Method for regulating OSNR in a fiber optic communication line
using Raman amplification
Field of the invention
The present invention relates to technologies of designing,
installing and regulating optical networks comprising high power optical
amplifiers, such as Raman amplifiers.
Background of the invention
There are a number of solutions proposed in the prior art for
calculating and regulating Optical Signal to Noise Ratio (OSNR) in
optical communication networks, in particular, there are a number of
approaches for controlling and regulating OSNR in optical lines
comprising Raman optical amplifiers.
Fig. 1 (prior art) shows a single span exemplary optical
communication system 10. In practice, such, systems may be composed
of several spans.
Let the illustrated system 10 initially comprises a multiplexer assembly
12 at the transmitting end of the system, a demultiplexer assembly 14 at
the receiving end of the system, an optical fiber link 15 extending
between an optical amplifier (EDFA) 13 the transmitting end and EDFA
17 of the receiving end for conveying the multiplexed optical signal, and
a backward Raman amplifier (BRA) 18 which is inserted close to the
receiving end of the link. The goal of the system designer is that OSNR at
the input of any single channel receiver at the receiving end of the link is
larger than the receiver OSNR Tolerance, being the minimum OSNR for
which the Bit Error Rate (BER) is still better than, say, a commonly
accepted standard value 10-12. The required OSNR must be greater than

the receiver OSNR tolerance +a margin selected by the system designer.
One of the possibilities to improve the system OSNR is to increase the
input power applied to the fiber up to the possible maximum, by using
output power of the EDFA's 13 booster. The possible maximum is
usually set by the system nonlinearity limit.
Those skilled in the art know that, at high power levels, nonlinear
phenomena like self-phase modulation (SPM), Cross-phase modulation
(XPM) and four-wave mixing (FWM) cause signal distortion and
performance (or BER) degradation in the system.
The non-linearity limit of a system should be understood as
follows. When a network works under the non-linearity limit, non-linear
penalty (performance degradation due to non-linear effects in the fiber)
does not exceed a value determined by a system designer (say, 1 or 2 dB).
Actually, crossing of the non-linearity limit can be expressed as such a
condition of the system when increasing the power applied to the fiber
leads to increase of a real OSNR required for the same stated BER.
Usually, when performance of an optical line cannot be further improved
by its own resources and without crossing the non-linearity limit, network
designers insert a Forward Raman Amplifier (FRA) in the line.
Fig. 1 therefore illustrates inserting a FRA 16 (shown as a dashed arrow)
at the beginning of the link 15.
A number of articles, for example 1) Essiambre et al. IEEE photon.
Techn. Lett. Vol.14, pp.914 (2002); 2) Perline and Winful. IEEE photon.
Techn. Lett. Vol.14, pp.1199 (2002) explain that the Forward Raman
amplification (FRA) enables the system designer to increase the effective
input power applied to the fiber, thus improving the system OSNR,
without crossing the nonlinear limit.

The above articles propose various but quite complex mathematical
equations which enable theoretically calculating the FRA power required
for a specific communication system. However, these and some other
previous works dealt with too general systems; it is very hard to employ
their methods of calculation, including many system parameters, to
practical systems.
To the best of the Applicant's knowledge, prior art does not give a
simple and effective advice of how to estimate the required gain of FRA
for obtaining a designed value of OSNR in real optical
telecommunication systems. Likewise, no recommendations are found for
effective OSNR regulation in real systems.
Object of the invention
It is therefore the object of the present invention to present a simple
tool to the system designer, enabling to effectively deploy FRA in an
optical communication line and perform adjustment of OSNR at the
receiving end of the line.
Summary of the invention
The problem of obtaining desired values of OSNR when designing an
optical line consists of at least three sub-problems:
a) selecting a proper Raman amplifier for an optical line, when
required;
b) adjusting OSNR at the receiving end of the line so as not to
become lower than the receiver tolerance; and
c) adjusting OSNR at the receiving end for various optical channels
transmitted via the line.

The Inventor has derived a formula for any real long transmission
system operating substantially close to its non-linearity limit, that shows
that the gain of a required Forward Raman Amplifier (FRA) can be
determined, with quite a high accuracy, solely by the desired value of
OSNR improvement, and that an almost linear regulation function can be
obtained for fine tuning of the OSNR by regulating the FRA gain.
In practice, the Inventor has found that any reasonable OSNR
improvement (say, up to 5 dB) can be achieved by a properly selected
value of the FRA gain.
The Inventor has also found that, when adding and regulating a
FRA in a long transmission system that operates substantially close to its
non-linearity limit, a desired OSNR increment practically does not
depend on gain of a Backward Raman Amplifier BRA (if comprised in
the system) and on many other parameters usually present in theoretical
equations described in the prior art references.
The long transmission systems should be understood as such
optical communication systems where a value of the power loss L in a
fiber span that extends between two optical network nodes respectively
associated with its transmitting end and its receiving end, is much greater
than a value of the working gain Gf of the FRA (Forward Raman
Amplifier) associated with the transmitting end:
L>> Gf
If a BRA (Backward Raman Amplifier) is already present in the same
system (span) at its receiving end, the above condition should be
understood as
L>>Max of (Gf,Gb),
where Gf is a value of working gain of the FRA,
Gb is a value of working gain of the BRA if present,

L - is power loss in the fiber span, being a passive fiber
characteristic that depends only on the fiber length and quality.
Preferably, the value of power loss L is at least one order of magnitude
higher (approximately by 10 dB) than the value of gain Gf which is
also called "on-off gain" (or of gain Gb, if BRA is present).
The gain of BRA is usually of the same order of magnitude as that of
the FRA. However, even in a rear case when Gb>>Gf, the condition of
long transmission systems still remains the same and can be just
rewritten as L>>Gb.
For example, the formula found out by the Inventor applies to an
optical span equipped with a FRA having gain Gf =10dB, wherein the
power loss L of an optical span is approximately 20 dB or more.
In the present description, the term "gain" will be used
intermittently with the term "on-off gain" accepted in the art.
In particular, under a set of assumptions that the Inventor considers
practically correct for realistic long transmission systems working close
to their non-linearity limit, the Inventor shows that, by introducing a FRA
at the transmitting end of a fiber span, OSNR of an optical signal at the
receiving end can be improved according to a function of OSNR
improvement ROSNS, being close to linear (or at least, approximatable to
linear portions):

where Gf is the FRA on-off gain and RNL is the FRA's so-called nonlinear
enhancement factor determined close to the following:

where μ=α/β,

α is the fiber attenuation at the signal wavelength (practically, the
average fiber attenuation at the C-band), known for each specific fiber,
β is the fiber attenuation of the Raman pump wavelengths (in practice,
the average value over the pump wavelengths),
and Γ(x) and Γ(x, y) are the Gamma and the incomplete Gamma
functions, respectively.
It should be noted that though the coefficients α and β may slightly
vary from fiber to fiber, their ratio μ=α/β remains almost constant. The
remaining components of the expression (2) can easily be obtained by
those skilled in the art.
Since a modern FRA comprises two Raman pumps, the
simultaneous operation of the pumps enables obtaining equal Raman gain
for each of the propagating signal wavelengths. Thereby, one and the
same equation (2) is practically applicable to each optical channel of a
multi-channel signal.
Further, the Inventor has shown mat for a practical interval of 0-
20dB of the FRA on-off gain, the function of OSNR improvement ROSNR at
the receiver end of the optical transmission line can be approximated as a
number of linear sections:

optionally, for an interval of 0 - 12 dB, the function can be approximated
as:


Suitable calculations and verifying experiments were performed and
have proven the proposed method.
In simple words, when designing a transmission line, the Inventor
proposes selecting, for a long fiber optic transmission line, a FRA capable
of reaching a certain "on-off" gain calculated according to Equation (1) in
order to improve OSNR of the line by a certain required amount.
According to that version, the Inventor proposes a method of
selecting a Forward Raman Amplifier (FRA) to be inserted at a
transmitting end of a given fiber optic transmission line, for providing
improvement of OSNR at a receiving end of said transmission line by no
less than a certain required improvement amount ROSNR, the method
comprises detennining a required value of (working) gain Gf of said FRA
by using a regulation function (ROSNR) of OSNR improvement
substantially close to that defined by the following expression:
where RNL is the FRA nonlinear enhancement factor:

where μ=α/β,
α is the fiber attenuation at the signal wavelength,
β is the fiber attenuation of the Raman pump wavelengths,
Γ(x) and Γ(x, y) are the Gamma and the incomplete Gamma
functions, respectively;
the method being applicable if the following two conditions are
satisfied:
the given fiber optic transmission line operates under a non-
linearity limit,

power loss L of the given fiber optic transmission line is much
greater than the determined gain Gf.
The FRA capable of reaching a value of gain not less than the
required gain Gf, can be considered as selected.
The method may further comprise inserting the selected FRA (i.e.
the FRA capable of reaching a value of gain not less than Gf) in the fiber
optic transmission line at the transmitting end.
Further, the Inventor proposes adding a step of regulating
(adjusting, fine tuning) of the OSNR at the receiving end of the
transmission line by adjusting gain of said FRA according to the
regulation function expressed by said equation (1).
Since any Raman amplifier comprises pumps, the gain adjustment
can be performed by controlling pumps of said FRA.
The Inventor also proposes an alternative method for regulating
OSNR in a real, given fiber optic transmission line comprising an existing
FRA at its transmitting end; the method comprises
regulating OSNR at the receiving end of said transmission line by
adjusting gain of said FRA using a regulation function substantially
expressed by the equation (1),
provided that the given transmission line operates without crossing
the non-linearity limit, and that L>> Gf, wherein:
Gf is a value of working (or actual) gain of the existing FRA,
L is a value of power loss in the given fiber transmission line.
For both of the methods proposed above, the power loss L should
be approximately one order of magnitude greater than the determined
gain Gf.

In case the given transmission line initially comprises a Backward
Raman Amplifier BRA, the transmission line should satisfy a condition
that the power loss L is much greater (for example, approximately one
order of magnitude greater) than the highest value among values of the Gf
and Gb, wherein Gb is a value of working (or actual) gain of the BRA.
The step of regulating OSNR actually comprises adjusting gain of
said FRA by an amount produced by said regulation function for a value
of a certain required improvement of OSNR.
Both the method of selecting a FRA, and the method of regulating
OSNR in the line comprising a FRA can be essentially simplified by
using a linear approximation of the regulation function (1).
It should be noted that the regulation function can be presented as a
sum of linear approximations according to equations 3,4, 5.
The methods can therefore be simplified by using a specific linear
section of the regulation function for practically required intervals of
FRA gains and OSNR increments.
Yet further, for a multi-channel optical traffic conveyed via said
transmission line, the Inventor proposes regulating the OSNR so as to
achieve said certain required improvement of OSNR in "the worst"
optical channel, wherein the worst optical channel is considered to be
such having the lowest OSNR at a currently used value of the FRA gain
Gf.
In one specific embodiment, the optical fiber transmission line
comprises a single optical fiber span extending between the transmitting
end and the receiving end of the line.
It should be added that the method can be applied to an optical system in
the form of the fiber optic transmission line comprising a number of
optical spans, each of the spans working close to the limit of non-linearity

and being equipped with, a FRA such that values of Gf of all said FRA are
substantially equal to one another; and wherein each of the spans satisfies
either the requirement L>> Gf, or L>>Max of( Gf, Gb ) in case any of the
optical spans is also equipped with a BRA. The OSNR of that system can
be then regulated according to the equation 1, equation 6, and/or the
equations 3,4,5, by synchronously regulating the FRA gains Gf of each
of the spans.
Generally speaking, the Inventor has found a method for selecting
a relation between a gain Gf of a Forward Raman Amplifier (FRA) at a
transmitting end of a fiber optic transmission line and an optical signal to
noise ratio (OSNR) at a receiving end of the fiber optic transmission line
satisfying the above-mentioned limitations for long lines; wherein
the method comprises selecting said relation using a regulation function
ROSRN either in the form of equation (1), or in the form of one or more
linear approximations for a practical range of the FRA gain 0 to 12 dB or
0 to 20.dB.
For example, the regulation function can be in the form of one or
more, or a sum of the following linear approximations:

In a more approximate case, the regulation function can be in the
form of a single linear approximation section covering a more limited
practical range of the FRA gain: R0SNR - 0.35Gf, odB > Gf, wherein:
Gf is a value of working gain of the existing FRA,
L is a value of power loss in the given fiber transmission line;
the method comprises
regulating OSNR at the receiving end of said transmission line by
adjusting gain of said FRA using a regulation function ROSNR substantially
expressed by the equation:

where RNL is a factor of the FRA, defined substantially close to the
expression:

where μ=α/β,
α is the fiber attenuation at the signal wavelength,
β is the fiber attenuation of the Raman pump wavelengths,
Γ(x) and Γ(x, y) are the Gamma and the incomplete Gamma functions,
respectively.
5. The method according to any one of the preceding claims, wherein
the given transmission line initially comprises a Backward Raman

Amplifier BRA and satisfies a condition that the power loss L is much
greater than the highest value among values of Gf and Gb, wherein Gb is a
value of working gain of the BRA.
6. The method according to any one of the preceding claims, wherein
the given transmission line satisfies the condition that the powerloss L is
approximately one order of magnitude greater than the determined gain
Gf or than the highest value among values of Gf and Gb, wherein Gb is a
value of working gain of the BRA.
7. The method according to any one of claims 3 to 6, wherein the step
of regulating OSNR comprises adjusting gain of said FRA by a value
produced by said regulation function for a value of a certain required
improvement of 6SNR.
8. The method according to any one of claims 3 to 7, wherein said
adjustment of the FRA gain is performed by controlling pumps of said
FRA.
9. A method according to any one of the preceding claims, wherein
said regulation function is used in the form of its linear approximation.
10. The method according to Claim 9, wherein the regulation function
is utilized in the form of one or more of the following linear
approximations for a practical range of the FRA gain 0 to 20 dB:


11. The method according to Claim 10, wherein the regulation function
is utilized in the form of the following linear approximation for a
practical range of the FRA gain 0 to 12 dB:

12. A method for selecting a relation between a gain Gf of a Forward
Raman Amplifier (FRA) at a transmitting end of a fiber optic
transmission line and an optical signal to noise ratio (OSNR) at a
receiving end of the fiber optic transmission line, provided that
said transmission line operates under a non-linearity limit, and
power loss L of the fiber optic transmission line is much greater than a
selected value of the gain Gf;
the method comprises selecting said relation using a regulation
function ROSNR in the form of one or more of the following approximated
linear sections covering a practical range of the FRA gain 0 to 20 dB:

13. A method for selecting a relation between a gain Gf of a Forward
Raman Amplifier (FRA) at a transmitting end of a fiber optic
transmission line and an optical signal to noise ratio (OSNR) at a
receiving end of the fiber optic transmission line, provided that
said transmission line operates under a non-linearity limit, and
power loss L of the fiber optic transmission line is much greater than a
selected value of the gain Gf;

the method comprises selecting said relation using a regulation
function ROSNR in the form of an approximated linear section covering a
practical range of the FRA gain 0 to 12 dB:

14. The method according to any one of Claims 3 to 13, wherein the
step of regulating OSNR of a multi-channel optical signal is performed
by regulating OSNR for an optical channel having the lowest OSNR at a
currently used value of the FRA gain Gf.
15. The method according to any one of the preceding claims, wherein
the optical fiber transmission line comprises a single optical fiber span
extending between the transmitting end and the receiving end of the line.
6. The method according to any one of claims 3 to 15, wherein the
optical fiber transmission line comprises a number of optical spans, each
of said spans working close to the limit of non-linearity and being
equipped with a FRA such that values of Gf of all said FRA are
substantially equal to one another; and wherein each of the spans satisfies
either the requirement in case any of the
optical spans is also equipped with a BRA;
the method comprises regulating OSNR of the line according to the
equation 1, equation 6, and/or the equations 3,4,5, by synchronously
regulating Gf of each of the spans.
17. A method for selecting a relation between a gain Gf of a Forward
Raman Amplifier (FRA) at a transmitting end of a fiber optic

transmission line and an optical signal to noise ratio (OSNR) at a
receiving end of the fiber optic transmission line, provided that
said transmission line operates under a non-linearity limit, and
power loss L of the fiber optic transmission line is much greater than a
selected value of the gain Gf;
the method comprises selecting said relation by using a regulation
function ROSNR of OSNR improvement, defined substantially close to the
following expression:

where RNL is a factor of the FRA, calculated substantially close to the
following:

where μ=α/β,
α is the fiber attenuation at the signal wavelength,
β is the fiber attenuation of the Raman pump wavelengths,
Γ(x) and Γ(x, y) are the Gamma and the incomplete Gamma functions,
respectively.

A method for selecting a relation between a gain Gf of a Forward Raman Amplifier (FRA) at a transmitting end of a fiber optic transmission line and an optical signal to noise ratio (OSNR) at a receiving end of the fiber optic transmission line satisfying limitations
for real long transmission lines. The method comprises selecting the relation using a regulation function ROSNR obtained either in the form of a simplified equation, or in the form of one or more linear approximation for practical ranges of the FRA gain.