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The QoT estimation in the PSE framework of TIP-OOPT
=======================================================
QoT-E including ASE noise and NLI accumulation
----------------------------------------------
The operations of PSE simulative framework are based on the capability to estimate the QoT of one
or more channels operating lightpaths over a given network route. For
backbone transport networks, we can suppose that transceivers are
operating polarization-division-multiplexed multilevel modulation
formats with DSP-based coherent receivers, including equalization. For
the optical links, we focus on state-of-the-art amplified and
uncompensated fiber links, connecting network nodes including ROADMs,
where add and drop operations on data traffic are performed. In such a
transmission scenario, it is well accepted
:cite:`vacondio_nonlinear_2012,bononi_modeling_2012,carena_modeling_2012,mecozzi_nonlinear_2012,secondini_analytical_2012,johannisson_perturbation_2013,dar_properties_2013,serena_alternative_2013,secondini_achievable_2013,poggiolini_gn-model_2014,dar_accumulation_2014,poggiolini_analytical_2011,savory_approximations_2013,bononi_single-_2013,johannisson_modeling_2014`
to assume that transmission performances are limited by the amplified
spontaneous emission (ASE) noise generated by optical amplifiers and and
by nonlinear propagation effects: accumulation of a Gaussian disturbance
defined as nonlinear interference (NLI) and generation of phase noise.
State-of-the-art DSP in commercial transceivers are typically able to
compensate for most of the phase noise through carrier-phase estimator
(CPE) algorithms, for modulation formats with cardinality up to 16, per
polarization state
:cite:`poggiolini_recent_2017,schmidt_experimental_2015,fehenberger_experimental_2016`.
So, for backbone networks covering medium-to-wide geographical areas, we
can suppose that propagation is limited by the accumulation of two
Gaussian disturbances: the ASE noise and the NLI. Additional impairments
such as filtering effects introduced by ROADMs can be considered as
additional equivalent power penalties depending on the ratio between the
channel bandwidth and the ROADMs filters and the number of traversed
ROADMs (hops) of the route under analysis. Modeling the two major
sources of impairments as Gaussian disturbances, and being the receivers
*coherent*, the unique QoT parameter determining the bit error rate
(BER) for the considered transmission scenario is the generalized
signal-to-noise ratio (SNR) defined as
.. math::
{\text{SNR}}= L_F \frac{P_{\text{ch}}}{P_{\text{ASE}}+P_{\text{NLI}}} = L_F \left(\frac{1}{{\text{SNR}}_{\text{LIN}}}+\frac{1}{{\text{SNR}}_{\text{NL}}}\right)^{-1}
where :math:`P_{\text{ch}}` is the channel power,
:math:`P_{\text{ASE}}` and :math:`P_{\text{NLI}}` are the power levels of the disturbances
in the channel bandwidth for ASE noise and NLI, respectively.
:math:`L_F` is a parameter assuming values smaller or equal than one
that summarizes the equivalent power penalty loss such as
filtering effects. Note that for state-of-the art equipment, filtering
effects can be typically neglected over routes with few hops
:cite:`rahman_mitigation_2014,foggi_overcoming_2015`.
To properly estimate :math:`P_{\text{ch}}` and :math:`P_{\text{ASE}}`
the transmitted power at the beginning of the considered route must be
known, and losses and amplifiers gain and noise figure, including their
variation with frequency, must be characterized. So, the evaluation of
:math:`{\text{SNR}}_{\text{LIN}}` *just* requires an accurate
knowledge of equipment, which is not a trivial aspect, but it is not
related to physical-model issues. For the evaluation of the NLI, several
models have been proposed and validated in the technical literature
:cite:`vacondio_nonlinear_2012,bononi_modeling_2012,carena_modeling_2012,mecozzi_nonlinear_2012,secondini_analytical_2012,johannisson_perturbation_2013,dar_properties_2013,serena_alternative_2013,secondini_achievable_2013,poggiolini_gn-model_2014,dar_accumulation_2014,poggiolini_analytical_2011,savory_approximations_2013,bononi_single-_2013,johannisson_modeling_2014`.
The decision about which model to test within the PSE activities was
driven by requirements of the entire PSE framework:
i. the model must be *local*, i.e., related individually to each network element (i.e. fiber span) generating NLI, independently of preceding and subsequent elements; and
ii. the related computational time must be compatible with interactive operations.
So, the choice fell on the Gaussian Noise
(GN) model with incoherent accumulation of NLI over fiber spans
:cite:`poggiolini_gn-model_2014`. We implemented both the
exact GN-model evaluation of NLI based on a double integral (Eq. (11) of
:cite:`poggiolini_gn-model_2014`) and its analytical
approximation (Eq. (120-121) of
:cite:`poggiolini_analytical_2011`). We performed several
validation analyses comparing results of the two implementations with
split-step simulations over wide bandwidths
:cite:`pilori_ffss_2017`, and results clearly showed that
for fiber types with chromatic dispersion roughly larger than 4
ps/nm/km, the analytical approximation ensures an excellent accuracy
with a computational time compatible with real-time operations.
The Gaussian Noise Model to evaluate the NLI
--------------------------------------------
As previously stated, fiber propagation of multilevel modulation formats relying on the polarization-division-multiplexing
generates impairments that can be summarized as a disturbance called nonlinear interference (NLI),
when exploiting a DSP-based coherent receiver, as in all state-of-the-art equipment.
From a practical point of view, the NLI can be modeled as an additive
Gaussian random process added by each fiber span, and whose strength depends on the cube of the input power spectral density and
on the fiber-span parameters.
Since the introduction in the market in 2007 of the first transponder based on such a transmission technique, the scientific
community has intensively worked to define the propagation behavior of such a trasnmission technique.
First, the role of in-line chromatic dispersion compensation has been investigated, deducing that besides being
not essential, it is indeed detrimental for performances :cite:`curri_dispersion_2008`.
Then, it has been observed that the fiber propagation impairments are practically summarized by the sole NLI, being all the other
phenomena compensated for by the blind equalizer implemented in the receiver DSP :cite:`carena_statistical_2010`.
Once these assessments have been accepted by the community, several prestigious research groups have started to work
on deriving analytical models able to estimating the NLI accumulation, and consequentially the generalized SNR that sets the BER,
according to the transponder BER vs. SNR performance.
Many models delivering different levels of accuracy have been developed and validated. As previously clarified, for the purposes
of the PSE framework, the GN-model with incoherent accumulation of NLI over fiber spans has been selected as adequate.
The reason for such a choice is first such a model being a "local" model, so related to each fiber spans, independently of
the preceding and succeeding network elements. The other model characteristic driving the choice is
the availability of a closed form for the model, so permitting a real-time evaluation, as required by the PSE framework.
For a detailed derivation of the model, please refer to :cite:`poggiolini_analytical_2011`, while a qualitative description
can be summarized as in the following.
The GN-model assumes that the channel comb propagating in the fiber is well approximated by unpolarized spectrally shaped
Gaussian noise. In such a scenario, supposing to rely - as in state-of-the-art equipment - on a receiver entirely compensating for linear propagation effects, propagation in the fiber only excites the four-wave mixing (FWM) process among the continuity of
the tones occupying the bandwidth. Such a FWM generates an unpolarized complex Gaussian disturbance in each spectral slot
that can be easily evaluated extending the FWM theory from a set of discrete tones - the standard FWM theory introduced back in the 90s by Inoue :cite:`Innoue-FWM`- to a continuity of tones, possibly spectrally shaped.
Signals propagating in the fiber are not equivalent to Gaussian noise, but thanks to the absence of in-line compensation for choromatic dispersion,
the become so, over short distances.
So, the Gaussian noise model with incoherent accumulation of NLI has estensively proved to be a quick yet accurate and conservative tool
to estimate propagation impairments of fiber propagation.
Note that the GN-model has not been derived with the aim of an *exact* performance estimation, but to pursue a conservative performance prediction. So, considering these characteristics, and the fact that the NLI is always a secondary effect with respect to the ASE noise accumulation, and - most importantly - that typically linear propagation parameters (losses, gains and noise figures) are known within
a variation range, a QoT estimator based on the GN model is adequate to deliver performance predictions in terms of a reasonable SNR range, rather than an exact value.
As final remark, it must be clarified that the GN-model is adequate to be used when relying on a relatively narrow bandwidth up to few THz. When exceeding such a bandwidth occupation, the GN-model must be generalized introducing the interaction with the Stimulated
Raman Scattering in order to give a proper estimation for all channels :cite:`cantono2018modeling`.
This will be the main upgrade required within the PSE framework.
.. bibliography:: biblio.bib

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.. GNpy documentation master file, created by
.. gnpy documentation master file, created by
sphinx-quickstart on Mon Dec 18 14:41:01 2017.
You can adapt this file completely to your liking, but it should at least
contain the root `toctree` directive.
Welcome to GNpy's documentation!
Welcome to gnpy's documentation!
================================
Gaussian Noise (GN) based modeling library for physical layer impairment evaluation in optical networks.
**gnpy is an open-source, community-developed library for building route planning
and optimization tools in real-world mesh optical networks.**
Summary
--------
We believe that openly sharing ideas, specifications, and other intellectual property is the key to maximizing innovation and reducing complexity
PSE WG Charter
--------------
- Goal is to build an end-to-end simulation environment which defines the network models of the optical device transfer functions and their parameters. This environment will provide validation of the optical performance requirements for the TIP OLS building blocks.
- The model may be approximate or complete depending on the network complexity. Each model shall be validated against the proposed network scenario.
- The environment must be able to process network models from multiple vendors, and also allow users to pick any implementation in an open source framework.
- The PSE will influence and benefit from the innovation of the DTC, API, and OLS working groups.
- The PSE represents a step along the journey towards multi-layer optimization.
`gnpy <http://github.com/telecominfraproject/gnpy>`_ is:
- a sponsored project of the `OOPT/PSE <http://telecominfraproject.com/project-groups-2/backhaul-projects/open-optical-packet-transport/>`_ working group of the `Telecom Infra Project <http://telecominfraproject.com>`_.
- fully community-driven, fully open source library
- driven by a consortium of operators, vendors, and academic researchers
- intended for rapid development of production-grade route planning tools
- easily extensible to include custom network elements
- performant to the scale of real-world mesh optical networks
Documentation
=============
The following pages are meant to describe specific implementation details and modeling assumptions behind GNpy.
The following pages are meant to describe specific implementation details and
modeling assumptions behind gnpy.
.. toctree::
:maxdepth: 2
gn_model
model
Indices and tables
==================
@@ -59,7 +55,7 @@ Contributors in alphabetical order
+----------+------------+-----------------------+----------------------------+
| Gilad | Goldfarb | Facebook | giladg@fb.com |
+----------+------------+-----------------------+----------------------------+
| James | Powell | Consultant | james@dontusethiscode.com |
| James | Powell | Telecom Infra Project | james.powell@telecominfraproject.com |
+----------+------------+-----------------------+----------------------------+
| Jeanluc | Auge | Orange | jeanluc.auge@orange.com |
+----------+------------+-----------------------+----------------------------+
@@ -68,3 +64,18 @@ Contributors in alphabetical order
| Vittorio | Curri | Politecnico di Torino | vittorio.curri@polito.it |
+----------+------------+-----------------------+----------------------------+
PSE WG Charter
--------------
- Goal is to build an end-to-end simulation environment which defines the
network models of the optical device transfer functions and their parameters.
This environment will provide validation of the optical performance
requirements for the TIP OLS building blocks.
- The model may be approximate or complete depending on the network complexity.
Each model shall be validated against the proposed network scenario.
- The environment must be able to process network models from multiple vendors,
and also allow users to pick any implementation in an open source framework.
- The PSE will influence and benefit from the innovation of the DTC, API, and
OLS working groups.
- The PSE represents a step along the journey towards multi-layer optimization.