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.

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$P_s\left(z\right)=P_{\mathrm{s0}}{e}^{-\alpha L}\left[\left(1+\frac{P_{\mathrm{p0}}g}{\alpha }\right)+\frac{P_{\mathrm{p0}}g}{\alpha }m\cos \left(\omega t\right)\right]$

[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

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/α

[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$R_k=\frac{R_{k-1}{P}_0}{\left(R_{k-1}+E_{k-1}\right)+x_1^{\prime }+x_2^{\prime }{A}_2{\beta }_2}{E}_k=\frac{\left(x_1^{\prime }+x_2^{\prime }{A}_2{\beta }_2+E_{k-1}\right)P_0}{\left(R_{k-1}+E_{k-1}\right)+x_1^{\prime }+x_2^{\prime }{A}_2{\beta }_2}$

[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$P_s\left(z\right)=P_{\mathrm{s0}}{e}^{-\alpha L}\left[\left(1+\frac{P_{\mathrm{p0}}g}{\alpha }\right)+\frac{P_{\mathrm{p0}}g}{\alpha }m\cos \left(\omega t\right)\right]$

[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

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/α 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$\begin{array}{cc}{R}_k=\frac{R_{k-1}{P}_0}{\left(R_{k-1}+E_{k-1}\right)+x_1^{\prime }+x_2^{\prime }{A}_2{\beta }_2}{E}_k=\frac{\left(x_1^{\prime }+x_2^{\prime }{A}_2{\beta }_2+E_{k-1}\right)P_0}{\left(R_{k-1}+E_{k-1}\right)+x_1^{\prime }+x_2^{\prime }{A}_2{\beta }_2}& 16\end{array}$

[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$\begin{array}{cc}\{\begin{array}{c}\frac{d{P}_p}{dz}+\alpha P_p-{\mathrm{gP}}_p{P}_s=0\\ \frac{d{P}_s}{dz}+\alpha P_s+{\mathrm{gP}}_p{P}_s=0\end{array}& \left(1\right)\end{array}$

[0041] where α is the fiber attenuation and g is the Raman gain coefficient between channel Pp and channelPs. For optical performance monitoring a sinusoidal dither (pilot tone) is added to each channel. If channel Pp is modulated by a single tone (sinusoidal dither m cos ωt) the equation for an undepleted channel can easily be obtained from the above equation as:

P p (z)=P0pe−az(1+m cos ωt)  (2)

[0042] in which P0p is the mean launch power. Substituting (2) into (1) gives rise into the following SRS Crosstalk for channel Ps due to the superimposed dither on channel Pp. 6$\begin{array}{cc}{P}_s\left(z\right)=P_{\mathrm{s0}}{e}^{-\alpha L}\left[\left(1+\frac{P_{\mathrm{p0}}g}{\alpha }\right)+\frac{P_{\mathrm{p0}}g}{\alpha }m\cos \left(\omega t\right)\right]& \left(3\right)\end{array}$

[0043] Compared to the situation without SRS, channel Ps sees a depletion of the mean level and some cross-talk from the Pp modulation. Modulation depth of the cross-talk m′ is given by: 7$\begin{array}{cc}{m}^{\prime }=\frac{{\mathrm{gP}}_{\mathrm{p0}}{P}_{\mathrm{s0}}}{\alpha }m& \left(4\right)\end{array}$

[0044] which is identical to the SRS impact on average power given by the second 8$\frac{{\mathrm{gP}}_{\mathrm{p0}}{P}_{\mathrm{s0}}}{\alpha },$

[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$\frac{{\mathrm{gP}}_{\mathrm{p0}}{P}_{\mathrm{s0}}}{\alpha }$

[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$\frac{{\mathrm{gP}}_{\mathrm{p0}}{P}_{\mathrm{s0}}}{\alpha }$

[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).

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 P0 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 P0β1+x1 where β1 is span fiber attenuation and x1 is the SRS error coming from step 1.

[0058] The power at the input of the following booster is given by:

[0059] (P0β1A1+x1A1)β2+x2 in which A1 is the dual gain, β2 is DCM attenuation and x2 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 P0 for all wavelengths the booster output power will be obtained as: 11$\begin{array}{cc}\frac{P_0^2}{P_0+x_1{A}_1{A}_2{\beta }_2+x_2{A}_2}+\frac{\left(x_1{A}_1{A}_2{\beta }_2+x_2{A}_2\right)P_0}{P_0+x_1{A}_1{\beta }_2{A}_2+x_2{A}_2}& \left(5\right)\end{array}$

[0060] in which A2 denotes the booster gain.

[0061] To derive equation (5) we first multiply the booster input power (P0β1A1+x1A1)β2+x2 by A2. Then we find a multiplier to flatten the power to P0. If η1 denotes this multiplier we should have

[(P0β1A1+x1A1)A2β2+x2A2]η1=P0  (6)

[0062] Therefore, 12$\begin{array}{cc}{\eta }_1=\frac{P_0}{\left[\left(P_0{\beta }_1{A}_1+x_1{A}_1\right)A_2{\beta }_2+x_2{A}_2\right]}& \left(7\right)\end{array}$

[0063] The booster output power will now be given by: 13$\begin{array}{cc}{P}_{\mathrm{Booster}1}=\left[P_0+x_1{A}_1{A}_2{\beta }_2+x_2{A}_2\right]\frac{P_0}{\left[P_0+x_1{A}_1{A}_2{\beta }_2+x_2{A}_2\right]}& \left(8\right)\end{array}$

[0064] In equation (8) we further assumed A1A2β1β2=1 meaning that the total loss in each span is equal to the total gain in that span.

[0065] Now we define: 14$R_1=\frac{P_0^2}{P_0+x_1{A}_1{A}_2{\beta }_2+x_2{A}_2}{E}_1=\frac{\left(x_1{A}_1{A}_2{\beta }_2+x_2{A}_2\right)P_0}{P_0+x_1{A}_1{\beta }_2{A}_2+x_2{A}_2}$

[0066] as the true power (R) and SRS error power (E) (induced by other channels). 15$\begin{array}{cc}{R}_k=\frac{R_{k-1}{P}_0}{\left(R_{k-1}+E_{k-1}\right)+x_1^{\prime }+x_2^{\prime }{A}_2{\beta }_2}{E}_k=\frac{\left(x_1^{\prime }+x_2^{\prime }{A}_2{\beta }_2+E_{k-1}\right)P_0}{\left(R_{k-1}+E_{k-1}\right)+x_1^{\prime }+x_2^{ \prime }{A}_2{\beta }_2}& \left(3\right)\end{array}$

[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$\begin{array}{cc}{P}_{\mathrm{Booster}2}=\left[P_{\mathrm{Booster}1}+x_1{A}_1{A}_2{\beta }_2+x_2{A}_2\right]\frac{P_0}{\left[P_{\mathrm{Booster}1}+x_1{A}_1{A}_2{\beta }_2+x_2{A}_2\right]}& \left(9\right)\end{array}$

[0068] Substituting equation (8) into (9) yields: 17$\begin{array}{cc}{P}_{\mathrm{Booster}2}=\frac{R_1{P}_0}{\left(R_1+E_1\right)+x_1{A}_1{\beta }_2{A}_2+x_2{A}_2}+\frac{P_0\left(x_1{A}_1{A}_2{\beta }_2+x_2{A}_2+E_1\right)}{\left(R_1+E_1\right)+x_1{A}_1{\beta }_2{A}_2+x_2{A}_2}& \left(10\right)\end{array}$

[0069] Continuing the same procedure will produce the following iterative approach for the kth booster:

P Booster k =R k +E k

[0070] where 18$\begin{array}{cc}{R}_k=\frac{R_{k-1}{P}_0}{\left(R_{k-1}+E_{k-1}\right)+x_1^{\prime }+x_2^{\prime }{A}_2{\beta }_2}{E}_k=\frac{\left(x_1^{\prime }+x_2^{\prime }{A}_2{\beta }_2+E_{k-1}\right)P_0}{\left(R_{k-1}+E_{k-1}\right)+x_1^{\prime }+x_2^{\prime }{A}_2{\beta }_2}& \left(3\right)\end{array}$

[0071] and

x1=β1x1′, x2=β2x2′

[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 (x1 and x2) 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.

Claims

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: 19Ps⁢(z)=Ps0⁢ⅇ-α⁢ ⁢L⁡[(1+Pp0⁢gα)+Pp0⁢gα⁢m⁢ ⁢cos⁢(ω⁢ ⁢t)]where α is the fiber attenuation and g is the Raman gain coefficient between channel Pp and channel Ps; 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: 4for k=1:2for i=1:Nchfor j=1:NchX(i)=X(i)+0.5*G*(j−i)*SpanP(j)*SpanTxP0;endSpanP(i)=SpanP(i)−X(i);endendto 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/α

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:

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: 21Ps⁡(z)=Ps0⁢e-α⁢ ⁢L⁡[(1+Pp0⁢gα)+Pp0⁢gα⁢m⁢ ⁢cos⁡(ωt)]where α is the fiber attenuation and g is the Raman gain coefficient between channel Pp and channel Ps; 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: 5for k=1:2for i=1:Nchfor j=1:NchX(i)=X(i)+0.5*G*(j−i)*SpanP(j)*SpanTxP0;endSpanP(i)=SpanP(i)−X(i);endendto 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/α

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 22Ps⁡(z)=Ps0⁢e-α⁢ ⁢L⁡[(1+Pp0⁢gα)+Pp0⁢gα⁢m⁢ ⁢cos⁡(ωt)]where α is the fiber attenuation and g is the Raman gain coefficient between channel Pp and channel Ps; and a network component having embedded computer readable code comprised of an iterative extended form of the two-channel equation substantially equal to: 6for k=1:2for i=1:Nchfor j=1:NchX(i)=X(i)+0.5*G*(j−i)*SpanP(j)*SpanTxP0;endSpanP(i)=SpanP(i)−X(i);endendto 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/α

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: