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Optics Express

Optics Express

  • Editor: Martijn de Sterke
  • Vol. 16, Iss. 20 — Sep. 29, 2008
  • pp: 15718–15727
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Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing

William Shieh and Keang-Po Ho  »View Author Affiliations


Optics Express, Vol. 16, Issue 20, pp. 15718-15727 (2008)
http://dx.doi.org/10.1364/OE.16.015718


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Abstract

In coherent optical systems employing electronic digital signal processing, the fiber chromatic dispersion can be gracefully compensated in electronic domain without resorting to optical techniques. Unlike optical dispersion compensator, the electronic equalizer enhances the impairments from the laser phase noise. This equalization-enhanced phase noise (EEPN) imposes a tighter constraint on the receive laser phase noise for transmission systems with high symbol rate and large electronically-compensated chromatic dispersion.

© 2008 Optical Society of America

1. Introduction

Recently, we have witnessed a dramatic resurgence of interests in coherent optical communications from both academia and industry [1

1. D. S. Ly-Gagnon, S. Tsukarnoto, K. Katoh, and K. Kikuchi, “Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation,” J. of Lightwave Technol. 24,12–21 (2006). [CrossRef]

5

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

]. The coherent optical systems offer unprecedented performance in spectral efficiency, receiver sensitivity, chromatic- and polarization-dispersion resilience. Additionally, coherent systems present some desirable features that are critical for future-generation reconfigurable networks in terms of their ease of installation, monitoring, and dynamic bandwidth provisioning. The allowable laser linewidth has been shown to increase with the transmission speed for coherent optical systems [2

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

, 6

6. L. G. Kazovsky, “Performance analysis and laser linewidth requirements for optical PSK heterodyne communication systems,” J. Lightwave Technol. 4, 415–425 (1986). [CrossRef]

8

8. K.-P. Ho, Phase-modulated Optical Communication Systems, (Springer, 2005), ch. 4.

]. This finding seems to cope very well with the current trend in optical communications where the 40-Gb/s systems have already been deployed in large scale and the research works have shown 100 Gb/s feasibility in the near horizon. The coherent optical communication systems are commonly based on the electronic digital signal processing for phase compensation and channel equalization that reaps the benefits provided by the powerful CMOS ASICs [1

1. D. S. Ly-Gagnon, S. Tsukarnoto, K. Katoh, and K. Kikuchi, “Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation,” J. of Lightwave Technol. 24,12–21 (2006). [CrossRef]

5

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

,9

9. H. Bulow, F. Buchali, and A. Klekamp, “Electronic dispersion compensation,” J. of Lightwave Technol. 26, 158–167 (2007). [CrossRef]

11

11. S. Tsukamoto, K. Katoh, and K. Kikuchi, “Unrepeated transmission of 20-Gb/s optical quadrature phase-shift-keying signal over 200-km standard single-mode fiber based on digital processing of homodynedetected signal for group-velocity dispersion compensation,” IEEE Photon. Technol. Lett. 18, 1016–1018 (2006). [CrossRef]

]. A dispersion map without per-span dispersion compensation is the preferred choice to provide the superior performance in nonlinearity [12

12. X. Chen, C. Kim, G. Li, and B. Zhou, “Numerical study of lumped dispersion compensation for 40-Gb/s return-to-zero differential phase-shift keying transmission,” IEEE Photon. Technol. Lett. 19, 568–570 (2007). [CrossRef]

13

13. E. Ip and J. M. Kahn, “Compensation of dispersion and nonlinear effects using digital back-propagation,” to be published in J. Lightwave Technol..

]. However, the analysis of the phase noise requirement is often performed without consideration of the large chromatic dispersion that may be present in these non-dispersion compensated systems [1

1. D. S. Ly-Gagnon, S. Tsukarnoto, K. Katoh, and K. Kikuchi, “Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation,” J. of Lightwave Technol. 24,12–21 (2006). [CrossRef]

3

3. R. Noé, “Phase noise tolerant synchronous QPSK/BPSK baseband type intradyne receiver concept with feedforward carrier recovery,” J. Lightwave Technol. 23, 802–808 (2005). [CrossRef]

, 6

6. L. G. Kazovsky, “Performance analysis and laser linewidth requirements for optical PSK heterodyne communication systems,” J. Lightwave Technol. 4, 415–425 (1986). [CrossRef]

8

8. K.-P. Ho, Phase-modulated Optical Communication Systems, (Springer, 2005), ch. 4.

]. This paper starts by laying out the communication system model involving the phase noise from both transmitter and receiver. The analysis of the phase noise impairment is then performed under the large residual channel dispersion. Due to the non-commutability of the phase noise and channel dispersion, a new source of impairment is identified that is originated from the receive laser phase noise enhanced by the electronic equalization. This (electronic) equalization-enhanced phase noise (EEPN) imposes a tighter constraint on the receive laser phase noise for the systems with large chromatic dispersion and high symbol rate. The EEPN does not exist for coherent or non-coherent optical systems employing optical dispersion compensation.

2. Channel model including the phase noise at both transmit and receive ends

Fig. 1. The communication channel model including the phase noise at both transmit and receive ends. CPE/C stands for carrier phase estimation and compensation.

At the receiver, the optical-to-electrical down conversion is performed, introducing an additional phase noise rotation of ejϕt(t) from the receive laser. The electrical filter he(t) is used to reverse the channel dispersion effect, and the signal is then passed into another filter hm(t) to match the pulse shaping function hps(t) for optimal performance. The combined responses of he(t) and hm(t) are commonly adjusted with an adaptive algorithm.

The output signal c(t) is sampled periodically at the symbol rate Ts, which gives the received signal ck. For this analysis, the convolution of hps(t) and hm(t) are assumed as the raised cosine response. The channel model can be altered by moving digital sampling immediately after the optical-to-electrical down-conversion and the subsequent filtering function he(t) and hm(t) can be performed digitally. This alternation does not change the performance of the system and will not affect our ensuing analysis.

The channel model relating the output to the input can be expressed as

c(t)=[r(t)ejϕr(t)]hehm+N(t)
(1)

where r(t) is the received baseband signal given by

r(t)=k=(ckejϕt(t)hps(tkTs))hf(t)
(2)

N′(t)is given by

N(t)=N(t)hehm
(3)

With no channel dispersion or with optical chromatic dispersion compensation, both hf(t) and he(t) are Dirac-delta function δ(t), the signal of (1) is thus simplified as

c(t)=k=[ckej[ϕt(t)+ϕr(t)]hps(tkTs)]+N(t)
(4)

where hps(t)=hpshm is the overall pulse shaping function, and for this analysis is assumed raised cosine function. The phase noise ej[ϕt(t)+ϕr(t)] has been commuted with m h (t) because of the short-duration of the pulse shaping function.

The sampling at the optimum timing points gives the received symbol ck of

ck=ckej[ϕt(kTs)+ϕr(kTs)]+N(kTs)
(5)

Various carrier phase estimation (CPE) algorithms such as phase-locked loop (PLL) and feed-forward carrier synchronization (FFCS) can be employed to estimate ϕt (kTs)+ϕr(kTs) [1

1. D. S. Ly-Gagnon, S. Tsukarnoto, K. Katoh, and K. Kikuchi, “Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation,” J. of Lightwave Technol. 24,12–21 (2006). [CrossRef]

8

8. K.-P. Ho, Phase-modulated Optical Communication Systems, (Springer, 2005), ch. 4.

, 14

14. F. M. Gardner, Phaselock Techniques, (2nd Ed., New York: John Wiley, 1979).

15

15. H. Meyr, M. Moeneclaey, and S. A. Fechtel, Digital Communication Receivers: Synchronization, Channel Estimation, and Signal Processing, (New York: John Wiley, 1997).

]. Assume that CPE has been processed and the estimated value of ϕt(kTs)+ϕr(kTs) is ϕ̂(kTs). The carrier phase compensation (CPC) is performed to recover the estimated transmitted symbol as

ĉk=ckejϕ̂(kTs)
(6)

The analysis of the difference between ϕ̂(kTs) and ϕt(kTs)+ϕr(kTs) is beyond the scope of this paper, and can be found in [1

1. D. S. Ly-Gagnon, S. Tsukarnoto, K. Katoh, and K. Kikuchi, “Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation,” J. of Lightwave Technol. 24,12–21 (2006). [CrossRef]

8

8. K.-P. Ho, Phase-modulated Optical Communication Systems, (Springer, 2005), ch. 4.

].

The analysis based on (5)–(6) has shown that for QPSK modulation, the laser linewidth and data period product is bounded at 1.3×10-4 [2

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

] for the 1 dB penalty at a BER of 10-3. This suggests that for the 40 and 100 Gb/s polarization-multiplexed systems, the maximum allowed laser linewidth is about 1.3 and 3.25 MHz that seems to be compatible with the conventional distributed-feedback (DFB) laser linewidth specification.

Nevertheless, the above analysis does not include the channel dispersion. For simplicity, the signal around t=0 with k=0 and ck=1 is considered. We obtain from (1)

r(t)=[(ejϕt(t)hps(t))hf(t)]ejϕt(t)
(7)

where r(t)r(t)ejϕt(t), and is the signal fed into the electronic equalizer. For illustrative purpose, the fiber dispersion hf(t) can be approximated with a set of discrete summation of many taps given by

hf(t)=i=MMhiδ(tiTs)
(8)

The tap spacing Ts should be smaller than the symbol period and is often set to half of the symbol period. Substituting (8) into (7), we arrive at

r(t)=i=MM(ejϕt(tiTs)hps(tiTs)hi)ejϕr(t)
=i=MMejϕt(tiTs)+jϕr(tiTs)hps(tiTs)hi(t)
(9)

where hi(t)ejΔi(t)hi, Δi(t)≡ϕr(t)-ϕr(t-iTs). The expression (9) shows that by moving the receive phase noise into the transmit end, the effective channel response can be considered as similar to yet different from hf(t), with each tap varying by an additional factor ej(ϕr(t)ϕr(tiTs)). Obviously when the channel dispersion is short, Δi(t) t is very small and can be assumed to be zero. However, when the channel is very dispersive, Δi(t) can be no longer approximated to be zero. A thorough analysis is required to understand the impact of the dispersion on the phase noise impairment. The expression (9) is further rearranged by Taylor expansion in Δi(t) and we have

r(t)=i=MM(ejϕt(tiTs)+jϕr(tiTs)hps(tiTs)hi(1+jΔi(t)))
=(ejϕt(t)+jϕr(t)hps)hf(t)+i=MMejϕt(tiTs)+jϕt(tiTs;)hps(tiTs)hi·jΔi(t)
(10)

The first-term resembles the conventional model that lumps together the transmit and receive laser phase noise, and can be processed as for the case with zero dispersion that is the system as shown earlier in (5) and (6). However, a second term emerges along with the signal, namely, an additional noise term due to the commuting between ejϕr(t) and hf(t). It is noted that the transmit laser phase noise ϕt(t) does not generate any additional impairment because it passes through both fiber channel of hf(t) and equalizer of he(t) that perfectly cancels the terms due to commuting. The second term of (10) is difficult to evaluate in the time-domain. Analysis of this noise impairment can be developed in the frequency-domain.

Fig. 2. The structure of a coherent receiver. The receiver response functions are modeled as summation of finite number of taps.

Aside from the point of view of lumping the transmit and receive phase noises, the origin of the EEPN can be illustrated as the receive phase noise passing through the equalizer response function as shown in Fig. 2. For simplicity, the signal around t=0 with k=0 and ck=1 is considered. The transmit phase noise is also omitted as it does not contribute to EEPN. In Fig. 2, the receive response function hehm is modeled with a set of discrete summation of many taps given by

hehm=i=MMhiδ(tiTs)
(11)

After sampling at t of 0, and removing the common phase of ϕr(0), the estimated transmit symbol is given by

ĉ0=1+nE
(12)
nE=i=MMr(iT)hi(ejΔi(0)1)
(13)

where Δi(t)≡ϕr(t)-ϕr(t-iTs). From (12) and (13), in additional to the original transmit symbol of 1, an additional noise term E n arises from the receive phase noise. From Fig. 2, the output signal c(t) is a summation of multiple copies of the signal with varying delay. The existence of the receive phase noise de-correlates the summing components of c(t) and subsequently contributes the additional noise.

3. Analytical results of the equalization-enhanced phase noise (EEPN)

The equalization-enhanced phase noise (EEPN) originates from the receive laser phase noise as discussed in Section 2. To simplify the analysis and focus on the EEPN impairment, the contribution from the transmit laser phase noise and additive amplifier noise are omitted. The received signal for k=0 and ck=1 is rewritten as

c(t)=[hps(t)hf(t)]ejϕr(t)[he(t)hm(t)]
(14)

By limiting to the 0th symbol, the analysis gives the evaluation of phase-noise-induced intra-symbol interference. The impact of phase-noise-induced inter-symbol interference can be deduced in the later part of this section. With the CPE to find the common phase of ϕr(0), the carrier phase compensated signal become

c(t)=c(t)ejϕr(0)=[hps(t)hf(t)]ej(ϕr(t)ϕr(0))[he(t)hm(t)]
(15)

The noise variance of c′(t)due to the EEPN is given by

σc2=E{c(t)2}E{c(t)}2.
(16)

where E{} stands for statistical average. Using a simplified notation of

h1(t)=hps(t)hf(t)
(17)
h2(t)=he(t)hm(t)
(18)

we have

E{c(t)}=h1(tt1)E{ej(ϕr(tt1)ϕr(0))}h2(t1)dt1
(19)

A very useful formula can be applied to transfer the integration from time- to frequencydomain. Denote the random variable

υ(t)=ejϕ(t)
(20)

The correlation function of υ(t) is [6]

Rυυ=E{υ(t1)υ*(t2)}=E{ejϕ(t1)jϕ(t2)}=S(f)ej2πf(t1t2)df
(21)

where S(f) is the spectral density of υ(t).

In optical communications, the phase noise is found to follow Wiener stochastic process [2

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

, 6

6. L. G. Kazovsky, “Performance analysis and laser linewidth requirements for optical PSK heterodyne communication systems,” J. Lightwave Technol. 4, 415–425 (1986). [CrossRef]

8

8. K.-P. Ho, Phase-modulated Optical Communication Systems, (Springer, 2005), ch. 4.

]. The Wiener phase noise is also a major phase noise component for the electronic oscillators [16

16. A. Demir, A. Mehrotra, and J. Roychowdhury, “Phase noise in oscillators: A unifying theory and numerical methods for characterization,” IEEE Trans. Circuits Syst. I 47, 655–674 (2000). [CrossRef]

17

17. T. H. Lee and A. Hajimiri, “Oscillator phase noise: A tutorial,” IEEE J. Solid-State Circuits 35, 326–336 (2000). [CrossRef]

]. For Wiener phase noise, S(f)is of Lorentzian line shape given by [6

6. L. G. Kazovsky, “Performance analysis and laser linewidth requirements for optical PSK heterodyne communication systems,” J. Lightwave Technol. 4, 415–425 (1986). [CrossRef]

]

S(f)=12πf3dBf2+(f3dB2)2
(22)

where f 3dB is the 3-dB laser linewidth.

Substituting (21) into (19), and converting the time-domain integration to frequency-domain, we arrive at

E{c(t)}=S(f)H2(f1)H1(f1f)ei2πftdf1df
(23)

where H 1(f) and H 2(f) are the frequency responses corresponding to the impulse responses of h 1(t) and h 2(t), respectively.

The similar procedure can apply to E{|c′(t)|2}, and the result is given by

E{|c(t)|2}=S(f)|H2(f1)H1(f1f)ei2πftdf1|2df
(24)

The expressions of (16), (23) and (24) evaluated at t of zero (or sampled at t of zero) give the complete formulation of the EEPN noise evaluation. Once the frequency-domain transfer functions are specified, expressions of (23) and (24) can be readily computed, and subsequently the noise variance can be obtained using (16).

We proceed to perform the analysis with all the transmitted symbols present and show the final result given by

E{c(t)}=k=E{ck}·ξ(tkTs)=ξ(t)
(25)
E{c(t)2}=k=ρk·ζ(tkTs)
(26)

where

ξ(t)=S(f)H2(f1)H1(f1f)ei2πftdf1df
(27)
ζ(t)=S(f)H2(f1)H1(f1f)ei2πftdf12df
(28)
ρk=E{|ck|2}
(29)

Each symbol is assumed to be zero-mean and independent and identically distributed (iid), and the evaluation is made for the 0th symbol with the symbol value ck of 1. The combination of (16), (27) and (28) evaluated at t of zero gives the complete formulation of the EEPN noise for a continuous signal with arbitrary number of symbols.

4. Numerical results of EEPN impairment

For numerical evaluation of the EEPN interference, the pulse-shaping transfer functions are assumed to be raised cosine with zero excessive bandwidth or the Nyquist filter:

Hps(f)=Hm(f)={1,B2fB20,f>B2,f<B2
(30)

where B is the signal symbol rate.

The fiber transfer function and its equalizer have the forms of

Hf(f)=ejπ·cf02Dt·f2,He(f)=ejπ·cf02Dt·f2
(31)

where f 0 is the laser center frequency, c is the speed of light, Dt is the accumulated chromatic dispersion. Noting that H 2(f)=He(f) Hm(f) and H 2(f)=He(f) Hm(f), by substituting (30) and (31) into (23) and (24), we arrive at

E{c(0)}=1α(1eα)
(32)
E{c(0)2}=12α2(e2α+2α1)
(33)

where απc(2f 2 0)-1 DtBf3dB. The expressions of (32) and (33) are derived with the normalization to 1 for |E{c′(0)}| and E{|c′(0)|2} at zero dispersion. Using the Taylor expansion of (32) and (33), and keeping the first-order of α, we have

E{c(0)}=1α(1eα)112α
(34)
ηE{c(0)}21α
(35)
E{c(0)2}=12α2(e2α+2α1)123α
(36)

where η defined in (35) is the normalized received signal power. Combing (35), and (36), and (16), we have

σc2=13α
(37)

In general, the EEPN has three effects on the systems, (i) it reduces the signal power by a factor of α, (ii) it induces an intra-symbol interference equal to α/3, and (iii) it also induces an inter-symbol interference, the magnitude of which is to be discussed in the following paragraph.

The amount of the inter-symbol interference can be simply deduced by the argument on conservation of energy. The optical channel modeled here is unitary regardless of the introduction of phase noise or chromatic dispersion. The energy loss for the signal will be converted into the gain for the noise or distortion. Assuming the identical distribution for each symbol, then the total noise is (1-η) for each symbol or is α from (35). This implies that the inter-symbol interference contributes two-third of the total noise. To be specific, the noise variances can be summarized as follows:

σT2=σIntra2+σInter2=α,σIntra2=13α,σInter2=23α
(38)

where σ 2 T, σ 2 Inter, and σ 2 Inter stand for total interference, intra-symbol interference, and inter-symbol interference, respectively. These interferences are proportional to dispersion, bit rate, and linewidth, which is in contrast to the phase noise impairment without dispersion where the phase noise induced degradation is reduced with the increase of the bit rate.

The impact of the EEPN can be evaluated in terms of its SNR penalty. Assuming the signal power is P, and the amplifier noise power n 0, the total effective SNR under influence of EEPN is

γ0=ηPPσT2+n0=ηγγσT2+1
(39)

where γ=P/n 0 is the SNR, and γ 0 is the effective system SNR with EEPN. The increase of the required SNR, ΔP due to the EEPN can be characterized as

ΔP=γγ0=γσT2+1ηγ0σT2+1η
(40)

The SNR penalty ΔP is often expressed in (dB) given by

ΔP(dB)=10log10(γ0σT2+1η)4.343·α(1+γ0)
(41)

The SNR penalty for transmission systems is studied for various reaches of 1000, 4000, 7000, and 10,000 km. The first two scenarios correspond to the terrestrial long-haul systems, and the second two scenarios to the undersea systems. Figs. 3(a) and (b) show the SNR penalty as a function of the linewidth at the symbol rate of 10 Gbaud and 25 Gbaud respectively. The 10 and 25 Gbaud correspond to the system data rates of 40 and 100 Gb/s with QPSK modulation and polarization multiplexing. At the symbol rate of 10 Gbaud/s and QPSK modulation, the feed-forward carrier synchronization (FFCS) requires a laser linewidth of smaller than 1.3 MHz for 1 dB penalty [2

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

]. At this linewidth of 1.3 MHz, the EEPN penalty is as small as 0.1 and 0.5 dB for the terrestrial system of 1000 and 4000 km, but reaches 1.2 dB for the 10,000-km system. Similarly, at the symbol rate of 25 Gbaud system, the FFCS requires a laser linewidth of 3.25 MHz. At this linewidth of 3.25 MHz, the penalty becomes very sizable for all the systems, and in particularly, incurs a penalty of 0.7, 3.0, 5.2, and 7.4 dB for 1000, 4000, 7000, and 10,000 km respectively. Fig. 4 plots the linewidth requirement for the 1 dB SNR penalty at the BER of 10-3 due to the EEPN interference. As the symbol rate increases, the linewidth requirement becomes more stringent, in sharp contrast with the FFCS requirement. The FFCS 1 dB penalty linewidth requirement is also shown for comparison in Fig. 4. The intercept of the FFCS and EEPN curves signifies the boundary for the two symbol rate regimes in which one of two effects is dominant. For instance, for 10,000-km transmission system, the EEPN and FFCS curve intercepts at the symbol rate of 10 Gbaud/s. Below 10 Gbaud/s, the FFCS residual noise will dominate. However, beyond the symbol rate of 10 Gbaud/s, the EEPN is the primary noise source. Although FFCS predicates that the lessening of the laser linewidth requirement beyond 10 Gbaud/s, due to the EEPN interference, as a matter of fact, the increase of the symbol rate will further tighten the requirement of laser linewidth. For instance, FFCS alone permits a laser linewidth of 12 MHz at the symbol rate of 100 Gbaud/s, but this will be preempted by the requirement of EEPN that requires the laser linewidth of 100 kHz, which is about 100 times more stringent. EEPN interference only becomes significant when the dispersion is large and the symbol rate is high. Nevertheless, the coherent systems that support symbol rate of 100 Gb/s and 10,000 km could be a reality for undersea systems with proper span engineering and powerful silicon digital signal processing.

Fig. 3. The SNR penalty from EEPN interference as a function of the linewidth at various reaches when the symbol rate is (a) 10 Gbaud/s, and (b) 25 Gbaud/s, respectively. This corresponds to 40 Gb/s and 100 Gb/s systems with QPSK modulation and polarization multiplexing. Chromatic dispersion of 17 ps/(nm·km) and SNR (γ0) of 9.8 dB are assumed.
Fig. 4. The required laser linewidth for 1 dB SNR penalty at a BER of 10-3 from EEPN interference for various reaches. The required laser linewidth at 1 dB SNR penalty from the feedback-forward carrier synchronizer (FFCS) is also shown as a comparison.

5. Conclusion

The system penalty has been studied for the EEPN impairment. The origin of the EEPN noise is elucidated and the analytical theory for EEPN is also developed based on continuous-time model. Not existent for coherent systems with optical dispersion compensation, EEPN impairment imposes a tighter constraint on the receive laser phase noise for coherent systems with high symbol rate and large electronic-compensated dispersion.

References and links

1.

D. S. Ly-Gagnon, S. Tsukarnoto, K. Katoh, and K. Kikuchi, “Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation,” J. of Lightwave Technol. 24,12–21 (2006). [CrossRef]

2.

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

3.

R. Noé, “Phase noise tolerant synchronous QPSK/BPSK baseband type intradyne receiver concept with feedforward carrier recovery,” J. Lightwave Technol. 23, 802–808 (2005). [CrossRef]

4.

H. Sun, K. -T. Wu, and K. Roberts, “Real-time measurements of a 40 Gb/s coherent system,” Opt. Express 16, 873–879 (2008). [CrossRef] [PubMed]

5.

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

6.

L. G. Kazovsky, “Performance analysis and laser linewidth requirements for optical PSK heterodyne communication systems,” J. Lightwave Technol. 4, 415–425 (1986). [CrossRef]

7.

S. Norimatsu and K. Iwashita, “Linewidth requirements for optical synchronous detection systems with nonnegligible loop delay time,” J. Lightwave Technol. 10, 341–349 (1992). [CrossRef]

8.

K.-P. Ho, Phase-modulated Optical Communication Systems, (Springer, 2005), ch. 4.

9.

H. Bulow, F. Buchali, and A. Klekamp, “Electronic dispersion compensation,” J. of Lightwave Technol. 26, 158–167 (2007). [CrossRef]

10.

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

11.

S. Tsukamoto, K. Katoh, and K. Kikuchi, “Unrepeated transmission of 20-Gb/s optical quadrature phase-shift-keying signal over 200-km standard single-mode fiber based on digital processing of homodynedetected signal for group-velocity dispersion compensation,” IEEE Photon. Technol. Lett. 18, 1016–1018 (2006). [CrossRef]

12.

X. Chen, C. Kim, G. Li, and B. Zhou, “Numerical study of lumped dispersion compensation for 40-Gb/s return-to-zero differential phase-shift keying transmission,” IEEE Photon. Technol. Lett. 19, 568–570 (2007). [CrossRef]

13.

E. Ip and J. M. Kahn, “Compensation of dispersion and nonlinear effects using digital back-propagation,” to be published in J. Lightwave Technol..

14.

F. M. Gardner, Phaselock Techniques, (2nd Ed., New York: John Wiley, 1979).

15.

H. Meyr, M. Moeneclaey, and S. A. Fechtel, Digital Communication Receivers: Synchronization, Channel Estimation, and Signal Processing, (New York: John Wiley, 1997).

16.

A. Demir, A. Mehrotra, and J. Roychowdhury, “Phase noise in oscillators: A unifying theory and numerical methods for characterization,” IEEE Trans. Circuits Syst. I 47, 655–674 (2000). [CrossRef]

17.

T. H. Lee and A. Hajimiri, “Oscillator phase noise: A tutorial,” IEEE J. Solid-State Circuits 35, 326–336 (2000). [CrossRef]

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: August 7, 2008
Revised Manuscript: September 3, 2008
Manuscript Accepted: September 15, 2008
Published: September 19, 2008

Citation
William Shieh and Keang-Po Ho, "Equalization-enhanced phase noise for coherent-detection systems using electronic digital signal processing," Opt. Express 16, 15718-15727 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-20-15718


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References

  1. D. S. Ly-Gagnon, S. Tsukarnoto, K. Katoh, and K. Kikuchi, "Coherent detection of optical quadrature phase-shift keying signals with carrier phase estimation," J. Lightwave Technol. 24, 12-21 (2006). [CrossRef]
  2. E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, "Coherent detection in optical fiber systems," Opt. Express 16, 753-791 (2008). [CrossRef] [PubMed]
  3. R. Noé, "Phase noise tolerant synchronous QPSK/BPSK baseband type intradyne receiver concept with feedforward carrier recovery," J. Lightwave Technol. 23, 802-808 (2005). [CrossRef]
  4. H. Sun, K. -T. Wu, and K. Roberts, "Real-time measurements of a 40 Gb/s coherent system," Opt. Express 16, 873-879 (2008). [CrossRef] [PubMed]
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  7. S. Norimatsu and K. Iwashita, "Linewidth requirements for optical synchronous detection systems with nonnegligible loop delay time," J. Lightwave Technol. 10, 341-349 (1992). [CrossRef]
  8. K.-P. Ho, Phase-modulated Optical Communication Systems, (Springer, 2005), ch. 4.
  9. H. Bulow, F. Buchali, and A. Klekamp, "Electronic dispersion compensation," J. Lightwave Technol. 26, 158 - 167 (2007). [CrossRef]
  10. M. G. Taylor, "Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments," IEEE Photon. Technol. Lett. 16, 674-676 (2004). [CrossRef]
  11. S. Tsukamoto, K. Katoh, and K. Kikuchi, "Unrepeated transmission of 20-Gb/s optical quadrature phase-shift-keying signal over 200-km standard single-mode fiber based on digital processing of homodyne-detected signal for group-velocity dispersion compensation," IEEE Photon. Technol. Lett. 18, 1016-1018 (2006). [CrossRef]
  12. X. Chen, C. Kim, G. Li, and B. Zhou, "Numerical study of lumped dispersion compensation for 40-Gb/s return-to-zero differential phase-shift keying transmission," IEEE Photon. Technol. Lett. 19, 568-570 (2007). [CrossRef]
  13. E. Ip and J. M. Kahn, "Compensation of dispersion and nonlinear effects using digital back-propagation," to be published in J. Lightwave Technol..
  14. F. M. Gardner, Phaselock Techniques, (2nd Ed., New York: John Wiley, 1979).
  15. H. Meyr, M. Moeneclaey, and S. A. Fechtel, Digital Communication Receivers: Synchronization, Channel Estimation, and Signal Processing, (New York: John Wiley, 1997).
  16. A. Demir, A. Mehrotra, and J. Roychowdhury, "Phase noise in oscillators: A unifying theory and numerical methods for characterization," IEEE Trans. Circuits Syst. I 47, 655-674 (2000). [CrossRef]
  17. T. H. Lee and A. Hajimiri, "Oscillator phase noise: A tutorial," IEEE J. Solid-State Circuits 35, 326-336 (2000). [CrossRef]

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