Method and apparatus for estimating the quality of an optical signal - Patents.com

Abstract

The method relating to the present invention, in which the effects of crosstalk are accurately estimated, involves estimating the upper limit of a bit error rate in an optical transmission unit of an optical transmission system which uses coherent detection and in which an optical sending unit and an optical reception unit are connected to each other via an optical transmission unit using a plurality of spatial resources. Said method includes the processes of: (A) calculating the amplitude of each crosstalk for different spatial resources in the optical transmission unit on the basis of a result of measuring optical power in the optical sending unit and the result of measuring optical power in the optical reception unit; (B) calculating the variance of additive white Gaussian noise in the optical transmission system from a signal-to-noise power ratio or an optical signal-to-noise power ratio obtained on the basis of an electrical signal after coherent demodulation and photoelectric conversion; and (C) varying the value of an independent variable in a formula for the bit error rate, which is expressed by the amplitude of each crosstalk, the variance of additive white Gaussian noise, and an independent variable different from the time axis, to search for the minimum value of said formula as the upper limit of the bit error rate.

Description

[Technical field]

[0001] The present invention relates to a technique for estimating the effect of leakage light (that is, crosstalk) that occurs in an optical transmission line including an optical switch. [Background technology]

[0002] Applications such as cloud computing and big data analysis, which have become more common in recent years, have contributed greatly to the development of data centers. According to a survey, the IP traffic in data centers worldwide is growing at a rate of more than 25% per year, and this trend is expected to continue in the future. On the other hand, since more than 75% of IP traffic in data centers is processed within the data center, there is an urgent need to expand the scale of networks in data centers and to reduce power consumption and increase bandwidth. Currently, large-scale networks are built within data centers by connecting multiple broadband electrical switches with terabit-class throughput. However, as Moore's Law draws to an end, the limits of miniaturization of electrical switches are beginning to be seen, making it difficult to achieve lower power consumption and wider bandwidth than before.

[0003] Due to the nature of circuit switching, optical switches are not suitable for flexible processing like packet switching performed by electrical switches, but they are very good in terms of energy efficiency, calculated as the ratio of power consumption to bandwidth. On the other hand, the performance of an optical switch is greatly affected by leakage light (i.e., crosstalk) between optical circuits, making it difficult to estimate and specify its maximum throughput and scale. Non-Patent Document 1 reports a study in which one interference signal is added to the main signal and the effects of the crosstalk are compared through experiments and numerical simulations. Similar issues are also seen as problems in optical transmission systems that use spatial multiplexing, and Patent Document 1 proposes a method of performance estimation that takes into account the variation in crosstalk.

[0004] However, most of the existing technologies, including those in Non-Patent Document 1 and Patent Document 1, use methods that consider the amplitude fluctuation of the interference signal to be a normal distribution (i.e., Gaussian approximation), and overestimate the degradation of signal quality due to crosstalk. The impact of overestimated crosstalk degradation requires extra margins in the design of optical transmission systems, which becomes an obstacle when maximizing system performance in terms of throughput, transmission distance, and switch scale. In addition, the conventional technologies in Non-Patent Document 1 and Patent Document 1 are targeted at optical transmission systems for one or an averaged one interference component, and cannot accurately analyze interactions occurring between optical interference of multiple signals. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] International Publication WO2013 / 0945678A1 [Patent Document 2] Japanese Patent No. 6400119 [Non-patent literature]

[0006] [Non-Patent Document 1] PJ Winzer, AH Gnauck, A. Konczykowska, F. Jorge, and J.-Y. Dupuy, "Penalties from In-Band Crosstalk for Advanced Optical Modulation Formats," Proc. European Conference and Exhibition on Optical Communication (ECOC), Paper Tu.5.B.7, 2011 [Non-Patent Document 2] S. Savory, "Digital coherent optical receivers: Algorithms and subsystems," IEEE Journal of Selected Topics in Quantum Electronics, vol.16, no.5, pp.1164-1179, 2010 [Non-Patent Document 3] K. Kikuchi, "Fundamentals of Coherent Optical Fiber Communications," IEEE / OSA Journal of Lightwave Technology, vol.34, no.1. pp.157-179, 2016 [Non-Patent Document 4] ITU-T Recommendation G.975.1, "Forward error correction for high bit-rate DWDM submarine systems" [Non-Patent Document 5] C. Clos, "A study of non-blocking switching networks," The Bell System Technical Journal, vol. 32, no. 2, pp. 406-424, 1953. Summary of the Invention [Problem to be solved by the invention]

[0007] Therefore, an object of the present invention, according to one aspect, is to provide a technique for accurately estimating the influence of crosstalk. [Means for solving the problem]

[0008] The estimation method according to the present invention is an estimation method for estimating an upper limit value of a bit error rate in an optical transmission section of an optical transmission system in which an optical transmitting section and an optical receiving section are connected to each other via an optical transmission section that utilizes a plurality of spatial resources and that uses coherent detection, and includes the steps of: (A) calculating the amplitude of each crosstalk for different spatial resources in the optical transmission section based on the measurement results of the optical power in the optical transmitting section and the measurement results of the optical power in the optical receiving section; (B) calculating the variance of additive white Gaussian noise in the optical transmission system from the signal-to-noise power ratio or the optical signal-to-noise power ratio obtained based on the electrical signal after coherent detection and photoelectric conversion; and (C) changing the value of the independent variable in a formula for the bit error rate represented by the amplitude of each crosstalk, the variance of the additive white Gaussian noise, and an independent variable different from the time axis, and searching for the minimum value of the formula as the upper limit value of the bit error rate. [Brief description of the drawings]

[0009] [Figure 1] FIG. 1 illustrates an example of a configuration of an optical transmission system according to a first embodiment. [Diagram 2] FIG. 2 is a diagram illustrating an example of a configuration of the optical transmitter according to the first embodiment. [Diagram 3] FIG. 3 is a diagram illustrating an example of a configuration of an optical receiver according to the first embodiment. [Figure 4] FIG. 4 is a diagram illustrating an example of a configuration of a photoelectric conversion unit according to the first embodiment. [Diagram 5] FIG. 5 is a diagram for explaining the effect of the embodiment. [Figure 6] FIG. 6 is a diagram showing crosstalk characteristics in the prior art. [Figure 7] FIG. 7 is a diagram illustrating crosstalk characteristics according to the embodiment. [Figure 8A] FIG. 8A is a diagram showing the process contents of the control method according to the first embodiment. [Figure 8B] FIG. 8B is a diagram illustrating an example of the relationship between the independent variable s and the BER. [Figure 8C] FIG. 8C is a diagram illustrating an example of a process of searching for a minimum value. [Figure 9] FIG. 9 is a diagram illustrating processing contents in the optical transmission system according to the first embodiment. [Figure 10] FIG. 10 is a diagram illustrating a configuration example of an optical transmission unit according to the second embodiment. [Figure 11] FIG. 11 is a diagram illustrating processing contents in the optical transmission system according to the second embodiment. [Figure 12] FIG. 12 is a diagram illustrating an example of a configuration of an optical transmission unit according to the third embodiment. [Figure 13] FIG. 13 is a diagram showing the process contents according to the fourth embodiment. [Figure 14] FIG. 14 is a diagram illustrating an example of a functional configuration of a computer when the control unit is implemented by a computer. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0010] [Embodiment 1] First, an example of an optical transmission system according to the present embodiment will be described. FIG. 1 shows an outline of the optical transmission system according to the present embodiment. The optical transmission system includes an optical transmitter 1, an input adjustment unit 2, an optical transmission unit 3, an output adjustment unit 4, an optical receiver 5, and a control unit 6. The optical transmitter 1 includes, for example, N optical transmitters (1-1 to 1-N). Similarly, the optical receiver 5 includes, for example, N optical receivers (5-1 to 5-N). The optical transmission unit 3 is premised on transmitting a plurality of optical signals using spatial resources, and examples thereof include an optical switch and a spatial multiplexing fiber such as a multi-core or multi-mode fiber. A single carrier or wavelength division multiplexing optical signal generated by the optical transmitter 1 is input to an input adjustment unit 2 for converting the signal into an input format suitable for the optical transmission unit 3. Examples of the input adjustment unit 2 include an input polarization adjustment function of a polarization-dependent optical switch and a conversion function for connecting a single mode fiber to a specific core or mode of a spatial multiplexing fiber.

[0011] The optical transmission unit 3 transmits optical signals assigned to each spatial resource, but even between spatial resources that are ideally independent, in reality, leakage light occurs, which becomes an interference component (i.e., crosstalk). The optical signal output from the optical transmission unit 3 is input to the output adjustment unit 4, which performs the reverse operation of that performed by the input adjustment unit 2. For example, it has an input polarization adjustment function for a polarization-dependent optical receiver, and a conversion function for connecting a specific core or mode of a spatial multiplexing fiber to a single mode fiber. The optical receiver 5 performs differential or coherent detection of the input optical signal.

[0012] The control unit 6 has a role of controlling the combination of each function included in the optical transmitter 1, the optical transmission unit 3, and the optical receiver 5, and includes a first control unit 6-1 for the optical transmitter 1, a second control unit 6-2 for the optical transmission line 3, a third control unit 6-3 for the optical receiver 5, and an optical interference estimation unit 6-4. The optical interference estimation unit 6-4 cooperates with the first control unit 6-1, the second control unit 6-2, and the third control unit 6-3 depending on conditions, and analyzes and estimates the influence of quality degradation caused by interference components generated in the optical transmission unit 3.

[0013] FIG. 2 is a diagram showing the configuration of the optical transmitter 1-1 included in the optical transmitter 1. The other optical transmitters 1-2 to 1-N have the same configuration. The optical transmitter 1-1 has a modulation format control unit 1-1-1, optical signal generation units 1-11 to 1-1m, a multiplexing unit 1-1-2, and a power detection unit 1-1-3. Note that m represents the number of wavelengths multiplexed. Each optical signal generation unit generates an optical signal based on the signal format set by the modulation format control unit 1-1-1. For example, the optical signal generation unit 1-11 has a light source unit 1-111, an optical modulation unit 1-112, and an electric signal generation unit 1-113.

[0014] The continuous light of optical wavelength λ1 output from the light source unit 1-111 is input to the optical modulation unit 1-112, which modulates the input continuous light using an electrical signal received from the electrical signal generation unit 1-113. The same process is performed in the optical signal generation units 1-12 to 1-1m, and the generated optical signals of optical wavelengths λ1 to λm are input to the multiplexing unit 1-1-2. The multiplexing unit 1-1-2 generates one optical wavelength division multiplexing (WDM) signal from the m input optical signals. When m is 1, the signal becomes a single carrier signal, and the multiplexing unit 1-1-2 can be omitted depending on the conditions. If necessary, the optical power of the single carrier or WDM signal output from the multiplexing unit 1-1-2 is measured in the power detection unit 1-1-3.

[0015] FIG. 3 is a diagram showing the configuration of the optical receiver 5-1 included in the optical receiver 5. The other optical receivers 5-2 to 5-N have a similar configuration. The optical receiver 5-1 has a power detection unit 5-12, a local light source 5-13, an opto-electrical conversion unit 5-14, an electrical signal analysis unit 5-15, a received signal adjustment unit 5-16, and a demodulation unit 5-17. When input to the optical receiver, the power detection unit 5-12 measures the optical power from the received optical signal as necessary. Both the received optical signal and the local light from the local light source 5-13 are input to the opto-electrical conversion unit 5-14, which then converts the received optical signal and the local light into an optical beam splitter signal. to The components are converted into electrical signals, which may be analog or digital.

[0016] The electrical signal analyzer 5-15 measures the signal power and signal-to-noise ratio (SNR) from the detected electrical signal as necessary. For example, the signal power is calculated from the mean square value of the electrical signal, and the SNR or optical signal-to-noise ratio (OSNR) is calculated from the detected electrical signal. The SNR is generally calculated in the upstream of the received signal conditioner 5-16 by taking the ratio of the signal power to the noise level (spectrum floor value) from the spectrum of the detected electrical signal. Since the SNR is defined as the signal-to-noise ratio per 1 Hz band, it can be converted to the OSNR defined in the noise band per 12.5 GHz by multiplying it by an appropriate coefficient.

[0017] The detected electrical signal is input to the reception signal conditioning unit 5-16, which removes distortion components contained in the signal as necessary. Examples of processing by the reception signal conditioning unit 5-16 include clock recovery, frequency offset compensation, polarization separation, and phase noise removal, as shown in Non-Patent Documents 2 and 3. The demodulation unit 5-17 demodulates the electrical signal from which distortion has been removed by the reception signal conditioning unit 5-16, and the processing result is output to an external function or process (not shown) as necessary.

[0018] Next, a configuration example of the photoelectric conversion unit 5-14 assumed in deriving the following formulas will be described with reference to FIG. 4. The photoelectric conversion unit 5-14 includes an optical 90-degree hybrid mixer 5-141, a photodetector 5-142, and a photodetector 5-143. An input optical signal E s The optical 90-degree hybrid mixer 5-141 outputs a composite (beat) component of the input light and the continuous light, which are out of phase with each other by 90 degrees, to the respective photodetectors 5-142 and 5-143. The photodetectors 5-142 and 5-143 convert the received beat light into an electrical signal I corresponding to the real part and imaginary part. r and I i Convert to.

[0019] [About the process of deriving the formula for calculating the bit error rate (BER)] The calculation in the optical interference estimation unit 6-4 is performed according to the formula obtained through the derivation process shown below. Here, the signal electric field E expressed by equation (1) s (t) and the local light E expressed by Eq. (2) L Consider the case where (t) and are input to the optical receiver 5. In this example, a single polarized signal or a single polarized component of a polarization multiplexed signal is the subject of the study.

number

number

[0020] When N interference components are added to a signal, the crosstalk-affected signal field E s,in (t) is expressed as follows:

number

[0021] Moreover, when the configuration example of the photoelectric conversion unit 5-14 is as shown in FIG. 4, the outputs of the optical 90-degree hybrid mixer 5-141 are as follows:

number

number

number

number

[0022] The loss of the coherent front end is L E , and the light receiving rate is Ra, then the equations (4) to (7) after photoelectric conversion are as follows:

number

number

number

number

[0023] Using equations (8) to (11), the output of the photoelectric conversion unit 5-14 corresponding to balanced optical detection is expressed by the following equations. Here, assuming an ideal coherent receiver, a=1, L E = 1, τ = 0, and t = t'.

number

number

[0024] Here, assuming an M-ary phase-modulated signal, A s (t)=1, θs (t)∈{π / M, 3π / M, 5π / M, ..., (2M-1) / M}. In addition, assuming that the received signal conditioning unit 5-16 performs waveform distortion equalization using ideal digital signal processing, ω s -ω L =0,θ L Let (t) = 0.

number

number

[0025] Here, θ s' (t) represents the phase rotation that occurs during waveform distortion compensation. The phase term of the crosstalk in the second term is the product of the frequency rotation and the random walk phase fluctuation, so it can be considered to have a uniform distribution in the range [-π,π]. Therefore, if the amplitude of the i-th crosstalk component is y, its distribution can be expressed by the following equation.

number

[0026] In this way, the amplitude distribution of a certain crosstalk can be considered as a sine function (arc-sine function). Since multiple crosstalks affect each other in equations (14) and (15), equation (16) is expanded to N crosstalks. If each crosstalk is considered to be independent and uncorrelated, the characteristic function M XT (s) is expressed by the following equation.

number

[0027] Next, the BER is calculated using the characteristics of equation (17). The real and imaginary parts are considered independent, and the derivation represents the BER of either of the components. [Number] Here, D1, D2, E1, E2 (where D1 > D2, E1 < E2) are decision thresholds, p0 is the occurrence probability of bit 0, p1 is the occurrence probability of bit 1, and Pr[·] is the probability density function for the random variable Z.

[0028] Let the noise component be Z = X + Y, where X is the distribution p x (u) of the distortion due to crosstalk, and Y is the noise of other additive white Gaussian processes. Here, let Y ~ N(μ, σ 2 ), and let the amplitude of crosstalk be u. Also, σ 2 is the variance of the additive white Gaussian noise. Since X and Y are independent, Equation (18) can be transformed as follows. [Number]

[0029] To solve Equation (19), first consider the following equation related to the first term. [Number] Introduce an arbitrary variable s and use the non-negativity of the squared difference (z - sσ 2 ) 2 ≥ 0 to derive the following relational expression. [Number]

[0030] By using the relationship of Equation (21), the upper limit of Equation (20) can be described by the following equation. [Number] The integral term of Equation (22) corresponds to the definition formula of the characteristic function using the transformation variable s. To rewrite Equation (22), similar to Equation (17), let the characteristic function of the interference component for the transmitted bit b ∈ {0, 1} be the following equation. [Number]

[0031] By substituting equation (23) into equation (22), the probability that the received symbol exceeds the threshold when bit 0 is transmitted is finally given by

number

number

[0032] If p0 = p1 = 0.5, the final upper limit of the BER is as follows:

number

[0033] In this example, four decision thresholds are assumed, but depending on the modulation method, there may be more than four. Below, we take binary phase shift keying (BPSK) and quadrature phase shift keying (QPSK) as examples to derive the BER in an environment where N interference components exist. If additive white Gaussian noise with the same variance is added to each symbol, the optimal decision threshold conditions are D1 = ∞, D2 = 0, E1 = 0, and E2 = ∞. Therefore, equation (26) can be transformed into the following equation.

number

[0034] The characteristic function of the interference component in equation (27) is the expected value of the combination of N interference components, and is expressed by the following equation.

number

number

[0035] In the derivation, it is assumed that bit 0 is assigned to symbol -1, and bit 1 is assigned to symbol 1. Up until now, the BER of the imaginary part and the real part have been considered independently. In the case of BPSK, it is sufficient to consider only one axis, so the noise power is relatively half the signal power. The BER of QPSK is treated independently for the real part and the imaginary part. Therefore, the BER of each is expressed by the following formula.

number

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[0036] On the other hand, when the Gaussian approximation used in the conventional technology is used, the BER is expressed by the following equations.

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[0037] In this embodiment, the crosstalk is mapped to an independent variable axis s different from the time axis t, and the square of the difference between the product of the independent variable and the variance of the additive white Gaussian noise and the total noise is non-negativity (z-sσ 2 ) 2 ≧0), and calculates an accurate upper limit of the BER using the product of the sine wave distribution (also called the inverse sine distribution) of the sum of the crosstalk amplitudes (e.g., equations (23), (28), and (29)). In contrast, the prior art simply approximates the crosstalk to an appropriate Gaussian distribution to calculate the BER.

[0038] In this embodiment, the linear mapping of an arbitrary function f(v) expressed by a certain variable v to an independent variable s is defined by the following equation.

number

[0039] [Advantages of this embodiment] FIG. 5 shows the results of plotting the relative BER against crosstalk (here, the root mean square of the leakage light amplitude) [dB] for the conventional technique, the present embodiment, and the analysis. -9 This means the BER obtained with the SNR required to obtain , and does not directly correspond to the BER calculated by equations (28) to (33). For convenience of explanation, the SNR caused by additive white noise is fixed at a specific value under all conditions in FIG. 5. Also, as can be seen from equations (28) to (31), the influence of degradation caused by interference components is the same for BPSK and QPSK, so only QPSK is targeted in FIG. 5. It can be confirmed that the results of this embodiment and the analysis are very consistent. On the other hand, the conventional technology shows a higher BER than the analysis in areas where the number of crosstalks is small or the amount of crosstalk is large.

[0040] Figure 6 shows the results of calculating the probability distribution of crosstalk amplitude when the conventional technology is applied. In Figure 6, the crosstalk number N is changed from 1 to 4, with the dotted line representing the conventional technology and the circles representing the analysis results. For example, when focusing on the result for N=1, the conventional technology and the analysis results show a tendency to differ greatly. The crosstalk amplitude has the properties of a sine function (also called an inverse sine function) shown in equation (16), whereas the conventional technology approximates this with a Gaussian function, and this influence causes deviation from the analysis. In other words, this means that although the influence of the sine function distribution on the BER is actually small, excessive degradation is estimated by regarding it as a Gaussian distribution.

[0041] FIG. 7 shows the result of calculating the probability distribution for the crosstalk amplitude when this embodiment is applied. As in FIG. 6, in FIG. 7, the crosstalk number N is changed from 1 to 4, the dashed line represents this embodiment, and the circle represents the analysis result. For any crosstalk number, the two show the same probability distribution. This suggests that the formula (28) and formula (29) calculated in this embodiment can accurately express the actual distribution. However, even in the conventional technology, as the crosstalk number N increases, the probability distribution approaches a Gaussian shape. In other words, if a certain degree of penalty is allowed, there are cases where the conventional technology can be applied when N is 4 or more. This tendency can also be confirmed in FIG. 5, and it can be confirmed that the difference between the conventional technology and this embodiment is relatively small when N=4.

[0042] [Function of the optical interference estimation unit 6-4] The optical interference estimation unit 6-4 estimates the influence of crosstalk from the derived formulas (28) to (31) etc. The details of the function of the optical interference estimation unit 6-4 will be described below. When the SNR and each crosstalk amplitude are known, an accurate BER can be estimated from formulas (28) to (31) etc. Note that the average value of the crosstalk amplitude may be obtained, and in that case, each crosstalk amplitude is treated as being the same value.

[0043] In the above example, the SNR and each crosstalk amplitude are assumed to be known, but if they are unknown, the measured results may be applied. For example, in an optical transmission system in which the first control unit 6-1, the second control unit 6-2, and the third control unit 6-3 can operate in cooperation with each other, the absolute value of the crosstalk amplitude is calculated from the square root of the difference between the optical power measured by the power detection unit 1-1-3 and the optical power measured by the power detection unit 5-12 for each path of the transmission line 3.

[0044] The SNR or OSNR may be calculated from the output of the electrical signal analyzer 5-15 using the method disclosed in Patent Document 2 or the like. 2However, if the electrical signal observed by the received signal conditioning unit 5-16 is normalized so that the absolute value of its amplitude is 1, the variance of the additive white Gaussian noise σ 2 is the inverse of the SNR. Based on this premise, we can calculate the variance of additive white Gaussian noise σ 2 The following description will be given on the assumption that these can be easily calculated. By applying these measured values ​​to equations (28) to (31), the same results as those shown in Fig. 5 can be obtained. Conversely, when the BER is known, the SNR and each crosstalk amplitude or its average value can be calculated back from equations (28) to (31) etc. Similarly, in this case, when either the crosstalk amplitude or the SNR is unknown, it is sufficient to measure either one of them using the above-mentioned method.

[0045] In this way, according to the present embodiment, the bit error rate, the variance of additive white Gaussian noise σ 2 , the quality of the signal, represented by the SNR or OSNR, or the respective crosstalk amplitude or its average value, can be accurately indicated.

[0046] Moreover, the processing result of the optical interference estimation unit 6-4 may be fed back to the optical transmitter 1 to control the efficient operation of the optical transmission system. When the SNR and each crosstalk amplitude or its average value are known, the BER can be estimated in advance in the optical interference estimation unit 6-4 before transmitting the optical signal. When the BER calculated by a certain modulation method exceeds a reference value, the condition can be changed to increase the transmission capacity while keeping the BER below the reference value. As an example, assume that the coding rate and coding method of the error correction code and the modulation multilevel degree of the symbol can be set. If the BER of the PSK signal is calculated from equations (23) and (26), or equations (28), (29), and (31) at a fixed coding rate, the calculation result exceeds the reference value. In this case, a PSK with higher resistance to crosstalk degradation is selected so that the BER is below the reference value. For example, as can be seen from equations (28) to (31), BPSK using binary symbols is twice as resistant to distortion and noise as QPSK using 4-value symbols. That is, control is performed so as to change from QPSK to BPSK.

[0047] The same process can be applied to the selection of the coding rate and coding method of the error correcting code. When a coding rate and coding method of a certain error correcting code are selected and the BER of the PSK signal is calculated for a fixed modulation level using equations (23) and (26), or equations (28), (29), and (31), the calculation result exceeds the reference value. In such a case, a coding rate and / or coding method with higher error correction accuracy is selected and set so that the BER is equal to or less than the reference value.

[0048] In the above, a method of selecting one of the coding rate of the error correcting code, the coding method of the error correcting code, and the modulation multi-level degree of the symbol has been described, but a combination of these may also be selected.

[0049] FIG. 8A shows an example of this processing procedure. First, the optical interference estimation unit 6-4 selects the coding rate and coding method of the error correction code before transmitting a signal (step S1), and further selects the modulation multi-level of the symbol (step S3). The optical interference estimation unit 6-4 calculates the BER according to equations (23) and (26) or equations (28)-(31) (step S5). The calculation of the BER will be specifically explained later with reference to FIG. 8C. The optical interference estimation unit 6-4 judges whether the calculated BER is equal to or lower than a reference value (step S7). If the calculated BER is equal to or lower than the reference value, the optical interference estimation unit 6-4 notifies the modulation scheme control unit 1-1-1 of the selected coding rate and coding method and the modulation multi-level of the symbol via the first control unit 6-1, and the modulation scheme control unit 1-1-1 controls each optical signal generation unit to select the coding rate and coding method and the modulation multi-level of the symbol. 1-11 1 to 1-1m (step S13).

[0050] On the other hand, if the calculated BER exceeds the reference value, the optical interference estimation unit 6-4 reselects the modulation multi-level of the symbol (step S9). If a different modulation multi-level is selectable, it is selected. If a different modulation multi-level cannot be selected, the same one may be selected. The optical interference estimation unit 6-4 also reselects the coding rate and coding method of the error correction code (step S11). If a different coding rate or coding method or both can be selected, they are selected, and if not, the same one is selected. Then the process returns to step S5.

[0051] By performing such processing, it becomes possible to communicate with a combination of the error correction code coding rate and coding method and the symbol modulation multilevel degree that are below the BER standard value. For example, in the field of optical fiber communications, after error correction decoding, the BER=10 -15 According to Non-Patent Document 4, the standard value of BER is BER<2×10 -3 It is possible to change the order of steps S1 and S3 and the order of steps S9 and S11. The above process may be performed by the first control unit 6-1 or the method control unit 1-1-1, or may be shared among a plurality of components. Furthermore, if the BER does not become equal to or less than the reference value in any combination of the coding rate and coding method of the error correction code and the modulation multi-level degree of the symbol, there is a problem with the reference value itself, so an error may be generated.

[0052] In this way, the effect of degradation due to crosstalk can be accurately analyzed and estimated, and by using the accurately estimated BER to adopt an appropriate modulation method in the optical transmitter 1, excess margins can be reduced and the transmission capacity of the optical transmission system can be increased.

[0053] Next, the calculation of the BER in step S5 will be described. In many cases, the relationship between the BER and the independent variable s is a downward convex curve as shown in FIG. 8B. That is, in order to calculate the BER, the value of the expression in the right-hand brackets in Equation (26), Equation (30), or Equation (31) is calculated while changing the independent variable s, thereby searching for the minimum value. For example, the minimum value may be searched for in a brute-force manner in the search range of the independent variable s, or the minimum value may be searched for by a general optimization algorithm such as the steepest descent method. For example, as shown in FIG. 8C, the optical interference estimation unit 6-4 sets a value for the independent variable s according to a predetermined algorithm or rule (step S101). Then, the optical interference estimation unit 6-4 calculates the BER for the current value of the independent variable s according to the expression in the right-hand brackets in Equation (26), Equation (30), or Equation (31) (step S103). After that, the optical interference estimation unit 6-4 determines whether or not a processing termination condition is satisfied (step S105). This termination condition is, for example, an upper limit of the number of calculations, but may be another termination condition determined by the optimization algorithm. If the termination condition is not satisfied, the process returns to step S101. On the other hand, if the termination condition is satisfied, the optical interference estimation unit 6-4 selects the minimum value of the calculated BER values ​​as a solution (step S107).

[0054] In this way, by performing the process shown in FIG. 8C or a similar process, the value in the parentheses on the right-hand side of equation (26), (30), or (31) is minimized while varying the independent variable s, so that the desired upper limit of the BER can be estimated.

[0055] An example of processing performed in the optical transmission system according to the present embodiment will be described with reference to FIG. 9. First, the optical interference estimation unit 6-4 judges whether the amplitude or the average value of each crosstalk is unknown (step S31). If the amplitude or the average value of each crosstalk is unknown, it is estimated using the power of the optical transmitter 1 and the optical receiver 5. Specifically, the optical interference estimation unit 6-4 transmits a control signal to the optical transmitter 1 via the first control unit 6-1 and to the optical receiver 5 via the third control unit 6-3. The optical transmitter 1 that receives the control signal measures the transmission optical power (step S23). Also, the optical receiver 5 that receives the control signal measures the reception optical power (step S25). For example, the transmission optical power detection unit 1-1-3 of the optical transmitter 1 measures the power of the generated continuous light, single carrier, or WDM signal. Also, the reception optical power detection unit 5-12 of the optical receiver 5 measures the reception optical power.

[0056] Then, the optical interference estimation unit 6-4 receives the transmitted optical power value from the optical transmitter 1 and the received optical power value from the optical receiver 5, and calculates the amplitude or the average value of each crosstalk based on the difference between the transmitted optical power value and the received optical power value (step S27).Then, the process proceeds to step S29.

[0057] When the amplitude or average value of each crosstalk is known or after step S27, the optical interference estimation unit 6-4 estimates the SNR, OSNR, or variance σ of the additive white Gaussian noise. 2 is unknown (step S29). If the OSNR, etc. are unknown, the optical interference estimation unit 6-4 transmits a control signal to the optical receiver 5 via the third control unit 6-3. The optical receiver 5 that receives the control signal transmits the spectrum calculated by the electrical signal analysis unit 5-15 to the optical interference estimation unit 6-4, and the optical interference estimation unit 6-4 estimates the SNR or OSNR using, for example, the method disclosed in Non-Patent Document 4 (step S31), and further calculates the variance σ of the additive white Gaussian noise from the SNR or OSNR using the above-mentioned method. 2 is estimated (step S33).

[0058] Then, the optical interference estimation unit 6-4 calculates the BER using equations (23) and (26), or equations (28) to (31) (step S35). In this step, the process of FIG. 8C is performed. Note that parameters other than the crosstalk amplitude and OSNR are assumed to be known. For example, the average voltage value V of the received symbols is a fixed value or the average value of the values ​​measured for each symbol. Then, the process proceeds to step S35.

[0059] When the OSNR and the like are known or after step S33, the optical interference estimation unit 6-4 judges whether or not to control the optical transmitter 1 (step S37). If the optical transmitter 1 is not to be controlled, the process ends. On the other hand, if the optical transmitter 1 is to be controlled, at least one of the coding rate and coding method of the error correction code and the modulation multilevel degree of the symbol is selected so that the BER becomes equal to or less than the reference value, and a method control is executed to set the coding rate and coding method of the error correction code and the modulation multilevel degree of the symbol in the optical transmitter 1 (step S39). Then, the process ends.

[0060] In this way, unknown parameters are measured and estimated, and known parameters are used as they are, making it possible to accurately calculate the BER. Note that the order of steps S21 to S27 and steps S29 to S33 may be interchanged.

[0061] [Embodiment 2] In the optical transmission system of Fig. 1, the optical transmission unit 3 shown in Fig. 10 may be adopted. The optical transmission unit 3 according to this embodiment includes input optical power detection units 3-101 to 3-10k, optical power adjustment units 3-201 to 3-20k, an optical switch unit 3-301, and output optical power detection units 3-401 to 3-40k, and in some cases, the optical power adjustment units 3-201 to 3-20k, the optical switch unit 3-301, and the output optical power detection units 3-401 to 3-40k. 3-401 3-40k are repeated for L stages, where k represents the number of input ports or output ports of the optical switch unit 3-301. Note that k may be different for each stage.

[0062] First, consider the case where L is 1. When the SNR and each crosstalk amplitude or its average value are known, an accurate BER can be estimated from equations (23) and (26), or equations (28) to (31). When each crosstalk amplitude or its average value is unknown, the absolute value of the crosstalk amplitude is calculated from the square root of the difference between the optical power measured by the input optical power detectors 3-101 to 3-10k and the optical power measured by the output optical power detectors 3-401 to 3-40k for each path of the optical switch unit 3-301.

[0063] Next, consider the case where L is 2 or more. When the SNR after L stages and each crosstalk amplitude or its average value are known or can be estimated, the upper limit of the BER can be estimated from equations (23) and (26), or equations (28) to (31). When the crosstalk amplitude after L stages or its average value is unknown, the absolute value of the crosstalk amplitude is calculated from the square root of the difference between the optical power measured by the input optical power detectors 3-101 to 3-10k and the optical power measured by the output optical power detectors 3-401 to 3-40k after L stages. By applying this concept to a switch construction method such as Non-Patent Document 5, the upper limit of the BER can be estimated even for large-scale optical switches connected in multiple stages.

[0064] Also, the process described in Fig. 8A in the first embodiment may be performed. That is, communication can be performed with a combination of the coding rate and coding method of the error correction code and the modulation multilevel degree of the symbol that makes the estimated BER equal to or less than a reference value.

[0065] Moreover, an example of processing performed in the optical transmission system according to the present embodiment will be described with reference to FIG. The difference from the first embodiment is that step S51 is executed instead of step S23, and step S53 is executed instead of step S25.

[0066] Specifically, the optical interference estimation unit 6-4 transmits a control signal to the input optical power detection units 3-101 to 3-10k and output optical power detection units 3-401 to 3-40k of the optical transmission line unit 3 that perform power measurement via the second control unit 6-2. The input optical power detection units 3-101 to 3-10k of the optical transmission line unit 3 that receive the control signal measure the input optical power to the optical transmission line 3 (step S51). Also, the output optical power detection units 3-401 to 3-40k of the optical transmission line 3 that receive the control signal measure the output optical power from the optical transmission line 3 (step S53). The optical interference estimation unit 6-4 receives the measured input optical power value and output optical power value from the input optical power detection units 3-101 to 3-10k and the output optical power detection units 3-401 to 3-40k, and calculates the difference between the input and output power in the optical transmission line 3 to obtain each crosstalk amplitude or its average value.

[0067] Thus, according to this embodiment, even if a single-stage optical switch or a large-scale optical switch connected in multiple stages is used, the same effect as in the first embodiment can be obtained. That is, it becomes possible to calculate a highly accurate BER. Note that in this embodiment, the process of FIG. 9 may be performed.

[0068] [Embodiment 3] In the optical transmission system of Fig. 1, another optical transmission section 3 shown in Fig. 12 may be adopted. The optical transmission section 3 according to this embodiment includes a spatial multiplexing optical fiber section 3-111, a spatial adjustment section 3-211, an optical power adjustment section 3-311 3-31k, output optical power detection units 3-411 to 3-41k, and a spatial adjustment unit 3-511. This order and combination can be changed, and in some cases these are repeated L stages. k represents the number of input ports or output ports of the spatial multiplexing optical fiber unit 3-111. Examples of the spatial multiplexing optical fiber unit 3-111 include a multicore fiber having multiple cores and a multimode fiber that propagates multiple modes.

[0069] A single carrier or WDM signal is input to the spatial multiplexing optical fiber unit 3-111, and input to the spatial adjustment unit 3-211 through the spatial multiplexing optical fiber unit 3-111. The spatial adjustment unit 3-211 has a role of converting each spatial resource into a single-core mode fiber. The power of the light converted by the spatial adjustment unit 3-211 is adjusted by the optical power adjustment units 3-311 to 3-31k, and then the optical power is measured by the output optical power detection units 3-411 to 3-41k.

[0070] When L is 1, the spatial adjustment unit 3-511 transmits an optical signal to each optical receiver. When L is 2 or more, the spatial adjustment unit 3-511 converts the input light into a format (multi-core or multi-mode) that can be input to the next spatial multiplexing optical fiber, and performs the role of a conversion function for connecting from a single mode fiber to a specific core or mode of the spatial multiplexing fiber. When L is 2 or more and L is the maximum value, the spatial adjustment unit 3-511 transmits an optical signal to each optical receiver in the same way as when L is 1. Note that when L is 2 or more and L is the maximum value, the output optical power detection unit 3-411 The sub-units 3-41k and the spatial adjustment unit 3-511 may be disposed on the receiver side.

[0071] In this embodiment, the BER can be accurately estimated from equations (23) and (26), or equations (28) to (31), as in the second embodiment. When each crosstalk amplitude or its average value is unknown, the absolute value of the crosstalk amplitude is calculated from the square root of the difference between the optical power measured by the transmission optical power detector 1-1-3 and the optical power measured by the output optical power detectors 3-411 to 3-41k. Similarly, when the SNR or OSNR is unknown, the SNR or OSNR is estimated from the frequency waveform (spectrum) calculated by the electrical signal analyzer 5-15 by the method disclosed in Non-Patent Document 4 or the like. A series of processes according to this embodiment is also the same as in FIG. 11. As described above, this embodiment is applicable to a single-stage spatial multiplexing optical fiber or a multi-stage-connected spatial multiplexing optical fiber, and the same effects as those of the first embodiment can be obtained.

[0072] [Embodiment 4] In the first to third embodiments, the BER is calculated from equations (23) and (26), or equations (28) to (31). However, as shown in Figures 5 to 7, it can be confirmed that as the number of interferences N increases, the penalty and distribution error between the conventional technology and the embodiments decrease. Therefore, when the number of interferences N exceeds a preset value, the calculations equivalent to the conventional technology shown in equations (32) and (33) may be applied.

[0073] That is, the interference estimation unit 6-4 judges whether the number of interferences N is equal to or less than the reference value (FIG. 13: step S71). If the number of interferences N is equal to or less than the reference value, the interference estimation unit 6-4 calculates the BER according to equations (23) and (26) or equations (28) to (31) (step S73). In this step, the processing shown in FIG. 8C is performed. Then, the processing ends. On the other hand, if the number of interferences N exceeds the reference value, the interference estimation unit 6-4 calculates the BER according to equations (32) and (33) (step S75). Then, the processing ends.

[0074] In this way, when the number of interferences N exceeds the reference value, the calculation of special functions such as the zeroth-order modified Bessel function required in equations (23) and (26) or equations (28) to (31) can be omitted, which makes it possible to reduce the scale of calculation and contributes to faster calculation processing and lower power consumption. However, the accuracy of BER will be slightly reduced.

[0075] Although the embodiments of the present invention have been described above, the present invention is not limited to these. Elements of each embodiment may be arbitrarily combined. Also, each embodiment may be implemented by removing any element. As for the processing flow, the order may be changed or multiple steps may be executed in parallel as long as the processing result does not change. Note that the BER estimation itself may be calculated by a computer of another system, not by a component inside the optical transmission system such as the optical interference estimation unit 6-4.

[0076] The control unit 6 described above is, for example, a computer device, and as shown in FIG. 14, includes a memory 2501, a CPU (Central Processing Unit) 2503, a hard disk drive (HDD: Hard Disk Drive) 2505, a display control unit 2507 connected to a display device 2509, a drive device 2513 for a removable disk 2511, an input device 2515, and a communication control unit 2517 for connecting to a network. Toga The HDD 2505 is connected to the memory 2501 via a bus 2519. The HDD 2505 may be a storage device such as a solid state drive (SSD). An operating system (OS) and an application program for implementing the processes in the embodiment of the present invention are stored in the HDD 2505, and are read from the HDD 2505 to the memory 2501 when executed by the CPU 2503. The CPU 2503 controls the display control unit 2507, the communication control unit 2517, and the drive device 2513 according to the processing contents of the application program to perform a predetermined operation. Data during processing is mainly stored in the memory 2501, but may be stored in the HDD 2505. For example, an application program for implementing the above-mentioned processes is distributed by being stored in a computer-readable removable disk 2511, and is installed in the HDD 2505 from the drive device 2513. The application program may also be installed in the HDD 2505 via a network such as the Internet and the communication control unit 2517. Such a computer device realizes the various functions described above through organic cooperation between hardware such as the CPU 2503 and memory 2501 described above and programs such as the OS and application programs.

[0077] The control unit 6 may be implemented in one device, or its functions may be distributed across multiple devices. The CPU may be a GPU (Graphics Processing Unit) or an FPGA (Field-Programmable Gate Array).

[0078] The above-described embodiment can be summarized as follows.

[0079] A method according to a first aspect of this embodiment includes a process in which an optical transmitting unit and an optical receiving unit are connected to each other via an optical transmission unit that utilizes a plurality of spatial resources and a control unit in an optical transmission system that uses coherent detection maps the amplitude of each crosstalk for different spatial resources in the optical transmission unit as a sinusoidal distribution onto an independent variable axis different from the time axis, and estimates the quality of an optical signal in the optical transmission unit using the product of the sinusoidal distribution formed by the sum of the crosstalk amplitudes based on the property that the square of the amplitude difference between the independent variable used in the mapping and the total noise is non-negative.

[0080] In this way, it becomes possible to estimate the quality of an optical signal with higher accuracy than the conventional technique in which the amplitude distribution of crosstalk is approximated as a normal distribution. As mentioned above, the quality is calculated by the bit error rate and the variance σ 2 , SNR or OSNR, and each crosstalk amplitude or the average value of the crosstalk amplitude.

[0081] In the above optical transmission system, when a phase-modulated signal is transmitted and received, the independent variable is s (s>0) and the variance of additive white Gaussian noise is σ 2 , the threshold for the gth symbol decision is D g (D g+1 >D g ), the threshold for the h-th symbol decision is E h (E h+1 >E h ), threshold D g The total number of G is the threshold E h Let H be the total number of bits, and let M be the characteristic function of crosstalk when transmitting bit b∈{0,1}. X|b (s), the number of crosstalks is N, the zeroth order modified Bessel function is J0(·), and the amplitude of the i-th crosstalk when transmitting each bit b∈{0,1} is A XT|b,i , and the bit error rate is expressed as BER by the formula

number

number

[0082] In this formula, the BER, the amplitude of the crosstalk, and the variance of the additive white Gaussian noise σ 2 The relationship between these two can be expressed as follows. Note that equation (26) can be generalized as the first equation above.

[0083] In the above optical transmission system, when a phase-modulated signal consisting of binary symbols (BPSK signal) or a phase-modulated signal consisting of four-value symbols (QPSK signal) is transmitted and received, the independent variable is s (s>0) and the variance of additive white Gaussian noise is σ 2 , the voltage value of the received symbol is V, the ensemble average is E(·), and the characteristic function of the crosstalk when transmitting bit b∈{0,1} is M X|b (s), the number of crosstalks is N, the zeroth order modified Bessel function is J0(·), and the amplitude of the kth crosstalk when each bit b∈{0,1} is transmitted is A XT|b,k , and the bit error rate is expressed as BER by the formula

number

number

number

number

[0084] When BPSK or QPSK is used, the BER and other parameters can be calculated with high accuracy by using the above formula.

[0085] Furthermore, the above-mentioned control unit may estimate the quality of the optical signal by using the average value of the amplitude of each crosstalk or the amplitude of all crosstalks estimated from the input / output optical power difference in the optical transmission unit or the optical power difference between the optical transmission unit and the optical reception unit. On the other hand, the above-mentioned control unit may estimate the variance σ of additive white Gaussian noise from the estimated signal-to-noise power ratio or the optical signal-to-noise power ratio. 2 and the variance of the estimated additive white Gaussian noise, σ 2 In this manner, the quality of the optical signal may be determined using values ​​obtained by measurement for unknown parameters.

[0086] Furthermore, the above method may further include a process in which the control unit sets at least one of a modulation method and an error correction code of the optical signal generated by the optical transmission unit based on the estimated optical signal quality. If the quality such as BER can be estimated with high accuracy in this way, it becomes possible to set an appropriate modulation method and an error correction code without allowing for an extra margin, and efficient optical communication in the optical transmission unit becomes possible.

[0087] For example, the method may further include a process in which the control unit sets a modulation method (e.g., a modulation multilevel degree) of the optical signal generated by the optical transmitting unit so that the bit error rate, which is the quality of the optical signal, is equal to or lower than a reference value when the error correction code of the optical signal generated by the optical transmitting unit is a specific error correction code. Also, the method may further include a process in which the control unit sets at least one of the coding rate and coding method of the error correction code of the optical signal generated by the optical transmitting unit so that the bit error rate, which is the quality of the optical signal, is equal to or lower than a reference value when the modulation method of the optical signal generated by the optical transmitting unit is a specific modulation method. Both the modulation method and the error correction code may be set, or only one of them may be set.

[0088] In addition, the control unit described above is configured to calculate the variance σ of additive white Gaussian noise with a known bit error rate. 2On the other hand, when the bit error rate and the average value of the amplitude of each crosstalk or the average value of the amplitude of all crosstalks are known, the control unit may calculate the variance σ of additive white Gaussian noise as the quality of the optical signal from the above equation. 2 The variance of the additive white Gaussian noise σ 2 Once this is obtained, the SNR and OSNR can be derived.

[0089] Furthermore, the above method may further include a process in which the control unit estimates the quality of the optical signal by an equation that approximates the amplitude distribution of the crosstalk as a normal distribution when the number N of crosstalks exceeds a reference value. As the difference from the calculation by the above-mentioned equation becomes small when the number N of crosstalks increases, the equation in the prior art may be adopted to reduce the amount of calculation.

[0090] Let Q[·] be the Q function, and the expected value of the crosstalk variance be σ x 2 Then, when the number of crosstalks N exceeds the reference value, the control unit described above uses the second formula representing the bit error rate BER:

number

number

[0091] An estimation method according to a second aspect of this embodiment is a method for estimating an upper limit value of a bit error rate in an optical transmission unit for an optical transmission system in which an optical transmitting unit and an optical receiving unit are connected to each other via an optical transmission unit that utilizes a plurality of spatial resources and that uses coherent detection, and includes the steps of: (A) calculating the amplitude of each crosstalk for different spatial resources in the optical transmission unit based on a measurement result of optical power in the optical transmitting unit and a measurement result of optical power in the optical receiving unit; (B) calculating the variance of additive white Gaussian noise in the optical transmission system from a signal-to-noise power ratio or an optical signal-to-noise power ratio obtained based on an electrical signal after coherent detection and photoelectric conversion; and (C) changing the value of an independent variable in a formula for the bit error rate, which is expressed by the amplitude of each crosstalk, the variance of the additive white Gaussian noise, and an independent variable different from the time axis, and searching for the minimum value of the formula as the upper limit value of the bit error rate.

[0092] By executing this estimation method, it becomes possible to obtain a highly accurate bit error rate (BER). For simplicity, the amplitude of each crosstalk may be the average value of the crosstalk amplitude.

[0093] It should be noted that the above formula can be expressed to include a zeroth order modified Bessel function for the independent variables and the amplitude of each crosstalk, which is different from the prior art.

[0094] In the above optical transmission system, when a phase-modulated signal is transmitted and received, the above formula is expressed as follows: the independent variable is s (s>0), the variance of additive white Gaussian noise is σ 2 , the threshold for the gth symbol decision is D g (D g+1 >D g ), the threshold for the h-th symbol decision is E h (E h+1 >E h ), threshold D g The total number of,G,is the threshold,E,. h Let H be the total number of bits, and let M be the characteristic function of crosstalk when transmitting bit b∈{0,1}. X|b(s), the number of crosstalks is N, the zeroth order modified Bessel function is J0(·), and the amplitude of the i-th crosstalk when transmitting each bit b∈{0,1} is A XT|b,i As,

number

number

[0095] In addition, in the above optical transmission system, when a phase-modulated signal consisting of binary symbols (BPSK signal) or a phase-modulated signal consisting of four-value symbols (QPSK signal) is transmitted and received, the above formula is such that the independent variable is s (s>0) and the variance of additive white Gaussian noise is σ 2 , the voltage value of the received symbol is V, the ensemble average is E(·), and the characteristic function of the crosstalk when transmitting bit b∈{0,1} is M X|b (s), the number of crosstalks is N, the zeroth order modified Bessel function is J0(·), and the amplitude of the kth crosstalk when each bit b∈{0,1} is transmitted is A XT|b,k As, In the case of the above BPSK signal,

number

number

number

number

[0096] When BPSK or QPSK is used, the BER and other parameters can be calculated with high accuracy by using the above formula.

[0097] The estimation method may further include a process of setting at least one of a modulation scheme and an error correction code of an optical signal generated by the optical transmitter based on the upper limit value of the bit error rate found.

[0098] Furthermore, the estimation method may further include a process of setting a modulation method of the optical signal generated by the optical transmitter so that the upper limit of the bit error rate is equal to or lower than a reference value when the error correction code of the optical signal generated by the optical transmitter is a specific error correction code. Also, the estimation method may further include a process of setting at least one of a coding rate and a coding method of the error correction code of the optical signal generated by the optical transmitter so that the upper limit of the bit error rate is equal to or lower than a reference value when the modulation method of the optical signal generated by the optical transmitter is a specific modulation method.

[0099] Furthermore, the above estimation method estimates the expected variance of crosstalk when the number of crosstalks N exceeds a criterion. Value and The method may further include a process of estimating an upper limit of the bit error rate using a second formula expressed as a function of the variance of additive white Gaussian noise.

[0100] Let V be the voltage value of the received symbol, Q[·] be the Q function, and let σ be the expected value of the variance of the crosstalk. x 2 In the case of a phase-modulated signal (BPSK signal) consisting of binary symbols, the second formula is expressed as follows:

number

number

[0101] A program for causing a processor to execute the above method can be created, and the program is stored in various storage media.

Claims

1. 1. A method for estimating an upper limit of a bit error rate in an optical transmission system using coherent detection, the method comprising: Calculating the amplitude of each crosstalk for different spatial resources in the optical transmission unit based on the measurement result of optical power in the optical transmission unit and the measurement result of optical power in the optical reception unit; calculating a variance of additive white Gaussian noise in the optical transmission system from a signal-to-noise power ratio or an optical signal-to-noise power ratio obtained based on the electrical signal after the coherent detection and photoelectric conversion; In a formula for a bit error rate, the formula is expressed by the amplitude of each crosstalk, the variance of the additive white Gaussian noise, and an independent variable different from a time axis, and a value of the independent variable is changed to search for a minimum value of the formula as an upper limit of the bit error rate. Estimation methods including processing.

2. The formula includes a zeroth order modified Bessel function for the independent variable and the amplitude of each crosstalk. The estimation method according to claim 1.

3. In the optical transmission system, a phase modulated signal is transmitted and received; The formula is: The independent variable is s (s>0), and the variance of the additive white Gaussian noise is σ ２ , the threshold value for the gth symbol decision is D ｇ (D ｇ＋１ >D ｇ ), the threshold value for the h-th symbol decision is E ｈ (E ｈ＋１ >E ｈ ), the threshold value D ｇ The total number of G is the threshold E ｈ Let H be the total number of bits, and let M be the characteristic function of crosstalk when transmitting bit b∈{0,1}. Ｘ｜ｂ (s), the number of crosstalks is N, and the zeroth order modified Bessel function is J ０ (·), the amplitude of the i-th crosstalk when transmitting each bit b∈{0, 1} is A ＸＴ｜ｂ，ｉ As, [0010] [0025] The estimation method according to claim 1,

4. In the optical transmission system, a phase modulated signal consisting of binary symbols (BPSK signal) or a phase modulated signal consisting of four-level symbols (QPSK signal) is transmitted and received; The formula is: The independent variable is s (s>0), and the variance of the additive white Gaussian noise is σ ２ , the voltage value of the received symbol is V, the ensemble average is E(·), and the characteristic function of the crosstalk when transmitting a bit b∈{0,1} is M Ｘ｜ｂ (s), the number of crosstalks is N, and the zeroth order modified Bessel function is J ０ (·), the amplitude of the kth crosstalk when transmitting each bit b∈{0, 1} is A ＸＴ｜ｂ，ｋ As, In the case of the above BPSK signal, [0030] and In the case of the QPSK signal, [0045] [0050] [006] The estimation method according to claim 1,

5. A process of setting at least one of a modulation method and an error correction code of an optical signal generated by the optical transmitting unit based on the upper limit value of the bit error rate found. The method of claim 1 , further comprising:

6. A process of setting a modulation method of an optical signal generated by the optical transmission unit so that an upper limit value of the bit error rate becomes equal to or lower than a reference value when an error correction code of the optical signal generated by the optical transmission unit is a specific error correction code. The method of claim 1 , further comprising:

7. A process of setting at least one of a coding rate and a coding method of an error correction code of an optical signal generated by the optical transmission unit so that an upper limit value of the bit error rate is equal to or lower than a reference value when the modulation method of the optical signal generated by the optical transmission unit is a specific modulation method. The method of claim 1 , further comprising:

8. If the number N of crosstalks exceeds a reference value, a process of estimating an upper limit of the bit error rate using a second formula expressed as a function of an expected value of the variance of the crosstalk and the variance of the additive white Gaussian noise. The method of claim 1 , further comprising:

9. Let V be the voltage value of the received symbol, Q[·] be the Q function, σ 2 be the variance of the additive white Gaussian noise, and σ be the expected value of the variance of the crosstalk. ｘ ２ As, The second formula is: In the case of a phase-modulated signal (BPSK signal) consisting of binary symbols, [0070] In the case of a phase-modulated signal (QPSK signal) consisting of four-value symbols, [0080] The estimation method according to claim 8, wherein

10. A program for causing a processor to execute the estimation method according to any one of claims 1 to 9.

11. An estimation device for estimating an upper limit of a bit error rate in an optical transmission system using coherent detection, in which an optical transmitter and an optical receiver are connected to each other via an optical transmission section that uses a plurality of spatial resources, comprising: a means for calculating an amplitude of each crosstalk for different spatial resources in the optical transmission section based on a measurement result of optical power in the optical transmission section and a measurement result of optical power in the optical reception section; a means for calculating a variance of additive white Gaussian noise in the optical transmission system from a signal-to-noise power ratio or an optical signal-to-noise power ratio obtained based on the electrical signal after the coherent detection and the photoelectric conversion; a means for searching for a minimum value of the bit error rate as an upper limit value of the bit error rate by changing a value of an independent variable in a formula for the bit error rate, the independent variable being expressed by the amplitude of each crosstalk, the variance of the additive white Gaussian noise, and an independent variable different from a time axis; An estimation device having the following:

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