Control device, optical transmission system, and control method

Abstract

Provided is a control device capable of controlling an intensity modulation signal to a desired quality during optical wavelength multiplex transmission that uses a wavelength band close to a zero dispersion wavelength. This control device controls an optical transmission system comprising: an optical transmitter that transmits a wavelength-multiplexed signal obtained by multiplexing a plurality of optical signals that have each been intensity-modulated and have mutually different wavelengths; and an optical transmission path that transmits the wavelength-multiplexed signal transmitted by the transmitter. Each of the plurality of optical signals is pre-equalized by using an intensity distortion amount, of the wavelength-multiplexed signal, based on a backpropagation characteristic of the optical transmission path, and the intensity of the optical signals pre-equalized by the control device is 0 or more.

Description

Control device, optical transmission system and control method

[0001] The present disclosure relates to a control device, an optical transmission system, and a control method.

[0002] An optical wavelength (optical frequency) multiplexing transmission technique using a wavelength band close to the zero-dispersion wavelength of an optical fiber is known.

[0003] For example, Non-Patent Document 1 discloses a technique of arranging wavelengths at unequal intervals in order to reduce four-wave mixing in optical wavelength division multiplexing transmission technology. Non-Patent Document 2 discloses a polarization interleaving technique that assigns different polarizations to wavelength pairs in order to reduce four-wave mixing in optical wavelength division multiplexing transmission technology. Patent Document 1 discloses a technique for evaluating in-phase crosstalk caused by four-wave mixing in the electrical domain, and adjusting the amplitude and phase during optical modulation in advance so as to reduce waveform deterioration.

[0004] Japanese Patent No. 4813963

[0005] F. Forghieri, R. W. Tkach, and A. R. Chraplyvy, "Reduction of four-wave mixing crosstalk in WDM systems using unequally spaced channels" IEEE Photonics Technology Letters, vol. 6, no. 6, pp. 754-756, Jun. 1994.X. Liu and Q. Fan, "Inter-Channel FWM Mitigation Techniques for 800G-LR4, 1.6T-LR8, 400G-ER4 and 5G Fronthaul Applications Based on O-Band WDM" Journal of Lightwave Technology, vol. 42, no. 3, pp. 1085-1094, Feb. 1, 2024.

[0006] However, the technologies described in Non-Patent Documents 1 and 2 require new configurations such as light sources, optical filters, or polarization rotation elements with wavelength grids different from 400 GbE (Gigabit Ethernet) or 800 GbE-FR, which could complicate the device configuration. Patent Document 1 cannot be applied to Ethernet, a communication standard that uses intensity-modulated signals, because the amplitude and phase during optical modulation are adjusted in advance.

[0007] The embodiments relating to this disclosure aim to provide a control device, an optical transmission system, and a control method that can control an intensity-modulated signal to a desired quality in optical wavelength division multiplexing transmission using a wavelength band close to the zero-dispersion wavelength.

[0008] A control device according to the embodiment of the present disclosure is a control device for controlling an optical transmission system comprising: an optical transmitter that transmits a wavelength-multiplexed signal obtained by multiplexing a plurality of optical signals with different wavelengths, each of which is intensity-modulated; and an optical transmission path that transmits the wavelength-multiplexed signal transmitted by the transmitter, wherein each of the plurality of optical signals is pre-equalized using the amount of intensity distortion of the wavelength-multiplexed signal based on the backpropagation characteristics of the optical transmission path, and the intensity of the optical signal pre-equalized by the control device is 0 or greater.

[0009] An optical transmission system according to an embodiment of this disclosure comprises the optical transmitter, the optical transmission path, the optical receiver, and the control device.

[0010] A control method according to an embodiment of the present disclosure is a control method by a control device for controlling an optical transmission system comprising: an optical transmitter that transmits a wavelength-multiplexed signal obtained by multiplexing a plurality of optical signals of different wavelengths, each of which is intensity-modulated; an optical transmission path that transmits the wavelength-multiplexed signal transmitted by the transmitter; and an optical receiver that receives the wavelength-multiplexed signal transmitted by the optical transmission path as an electrical signal, wherein the control device pre-equals each of the plurality of optical signals using the amount of intensity distortion of the wavelength-multiplexed signal based on the backpropagation characteristics of the optical transmission path, and the intensity of the optical signal pre-equalized by the control device is 0 or greater.

[0011] According to embodiments of this disclosure, it is possible to provide a control device, an optical transmission system, and a control method that can control an intensity-modulated signal to a desired quality in optical wavelength division multiplexing transmission using a wavelength band close to the zero-dispersion wavelength.

[0012] This is a block diagram showing the overall configuration of an optical transmission system equipped with a control device according to the first embodiment. This is a block diagram showing the functional configuration of the transmitting electrical processing unit in an optical transmission system equipped with a control device according to the first embodiment. This is a block diagram showing the functional configuration of the nonlinear pre-equalization unit in an optical transmission system equipped with a control device according to the first embodiment. This is a block diagram showing the functional configuration of the backpropagation calculation unit in an optical transmission system equipped with a control device according to the first embodiment. This is a block diagram showing the functional configuration of the intensity strain acquisition unit in an optical transmission system equipped with a control device according to the first embodiment. This is a block diagram showing the functional configuration of the linear backpropagation intensity separation unit in an optical transmission system equipped with a control device according to the first embodiment. This is a block diagram showing a first example of the configuration of the optical transmitting unit in an optical transmission system equipped with a control device according to the first embodiment. This is a block diagram showing a second example of the configuration of the optical transmitting unit in an optical transmission system equipped with a control device according to the first embodiment. This is a block diagram showing a first example of the configuration of the optical wavelength multiplexing unit in an optical transmission system equipped with a control device according to the first embodiment. This is a block diagram showing a second example of the configuration of the optical wavelength multiplexing unit in an optical transmission system equipped with a control device according to the first embodiment. This is a block diagram showing the configuration of the optical transmission path in an optical transmission system equipped with a control device according to the first embodiment. This is a block diagram showing the configuration of the optical wavelength multiplexing separation unit in an optical transmission system equipped with a control device according to the first embodiment. This is a block diagram showing the configuration of the optical receiving unit in an optical transmission system equipped with a control device according to the first embodiment. This is a block diagram showing the functional configuration of the receiving electrical processing unit in an optical transmission system equipped with a control device according to the first embodiment. This figure shows the eye pattern of pre-equalized intensity obtained in an optical transmission system equipped with the control device according to the first embodiment. This figure shows a first example of an eye pattern obtained without pre-equalization in an optical transmission system equipped with the control device according to the first embodiment. This figure shows the intensity and frequency histogram obtained in Figure 16A. This figure shows a first example of an eye pattern obtained with pre-equalization in an optical transmission system equipped with the control device according to the first embodiment. This figure shows the intensity and frequency histogram obtained in Figure 16C. This figure shows an example of an eye pattern with an extinction ratio of 6 dB and an input power of 5 dBm in an optical transmission system equipped with the control device according to the first embodiment.This figure shows an example of an eye pattern with an extinction ratio of 6 dB and an input power of 10 dBm in an optical transmission system equipped with a control device according to the first embodiment. This figure shows an example of an eye pattern with an extinction ratio of 6 dB and an input power of 12.5 dBm in an optical transmission system equipped with a control device according to the first embodiment. This figure shows an example of an eye pattern with an extinction ratio of 10 dB and an input power of 5 dBm in an optical transmission system equipped with a control device according to the first embodiment. This figure shows an example of an eye pattern with an extinction ratio of 10 dB and an input power of 10 dBm in an optical transmission system equipped with a control device according to the first embodiment. This figure shows an example of an eye pattern with an extinction ratio of 10 dB and an input power of 12.5 dBm in an optical transmission system equipped with a control device according to the first embodiment. This figure shows an example of an eye pattern with an extinction ratio of 100 dB and an input power of 5 dBm in an optical transmission system equipped with a control device according to the first embodiment. This figure shows an example of an eye pattern with an extinction ratio of 100 dB and an input power of 10 dBm in an optical transmission system equipped with a control device according to the first embodiment. This figure shows an example of an eye pattern with an extinction ratio of 100 dB and an input power of 12.5 dBm in an optical transmission system equipped with a control device according to the first embodiment. This figure shows a second example of an eye pattern obtained without pre-equalization in an optical transmission system equipped with the control device according to the first embodiment. This figure shows an example of simulation results of the BER curve with respect to received power in an optical transmission system equipped with the control device according to the first embodiment. This figure shows an example of simulation results of sensitivity improvement for different input power and polarization conditions in an optical transmission system equipped with the control device according to the first embodiment. This figure shows an example of simulation results of the dependence of step size and number of stages in an optical transmission system equipped with the control device according to the first embodiment. This figure shows a first example of signal control processing of the control device according to the first embodiment. This figure shows a second example of signal control processing of the control device according to the first embodiment. This is a flowchart showing the parameter set determination process of the control device according to the first embodiment. This figure shows an example of simulation results of the dependence of BER on transmission distance in an optical transmission system equipped with the control device according to the first embodiment.This figure shows an example of the simulation results of the dependence of BER on quadratic dispersion in an optical transmission system equipped with a control device according to the first embodiment. This figure shows an example of the simulation results of the dependence of BER on dispersion gradient in an optical transmission system equipped with a control device according to the first embodiment. This figure shows an example of the simulation results of the dependence of BER on nonlinear coefficients in an optical transmission system equipped with a control device according to the first embodiment. This is a block diagram of the nonlinear pre-equalization unit of an optical transmission system equipped with a control device according to the second embodiment. This is a block diagram of the backpropagation calculation unit of an optical transmission system equipped with a control device according to the second embodiment.

[0013] The embodiments for implementing this disclosure will be described in detail below with reference to the drawings. The embodiments described below are examples for realizing the technical concept of the invention and do not limit this disclosure to the configurations and numerical values ​​described. In each drawing, the same components are denoted by the same reference numerals, and redundant explanations are omitted as appropriate.

[0014] [First Embodiment] <Configuration of an optical transmission system equipped with a control device according to the first embodiment> (Overall configuration) Figure 1 is a block diagram showing the overall configuration of an optical transmission system 100 equipped with a control device according to the first embodiment. The optical transmission system 100 includes an optical transmitter 1 that transmits a wavelength-multiplexed signal obtained by multiplexing a plurality of optical signals with different wavelengths, each of which is intensity-modulated; an optical transmission path 2 that transmits the wavelength-multiplexed signal transmitted by the optical transmitter 1; and a control device 4 that controls the optical transmission system 100. In the example shown in Figure 1, the optical transmission system 100 further includes an optical receiver 3 that receives the wavelength-multiplexed signal transmitted by the optical transmission path 2 as an electrical signal.

[0015] The optical transmission system 100 is an optical transmission system that uses optical wavelength (optical frequency) multiplexing transmission technology that uses a wavelength band close to the zero-dispersion wavelength of an optical fiber.

[0016] For example, in optical wavelength division multiplexing (WDM) transmission technology that uses the bandwidth around the zero-dispersion wavelength of optical fibers, intensity distortion may occur in the transmitted WDM signal due to nonlinear optical effects, mainly quadruple-wave mixing. Quadruple-wave mixing is a phenomenon in which light of wavelengths other than the three different wavelengths is newly generated when light of three different wavelengths is mixed. Due to nonlinear optical effects, mainly quadruple-wave mixing, crosstalk occurs between multiple optical signals in the WDM signal, making it easier for intensity distortion to occur in the WDM signal. In particular, in Ethernet, a communication standard that uses intensity-modulated signals, intensity distortion in the WDM signal makes it difficult to control the intensity-modulated signal to the desired quality.

[0017] In the first embodiment of this disclosure, the control device 4 pre-equals each of a plurality of optical signals using the intensity distortion amount of the wavelength-multiplexed signal based on the backpropagation characteristics of the optical transmission path 2. Pre-equalization means correcting the distortion of the wavelength-multiplexed signal transmitted through the optical transmission path 2 by adjusting each of the plurality of optical signals in advance on the transmitting side. In the control device 4, the intensity of the pre-equalized optical signal is 0 or greater. Through such pre-equalization, the control device 4 can correct the intensity distortion of the wavelength-multiplexed signal, which is an intensity-modulated signal, in optical wavelength-multiplexed transmission near the zero-dispersion wavelength, and control the intensity-modulated signal to a desired quality. The desired quality of the intensity-modulated signal is, for example, the same quality. From another viewpoint, the control device 4 can control the quality of the intensity-modulated signal and improve the quality of the worst intensity-modulated signal. By controlling the intensity-modulated signal to a desired quality, the control device 4 can achieve longer distances and higher capacity optical signal transmission of the intensity-modulated signal.

[0018] In the example shown in Figure 1, the optical transmitter 1 comprises a transmitting electrical processing unit 1-1, optical transmitting units 1-21 through 1-2n, and an optical wavelength division multiplexing unit 1-3. Hereinafter, n represents a natural number. "2n" represents a number formed by concatenating 2 and n. For example, when n is 1, it represents "21", and when n is 3, it represents "23". This same principle applies to subsequent notations that concatenate numbers and "n" (for example, 140n).

[0019] The transmitting electrical processing unit 1-1 performs digital signal processing (DSP) that uses a specific modulation format or corrects waveform distortion. The transmitting electrical processing unit 1-1 converts binary data into analog electrical signals that are supplied from the optical transmitting unit 1-21 to each of the optical transmitting units 1-2n. The optical transmission system 100 assumes that it receives binary data using error correction coding (FEC). However, error correction coding processing may be included in the digital signal processing performed by the transmitting electrical processing unit 1-1.

[0020] Optical transmitting units 1-21 to 1-2n each modulate the electrical signal supplied from the transmitting electrical processing unit 1-1 using an optical modulator or a direct-modulating laser, and output it as an optical signal of a predetermined wavelength. In the optical transmission system 100, since an Ethernet optical transceiver is assumed, the optical transmitter 1 uses intensity modulation as the modulation method. In particular, the optical transmitter 1 can achieve more efficient optical transmission by using PAM4 (4-level Pulse Amplitude Modulation) or PAM8 (8-level Pulse Amplitude Modulation).

[0021] The optical wavelength division multiplexing (WDM) unit 1-3 combines optical signals of different wavelengths output from optical transmission units 1-21 to 1-2n into a single optical fiber using Wavelength Division Multiplexing (WDM) technology. The optical wavelength division multiplexing unit 1-3 can then combine the resulting WDM signal into the optical fiber of the optical transmission path 2 described below.

[0022] The optical transmission line 2 is composed of a group of optical fibers, each comprising multiple optical fibers. Each of the multiple optical fibers connects the optical transmitter 1 and the optical receiver 3, and transmits the wavelength-division multiplexed signal multiplexed by the optical wavelength division multiplexing units 1-3. The optical transmission line 2 may further include an optical amplifier or optical dispersion compensator to compensate for the degradation of the optical signal during transmission.

[0023] In the example shown in Figure 1, the optical receiver 3 comprises an optical wavelength multiplexing / decompression unit 3-1, optical receiving units 3-21 to 3-2n, and an electrical receiving processing unit 3-3.

[0024] The optical wavelength division multiplexing (WDM) separation unit 3-1 separates the WDM optical signal sent from the optical transmission line 2 into wavelengths. The WDM separation unit 3-1 outputs the separated optical signals from the optical receiving unit 3-21 corresponding to each wavelength to the optical receiving unit 3-2n.

[0025] Optical receiving units 3-21 and 3-2n each receive optical signals of corresponding wavelengths and perform photoelectric conversion using photodetectors such as photodiodes (PDs). The receiving electrical processing unit 3-3 performs digital signal processing, including bit restoration, on the electrical signals output from each of the optical receiving units 3-21 and 3-2n. The receiving electrical processing unit 3-3 may also perform digital signal processing, including error correction decoding, as needed.

[0026] The control device 4 can control the overall operation of the optical transmitter 1 and the optical receiver 3. In the example shown in Figure 1, the control device 4 has the following functional configuration: an optical transmitter control unit 4-1, a signal control unit 4-2, and an optical receiver control unit 4-3.

[0027] Each function of the control device 4 is realized by executing instruction codes stored in memory using electronic circuits, or by performing various processes using electronic circuits designed for special purposes. Examples of electronic circuits include a CPU (Central Processing Unit), FPGA (Field Programmable Gate Array), ASIC (Application Specific Integrated Circuit), or DSP. The control device 4 may also include memory such as ROM (Read Only Memory), RAM (Random Access Memory), or HDD (Hard Disk Drive). Furthermore, some of the functions of the control device 4 may be provided by devices or equipment other than the control device 4, such as the transmitting electrical processing unit 1-1 or the receiving electrical processing unit 3-3, and may be realized by distributed processing between the control device 4 and the devices or equipment other than the control device 4.

[0028] The optical transmitter control unit 4-1 controls each component of the optical transmitter 1 and sets transmission conditions for each wavelength of multiple optical signals with different wavelengths, in accordance with the conditions of the optical transmission path 2. The signal control unit 4-2 performs synchronization between the optical transmitter 1 and the optical receiver 3, or parameter control between the optical transmitter 1 and the optical receiver 3. The optical receiver control unit 4-3 controls each component of the optical receiver 3 and controls the signal quality or optimizes the reception sensitivity.

[0029] (Optical Transmitter 1) (Transmitting Electrical Processing Unit 1-1) Figure 2 is a block diagram showing the functional configuration of the transmitting electrical processing unit 1-1 of the optical transmitter 1. The transmitting electrical processing unit 1-1 performs the process of converting the input binary data B1 to binary data Bn and the corresponding modulated data M1 to modulated data Mn under the control of the optical transmitter control unit 4-1 of the control device 4.

[0030] In the example shown in Figure 2, the transmitting electrical processing unit 1-1 includes a symbol mapping unit 1-11, a polarization adjustment unit 1-12, a waveform shaping unit 1-13, a nonlinear pre-equalization unit 1-14, an intensity field conversion unit 1-15, a sampling rate adjustment unit 1-16, and a DA conversion (Digital-to-Analog Conversion) unit 1-17.

[0031] Each function of the transmitting electrical processing unit 1-1 is realized by executing instruction codes stored in memory using electronic circuits, or by performing various processes using electronic circuits designed for special purposes. The transmitting electrical processing unit 1-1 may be equipped with memory such as ROM, RAM, or HDD. Some of the functions of the transmitting electrical processing unit 1-1 may be provided by devices or equipment other than the transmitting electrical processing unit 1-1, such as the control device 4 or the receiving electrical processing unit 3-3, and may be realized by distributed processing between the transmitting electrical processing unit 1-1 and the devices or equipment other than the transmitting electrical processing unit 1-1.

[0032] The symbol mapping unit 1-11 converts each of the input binary data B1 to Bn into a symbol sequence suitable for a multi-level intensity modulation scheme. Specifically, for example, in the case of PAM4, the symbol mapping unit 1-11 converts the binary data B1 to Bn, each of which is 2 bits, so that each corresponds to one symbol.

[0033] The polarization adjustment unit 1-12 adjusts the polarization state of each of the multiple optical signals as a pre-processing step before the pre-equalization process of each of the multiple optical signals. For example, the polarization adjustment unit 1-12 performs processing to simulate the polarization state input to the optical wavelength division multiplexing unit 1-3 of the optical transmitter 1. By controlling the polarization adjustment unit 1-12, the control device 4 can perform nonlinear pre-equalization in combination with polarization interleaving technology, which assigns parallel or vertical polarization according to the set of optical signals. Note that when transmitting the same polarization, the transmitting electrical processing unit 1-1 does not necessarily need to have the polarization adjustment unit 1-12.

[0034] The waveform shaping unit 1-13 optimizes the time-domain waveform of the transmitted optical signal and performs shaping filter processing to suppress inter-symbol interference (ISI). In particular, the waveform shaping unit 1-13 can optimize the time-domain waveform of the transmitted optical signal by using Nyquist pulse shaping or a roll-off filter. This makes it possible to efficiently utilize the signal bandwidth in the frequency domain.

[0035] The waveform shaping unit 1-13 may include a function to compensate for the effects of the frequency characteristics or bandwidth limitations of the optical transmission path 2 before the optical signal to be transmitted is input to the optical modulator. For example, the waveform shaping unit 1-13 can use pre-emphasis technology to compensate for the attenuation of high-frequency components and reduce linear signal waveform degradation during reception. By amplifying the signal strength of specific frequency components using pre-emphasis technology, the effects of frequency dependence are reduced, enabling more uniform signal transmission.

[0036] The nonlinear pre-equalization unit 1-14 performs pre-equalization to compensate for intensity distortion caused by optical nonlinear effects occurring in the optical transmission path 2. The pre-equalization by the nonlinear pre-equalization unit 1-14 is a process that reduces the degradation of the quality of the wavelength-division multiplexed signal received by the optical receiver 3 by performing appropriate intensity correction calculations based on the nonlinear characteristics of the optical fiber obtained in advance by simulation or measurement. Under the control of the optical transmitter control unit 4-1 of the control device 4, the nonlinear pre-equalization unit 1-14 acquires intensity distortion information from the complex electric field amplitude obtained by backpropagation calculation and corrects the symbol mapping result based on the acquired intensity distortion information. This makes it possible to pre-equalize the nonlinear intensity distortion of the wavelength-division multiplexed signal using only binary data Bn and optical transmission parameters from binary data B1. Note that "acquisition" may mean acquisition by calculation.

[0037] The intensity-field conversion unit 1-15 converts the input intensity into an electric field format that can be received by the optical modulator or directly modulated laser. The intensity-field conversion unit 1-15 performs the conversion by calculating the square root of the input intensity. Note that if the input format of the optical modulator or directly modulated laser is intensity, the transmitting electrical processing unit 1-1 does not necessarily have to include the intensity-field conversion unit 1-15.

[0038] The sampling rate adjustment unit 1-16 converts the sampling rate to match the specifications of the DA conversion unit 1-17 located at the output terminal of the optical transmitter 1. While the main calculations in the transmitting electrical processing unit 1-1 are processed at more than twice the symbol rate, the sampling rate of the DA conversion unit 1-17 is often less than twice the symbol rate. Therefore, a correction is necessary between the processing rate and the physical sampling rate.

[0039] The DA conversion unit 1-17 performs a DA conversion of the symbol data, which has undergone the signal processing in the preceding stage, into an analog electrical signal. During the DA conversion by the DA conversion unit 1-17, the appropriate bit resolution and sampling rate can be selected to ensure a signal quality suitable for an optical modulator. The DA conversion unit 1-17 primarily targets signal generation of 100 Gbaud or higher using a high-speed DA converter.

[0040] The optical transmitter control unit 4-1 of the control device 4 controls each component of the optical transmitter 1. Specifically, the optical transmitter control unit 4-1 controls the modulation order and symbol mapping table for the symbol mapping unit 1-11, and controls the polarization information according to the configuration of the optical wavelength division multiplexing unit 1-3 for the polarization adjustment unit 1-12. The optical transmitter control unit 4-1 also controls the filter parameters necessary for waveform shaping or pre-emphasis for the waveform shaping unit 1-13. Furthermore, the optical transmitter control unit 4-1 controls the optical transmission path parameters, backpropagation parameters, optical transmission power, wavelength division multiplexing conditions, and signal quality for the nonlinear pre-equalization unit 1-14. In addition, the optical transmitter control unit 4-1 controls the rate conversion ratio for the sampling rate adjustment unit 1-16 and controls the setting conditions such as the bit resolution or output amplitude value of the DA conversion unit 1-17.

[0041] (Nonlinear Pre-equalization Unit 1-14) Figure 3 is a block diagram showing the functional configuration of the nonlinear pre-equalization unit 1-14 provided in the transmitting electrical processing unit 1-1. In the example shown in Figure 3, the nonlinear pre-equalization unit 1-14 includes an input processing rate adjustment unit 1-1401 to an input processing rate adjustment unit 1-140n, an electrical frequency synthesis unit 1-142, a backpropagation calculation unit 1-143, and a linear backpropagation signal duplication unit 1-144. The nonlinear pre-equalization unit 1-14 also includes an intensity strain acquisition unit 1-145, a linear backpropagation intensity separation unit 1-146, an intensity correction unit 1-1471 to an intensity correction unit 1-147n, and a nonlinear correction unit 1-1481 to a nonlinear correction unit 1-148n.

[0042] Each of the input processing rate adjustment units 1-1401 to 1-140n performs upsampling on the data streams of each of the multiple electrical signals corresponding to the multiple optical signals received from the symbol mapping unit 1-11 or the polarization adjustment unit 1-12, in order to convert them to the sampling rate required for the backpropagation calculation. The upsampling rate depends heavily on the backpropagation distance or input power, and it is desirable to have the largest possible value. From the viewpoint of reducing the computational load or computation time, it is preferable to set the upsampling rate to 2 to 2.5 times or more the total bandwidth of the wavelength division multiplexed signal.

[0043] The electrical frequency combining unit 1-142 shifts the center frequency in the frequency domain or applies a frequency shift and phase rotation in the time domain to multiple electrical signals input from each of the input processing rate adjustment units 1-1401 to 1-140n. As a result, the electrical frequency combining unit 1-142 can generate an electrical frequency multiplexed signal by applying a desired frequency shift to the multiple electrical signals and adding the sampling rate signals.

[0044] The backpropagation calculation unit 1-143 takes the transmission path length, loss coefficient, nonlinear coefficient, dispersion value, and dispersion slope as input variables and solves a nonlinear propagation equation with the signs of the parameters of the optical transmission path 2 reversed. Through this, the backpropagation calculation unit 1-143 obtains electric field information of the wavelength-division multiplexed signal based on the backpropagation of the optical transmission path 2. The transmission path length, loss coefficient, nonlinear coefficient, dispersion value, and dispersion slope are all parameters of the optical transmission path 2. For example, the backpropagation calculation unit 1-143 performs processing corresponding to the propagation of a linear or nonlinear wavelength-division multiplexed signal in the reverse direction in an optical transmission path equivalent to the optical transmission path 2.

[0045] The propagation characteristics of an optical fiber are obtained by solving a nonlinear propagation equation with transmission path length, loss coefficient, dispersion value, and dispersion gradient as coefficients. The backpropagation calculation unit 1-143 determines the complex electric field amplitude to reduce nonlinear waveform degradation by providing a desired signal waveform as the final state to the nonlinear propagation equation with the sign-inverted loss coefficient, dispersion value, and dispersion gradient as coefficients. With respect to the backpropagation of a linear wavelength-multiplexed signal, the backpropagation calculation unit 1-143 can calculate the waveform at the transmitting side by providing the optical intensity waveform at the receiving side as boundary conditions for the nonlinear propagation equation with the dispersion value and dispersion gradient set to zero. The output of the backpropagation calculation unit 1-143 is sent as a nonlinear backpropagation signal NR to the intensity-distortion acquisition unit 1-145.

[0046] The linear backpropagation signal replication unit 1-144 replicates the amplitude and phase of the light having the inverse characteristics of linear waveform distortion obtained by the backpropagation calculation unit 1-143, and converts it into a format that can be used in parallel by subsequent processing units.

[0047] The intensity strain acquisition unit 1-145 acquires the amount of intensity strain of the wavelength division multiplexed signal based on the backpropagation characteristics of the optical transmission path 2, based on the phase information of the electric field information acquired by the backpropagation calculation unit 1-143. The intensity strain acquisition unit 1-145 separates the electrical signals after nonlinear backpropagation calculation and linear backpropagation calculation for each lane, and performs a process to acquire only the intensity strain generated by nonlinear optical effects based on the intensity of the separated electrical signals after backpropagation calculation.

[0048] The linear backpropagation intensity separation unit 1-146 separates the electrical signals after the linear backpropagation calculation for each lane, thereby outputting information regarding the intensity of each of the multiple electrical signals to a subsequent processing unit.

[0049] Each of the intensity correction units 1-1471 to 1-147n controls the intensity of each of the multiple electrical signals to improve the signal quality, based on the nonlinear intensity strain acquired by the intensity strain acquisition unit 1-145 and the information of each of the multiple electrical signals obtained from the linear backpropagation intensity separation unit 1-146.

[0050] Each of the nonlinear correction units 1-1481 to 1-148n transforms the input / output characteristics using a nonlinear function so that the light intensity, which has been pre-compensated for intensity distortion in the intensity correction unit 1-147, becomes a value greater than or equal to 0. Through the transformation by the nonlinear correction units 1-1481 to 1-148n, the intensity field conversion unit 1-15 can receive multiple electrical signals. The outputs of each of the nonlinear correction units 1-1481 to 1-148n are sent to the intensity field conversion unit 1-15 as a nonlinear pre-equalization signal P1 and a nonlinear pre-equalization signal Pn.

[0051] The control device 4 can obtain the intensity distortion amount of the wavelength-division multiplexed signal based on the backpropagation characteristics of the optical transmission path 2 by controlling the operation of the nonlinear pre-equalization unit 1-14. Furthermore, by controlling the operation of the nonlinear pre-equalization unit 1-14 and going through a series of processes from the backpropagation calculation unit 1-143 to the intensity correction unit 1-147, the control device 4 can pre-correct the intensity distortion that occurs in the optical transmission path 2. As a result, the optical transmission system 100 can transmit intensity-modulated signals with high quality.

[0052] (Backpropagation Calculation Unit 1-143) Figure 4 is a block diagram showing the functional configuration of the backpropagation calculation unit 1-143. The backpropagation calculation unit 1-143 processes the input electrical signal and generates an electrical signal with nonlinear and linear distortions as if it had propagated in the reverse direction through the optical transmission path 2.

[0053] In the example shown in Figure 4, the backpropagation calculation unit 1-143 comprises a nonlinear backpropagation unit 1-1432 and a linear backpropagation unit 1-1433. The nonlinear backpropagation unit 1-1432 includes an input electrical signal replication unit 1-1431 and an N-stage cascaded first wavelength dispersion compensation unit 1-14321, an electrical signal replication unit 1-14322, an intensity detection unit 1-14323, a nonlinear phase calculation unit 1-14324, a multiplication unit 1-14325, and a subsequent wavelength dispersion compensation unit 1-14326. The linear backpropagation unit 1-1433 includes a second wavelength dispersion compensation unit 1-14331.

[0054] The input electrical signal duplication unit 1-1431 duplicates the input electrical frequency multiplexed signal FM into two copies. The output of the input electrical signal duplication unit 1-1431 is sent to the subsequent nonlinear backpropagation unit 1-1432 and linear backpropagation unit 1-1433, respectively.

[0055] In the nonlinear backpropagation unit 1-1432, the first wavelength dispersion compensation unit 1-14321 compensates for the wavelength dispersion of the input wavelength-division multiplexed signal using the nonlinear propagation equation. From another perspective, the first wavelength dispersion compensation unit 1-14321 corrects the phase change due to wavelength dispersion in the input signal. Signals propagating through optical fibers have different propagation speeds for each wavelength. This causes a temporal spread (i.e., dispersion) of the signal waveform. The first wavelength dispersion compensation unit 1-14321 can compensate for wavelength dispersion by obtaining the inverse response of the wavelength-dependent phase characteristics caused by optical fiber transmission due to the dispersion of the signal waveform. Note that "the input wavelength-division multiplexed signal" refers to the wavelength-division multiplexed signal that is repeatedly input to the nonlinear backpropagation unit 1-1432 when performing backpropagation calculations using the nonlinear backpropagation unit 1-1432.

[0056] The electrical signal duplication unit 1-14322 duplicates the input electrical frequency multiplexed signal FM into two copies, similar to the input electrical signal duplication unit 1-1431. The outputs of the electrical signal duplication unit 1-14322 are sent to the subsequent intensity detection unit 1-14323 and multiplication unit 1-14325, respectively.

[0057] The intensity detection unit 1-14323 detects the intensity of the input wavelength division multiplexing signal from the output of the first wavelength dispersion compensation unit 1-14321. For example, the intensity detection unit 1-14323 calculates the intensity of the complex amplitude signal passed from the electrical signal replication unit 1-14322. In the complex amplitude signal, the real part is E ｒ It is expressed as (t), and the imaginary part is E ｉ It is expressed as (t). The intensity I(t) is I(t) = |E ｒ (t) | ２ +|E ｉ (t) | ２ It is calculated from the following. The intensity I(t) serves as basic information for adding the effect of nonlinear distortion in the subsequent nonlinear phase calculation unit 1-14324 and multiplication unit 1-14325.

[0058] The nonlinear phase calculation unit 1-14324 calculates the phase information of the input wavelength division multiplexed signal according to the intensity detected by the intensity detection unit 1-14323. For example, the nonlinear phase calculation unit 1-14324 calculates the amount of phase shift caused by nonlinear optical effects based on the signal intensity obtained from the intensity detection unit 1-14323. For example, in optical fiber transmission, the optical refractive index change is larger in regions with higher intensity, resulting in a phase change. Taking this phenomenon into consideration, the nonlinear phase calculation unit 1-14324 calculates the nonlinear coefficient γ representing the intensity of the nonlinear effect and the effective length L of the optical fiber through which the signal is transmitted. ｅｆｆ Using the signal intensity I(t), the correction value Δφ(t) = γ・L ｅｆｆ Calculate I(t).

[0059] The multiplication unit 1-14325 multiplies the phase information of the wavelength division multiplexed signal calculated by the nonlinear phase calculation unit 1-14324 with the output of the first wavelength dispersion compensation unit 1-14321. From another perspective, the multiplication unit 1-14325 performs a calculation to correct the phase of the complex amplitude signal based on the phase shift amount obtained from the nonlinear phase calculation unit 1-14324. Corrected signal EＮＳ (t) is expressed using the complex amplitude E(t) before correction as E ＮＳ (t) = E(t)·exp[-j·Δφ(t)]. Through the processing performed by the multiplier 1-14325, the phase shift caused by the nonlinear optical effect is corrected.

[0060] Unlike the first chromatic dispersion compensator 1-14321, the post-stage chromatic dispersion compensator 1-14326 performs correction in consideration of the signal state after nonlinear correction. This enables calculation and correction of the phase shift amount caused by the nonlinear optical effect with higher accuracy.

[0061] The nonlinear back-propagation unit 1-1432 repeatedly executes a series of processes of the first chromatic dispersion compensator 1-14321, the electrical signal duplicator 1-14322, the intensity detector 1-14323, the nonlinear phase calculator 1-14324, the multiplier 1-14325 and the post-stage chromatic dispersion compensator 1-14326 N times. This allows numerically solving the nonlinear propagation equation representing signal propagation in an optical fiber.

[0062] The numerical solution method for the nonlinear propagation equation by the nonlinear back-propagation unit 1-1432 is a type of split-step method. The split-step method is a method that improves calculation efficiency by separating the linear chromatic dispersion effect in signal propagation from the influences of nonlinear self-phase modulation, cross-phase modulation, four-wave mixing and the like, and applying them alternately. The split-step method can calculate the influence of nonlinear effects in signal propagation through optical fibers with high accuracy (see, for example, the non-patent literature: Govind P. Agrawal, "Nonlinear Fiber Optics," Academic Press.). However, when N sections are considered, it is necessary to set the transmission distance used in the first chromatic dispersion compensator 1-14321, the nonlinear phase calculator 1-14324 and the post-stage chromatic dispersion compensator 1-14326 to 1 / N.

[0063] The nonlinear backpropagation unit 1-1432 can also execute the processing of the first wavelength dispersion compensation unit 1-14321, the intensity detection unit 1-14323, the nonlinear phase calculation unit 1-14324, and the multiplication unit 1-14325 only once, instead of repeating them N times. In this case as well, the nonlinear propagation equation representing signal propagation in optical fiber can be solved numerically. Note that in the case of long-distance transmission, reducing the number of processing iterations results in a rough approximation and thus a larger error, but in the case of short-distance transmission, it may be possible to solve the equation numerically while maintaining a certain level of accuracy even with a reduced number of processing iterations.

[0064] The control device 4 can solve the nonlinear propagation equation by controlling the operation of the nonlinear backpropagation unit 1-1432 and obtain electric field information of the wavelength-division multiplexed signal based on the backpropagation of the optical transmission path 2. The above configuration of the nonlinear backpropagation unit 1-1432 is an example and can be changed as appropriate. For example, Figure 4 illustrates a configuration in which the first wavelength dispersion compensation unit 1-14321 and the subsequent wavelength dispersion compensation unit 1-14326 are arranged symmetrically, but the first wavelength dispersion compensation unit 1-14321 and the subsequent wavelength dispersion compensation unit 1-14326 may be combined into a single configuration. In this case, the combined single configuration corresponds to the subsequent wavelength dispersion compensation unit 1-14326. Furthermore, linearly multiplicative coefficients such as losses or gains due to optical fibers and optical amplifiers can also be included in the first wavelength dispersion compensation unit 1-14321 and the subsequent wavelength dispersion compensation unit 1-14326.

[0065] The linear backpropagation unit 1-1433 takes the transmission path length, loss coefficient, dispersion value, and dispersion gradient as input variables and solves the linear propagation equation with the signs of the parameters of the optical transmission path 2 reversed to obtain electric field information of the wavelength-division multiplexed signal based on the backpropagation of the optical transmission path 2, assuming that the nonlinear coefficients are zero. The linear backpropagation unit 1-1433 uses the acquired electric field information to obtain the intensity strain amount. The control device 4 can obtain the complex electric field amplitude necessary for nonlinear preequalization.

[0066] In the linear backpropagation unit 1-1433, the second wavelength dispersion compensation unit 1-14331 can perform operations corresponding to the operations of the first wavelength dispersion compensation unit 1-14321 and the subsequent wavelength dispersion compensation unit 1-14326, which are connected in cascaded order N times. The second wavelength dispersion compensation unit 1-14331 compensates for the wavelength dispersion of the input wavelength division multiplexed signal using the linear propagation equation. The nonlinear pre-equalization unit 1-14 can acquire the intensity distortion amount using the output of the second wavelength dispersion compensation unit 1-14331.

[0067] The function of the linear backpropagation unit 1-1433 can be realized by setting the fiber length of the first wavelength dispersion compensation unit 1-14321 or the subsequent wavelength dispersion compensation unit 1-14326 to be the same as the optical transmission path length. The effect of wavelength dispersion appears as linear distortion. The processing by the linear backpropagation unit 1-1433 can be performed in a single calculation. The backpropagation calculation unit 1-143 can perform wavelength dispersion compensation processing all at once by having the linear backpropagation unit 1-1433.

[0068] As described above, the backpropagation calculation unit 1-143 numerically solves the nonlinear propagation equation and the linear propagation equation corresponding to propagation in the opposite direction to the actual propagation direction along the optical transmission path 2. This allows the complex electric field amplitude necessary for nonlinear preequalization using the intensity correction unit 1-147n from the intensity strain acquisition unit 1-145, the linear backpropagation intensity separation unit 1-146, the intensity correction unit 1-1471, and the nonlinear correction unit 1-148n from the nonlinear correction unit 1-1481 to the nonlinear correction unit 1-148n.

[0069] (Intensity Strain Acquisition Unit 1-145) Figure 5 is a block diagram showing the functional configuration of the intensity strain acquisition unit 1-145. The intensity strain acquisition unit 1-145 uses nonlinear backpropagation signals and linear backpropagation signals to calculate the intensity strain necessary for pre-equalization to improve the transmission quality of the intensity modulated signal.

[0070] In the example shown in Figure 5, the intensity strain acquisition unit 1-145 includes a nonlinear backpropagation signal electrical frequency separation unit 1-1451, a linear backpropagation signal electrical frequency separation unit 1-1452, and output processing rate adjustment units 1-14531 to 1-1453n. The intensity strain acquisition unit 1-145 also includes output processing rate adjustment units 1-14541 to 1-1454n, intensity generation units 1-14551 to 1-1455n, intensity generation units 1-14561 to 1-1456n, and subtraction units 1-14571 to 1-1457n.

[0071] The nonlinear backpropagation signal electrical frequency separation unit 1-1451 and the linear backpropagation signal electrical frequency separation unit 1-1452 have the function of separating the input nonlinear backpropagation signal NR and linear backpropagation signal LR into multiple signals (hereinafter sometimes referred to as wavelength channels) corresponding to different wavelengths. This function corresponds to the inverse operation function of the electrical frequency synthesis unit 1-142. Specifically, this function broadcasts the input electrical frequency multiplexed signal to each lane, shifts the center frequency in the frequency domain, or applies frequency shift and phase rotation in the time domain, and extracts only the required frequency band from the center frequency. Digital filters can be used for waveform adjustment operations. Examples of filter shapes include Chebyshev filters, Bessel filters, Nyquist filters, and rectangular filters. These digital filters have the function of removing signals above the desired frequency band. Processing by digital filters corresponds to the process of selecting multiple desired wavelength channels from the optical frequency multiplexed signal.

[0072] Following the nonlinear backpropagation signal electrical frequency separation unit 1-1451 and the linear backpropagation signal electrical frequency separation unit 1-1452, output processing rate adjustment units 1-14531 to 1-1453n and output processing rate adjustment units 1-14541 to 1-1454n are arranged. Output processing rate adjustment units 1-14531 to 1-1453n and output processing rate adjustment units 1-14541 to 1-1454n perform the reverse operation of the input processing rate adjustment unit 1-140.

[0073] Each of the output processing rate adjustment units 1-14531 to 1-1453n and 1-14541 to 1-1454n performs downsampling to convert the sampling rate for the data stream of each wavelength channel received from the nonlinear backpropagation signal electrical frequency separation unit 1-1451 and the linear backpropagation signal electrical frequency separation unit 1-1452. From the viewpoint of not causing problems in other signal processing and reducing the number of samples to be retained, it is preferable to match the downsampling rate to twice the normal symbol rate. The downsampling rate may also be determined in accordance with the sampling rate of the DA conversion unit 1-17. When the downsampling rate is determined in accordance with the sampling rate of the DA conversion unit 1-17, the transmission electrical processing unit 1-1 shown in Figure 2 above does not necessarily have to include the sampling rate adjustment unit 1-16.

[0074] Each of the intensity generation units 1-14551 to 1-1455n and 1-14561 to 1-1456n converts the complex electric field amplitudes obtained from the corresponding output processing rate adjustment units 1-14531 to 1-1453n and 1-14541 to 1-1454n, respectively, after nonlinear backpropagation and linear backpropagation at the desired sampling rate into intensity. Specifically, this process of converting the complex electric field amplitude into intensity involves representing the complex amplitude signal on a two-dimensional complex plane, performing a conversion process, and mapping it to a one-dimensional intensity signal.

[0075] For example, the time function of a complex amplitude is expressed as E(t) = A(t)・exp[jθ(t)], where E(t) is the complex amplitude, A(t) is the amplitude component (corresponding to the square root of the intensity), θ(t) is the phase component of the signal, and j is the imaginary unit. The process of mapping a complex amplitude E(t) on the complex plane to a one-dimensional space is I(t) = |E(t)| ２ = |A(t)| ２This corresponds to the following: By squaring the norm of the complex amplitude E(t), we can obtain a time-varying one-dimensional intensity I(t). Through this mapping process, the complex amplitude component is converted into intensity information corresponding to physical energy.

[0076] The intensity generation units 1-14551 to 1-1455n and 1-14561 to 1-1456n perform this conversion process sequentially or in blocks at each time point or sample corresponding to t, thereby acquiring a one-dimensional intensity waveform unfolded on the time axis.

[0077] Subtraction units 1-14571 through 1-1457n analyze intensity fluctuations affected by nonlinear distortion. Subtraction units 1-14571 through 1-1457n subtract the intensity of the field information after linear backpropagation, calculated by intensity generation units 1-14561 through 1-1456n, from the intensity of the field information after nonlinear backpropagation, calculated by intensity generation units 1-14551 through 1-1455n. As a result, the energy distribution of the intensity distortion component is directly represented on the t-axis corresponding to each time or sample, and the nonlinear intensity distortion NDn is separated from the nonlinear intensity distortion ND1 included in the intensity information. Subtraction units 1-14571 through 1-1457n output the corresponding nonlinear intensity distortion NDn from the corresponding nonlinear intensity distortion ND1. The nonlinear pre-equalization unit 1-14 shown in Figure 2 above receives the outputs from subtraction unit 1-14571 and subtraction unit 1-1457n, and performs nonlinear distortion correction processing in intensity correction unit 1-147. In other words, the control device 4 controls the nonlinear pre-equalization unit 1-14, converts the electric field information obtained by solving the nonlinear propagation equation and the linear propagation equation into intensity, and performs pre-equalization by subtracting the intensity distortion amount from the intensity of the electric field information after linear backpropagation. As a result, the control device 4 can improve the quality of the signal.

[0078] (Linear backpropagation intensity separation unit 1-146) Figure 6 is a block diagram showing the functional configuration of the linear backpropagation intensity separation unit 1-146. The linear backpropagation intensity separation unit 1-146 generates and separates intensity information from the complex electric field amplitude affected by linear degradation by propagating in the reverse direction through the optical transmission path 2.

[0079] In the example shown in Figure 6, the linear backpropagation intensity separation unit 1-146 comprises a linear backpropagation signal electrical frequency separation unit 1-1461, output processing rate adjustment units 1-14621 to 1-1462n, and intensity generation units 1-14631 to 1-1463n.

[0080] The linear backpropagation signal electrical frequency separation unit 1-1461 separates the linear backpropagation signal LR into data streams for each wavelength channel. The linear backpropagation signal electrical frequency separation unit 1-1461 can be configured in the same way as the linear backpropagation signal electrical frequency separation unit 1-1452 shown in Figure 5 above.

[0081] Each of the output processing rate adjustment units 1-14641 to 1-1464n adjusts the symbol rate for each data stream through downsampling or interpolation processing. Each of the output processing rate adjustment units 1-14641 to 1-1464n can be configured in the same way as the output processing rate adjustment units 1-14541 to 1-1454n shown in Figure 5 above.

[0082] Each of the intensity generation units 1-14661 to 1-1466n extracts the amplitude information of the signal in each data stream through squaring and converts the complex electric field amplitude of each wavelength channel obtained by linear backpropagation into an intensity signal. Each of the intensity generation units 1-14661 to 1-1466n outputs the linear backpropagation intensity LD1 to the linear backpropagation intensity LDn, which are the converted intensity signals. Each of the linear backpropagation intensity LD1 to the linear backpropagation intensity LDn is used in the subsequent intensity correction unit 1-147 to perform pre-equalization. The intensity generation units 1-14661 to 1-1466n can be configured in the same way as the intensity generation units 1-14561 to 1-1456n shown in Figure 5 above.

[0083] (Optical Transmitting Units 1-21 to 1-2n) Figure 7 is a block diagram showing a first example of the configuration of optical transmitting units 1-21 to 1-2n. Since optical transmitting units 1-21 to 1-2n all have the same configuration, they may be collectively referred to as optical transmitting unit 1-2 when not distinguishing between them. In addition, Figure 7 and Figure 8, which will be described below, will be explained using one optical transmitting unit 1-2 as a representative example.

[0084] In the first example shown in Figure 7, the optical transmitting unit 1-2 includes an electrical amplification unit 1-2101, a bias control unit 1-2102, a light source unit 1-2103, an optical modulation unit 1-2104, and an optical power adjustment unit 1-2105. Furthermore, the optical transmitting unit 1-2 according to the first example is provided with an interface to a transmitting electrical processing unit 1-1 for receiving electrical signals or to an optical transmitter control unit 4-1 for controlling the entire optical transmitter 1.

[0085] The transmitting electrical processing unit 1-1 receives the input signal to be modulated and generates an electrical signal according to the desired modulation scheme. This electrical signal is amplified to a predetermined amplitude level by the electrical amplification unit 1-2101. The electrical signal amplified by the electrical amplification unit 1-2101 is supplied to the optical modulation unit 1-2104.

[0086] The light source unit 1-2103 provides the optical carrier (carrier wave) in the external modulation scheme. For example, a semiconductor laser can be used as the light source unit 1-2103. However, a fiber laser or other light source may also be used as the light source unit 1-2103.

[0087] The optical modulation unit 1-2104 modulates the intensity of the optical carrier in accordance with the electrical signal. The optical modulation unit 1-2104 includes a Mach-Zehnder interferometer (MZI) type modulator and LiNbO ３ A lithium niobate modulator or an optical ring resonator type modulator can be used.

[0088] The bias control unit 1-2102 optimally controls the operating point of the optical modulation unit 1-2104. The bias control unit 1-2102 compensates for fluctuations in the operating point of the external modulator due to temperature changes or device characteristic drift, maintaining stable modulation characteristics. The optical signal modulated by the bias control unit 1-2102 is supplied to the optical power adjustment unit 1-2105.

[0089] The optical power adjustment unit 1-2105 adjusts the output optical power of the transmitted optical signal to ensure appropriate optical transmission power. For example, the optical power adjustment unit 1-2105 can use a variable optical attenuator (VOA) to adjust the transmitted optical intensity. The operation of the entire optical transmitter 1 is controlled by the optical transmitter control unit 4-1. The optical transmitter control unit 4-1 monitors the operating status of each component of the optical transmitter 1, outputs control signals, and maintains high quality of the transmitted signal.

[0090] Figure 8 is a block diagram showing a second example of the configuration of optical transmitting units 1-21 to 1-2n. In the second example shown in Figure 8, optical transmitting units 1-2 each use a direct modulation laser (DML) and modulate the optical signal without using an external modulator.

[0091] In the second example shown in Figure 8, the optical transmitting unit 1-2 includes an electrical amplification unit 1-2111, a bias control unit 1-2112, an optical power adjustment unit 1-2114, and a light source unit 1-2113. The electrical amplification unit 1-2111 has the same function as the electrical amplification unit 1-2101 shown in Figure 7. The bias control unit 1-2112 has the same function as the bias control unit 1-2102 shown in Figure 7. The light source unit 1-2113 has the same function as the light source unit 1-2103 shown in Figure 7. The optical power adjustment unit 1-2114 has the same function as the optical power adjustment unit 1-2105 shown in Figure 7. Furthermore, in the optical transmitting unit 1-2 according to the second example, an interface is provided with the transmitting electrical processing unit 1-1 or the optical transmitter control unit 4-1 for controlling the entire optical transmitter 1 in order to receive electrical signals.

[0092] The light source unit 1-2113 directly modulates the intensity of light in accordance with the supplied electrical signal. A directly modulable semiconductor laser can be used in the light source unit 1-2113. For example, a DFB (Distributed Feedback) laser can be used in the light source unit 1-2113. However, a DBR (Distributed Bragg Reflector) or FP (Fabry-Perot) laser may also be used in the light source unit 1-2113. By using a directly modulable semiconductor laser in the light source unit 1-2113, it becomes possible to modulate the intensity of the optical signal without using an external modulator. Furthermore, by not using an external modulation method, the configuration of the optical transmission unit 1-2 can be simplified, and the cost or power consumption of the optical transmission system 100 can be reduced.

[0093] The optical wavelength division multiplexing (WDM) units 1-3 multiplex multiple optical signals of different wavelengths for transmission through a single optical fiber. Wavelength division multiplexing (WDM) technology can be applied to the optical wavelength division multiplexing units 1-3. In particular, by using LAN-WDM (Local Area Network Wavelength Division Multiplexing) technology for data center communications, multiple wavelength channels can be densely integrated, enabling high-speed and high-capacity optical transmission.

[0094] (Optical Wavelength Division Multiplexing Unit 1-3) The optical wavelength division multiplexing unit 1-3 receives multiple intensity-modulated signals, adjusts the polarization state of each optical signal, combines them in a manner assigned to a predetermined wavelength channel, and outputs them via a single optical fiber.

[0095] Figure 9 is a block diagram showing a first example of the configuration of the optical wavelength multiplexing unit 1-3. In the first example shown in Figure 9, the optical wavelength multiplexing unit 1-3 includes optical polarization adjustment units 1-3011 to 1-301n and optical multiplexing unit 1-302.

[0096] Optical polarization adjustment units 1-3011 to 1-301n each receive intensity modulated signals IM1 and IMn, respectively. Optical polarization adjustment units 1-3011 to 1-301n adjust the polarization state of each wavelength channel input to the optical wavelength division multiplexing unit 1-3 to a predetermined standard. In the optical transmission system 100, optical signals are input in a vertical or parallel polarization state. By having optical polarization adjustment units 1-3011 to 1-301n, the optical transmission system 100 can perform appropriate polarization control when polarization interleaving technology is applied. The input polarization state is predetermined as either vertical polarization or parallel polarization. Optical polarization adjustment units 1-3011 to 1-301n adjust the input polarization state to a predetermined polarization state using passive devices such as waveplates or phase plates. For example, optical polarization adjustment units 1-3011 to 1-301n can adjust linear polarization, circular polarization, or elliptical polarization by combining a quarter-wave plate (λ / 4 plate) or a half-wave plate (λ / 2 plate), respectively.

[0097] The optical multiplexer 1-302 combines the polarization-adjusted optical signals based on predetermined wavelength channels and outputs them as a single wavelength-multiplexed signal WM. For example, the optical multiplexer 1-302 can combine each wavelength component based on predetermined wavelength channels by using an arrayed waveguide grating (AWG), an optical coupling element (coupler), or equivalent optical combining means. The intensity-modulated signals IM1 to IMn are signals supplied from different optical transmitters 1-21 and 1-2n, respectively, and correspond to wavelength channels or grids compliant with ITU-T or IEEE, which have predetermined wavelength bands.

[0098] Figure 10 is a block diagram showing a second example of the configuration of the optical wavelength division multiplexing unit 1-3. In the second example shown in Figure 10, the optical wavelength division multiplexing unit 1-3 generates a wavelength division multiplexed signal by wavelength division multiplexing an intensity-modulated signal onto a subwavelength group composed of orthogonal polarizations, adjusting each polarization, and then recombining them using polarization multiplexing.

[0099] In the second example shown in Figure 10, the optical wavelength multiplexing unit 1-3 includes optical multiplexing units 1-3111 and 1-3112, optical polarization adjustment unit 1-312, and optical polarization adjustment unit 1-313.

[0100] Optical multiplexers 1-3111 and 1-3112 are equipped with optical fiber input ports that receive intensity modulated signals IMn from intensity modulated signals IM1 of different wavelengths. Optical multiplexers 1-3111 and 1-3112 are wavelength multiplexed into subwavelength groups, similar to optical multiplexer 1-302.

[0101] Optical polarization adjustment units 1-312 and 1-313 pass each subwavelength signal formed as a subwavelength group through a waveplate or phase plate and adjust each signal so that it is in a desired polarization state or a state where each signal is orthogonal to the others. The polarized subwavelength signals are then combined again in the optical polarization multiplexing unit 1-314. In the optical polarization multiplexing unit 1-314, the subwavelength signals are combined using orthogonal polarization to generate the final wavelength multiplexed signal WM.

[0102] As described above, the optical polarization multiplexing unit 1-314 can send a stable and high-quality wavelength multiplexed signal WM to the optical transmission line 2 by using a polarization adjustment element or a wavelength combining element. Note that if polarization interleaving technology is not applied, the optical wavelength multiplexing unit 1-3 does not necessarily need to include the optical polarization adjustment units 1-3011, 1-301n, 1-312, and 1-313.

[0103] (Optical transmission line 2) Figure 11 is a block diagram showing the configuration of optical transmission line 2. Optical transmission line 2 transmits wavelength division multiplexing signals WM. In the example shown in Figure 11, optical transmission line 2 comprises an L-stage cascaded optical fiber 2-1, an optical loss compensation unit 2-2, an optical signal extraction unit 2-3, and a dispersion compensation unit 2-4.

[0104] The optical fiber 2-1 can be a single-mode fiber (SMF) with a core diameter of approximately 8 μm to approximately 10 μm and a cladding diameter of 125 μm. The optical loss compensation unit 2-2 can be an erbium-doped optical fiber amplifier (EDFA) or a semiconductor optical amplifier (SOA), etc. The erbium-doped optical fiber amplifier increases the intensity of the optical signal to maintain signal quality when the transmission distance exceeds a certain level.

[0105] The optical signal extraction section 2-3 can utilize a thin-film interference filter and a wavelength-selective switching (WSS) module. The thin-film interference filter selectively passes a specific wavelength band, removing unwanted wavelength components and thereby improving the signal-to-noise ratio (SNR). The dispersion compensation section 2-4 can utilize dispersion-shift fibers, dispersion-compensating fibers, and a phase-controllable wavelength-selective switching (WSS) module, etc. With these configurations, the optical transmission path 2 can compensate for the effects of group delay dispersion and suppress the temporal spread of the signal.

[0106] The dispersion compensation unit 2-4 ensures the dispersion of signals transmitted through the optical transmission path 2. The dispersion compensation unit 2-4 is appropriately positioned according to the transmission section. The dispersion compensation unit 2-4 is particularly effective in high data rate communications.

[0107] In the optical transmission path 2, the optical fiber 2-1, optical loss compensation unit 2-2, optical signal extraction unit 2-3, and dispersion compensation unit 2-4 are connected in an L-stage cascade, allowing each element to complement the others. This improves the transmission performance of the wavelength division multiplexing signal WM. Each component can be arbitrarily combined and arranged as appropriate according to the requirements of the optical transmission system 100. For example, in optical connections or Ethernet standards within a data center, only a 2km or 10km optical fiber 2-1 can be used as the minimum component (L=1) from the viewpoint of cost and space reduction. Also, under certain circumstances, a semiconductor optical amplifier (SOA) can be used as the optical loss compensation unit 2-2. By arbitrarily combining and appropriately arranging each component of the optical transmission path 2, the transmission efficiency of the optical transceiver can be improved while appropriately compensating for the intensity of the optical signal.

[0108] (Optical Wavelength Multiplexing Decomposition Unit 3-1) Figure 12 is a block diagram showing the configuration of the optical wavelength multiplexing decomposition unit 3-1. The optical wavelength multiplexing decomposition unit 3-1 separates the wavelength multiplexed signal WM into multiple wavelength components and sends each separated wavelength component from the optical receiving unit 3-21 to the optical receiving unit 3-2n. In the example shown in Figure 12, the optical wavelength multiplexing decomposition unit 3-1 includes an optical demultiplexing unit 3-101 and an optical signal extraction unit 3-101n derived from a plurality of optical signal extraction units 3-1011.

[0109] The optical demultiplexer 3-101 receives a wavelength-division multiplexed signal WM. The optical demultiplexer 3-101 duplicates the input wavelength-division multiplexed signal into n copies and distributes the n duplicated signals to the corresponding lanes. The optical demultiplexer 3-101 supplies the same wavelength-division multiplexed signal WM to each lane.

[0110] Optical signal extraction units 3-1011 to 3-101n extract the optical received signal ORn from the optical received signal OR1 of a corresponding specific wavelength component and send it from the subsequent optical receiving unit 3-21 to optical receiving unit 3-2n. Each of the optical signal extraction units 3-1011 to 3-101n can selectively extract only the desired wavelength component by, for example, being equipped with a band-pass filter (BPF). Furthermore, each of the optical signal extraction units 3-1011 to 3-101n can, if necessary, be equipped with an optical amplifier to appropriately adjust the light intensity of the extracted optical received signal ORn from the optical received signal OR1. By adjusting the light intensity, the optical received signal ORn is appropriately separated from the optical received signal OR1 and supplied from the optical receiving unit 3-21 to optical receiving unit 3-2n.

[0111] For example, a combination of an optical coupler and a filter can be used in the optical wavelength division multiplexing (WDM) separation unit 3-1. When using a combination of an optical coupler and a filter, the optical coupler splits the signal into multiple branched optical signals, and each branched optical signal passes through a corresponding bandpass filter, thereby selectively extracting specific wavelength components from the WDM signal. Alternatively, an AWG (Arrayed Waveguide Grating) can be used in the WDM separation unit 3-1. When an AWG is used as the WDM separation unit 3-1, the processing of the optical demultiplexing unit 3-101, the optical signal extraction unit 3-1011, and the optical signal extraction unit 3-101n can be performed together by a single processing unit. In this case, the WDM signal is supplied to the input port of the AWG, and optical signals of different wavelengths are separated and output from each output port of the AWG. By using an AWG as the WDM separation unit 3-1, wavelength separation can be performed in a more compact configuration compared to when a combination of an optical coupler and a filter is used.

[0112] (Optical Receiving Unit 3-21) Figure 13 is a block diagram showing the configuration of the optical receiving unit 3-21. Note that optical receiving units 3-21 through 3-2n each have the same configuration. Therefore, optical receiving units 3-21 through 3-2n are sometimes collectively referred to as the optical receiving unit 3-21. Also, in Figure 13, the optical receiving unit 3-21 will be described as representative. The optical receiving unit 3-21 receives the optical reception signal OR1 supplied from the optical wavelength division multiplexing / decompression unit 3-1 as input and converts the optical reception signal OR1 into an electrical signal.

[0113] In the example shown in Figure 13, the optical receiving unit 3-21 includes an optical waveform adjustment unit 3-211, a received optical power detection unit 3-212, and a photoelectric conversion unit 3-213. The optical received signal OR1 is supplied from the input terminal of the optical receiving unit 3-21 and is first input to the optical waveform adjustment unit 3-211.

[0114] The optical waveform adjustment unit 3-211 corrects the waveform of the received optical signal OR1 and shapes it into an optical signal OR1 suitable for subsequent processing. For example, by including an optical filter or wavelength selector element, the optical waveform adjustment unit 3-211 can appropriately correct the spectral characteristics of the received optical signal OR1 and improve the signal quality. Furthermore, by further including an optical amplifier, the optical waveform adjustment unit 3-211 can increase the light intensity of the optical signal OR1 and reduce signal degradation in subsequent processing. The optical signal OR1 that has passed through the optical waveform adjustment unit 3-211 is supplied to the received optical power detection unit 3-212.

[0115] The received optical power detection unit 3-212 detects the light intensity of the input optical received signal OR1 and is used to ensure that processing by the subsequent photoelectric conversion unit 3-213 is carried out properly and to evaluate the signal quality. For example, the received optical power detection unit 3-212 may be equipped with an optical power monitor. The optical power monitor extracts a portion of the optical received signal OR1 via an optical splitter and measures the light intensity with a photodetector. Furthermore, the received optical power detection unit 3-212 can properly adjust the gain of the optical amplifier provided in the optical waveform adjustment unit 3-211 by performing feedback control according to the light intensity. The optical received signal OR1 that has passed through the received optical power detection unit 3-212 is input to the photoelectric conversion unit 3-213.

[0116] The photoelectric conversion unit 3-213 converts the received optical signal OR1 into an electrical signal. For example, a photodiode can be used in the photoelectric conversion unit 3-213. The photodiode converts the optical signal OR1 into an electrical signal and outputs a received electrical signal ER1. A PIN photodiode or an avalanche photodiode (APD) can be used as the photodiode. Because APDs can perform highly sensitive reception even when the intensity of the optical signal OR1 is low, they are suitable for long-distance transmission or reception of low-power optical signals.

[0117] The photoelectric conversion unit 3-213 may include an electrical amplifier. The electrical amplifier amplifies the amplitude of the received electrical signal ER1 after photoelectric conversion and adjusts it to an amplitude that can be appropriately processed by the subsequent digital processing circuit. For example, a transimpedance amplifier (TIA) or a limiting amplifier (LA) can be used as the electrical amplifier. A TIA can amplify the weak current signal from the photodiode while converting it to a voltage signal, and is particularly effective in improving reception sensitivity at low light intensity. The method of receiving intensity using a photodiode is called direct detection, and mathematically corresponds to the process of taking the square. On the other hand, an LA contributes to the stabilization of the signal amplitude and enables signal processing suitable for high-speed data transmission.

[0118] The received electrical signal ER1 converted by the photoelectric conversion unit 3-213 is output from the output terminal of the optical receiving unit 3-21 and supplied to the subsequent received electrical processing unit 3-3. In the received electrical processing unit 3-3, post-processing related to demodulation is performed to restore the data. The configuration of the optical receiving unit 3-21 can be appropriately changed according to the type of optical received signal OR1 or the required specifications of the optical transmission system 100. As described above, the optical receiving unit 3-21 can appropriately shape the received optical received signal OR1 and perform stable photoelectric conversion while monitoring the optical power.

[0119] (Received Electrical Processing Unit 3-3) Figure 14 is a block diagram showing the functional configuration of the received electrical processing unit 3-3. The received electrical processing unit 3-3 receives the received electrical signal ERn from the received electrical signal ER1, performs predetermined electrical processing on each signal, and outputs the received binary data RBn from the received binary data RB1.

[0120] In the example shown in Figure 14, the receiving electrical processing unit 3-3 includes a DA conversion unit 3-301, a clock control unit 3-302, a symbol rate adjustment unit 3-303, a waveform shaping unit 3-304, a symbol demapping unit 3-305, and a signal analysis unit 3-306.

[0121] Each function of the receiving electrical processing unit 3-33 is realized by executing instruction codes stored in memory using electronic circuits, or by performing various processes using electronic circuits designed for special purposes. The receiving electrical processing unit 3-33 may include memory such as ROM, RAM, or HDD. Some of the functions of the receiving electrical processing unit 3-33 may be provided by devices or equipment other than the receiving electrical processing unit 3-33, and may be realized by distributed processing between the receiving electrical processing unit 3-33 and devices or equipment other than the receiving electrical processing unit 3-33.

[0122] The DA conversion unit 3-301 converts the received electrical signal ERn from the input received electrical signal ER1 into a corresponding digital signal. The DA conversion unit 3-301 converts the received electrical signal, which was input as an analog signal, into a format suitable for the subsequent digital processing circuit. The output of the DA conversion unit 3-301 is sent to the clock control unit 3-302.

[0123] The clock control unit 3-302 performs clock synchronization processing on the digital signal from the DA conversion unit 3-301 to correct the phase difference with the reference clock. Specifically, the clock control unit 3-302 uses a delay-locked loop (DLL) or a phase-locked loop (PLL) to synchronize the phase of the input signal with the internal clock. This improves the time-axis accuracy in subsequent digital signal processing. The output of the clock control unit 3-302 is sent to the symbol rate adjustment unit 3-303.

[0124] The symbol rate adjustment unit 3-303 converts the symbol rate of the input signal to a predetermined rate. For example, when received signals are supplied from multiple transmitters having different symbol rates, the symbol rate adjustment unit 3-303 can convert the received signals to a unified symbol rate. Specifically, the symbol rate adjustment unit 3-303 can perform appropriate rate conversion using techniques such as decimation or interpolation. The output of the symbol rate adjustment unit 3-303 is sent to the waveform shaping unit 3-304.

[0125] The waveform shaping unit 3-304 performs waveform shaping processing on the output from the symbol rate adjustment unit 3-303 to improve the signal quality. The waveform shaping unit 3-304 can use digital filters such as FFE (Feed-Forward Equalizer) for waveform shaping. The FFE performs adaptive filtering in the time domain and corrects the channel's impulse response to reduce inter-symbol interference (ISI). Furthermore, by using the LMS (Least Mean Squares) algorithm as the adaptive filter, correction according to the channel characteristics can be performed. The output of the waveform shaping unit 3-304 is sent to the symbol demapping unit 3-305.

[0126] The symbol demapping unit 3-305 applies a predetermined demodulation process to the output from the waveform shaping unit 3-304 and outputs received binary data RB1 to received binary data RBn. For the predetermined demodulation process, for example, PAM demodulation can be used. In PAM demodulation, the amplitude value of each received symbol is determined and converted to digital data based on a predetermined threshold. For example, in OOK, bits are assigned based on high and low binary levels, and in quaternary PAM (PAM4), bits are assigned based on four amplitude levels. After the demodulation process is completed, the signal analysis unit 3-306 calculates an index of the quality of the received signal.

[0127] The signal analysis unit 3-306 evaluates the bit error rate (BER), Q-factor, and signal-to-noise ratio (SNR) of the received signal to analyze the signal quality. The analysis performed by the signal analysis unit 3-306 allows for monitoring of the system's operating status and adaptive correction processing as needed. Furthermore, a configuration for decoding error correction codes (FEC) may be included after the signal analysis unit 3-306. Performing further decoding of the error correction code (FEC) on the demodulated signal can further improve the signal quality.

[0128] The optical receiver control unit 4-3 controls the operation of the receiving electrical processing unit 3-3 by setting parameters or supplying control signals. The optical receiver control unit 4-3 controls, for example, the resolution of the DA conversion unit 3-301, the synchronization parameters of the clock control unit 3-302, the conversion ratio of the symbol rate adjustment unit 3-303, the filter coefficients of the waveform shaping unit 3-304, the demodulation method and threshold processing of the symbol demapping unit 3-305.

[0129] As described above, the receiving electrical processing unit 3-3 sequentially performs DA conversion, clock synchronization, symbol rate adjustment, waveform shaping, demodulation processing, and signal analysis on the received electrical signals ER1 to ERn, thereby obtaining the received binary data RBn from the received binary data RB1, calculating BER, Q value, and SNR, and evaluating the quality of the received signal.

[0130] <Nonlinear Pre-equalization Processing of Optical Transmission System 100> Next, the nonlinear pre-equalization processing of the optical transmission system 100 will be described. Specifically, the calculation of the backpropagation characteristics of the optical transmission path 2 using the nonlinear propagation equation, the calculation of intensity strain by the intensity strain acquisition unit 1-145, and the signal processing by the nonlinear correction unit 1-1481 to the nonlinear correction unit 1-148n will be described in detail.

[0131] The nonlinear propagation equation used to describe wave propagation in optical fibers and nonlinear media is called the Nonlinear Schrödinger Equation (NLSE), and is modeled as shown in equation (1), for example (see, for example, the non-patent document "E. Mateo and G. Li, "Compensation of interchannel nonlinearities using enhanced coupled equations for digital backward propagation," Applied Optics, vol. 48, no. 25, pp. F6-F10, 2009").

[0132]

[0133] In equation (1), each term on the left side represents the main signal field E at the m-th wavelength with respect to the transmission distance z.ｍ This shows the change in (z, t), where α represents the loss coefficient in the optical fiber, and β ２ and β ３ The `γ` and `δk` coefficients represent the dispersion coefficients that show the effects of quadratic and cubic variances that contribute to the temporal spread of the optical signal. Furthermore, γ represents a nonlinear coefficient, and δk ｒｓｌｍ The θ-θ parameter represents the phase matching parameter. The fifth term on the left side represents the nonlinear effect considering self-phase modulation and cross-phase modulation. The fifth term on the left side also represents the nonlinear effect due to four-wave mixing considering the interaction of multiple wavelength channels. l = r + s - m, [m, r, s] ∈ H and r ≠ s ≠ m. This ensures that the waves newly generated by four-wave mixing exist within the analysis bandwidth of the wavelength division multiplexing signal WM, and that the effects of nonlinear interactions can be appropriately represented while considering the degree of frequency and phase matching.

[0134] The constraint r≠s≠m is a constraint to exclude self-phase modulation and cross-phase modulation, and it is a constraint to clarify how four-wave mixing interacts. Phase matching parameter δk ｒｓｌｍ This is expressed by the following equation (2): Phase matching parameter δk ｒｓｌｍ This is important for demonstrating phase and frequency matching.

[0135] In equation (2), Δω represents the angular frequency difference and is defined as Δω = 2π・Δf using the channel spacing Δf. Equation (1) can be simplified to equation (3) using the linear operator D^, the phase modulation operator N^, and the four-wave mixing operator F^.

[0136] Here, each operator corresponds to the following expressions (4), (5), and (6).

[0137]

[0138]

[0139]

[0140] Since the newly generated four-wave mixing component has a power significantly lower than the signal component, the effects of self-phase modulation and cross-phase modulation can be ignored. However, the effect of wavelength dispersion remains, and therefore, the following equation (7) must be considered for the four-wave mixing operator F^.

[0141]

[0142] From equations (3) and (7), the E obtained after propagation through the small interval h is obtained. ｍ (z+h, t) can be approximately calculated using the following equation (8) (see Non-Patent Literature "E. Mateo and G. Li, "Compensation of interchannel nonlinearities using enhanced coupled equations for digital backward propagation," Applied Optics, vol. 48, no. 25, pp. F6-F10, 2009" and Non-Patent Literature "DS Millar, S. Makovejs, C. Behrens, S. Hellerbrand, RI Killey, P. Bayvel, and Seb J. Savory, "Mitigation of fiber nonlinearity using a digital coherent receiver," IEEE Journal of Selected Topics in Quantum Electronics, vol. 14, no. 5, pp. 1063-1074, 2008").

[0143]

[0144] In equation (8), the approximation accuracy from the second equation to the third equation is affected by the magnitude of h. h is called the step size. If h is too small, the calculation time increases; if it is too large, numerical instability occurs, and accurate results cannot be obtained. Therefore, it is important to select h appropriately. The optical transmission system 100 uses a direct detection method. Therefore, the intensity-modulated signal obtained at the receiver is expressed by the following equation (8).

[0145]

[0146] Here, in order to distinguish between the main signal and the distortion term caused by the four-wave mixing, the main signal intensity is set to l ｍ Main signal field E ｍ The product of (z, t) and the optical field newly generated by the four-wave mixing is I ｓｉｇ－ＦＷＭ The light intensity newly generated by the four-wave mixing is I ＦＷＭ Let's assume that. ｓｉｇ－ＦＷＭ and I ＦＷＭ This corresponds to nonlinear inter-channel crosstalk due to four-wave mixing, and since F^ is the product of complex electric fields involved in the interaction, it can be qualitatively understood that the greater the intensity in the eye pattern, the more the distortion is emphasized. The result of propagation in the reverse direction through optical transmission path 2 is obtained from equation (1) by inverting the loss coefficient, dispersion coefficient, and nonlinear coefficient. Therefore, based on equation (8), the complex electric field amplitude E after reverse propagation is obtained. ｍ，ＢＰ (z+h, t) is expressed by the following equation (10).

[0147]

[0148] The digital backpropagation method is a method of applying equation (10) in the forward direction to the optical transmission path 2. E propagated by h ｍ，ＤＢＰ (z+h, t) is expressed by the following equation (11-1).

[0149]

[0150] Assuming that the four-wave mixing is approximately reversible in the small interval h, the following equation (11-2) holds. Therefore, equation (11-1) can be expressed as the following equation (12). Equation (12) is given by the original main signal field E ｍ This means that (z, t) is restored.

[0151]

[0152]

[0153] Equations (11-1) and (12) support the idea that the digital backpropagation method with optical amplitude and phase modulation is an ideal preequalization. Next, we consider preequalization by backpropagation intensity. Preequalization by backpropagation intensity is given by Equation (11) ｍ，ＤＢＰ (z+h, t) is |E ｍ，ＤＢＰThis is equivalent to replacing it with (z+h, t)|. The intensity of the complex electric field amplitude |E| obtained by applying the digital backpropagation method. ｍ，ＤＢＰ (z+h, t) | ２ This can be expressed by the following equation (13).

[0154]

[0155] When the complex electric field amplitude calculated by the digital backpropagation method is transmitted as the square root of its intensity, that is, |E| in equation (13) ｍ，ＤＢＰ (z+h, t)| is E in equation (11-1) ｍ，ＤＢＰ The solution when substituted with (z+h, t) is expressed by the following equation (14-1).

[0156]

[0157] In the optical receiver 3, square detection is performed, and the information used for signal analysis is the intensity of equation (14-1) above. Therefore, the received intensity is expressed by equation (15-1), using the following equation (14-2), which is a real number.

[0158]

[0159]

[0160] Generally, the main signal intensity is 10 to 20 times or more the intensity of the light newly generated by the four-wave mixing. Therefore, equations (15-2) and (15-3) generally hold true.

[0161]

[0162]

[0163] Since we are assuming an intensity-modulated signal, |E ｍ (z, t) | = E ｍ (z, t). Therefore, in equation (15-1), the following equation (16-1) holds.

[0164]

[0165] Comparing equation (9) and equation (16-1), except for the following equation (16-2), which is the dispersion term, the main signal field E ｍ The product of (z, t) and the newly generated optical field I from the four-wave mixing ｓｉｇ－ＦＷＭand the newly generated light intensity I from the four-wave mixing ＦＷＭ Each effect is doubled. Therefore, using the intensity of the backpropagated complex electric field amplitude may result in greater waveform distortion than an eye pattern without pre-equalization. Quantitatively, by converting the phase-inverted complex electric field amplitude to intensity using the digital backpropagation method as shown in equation (10), it acts as a nonlinear distortion similar to that during forward propagation, as shown in equation (13). This can be interpreted as adding the same amount of nonlinear distortion as when the optical transmission path 2 propagates twice the distance. From the above, it appears difficult to pre-equalize or compensate at the receiving end for nonlinear optical effects, mainly caused by four-wave mixing that affect the complex plane, using intensity modulation and direct detection, which result in the loss of phase information.

[0166]

[0167] In the optical transmission system 100, it is noted that even nonlinear distortion appearing on the complex plane is converted into intensity distortion upon reception, and the intensity distortion is subtracted in advance in the optical transmitter 1. In the optical transmission system 100, nonlinear backpropagation E ｍ，ＤＢＰ (z+h, t) and linear backpropagation E ｍ，ＣＤＣ The complex electric field amplitude obtained from (z+h, t) is converted to intensity, and the difference is calculated as shown in equation (17-1). This gives the intensity distortion |E| generated at the receiving end. ｍ，ＦＷＭ－ｅｓｔ Information regarding (z+h, t)| is acquired in advance by the optical transmitter 1.

[0168]

[0169] Next, in intensity modulation schemes or propagation in optical fibers, the following two conditions are met in many situations. Firstly, since the main signal intensity is 10 to 20 times or more the light intensity newly generated by the four-wave mixing, equations (17-2) and (17-3) are met, and equation (17-4) is satisfied.

[0170]

[0171]

[0172]

[0173]

[0174]

[0175] Secondly, in order to guarantee a one-to-one relationship between the electric field after intensity modulation and the electric field of direct detection, a DC bias must be added to the transmitted intensity signal and satisfy equation (17-5). In Ethernet optical transceivers or directly modulated lasers, extinction is often insufficient, and equation (17-6) holds true as a realistic extinction ratio of 10 dB or less. Considering the conditions of equations (17-4) and (17-6), using the output result of equation (17-1), the intensity of the pre-equalized signal |E as shown in equation (18) ｍ，Ｐｒｅｃｏｍｐ (z+h, t) | ２ You can obtain it.

[0176]

[0177] Perform a square root operation on the pre-equalization intensity obtained by equation (18), and in the same way as in the derivation of equation (14-1), E in equation (11) ｍ，ＤＢＰ (z+h, t) to |E ｍ，Ｐｒｅｃｏｍｐ Replace it with (z+h, t)|. This gives the transmission characteristics E of the pre-equalized signal. ｍ，Ｐｒｅｃｏｍｐ (z + 2h, t) is expressed by equation (19).

[0178]

[0179] The signal of interest in the optical receiver 3 is E ｍ，Ｐｒｅｃｏｍｐ This is the intensity at (z + 2h, t). Therefore, the intensity information obtained after transmitting the pre-equalized signal is expressed by the following equation (20).

[0180]

[0181] In equation (20), the main signal term after direct detection is |E ｍ (z, t) | ２ Only is obtained. From this, the strength strain |E obtained based on the conditions of equations (17-4) and (17-6) is obtained. ｍ，ＦＷＭ－ｅｓｔ (z, t) | ２ Linear backpropagation strength | E ｍ，ＣＤＣ (z, t) | ２ By correcting for this, it can be seen that pre-equalization can be performed using only intensity modulation.

[0182] <Verification and Consideration of Operation of Optical Transmission System 100> Figure 15 shows an example of the eye pattern of pre-equalized intensity obtained by the optical transmission system 100. Figure 15 shows the eye pattern of the intensity signal obtained by pre-equalizing the signal on the central short wavelength side of the four wavelengths. In the example shown in Figure 15, four PAM4 signals modulated at 200 Gbaud were wavelength-multiplexed at 400 GHz intervals, and the generated optical wavelength-multiplexed signal was transmitted over 10 km near zero dispersion using a single-mode fiber. The extinction ratio of the PAM4 signal was set to 6 dB in accordance with the general Ethernet standard. Considering the effect of four-wave mixing, where distortion increases with higher intensity levels, it was found that pre-equalization was performed to make the eye pattern smaller at low intensity levels and larger at high intensity levels, as shown in Figure 15.

[0183] Figures 16A to 16D show the eye patterns and histograms of intensity signals obtained by extracting the signal on the central short wavelength side of the four wavelengths when intensity modulated signals with and without pre-equalization are transmitted forward to the optical transmission line 2. Figure 16A is a first example of the eye pattern obtained without pre-equalization in the optical transmission system 100. Figure 16B is a histogram of intensity and frequency obtained in Figure 16A. Figure 16C is a first example of the eye pattern obtained with pre-equalization in the optical transmission system 100. Figure 16D is a histogram of intensity and frequency obtained in Figure 16C.

[0184] As shown in Figures 16A to 16D, it was found that pre-equalization equalizes the intervals between intensity levels to some extent, suppressing the effects of nonlinear inter-channel crosstalk due to four-wave mixing. In pre-equalization in the optical transmission system 100, the square root operation is performed on the intensity in equation (18), and the intensity obtained by pre-equalization is converted into an electric field. Therefore, equation (18) must be greater than or equal to 0.

[0185] In intensity modulation, it was assumed that equation (17-6) generally holds true. Here, we will specifically consider the boundary conditions of equation (17-6). Figures 17A to 17I show the intensity signals obtained by pre-equalizing the signal on the central short wavelength side of the four wavelengths when the extinction ratio and the input power per channel to the optical transmission line are changed, i.e., |Em, Precomp(z+h,t)| ２ An example of the simulation results for the eye pattern is shown. However, since the waveform broadening due to wavelength dispersion may greatly increase the effect of intensity distortion, the effect of wavelength dispersion was included in the simulation from Figure 17A to Figure 17I.

[0186] Figure 17A shows an example of an eye pattern in the optical transmission system 100 with an extinction ratio of 6 dB and an input power of 5.0 dBm. Figure 17B shows an example of an eye pattern in the optical transmission system 100 with an extinction ratio of 6 dB and an input power of 10.0 dBm. Figure 17C shows an example of an eye pattern in the optical transmission system 100 with an extinction ratio of 6 dB and an input power of 12.5 dBm. Figure 17D shows an example of an eye pattern in the optical transmission system 100 with an extinction ratio of 10 dB and an input power of 5.0 dBm. Figure 17E shows an example of an eye pattern in the optical transmission system 100 with an extinction ratio of 10 dB and an input power of 10.0 dBm. Figure 17F shows an example of an eye pattern in the optical transmission system 100 with an extinction ratio of 10 dB and an input power of 12.5 dBm. Figure 17G shows an example of an eye pattern in the optical transmission system 100 with an extinction ratio of 100 dB and an input power of 5.0 dBm. Figure 17H ​​shows an example of an eye pattern in the optical transmission system 100 with an extinction ratio of 100 dB and an input power of 7.5 dBm. Figure 17I shows an example of an eye pattern in the optical transmission system 100 with an extinction ratio of 100 dB and an input power of 10.0 dBm.

[0187] In the region below a realistic extinction ratio of 10 dB, it was found that the pre-equalization intensity is greater than or equal to 0 as long as the input power does not exceed 10 dBm. On the other hand, in the case of a very large extinction ratio of 100 dB, it was found that the pre-equalization intensity enters the negative region when the input power exceeds 5.0 dBm. However, since the possible negative values ​​are very small compared to the maximum positive value, it was found that performance improvement through pre-equalization can generally be expected by adding the nonlinear correction shown later.

[0188] Figure 18 shows a second example of an eye pattern obtained without pre-equalization in the optical transmission system 100. Figure 18 shows the eye pattern of the intensity signal obtained by extracting the signal on the central short wavelength side of the four wavelengths after transmission at an input power of 7.5 dBm with an extinction ratio of 100 dB when no pre-equalization is performed. Compared with Figure 17H ​​described above, which is under the same conditions as the simulation in Figure 18, pre-equalization is performed to make the eye pattern smaller at high intensity levels and larger at low intensity levels. From this, it was found that the signal quality at the optical receiver 3 can be improved in the optical transmission system 100 by performing pre-equalization considering the effect of wavelength dispersion.

[0189] Next, we considered how equation (18) can provide a constraint for reversible operation in the subsequent intensity and field conversion when the extinction ratio or input power to the optical fiber is very large. This constraint means that the field obtained from equation (18) cannot take a complex number in order for intensity modulation to be established. In order to improve signal performance by increasing the extinction ratio or input power to the optical fiber, a correction is required so that equation (18) becomes a value greater than or equal to 0. In the optical transmission system 100, a normalized linear function f(x) was used as an example. The normalized linear function f(x) is a function defined by the following equation (21). By performing a nonlinear transformation using the normalized linear function f(x), the input variable is always transformed to a positive value.

[0190]

[0191] Specifically, a normalized linear function is used for the pre-equalization intensity f(|E) ｍ，Ｐｒｅｃｏｍｐ (z+h, t) | ２By performing a nonlinear correction that results in ), intensity modulation can be achieved through subsequent intensity and field conversion under any extinction ratio or input power conditions. In other words, the control device 4 uses a normalized linear function to pre-equalize each of the multiple optical signals, thereby enabling intensity modulation through subsequent intensity and field conversion under any extinction ratio or input power conditions, and facilitating pre-equalization.

[0192] For the sake of simplicity, equations (8) through (21) assume that the optical transmission path 2 is calculated from a one-step nonlinear Schrödinger equation. However, in actual calculations of the optical transmission path 2, it is preferable to use the split-step method to improve calculation accuracy. Here, E ｍ，ＤＢＰ (z+h, t) is calculated from the nonlinear backpropagation unit 1-1432, which includes the first wavelength dispersion compensation unit 1-14321, electrical signal replication unit 1-14322, intensity detection unit 1-14323, nonlinear phase calculation unit 1-14324, multiplication unit 1-14325, and subsequent wavelength dispersion compensation unit 1-14326, all of which are cascaded in N stages as shown in Figure 4 above.

[0193] E ｍ，ＣＤＣ (z+h, t) is calculated from the linear backpropagation section 1-1433, which includes the second wavelength dispersion compensation section 1-14331. When an N-stage cascade is connected, it is necessary to apply dispersion compensation corresponding to the optical transmission path length L. In this case, the first wavelength dispersion compensation section 1-14321 and the subsequent wavelength dispersion compensation section 1-14326 are expressed by the following equation (22) using a step size h = L / N and a linear operator D^.

[0194]

[0195] When performing dispersion compensation in the frequency domain, the Fourier transform F and the inverse Fourier transform F are used. －１ It can be expressed using the following equation (23).

[0196]

[0197] On the other hand, the output field E of the second wavelength dispersion compensation unit 1-14331 ｍ，Ｂｌｕｋ－ＣＤＣ For (z + L, t), it can be expressed by the following equations (24) and (25).

[0198]

[0199]

[0200] The intensity strain acquisition unit 1-145 shown in Figure 3 above uses E obtained from the backpropagation calculation unit 1-143. ｍ，ＤＢＰ (z + L, t) and E ｍ，ＣＤＣ From (z + L, t), using the strength generation unit 1-1455 shown in Figure 5 above, |E ｍ，ＤＢＰ (z+h, t) | ２ Using the strength generation unit 1-1456 | E ｍ，ＣＤＣ (z+h, t) | ２ Each of these is calculated. Then, using the subtraction unit 1-1457, the strength strain |E shown in equation (17) is calculated. ｍ，ＦＷＭ－ｅｓｔ (z+h, t) | ２ This is calculated. Meanwhile, the linear backpropagation intensity separation unit 1-146 is |E ｍ，ＣＤＣ (z+h, t) | from | E ｍ，ＣＤＣ (z+h, t) | ２ Calculate.

[0201] The optical transmission system 100 receives |E from the intensity strain acquisition unit 1-145 and the linear backpropagation intensity separation unit 1-146. ｍ，ＦＷＭ－ｅｓｔ (z+h, t) | ２ and | E ｍ，ＣＤＣ (z+h, t) | ２ This is provided to the intensity correction unit 1-147. The intensity correction unit 1-147 performs the calculation corresponding to equation (18). This results in the pre-equalized intensity |E ｍ，Ｐｒｅｃｏｍｐ (z+h, t) | ２ This is obtained. Finally, in the nonlinear correction units 1-1481 to 1-148n, a nonlinear conversion of the input and output is performed, for example, on the condition that it is 0 or greater, corresponding to equation (21). As a result, the optical transmission system 100 is able to |E under any conditions. ｍ，Ｐｒｅｃｏｍｐ (z+h, t) | ２ The intensity can be modulated.

[0202] In the optical transmission system 100, the main signal intensity is sufficiently smaller than the electric field or intensity of the nonlinear distortion mainly caused by the four-wave mixing, and a nonlinear correction is applied so that the pre-equalized intensity does not lie on the complex plane in intensity modulation, adding the constraint that the intensity of the pre-equalized optical signal is 0 or greater. This makes it possible to pre-correct the intensity distortion of the nonlinear crosstalk between wavelength channels caused by the four-wave mixing generated in the optical receiver 3 using the transmitted intensity-modulated signal. Furthermore, in the optical transmission system 100, the phase matching condition is included in equation (2), and the linear operator D^ is included in equation (18). For this reason, the first embodiment of this disclosure can eliminate the assumption that the light related to the four-wave mixing is in phase, or that the wavelength dispersion or dispersion gradient is 0, and is therefore widely applicable to optical transmission systems using wavelengths close to the general zero-dispersion wavelength.

[0203] In the optical transmission system 100, the optical transmitter 1 transmits information E for each wavelength channel. ｍ While (z, t) is used, the Ethernet standard stores binary data or signal information for each wavelength channel in a single optical transceiver. Therefore, all wavelength channel data can be easily accessed.

[0204] It is also conceivable that the control target of the control device 4 according to the first embodiment of this disclosure may be the optical receiver 3 instead of the optical transmitter 1. However, the light generated by the four-wave mixing may extend over a wider range than the total bandwidth of the optical receiver 3. Therefore, it is not possible to estimate the interaction of the four-wave mixing caused by light outside the receiver bandwidth. Accordingly, in the optical transmission system 100, it is more preferable to perform pre-equalization at the optical transmitter 1 from the viewpoint of compensation accuracy. For the sake of explanation, it was assumed that the linear operator D^, the phase modulation operator N^, and the four-wave mixing operator F^ are independent of wavelength m, but the pre-equalization accuracy can be improved by using operators corresponding to each wavelength m. Thus, in the first embodiment of this disclosure, it is possible to provide a control device 4, an optical transmission system 100, and a control method that can control the intensity-modulated signal to a desired quality in optical wavelength division multiplexing transmission using a wavelength band close to the zero-dispersion wavelength.

[0205] <Evaluation of transmission characteristics by optical transmission system 100> In order to evaluate the transmission characteristics of nonlinear preequalization in optical transmission system 100, a 1.6-Tb / s class O-band DWDM optical communication system was constructed, and the signal quality was numerically verified under three input polarization conditions: same polarization XXXX, alternating polarization XYXY, and paired polarization XYYX.

[0206] For the numerical simulation, a system consisting of four channels of 200 Gbaud PAM-4 signals was used. The wavelengths of each wavelength channel were four wavelengths symmetrical around the zero-dispersion wavelength of 1310 nm. The spacing between the wavelength channels was set to 400 GHz. To digitally compensate for inter-wavelength channel crosstalk caused by four-wave mixing, the nonlinear pre-equalization unit 1-14 upsampled the input PAM-4 signal to 8 Sa / symm and digitally constructed the WDM bandwidth.

[0207] The optical signal was to be transmitted via a 10 km single-mode fiber. This single-mode fiber has a loss coefficient α = 0.3 dB / km, a nonlinear coefficient γ = 1.8 / W / km, and β ２ The related variance parameters D = 0 ps / nm / km, and β ３ The related dispersion gradient S = 0.09 ps / nm ２ It was designed to have the characteristic of being / km.

[0208] The input optical power was adjusted to investigate the effects of optical fiber nonlinearity, and the extinction ratio for each wavelength channel was set to 6 dB based on Ethernet standards. The propagation characteristics of the optical signal were modeled by numerically solving the coupled nonlinear Schrödinger equation using the split-step Fourier method. At this time, the input signal was upsampled again at 512 Sa / symm to obtain a total electric field representation. After optical transmission, the received optical signal was separated by a wavelength demultiplexer, detected by a photodetector, and then processed using standard digital signal processing techniques. Specifically, a 51-tap feedforward equalizer (FFE) was used to evaluate the BER. The receiver operating parameters were set to match the operating parameters described in Non-Patent Literature 2. In order to evaluate the nonlinear distortion under the worst conditions, the maximum BER among the four channels was evaluated while excluding the effects of polarization mode dispersion (PMD).

[0209] Figure 19 shows an example of the simulation results of the BER curve with respect to the received power in the optical transmission system 100. Figure 19 shows a comparison of the BER characteristics with and without pre-equalization by the optical transmission system 100 in the transmission of a 4-ch. ×200 Gbaud PAM4 signal. In calculating the BER, 100 propagation simulations were performed for different optical fiber conditions, and the average value was used. In this evaluation, three types of input polarization states were adopted: (i) all wavelength channels with the same polarization (XXXX), (ii) alternating polarization (XYXY), and (iii) pair polarization (XYYX). In each polarization state, the input optical power to the optical fiber for each wavelength channel was set to 4.5 dBm, 9.0 dBm, and 9.5 dBm. Pre-equalization in the optical transmission system 100 was implemented in a single-stage configuration to reduce the computational load on the optical transmitter 1 side.

[0210] In Figure 19, graph 191, enclosed in a dashed-dotted circle, shows the simulation results when pre-equalization is performed. Graph 192, enclosed in a double-dotted-dotted circle, shows the simulation results when pre-equalization is not performed. In graph 191, BER decreases smoothly with increasing received light intensity, and BER saturation does not occur even in the high-power region. On the other hand, in graph 192, the improvement in BER saturates, and 10 －３ It plateaued around that point. In particular, in the case of alternating polarization (XYXY), although the gain of nonlinear preequalization is relatively small, BER = 3.8 × 10 －３ We were able to confirm an improvement in reception sensitivity of 1.8 dB.

[0211] Figure 20 shows an example of simulation results for improving sensitivity in the optical transmission system 100 under different input power and polarization conditions. Figure 20 shows the amount of improvement in received sensitivity when nonlinear preequalization is applied to a single-stage configuration in the optical transmission system 100. Figure 20 also shows the results measured by changing the fiber input optical power in 4-ch. × 200-Gbaud PAM4 signal transmission.

[0212] The simulation results in Figure 20 show that the nonlinear preequalization in the optical transmission system 100 is effective in all of the evaluated input polarization states and exhibits high system robustness in any polarization interleaving scheme. Furthermore, the simulation results in Figure 20 suggest that an improvement of 3 dB or more in receiving sensitivity can be expected, and this improvement suggests the possibility of doubling the symbol rate or doubling the transmission distance.

[0213] Next, we investigated the effect of the number of nonlinear preequalization stages on the BER characteristics. Figure 21 shows an example of the simulation results of the dependence of step size and number of stages in the optical transmission system 100. In the simulation in Figure 21, the BER characteristics were analyzed with a low nonlinear tolerance co-polarization (XXXX) configuration, with the fiber input optical power set to 4.5 dBm and the received optical power to -10 dBm. As a result, changing the number of nonlinear preequalization stages and the step size of the backpropagation process had almost no effect on the system's BER characteristics. This suggests that the interaction between chromatic dispersion (CD) and fiber nonlinear effects is extremely small near the zero-dispersion wavelength of a single-mode fiber.

[0214] The nonlinear pre-equalization unit 1-14 of the optical transmission system 100 shown in Figure 2 above can effectively compensate for the interaction caused by four-wave mixing (FWM) between wavelength channels through a single-step backpropagation calculation. This significantly reduces computational costs while achieving equivalent compensation performance compared to conventional methods using multi-stage configurations, such as those represented by digital backpropagation methods.

[0215] <Processing of Control Device 4 when Parameters are Unknown> In the above explanation, it was assumed that the parameters of the optical transmission path 2 are known. However, there may be cases where the correct values ​​of the fiber length, loss coefficient, dispersion coefficient, dispersion gradient, and nonlinear coefficient are unknown. Even in such situations, the control device 4 can perform nonlinear preequalization in cooperation with the optical receiver 3. For example, in order to achieve adaptive parameter adjustment between the optical transmitter 1 and the optical receiver 3, the control device 4 can perform negotiation between the optical transmitter 1 and the optical receiver 3 via the signal control unit 4-2. Specifically, even when the parameters of the optical transmission path 2 are unknown, the optical transmission system 100 can be set to the best performance by performing the processing shown in Figures 22 to 24 below.

[0216] (First example of signal control processing) Figure 22 shows a first example of signal control processing by the control device 4. As shown in Figure 22, the control device 4 has an optical receiver control unit 4-3, an optical transmitter control unit 4-1, and a signal control unit 4-2 that work together to optimize the operating parameters of the transmitting and receiving sides, thereby improving the quality of communication. The details of the signal control processing in the control device 4 will be described below.

[0217] In the first example shown in Figure 22, the process of optimizing signal control is initiated by executing a predetermined signal test cycle. Specifically, the optical transmitter control unit 4-1 sets the operating parameters of the optical transmitter 1 via the signal control unit 4-2 and transmits a test signal to the optical receiver 3. In response to this transmission, the optical receiver control unit 4-3 analyzes the received signal and optimizes the operating parameters on the receiving side. In the signal control optimization process, the optimal set of parameters between the optical transmitter 1 and the optical receiver 3 is determined by repeating the signal test cycle multiple times. After receiving the test signal, the optical receiver control unit 4-3 evaluates the quality of the received signal, and the optical transmitter control unit 4-1 performs adaptive parameter adjustments. This evaluation process includes, for example, measurements of BER, received optical power, Q value, or SNR.

[0218] Next, we will explain the negotiation between the optical transmitter 1 and the optical receiver 3. In the optical transmission system 100, negotiation takes place between the optical transmitter 1 and the optical receiver 3 in order to properly adjust the parameters of the optical transmitter 1 and the optical receiver 3. As shown in Figure 22, parameter adjustment information is exchanged between the optical transmitter control unit 4-1 and the optical receiver control unit 4-3, and the optimal operating conditions for the optical transmitter 1 and the optical receiver 3 are determined.

[0219] First, the optical transmitter control unit 4-1 issues a parameter change request for the optical transmitter 1 via the signal control unit 4-2. Next, the optical receiver control unit 4-3 analyzes the results of receiving the test signal and determines the optimal set of parameters. The parameter information determined on the receiving side is transmitted to the optical transmitter control unit 4-1 via the signal control unit 4-2. Based on this information, the optical transmitter control unit 4-1 sets the optimal signal output conditions.

[0220] After the optimal parameters are determined, the actual transmission of the data signal begins. This negotiation allows both the optical transmitter 1 and the optical receiver 3 to adjust their operating parameters in coordination, improving the overall performance of the optical transmission system 100. In the optical transmission system 100, the negotiation order between the optical transmitter 1 and the optical receiver 3 is not necessarily fixed and can be changed as appropriate. After the entire signal test cycle has been completed, a nonlinear pre-equalization signal is transmitted.

[0221] (Second example of signal control processing) Figure 23 shows a second example of signal control processing by the control device 4. In the second example shown in Figure 23, the control device 4 can negotiate between the optical transmitter control unit 4-1 and the optical receiver control unit 4-3 without going through the signal control unit 4-2, and adaptively adjust the operating parameters of the optical transmitter 1 and the optical receiver 3.

[0222] In the second example shown in Figure 23, the process of optimizing signal control is first initiated by performing a predetermined signal test cycle. The optical transmitter control unit 4-1 transmits a test signal to the optical receiver 3. The signal quality is evaluated on the optical receiver 3 side. The optical receiver control unit 4-3 analyzes the received parameters and performs adaptive adjustments. In the second example, the test signal cycle is repeated multiple times to establish optimal operating conditions between the optical transmitter 1 and the optical receiver 3. During the signal test, BER, Q value, SNR, etc., are measured, and the optical receiver 3 side receives feedback on the optimal parameters. In the second example shown in Figure 23, the optical transmitter control unit 4-1 and the optical receiver control unit 4-3 communicate directly to determine the optimal parameters.

[0223] Next, adjustments are made between the optical transmitter 1 and the optical receiver 3. First, the optical transmitter control unit 4-1 transmits a test signal, and the optical receiver control unit 4-3 evaluates the quality of the received signal. Based on the quality of the received signal, the optical receiver control unit 4-3 makes adaptive adjustments and feeds the results back to the optical transmitter control unit 4-1. Reflecting the analysis results from the receiving side, the optical transmitter control unit 4-1 optimizes the parameters of the transmitted signal.

[0224] Finally, after the optimal parameters are established, full-scale data transmission and reception begins. In the second example, the optical transmitter 1 and optical receiver 3 communicate directly without going through the signal control unit 4-2, enabling faster adaptive control.

[0225] (Parameter Optimization Process) The control device 4 can improve communication quality and optimize transmission characteristics by dynamically optimizing parameters. The control device 4 can determine the optimal parameter set by selecting and adjusting parameters step by step according to the procedure in the flowchart shown in Figure 24.

[0226] Figure 24 is a flowchart showing the parameter set determination process by the control device 4. The control device 4 adaptively adjusts the parameters according to the state of the communication path and transmission / reception conditions, and performs the process shown in Figure 24 periodically or as needed. The control device 4 starts the process shown in Figure 24 as appropriate when the optical transmission system 100 is started up or in response to changes in communication conditions.

[0227] First, in step S11, the control device 4 selects a range for various parameters as the initial stage of the optimization process. The control device 4 sets the transmission distance, loss coefficient, dispersion coefficient, dispersion gradient, and nonlinear coefficient as the main parameters that determine the transmission characteristics. The control device 4 determines the selection range for the above parameters and decides on a combination of parameters to be applied experimentally.

[0228] Next, in step S12, the control device 4 selects the transmission distance. The control device 4 considers a range of transmission distances assuming short-distance transmission (for example, around 10 km) and can search for the optimal parameter set according to each distance.

[0229] Subsequently, in step S13, the control device 4 selects a loss value. The control device 4 can evaluate parameters for different loss values in consideration of the attenuation characteristics of an optical fiber. For example, in the case of a single-mode fiber, the loss coefficient α is set to be 0.2 dB / km or more and 0.3 dB / km or less. Selection of a loss value is closely related to transmission distance and is an important factor when determining an appropriate optical power level. Since a dispersion parameter, a dispersion slope, and a nonlinear coefficient greatly affect the quality of a pre-equalized signal, nonlinear distortion can be suppressed by setting optimal parameters through the same procedure.

[0230] Subsequently, in step S14, the control device 4 selects a nonlinear parameter, a dispersion parameter, and a dispersion slope respectively. For example, in the case of a single-mode fiber, at a wavelength close to the zero-dispersion wavelength, the nonlinear coefficient γ is 1.8 / W / km, and β ２ the related dispersion parameter D is 0 ps / nm / km, and β ３ the related dispersion slope s is 0.09 ps / nm ２ / km. The optical transmission system 100 sets a search range to include these values.

[0231] Note that the processing order of steps S12 to S14 can be changed as appropriate, and the processing of steps S12 to S14 may be performed in parallel.

[0232] Subsequently, in step S15, the control device 4 measures and records the signal quality for each selected parameter. As a measurement index, BER, a Q value, SNR, or the like can be used.

[0233] Subsequently, in step S16, the control device 4 determines whether there is any remaining selection range. If it is determined in step S16 that there is a remaining selection range (NO in step S16), the control device 4 performs the operations from step S12 again, and repeats the process until it is determined in step S16 that there is no remaining selection range. On the other hand, if it is determined in step S16 that there is no remaining selection range (YES in step S16), in step S17, the control device 4 determines the parameter. Thereafter, the control device 4 ends the processing.

[0234] As described above, the control device 4 can perform the parameter set determination process. From another perspective, the control device 4 controls the optical receiver 3 and determines the transmission path length, loss coefficient, nonlinear coefficient, dispersion value, and dispersion slope, or any combination thereof, based on the quality of each of the multiple optical signals separated in the wavelength domain by the optical receiver 3 from the wavelength division multiplexed signal WM output from the optical transmission path 2. This enables improvement of communication quality through adaptive parameter selection, or comprehensive optimization of nonlinear compensation and dispersion compensation. After the parameters are determined, they are used for optical transmission by the optical transmission system 100.

[0235] The control device 4 can also determine the number of repetitions for each of the processes of the first wavelength dispersion compensation unit 1-14321, the intensity detection unit 1-14323, the nonlinear phase calculation unit 1-14324, and the multiplication unit 1-14325, according to the quality of each of the multiple optical signals separated in the wavelength domain by the optical receiver 3 from the wavelength division multiplexed signal WM output from the optical transmission line 2. This makes it possible to improve the calculation accuracy of solving the nonlinear propagation equations and linear propagation equations while shortening the calculation time.

[0236] (Verification of the effectiveness of the determined parameters) The results of the reliability verification of the determined parameters will be explained with reference to Figures 25A, 25B, 25C, and 25D. Figure 25A is a diagram showing an example of the simulation results of the dependence of BER on the transmission distance in the optical transmission system 100. Figure 25B is a diagram showing an example of the simulation results of the dependence of BER on the second-order dispersion in the optical transmission system 100. Figure 25C is a diagram showing an example of the simulation results of the dependence of BER on the dispersion gradient in the optical transmission system 100. Figure 25D is a diagram showing an example of the simulation results of the dependence of BER on the nonlinear coefficients in the optical transmission system 100.

[0237] Figures 25A, 25B, 25C, and 25D show the dependence of each parameter obtained when the same polarization signal is received at -8 dBm under the same conditions as in Figure 19 described above. As shown in Figures 25A, 25B, 25C, and 25D, the actual parameters of the optical fiber are a transmission distance of 10 km, a dispersion parameter D of 0 ps / nm / km, and a dispersion gradient s of 0.09 ps / nm. ２ A generally low BER was obtained when the nonlinear coefficient γ was around 1.8 / W / km. From this, the effectiveness of the process described above with reference to Figures 22 to 24 was verified.

[0238] As explained above, in a wavelength division multiplexing optical transmission system that transmits multiple wavelength channels using intensity modulation with wavelengths close to zero-dispersion wavelengths, the control device 4 pre-corrects intensity distortion due to nonlinear optical effects, mainly four-wave mixing, at the optical transmitter 1. This makes it possible to control the signal quality of the received signal obtained after optical transmission to the desired quality. The amount of improvement in signal quality is at least 1.8 dB in the example shown in Figure 19 above, and 3 dB or more in the standard example shown in Figure 20 above. By improving the signal quality, the transmission capacity can be further increased and the transmission distance can be further extended. In addition, by performing the processing shown in Figures 22 to 24 above, the control device 4 can obtain the optimal combination of fiber length, loss coefficient, dispersion coefficient, dispersion gradient, and nonlinear coefficient for BER. This allows for flexible response to the reconstruction of the optical transmission system 100 due to the addition or deletion of the optical transmitter 1, optical transmission line 2, or optical receiver 3, and makes it easier to reduce the operational management costs of the optical transmitter 1, optical receiver 3, or optical transmission system 100.

[0239] [Second Embodiment] Next, an optical transmission system having a control device according to the second embodiment of this disclosure will be described. Note that names and reference numerals identical to those in the embodiments already described indicate the same or similar components or configurations, and detailed explanations will be omitted as appropriate.

[0240] Figure 26 is a block diagram showing the nonlinear preequalization unit 1-14a of an optical transmission system equipped with a control device according to the second embodiment of this disclosure. The nonlinear preequalization unit 1-14a differs from the nonlinear preequalization unit 1-14 of the control device 4 according to the first embodiment of this disclosure in that it includes a backpropagation calculation unit 1-143a and a subtraction unit 1-148an from a subtraction unit 1-148a1.

[0241] Subtraction units 1-148na from 1-1481a control the signal intensity for each wavelength channel to improve signal quality by subtracting the nonlinear backpropagation intensity from the linear backpropagation intensity calculated by intensity generation units 1-14551 and 1-1456n.

[0242] Figure 27 is a block diagram showing the backpropagation calculation unit 1-143a. In the example shown in Figure 27, the backpropagation calculation unit 1-143a differs from the backpropagation calculation unit 1-143 of the control device 4 according to the first embodiment of this disclosure in that it includes a linear propagation unit 1-1433a. The linear propagation unit 1-1433a differs from the linear backpropagation unit 1-1433 of the control device 4 according to the first embodiment of this disclosure in that it includes an electrical amplitude adjustment unit 1-14332a.

[0243] The electrical amplitude adjustment unit 1-14332a controls the scale of the complex electric field amplitude, which has been compensated for wavelength dispersion and obtained from the second wavelength dispersion compensation unit 1-14331, so that it becomes the desired amplitude value. The processing by the nonlinear pre-equalization unit 1-14a corresponds to performing the processing corresponding to equation (18) above from the back-propagated complex electric field amplitude or intensity information without going through equation (17) above. Specifically, the processing by the nonlinear pre-equalization unit 1-14a is as shown in equation (26), from equation (18) and equation (17-1) to E ｍ，ＦＷＭ－ｅｓｔ Remove (z+h, t), E ｍ，ＣＤＣ (z+h, t) and E ｍ，ＤＢＰ This is a calculation process that directly calculates the pre-equalized intensity from (z+h, t). In this case, the electrical amplitude adjustment unit 1-14332a is √(2) × E ｍ，ＣＤＣ Adjust the amplitude value so that it becomes (z + h, t).

[0244]

[0245] In other words, the control device according to the second embodiment of this disclosure can perform pre-equalization by controlling the nonlinear pre-equalization unit 1-14a to adjust the electric field information at the output of the second wavelength dispersion compensation unit 1-14331, converting the electric field information obtained by solving the nonlinear propagation equation and the linear propagation equation into intensity, and subtracting the intensity of the electric field information after nonlinear backpropagation from the intensity obtained from the adjusted electric field information.

[0246] In the second embodiment of this disclosure, the same effects as those of the first embodiment of this disclosure can be obtained.

[0247] Although preferred embodiments have been described in detail above, the embodiments of this disclosure described above are not limited to those described above, and various modifications and substitutions can be made to the embodiments of this disclosure described above without departing from the scope of the claims.

[0248] The ordinal numbers, quantities, and other figures used in the description of the embodiments of this disclosure are all illustrative to specifically illustrate the technology of this disclosure, and this disclosure is not limited to the illustrative figures. Furthermore, the connection relationships between the components are illustrative to specifically illustrate the technology of this disclosure, and are not limited to the connection relationships that realize the functions of this disclosure.

[0249] Embodiments of this disclosure may include, for example, the following: <1> A control device for controlling an optical transmission system comprising: an optical transmitter that transmits a wavelength-multiplexed signal obtained by multiplexing a plurality of optical signals of different wavelengths, each of which is intensity-modulated; and an optical transmission path that transmits the wavelength-multiplexed signal transmitted by the optical transmitter, wherein each of the plurality of optical signals is pre-equalized using an intensity distortion amount of the wavelength-multiplexed signal based on the backpropagation characteristics of the optical transmission path, and the intensity of the optical signal pre-equalized by the control device is 0 or greater. <2> The control device according to <1>, wherein the transmission path length, loss coefficient, nonlinear coefficient, dispersion value, and dispersion slope of the optical transmission path are input variables, and electric field information of the wavelength-multiplexed signal based on backpropagation of the optical transmission path is obtained by solving a nonlinear propagation equation with the signs of the parameters of the optical transmission path reversed, and the intensity distortion amount is obtained based on the obtained electric field information. <3> The control device described in <2> comprises: a first wavelength dispersion compensation unit that compensates for the wavelength dispersion of the input wavelength division multiplexed signal using the nonlinear propagation equation; an intensity detection unit that detects the intensity of the input wavelength division multiplexed signal from the output of the first wavelength dispersion compensation unit; a nonlinear phase calculation unit that calculates phase information of the input wavelength division multiplexed signal according to the intensity detected by the intensity detection unit; and a multiplication unit that multiplies the phase information of the wavelength division multiplexed signal calculated by the nonlinear phase calculation unit by the output of the first wavelength dispersion compensation unit, wherein the solution to the nonlinear propagation equation is obtained by repeatedly executing the processing of the first wavelength dispersion compensation unit, the intensity detection unit, the nonlinear phase calculation unit, and the multiplication unit. <4> The control device according to <2> or <3> above, wherein the transmission path length, the loss coefficient, the dispersion value, and the dispersion gradient are input variables, and a linear propagation equation is obtained by inverting the signs of the parameters of the optical transmission path, thereby obtaining electric field information of the wavelength division multiplexed signal based on the back propagation of the optical transmission path assuming that the nonlinear coefficient is 0, and the intensity distortion amount is obtained based on the obtained electric field information. <5> The control device according to <4> above, further comprising a second wavelength dispersion compensation unit that compensates for the wavelength dispersion of the input wavelength division multiplexed signal using the linear propagation equation, and the intensity distortion amount is obtained using the output of the second wavelength dispersion compensation unit.<6> The control device according to <5>, wherein the electric field information obtained by solving the nonlinear propagation equation and the linear propagation equation respectively is converted into intensity, the difference in intensity of the converted electric field information is calculated, and the intensity strain amount is obtained by subtracting the intensity of the electric field information after linear backpropagation from the intensity of the electric field information after nonlinear backpropagation. <7> The control device according to <6>, wherein pre-equalization is performed by subtracting the intensity strain amount from the intensity of the electric field information after linear backpropagation. <8> The control device according to <4>, further comprising a second wavelength dispersion compensation unit that compensates for the wavelength dispersion of the input wavelength division multiplexed signal using the linear propagation equation, adjusting the electric field information at the output of the second wavelength dispersion compensation unit, converting the electric field information obtained by solving the nonlinear propagation equation and the linear propagation equation respectively into intensity, and pre-equalizing is performed by subtracting the intensity of the electric field information after nonlinear backpropagation from the intensity obtained from the adjusted electric field information. <9> The optical transmission system further comprises an optical receiver that receives the wavelength division multiplexed signal transmitted by the optical transmission path as an electrical signal, and determines the transmission path length, the loss coefficient, the nonlinear coefficient, the dispersion value, and the dispersion slope, or any combination thereof, based on the quality of each of the plurality of optical signals separated in the wavelength domain by the optical receiver from the optical wavelength division multiplexed signal output from the optical transmission path, and is the control device described in <2>. <10> The control device described in <3> executes the processing of the first wavelength dispersion compensation unit, the intensity detection unit, the nonlinear phase calculation unit, and the multiplication unit once. <11> The optical transmission system further comprises an optical receiver that receives the wavelength division multiplexed signal transmitted by the optical transmission path as an electrical signal, and determines the number of times to repeat the processing of the first wavelength dispersion compensation unit, the intensity detection unit, the nonlinear phase calculation unit, and the multiplication unit according to the quality of each of the plurality of optical signals separated in the wavelength domain by the optical receiver from the optical wavelength division multiplexed signal output from the optical transmission path, and is the control device described in <3>. <12> The control device according to any one of <1> to <11>, further comprising a polarization adjustment unit that adjusts the polarization state of each of the multiple optical signals as a pre-processing step for the process of pre-equalizing each of the multiple optical signals.<13> A control device according to any one of <1> to <12>, wherein each of the plurality of optical signals is pre-equalized using a normalized linear function. <14> An optical transmission system comprising the optical transmitter, the optical transmission path, and the control device according to any one of <1> to <13>. <15> A control method by a control device for controlling an optical transmission system comprising an optical transmitter that transmits a wavelength division multiplexed signal obtained by multiplexing a plurality of optical signals of different wavelengths, each of which is intensity-modulated; an optical transmission path that transmits the wavelength division multiplexed signal transmitted by the optical transmitter; and an optical receiver that receives the wavelength division multiplexed signal transmitted by the optical transmission path as an electrical signal, wherein the control device pre-equalizes each of the plurality of optical signals using an intensity distortion amount of the wavelength division multiplexed signal based on the backpropagation characteristics of the optical transmission path, and the intensity of the optical signal pre-equalized by the control device is 0 or greater.

[0250] This application claims priority based on Japanese Patent Application No. 2025-053670, filed with the Japan Patent Office on 27 March 2025, and includes the entire contents of that Japanese Patent Application.

[0251] 1 Optical Transmitter 1-1 Transmitting Electrical Processing Unit 1-21 to 1-2n Optical Transmitting Unit 1-2101, 1-2111 Electrical Amplification Unit 1-2102, 1-2112 Bias Control Unit 1-2103, 1-2113 Light Source Unit 1-2104 Optical Modulation Unit 1-2114 Optical Power Adjustment Unit 1-2105 Optical Power Adjustment Unit 1-3 Optical Wavelength Division Multiplexing Unit 1-3011 to 1-301n Optical Polarization Adjustment Unit 1-302, 1-3111, 1-3112 Optical Multiplexing Unit 1-312, 1-313 Optical Polarization Adjustment Unit 1-314 Optical Polarization Division Multiplexing Unit 1-11 Symbol Mapping Unit 1-12 Polarization Adjustment Unit 1-13 Waveform Shaping Unit 1-14, 1-14a Nonlinear Pre-equalization Unit 1-1401 to 1-140n Input processing rate adjustment unit 1-142 Electrical frequency synthesis unit 1-143, 1-143a Backpropagation calculation unit 1-1431 Input electrical signal duplication unit 1-1432 Nonlinear backpropagation unit 1-14321 First wavelength dispersion compensation unit 1-14322 Electrical signal duplication unit 1-14323 Intensity detection unit 1-14324 Nonlinear phase calculation unit 1-14325 Multiplication unit 1-14326 Subsequent wavelength dispersion compensation unit 1-1433 Linear backpropagation unit 1-14331 Second wavelength dispersion compensation unit 1-145 Intensity distortion acquisition unit 1-1451 Nonlinear backpropagation signal electrical frequency separation unit 1-1452 Linear backpropagation signal electrical frequency separation unit 1-14531 to 1-1453n, 1-14541 to 1-1454n Output processing rate adjustment unit 1-14551 to 1-1455n, 1-14561 to 1-1456n Intensity generation unit 1-14571 to 1-1457n, 1-148a1 to 1-148an Subtraction unit 1-146 Linear backpropagation intensity separation unit 1-1461 Linear backpropagation signal electrical frequency separation unit 1-14621 to 1-1462n Output processing rate adjustment unit 1-14631 to 1-1463n Intensity generation unit 1-1471 to 1-147n Intensity correction unit 1-1481 to 1-148n Nonlinear correction unit 1-15 Intensity field conversion unit 1-16 Sampling rate adjustment unit 1-17 1. DA conversion unit 2. Optical transmission line 2-1. Optical fiber 2-2. Optical loss compensation unit 2-3. Optical signal extraction unit 2-4. Dispersion compensation unit 3. Optical receiver 3-1. Optical wavelength division multiplexing / decompression unit 3-101. Optical decompression unit 3-1011 to 3-101n. Optical signal extraction unit 3-21 to 3-2n. Optical receiver unit3-211 Optical waveform adjustment unit 3-212 Received optical power detection unit 3-213 Photoelectric conversion unit 3-3 Received electrical processing unit 3-301 DA conversion unit 3-302 Clock control unit 3-303 Symbol rate adjustment unit 3-304 Waveform shaping unit 3-305 Symbol demapping unit 3-306 Signal analysis unit 4 Control device 4-1 Optical transmitter control unit 4-2 Signal control unit 4-3 Optical receiver control unit 100 Optical transmission system 191, 192 Graphs B1 to Bn Bivalidation data ER1 to ERn Received electrical signal FM Electrical frequency multiplexed signal IM1 to IMn Intensity modulated signal LD1 to LDn Linear backpropagation intensity LR Linear backpropagation signal M1 to Mn Modulation data ND1 to NDn Nonlinear intensity distortion NR Nonlinear backpropagation signal OR1 to ORn: Optical received signal; OT: Optical transmitted signal; P1 to Pn: Nonlinear pre-equalized electrical signal; RB1 to RBn: Received binary data; WM: Wavelength division multiplexed signal.

Claims

1. A control device for controlling an optical transmission system comprising: an optical transmitter that transmits a wavelength-multiplexed signal obtained by multiplexing a plurality of optical signals with different wavelengths, each of which is intensity-modulated; and an optical transmission path that transmits the wavelength-multiplexed signal transmitted by the optical transmitter, wherein the control device pre-equals each of the plurality of optical signals using the amount of intensity distortion of the wavelength-multiplexed signal based on the backpropagation characteristics of the optical transmission path, and the intensity of the optical signals pre-equalized by the control device is 0 or greater.

2. The control device according to claim 1, wherein the transmission path length, loss coefficient, nonlinear coefficient, dispersion value, and dispersion slope of the optical transmission path are used as input variables, and a nonlinear propagation equation is solved by inverting the signs of the parameters of the optical transmission path to obtain electric field information of the wavelength division multiplexed signal based on the back propagation of the optical transmission path, and the intensity strain amount is obtained based on the obtained electric field information.

3. The control device according to claim 2, comprising: a first wavelength dispersion compensation unit that compensates for the wavelength dispersion of the input wavelength division multiplexed signal using the nonlinear propagation equation; an intensity detection unit that detects the intensity of the input wavelength division multiplexed signal from the output of the first wavelength dispersion compensation unit; a nonlinear phase calculation unit that calculates phase information of the input wavelength division multiplexed signal according to the intensity of the wavelength division multiplexed signal detected by the intensity detection unit; and a multiplication unit that multiplies the phase information of the wavelength division multiplexed signal calculated by the nonlinear phase calculation unit by the output of the first wavelength dispersion compensation unit, wherein the solution to the nonlinear propagation equation is obtained by repeatedly executing the processing of the first wavelength dispersion compensation unit, the intensity detection unit, the nonlinear phase calculation unit, and the multiplication unit.

4. The control device according to claim 2 or 3, wherein the electric field information is obtained based on the back propagation of the optical transmission path assuming that the nonlinear coefficient is 0, by solving a linear propagation equation with the signs of the parameters of the optical transmission path reversed, using the transmission path length, the loss coefficient, the dispersion value, and the dispersion gradient as input variables, and based on the obtained electric field information, the intensity strain amount is obtained.

5. The control device according to claim 4, comprising a second wavelength dispersion compensation unit that compensates for the wavelength dispersion of the input wavelength division multiplexed signal using the linear propagation equation, and the intensity distortion amount is obtained using the output of the second wavelength dispersion compensation unit.

6. The control device according to claim 5, comprising: converting the electric field information obtained by solving the nonlinear propagation equation and the linear propagation equation into intensity; calculating the difference in intensity of the converted electric field information; and obtaining the intensity strain amount by subtracting the intensity of the electric field information after linear backpropagation from the intensity of the electric field information after nonlinear backpropagation.

7. The control device according to claim 6, wherein pre-equalization is performed by subtracting the intensity strain amount from the intensity of the electric field information after linear backpropagation.

8. The control device according to claim 4, comprising a second wavelength dispersion compensation unit that compensates for the wavelength dispersion of the input wavelength division multiplexed signal using the linear propagation equation, adjusting the electric field information at the output of the second wavelength dispersion compensation unit, converting the electric field information obtained by solving the nonlinear propagation equation and the linear propagation equation, respectively, into intensity, and performing pre-equalization by subtracting the intensity of the electric field information after nonlinear backpropagation from the intensity obtained from the adjusted electric field information.

9. The control device according to claim 2, wherein the optical transmission system further comprises an optical receiver that receives the wavelength-multiplexed signal transmitted by the optical transmission path as an electrical signal, and determines the transmission path length, the loss coefficient, the nonlinear coefficient, the dispersion value, and the dispersion slope, or any combination thereof, based on the quality of each of the plurality of optical signals separated in the wavelength domain by the optical receiver from the optical wavelength-multiplexed signal output from the optical transmission path.

10. The control device according to claim 3, wherein the processing of the first wavelength dispersion compensation unit, the intensity detection unit, the nonlinear phase calculation unit, and the multiplication unit is performed once.

11. The control device according to claim 3, wherein the optical transmission system further comprises an optical receiver that receives the wavelength multiplexed signal transmitted by the optical transmission path as an electrical signal, and the number of repetitions of the processing of the first wavelength dispersion compensation unit, the intensity detection unit, the nonlinear phase calculation unit, and the multiplication unit is determined according to the quality of each of the multiple optical signals separated in the wavelength domain by the optical receiver from the optical wavelength multiplexed signal output from the optical transmission path.

12. The control device according to claim 1, further comprising a polarization adjustment unit that adjusts the polarization state of each of the multiple optical signals as a pre-processing step for the process of pre-equalizing each of the multiple optical signals.

13. The control device according to claim 1, wherein each of the multiple optical signals is pre-equalized using a normalized linear function.

14. An optical transmission system comprising the optical transmitter, the optical transmission path, and the control device according to claim 1.

15. A control method by a control device for controlling an optical transmission system comprising: an optical transmitter that transmits a wavelength-multiplexed signal obtained by multiplexing a plurality of optical signals of different wavelengths, each of which is intensity-modulated; an optical transmission path that transmits the wavelength-multiplexed signal transmitted by the optical transmitter; and an optical receiver that receives the wavelength-multiplexed signal transmitted by the optical transmission path as an electrical signal, wherein the control device pre-equals each of the plurality of optical signals using the amount of intensity distortion of the wavelength-multiplexed signal based on the backpropagation characteristics of the optical transmission path, and the intensity of the optical signals pre-equalized by the control device is 0 or greater.

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