## Novel figure of merit to compare fibers in coherent detection systems with uncompensated links |

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

*FoM*) have been proposed encompassing the effects of both nonlinearity and loss [1,2]. With the introduction of coherent detection and electronic dispersion compensation [3

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]

*FoM*definition taking into account the effects of chromatic dispersion on system performance, extending results presented in [6] to channel spacing larger than the symbol rate. The presented closed-form of

*FoM*is based on a model for the impact of non-linear propagation proposed in [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]

*FoM*definition based on the system margin. Then, in Sec. 3, we recall the model of nonlinear interference [6] to obtain a closed-form expression of

*FoM*at the Nyquist limit, i.e., for channel spacing (

*Δf*) equal to the symbol rate (

*R*). In Sec. 4, we compare the proposed

_{S}*FoM*with the ones earlier presented in the literature [1,2] showing how it is fundamental to include the role of chromatic dispersion in order to obtain a fair comparison between different fiber types. In order to validate the proposed

*FoM*we simulated a 10 channels Nyquist WDM PM-QPSK link and, in Sec. 5, displayed how simulative estimates of

*FoM*based on system margin are in excellent agreement with the proposed closed-form expression. In Sec. 6, we tested by simulation the applicability of the proposed

*FoM*to channel spacings larger than the Nyquist limit, showing that the presented

*FoM*works properly also in such scenarios. Finally, in Sec. 7, we validate experimentally the performance prediction obtained through the new

*FoM*for different fiber types and in conclusion (Sec. 8) we discuss the obtained results.

## 2. The figure of merit based on system margin

_{target}. In such a scenario we can define the following parameters.

- • Fiber loss
*A*: it is the intrinsic loss introduced by each fiber span, i.e.,_{fiber}*A*[dB], where α_{fiber}= α_{dB}·L_{s}_{dB}is the fiber loss coefficient expressed in dB/km and L_{s}is the span length expressed in km. - • Span budget
*A*: it is the maximum tolerable loss per span in order to keep the system in-service, i.e., BER ≤ BER_{max}_{target}.

*system margin*as the tolerable excess span loss with respect to fiber loss:

*system margin*strongly depends on the dispersion map, modulation format and data-rate, therefore it cannot be used as universal parameter

*to weight*the performance of a fiber type. If we focus our analysis on transmission based on coherently-received modulation formats, we know that the optimal links are uncompensated [4

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]

*FoM*) for uncompensated links transmitting coherently-received modulation formats, the system margin, i.e.:

*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

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

*FoM*definition proposed in Eq. (2) has a general validity, provided that it is applied to uncompensated links transmitting coherently-received modulation formats. In general, the

*FoM*can be estimated by simulation or measurements. In this section, we demonstrate that a closed-form expression for the

*FoM*can be derived for multichannel transmission with channel spacing equal to the symbol rate

*R*.

_{s}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]

*OSNR*that accounts for nonlinear interference (NLI) as additional Gaussian noise with equivalent noise power

_{NL}*P*, so that:

_{NLI}*N*is the number of spans,

_{s}*A*is the span loss,

*F*is the EDFA noise figure,

*h*is Plank’s constant,

*ν*[Hz] is the operating center frequency and

*B*[Hz] is the reference noise-bandwidth for

_{n}*OSNR*measurement. At the Nyquist limit, i.e., when the channel spacing

*Δf*[Hz] is equal to the symbol-rate

*R*[symbol/s] and channel spectra are rectangular,

_{s}*P*[W] in a bandwidth

_{NLI}*B*can be accurately approximated through the following expression [7

_{n}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]

*γ*[1/W/km] is the nonlinear coefficient,

*L*[km] is the fiber-span effective length,

_{eff}*P*[W] is the transmitted power per channel,

_{Tx,ch}*β*[ps

_{2}^{2}/km] is the dispersion coefficient and

*N*is the number of transmitted channels. The effective length is defined aswhere

_{ch}*L*[km] is the span length and

_{s}*α*[1/km] is the fiber loss coefficient.

*OSNR*, the span loss

_{NL}*A*resulting for a given target

*OSNR*can be evaluated as a function of all system parameters. Maximizing

_{target}*A*with respect to the transmitted power

*P*, the following expression for the maximum span budget, valid for practical scenarios with

_{Tx,ch}*A*>> 1, is obtained:where

_{max}*OSNR*is the one yielding a required target BER for a given modulation format.

_{target}*FoM*in the following closed-form:

*F, N*and the span length

_{s}, OSNR_{target}*L*) 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

_{s}*B*=

_{WDM}*N*(e.g., C-band and

_{ch}·R_{s}*R*= 30 Gbaud, means

_{s}*N*), log

_{ch}≈160*(πN*log

_{ch}^{2})>>*(|β*Hence, the term log

_{2}|L_{eff}R_{s}^{2}).*(|β*becomes negligible, and the term

_{2}|L_{eff}R_{s}^{2})*R*/log

_{s}^{2}*(πN*is fiber-independent and cancels out when calculating

_{ch}^{2})*FoM*expression in more compact form: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

*L*(see Eq. (6)) where

_{eff}/L_{D}*L*is the dispersion length defined as

_{D}*L*=

_{D}*1*/ (

*|β*). 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.,

_{2}|R_{s}^{2}*N*= 10). Moreover, such an inaccuracy decreases with the increasing of dispersion.

_{ch}## 4. Earlier *FoM* definitions and fiber comparison

*FoM*(Eqs. (8) and (9)), we compared it with two earlier

*FoMs*proposed in the literature [1,2]:

*A*) rather than the nonlinear parameter

_{eff}*γ = 2π·n*(

_{2}/*λ·A*). We have replaced

_{eff}*A*with

_{eff}*γ*to ease the comparison with the one we propose.

*FoM*takes into account only the scaling in the nonlinear coefficient together with the difference in span loss.

_{1}*FoM*is an upgrade of

_{2}*FoM*considering also the interplay between nonlinearity and loss through the effective length. The

_{1}*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.

*FoM*s 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 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.

*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.

*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,

*ΔFoM*and

_{1}*ΔFoM*display a mismatch larger than 4 dB with respect to the

_{2}*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.

*ΔFoM*on fiber dispersion, in Fig. 1 we plotted it with respect to

*β*for three different pairs of (

_{2}*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

*FoM*definition, we carried out an analysis aimed at calculating by simulation the

*FoM*for different fiber types and comparing such results with the closed-form expressions of Eqs. (8) and (9). For simulations we used the same set-up described in [8] with

*Δf = R*in order to have a reference system scenario used also for the experimental validation that is presented in Sec. 7. The channel comb was made of 10 optically-shaped Nyquist-WDM PM-QPSK channels at

_{s}*R*= 30 Gbaud (120 Gbps) spaced

_{S}*Δf = R*The link was a 8 spans uncompensated link with each span made of

_{S}.*L*= 100 km of fiber, a variable optical attenuator (VOA) and an EDFA completely recovering the span loss.

_{S}*BER*was established to be

*BER*= 3·10

_{target}^{−3}corresponding to

*OSNR*= 16.3 dB that includes realistic Tx impairments and crosstalk by fitting to the back-to-back performance of the experimental set-up.

_{target}*P*from −5 up to + 7 dBm and varied the attenuation of the VOA in order to evaluate the maximum span loss, the span budget

_{tx,ch}*A*, ensuring the transmission operating below

_{max}*BER*after 8 spans. Results are plotted in Fig. 2 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.

_{target}*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 = R*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.

_{s}## 6. Extension of *FoM* definition to *Δf > R*_{s}

_{s}

*FoM*is so far proposed and validated only for links operated at the Nyquist limit, i.e., multi-channel systems based on

*Δf = R*The reason is that for such scenarios the NLI presents an easy-to-be-handled closed-form expression [7

_{S}.**23**(11), 742–744 (2011). [CrossRef]

*FoM*definition to channel spacings larger than the symbol rate. To pursue such an objective, we considered the same system scenario used for the simulative validation presented in Sec. 5 and redid simulations enlarging the channel spacing from 30 GHz (

*Δf = R*) up to 50 GHz (

_{S}*Δf = 5/3·R*). For each considered scenario, we swept the transmitted power per channel and varied the VOA level in order to estimate by simulation the maximum span budget at the link receiver for

_{S}*BER*= 3·10

_{target}^{−3}. Then, from the collected results we were able to evaluate the

*FoM*according to Eq. (2) for each scenario, and considering the SSMF as a reference we derived

*ΔFoM*vs.

*Δf*for PSCF and NZDSF.

*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

*FoM*. The experimental set-up was the same as described in [8] with ten 30 Gbaud (120 Gbps) PM-QPSK optically-shaped channels.

*L*= 102 km (SSMF) and

_{s}*L*= 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

_{s}*Δf = 1.1·R*, i.e., 33 GHz.

_{s}*P*for BER = 3·10

_{Tx}^{−3}, after 8 spans propagation, are shown in Fig. 4b together with the analytical prediction based on the NLI model [9]. 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*= −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

*FoM*and

_{1}*FoM*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

_{2}*FoM*definition in order to fairly compare fiber types over a wide range of chromatic dispersion values.

## 7. Conclusions

**23**(11), 742–744 (2011). [CrossRef]

*FoM*. We validated it by simulation and experimentally and we proved it can be applied also to system scenarios based on channel spacings larger than the Nyquist limit.

## Acknowledgments

^{TM}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. |

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. |

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. |

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

- A. Pilipetskii, “Nonlinearity management and compensation in transmission systems,” OFC 2009, paper OTuL5.
- Y. Yamamoto, M. Hirano, and T. Sasaki, “A new class of optical fiber to support large capacity transmission,” OFC 2011, paper OWA6.
- 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]
- 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]
- 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.
- 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.
- 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]
- 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.
- 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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