PM) and a 7 % Forward Error Correction (FEC) overhead, such symbol rate corresponds to 100 Gb/s and 200 Gb/s per channel transmission using Quadrature Phase-Shift Keying (QPSK) and 16-Quadrature Amplitude Modulation (QAM) modulation formats respectively. Fiber nonlinearity and polarization effects are neglected for simplicity.

Fig 1. A coherent communication system in presence of both transmitter (Tx) phase noise ejϕt(t) and receiver (Rx) phase noise ejϕr(t) . The received signal is sampled and passed into a finite-impulse response (FIR) filter w followed by a carrier recovery (CR) unit to produce the symbol estimate n.

The information symbols are first passed through a pulse-shaping filter b(t) to form the transmitted signal

A(t)=nxnb(tnT0)
(1)

y(t)=nxnq(tnT0)+ν(t)
(2)

where q(t) = p(t)* g(t) = p(t)* h(t)*b(t) and ν(t) = p(t)*n(t).In this formulation, ‘*’ denotes convolution, and h(t) and p(t) respectively denote the impulse response characterizing a channel with chromatic dispersion and electrical low pass filter after photo-detection respectively. The received signal is then sampled to form ym = y(mT) where T is the sampling period and S=T0/T is the over-sampling rate. To compensate for CD and demodulate the kth transmitted symbol xk, a vector of received samples

y=[ySk+LySk+L1ySkL+1ySkL]T
(3)

with length N=2L+1 is formed and passed through a equalizer, or, a linear finite impulse response (FIR) filter, w. In absence of laser phase noise, the estimate of the transmitted symbol k is simply given by

x̂k=wTy.
(4)

According to the minimum mean-squared error (MMSE) criterion, the optimal linear FIR filter lin w lin is derived as

wlin=(E[y*yT])1E[xky*]=A1α
(5)

where A and α are given by [2

2. E. Ip and J. M. Kahn, “Digital equalization of Chromatic Dispersion and Polarization Mode Dispersion,” IEEE/OSA J. Lightwave Technol. 25(8), 2033–2043 (2007). [CrossRef]

]

A(l,m)=E[ySk+Ll*ySk+Lm]=nq*((Sk+Ll)TnT0)q((Sk+Lm)TnT0)
+N0p*(tlT)p(tmT)dt
(6)

and

α(l)=E[xkySk+Ll*]=q*((Sk+Ll)TkT0).
(7)

Denoting the estimation error as ε = nxn and the phase error as θ = arg(n) −arg(xn), the corresponding mean-squared error becomes

MSE1=E[ε2]=E[xkαHA1y2]=1αHA1α
(8)

and the phase noise variance σ 2 θ is given by

σθ2=E[θ2]12E[ε2]
(9)

for large optical signal-to-noise ratio (OSNR).

With laser phase noise ϕr(t), the spectrum of a laser ejϕr(t) can be modeled as a Lorentzian lineshape with 3-dB linewidth Δυ in which

E[ej(ϕr(t1)ϕr(t2))]=exp(πΔυt1t2).
(10)

Equivalently, the phase noise ϕr(t) can be modeled as a Wiener process in which ϕr(t 2)−ϕr(t 1) is Gaussian distributed with zero mean and variance σ 2 p = 2πΔυt 1t 2∣. In presence of receiver (Rx) or LO phase noise and uncompensated CD, the received signal becomes

y(t)=([nxng(tnT0)+n(t)]ejϕr(t))*p(t).
(11)

Due to the fact that the multiplication and convolution operations are not commutable, introduction of Rx phase noise prior to electronic CD compensation prevents complete equalization of CD and results in additional impairments. Referred to as equalization-enhanced phase noise (EEPN) [20

20. C. Xie, “Local oscillator phase noise induced penalties in optical coherent detection systems using electronic chromatic dispersion compensation,” in Proceedings OFC/NFOEC, San Diego, CA, 2009, Paper OMT4.

], this effect is otherwise not present if optical dispersion compensation techniques are used. To highlight the system impact of EEPN alone and provide a performance upper bound for all carrier recovery techniques in presence of EEPN, we will assume perfect knowledge of the laser phase noise ejϕt(kT0) and ejϕr(kT0) at the carrier recovery (CR) unit so that the estimate of the transmitted symbol is given by x̂k=wTy·(ej(ϕt(kT0)+ϕr(kT0))) in this section. The effect of EEPN on practical carrier recovery techniques will be studied in later sections. From Appendix A, the pdf of EEPN for a given transmitted symbol xk is given by

f(εxk)=1CL·xCL14π2ΔυTΛ(X)exp(14πΔυT[Re{ε} Im{ε}]Λ(X)1[Re{ε}Im{ε}]T)
(12)

where X = […x k−2,x k−1,x k+1,x k+2…], C is the set {1, −1} for BPSK and {1, −1, j, −j} for QPSK formats etc. Figure 2 (a)–(c) illustrate the pdf of EEPN for various laser linewidths and transmission distance for QPSK systems with electronic dispersion compensation. The EEPN induces more phase noise on k than amplitude noise, resulting in the pdf being elliptical in nature. In presence of ASE noise, the pdf is more circular-like as shown in Figure 2 (d), indicating the relative significance of complex circularly symmetric ASE noise compared with EEPN.

Fig. 2. Pdf of EEPN for (a) Δυ = 5MHz, 6800 ps/nm uncompensated CD, no ASE noise; (b) Δυ = 5MHz, 13600 ps/nm uncompensated CD, no ASE noise; (c) Δυ = 10 MHz, 13600 ps/nm uncompensated CD, no ASE noise and (d) Δυ = 10 MHz, 13600 ps/nm uncompensated CD, OSNR = 13 dB. The modulation format is QPSK.

Fig. 3. Phase noise variance vs. OSNR for a transmission distance of 1200 km using optical and electronic dispersion compensation. The LO linewidth is 3 MHz. In presence of Rx phase noise and electronic dispersion compensation, the overall phase noise variance increases significantly.
Fig.4. Phase noise variance vs. OSNR for a QPSK system with electronic dispersion compensation for various LO linewidths. The propagation distance is 3200 km.
Fig. 5. Mean-squared error vs. OSNR for (a) 16-QAM and (b) 64-QAM systems with electronic dispersion compensation for various LO linewidths. The propagation distance is 1600 km.

B. EEPN Induced Phase and Amplitude Noise

The interaction between Rx phase noise and electronic CD compensation produces additional phase distortions as well as amplitude distortions. To look further into the nature of equalization-enhanced impairments in general, we studied the variances of the amplitude noise Var(∣k∣) as well as phase noise σ 2 θ induced by EEPN for a QPSK system and simulation results are shown in Figure 6. From the figure, it can be seen that the interaction between Rx phase noise and electronic CD compensation induces more phase noise than amplitude noise even at high OSNR, in contrast to systems corrupted by AWGN alone. For various values of OSNR and uncompensated CD, the EEPN induced phase noise variance is approximately twice the amplitude noise variance, indicating that EEPN induced phase noise rather than amplitude noise is a more dominant transmission impairment for systems using electronic CD compensation.

Fig. 6. Amplitude and phase noise variance vs. OSNR in presence of electronic CD compensation with a LO linewidth of 3MHz for a QPSK system. The length of propagation is 1200 km. Inset: corresponding received signal constellation diagram showing asymmetric noise distribution.

C. EEPN from transmitter laser

Fig. 7. Phase noise variance using electronic CD compensation for various laser linewidths and propagation distance for a QPSK system. A laser linewidth of 1MHz corresponds to a 0 MHz Tx linewidth and 1 MHz Rx linewidth for the ‘Rx only’ case and 1 MHz linewidth for both lasers for the ‘Rx, Tx’ case.

3. Optimal Equalization in Presence of EEPN

In presence of EEPN, the linear MMSE equalizer w lin previously studied for CD compensation is no longer optimal as the derivation of w lin does not take into account the statistics of the Rx phase noise. In this case, the received signal is given by

y(t)=([nxng(tnT0)+n(t)]·ejϕr(t))*p(t)=(nxng(τnT0))ejϕr(τ)p(tτ)dτ+(n(t)ejϕr(t))*p(t).
(13)

Taking into account the statistics of ejϕr(t) , the optimal linear MMSE estimate can now be expressed as n = α T PN A −1 PN y = w T PN y where

APN(l,m)=E[ySk+Ll*ySk+Lm]
={ng*(τ1nT0)g(τ2nT0)p*((Sk+Ll)Tτ1)p((Sk+Lm)Tτ2).
E[ej(ϕr(τ2)ϕr(τ1))]dτ1dτ2}+N0p*(tlT)p(tmT)dt
={ng*(τ1nT0)g(τ2nT0)p*((Sk+Ll)Tτ1)p((Sk+Lm)Tτ2).
eπΔυτ2τ1dτ1dτ2}+N0p*(tlT)p(tmT)dt
(14)

and

αPN(l)=E[xkySk+Ll*]=g*(τkT0)p*((Sk+Ll)Tτ)eπΔυτkT0dτ.
(15)

Since p(t) is a low-pass filter that filters out-of-band noise and laser linewidth is at most in the order of MHz for practical optical communication systems, it can be shown (from the Appendix B) that

(g(t)·ejϕr(t))*p(t)(g(t)*p(t))·ejϕr(t)=q(t)ejϕr(t)
(16)

and thus we can approximate the received signal as

y(t)=(nxnq(tnT0))·ejϕr(t)+(n(t)·ejϕr(t))*p(t).
(17)

In this case,

APN(l,m)=E[ySk+Ll*ySk+Lm]=nq*((Sk+Ll)TnT0)q((Sk+Lm)TnT0)eπΔυlmT
+N0p*(tlT)p(tmT)dt
(18)

and

αPN(l)=q*((Sk+Ll)T)eπΔυLlT.
(19)

Figure 8 shows the magnitude of the optimal filter tap coefficients w PN with a LO linewidth of 3 MHz and w lin with zero LO linewidth, both for a QPSK system with a transmission distance of 1200 km. One can see that with the received vector y corrupted by EEPN, the exponential decay terms in α PN , A −1 PN that capture the LO phase noise statistics result in samples of y further away from the center having bigger ‘weights’. However, as the samples further away from the center are more corrupted by LO phase noise, they became less relevant for the detection of the bit of interest and therefore system performance degrades with EEPN. Note also that in presence of EEPN, the samples with the largest weight are shifted from 98 to 95 samples from the center of the filter.

If we use the filter w lin to compensate CD in presence of EEPN, the mean-squared error will be given by

MSE2=E[xkαTA1y2]=12E[xkyH]A1α+αHA1E[y*yT]A1α
=12αPNHA1α+αHA1APNA1α.
(20)

With the optimal FIR coefficients w PN for CD compensation in presence of EEPN, the corresponding mean-squared error will be given by

MSE3=E[xkαPNTAPN1y2]=1αPNHAPN1αPN.
(21)
Fig. 8. Magnitude of MMSE filter tap coefficients for a QPSK system with electronic CD compensation and a LO linewidth of 3 MHz. The transmission distance is 1200 km; the over-sampling rate is 2;the OSNR is 21 dB; the length of the filter is 539 with tap index of 0 corresponding to the center tap.

Fig. 9. Mean-squared error with various FIR filters for a QPSK system with electronic CD compensation. The length of propagation is 1200 km and the LO linewidth is 3MHz.

4. EEPN Impact on Carrier Phase Recovery

Carrier phase recovery using phase-locked loop or other feedback-based techniques used to be common for traditional copper-wire and wireless communication systems. However, with the advent of DSP and the extremely low tolerance of propagation delay in feedback-based systems with high symbol rate, carrier phase recovery using DSP-based feed-forward techniques are currently receiving a lot of attention in coherent systems and therefore the effect of EEPN on such carrier phase recovery techniques becomes an important issue. Feedforward carrier recovery techniques can be implemented either with decision-directed (DD) or non-decision-aided (NDA) approaches. In this paper, we will focus on the effect of EEPN on the Viterbi-Viterbi algorithm for QPSK systems. Figure 10 shows the carrier phase ϕ(t) = ϕt(t) + ϕr(t) together with the tracked phase for systems with optical or electrical CD compensation for a 1200-km link. To achieve phase tracking, the Viterbi-Viterbi algorithm is performed on the CD-equalized samples and the phases of the resulting output are passed through a Wiener filter described in Eq. (26) of [14

14. E. Ip and J. M. Kahn, “Feedforward carrier recovery for coherent optical communications,” IEEE/OSA J. Lightwave Technol. 25(9), 2675–2692 (2007). [CrossRef]

] whose output is the MMSE estimate of the carrier phase. The tracked phase without EEPN is also shown as reference. As shown in Figure 9, it can be seen that in presence of EEPN, the tracked phase will have larger errors compared with systems using optical CD compensation. As the EEPN results in larger errors in carrier phase estimates, it will cause more cycle slips as it is more likely to have neighboring phases differ by 2π/4 = π/2, which is depicted in Figure 11.

Fig. 10. True carrier phase vs. tracked carrier phase for a QPSK system with a linewidth of 3 MHz for both the transmitter and receiver laser. The transmission distance is 1200 km. The tracking error is larger for systems with EEPN.
Fig. 11. True carrier phase vs. tracked carrier phase for a QPSK system with a linewidth of 3 MHz for both the transmitter and receiver laser. The transmission distance is 1200 km. In presence of EEPN, the tracked carrier phase is more likely to have cycle slips.
Fig. 12. Probability of cycle slips vs. OSNR for a QPSK system with 1200 km transmission. The linewidths of the transmitter and receiver laser are 3 MHz.

5. Conclusions

APPENDIX A: Pdf of EEPN

In the absence of ASE noise and Tx laser phase noise, (11) becomes y(t)=([nxng(tnT0)]ejϕr(t))*p(t)(nxnq(tnT0))ejϕr(t)

where the validity of the approximation is explained in Appendix B. The received samples are then

ym=[nxnq(mTnT0)]ejϕr(mT)[nxnq(mTnT0)][1+jϕr(mT)]
=nxnq(mTnT0)+jϕr(mT)nxnq(mTnT0)
=Qm+Qmjϕr(mT).

Let Δm−m = ϕr(mT) − ϕr(m′T) and w lin = [wL w L−1w −L+1 w −L]T. In this case, the estimation error for the k th transmitted symbol is given by

ε=x̂kxk=wlinTy·(ejϕr(kT0))xk
=[jQSk+LΔLJQSk+L1ΔL1JQSkL+1ΔL+1JQSkLΔL]Twlin
=jwLQSk+LΔL+jwL1QSk+L1ΔL1+jwL+1QSkL+1ΔL+1+jwLQSkLΔL
=i=L1riΔi+0+i=1LriΔi
=i=L1[(ΔiΔi+1)m=Lirm]+i=1L[(ΔiΔi1)m=iLrm]

where ri=jwiQSk+i, and Δi − Δi±1 are independent Gaussian random variables with zero mean and variance 2πΔυT. For a given xk, r−L, r −L+1, ⋯, r L−1, rL are functions of the neighboring symbols X = […x k−2,x k−1,x k+1,x k+2 …]. Therefore, for a given neighboring symbol sequence X, ε will be a complex Gaussian random variable with zero mean and covariance matrix

2πΔυ TΛ(X) where

Λ(X)=[i=L1(m=LiRe{rm})2+i=1L(m=iLRe{rm})2i=L1(m=LiRe{rm}m=LiIm{rm})+i=1L(m=iLRe{rm}m=iLIm{rm})i=L1(m=LiRe{rm}m=LiIm{rm})+i=1L(m=iLRe{rm}m=iLIm{rm})i=L1(m=LiIm{rm})2+i=1L(m=iLIm{rm})2].

Therefore, for a given xk, the pdf of EEPN is given by

f(εxk)=1CL·xCL14π2ΔυTΛ(X)exp(14πΔυT[Re{ε}Im{ε}]Λ(X)1[Re{ε}Im{ε}]T) where C is the set {1, −1} for BPSK and {1, −1, j, −j} for QPSK formats etc. and ∣ C ∣ denotes the cardinality of C. Note that in presence of ASE noise with variance σ 2 per quadrature, Λ(X) can be replaced by Λ(X) +σ 2 I.

APPENDIX B: Proof of (g(t)·ejϕr(t))*p(t)≈q(t)ejϕr(t)

Denote u(t)=(g(t)·ejϕr(t))*p(t) , the Fourier Transform of u(t) is given by U(f) = (G(f)*Φ(f))·P(f)

where Φ(f) is the Fourier Transform of ejϕr(t) . Now, U(f)=P(f)Φ(f1)G(ff1)df1P(f)Δυ2Δυ2Φ(f1)G(ff1)df1 as the bandwidth of ejϕr(t) is approximately Δυ. Since the bandwidth of the low-pass filter P(f) is in the order of 30 GHz for a symbol rate of 27.59 GSym/s and Δυ is at most several MHz in practice,

P(f)P(ff1)forf1Δυ2.
(B.1)

In this case,

U(f)P(f)Δυ2Δυ2Φ(f1)G(ff1)df1
Δυ2Δυ2Φ(f1)P(ff1)G(ff1)df1
=Δυ2Δυ2Φ(f1)Q(ff1)df1=Q(f)*Φ(f).
(B.2)

Therefore, by taking the inverse Fourier Transform, we obtain u(t)q(t)·ejϕr(t) . Note that this is an alternative way to illustrate the origins of EEPN. Consider replacing P(f) with H1(f)=ej4π2f2β2L2 that characterize compensation of accumulated CD in a transmission link. For any given Δυ, H −1(f) ≠ H −1(ff1) for ∣f 1∣ ≤ Δυ/2 whenever β 2 L is large enough and hence (B.2) will not follow and multiplication and convolution will not commute. Therefore, the effect of EEPN will always scale up with accumulated CD independent of laser linewidth.

Acknowledgements

The authors would like to acknowledge the support of the Hong Kong Government General Research Fund (GRF) under project number 522009.

References and links

1.

E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, “Coherent detection in optical fiber systems,” Opt. Express 16(1), 753–791 (2008). [CrossRef] [PubMed]

2.

E. Ip and J. M. Kahn, “Digital equalization of Chromatic Dispersion and Polarization Mode Dispersion,” IEEE/OSA J. Lightwave Technol. 25(8), 2033–2043 (2007). [CrossRef]

3.

M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon.Technol. Lett. 16(2), 674–676 (2004). [CrossRef]

4.

G. Goldfarb and G. Li, “Chromatic dispersion compensation using digital IIR filtering with coherent detection,” IEEE Photon. Technol. Lett. 19(13), 969–971 (2007). [CrossRef]

5.

K. Roberts, C. Li, L. Strawczyski, M. O. Sullivan, and I. Hardcastle, “Electronic precompensation of optical nonlinearity,” IEEE Photon. Technol. Lett.18(13), 403–405 (2006). [CrossRef]

6.

F. Buchali and H. Bulow, “Adaptive PMD Compensation by Elecgtrical and Optical Techniques,” IEEE/OSA J. Lightwave Technol. 22(4), 1116–1126 (2004). [CrossRef]

7.

D. Schlump, B. Wedding, and H. Bulow, “Electronic equalization of PMD and chromatic dispersion induced distortion after 100 km standard fibre at 10Gb/s,” in Proceedings ECOC, Madrid, Spain, 1998, pp. 535–536.

8.

J. M. Gené, P. J. Winzer, S. Chandrasekhar, and H. Kogelnik, “Simultaneous compensation of Polarization Mode Dispersion and chromatic dispersion using electronic signal processing,” IEEE/OSA J. Lightwave Technol. 26(7), 1735–1741 (2007). [CrossRef]

9.

H. Bulow, F. Buchali, and A. Klekamp, “Electronic dispersion compensation,” IEEE/OSA J. Lightwave Technol. 26(1), 158–167 (2008). [CrossRef]

10.

E. Ip and J. M. Kahn, “Compensation of Dispersion and Nonlinear Impairments Using Digital Backpropagation,” IEEE/OSA J. Lightwave Technol. 26(20), 3416–3425 (2008). [CrossRef]

11.

X. Li, X. Chen, G. Goldfarb, E. Mateo, I. Kim, F. Yaman, and G. Li, “Electronic post-compensation of WDM transmission impairments using coherent detection and digital signal processing,” Opt. Express 16(2), 880–888 (2008). [CrossRef] [PubMed]

12.

K. Kikuchi, “Electronic post-compensation for nonlinear phase fluctuations in a 1000-km 20-Gbit/s optical quadrature phase-shift keying transmission system using the digital coherent receiver,” Opt. Express 16(1), 889–896 (2008). [CrossRef] [PubMed]

13.

A.P.T. Lau and J. M. Kahn, “Signal design and detection in presence of nonlinear phase noise,” IEEE/OSA J. Lightwave Technol.25(10), 3008–3016 (2007). [CrossRef]

14.

E. Ip and J. M. Kahn, “Feedforward carrier recovery for coherent optical communications,” IEEE/OSA J. Lightwave Technol. 25(9), 2675–2692 (2007). [CrossRef]

15.

D. S. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, “Coherent Detection of Optical Quadrature Phase-Shift Keying Signals With Carrier Phase Estimation,” IEEE/OSA J. Lightwave Technol. 24(1), 12–21 (2006). [CrossRef]

16.

R. Noe, “Phase noise-tolerant synchronous QPSK/BPSK baseband-type intradyne receiver concept with feedforward carrier recovery,” IEEE/OSA J. Lightwave Technol. 23(2), 802–808 (2006). [CrossRef]

17.

S. J. Savory, G. Gavioli, R. I. Killey, and P. Bayvel, “Electronic compensation of chromatic dispersion using a digital coherent receiver,” Opt. Express 15(5), 2120–2126 (2007). [CrossRef] [PubMed]

18.

G. Charlet, M. Salsi, P. Tran, M. Bertolini, H. Mardoyan, J. Renaudier, O. Bertran-Pardo, and S. Bigo, “72×100 Gb/s transmission over transoceanic distance, using large effective area fiber, hybrid Raman-Erbium amplification and coherent detection,” in Proceedings OFC/NFOEC, San Diego, CA, 2009, Paper PDPB6.

19.

W. Shieh and K.P. Ho, “Equalization-enhanced phase noise for coherent detection systems using electronic digital signal processing,” Opt. Express 16(20), 15718 – 15727 (2008). [CrossRef] [PubMed]

20.

C. Xie, “Local oscillator phase noise induced penalties in optical coherent detection systems using electronic chromatic dispersion compensation,” in Proceedings OFC/NFOEC, San Diego, CA, 2009, Paper OMT4.

21.

C. Xie, “WDM coherent PDM-QPSK systems with and without inline optical dispersion compensation,” Optics Express 17(6), 4815–4823 (2009). [CrossRef] [PubMed]

OCIS Codes
(060.1660) Fiber optics and optical communications : Coherent communications
(060.5060) Fiber optics and optical communications : Phase modulation

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: February 19, 2010
Revised Manuscript: April 5, 2010
Manuscript Accepted: June 29, 2010
Published: July 29, 2010

Citation
Alan Pak Tao Lau, Thomas Shun Rong Shen, William Shieh, and Keang-Po Ho, "Equalization-enhanced phase noise for 100Gb/s transmission and beyond with coherent detection," Opt. Express 18, 17239-17251 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-16-17239


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References

  1. E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, "Coherent detection in optical fiber systems,’’Opt. Express 16(1), 753-791 (2008). [CrossRef] [PubMed]
  2. E. Ip and J. M. Kahn, "Digital equalization of Chromatic Dispersion and Polarization Mode Dispersion," IEEE/OSAJ. Lightwave Technol. 25(8), 2033-2043 (2007). [CrossRef]
  3. M. G. Taylor, "Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments," IEEE Photon.Technol. Lett. 16(2), 674-676 (2004). [CrossRef]
  4. G. Goldfarb and G. Li, "Chromatic dispersion compensation using digital IIR filtering with coherent detection," IEEE Photon. Technol. Lett. 19(13), 969-971 (2007). [CrossRef]
  5. K. Roberts, C. Li, L. Strawczyski, M. O. Sullivan, and I. Hardcastle, "Electronic precompensation of optical nonlinearity," IEEE Photon. Technol. Lett. 18(13), 403-405 (2006). [CrossRef]
  6. F. Buchali and H. Bulow, "Adaptive PMD Compensation by Elecgtrical and Optical Techniques," IEEE/OSAJ. Lightwave Technol. 22(4), 1116-1126 (2004). [CrossRef]
  7. D. Schlump, B. Wedding, and H. Bulow, "Electronic equalization of PMD and chromatic dispersion induced distortion after 100 km standard fibre at 10Gb/s," in Proceedings ECOC, Madrid, Spain, 1998, pp. 535-536.
  8. J. M. Gené, P. J. Winzer, S. Chandrasekhar, and H. Kogelnik, "Simultaneous compensation of Polarization Mode Dispersion and chromatic dispersion using electronic signal processing," IEEE/OSAJ. Lightwave Technol. 26(7), 1735-1741 (2007). [CrossRef]
  9. H. Bulow, F. Buchali and A. Klekamp, "Electronic dispersion compensation," IEEE/OSAJ. Lightwave Technol. 26(1), 158-167 (2008). [CrossRef]
  10. E. Ip and J. M. Kahn, "Compensation of Dispersion and Nonlinear Impairments Using Digital Backpropagation," IEEE/OSAJ. Lightwave Technol. 26(20), 3416-3425 (2008). [CrossRef]
  11. X. Li, X. Chen, G. Goldfarb, E. Mateo, I. Kim, F. Yaman, and G. Li, "Electronic post-compensation of WDM transmission impairments using coherent detection and digital signal processing," Opt. Express 16(2), 880-888 (2008). [CrossRef] [PubMed]
  12. K. Kikuchi, "Electronic post-compensation for nonlinear phase fluctuations in a 1000-km 20-Gbit/s optical quadrature phase-shift keying transmission system using the digital coherent receiver," Opt. Express 16(1), 889-896 (2008). [CrossRef] [PubMed]
  13. A.P.T. Lau and J. M. Kahn, "Signal design and detection in presence of nonlinear phase noise," J. Lightwave Technol. 25(10), 3008-3016 (2007). [CrossRef]
  14. E. Ip and J. M. Kahn, "Feedforward carrier recovery for coherent optical communications," J. Lightwave Technol. 25(9), 2675-2692 (2007). [CrossRef]
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