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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 1 — Jan. 2, 2012
  • pp: 339–346
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Novel figure of merit to compare fibers in coherent detection systems with uncompensated links

Andrea Carena, Vittorio Curri, Gabriella Bosco, Roberto Cigliutti, Enrico Torrengo, Pierluigi Poggiolini, Antonino Nespola, Dario Zeolla, and Fabrizio Forghieri  »View Author Affiliations


Optics Express, Vol. 20, Issue 1, pp. 339-346 (2012)
http://dx.doi.org/10.1364/OE.20.000339


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Abstract

We introduce an improved fiber figure of merit (FoM) in order to compare different fiber types used in uncompensated links for transmission of coherently-received modulation formats. The role of fiber dispersion in enhancing system performance is shown and verified by simulations and experiments, confirming the need for the inclusion of dispersion parameter in a FoM definition allowing to compare fiber types with relevant different dispersion parameters. Applicability of the proposed FoM has been demonstrated for channel spacing from the Nyquist limit up to 5/3 the symbol rate.

© 2011 OSA

1. Introduction

Since the beginning of optical communications, fiber manufacturer have tried to give their contribution to system performance improvement by designing new fiber types with parameters tailored to reduce the impact of propagation effects. After the development of the standard single-mode fiber (SSMF), fibers with low dispersion were introduced to ease in-line optical dispersion compensation. Then, fibers with large effective area to reduce the impact of nonlinear effects were developed, and recently new fibers with low loss and even larger effective area have been introduced in the market.

2. The figure of merit based on system margin

  • Fiber loss Afiber: it is the intrinsic loss introduced by each fiber span, i.e., Afiber = αdB·Ls [dB], where αdB is the fiber loss coefficient expressed in dB/km and Ls is the span length expressed in km.
  • Span budget Amax: it is the maximum tolerable loss per span in order to keep the system in-service, i.e., BER ≤ BERtarget.

Using these two parameters we can then define the system margin as the tolerable excess span loss with respect to fiber loss:

μdB=Amax|dBAfiber
(1)

FoM=^Amax|dBAfiber
(2)

In general, the FoM is difficult to be interpreted as an absolute quality parameter, therefore, it can be useful to refer to a differential FoM (ΔFoM) defined with respect to a reference fiber as

ΔFoM=FoMFoMref
(3)

3. Closed-form expression for channel spacing equal to the symbol rate

OSNRNL=PTx,chPASE+PNLI
(4)

The amount of ASE noise at the receiver (Rx) is
PASE=Ns(A1)FhνBn
(5)
where Ns is the number of spans, A is the span loss, F is the EDFA noise figure, h is Plank’s constant, ν [Hz] is the operating center frequency and Bn [Hz] is the reference noise-bandwidth for OSNR measurement. At the Nyquist limit, i.e., when the channel spacing Δf [Hz] is equal to the symbol-rate Rs [symbol/s] and channel spectra are rectangular, PNLI [W] in a bandwidth Bn can be accurately approximated through the following expression [7

7. P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical modeling of non-linear propagation in uncompensated optical transmission links,” IEEE Photon. Technol. Lett. 23(11), 742–744 (2011). [CrossRef]

]:
PNLI(23)3πNsγ2Nch2Leff2PTx,ch3log(π2|β2|LeffNch2Rs2)π2|β2|LeffNch2Rs2BnRs
(6)
where γ [1/W/km] is the nonlinear coefficient, Leff [km] is the fiber-span effective length, PTx,ch [W] is the transmitted power per channel, β2 [ps2/km] is the dispersion coefficient and Nch is the number of transmitted channels. The effective length is defined as
Leff=(1e2αLs)/2α
(7)
where Ls [km] is the span length and α [1/km] is the fiber loss coefficient.

Substituting Eqs. (5) and (6) into the expression of OSNRNL, the span loss A resulting for a given target OSNRtarget can be evaluated as a function of all system parameters. Maximizing A with respect to the transmitted power PTx,ch, the following expression for the maximum span budget, valid for practical scenarios with Amax >> 1, is obtained:
Amax12πRsFhν(BnRsNsOSNRtarget)32|β2|LeffRs2log(|β2|LeffRs2)+log(π2Nch2)γLeff
(8)
where OSNRtarget is the one yielding a required target BER for a given modulation format.

According to definition reported in Eq. (2), using Eq. (8) we can express the FoM in the following closed-form:

FoM=10log10{|β2|LeffRs2log(|β2|LeffRs2)+log(π2Nch2)}10log10{γLeff}αdBLs
(9)

Note that various system parameters (F, Ns, OSNRtarget and the span length Ls) giving the first factor of Eq. (8) do not appear in Eq. (9) because they can be neglected as they exactly cancel out when calculating ΔFoM. Analyzing in detail Eq. (9), we observe that for a large occupied bandwidth BWDM = Nch·Rs (e.g., C-band and Rs = 30 Gbaud, means Nch≈160), log(πNch2)>>log(|β2|LeffRs2). Hence, the term log(|β2|LeffRs2) becomes negligible, and the term Rs2/log(πNch2) is fiber-independent and cancels out when calculating ΔFoM. As a result, for practical scenarios using several channels, we can re-write the FoM expression in more compact form:
FoM10log10{|β2|Leff}10log10{γLeff}αdBLs
(10)
which is dependent only on fiber parameters and independent of all other system parameters. This property has in fact a quite fundamental meaning: ΔFoM, i.e., the gain or loss of system margin when replacing one fiber with a different one, is independent of the system on which fibers are compared and therefore qualifies as a very powerful and general indicator of fiber performance. In addition, Eq. (10) clearly highlights how different fiber parameters impact the FoM. Obviously non-linearity makes it worse whereas dispersion improves it, although with different weights: a doubling of non-linearity causes a 3 dB decrease of FoM whereas a doubling of dispersion causes a 1.5 dB improvement. Note that dispersion, whose inclusion is the principal novelty in our FoM definition, improves it because of its impact on the generation of nonlinearity given by the ratio Leff/LD (see Eq. (6)) where LD is the dispersion length defined as LD = 1/ (2|Rs2). As a final comment it is important to remark that the use of the simplified expression of Eq. (10), instead of complete expression given by Eq. (9), implies always a limited inaccuracy within fractions of dBs, even for a small number of channels (e.g., Nch = 10). Moreover, such an inaccuracy decreases with the increasing of dispersion.

4. Earlier FoM definitions and fiber comparison

After introducing the original closed-form expression for the FoM (Eqs. (8) and (9)), we compared it with two earlier FoMs proposed in the literature [1

1. A. Pilipetskii, “Nonlinearity management and compensation in transmission systems,” OFC 2009, paper OTuL5.

,2

2. Y. Yamamoto, M. Hirano, and T. Sasaki, “A new class of optical fiber to support large capacity transmission,” OFC 2011, paper OWA6.

]:

FoM1=10log10(γ)αdBL,sFoM2=10log10(γLeff)αdBLs.

Note that their original expressions used the effective area (Aeff) rather than the nonlinear parameter γ = 2π·n2/(λ·Aeff). We have replaced Aeff with γ to ease the comparison with the one we propose. FoM1 takes into account only the scaling in the nonlinear coefficient together with the difference in span loss. FoM2 is an upgrade of FoM1 considering also the interplay between nonlinearity and loss through the effective length. The FoM we propose in Eq. (10) is therefore a further upgrade that takes into account the simultaneous effect of nonlinearity and fiber dispersion, together with fiber loss.

We compared the three FoMs considering different fiber types: a standard single mode fiber (SSMF), a pure silica core fiber (PSCF) and a non-zero dispersion-shifted fiber (NZDSF). Fiber parameters are displayed in Table 1

Table 1. Fiber parameters and ΔFoM comparison with Ls = 100 km.

table-icon
View This Table
together with ΔFoM values, where SSMF has been selected as the reference fiber. Chromatic dispersion of the NZDSF is very low, therefore it can be considered as a worst-case.

Note that for the FoM we propose, results are shown either using the simplified expression given by Eq. (10), or using the complete expression (Eq. (9)) with only 10 channels. It can be observed that for large dispersion (PSCF) there are no differences, while reducing dispersion a limited difference appears: −7 dB against −6.2 for NZDSF.

Analyzing Table 1, for the PSCF it can be observed that the three ΔFoMs present small differences limited within 0.7 dB. While, for the NZDSF, whose dispersion value is much smaller than the reference fiber (SSMF) one, ΔFoM1 and ΔFoM2 display a mismatch larger than 4 dB with respect to the ΔFoM we propose. Such a large difference confirms the need for the inclusion of the dispersion parameters in a FoM definition that allows fair comparison between fibers presenting large differences in transmission parameters.

In order to highlight the dependence of ΔFoM on fiber dispersion, in Fig. 1
Fig. 1 ΔFoM as a function of dispersion, for span length Ls = 100 km, with fiber loss and non-linearity as parameters. Labeled dots represent the fibers listed in Table 1
we plotted it with respect to β2 for three different pairs of (α, γ) values, again taking as reference the SSMF of Table 1. It can be clearly observed that on the dispersion range of practical transmission fibers the FoM varies over a range of 6 dB independently of the value of nonlinear and loss coefficients. This plot gives a further confirmation of the need to properly include dispersion in a quality parameter allowing comparison between fiber types.

5. Simulative validations

We considered the three fiber types (SSMF as reference, PSCF and NZDSF) whose parameters are reported in Table 1. The target BER was established to be BERtarget = 3·10−3 corresponding to OSNRtarget = 16.3 dB that includes realistic Tx impairments and crosstalk by fitting to the back-to-back performance of the experimental set-up.

For each considered fiber type we swept the transmitted power per channel Ptx,ch from −5 up to + 7 dBm and varied the attenuation of the VOA in order to evaluate the maximum span loss, the span budget Amax, ensuring the transmission operating below BERtarget after 8 spans. Results are plotted in Fig. 2
Fig. 2 Simulative results of maximum span budget vs. the power per channel for the fibers whose parameters are listed in Table 1 used in the considered 8 spans, PM-QPSK, RS = 30 Gbaud,10 channel system with Δf = Rs. Evaluations of FoM according to Eq. (2) are reported on the graph.
for the three fiber types. The plotted curves display the expected qualitative parabolic behavior characterized by an optimal power representing the best trade-off between advantages of power enlargement ad detrimental effects of nonlinearities. Also the hierarchy between fibers is the expected one showing performance advantages with the increasing of fiber dispersion due to beneficial effects of chromatic dispersion in mitigating nonlinearities.

From a quantitative evaluation of maxima for each curve, and with the knowledge of the fiber loss parameter and span length, the FoM can be easily evaluated using Eq. (2). Calculations are reported on the graph showing FoM = 12.1 dB for the PSCF, FoM = 8.0 dB for the SSMF and FoM = 1.7 dB for the NZDSF. Considering the SSMF as a reference, we can evaluate ΔFoM, obtaining ΔFoM = 4.1 dB for the PSCF and ΔFoM = −6.3 dB for the NZDSF: results in excellent agreement with the ones based on the closed-form expressions presented in Table 1. Such an agreement validates the proposed FoM for Δf = Rs and confirms the need of inclusion of dispersion in giving a proper hierarchy to fiber types used to transmit coherently-received modulation formats on uncompensated links.

6. Extension of FoM definition to Δf > Rs

Results of this analysis are pictorially presented in Fig. 3
Fig. 3 Simulative evaluations of ΔFoM for the fibers whose parameters are listed in Table 1 used in the considered 8 spans, PM-QPSK, RS = 30 Gbaud,10 channels system with Δf = 1·Rs up to Δf = 5/3·Rs
as ΔFoM vs. Δf for the considered fibers. It can be clearly observed that the behavior of the curves is practically flat with respect to Δf and the constant level is in excellent agreement with the values predicted by Eqs. (8) and (9) reported in Table 1, last column. This result confirms the applicability of the proposed FoM definition also to system scenarios based on channel spacing larger than the Nyquist limit. And from a physical interpretation point of view, it says that the scaling of performance hierarchy between fibers with respect to loss, dispersion and nonlinearity is independent of the channel spacing.

7. Experimental validation

As a further validation, we carried out experiments aiming at measuring the maximum achievable span budget and consequently evaluate the FoM. The experimental set-up was the same as described in [8

8. E. Torrengo, R. Cigliutti, G. Bosco, A. Carena, V. Curri, P. Poggiolini1, A. Nespola, D. Zeolla, and F. Forghieri. “Experimental validation of an analytical model for nonlinear propagation in uncompensated optical links,” ECOC 2011, paper We.7.B.2.

] with ten 30 Gbaud (120 Gbps) PM-QPSK optically-shaped channels.

We tested experimentally SSMF and NZDSF with parameters specified in Table 1. Span lengths were Ls = 102 km (SSMF) and Ls = 100 km (NZDSF). In order to reduce the linear crosstalk between channels, we did not consider the Nyquist limit case and we used a channel spacing Δf = 1.1·Rs, i.e., 33 GHz.

Results in terms of maximum span budget vs. PTx for BER = 3·10−3, after 8 spans propagation, are shown in Fig. 4b
Fig. 4 Simulative (a) and experimental (b) evaluations of maximum span budget for the fibers whose parameters are listed in Table 1 used in the considered 8 spans link, PM-QPSK, RS = 30 Gbaud,10 channels system with Δf = 1.1·Rs (33 GHz). Together with experimental results plotted as points (b), NLI model [9] results are plotted as continuous lines.
together with the analytical prediction based on the NLI model [9

9. P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “A simple and accurate model for non-linear propagation effects in uncompensated coherent transmission links,” ICTON 2011, paper We.B1.3.

]. The measured maximum span budgets were 31.2 dB and 25.7 dB, for SSMF and NZDSF, respectively. In Fig. 4a simulative results are presented for the same scenario, i.e., for Δf = 33 GHz, for three fiber types. The excellent agreement between simulations, experiments and theory can be clearly observed giving a further cross-validation of both theoretical predictions and simulative algorithms. Calculating from the experimental results the system margin difference according to Eq. (1), we obtained a ΔFoM of −6.1 dB for NZDSF vs. SSMF. Comparing this measurement with the analytical result of Table 1 (ΔFoM = −6.2 dB) and the simulative calculation (ΔFoM = −6.3 dB), we can observe that differences are of the order of fractions of dBs, i.e., they are within the inaccuracy of both experiments and simulations. Hence, we can conclude that also the experiments confirm the validity of the proposed FoM within a scenario of channel spacing larger than the Nyquist limit. Note that, instead, the ΔFoMs calculated according to FoM1 and FoM2 definitions are −3.0 dB and −2.8 dB, respectively, as reported in Table 1. Clearly, they greatly underestimate propagation penalty confirming the need of inclusion of dispersion effect in FoM definition in order to fairly compare fiber types over a wide range of chromatic dispersion values.

7. Conclusions

We compared the proposed FoM to earlier definitions proposed in the technical literature showing how it is fundamental to include the role of fiber dispersion within a figure of merit allowing a fair comparison between fiber types over a wide range of chromatic dispersion.

Acknowledgments

This work was supported by CISCO Systems within a SRA contract. The simulator OptSimTM was supplied by RSoft Design Group Inc.

References and links

1.

A. Pilipetskii, “Nonlinearity management and compensation in transmission systems,” OFC 2009, paper OTuL5.

2.

Y. Yamamoto, M. Hirano, and T. Sasaki, “A new class of optical fiber to support large capacity transmission,” OFC 2011, paper OWA6.

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.

V. Curri, P. Poggiolini, A. Carena, and F. Forghieri, “Dispersion compensation and mitigation of non-linear effects in 111 Gb/s WDM coherent PM-QPSK systems,” IEEE Photon. Technol. Lett. 20(17), 1473–1475 (2008). [CrossRef]

5.

D. van den Borne, V. Sleiffer, M. Alfiad, S. Jansen and T. Wuth, “POLMUX-QPSK modulation and coherent detection: the challenge of long-haul 100G transmission,” ECOC 2009, paper 3.4.1.

6.

A. Carena, V. Curri, G. Bosco, R. Cigliutti, E. Torrengo, P. Poggiolini, A.Nespola, D. Zeolla, and F. Forghieri “A novel figure of merit to compare fibers in coherent detection systems with uncompensated links,” ECOC 2011, paper Th.12.LeCervin.5.

7.

P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical modeling of non-linear propagation in uncompensated optical transmission links,” IEEE Photon. Technol. Lett. 23(11), 742–744 (2011). [CrossRef]

8.

E. Torrengo, R. Cigliutti, G. Bosco, A. Carena, V. Curri, P. Poggiolini1, A. Nespola, D. Zeolla, and F. Forghieri. “Experimental validation of an analytical model for nonlinear propagation in uncompensated optical links,” ECOC 2011, paper We.7.B.2.

9.

P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “A simple and accurate model for non-linear propagation effects in uncompensated coherent transmission links,” ICTON 2011, paper We.B1.3.

OCIS Codes
(060.1660) Fiber optics and optical communications : Coherent communications
(060.2330) Fiber optics and optical communications : Fiber optics communications
(060.2400) Fiber optics and optical communications : Fiber properties

ToC Category:
Fibers, Fiber Devices, and Amplifiers

History
Original Manuscript: September 30, 2011
Revised Manuscript: November 28, 2011
Manuscript Accepted: November 29, 2011
Published: December 21, 2011

Virtual Issues
European Conference on Optical Communication 2011 (2011) Optics Express

Citation
Andrea Carena, Vittorio Curri, Gabriella Bosco, Roberto Cigliutti, Enrico Torrengo, Pierluigi Poggiolini, Antonino Nespola, Dario Zeolla, and Fabrizio Forghieri, "Novel figure of merit to compare fibers in coherent detection systems with uncompensated links," Opt. Express 20, 339-346 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-1-339


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References

  1. A. Pilipetskii, “Nonlinearity management and compensation in transmission systems,” OFC 2009, paper OTuL5.
  2. Y. Yamamoto, M. Hirano, and T. Sasaki, “A new class of optical fiber to support large capacity transmission,” OFC 2011, paper OWA6.
  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. V. Curri, P. Poggiolini, A. Carena, and F. Forghieri, “Dispersion compensation and mitigation of non-linear effects in 111 Gb/s WDM coherent PM-QPSK systems,” IEEE Photon. Technol. Lett.20(17), 1473–1475 (2008). [CrossRef]
  5. D. van den Borne, V. Sleiffer, M. Alfiad, S. Jansen and T. Wuth, “POLMUX-QPSK modulation and coherent detection: the challenge of long-haul 100G transmission,” ECOC 2009, paper 3.4.1.
  6. A. Carena, V. Curri, G. Bosco, R. Cigliutti, E. Torrengo, P. Poggiolini, A.Nespola, D. Zeolla, and F. Forghieri “A novel figure of merit to compare fibers in coherent detection systems with uncompensated links,” ECOC 2011, paper Th.12.LeCervin.5.
  7. P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “Analytical modeling of non-linear propagation in uncompensated optical transmission links,” IEEE Photon. Technol. Lett.23(11), 742–744 (2011). [CrossRef]
  8. E. Torrengo, R. Cigliutti, G. Bosco, A. Carena, V. Curri, P. Poggiolini1, A. Nespola, D. Zeolla, and F. Forghieri. “Experimental validation of an analytical model for nonlinear propagation in uncompensated optical links,” ECOC 2011, paper We.7.B.2.
  9. P. Poggiolini, A. Carena, V. Curri, G. Bosco, and F. Forghieri, “A simple and accurate model for non-linear propagation effects in uncompensated coherent transmission links,” ICTON 2011, paper We.B1.3.

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