U.S. patent application number 10/013679 was filed with the patent office on 2002-08-22 for iterative approach to stimulated raman scattering (srs) error estimation.
Invention is credited to Harley, James, Seydnejad, Saeid.
Application Number | 20020113955 10/013679 |
Document ID | / |
Family ID | 4167940 |
Filed Date | 2002-08-22 |
United States Patent
Application |
20020113955 |
Kind Code |
A1 |
Seydnejad, Saeid ; et
al. |
August 22, 2002 |
Iterative approach to Stimulated Raman Scattering (SRS) error
estimation
Abstract
Iterative approach to Stimulated Raman Scattering (SRS) error
estimation in an optical fiber network comprised of determining a
multi-channel SRS error value for each pairing of all possible
pairings of all the channels by inputting measured channel power
levels into a two-channel equation and further calculating the SRS
error in a single fiber span for all channels by extending the
two-channel equation in an iterative form for calculating the SRS
error in a single fiber span for all channels. An embodiment of the
invention further comprising determining for each channel over
multiple fiber spans the amount of total SRS error value at every
span based on the calculated SRS error value of its previous span
to determine the SRS error accumulated over a multi-span
network.
Inventors: |
Seydnejad, Saeid; (Ottawa,
CA) ; Harley, James; (Ottawa, CA) |
Correspondence
Address: |
Gowling Lafleur Henderson LLP
Suite 2600
160 Elgin Street
Ottawa
ON
K1P 1C3
CA
|
Family ID: |
4167940 |
Appl. No.: |
10/013679 |
Filed: |
December 13, 2001 |
Current U.S.
Class: |
356/73.1 |
Current CPC
Class: |
G01N 21/65 20130101;
G01N 2021/655 20130101 |
Class at
Publication: |
356/73.1 |
International
Class: |
G01N 021/00 |
Foreign Application Data
Date |
Code |
Application Number |
Dec 18, 2000 |
CA |
2,328,752 |
Claims
What is claimed is:
1. An iterative method for Stimulated Raman Scattering (SRS) error
estimation in an optical fiber network, the network characterized
in that it comprises the infrastructure required to measure the
power levels of all optical channels using a pilot tone monitoring
technique, the method comprising the steps of: (i) determining the
multi-channel SRS error value for each pairing of all possible
pairings of all the channels by inputting measured values of
channel power levels into a two-channel equation substantially
equal to: 19 P s ( z ) = P s0 - L [ ( 1 + P p0 g ) + P p0 g m cos (
t ) ] where .alpha. is the fiber attenuation and g is the Raman
gain coefficient between channel P.sub.p and channel P.sub.s; and
(ii) calculating the SRS error in a single fiber span for all
channels by extending the two-channel equation in an iterative form
substantially equal to:
4 for k=1:2 for i=1:Nch for j=1:Nch
X(i)=X(i)+0.5*G*(j-i)*SpanP(j)*SpanTxP0; end
SpanP(i)=SpanP(i)-X(i); end end
to estimate the SRS error in a single span. where Nch=Number of
channels SpanTxP0=Launch power into the fiber (equal power per
wavelength is assumed) SpanP(j)=output power at channel j X(i)=SRS
error in channel i G=g/.alpha.
2. The method according to claim 1, further comprising determining
for each channel over multiple fiber spans the amount of total SRS
error value at every span based on the calculated SRS error value
of its previous span so as to determine the SRS error accumulated
over a multi-span network, the method comprising an iterative form
of the two-channel equation substantially equal to: 20 R k = R k -
1 P 0 ( R k - 1 + E k - 1 ) + x 1 ' + x 2 ' A 2 2 E k = ( x 1 ' + x
2 ' A 2 2 + E k - 1 ) P 0 ( R k - 1 + E k - 1 ) + x 1 ' + x 2 ' A 2
2
3. A system for Stimulated Raman Scattering (SRS) error estimation
in an optical fiber network, the network characterized in that it
comprises the infrastructure required to measure the power levels
of all optical channels using a pilot tone monitoring technique,
the system comprising: means for determining the multi-channel SRS
error value for each pairing of all possible pairings of all the
channels by inputting measured values of channel power levels into
a two-channel equation substantially equal to: 21 P s ( z ) = P s0
e - L [ ( 1 + P p0 g ) + P p0 g m cos ( t ) ] where .alpha. is the
fiber attenuation and g is the Raman gain coefficient between
channel P.sub.p and channel P.sub.s; and means for calculating the
SRS error in a single fiber span for all channels by extending the
two-channel equation in an iterative form substantially equal
to:
5 for k=1:2 for i=1:Nch for j=1:Nch
X(i)=X(i)+0.5*G*(j-i)*SpanP(j)*SpanTxP0; end
SpanP(i)=SpanP(i)-X(i); end end
to estimate the SRS error in a single span where Nch=Number of
channels SpanTxP0=Launch power into the fiber (equal power per
wavelength is assumed) SpanP(j)=output power at channel j X(i)=SRS
error in channel i G=g/.alpha.
4. The system according to claim 3, further comprising a means for
determining for each channel over multiple fiber spans the amount
of total SRS error value at every span based on the calculated SRS
error value of its previous span so as to determine the SRS error
accumulated over a multi-span network, the system comprising an
iterative form of the two-channel equation substantially equal
to:
5. A system for Stimulated Raman Scattering (SRS) error estimation
in an optical fiber network, the network characterized in that it
comprises the infrastructure required to measure the power levels
of all optical channels using a pilot tone monitoring technique,
the system comprising: a network component having embedded computer
readable code comprising a two-channel equation for determining a
multi-channel SRS error value for each pairing of all possible
pairings of all the channels by inputting the measured channel
power levels into the equation, the equation substantially equal to
22 P s ( z ) = P s0 e - L [ ( 1 + P p0 g ) + P p0 g m cos ( t ) ]
where .alpha. is the fiber attenuation and g is the Raman gain
coefficient between channel P.sub.p and channel P.sub.s; and a
network component having embedded computer readable code comprised
of an iterative extended form of the two-channel equation
substantially equal to:
6 for k=1:2 for i=1:Nch for j=1:Nch
X(i)=X(i)+0.5*G*(j-i)*SpanP(j)*SpanTxP0; end
SpanP(i)=SpanP(i)-X(i); end end
to estimate the SRS error in a single span where Nch=Number of
channels SpanTxP0=Launch power into the fiber (equal power per
wavelength is assumed) SpanP(j)=output power at channel j X(i)=SRS
error in channel i G=g/.alpha.
6. The approach according to claim 5, further comprising a network
component having embedded computer readable code capable of
determining for each channel over multiple fiber spans the amount
of total SRS error value at every span based on the calculated SRS
error value of its previous span so as to determine the SRS error
accumulated over a multi-span network, the code comprised of an
iterative form of the two-channel equation substantially equal to:
23 R = R k - 1 P 0 ( R k - 1 + E k - 1 ) + x 1 ' + x 2 ' A 2 2 E k
= ( x 1 ' + x 2 ' A 2 2 + E k - 1 ) P 0 ( R k - 1 + E k - 1 ) + x 1
' + x 2 ' A 2 2
Description
FIELD OF THE INVENTION
[0001] The present invention relates to maintenance of an optical
fiber network and more specifically to Stimulated Raman Scattering
(SRS) error estimation.
BACKGROUND OF THE INVENTION
[0002] Today's optical fiber networks carry many channels along
their optical fibers. A significant challenge in maintaining these
networks is the problem of power level estimation within these
channels at every point in the network or in other words optical
performance monitoring. A simple tool for optical performance
monitoring and channel identification in DWDM (Dense Wave Division
Multiplexing) systems is to add small signal sinusoidal dithers
(pilot tones) to optical carriers. Consequently, each optical
carrier has a unique sinusoidal dither whose amplitude is
proportional to the average power of its carrier. These pilot tones
are superimposed to the average power of the optical channel and
can be separated and analysed easily. The presence of a specific
dither at a particular point in the network therefore indicates the
presence of its corresponding wavelength and its amplitude will
show the average optical power.
[0003] This is true when each dither travels solely with its
optical carrier. However, an effect known as Stimulated Raman
Scattering (SRS) precipitates an inter-channel energy transfer that
interferes with the ability to accurately estimate power levels
through pilot tones. This inter-channel energy transfer occurs from
smaller wavelengths to larger wavelengths causing larger wavelength
power levels to increase. SRS not only causes an interaction
between the average power of each channel but also brings about a
transfer of dithers between different channels. Therefore, some of
the dither of each channel is transferred to other channels and
hence its amplitude will not be proportional to the power of its
carrier any more. This causes inaccuracy in power level estimation
using pilot tones.
[0004] SRS energy transfer, or SRS error, largely depends upon the
number of channels in the network. The more channels present the
more energy transfer occurring. In a multi-span optical networks,
in addition to the number of channels, the number of spans
contributes significantly. In such a system SRS error is
accumulated over all the spans causing an even more severe
degradation in power level estimation.
[0005] In a multi-span system estimation of the SRS error needs two
steps to be taken. In the first step an estimate of the SRS error
in one span should be obtained. Using the results of the first
step, in the second step the accumulation of the SRS error over all
spans should be considered. Once the total error is estimated a
compensation algorithm can be developed to correct for the
inaccuracy in pilot tone power estimation due to SRS.
[0006] For the foregoing reasons, a need exists for an improved
method of SRS error estimation in a single span of an optical fiber
network that can be applied to a multi-span approach of SRS error
estimation within a multi-span network.
SUMMARY OF THE INVENTION
[0007] The present invention is directed to an iterative method for
Stimulated Raman Scattering (SRS) error estimation in an optical
fiber network, the network characterized in that it comprises the
infrastructure required to measure the power levels of all optical
channels using a pilot tone monitoring technique, the method
comprising the steps of determining the multi-channel SRS error
value for each pairing of all possible pairings of all the channels
by inputting measured values of channel power levels into a
two-channel equation substantially equal to 1 P s ( z ) = P s0 - L
[ ( 1 + P p0 g ) + P p0 g m cos ( t ) ]
[0008] and calculating the SRS error in a single fiber span for all
channels by extending the two-channel equation in an iterative form
substantially equal to
1 for k=1:2 for i=1:Nch for j=1:Nch
X(i)=X(i)+0.5*G*(j-i)*SpanP(j)*SpanTxP0; end
SpanP(i)=SpanP(i)-X(i); end end
[0009] to estimate the SRS error in a single span.
[0010] where Nch=Number of channels
[0011] SpanTxP0=Launch power into the fiber (equal power per
wavelength is
[0012] assumed) SpanP(j)=output power at channel j
[0013] X(i)=SRS error in channel i
[0014] G=g/.alpha.
[0015] In an aspect of the invention, the method comprises
determining for each channel over multiple fiber spans the amount
of total SRS error value at every span based on the calculated SRS
error value of its previous span so as to determine the SRS error
accumulated over a multi-span network, the method comprising an
iterative form of the two-channel equation substantially equal to 2
R k = R k - 1 P 0 ( R k - 1 + E k - 1 ) + x 1 ' + x 2 ' A 2 2 E k =
( x 1 ' + x 2 ' A 2 2 + E k - 1 ) P 0 ( R k - 1 + E k - 1 ) + x 1 '
+ x 2 ' A 2 2
[0016] The advantage of using this iterative approach is to account
for the power depletion in a practical manner. This iterative
approach is very suitable for software implementation and provides
adequate accuracy in power readings up to 40 optical channels.
[0017] Other aspects and features of the present invention will
become apparent to those ordinarily skilled in the art upon review
of the following description of specific embodiments of the
invention in conjunction with the accompanying figures.
BRIEF DESCRIPTION OF THE DRAWINGS
[0018] These and other features, aspects, and advantages of the
present invention will become better understood with regard to the
following description, appended claims, and accompanying drawings
where:
[0019] FIG. 1 is a flow chart showing the iterative method for
Stimulated Raman Scattering (SRS) error estimation in an optical
fiber network;
[0020] FIG. 2 is a flow chart showing the iterative method for
Stimulated Raman Scattering (SRS) error estimation in an optical
fiber network further including a multi-span solution;
[0021] FIG. 3 is a flow chart showing the system for Stimulated
Raman Scattering (SRS) error estimation in an optical fiber
network;
[0022] FIG. 4 is a flow chart showing the system for Stimulated
Raman Scattering (SRS) error estimation in an optical fiber network
further including a multi-span solution;
[0023] FIG. 5 is a graph displays the results of this approach for
40 channels with 6.0o dBm average power per wavelength in an 80km
NDSF fiber; and
[0024] FIG. 6 is a graph illustrating the SRS error in pilot tone
power estimation for 40 channels 6-span NDSF system with 6.0 dBm
launch power per wavelength.
DETAILED DESCRIPTION OF THE PRESENTLY PREFERRED EMBODIMENT
[0025] As shown in FIG. 1, the present invention is directed to an
iterative method for Stimulated Raman Scattering (SRS) error
estimation in an optical fiber network, the network characterized
in that it comprises the infrastructure required to measure the
power levels of all optical channels using a pilot tone monitoring
technique, the method comprising the steps of determining the
multi-channel SRS error value for each pairing of all possible
pairings of all the channels by inputting measured values of
channel power levels into a two-channel equation substantially
equal to 3 P s ( z ) = P s0 - L [ ( 1 + P p0 g ) + P p0 g m cos ( t
) ]
[0026] 12 and calculating the SRS error in a single fiber span for
all channels by extending the two-channel equation in an iterative
form substantially equal to
2 for k=1:2 for i=1:Nch for j=1:Nch
X(i)=X(i)+0.5*G*(j-i)*SpanP(j)*SpanTxP0; end
SpanP(i)=SpanP(i)-X(i); end end
[0027] to estimate the SRS error in a single span.
[0028] where Nch= Number of channels
[0029] SpanTxP0= Launch power into the fiber (equal power per
wavelength is
[0030] assumed) SpanP(j)=output power at channel j
[0031] X(i)=SRS error in channel i
[0032] G=g/.alpha. 14
[0033] As shown in FIG. 2, in an embodiment of the invention, the
method comprises determining for each channel over multiple fiber
spans the amount of total SRS error value at every span based on
the calculated SRS error value of its previous span so as to
determine the SRS error accumulated over a multi-span network, the
method comprising an iterative form of the two-channel equation
substantially equal to 4 R k = R k - 1 P 0 ( R k - 1 + E k - 1 ) +
x 1 ' + x 2 ' A 2 2 E k = ( x 1 ' + x 2 ' A 2 2 + E k - 1 ) P 0 ( R
k - 1 + E k - 1 ) + x 1 ' + x 2 ' A 2 2 16
[0034] By applying an iterative approach the two wavelength
solution can be extended for an arbitrary number of channels,
permitting the effect of power depletion to be included in the
results.
[0035] Two factors should be taken into account when determining
SRS error over a multi-span network. First, how the SRS error is
manifested in one span and second, how the SRS error is accumulated
over multiple spans. The contribution of both of these factors can
be calculated by an appropriate iterative approach as described
below.
[0036] For this purpose, an iterative approach is first applied to
find the amount of SRS error in a single span. Next, an iterative
algorithm is designed to calculate the amount of SRS error
accumulated over multiple spans by considering the role of the dual
and booster amplifiers in the system.
[0037] With respect to this second iterative approach, it is
assumed that every dual amplifier has a flat gain and every booster
amplifier has a flat power distribution. The total amount of SRS
error at every span is then calculated based on the error of its
previous span. Finally, the total SRS error is used to compensate
for the inaccuracy in power readings.
[0038] When a set of optical channels travels through a fiber,
Stimulated Raman Scattering (SRS) causes an energy transfer from
shorter to longer wavelengths. This energy transfer causes an
inaccuracy in the estimated power readings. In a multi-span system
the SRS error in each span is accumulated at the end of the system.
In this report an iterative approach is proposed to calculate the
amount of SRS error for one span. Then a recursive equation will be
developed to obtain the accumulation of the SRS error in a
multi-span system.
[0039] Step 1: SRS error estimation in one span:
[0040] In this step we solve the SRS differential equation for two
channels only. Then we extend the results for a multi-channel
system. The SRS describing equation for two wavelengths in a single
fiber is given by: 5 { P p z + P p - gP p P s = 0 P s z + P s + gP
p P s = 0 ( 1 )
[0041] where .alpha. is the fiber attenuation and g is the Raman
gain coefficient between channel P.sub.p and channelP.sub.s. For
optical performance monitoring a sinusoidal dither (pilot tone) is
added to each channel. If channel P.sub.p is modulated by a single
tone (sinusoidal dither m cos .omega.t) the equation for an
undepleted channel can easily be obtained from the above equation
as:
P.sub.p(z)=P.sub.0pe.sup.-az(1+m cos .omega.t) (2)
[0042] in which P.sub.0p is the mean launch power. Substituting (2)
into (1) gives rise into the following SRS Crosstalk for channel
P.sub.s due to the superimposed dither on channel P.sub.p. 6 P s (
z ) = P s0 - L [ ( 1 + P p0 g ) + P p0 g m cos ( t ) ] ( 3 )
[0043] Compared to the situation without SRS, channel P.sub.s sees
a depletion of the mean level and some cross-talk from the P.sub.p
modulation. Modulation depth of the cross-talk m' is given by: 7 m
' = gP p0 P s0 m ( 4 )
[0044] which is identical to the SRS impact on average power given
by the second 8 gP p0 P s0 ,
[0045] term in (3). Recalling that the inaccuracy in pilot tone
power level estimation comes from the fact that the mean level of
the average power is changed due to SRS according to 9 gP p0 P
s0
[0046] whereas the dither amplitude as detected by the pilot tone
monitoring apparatus does not see any change. The difference is
actually the SRS inaccuracy in pilot tone power level estimation
technique. For the two channel case this error is equal to 10 gP p0
P s0
[0047] but for a multi-channel system (DWDM system) this simple
solution is not valid. This is because the SRS energy transfer from
the first channel to the second channel increases the power of the
second channel and therefore will contribute to the SRS error
between the second channel and the third channel. The same concept
is also true for all other channels in the system. Therefore, we
have to extend the above results in a way to accommodate the
presence of more than two channels.
[0048] In order to get a better estimate of the SRS energy transfer
while taking advantage of using the simple solution of equation (3)
we can implement an iterative approach which incrementally
calculates the SRS energy transfer between each pair and
subsequently calculates the impact between other pairs based on
this incremental change. The following pseudo-code shows this
approach for a single fiber based on equation (3).
3 for k=1:2 for i=1:Nch for j=1:Nch
X(i)=X(i)+0.5*G*(j-i)*SpanP(j)*SpanTxP0; end
SpanP(i)=SpanP(i)-X(i); end end
[0049] In the above notation we have:
[0050] Nch=Number of channels
[0051] SpanTxP0=Launch power into the fiber (equal power per
wavelength is assumed)
[0052] SpanP(j)=output power at channel j
[0053] X(i)=SRS error in channel i
[0054] In this code the SRS contribution of each channel on all
other channels is first calculated in the internal loop. Then the
external loop uses the modified power levels to calculate the total
SRS error for each channel. FIG. 5 displays the results of this
approach for 40 channels with 6.0o dBm average power per wavelength
in an 80 km NDSF fiber.
[0055] Step 2: Accumulation of SRS error in a multi-pan system
[0056] Once the SRS error for each channel over one span is given
we can calculate the total SRS error in a multi-span system. To
simplify the calculations we assume all spans are identical with a
series combination of fiber, dual amplifier, DCM and booster
amplifier. Furthermore, we assume a flat gain characteristic for
dual amplifier and a flat output power distribution for the booster
amplifier.
[0057] Now consider the first span. If P.sub.0 denotes the input
power into the fiber per wavelength then dual input power which is
located at the end of the first span fiber will be equal to
P.sub.0.beta..sub.1+x.su- b.1 where .beta..sub.1 is span fiber
attenuation and x.sub.1 is the SRS error coming from step 1.
[0058] The power at the input of the following booster is given
by:
[0059]
(P.sub.0.beta..sub.1A.sub.1+x.sub.1A.sub.1).beta..sub.2+x.sub.2 in
which A.sub.1 is the dual gain, .beta..sub.2 is DCM attenuation and
x.sub.2 is the SRS error in DCM. Recalling that the DCM module
comprises an internal fiber which adds to the overall SRS error.
Since we have assumed that the booster flattens the power to
P.sub.0 for all wavelengths the booster output power will be
obtained as: 11 P 0 2 P 0 + x 1 A 1 A 2 2 + x 2 A 2 + ( x 1 A 1 A 2
2 + x 2 A 2 ) P 0 P 0 + x 1 A 1 2 A 2 + x 2 A 2 ( 5 )
[0060] in which A.sub.2 denotes the booster gain.
[0061] To derive equation (5) we first multiply the booster input
power
(P.sub.0.beta..sub.1A.sub.1+x.sub.1A.sub.1).beta..sub.2+x.sub.2 by
A.sub.2. Then we find a multiplier to flatten the power to P.sub.0.
If .eta..sub.1 denotes this multiplier we should have
[(P.sub.0.beta..sub.1A.sub.1+x.sub.1A.sub.1)A.sub.2.beta..sub.2+x.sub.2A.s-
ub.2].eta..sub.1=P.sub.0 (6)
[0062] Therefore, 12 1 = P 0 [ ( P 0 1 A 1 + x 1 A 1 ) A 2 2 + x 2
A 2 ] ( 7 )
[0063] The booster output power will now be given by: 13 P Booster
1 = [ P 0 + x 1 A 1 A 2 2 + x 2 A 2 ] P 0 [ P 0 + x 1 A 1 A 2 2 + x
2 A 2 ] ( 8 )
[0064] In equation (8) we further assumed
A.sub.1A.sub.2.beta..sub.1.beta.- .sub.2=1 meaning that the total
loss in each span is equal to the total gain in that span.
[0065] Now we define: 14 R 1 = P 0 2 P 0 + x 1 A 1 A 2 2 + x 2 A 2
E 1 = ( x 1 A 1 A 2 2 + x 2 A 2 ) P 0 P 0 + x 1 A 1 2 A 2 + x 2 A
2
[0066] as the true power (.sup.R) and SRS error power (.sup.E)
(induced by other channels). 15 R k = R k - 1 P 0 ( R k - 1 + E k -
1 ) + x 1 ' + x 2 ' A 2 2 E k = ( x 1 ' + x 2 ' A 2 2 + E k - 1 ) P
0 ( R k - 1 + E k - 1 ) + x 1 ' + x 2 ' A 2 2 ( 3 )
[0067] For the second span we inject the booster 1 output power
(equation 8) to the next set of span fiber, dual amplifier, DCM,
and booster amplifier. Along the same line of derivation it is easy
to show the output power of the second booster at the end of the
second span is given by: 16 P Booster 2 = [ P Booster 1 + x 1 A 1 A
2 2 + x 2 A 2 ] P 0 [ P Booster 1 + x 1 A 1 A 2 2 + x 2 A 2 ] ( 9
)
[0068] Substituting equation (8) into (9) yields: 17 P Booster 2 =
R 1 P 0 ( R 1 + E 1 ) + x 1 A 1 2 A 2 + x 2 A 2 + P 0 ( x 1 A 1 A 2
2 + x 2 A 2 + E 1 ) ( R 1 + E 1 ) + x 1 A 1 2 A 2 + x 2 A 2 ( 10
)
[0069] Continuing the same procedure will produce the following
iterative approach for the kth booster:
P.sub.Booster k=R.sub.k+E.sub.k
[0070] where 18 R k = R k - 1 P 0 ( R k - 1 + E k - 1 ) + x 1 ' + x
2 ' A 2 2 E k = ( x 1 ' + x 2 ' A 2 2 + E k - 1 ) P 0 ( R k - 1 + E
k - 1 ) + x 1 ' + x 2 ' A 2 2 ( 3 )
[0071] and
x.sub.1=.beta..sub.1x.sub.1', x.sub.2=.beta..sub.2x.sub.2'
[0072] In other words the power for each wavelength has two
components the actual power and the power induced in the channel by
SRS. Note that the SRS induced errors in each span (x.sub.1 and
x.sub.2) are provided by step 1 whereas SRS error accumulation over
multiple spans is calculated by step 2. Using these two steps
together enables us to estimate the total SRS error for each
channel for a DWDM multi-span system. FIG. 6 illustrates the SRS
error in pilot tone power estimation for 40 channels 6-span NDSF
system with 6.0 dBm launch power per wavelength.
[0073] Although the present invention has been described in
considerable detail with reference to certain preferred versions
thereof, other versions are possible. Therefore, the spirit and
scope of the appended claims should not be limited to the
description of the preferred versions contained herein.
[0074] All the features disclosed in this specification (including
any accompanying claims, abstract, and drawings) maybe replaced by
alternative features serving the same, equivalent or similar
purpose, unless expressly stated otherwise. Thus, unless expressly
stated otherwise, each feature disclosed is one example only of a
generic series of equivalent or similar features.
* * * * *