Method and network control device for optimizing performance of a multi-span optical fiber network

Abstract

The present invention relates to a method for optimizing performance of a multi-span optical fiber network. Each span has an associated optical transmission fiber connected to an associated optical amplifier. Gain and output power of the associated optical amplifier are respectively controlled independently. An amplifier noise figure respectively depends on the gain of the associated optical amplifier, with each associated optical amplifier further connected to launch optical signals into a remainder of a corresponding optical transmission line. The method includes the steps of for each span, computing the amplifier noise figure and a non-linear noise generated in the span based on information about the span and using the computed amplifier noise figure and the computed non-linear noise to compute an optimum launch power, and optimizing performance of the multi-span optical fiber network based on the computed optimum launch powers of all spans.

Claims

1. A method for optimizing performance of a multi-span optical fiber network, wherein each span has an associated optical transmission fiber connected to an associated optical amplifier, wherein gain and output power of the associated optical amplifier are respectively controlled independently, and wherein an amplifier noise figure respectively depends on the gain of the associated optical amplifier, wherein each associated optical amplifier is further connected to launch optical signals into a remainder of a corresponding optical transmission line, and wherein the method comprises the steps of: for each span, computing the amplifier noise figure and a non-linear noise generated in the span based on information about the span and using the computed amplifier noise figure and the computed non-linear noise to compute an optimum launch power; and optimizing performance of the multi-span optical fiber network based on the computed optimum launch powers of all spans, wherein: the step of optimizing performance of the multi-span optical fiber network based on the computed optimum launch powers of all spans further comprises the step of: separately optimizing performance of each span by setting the gain of an amplifier associated with a particular span and the output power of an amplifier associated with a span that is immediately preceding the particular span based on the computed optimum launch power of the particular span, and by setting the gain of the amplifier associated with the particular span based on an optimum gain that is derived from the computed optimum launch power of the particular span.

2. The method according to claim 1, wherein the information about the span includes a span length, information about the associated transmission fiber, information about an optical amplifier associated with a previous span, a symbol rate of a corresponding transceiver and a frequency spacing between channels transmitted on the previous span.

3. The method according to claim 1, wherein the step of optimizing performance of the multi-span optical fiber network based on the computed optimum launch powers of all spans further comprises the steps of: for each span, using the computed optimum launch power to calculate a maximum generalized optical signal-to-noise ratio of the span; and using the calculated maximum generalized optical signal-to-noise ratios of all spans to optimize the performance of the multi-span optical fiber network.

4. The method according to claim 1, wherein linear equivalents of the information about the span are used to compute the amplifier noise figure.

5. The method according to claim 1, wherein the performance of the multi-span optical fiber network is optimized during a planning phase of a network deployment, wherein usual values are chosen for the information about the span, and optionally, wherein in the multi-span optical fiber network pairs of nodes of the network are associated with distinct bands of optical channels used for communication between the pairs of nodes, wherein a maximum generalized optical signal-to-noise ratio is calculated for the central channel based on the computed optimum launch powers of all spans of the central channel, and wherein the maximum generalized optical signal-to-noise ratio of the central channel is used to optimize the performance of the multi-span optical fiber network.

6. The method according to claim 1, wherein the performance of the multi-span optical fiber network is optimized as part of a network turn-up and commissioning, wherein exact values are chosen for the information about the span, and optionally, wherein in the multi-span optical fiber network pairs of nodes of the network are associated with distinct bands of optical channels used for communication between the pairs of nodes, wherein a maximum generalized optical signal-to-noise ratio is separately calculated for each channel based on the computed optimum launch powers of all spans of the respective channel, wherein a worst generalized optical signal-to-noise ratio is determined from the calculated maximum generalized optical signal-to-noise ratios of the channels, and wherein the worst generalized optical signal-to-noise ratio is used to optimize the performance of the multi-span optical fiber network.

7. A network control device for optimizing performance of a multi-span optical fiber network in which each span has an associated optical transmission fiber connected to an associated optical amplifier, wherein gain and output power of the associated optical amplifier are respectively controlled independently, and wherein an amplifier noise figure respectively depends on the gain of the associated optical amplifier, wherein each associated optical amplifier is further connected to launch optical signals into a remainder of a corresponding optical transmission line, and wherein the network control device comprises a computing means which is configured to, for each span, compute the amplifier noise figure and a non-linear noise generated in the span based on information about the span and use the computed amplifier noise figure and the computed non-linear noise to compute an optimum launch power, and an optimizing means which is configured to optimize performance of the multi-span optical fiber network based on the computed optimum launch powers of all spans, wherein the optimizing means comprises a controlling means which is configured to separately optimize performance of each span by setting the gain of an amplifier associated with a particular span and the output power of an amplifier associated with a span that is immediately preceding the particular span based on the computed optimum launch power of the particular span, and by setting the gain of the amplifier associated with the particular span based on an optimum gain that is derived from the computed optimum launch power of the particular span.

8. The network control device according to claim 7, wherein the information about the span includes a span length, information about the associated transmission fiber, information about an optical amplifier associated with a previous span, a symbol rate of a corresponding transceiver and a frequency spacing between channels transmitted on the previous span.

9. The network control device according to claim 7, wherein the optimizing means further comprises a calculating means which is configured to, for each span, use the computed optimum launch power to calculate a maximum generalized optical signal-to-noise ratio of the span, and wherein the optimizing means is configured to use the calculated maximum generalized optical signal-to-noise ratios of all spans to optimize the performance of the multi-span optical fiber network.

10. The network control device according to claim 7, wherein the computing means is configured to use linear equivalents of the information about the span to compute the amplifier noise figure.

11. The network control device according to claim 7, wherein the network control device is configured to optimize the performance of the multi-span optical fiber network during a planning phase of a network deployment, wherein the network control device further comprises a memory in which usual values for the information about the span are stored, and optionally, wherein in the multi-span optical fiber network pairs of nodes of the network are associated with distinct bands of optical channels used for communication between the pairs of nodes, wherein the network control device is configured to calculate a maximum generalized optical signal-to-noise ratio for the central channel based on the computed optimum launch powers of all spans of the central channel and to use the maximum generalized optical signal-to-noise ratio of the central channel to optimize the performance of the multi-span optical fiber network.

12. The network control device according to claim 7, wherein the network control device is configured to optimize the performance of the multi-span optical fiber network as part of a network turn-up and commissioning, wherein the network control device further comprises a first determining means which is configured to determine exact values for the information about the span, and optionally, wherein in the multi-span optical fiber network pairs of nodes of the network are associated with distinct bands of optical channels used for communication between the pairs of nodes, wherein the network control device is configured to separately calculate a maximum generalized signal-to-noise ratio for each channel based on the computed optimum launch powers of all spans of the respective channel, wherein the network control device further comprises a second determining means to determine a worst generalized optical signal-to-noise ratio from the calculated maximum generalized optical signal-to-noise ratios of the channels, and wherein the optimizing means is configured to use the worst generalized optical signal-to-noise ratio to optimize the performance of the multi-span optical fiber network.

13. A program product comprising a computer-readable storage medium that stores non-transitory code executable by a processor, the executable code comprising code which, when executed by the processor, causes the processor to: (a) for each span in a multi-span optical fiber network, wherein each span has an associated optical transmission fiber connected to an associated optical amplifier, wherein gain and output power of the associated optical amplifier are respectively controlled independently, and wherein an amplifier noise figure respectively depends on the gain of the associated optical amplifier, wherein each associated optical amplifier is further connected to launch optical signals into a remainder of a corresponding optical transmission line, to compute the amplifier noise figure and a non-linear noise generated in the span based on information about the span and to use the computed amplifier noise figure and the computed non-linear noise to compute an optimum launch power; and (b) to optimize performance of the multi-span optical fiber network based on the computed optimum launch powers of all spans, wherein step (b) comprises separately optimizing performance of each span by setting the gain of an amplifier associated with a particular span and the output power of an amplifier associated with a span that is immediately preceding the particular span based on the computed optimum launch power of the particular span, and by setting the gain of the amplifier associated with the particular span based on an optimum gain that is derived from the computed optimum launch power of the particular span.

14. The method according to claim 2, wherein the step of optimizing performance of the multi-span optical fiber network based on the computed optimum launch powers of all spans further comprises the steps of: for each span, using the computed optimum launch power to calculate a maximum generalized optical signal-to-noise ratio of the span; and using the calculated maximum generalized optical signal-to-noise ratios of all spans to optimize the performance of the multi-span optical fiber network.

15. The method according to claim 1, wherein the step of optimizing performance of the multi-span optical fiber network based on the computed optimum launch powers of all spans further comprises the steps of: for each span, using the computed optimum launch power to calculate a maximum generalized optical signal-to-noise ratio of the span; and using the calculated maximum generalized optical signal-to-noise ratios of all spans to optimize the performance of the multi-span optical fiber network.

16. The network control device according to claim 8, wherein the optimizing means comprises a controlling means which is configured to separately optimize performance of each span by setting the gain of an amplifier associated with a particular span and the output power of an amplifier associated with a span that is immediately preceding the particular span based on the computed optimum launch power of the particular span.

17. The network control device according to claim 8, wherein the optimizing means further comprises a calculating means which is configured to, for each span, use the computed optimum launch power to calculate a maximum generalized optical signal-to-noise ratio of the span, and wherein the optimizing means is configured to use the calculated maximum generalized optical signal-to-noise ratios of all spans to optimize the performance of the multi-span optical fiber network.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Embodiments of the invention will now be described with reference to the drawings.

(2) FIG. 1 illustrates an example section of an optical fiber network;

(3) FIG. 2 illustrates a system that includes a network control device for optimizing performance of a multi-span optical fiber network according to embodiments of the invention;

(4) FIG. 3 illustrates a flowchart of a method for optimizing performance of a multi-span optical fiber network according to a first embodiment of the invention;

DESCRIPTION OF THE INVENTION

(5) FIG. 1 illustrates an example section 1 of an optical fiber network. The network is a wavelength-division multiplexing (WDM) Network.

(6) As shown in FIG. 1, an ingress WDM node 2 is connected to an egress WDM node 3 via spans 4 of optical fiber. The spans 4 of optical fiber are coupled via optical amplifiers 5. An amplifier 5 in the ingress node 2 is optically coupled to the first span 4 of optical fiber. An amplifier 5 in the egress node 3 is optically coupled to the final span 4 of optical fiber.

(7) The optical amplifiers 5 shown in FIG. 1 are optical amplifiers with independent gain and output power controls and amplifier noise figure dependence on amplifier gain. In this regard, FIG. 1 also shows variable-gain amplifier 6 and corresponding variable optical attenuators (VOA) 7, wherein the output power is respectively controlled using the respective variable optical attenuator 7. Here, the actual amplifier 6 and the variable optical attenuator 7 are respectively shown being separated from each other. However, each optical amplifier with independent gain and output power control may also be an amplifier in which a variable attenuator is integrated. The optical amplifiers 5 can for example be erbium-doped fiber amplifiers (EDFAs) which ensure that the amplifier operates with the lowest possible noise figure regardless of the launch power. However, the optical amplifiers 5 can for example also be hybrid Raman-EDFAs, in particular amplifiers comprised of a combination of a Raman amplifier connected to the input of an EDFA, wherein the Raman amplifier can be discrete or distributed. Therein, one or both amplifier stages could also be semiconductor amplifiers.

(8) One can index the spans 4 and the optical amplifier devices by an index i, with N representing the total number of spans of optical fiber coupling the ingress node 2 to the egress node 3.

(9) Network operators have a strong interest in making most efficient use of their investments in the network infrastructure, and therefore, a strong interest in achieving the highest transmission capacity through the fiber optical transmission lines in the network. Therein, for most fiber optical transmission lines impairments determining the total capacity of the fiber within a given bandwidth are amplified spontaneous emission (ASE) noise from optical amplifiers 5 along the line and fiber nonlinear effects. It is also known that the power of the optical signal launched into each span 4 is a critical parameter of the system, which determines the capacity that can be attained. Low power launched into the fiber yields low optical signal-to-noise ratio (OSNR), which reduces the available transmission rate. High power launched into the fiber produces nonlinear distortions. Thus, low launch power increases the amplified spontaneous emission noise, while high launch power increases nonlinear noise, and an optimum launch power into each span 4 exists where the performance of a signal is maximized.

(10) Therefore, the optimization of the launch power is important to optimize the performance of the network. However, known methods to determine the optimum launch power are based on a simplified optimization approach, wherein the noise figure of the optical amplifiers is assumed to be constant regardless of the amplifier gain value used to compensate the span loss, regardless of the tilt setting the amplifier, and assumed to be constant for all channels. However, this over-simplification leads to an error in the estimation of the optimum launch power, in particular as there are optical amplifiers known with independent gain and output power controls. Therefore, there is a need for a method for optimizing performance of a multi-span optical fiber network, wherein the determination of the optimum launch power is as precise as possible.

(11) FIG. 2 illustrates a system 10 that includes a network control device 11 for optimizing performance of a multi-span optical fiber network according to embodiments of the invention.

(12) As shown in FIG. 2, the multi-span optical fiber network comprises a section 1 of an optical fiber network as shown in FIG. 1, wherein the same elements as in FIG. 1 are given the same reference numbers as in FIG. 1 and are not discussed in any further detail here.

(13) The system 10 further comprises a network control device 11, wherein the network control device 11 comprises a computing means 12 which is configured to, for each span, compute an amplifier noise figure and a non-linear noise generated in the span based on information about the span and to use the computed amplifier noise figure and the computed non-linear noise to compute an optimum launch power, and an optimizing means 13 which is configured to optimize performance of the multi-span optical fiber network based on the computed optimum launch powers of all spans.

(14) Therein, that the parameters and, in particular, that the amplifier noise figure and a non-linear noise generated in each span are computed means that these parameters, respectively information characterizing the parameters are derived respectively calculated by methods of functional analysis and numerical mathematics.

(15) Thus, a network control device 11 for optimizing a multi-span optical fiber network is provided which is as precise as possible, as all relevant parameters that can impact the value of the optimum launch power are taken into account. In particular, the amplifier noise figure is not assumed to be constant but for each span information characterizing the amplifier noise figure is defined. Therein, the information about the span preferably includes all relevant parameters of the fiber and information about components which can impact the value of the optimum launch power. Further, as the optimum launch power is separately computed for each span, a global transmission fiber line optimization problem can be reduced to a local per span optimization problem, which makes the optimization numerically very fast, while supporting multi-span transmission fiber lines with different types of fiber in different spans. Therefore, the network control device also addresses the problem that communication systems often evolve and grow during their lifetime, wherein, due to their evolution and growth, these infrastructures often combine different technologies which can produce optical fiber transmission lines that are span-wise heterogeneous.

(16) According to the embodiments of FIG. 2, the information about the span includes a span length, information about the associated transmission fiber, information about an optical amplifier associated with a previous span, a symbol rate of a corresponding transceiver and a frequency spacing between channels transmitted on the previous span.

(17) The optimizing means 13 further comprises a controlling means 14 which is configured to separately optimize the performance of each span by setting the gain of an amplifier associated with a particular span and the output power of an amplifier associated with a span that is immediately preceding the particular span based on the computed optimum launch power of the particular span. In particular, by setting the output power of an amplifier associated with a span immediately preceding the particular span based on the computed optimum launch power of the particular span, it can be ensured that this optimum launch power is in fact launched into the particular span. Further, power losses in the particular span at the optimum launch power can be compensated by setting the gain of the amplifier based on the computed optimum launch power.

(18) Further, the computing means 12 is configured to use linear equivalents of the information about the span to compute the amplifier noise figure.

(19) The network control device 11 is further configured to optimize the performance of the multi-span optical fiber network during a planning phase of a network deployment. Therein, the planning phase is a phase during the network planning and design, in which it is, among others, determined whether a predefined system infrastructure, sites, and an operational environment can support a proposed system. As shown in FIG. 2, the network control device further comprises a memory 15 in which usual values for the information about the span are stored. That usual values are chosen for the information about the span means that the values are chosen in such a way that they are common for a comparable usual span, respectively that either design or manufacturing data is chosen for the values. For example, a dependence between noise figure and gain can be chosen that represents a usual amplifier of the same type. Further, the values may be provided by a carrier to a system vendor during design stage.

(20) In the multi-span optical fiber network pairs of nodes of the network are associated with distinct bands of optical channels used for communication between the pairs of nodes. Therein, the network control device 11 according to the embodiments of FIG. 2 is, in particular, configured to, during a planning phase of a network deployment, calculate a maximum generalized optical signal-to-noise ratio for the central channel based on the computed optimum launch powers of all spans of the central channel and to use the maximum generalized optical signal-to-noise ratio of the central channel to optimize the performance of the multi-span optical fiber network.

(21) According to the embodiments of FIG. 2, the network control device 11 is further configured to optimize the performance of the multi-span optical fiber network as part of a network turn-up and commissioning. Therein, network turn-up and commissioning means the phase after the system equipment has been deployed, during which a series of steps are taken to prove that the system actually meets the specific requirements. As shown in FIG. 2, the network control device 11 further comprises a first determining means 16 which is configured to determine exact values for the information about the span.

(22) Therein, the network control device 11 is configured to, during network turn-up and commissioning, separately calculate a maximum generalized signal-to-noise ratio for each channel based on the computed optimum launch powers of all spans of the respective channel.

(23) As shown in FIG. 2, the network control device further comprises a second determining means 17 to determine a worst generalized optical signal-to-noise ratio from the calculated maximum generalized optical signal-to-noise ratios of the channels, wherein the optimizing means 14 is configured to use the worst generalized optical signal-to-noise ratio to optimize the performance of the multi-span optical fiber network.

(24) FIG. 3 illustrates a flowchart of a method 20 for optimizing performance of a multi-span optical fiber network according to a first embodiment of the invention.

(25) In particular, FIG. 3 shows a method 20 for optimizing performance of a multi-span optical fiber network, wherein each span has an associated optical transmission fiber connected to an associated optical amplifier, wherein gain and output power of the associated optical amplifier are respectively controlled independently, and wherein an amplifier noise figure respectively depends on the gain of the associated optical amplifier, wherein each associated optical amplifier is further connected to launch optical signals into a remainder of a corresponding optical transmission line. The method 20 comprises the steps of, for each span, computing the amplifier noise figure and computing non-linear noise generated in the span based on information about the span 21 and using the computed amplifier noise figure and the computed non-linear noise to compute an optimum launch power 22, and, optimizing performance of the multi-span optical fiber network based on the computed optimum launch powers of all spans.

(26) Therein, that gain and output power of the associated optical amplifier are respectively controlled independently, wherein an amplifier noise figure respectively depends on the gain of the associated optical amplifier, means that the associated optical amplifier is an optical associated amplifier with independent gain and output power controls and amplifier noise figure dependence on amplifier gain. Therein, for example the control of the output power can be integrated in the optical amplifier but can also be established independently of the optical amplifier. Further, that the parameters and, in particular, that the amplifier noise figure and a non-linear noise generated in each span are computed means that these parameters, respectively information characterizing the parameters are derived respectively calculated by methods of functional analysis and numerical mathematics.

(27) According to the embodiment of FIG. 3, the information about the span includes a span length, information about the associated transmission fiber, information about an optical amplifier associated with a previous span, a symbol rate of a corresponding transceiver and a frequency spacing between channels transmitted on the previous span.

(28) In particular, according to the embodiment of FIG. 3, the information about the span includes the following variables:

(29) amplifier gain respectively the amplifier gain dependence on signal power G.sub.i (dB), amplifier noise figure NF.sub.i (dB), fiber span loss in the ith-span Loss.sub.i (dB), channel power into the span optical power P.sub.i (dBm), the max output power level respectively the signal max power per channel P.sub.max_per_ch,i and ASE noise power P.sub.ase,i (dBm) (scaled to 0.1 nm/12.5 GHz bandwidth).

(30) Therein, the spans and the optical amplifier devices are indexed by the index i, with N representing the total number of spans of optical fiber.

(31) The ASE noise power can be determined based on the standard equation
P.sub.ase,i (dBm)=G.sub.i (dB)+NF.sub.i (dB)−57.9  (1).

(32) Further, the max output power level depends on the amplifier type.

(33) According to the embodiment of FIG. 3, further linear equivalents of the information about the span are used to compute the amplifier noise figure. In particular, in addition to the above-stated variables in decibel units, their linear counterparts can be defined as
G.sub.i=span amp gain (normalized linear units)=10.sup.0.1*G.sup.i .sup.(dB)  (2)
Loss.sub.i=span loss (normalized linear units)=10.sup.−0.1*Loss.sup.i .sup.(dB)  (3)
NF.sub.i=span amp noise figure (normalized linear units)=10.sup.0.1*NF.sup.i .sup.(dB)  (4)
P.sub.i=signal power (linear units W)=10.sup.0.1*P.sup.i .sup.(dBm)/1000  (5)
P.sub.max_per_ch,i=signal power (linear units W)=10.sup.0.1*P.sup.max_per_ch,i .sup.(dBm)/1000  (6)
P.sub.ase,i=ASE noise power(linear units W)=10.sup.0.1*P.sup.ase,i .sup.(dBm)/1000=G.sub.iNF.sub.i10.sup.−8.79  (7)

(34) The amplifier gain dependence on signal power can be given in both dB- and linear units:

(35) $\begin{array}{cc}{G}_i\left(\mathrm{dB}\right)=P_{\mathrm{max\_per}\mathrm{\_ch},i}\left(\mathrm{dBm}\right)-P_{i_{\mathrm{out}}}\left(\mathrm{dBm}\right)=P_{\mathrm{max\_per}\mathrm{\_ch},i}\left(\mathrm{dBm}\right)-\left(P_i\left(\mathrm{dBm}\right)-{\mathrm{Loss}}_i\left(\mathrm{dB}\right)\right)& \left(8a\right)\\ G_i=\frac{P_{\mathrm{max\_per}\mathrm{\_ch},i}}{P_{i}Los{s}_i}& \left(8b\right)\end{array}$

(36) In formulas (1) and (7), the factor (G.sub.i−1) was replaced by G.sub.i for simplicity. Further, the factor 10.sup.−8.79 was derived from the standard expression composed of physical constants
−8.79=LOG 10(h*ν*12.5E9 Hz),

(37) wherein ν=193.8 THz (1546.9 nm) is the central wavelength in C-band, h is planck's constant, and wherein E9 stands for 10.sup.9.

(38) Further, the noise figure for usual amplifiers depends on the gain, wherein a 3rd order polynomial gain expression can be used for the dependency, wherein the polynomial coefficients are fitted for each amplifier type separately. In particular, the polynomial coefficients are obtained in several steps of amplifier measurement characterization, wherein first the noise figure is characterized at fixed amplifier gain and tilt over an amplifier bandwidth over multiple modules. Then, for each module, the worst respectively maximum value of the noise figure is identified at some wavelength and the worst values are averaged over all characterized modules and result in a single worst value at fixed gain and tilt. Thereafter, the process is repeated at various gain values wherein characterization data of a resulting plot of noise figure versus gain is fitted with a cubic polynomial with specific coefficients, which depend on the amplifier type. In particular, the noise figure can be defined as follows:
NF (dB)=A.sub.0+A.sub.1G (dB)+A.sub.2G (dB).sup.2+A.sub.3G (dB).sup.3  (9a)
NF(G)=10.sup.0.1*(A.sup.0.sup.+A.sup.1.sup.10*LOG 10(G)+A.sup.2.sup.(10*LOG 10(G)).sup.2.sup.+A.sup.3.sup.(10*LOG 10(G)).sup.3.sup.)  (9b)

(39) Therein, the optimum launch power is then obtained by taking the first derivative of the inverse generalized optical signal-to-noise ratio with respect to the signal power P.sub.i and equating the result to zero, wherein the spans and the optical amplifier devices are indexed by the index i, with N representing the total number of spans of optical fiber.

(40) $\begin{array}{cc}\frac{1}{{\mathrm{GOSNR}}_i}=\frac{1}{{\mathrm{OSNR}}_i}+{\mathrm{VAR}}_{{\mathrm{NLI}}_i}=\frac{P_{\mathrm{ase},i}}{P_{\mathrm{max\_per}\mathrm{\_ch},i}}+{\eta }_i{P}_i^2& \left(10\right)\end{array}$

(41) In formula (11), GOSNR.sub.i, OSNR.sub.i, and the normalized nonlinear variance VAR.sub.NLI were respectively defined after the i-th optical amplifier and before the built-in optical attenuator.

(42) Further, the expression VAR.sub.NL.sub.i=η.sub.iP.sub.i.sup.2 for the normalized variance can be obtained by defining the nonlinear noise power at the ith-span before the optical amplifier with nonlinear efficiency η.sub.l being defined by the standard equation

(43) $\begin{array}{cc}{P}_{{\mathrm{NLI}}_i}={\eta }_i{P}_i^{3}Los{s}_i,\mathrm{with}& \left(11\right)\end{array}$$\begin{array}{cc}{\eta }_i={B_n\left(\frac{2.}{3.}\right)}^3\frac{{\gamma }^2\left(1/R_s^3\right)L_{\mathrm{eff}}^2}{\pi .Math.{\beta }_2.Math.L_{\mathrm{eff},a}}a\sin h\left(\frac{{\pi }^2}{2}.Math.{\beta }_2.Math.L_{\mathrm{eff},a}{R}_s^2{N}_{\mathrm{ch}}^{2\frac{R_S}{\Delta f}}\right),& \left(12\right)\end{array}$

(44) wherein the nonlinear efficiency is scaled to the bandwidth B.sub.n=12.5 GHz, R.sub.s is the modulated signal symbol rate, N.sub.ch is the number of channels, Δf is the channel slot, L.sub.eff is the effective loss length, L.sub.eff,a, is the asymptotic effective loss length, β.sub.2 is the fiber group-velocity dispersion parameter, and wherein γ is the fiber nonlinear coefficient.

(45) The result of formula (11) is then multiplied by gain G.sub.i and divided by the signal max power per channel P.sub.max_per_ch,i.

(46) ${\mathrm{VAR}}_{{\mathrm{NLI}}_i}={\eta }_i{P}_i^{3}Los{s}_i\frac{G_i}{P_{\mathrm{max\_per}\mathrm{\_ch},i}}={\eta }_i{P}_i^2,$

(47) wherein, as defined in formula (8b),

(48) $G_i=\frac{P_{\mathrm{max\_per}\mathrm{\_ch},i}}{P_{i}Los{s}_i}.$

(49) Similarly, the expression in

(50) $\frac{P_{\mathrm{ase},i}}{P_{\mathrm{max\_per}\mathrm{\_ch},i}}$
formula (9) can be transformed by

(51) $\frac{P_{\mathrm{ase},i}}{P_{\mathrm{max\_per}\mathrm{\_ch},i}}=\frac{P_{\mathrm{ase},i}/G_i}{P_{\mathrm{max\_per}\mathrm{\_ch},i}/G_i}=\frac{P_{\mathrm{ase},i}/G_i}{P_{\mathrm{i\_ou}t}}=\frac{P_{\mathrm{ase},i}}{P_{i}Los{s}_i{G}_i}.$

(52) Based on these simplifications, formula (9) can be transformed in

(53) $\begin{array}{cc}\frac{1}{GOSN{R}_i}=\frac{P_{\mathrm{ase},i}}{P_{i}Los{s}_i{G}_i}+{\eta }_i{P}_i^2=\frac{N{F}_{i}10^{-8.79}}{P_{i}Los{s}_i}+{\eta }_i{P}_i^2.& \left(13\right)\end{array}$

(54) Taking the first derivative of formula (13) with respect to the signal power P.sub.i and equating the result to zero then results in

(55) $\begin{array}{cc}\frac{d}{dP}\left(\frac{1}{\mathrm{GOSNR}}\right)=\frac{\frac{dNF}{\mathrm{dP}}10^{-8.79}}{P\mathrm{Loss}}-\frac{NF10^{-8.79}}{P^2\mathrm{Loss}}+2\eta P=0,& \left(14a\right)\end{array}$

(56) wherein formula (14a) can be simplified to

(57) 0$\begin{array}{cc}2\eta P^3\mathrm{Loss}-\mathrm{NF1}{0}^{-8.79}=RHS=-10^{-8.79}\frac{\mathrm{dNF}}{\mathrm{dP}}P.& \left(14b\right)\end{array}$

(58) In equations (14a) and (14b), the span index i has been omitted for notification simplicity.

(59) Further, NF is a nested function of the signal power. Therein, its derivative with respect to the signal power is a complex function, wherein

(60) $$\begin{gathered} \begin{array}{cc}\frac{\mathrm{dNF}}{\mathrm{dP}}=\frac{\mathrm{dNF}}{\mathrm{dG}}\frac{\mathrm{dG}}{\mathrm{dP}}, \\ \mathrm{with}& \left(15\right)\end{array} \end{gathered}$$$\begin{array}{cc}\frac{d{G}_i}{d{P}_i}=-\frac{G_i}{P_i}=\frac{P_{\mathrm{max\_per}\mathrm{\_ch},i}}{P_i^{2}Los{s}_i}\mathrm{and}& \left(16\right)\end{array}$$\begin{array}{cc}\frac{\mathrm{dNF}}{\mathrm{dG}}=\frac{NF\left(G\right)}{G}\frac{\mathrm{dNF}\left(\mathrm{dB}\right)}{\mathrm{dG}\left(\mathrm{dB}\right)}=\frac{NF\left(G\right)}{G}\left(A_1+2A_{2}10\mathrm{LOG}10\left(G\right)+3{A_3\left(10\mathrm{LOG}10\left(G\right)\right)}^2\right).& \left(17\right)\end{array}$

(61) Combining formulas (15), (16) and (17) results in

(62) $\begin{array}{cc}\frac{dNF}{dP}=-\frac{NF\left(G\right)}{P}\frac{dNF\left(\mathrm{dB}\right)}{dG\left(\mathrm{dB}\right)}=-\frac{NF\left(G\right)}{P}\left(A_1+2A_{2}10\mathrm{LOG}10\left(G\right)+3{A_3\left(10\mathrm{LOG}10\left(G\right)\right)}^2\right).& \left(18\right)\end{array}$

(63) Combining formulas (14b) and (18) then results in the transcendental equation

(64) $\begin{array}{cc}\frac{2\eta P^3\mathrm{Loss}}{10^{-8.79}NF\left(G\right)}=\left(1+A_1+2A_{2}G\left(\mathrm{dB}\right)+3A_3{G\left(\mathrm{dB}\right)}^2\right).& \left(19\right)\end{array}$

(65) In formula (19), the span index i has been omitted for notification simplicity.

(66) By numerically solving the system of the two coupled equations (8b) and (19), optimal values for both the signal power P.sub.i and the related amplifier gain G.sub.i can be determined.

(67) Therein, full spectral loading is assumed. This assumption could, however, be removed as optimization could also be done for a subset of channels. Further, uniform signal power is assumed across the amplifier bandwidth.

(68) Further, the impact of the amplifier output tilt on the noise figure and its impact on channel optimization could be taken into account by replacing the variable gain G (dB) in formula (9a) with gain_caldB G.sub.cal,i, which depends on both the gain in decibel units and the tilt via the tilt dependence function TiltdB, which depends, among others, on the channel input signal power averaged over the channel plan.

(69) According to the embodiment of FIG. 3, after, for each span, the optimum launch power has been computed, the computed optimum launch power is used to calculate a maximum generalized optical signal-to-noise ratio of the span in step 23.

(70) To calculate the maximum generalized optical signal-to-noise ratio, the optimal values P.sub.opt and G.sub.opt, which have been derived by numerically solving formulas (8b) and (19), and the corresponding value of the noise figure NF.sub.i can be used to compute the following formulas:

(71) $\begin{array}{cc}\mathrm{Span}{\mathrm{OSNR}}_i{O\mathrm{SNR}}_i=\frac{P_{\mathrm{max\_per}\mathrm{\_ch},i}}{P_{ase,i}}=\frac{P_{\mathrm{max\_per}\mathrm{\_ch},i}}{G_{i}N{F}_{i}10^{-8.79}}=\frac{P_i{\mathrm{Loss}}_i}{N{F}_{i}10^{-8.79}}& \left(20\right)\end{array}$$$\begin{gathered} \begin{array}{cc}\mathrm{Span}\mathrm{MAX}{\mathrm{GOSNR}}_i \\ \frac{1}{{\mathrm{MAXGOSNR}}_i}=\frac{1}{{\mathrm{OSNR}}_i}+{\eta }_i{P}_i^2=\frac{1}{{\mathrm{OSNR}}_i}\left(\frac{3}{2}-P_i\frac{dN{F}_i}{d{P}_i}/N{F}_i\right)& \left(21\right)\end{array} \end{gathered}$$

(72) Further, Link MAX GOSNR.sub.link can be calculated by summation over all spans

(73) $\begin{array}{cc}\frac{1}{{\mathrm{MAXGOSNR}}_{\mathrm{link}}}=\underset{i=1}{\overset{N_s}{.Math.}}\frac{1}{M\mathrm{AXGOSN}{R}_i}=\underset{i=1}{\overset{N_s}{.Math.}}\frac{1}{\mathrm{OSN}{R}_i}\left(\frac{3}{2}-P_i\frac{dN{F}_i}{d{P}_i}/N{F}_i\right)& \left(22\right)\end{array}$

(74) As common optical communication systems also have two booster amplifiers that are responsible for loss compensation in terminal equipment and loss compensation in reconfigurable optical add-drop multiplexers, the values of the link optical signal-to-noise ratio and generalized optical signal-to-noise ratio can be affected, wherein this impact can be accounted for when computing the maximum generalized optical signal-to-noise ratio of the corresponding transmission line by adding a sum over all booster amplifiers

(75) $\frac{1}{{\mathrm{MAXGOSNR}}_{\mathrm{link}}}=>\frac{1}{{\mathrm{MAXGOSNR}}_{\mathrm{link}}}+\underset{k=1}{\overset{N_{b\mathrm{oosters}}}{.Math.}}\frac{1}{{\mathrm{OSNR}}_k},$

(76) wherein N.sub.boosters is the number of boosters in the optical communication system.

(77) The maximum generalized optical signal-to-noise ratios of all spans, respectively the maximum generalized optical signal-to-noise ratio of the corresponding transmission line, respectively the maximum of the signal performance metric can then be used in step 24 to optimize the performance of the multi-span optical fiber network. Therein, the maximum generalized optical signal-to-noise ratio results in the optimization of signal primary measurable characteristics, as the maximization of the signal-to-noise ratio and the parameter Q, as well as the minimization of the bit-error rate BER.

REFERENCE SIGNS

(78) 1 section 2 ingress node 3 egress node 4 span 5 amplifier with independent gain and output power control 6 amplifier with variable gain 7 variable optical attenuator 10 system 11 network control device 12 computing means 13 optimizing means 14 controlling means 15 memory 16 first determining means 17 second determining means 20 method 21 method step 22 method step 23 method step 24 method step