JP5147582B2 - Reception device, compensation arithmetic circuit, and reception method - Google Patents

Description

In the present invention, in order to compensate for nonlinear waveform distortion due to nonlinear interaction between a plurality of carriers (carriers and subcarriers), the nonlinear waveform distortion is approximated by a waveform degradation model due to four-wave mixed light crosstalk or the like. The present invention relates to a receiving apparatus, a compensation arithmetic circuit, and a receiving method, which can linearize and simplify the non-linear equation and can realize complicated waveform distortion compensation with a simple electric arithmetic circuit.
About.

  The optical fiber transmission line has four-wave mixing (FWM: Four Wave Mixing), cross-phase modulation (XPM), self-phase modulation (FPM) due to the optical Kerr effect whose refractive index changes in proportion to the light intensity. Induces optical nonlinear effects such as SPM (Self Phase Modulation).

  As a result, a phenomenon in which the optical electric field phase of each signal light is distorted by the signal light of its own channel and a phenomenon of distortion by the optical signals of other channels occurs. In the modulation method in which data is placed on the phase of the optical electric field, the waveform of the received signal is distorted by the signal light of the own channel or another channel, which causes an error in data discrimination. Further, since the distortion of the phase waveform of the optical signal is converted into the distortion of the amplitude waveform through the wavelength dispersion of the transmission line, a data discrimination error is caused even in the modulation method in which data is put on the amplitude of the optical electric field waveform.

  These nonlinear waveform distortions cause interference between symbols within a channel and interference between symbols between channels and degrade transmission characteristics. Since the deterioration of transmission characteristics due to nonlinear waveform distortion becomes conspicuous as the optical power increases, the conventional optical transmission system suppresses it by limiting the input optical power to the optical fiber transmission line. On the other hand, if the input power of the optical fiber transmission line is reduced, the signal-to-noise ratio (SNR) of the signal light received at the receiving end will be reduced. Causes an error.

  Therefore, it is desirable to set the input power to the optical fiber transmission line so that the sum of the characteristic degradation due to nonlinear waveform distortion and the characteristic degradation due to the degradation of the incoming SNR is minimized. However, the nonlinear waveform distortion largely depends on the characteristics of the zero dispersion wavelength and chromatic dispersion of the transmission line fiber. In particular, a dispersion-shifted fiber (DSF) has a zero-dispersion wavelength band in the wavelength band (C-band) of 1530 nm to 1565 nm, and of course for C-band WDM (Wavelength Division Multiplexing) signal light. In addition, for WDM signal light in the wavelength band (L band) of 1570 nm to 1605 nm, the zero-dispersion wavelength is close and waveform deterioration is serious. Even in the case of non-zero dispersion shifted fibers (NZ-DSF), waveform degradation occurs in WDM transmission in the L band.

  For this reason, conventionally, the input power to the optical fiber transmission line is set by predicting the magnitude of this waveform degradation from the statistical data of the zero dispersion wavelength and chromatic dispersion characteristics of the already installed optical fiber transmission line. Was. However, since the dispersion characteristics of the optical fiber transmission line differ depending on the individual, the design was made with an extra margin in mind in order to design the signal transmission quality with high reliability. Therefore, in order to design the signal transmission quality with high reliability, it has been a cause of high cost and limited performance. Even with a large margin, transmission design may not be possible depending on the characteristics of the laid fiber.

  In addition, in order to suppress nonlinear waveform distortion with a margin, the design is such that the input power to the optical fiber transmission line is reduced below the optimum value, leading to a decrease in incoming SNR and limiting the transmission distance and transmission capacity. It was. Therefore, a measure for compensating for non-linear waveform distortion has been demanded in order to increase the allowable transmission distance and transmission capacity of the transmission system.

  By the way, among the three nonlinear waveform degradations of SPM, FWM, and XPM in optical fiber transmission, SPM is the main cause of waveform distortion that occurs in signal light of a single carrier wave. Conventionally, a method for compensating for non-linear waveform distortion in signal light of a single carrier by SPM has been proposed (see, for example, Non-Patent Document 1). Furthermore, a method for compensating for the “Gordon-Mollenauer effect” in which intensity noise due to ASE noise via SPM is converted to phase noise has also been proposed (see, for example, Non-Patent Document 2). Until now, there has been no method for compensating waveform distortion of signal light of a plurality of carrier waves.

  Further, in the waveform distortion compensation of the signal light of a single carrier wave, it is a principle to compensate by giving an effect opposite to that of SPM. The SPM is an effect that the optical phase rotates in proportion to the intensity waveform of the signal light. To explain in brief, by giving a reverse phase rotation in proportion to the optical intensity waveform and returning the phase rotation. This is the principle of compensating for waveform distortion.

However, because the intensity waveform changes in the optical fiber transmission line due to the chromatic dispersion of the optical fiber transmission line, the intensity waveform acquired at the receiving end is different from the intensity waveform at the time when the nonlinear distortion occurs. A sufficient compensation effect cannot be obtained. In addition, even when nonlinear distortion compensation calculation is performed after returning the intensity waveform change due to chromatic dispersion, the intensity waveform change due to chromatic dispersion and nonlinear phase rotation occur at the same time. In some cases, sufficient compensation accuracy cannot be obtained.
RI Kelley, et al., "Electronic dispersion compensation by signal predistorsion using a dual drive Mach-Zehender modulator," OFC2005, OThJ2, 2005 K. Kikuchi, et al., OFC / NFOEC2007, OTuA2, Anaheim, CA, Mar. 2007.

  As described above, in an optical fiber transmission system, an optical amplifier is relayed to transmit an optical signal in order to compensate for attenuation of the optical signal due to transmission path loss. In this case, when the input optical power of the optical fiber is increased, the signal-to-noise ratio increases, and the distance that can be transmitted as light increases. Therefore, when configuring a network economically, it is desirable to set a large input power to the optical fiber transmission line. However, when the input power to the optical fiber is increased, the signal light waveform is distorted due to the nonlinear effect, resulting in a problem that the transfer characteristic is deteriorated.

  Further, since the nonlinear waveform distortion differs depending on the individual difference in the transmission line optical fiber characteristics, an extra margin is designed in order to design the signal transmission quality with high reliability. Therefore, in order to design the signal transmission quality with high reliability, it has been the cause of high cost and limited performance. So far, methods for providing nonlinear waveform distortion have been impaired, but signal light consisting of a single carrier wave has been targeted. In recent years, with the increase in transmission bit rate, attention has been paid to a method of transmitting using a plurality of carrier waves, and nonlinear waveform deterioration has been a problem in that.

  The present invention has been made in view of the above problems, and an object of the present invention is to approximate nonlinear waveform distortion caused by nonlinear interaction between a plurality of carrier waves by a waveform degradation model due to four-wave mixed light crosstalk, etc. It is an object of the present invention to provide a receiver, a compensation arithmetic circuit, and a reception method capable of linearizing and simplifying the nonlinear equations of the waveform deterioration model and realizing complex waveform distortion compensation with a simple electric arithmetic circuit. .

The first aspect is a receiving apparatus that receives signal light multiplexed with a plurality of frequency carriers encoded by transmission information or independent polarization carriers in an optical transmission system using an optical fiber transmission line. A separation device that separates a signal for each carrier according to the frequency or polarization of the signal light, and a phase synchronization unit that performs synchronization processing of a symbol phase between a plurality of carriers output from the separation device; Based on a carrier wave signal that has been subjected to synchronization processing by the phase synchronization unit, non-linear waveform distortion of the multiplexed signal light in the optical fiber transmission line is modeled and calculated by a predetermined model including four-wave mixing crosstalk. And a compensation computation unit that performs computation to compensate for the nonlinear waveform distortion, and the computation processing in the phase synchronization unit and the compensation computation unit is performed in an electrical computation circuit Ri is configured to execute it, a receiving apparatus according to claim.

In addition, in the second aspect , in an optical transmission system using an optical fiber transmission line, reception of signal light multiplexed with a plurality of frequency carriers encoded by transmission information or independent polarization carriers is performed. A polarization separation device that separates polarization-multiplexed signal light into two by polarization, a separation device that separates a signal for each individual carrier wave by frequency, and each output from the separation device A polarization separation calculation unit that receives two polarization reception signals for each frequency carrier wave, removes interference between the two polarization reception signals that are input, and separates the polarization signals into two independent signals; In the optical fiber transmission line, based on a phase synchronization unit that performs phase synchronization processing between a plurality of carriers output from the polarization separation calculation unit, and a carrier signal that has been subjected to synchronization processing by the phase synchronization unit. Multiplexing A non-linear waveform distortion of the measured signal light by modeling with a predetermined model including four-wave mixing crosstalk, and a compensation calculation unit that performs a calculation to compensate for the non-linear waveform distortion, the polarization separation calculation unit The receiving device is configured to execute arithmetic processing in the phase synchronization unit and the compensation arithmetic unit by an electric arithmetic circuit.

A third aspect is a compensation arithmetic circuit constituting the compensation arithmetic unit in the receiver described above , wherein the frequency-multiplexed and polarization-multiplexed signal light is generated in a non-linear waveform during propagation in an optical fiber transmission line. Distortion is modeled by waveform distortion due to four-wave mixing crosstalk that occurs between signal light of multiple frequencies and signal light of different polarizations, and the relationship between the waveform of the received signal and the transmitted signal is related by a multi-dimensional nonlinear equation, A compensation arithmetic circuit comprising an electric arithmetic circuit for calculating a transmission signal from a reception signal by solving the multi-dimensional nonlinear equation.

A fourth aspect is the compensation arithmetic circuit described above , wherein the non-linear waveform distortion that occurs during propagation of the frequency-multiplexed and polarization-multiplexed signal light in an optical fiber transmission line, signal light having a plurality of frequencies, and Modeled by waveform distortion due to four-wave mixed crosstalk that occurs between signal lights of different polarizations, and the relationship between the waveform of the received signal and the transmitted signal is related by a multi-dimensional nonlinear equation, and transmitted from the received waveform based on the multi-dimensional nonlinear equation When estimating the waveform sequentially, the n-th transmission waveform estimation value output from the n-th transmission waveform estimation step is temporarily used as a transmission waveform of a part of the multi-dimensional nonlinear equation, A multi-dimensional nonlinear equation is linearized to have an n + 1-th transmission waveform estimation step for estimating an (n + 1) -th transmission waveform, and to be configured by an arithmetic circuit that sequentially estimates a compensation waveform. A compensation operation circuit to symptoms.

Further, the fifth aspect is the compensation arithmetic circuit described above , wherein in the first-stage transmission waveform estimation step, a reception waveform before compensation is used as an initial value and a part of the transmission waveform of the multi-linear nonlinear equation It is a compensation arithmetic circuit characterized by having an arithmetic circuit used as a.

A sixth aspect is the compensation arithmetic circuit described above , wherein in the first-stage transmission waveform estimation step, a predetermined arbitrary waveform is used as an initial value and a part of the multi-dimensional nonlinear equation. It is a compensation arithmetic circuit characterized by including an arithmetic circuit used as a transmission waveform.

A seventh aspect is the compensation arithmetic circuit described above , wherein the non-linear waveform distortion generated during propagation of the frequency-multiplexed and polarization-multiplexed signal light in an optical fiber transmission line is reduced to signal light having a plurality of frequencies, and Modeled by waveform distortion due to four-wave mixing crosstalk that occurs between signal lights of different polarizations, and the relationship between the nonlinear distortion fluctuation amount of the received waveform and the transmission waveform is related by a multi-dimensional nonlinear equation, and the nonlinear distortion fluctuation amount is sequentially determined. The n-th stage compensation waveform output from the n-th fluctuation amount estimation step is temporarily used as a transmission waveform that is part of the multi-dimensional nonlinear equation, and the multi-dimensional nonlinear equation is linearized. And receiving the output value from the (n + 1) th stage fluctuation amount estimating step for estimating the nonlinear distortion fluctuation amount of the received waveform at the (n + 1) th stage and the (n + 1) th fluctuation amount estimating step. And an n + 1-th stage fluctuation amount compensation step for outputting a waveform after compensating for the (n + 1) -th stage nonlinear distortion, and comprising a calculation circuit that sequentially estimates the compensation waveform. This is a characteristic compensation operation circuit.

Further, an eighth aspect is the compensation arithmetic circuit described above , wherein in the first stage fluctuation amount estimation step, the received waveform before compensation is temporarily used as a transmission waveform that is a part of the multi-dimensional nonlinear equation. It is a compensation arithmetic circuit characterized by comprising an arithmetic circuit to be used.

A ninth aspect is the compensation arithmetic circuit described above , wherein in the first stage fluctuation amount estimation step, a predetermined arbitrary waveform is used as an initial value and a part of the multi-dimensional nonlinear equation. It is a compensation arithmetic circuit characterized by comprising an arithmetic circuit characterized by being used as a transmission waveform.

The tenth aspect is the compensation arithmetic circuit described above , wherein in the first-stage fluctuation amount estimation step, a value used as an initial value is changed to detect a value that provides a correction effect. A compensation arithmetic circuit including a circuit.

Also, aspects of the eleventh, a compensation operation circuit described above, the frequency-multiplexed and polarization-multiplexed signal light to the nonlinear waveform distortion generated in the optical fiber transmission path propagation, the signal light of the plurality of frequency It is modeled by self-phase modulation in which the optical phase of the signal light electric field rotates in proportion to the intensity of the synthesized time waveform and the time waveform of the orthogonal polarization, and the pre-transmission waveform and the post-transmission waveform are modeled by the self-phase modulation model. The compensation arithmetic circuit is characterized by comprising an arithmetic circuit characterized by associating the relationship with a nonlinear equation and estimating a pre-transmission waveform from a post-transmission waveform.

Further, a twelfth aspect is the compensation operation circuit described above, the wavelength dispersion in the optical fiber transmission line, and the loss is described by a linear transfer function, the linear waveform distortion that applies an inverse function of the transfer function Computation for pre-transmission waveform estimation that pre-transmission waveform is estimated from post-transmission waveform by repeatedly performing compensation computation and compensation calculation of nonlinear waveform distortion calculated by a predetermined model including the four-wave mixing crosstalk model It is a compensation arithmetic circuit characterized by comprising a circuit.

The thirteenth aspect depends on the chromatic dispersion of the optical fiber transmission line used in the calculation for compensating the nonlinear distortion, the chromatic dispersion slope, the transmission parameter including the nonlinear constant, and the relative phase between the carriers of the multiplexed signal light. the compensation parameters learned that, it comprises a compensation parameter learning unit for inputting the compensation parameter value to the compensation operation circuit, a compensation operation circuit described above, wherein.

Further, the fourteenth aspect is a multimode local light generation unit that outputs continuous light of a plurality of frequencies, a component that inputs local light and input signal light of the plurality of frequencies, and whose optical phases are the same. Optical 90-degree hybrid that is separated into orthogonal components and output to different ports, output light from the optical 90-degree hybrid is input, and each optical separator is separated for each wavelength by a chromatic dispersion medium; A photoelectric converter that inputs output light from the optical separator and converts each of the light into an electric signal, and an analog / digital converter that converts the electric signal of the photoelectric converter into a digital signal. The receiving apparatus according to the above , characterized in that:

In the fifteenth aspect , a multi-mode local light generation unit that outputs continuous light having a plurality of frequencies as local light and an input signal light are input, separated for each wavelength by a chromatic dispersion medium, and output to different ports. A signal light separator, a local light output from the multi-mode local light generator, and a local light separator that separates each wavelength by a chromatic dispersion medium and outputs it to different ports; and the signal The output light from each port of the optical light separator and the output light from each port of the local light separator are input and separated into a component orthogonal to the component in which both optical phases match. Optical 90-degree hybrids of the respective carriers output to different ports, respective photoelectric converters for converting the output light from the respective optical 90-degree hybrids into electric signals, and the respective photoelectric conversions And each of the analog-digital converter for converting an electrical signal vessels into a digital signal, a receiving apparatus according to, characterized in that it comprises a.

Further, the sixteenth aspect is an optical signal separator that receives input signal light, separates the signals for each wavelength by a wavelength dispersion medium, and outputs them to different ports, and a plurality of stations that output continuous light having different frequencies. A component that is inputted with the light emitted from the respective ports of the light emission generation unit, the signal light optical separator, and the output light from each of the local light generation units, and is a component that is orthogonal to the component in which both optical phases match 90-degree hybrids that are separated and output to different ports, respective photoelectric converters that convert the output light from the respective wavelength separators into electrical signals, and electrical signals from the respective photoelectric converters are converted into digital signals Each of the analog-to-digital converters for converting to the above- described receiving device is the receiving device described above .

In the seventeenth aspect , the local light generation unit that outputs continuous light having one frequency component, the local light and the input signal light are input, and a component that is orthogonal to a component in which both optical phases coincide with each other Separated output 90 degree hybrid, each photoelectric converter that converts the output light from the 90 degree hybrid light into electrical signal, and output signal from the photoelectric converter is separated into a plurality of electrical signals according to frequency The receiving device according to the above , further comprising: an electrical filter that converts the output electrical signal from each electrical filter into a digital signal.

According to an eighteenth aspect , a local light generation unit that outputs continuous light having a component of one frequency, a component that receives the local light and input signal light, and that is orthogonal to a component in which both optical phases coincide with each other Optical 90-degree hybrid that is output separately, a photoelectric converter that converts output light from the optical 90-degree hybrid into an electrical signal, and an analog / digital converter that converts the electrical signal of the photoelectric converter into a digital signal When a receiving apparatus according to, characterized in that it comprises a digital filter for separating a plurality of channels by frequency an output signal from said respective analog-to-digital converter.

In addition, in a nineteenth aspect , in an optical transmission system using an optical fiber transmission path, reception of signal light multiplexed with a plurality of frequency carriers encoded by transmission information or independent polarization carriers is performed. A method for receiving the signal light in an apparatus, comprising: a separation procedure for separating a signal for each carrier according to a frequency or polarization of the signal light; and a symbol phase between a plurality of carriers output by the separation procedure A four-wave mixing crosstalk is included in the non-linear waveform distortion of the multiplexed signal light in the optical fiber transmission line based on the phase synchronization procedure for performing the synchronization processing and the carrier wave signal subjected to the synchronization processing by the phase synchronization procedure. And a compensation calculation procedure for performing calculation for compensating for the nonlinear waveform distortion while modeling and calculating with a predetermined model. It is.

In the receiving apparatus of the first aspect , in order to compensate for nonlinear waveform distortion due to nonlinear interaction between a plurality of carrier waves, preprocessing of symbol phase synchronization between the plurality of carrier waves is performed, and then the nonlinear waveform distortion is reduced to four light waves. It is approximated by a waveform degradation model due to mixed optical crosstalk, etc., and the nonlinear equation of this waveform degradation model is simplified by linearizing it by a successive approximation method, etc., and this simplified waveform distortion model compensates for complex waveform distortion. As a result, the nonlinear compensation calculation can be realized with a simple electric calculation circuit.

In the receiving device of the second mode , the polarization multiplexed signal light is separated into two by the polarization separation device, and the interference between the two polarizations for each carrier frequency by the polarization separation operation unit. In order to compensate for non-linear waveform distortion between multiple carriers, pre-processing of phase synchronization between the carriers is performed, and the non-linear waveform distortion is approximated by a waveform degradation model such as four-wave mixed-light crosstalk. Then, the nonlinear equation of the waveform deterioration model is simplified by linearizing it by a successive approximation method or the like, and the waveform distortion is compensated by the simplified waveform distortion model. As a result, the nonlinear compensation calculation can be realized with a simple electric calculation circuit.

Further, in the compensation arithmetic circuit of the third aspect , nonlinear waveform distortion generated during propagation of frequency multiplexed and polarization multiplexed signal light in the optical fiber transmission line is modeled by waveform distortion due to four-wave mixing crosstalk, and the received signal and Since the relationship of the waveform of the transmission signal is related by a multi-dimensional nonlinear equation and the transmission signal is obtained from the received signal by solving this multi-dimensional nonlinear equation, the non-linear compensation calculation is realized by a simple electric arithmetic circuit. A compensation arithmetic circuit can be provided.

Further, in the compensation arithmetic circuit of the fourth aspect , the nonlinear waveform distortion generated during propagation of the frequency multiplexed and polarization multiplexed signal light in the optical fiber transmission line is modeled by the waveform distortion caused by the four-wave mixing crosstalk, and the received signal and The waveform relationship of the transmission signal is related by a multi-dimensional nonlinear equation, and the n-th transmission waveform estimation value output from the n-th transmission waveform estimation step is temporarily used as a partial transmission waveform of the multi-dimensional nonlinear equation. Thus, the multi-linear equation is linearized to have the (n + 1) th transmission waveform estimation step for estimating the (n + 1) th transmission waveform, so that the nonlinear compensation calculation can be realized with a simple electric calculation circuit. An arithmetic circuit can be provided.

Further, in the compensation operation circuit of the fifth aspect , in the first transmission waveform estimation step, the reception waveform before compensation is used as a partial transmission waveform of the multi-dimensional nonlinear equation as an initial value. A transmission waveform with higher accuracy can be estimated.

In the compensation calculation circuit of the sixth aspect , since an arbitrary waveform is used as a partial transmission waveform of the multi-dimensional nonlinear equation as an initial value in the first transmission waveform estimation step, A desired initial value can be set according to the form, parameters, etc. of the multi-dimensional nonlinear equation.

In the compensation calculation circuit of the seventh aspect , the relationship between the nonlinear distortion fluctuation amount of the reception waveform and the transmission waveform modeled by the four-wave mixed crosstalk is related by the multi-dimensional nonlinear equation, and the nth fluctuation amount is obtained. The n + 1-th stage fluctuation amount for linearizing the multi-dimensional nonlinear equation using the n-th stage compensation waveform output from the compensation step as a partial transmission waveform and estimating the distortion fluctuation amount of the (n + 1) -th stage received waveform. An estimation step and an (n + 1) th stage fluctuation amount compensation step for subtracting the output value from the (n + 1) th fluctuation amount estimation step from the received data and outputting a waveform after the (n + 1) th stage nonlinear distortion compensation. As a result, the nonlinear compensation calculation can be easily performed using the recurrence formula based on the distortion fluctuation amount, and the convergence to the estimation result can be accelerated.

In the compensation operation circuit of the eighth aspect , the received waveform before compensation is temporarily used as part of the transmission waveform of the multi-linear nonlinear equation in the first-stage fluctuation amount estimation step for obtaining the distortion fluctuation amount. As a result, the received waveform before compensation is selected as the initial value, and the nonlinear compensation calculation can be easily performed using the recurrence formula based on the distortion fluctuation amount.

In the compensation operation circuit of the ninth aspect , an arbitrary waveform is used as an initial value as a part of the transmission waveform of the multi-dimensional nonlinear equation in the first-stage transmission waveform estimation step for obtaining the distortion fluctuation amount. As a result, an arbitrary waveform can be selected as an initial value, and a nonlinear compensation calculation can be easily performed using a recurrence formula based on a distortion fluctuation amount.

In the compensation arithmetic circuit according to the tenth aspect , the value used as the initial value is changed in the first fluctuation amount estimation step so as to detect the value that provides the correction effect. By selecting an appropriate initial value, it becomes possible to perform compensation for nonlinear waveform distortion with high accuracy, such as speeding up convergence.

In the compensation arithmetic circuit of the eleventh aspect , the nonlinear waveform distortion generated during propagation in the optical fiber transmission line is modeled by self-phase modulation, the relationship between the waveform before transmission and the waveform after transmission is related by a nonlinear equation, and transmission Since the pre-transmission waveform is estimated from the post waveform, the transmission waveform can be estimated using the self-phase modulation phase rotation model.

In the compensation operation circuit of the twelfth aspect , the chromatic dispersion and loss in the optical fiber transmission line are described by a linear transfer function, and a linear waveform distortion compensation operation for applying an inverse function of the transfer function, and four-wave mixing Since the waveform before transmission is estimated from the post-transmission waveform by repeatedly performing the compensation calculation of the non-linear waveform distortion by the crosstalk model or the self-phase modulation phase rotation model, the split step method is used thereby. The transmission waveform can be estimated.

In the compensation calculation circuit of the thirteenth aspect , the chromatic dispersion of the optical fiber transmission line used for the nonlinear compensation calculation, the chromatic dispersion slope, the transmission parameter including the nonlinear constant, and the relative phase between the carriers of the multiplexed signal light are set. Since the compensation parameter learning unit for learning the dependent compensation parameter is provided, it is possible to acquire a compensation parameter necessary for performing compensation performance for estimating the transmission waveform from the multi-dimensional nonlinear equation.

Further, in the receiver of the fourteenth aspect , the multi-mode local light generator and the optical 90-degree hybrid are separated into components orthogonal to the components having the same optical phase for each carrier frequency and output to different ports, In addition, since the output light from the optical 90-degree hybrid is separated for each frequency (wavelength) by an optical separator using a wavelength dispersion medium, this allows without using an electric filter (digital filter, etc.) The carrier wave can be separated in the optical system.

In the receiver of the fifteenth aspect , the input signal light is separated for each wavelength and output to different ports, and the output light from the multimode local light generation unit is input for each wavelength. And the light output from each port of the signal light separator and the output from each port of the local light separator. Since the optical 90-degree hybrid of each carrier wave that inputs light and separates into a component orthogonal to a component in which both optical phases match and outputs to a different port is provided, an electric filter (digital filter) Etc.), the carrier wave can be separated in the optical system.

Further, in the receiver of the sixteenth aspect , a signal light optical separator that separates the input signal light for each wavelength and outputs it to different ports, and a plurality of local light generators that output continuous light of different frequencies, In addition, the output light from each port of the signal light separator and the output light from each local light generation unit are input and separated into a component that is orthogonal to the component in which both optical phases match Thus, since a plurality of optical 90-degree hybrids that output to different ports are provided, it is possible to separate the carrier waves in the optical system without using an electrical filter (such as a digital filter).

In the receiver of the seventeenth aspect , the local light generation unit that outputs continuous light of one frequency, the local light and the input signal light are input, and the component that is orthogonal to the component in which both optical phases match The optical 90-degree hybrid that is separated and output, and the output light from the optical 90-degree hybrid is converted into an electrical signal by a photoelectric converter, and the output signal from the photoelectric converter is converted into a plurality of electrical signals by frequency using an electrical filter. Thus, the carrier wave can be separated for each frequency by using the electric filter.

In the eighteenth aspect of the receiving device, the local light generation unit that outputs continuous light of one frequency, the local light and the input signal light are input, and the component that is orthogonal to the component in which both optical phases coincide with each other A 90-degree optical hybrid that outputs the light separately and converts the output light from the optical 90-degree hybrid into an electrical signal by a photoelectric converter, and the output signal from the photoelectric converter is converted into a plurality of electrical signals by frequency using a digital filter. Thus, the carrier wave can be separated for each frequency using the digital filter.

Further, in the reception method of the nineteenth aspect , in order to compensate for nonlinear waveform distortion due to nonlinear interaction between a plurality of carrier waves, preprocessing for symbol phase synchronization between the plurality of carrier waves is performed, and then the nonlinear waveform distortion is reduced. It is approximated by a waveform degradation model due to four-wave mixed light crosstalk, etc., and the nonlinear equation of this waveform degradation model is simplified by linearizing it by a sequential approximate solution, etc., and this simplified waveform distortion model Since the compensation is performed, the nonlinear compensation calculation can be realized by a simple electric calculation circuit.

  Embodiments of the present invention will be described below with reference to the accompanying drawings.

[Description of the form of signal light to which the present invention is applied]
First, the form of signal light to which the receiving apparatus of the present invention is applied will be described. In the receiving apparatus of the present invention, a signal obtained by multiplexing optical carriers (optical carriers and subcarriers) having a plurality of frequencies encoded with transmission information, or optical carriers (optical carriers and subcarriers) having independent polarizations. Assume that light is received.

  For example, as such signal light, there is wavelength division multiplexing (WDM) signal light in which optical carriers of different wavelengths are individually modulated and multiplexed using a wavelength dispersion medium. Further, the present invention can also be applied to multicarrier signal light that transmits one client information by separating it into signal lights of a plurality of carriers and subcarriers whose frequencies are close to each other.

  Also, orthogonal frequency division multiplexing (multiple carriers) is used to multiplex a plurality of carrier waves, and are multiplexed at a high density until the modulation frequency (bit rate) of each carrier becomes approximately the same as the frequency interval of the carriers. There is an OFDM (Orthogonal Frequency Division Multiplexing) signal. These signal lights are physically in a signal light format in which a plurality of frequencies are multiplexed, and can be expressed by the conceptual diagram shown in FIG.

  FIG. 1A is a conceptual diagram of multicarrier signal light, in which a plurality of carriers Ch-1, Ch-2, Ch-3, and Ch-4 are modulated, and signal lights E1, E2, E3, and E4 are modulated. A multiplexed example is shown. FIG. 1B is a conceptual diagram of multicarrier / polarization multiplexed signal light, and is a conceptual diagram of signal light in which multicarrier signal light or OFDM signal light is further polarization multiplexed. As shown in FIG. 1B, polarization multiplexed signal light in which different signal lights are allocated and transmitted to independent polarizations is also assumed as an application destination of the present invention.

[First Embodiment]
(Description of configuration example of receiving apparatus)
Next, the configuration of the receiving apparatus according to the first embodiment of the present invention will be described. In the conventional optical fiber transmission system, the nonlinearity of the transmission line fiber causes the received waveform to be distorted and deteriorates the transmission characteristics. This waveform distortion is uniquely determined depending on the transmitted optical electric field waveform, and the waveform distortion can be predicted from the received waveform. That is, the principle is to predict the nonlinear waveform distortion received using the reception waveform of the adjacent channel and compensate for the waveform distortion, whether it is transmission of WDM signal light, transmission of OFDM signal or multicarrier signal. Is possible.

  In the first embodiment of the present invention, nonlinear waveform deterioration is approximated by a waveform deterioration model by FWM crosstalk (four-wave mixed crosstalk) to simplify the description of waveform deterioration. FWM crosstalk is modeled as a phenomenon in which an optical electric field proportional to the product of the optical electric fields of three carriers and subcarriers having different frequencies or polarizations is generated.

  Of the three, two carriers and subcarriers may be degenerated and become the same subcarrier and carrier. The FWM crosstalk optical field generated by the FWM is superimposed on the optical field of another carrier or subcarrier, and the photoelectrolytic waveform is distorted.

  FIG. 2 shows, as an example, the relationship between the carrier, the subcarrier, and the carrier on which the FWM crosstalk is superimposed, the frequency of the subcarrier, and the polarization.

In FIG. 2A, an FWM cross is generated in the optical field E4 of the channel Ch-4 by the optical fields E1, E2, and E3 generated by the three channels Ch-1, Ch-2, and Ch-3 having different frequencies (wavelengths). An example in which a talk (E3 × E2 × E1 ^* ) occurs is shown. In FIG. 2B, an FWM crosstalk (E1X × E2X × E1Y ^* ) is generated in the optical electric field E2Y by the X-polarized light electric field E1X, the Y-polarized light electric field E1Y, and the X-polarized light electric field E2X ^. Shows an example of the occurrence of. 2A shows the occurrence of FWM crosstalk between signal lights having a plurality of frequencies, and FIG. 2B shows FWM crosstalk between signal lights having a plurality of frequencies and signal lights having different polarizations. It shows the occurrence.

  In this case, the FWM crosstalk optical electric field waveform at the output end of the optical fiber transmission line can be expressed using the optical electric field waveform at the input end of the optical fiber transmission line, that is, the intensity and phase of the optical electric field (next) Reference 1).

  [Reference 1] P.O. Hill, “cw-three wave mixing in single mode optical fibers,” J. Appl. Phys., 5098.

  At the receiving end of the carrier or subcarrier that has received FWM crosstalk, an optical electric field waveform obtained by adding the optical electric field waveform of the FWM crosstalk to the optical electric field waveform of the main signal is input to the receiver. In other words, since the optical electric field waveform obtained by adding the optical frequency waveform of the surrounding frequency, the polarized carrier and the subcarrier to the optical electric field waveform of the main signal is received, the received optical field of each carrier and subcarrier is received. Is described by a third-order nonlinear simultaneous equation of these transmitted optical fields. In the compensation arithmetic circuit that compensates for nonlinear waveform degradation, the optical receiver observes the waveform output from the optical fiber transmission path of each carrier and subcarrier, and generates a transmission electric field waveform that becomes the received waveform of the nonlinear simultaneous equations. It is obtained by solving the nonlinear simultaneous equations.

FIG. 3 is a diagram illustrating a configuration example of a receiving apparatus according to an embodiment of the present invention.
In the receiving apparatus shown in FIG. 3, the input signal light including a plurality of carrier waves is input to the optical 90-degree hybrid 102 together with the local light output from the local light generation unit 11.

  The optical 90-degree hybrid 101 has a function of inputting multicarrier local light and input signal light, separating them into components orthogonal to the components having the same optical phase, and outputting them to different ports. The output of the light 90-degree hybrid 101 is input to the photoelectric converters 201 and 202. For example, the system of the photoelectric converter 201 and the analog / digital converter (ADC) 301 is a signal system whose optical phase is the same phase component as the local light, and the system of the photoelectric converter 202 and the analog / digital converter (ADC) 302. Is a signal system of components orthogonal to the local light.

  The optical 90-degree hybrid 101 includes, for example, a multiplexer 110 that is a directional coupler shown in FIG. 4, and the multiplexer 110 mixes the signal light and the optical field of the local light and mixes them. The signal output from the two output ports of the wave detector 110 is detected by the differential photo-detector 211 in the photoelectric converter 201, so that the signal light and the station are detected by the square detection characteristics of the differential photo-detector 211. A product (cross-term) of light emission electric field is generated.

  This cross term has a term that depends on the phase difference between the signal light and the local light, and the two output ports from the multiplexer 110 have different dependencies on the phase difference. Therefore, when the optical frequencies of the signal light and the local light are close to each other, the phase difference between the signal light and the local light can be compared by taking the difference between them. Specifically, the intensity of the same phase component as that of the signal light is output based on the phase of the local light.

  In this manner, the electric signals output from the photoelectric converters 201 and 201 shown in FIG. 3 become an electric spectrum obtained by down-converting the optical spectrum of the signal light around the frequency of local light.

  The frequency band of this spectrum is limited by the response frequency band of the photoelectric converters 201 and 202, and a photoelectric converter having a frequency band of about 50 GHz is also commercially available. If this is used, an optical frequency difference of about 50 GHz can be obtained. Can support even in some cases. Here, it is assumed that the signal light is composed of carrier waves having a plurality of frequencies, and the frequency difference between the high-frequency end of the signal light and the local light, and the low-frequency end and the local light. However, it is necessary to select the photoelectric converter so that it is within the frequency band of the photoelectric converter.

  In FIG. 3, photocurrents output from the photoelectric converters 201 and 202 are converted into digital signals by analog / digital converters (ADC) 301 and 302, respectively. Usually, optical power of about several milliwatts is input to the photoelectric converters 201 and 202. Therefore, even if the conversion efficiency of the photoelectric converters 201 and 202 is assumed to be about 1 A / W, the average photoelectric flow rate is about several mA. is there. It is also necessary to change the impedance. Therefore, amplification is performed using a transimpedance amplifier so that sufficient voltage and impedance can be obtained as inputs to the analog / digital converters (ADC) 301 and 302. Also, the optical input power to the receiving device may change depending on the transmission path conditions, and an amplifier that keeps the output voltage constant even when the input changes so that it can be received without being affected by such changes. Use. This amplifier is called a limiting amplifier and is also used in a conventional receiver, and the technology is mature.

  When signals from the photoelectric converters 201 and 202 are input to the analog / digital converters (ADC) 301 and 302, the analog electric waveform is time-sampled and converted into a digital signal. The frequency band of the analog / digital converters (ADC) 301 and 302 is also a factor that limits the signal band.

  After the signal is converted into a digital signal, it is input to digital filters 401 and 402 that separate each carrier and subcarrier. As a method for realizing carrier separation relatively easily, there is FFT (Fast Fourier Transform) used for subcarrier separation of OFDM signals.

  FIG. 5 shows a configuration example of the digital filters 401 and 402. As shown in FIG. 5, the digital filter includes a serial / parallel conversion circuit 411 and an FFT 412. The FFT 412 includes N port inputs and N port outputs. Each input port corresponds to a time sequence. When a discrete sampling time signal is input, the discrete time signal is subjected to Fourier transform. It is a signal processing circuit in which a frequency spectrum is output from each output port. Here, serial data that is temporally continuous is divided at certain frame time intervals, rearranged in parallel by the serial-parallel conversion circuit 411, and input to the input port of the FFT 412.

  As a result, the discrete Fourier transformed spectrum signal is output from the output port of the FFT 412. Therefore, the carrier (subcarrier) interval of the input signal and the frequency interval of the discrete frequency spectrum of the FFT can be set to be equal for each carrier (subcarrier). That is, this is a case where the serial / parallel conversion frame period is equal to the carrier interval, and the bit rate of each carrier is equal to the frame interval. In some OFDM signals, a guard interval (GI) may be added. This is to add the same signal as the head of the frame by copying it at the end of the frame for each frame period, and to suppress intersymbol interference beyond the frame. In this case, the carrier separation is performed after the guard interval (GI) is removed before the FFT as in the conventional OFDM.

  The digital filters 401 and 402 and the nonlinear compensation calculation units 501 and 502 are electric calculation circuits that perform calculation using an electric calculation circuit (for example, a DSP (Digital Signal Processor)). The nonlinear compensation calculation units 501 and 502 include a phase synchronization unit 503 for achieving phase synchronization of signal bit phases (for example, symbol phase in orthogonal frequency division multiplexing) between a plurality of carrier subs and subcarriers, and nonlinear compensation. A compensation calculation unit 504 that executes calculation is included. (An example of phase synchronization processing performed by the phase synchronization unit 503 will be described later).

  The nonlinear compensation calculation units 51 and 502 include a compensation parameter learning unit 505. The compensation parameter learning unit 505 includes chromatic dispersion, chromatic dispersion slope of an optical fiber transmission line used for nonlinear compensation calculation, It has a function of learning any one parameter or all parameters among transmission parameters including nonlinear constants and compensation parameters depending on the relative phase between carriers of multiplexed signal light.

  In FIG. 3, the portion constituted by the optical 90-degree hybrid 101, the local light generation unit 11, the photoelectric converters 201 and 202, the analog / digital converters (ADC) 301 and 302, and the digital filters 401 and 402 is described above. It corresponds to the separation device. Further, the phase synchronization unit 503 in the nonlinear compensation calculation units 501 and 502 corresponds to the above-described phase synchronization unit, the compensation calculation unit 504 in the nonlinear compensation calculation units 501 and 502 corresponds to the above-described compensation calculation unit, The compensation parameter learning unit 505 corresponds to the above compensation parameter learning unit. In addition, the electric calculation circuit constituting the compensation calculation unit 504 corresponds to the above-described compensation calculation circuit.

Then, the signal light is separated for each carrier wave of each frequency by this separation device (optical 90-degree hybrid 101, digital filter 401, etc.), and the phase synchronization unit performs pre-processing of phase synchronization between a plurality of carrier waves. In the compensation calculation unit, the nonlinear waveform distortion is approximated by a waveform degradation model due to four-wave mixed light crosstalk, etc., and the nonlinear equation of this waveform degradation model is simplified by linearizing it with a successive approximation method, etc. Compensate for complex waveform distortion by using the waveform distortion model. The compensation parameter learning unit also includes a transmission parameter including the chromatic dispersion, chromatic dispersion slope, and nonlinear constant of the optical fiber transmission line used in the nonlinear compensation calculation, and a compensation parameter depending on the relative phase between the carriers of the multiplexed signal light. The compensation parameter is used when performing compensation computation of nonlinear waveform distortion in the compensation computation unit.
(The compensation parameter learning unit will be described again in FIG. 13).

  In the above description, the nonlinear compensation calculation unit 501 is described as including the phase synchronization unit 503. However, the present invention is not limited to this. For example, the phase synchronization unit 503 may be provided between the digital filter 401 and the nonlinear compensation calculation unit 501 (also in other receiving apparatuses in FIGS. 6, 16, and FIGS. 19 to 34 described later). A phase synchronization unit may be arranged before the nonlinear compensation calculation unit).

  FIG. 6 is a diagram illustrating a modification of the circuit configuration of the receiving apparatus illustrated in FIG. 1, and illustrates an example of a receiving apparatus that performs carrier separation using an optical dispersion medium. As shown in the figure, it is possible to separate each carrier using a light dispersion medium.

  In the configuration example shown in FIG. 6, the optical hybrid 121 (for example, optical 90-degree hybrid) is separated into local light, in-phase component, and quadrature component, and then each component is separated using a light dispersion medium. The carriers 131 and 132 separate the carrier.

  At this time, since local light is required for each carrier, local light that outputs a plurality of carriers having the frequency component is necessary for the carrier frequency of the signal light to be separated. 12 is provided. In this case, the difference between the frequency of signal light and the frequency of local light may be within the transmission band of each channel of the light dispersion medium and within the band of photoelectric conversion. Examples of the light dispersion medium include an element generated on a glass substrate by a planar optical circuit (PLC) technology, a wavelength separation element composed of a spatial optical system, an arrayed waveguide grating (AWG), WSS, and the like. and so on.

  In FIG. 6, a portion configured by the optical hybrid 121, the multimode local light generation unit 12, and the optical separators 131 and 132 corresponds to the above-described separator. Further, the nonlinear compensation calculation unit 501 includes the phase synchronization unit 503, the compensation calculation unit 504, and the compensation parameter learning unit 505 (not shown in FIG. 6) shown in FIG.

(Explanation of phase synchronization (signal bit phase estimation) between multiple carriers)
Here, an example of phase synchronization processing performed using the phase synchronization unit 503 in the nonlinear compensation calculation unit 501 described above will be described.
The carrier-separated parallel digital signal is compensated for time delay (skew) between subcarriers and carriers. This is because when the distance from the output end of the optical fiber transmission line to the nonlinear compensation calculation unit 501 differs depending on the carrier and subcarrier, the propagation position where the main nonlinear waveform degradation occurs, and the output end of the optical fiber transmission line This is because the distance between the carrier and the subcarrier may differ depending on the influence of chromatic dispersion and branching / multiplexing of the relay node.

  In this way, when there is a bit phase delay dependent on carrier and subcarrier, the phase of the signal bit of each adjacent carrier and subcarrier is estimated at the position where nonlinear waveform degradation has occurred, and nonlinear compensation is performed between the bits. Perform the operation. As a method, generally, a known pattern can be transmitted for each carrier and estimated from a change in a received signal. Further, if the signal light is turned off only for a certain channel, it is possible to detect the skew by directly detecting the FWM crosstalk generated in the channel at the receiving end.

  FIG. 7 shows an example of a transmission pattern and a reception pattern for detecting skew. FIG. 7A shows an example of a transmission pattern, and FIG. 7B shows an example of a reception pattern. Here, the receiving end receives the patterns of channels Ch-1, Ch-2, and Ch-3, and estimates the skew from the correlation with the FWM crosstalk light generated in channel Ch-4.

  In the case of the figure, since the FWM crosstalk generated in the channel Ch-4 is expressed by the product of the channels Ch-1, Ch-2, and Ch-3, the reception patterns of Ch-1, Ch-2, and Ch-3 are shown. The bit phase relationship in which the FWM crosstalk pattern of the channel Ch-4 is generated can be estimated. This method will also be described in the compensation parameter estimation method described later.

(Explanation of nonlinear compensation calculation method)
When the optical frequency is expressed as v0 + nΔv using the channel number n of the carrier and the subcarrier, the output is performed using the optical electric field waveforms E _T1 , E _Tm , E _Tn at the optical fiber input end of each carrier. The end FWM optical electric field waveform ΔE _k is expressed by the following equation (1). Here, φk represents a fixed component that does not change due to data modulation in the optical phase of the carrier and subcarrier channel number k.

Since this is added to the main signal, the received signal _ERK subjected to nonlinear distortion is expressed by the following equation.

  FWM generated by a combination of l, m, and n is crosstalk of the kth carrier and subcarrier. Combinations occur for various carriers and subcarriers. Among these, the relationship between the transmission waveform and the reception waveform is described by applying Equation (1) to the combination that results in FWM crosstalk that causes major waveform degradation. In the relational expression, the reception waveform of each carrier (subcarrier) and each polarization is represented by the product and sum of the transmission waveforms of each carrier (subcarrier) and polarization.

For example, with respect to signal light of four different frequency carriers and subcarriers, transmission waveforms E _T1 , E _T2 , E _T3 , E _T4 and reception waveforms E _R1 , E _R2 , E _R3 , including phase modulation by transmission data, The relationship of _ER4 can be modeled by the following equation. Here, φ ₁ , φ ₂ , φ ₃ , and φ ₄ represent the optical phase of the light source of each carrier, κ represents the nonlinear coupling coefficient, and φD _lmn represents the optical phase rotation due to wavelength dispersion.

Therefore, the transmission waveforms E _T1 , E _T2 , E _T3 , and E _T4 are estimated from the reception waveforms E _R1 , E _R2 , E _R3 , and E _R4 using the relational expression of the reception waveform and the transmission waveform as described above.

(Explanation of non-linear compensation calculation method using fluctuation difference)
In this case, there is a method for obtaining a difference between the reception signal and the transmission signal and a variation amount instead of directly obtaining the transmission signal from the reception signal. In this case, when the amount of fluctuation and _{ΔE k, E Tk, E Rk} , relationship Delta] E _k is the following equation (4). Here, the amount of variation ΔE _k is sequentially estimated with high accuracy using an approximate solution of a multi-dimensional nonlinear equation.

In this way, rather than directly from the received waveform E _R determine the transmission waveform E _T, for obtaining the difference, by giving a range of limit condition, there are advantages such as allowing estimation with high accuracy.

  Further, it is possible to speed up the convergence by assuming a condition such that the fluctuation amount ΔE is smaller than that of the main signal. In addition, although an initial value is assumed in the numerical approximate solution method, it is possible to select a more appropriate initial value (an arbitrary predetermined initial value) by using the condition of ΔE.

  For example, in the first step of obtaining the distortion fluctuation amount, the received waveform before compensation can be temporarily used as a transmission waveform of a part of the multi-dimensional nonlinear equation, and the first stage fluctuation amount estimation. In the step, the value used as the initial value can be changed to detect a value that provides a correction effect. Thus, by selecting an appropriate initial value, it becomes possible to perform nonlinear waveform distortion compensation calculation with high accuracy, such as speeding up convergence.

(Explanation of the method for obtaining approximate solution by variation difference method)
Waveform distortion due to the FWM crosstalk model is expressed by adding the crosstalk optical waveform to the optical waveform of the main signal at the transmitting end. Accordingly, the waveform E _RK of the receiver by subtracting the crosstalk variation amount Delta] E _K, it is possible to obtain the waveform E _TK at the transmitting end. Further, the crosstalk fluctuation amount ΔE _k can be estimated from the waveform _ERK at the receiving end. Since it is a nonlinear equation and difficult to solve directly, it is estimated using a sequential approximate solution.

_Assuming that the n- ^th estimated transmission waveform E _Tk ⁽ⁿ⁾ and the n-th estimated crosstalk fluctuation amount ΔE _k ⁽ⁿ⁾ , the recurrence formulas represented by the following equations (5) and (6) are used. An approximate solution can be obtained.

In equations (5) and (6), φ1, φ2, φ3, and φ4 represent the optical phase of the light source of each carrier, κ represents a nonlinear coupling coefficient, and φD _lmn represents the optical phase rotation due to wavelength dispersion.

FIG. 8 is a diagram showing a calculation configuration for sequentially solving a nonlinear equation, and shows a state in which an approximate solution is obtained using the above recurrence formula. However, the 0th-order estimated crosstalk fluctuation amount ΔE _k ⁽⁰⁾ is an initial value and gives an appropriate value.

  In the example shown in FIG. 8, 0 (zero) is given as an initial value.

That is, in FIG. 8, first-order compensation calculation 511_1 from the received waveform _{E R1,} based on the first equation of equation (6) described above, calculates first-order distortion variation Delta] E ₁ a ⁽¹⁾ To estimate. Similar to the first-order compensation calculation 511_1, the first-order compensation calculations 511_2, 511_3, and 511_4 are based on the received waveforms E _R2 , E _R3 , and E _R4 , the second and third formulas of the above-described formula (6). Based on the fourth equation, first-order distortion fluctuation amounts ΔE ₂ ⁽¹⁾ , ΔE ₃ ⁽¹⁾ , ΔE ₄ ⁽¹⁾ are calculated and estimated, respectively.

Then, the subtracter 513_1 is (5) based on the first equation of equation subtracts the estimated variation Delta] E ₁ ⁽¹⁾ from the received waveform _{E R1,} calculates _E ^{T1 (1).} Subtractor 513_2 is (5) based on the second equation of Formula subtracts the variation Delta] E ₂ was estimated from the received waveform _{E R2 ^(1),} and calculates _E ^{T2 (1).} Subtractor 513_3 is (5) based on the third expression of equation subtracts the variation Delta] E ₃ were estimated from the received waveform _{E R3 ^(1),} and calculates _E ^{T3: (1)} the subtractor 513-4 is , (5) based on the fourth equation of formula subtracts the variation Delta] E ₄ was estimated from the received waveform _{E R4 ^(1),} and calculates _E ^{T4 (1).}

Subsequently, the second-order compensation calculation 512_1 is based on the estimated waveforms E _T1 ⁽²⁾ , E _T2 ⁽²⁾ , E _T2 ⁽³⁾ , and E _T4 ^(4). Based on this, the second-order distortion fluctuation amount ΔE ₁ ⁽²⁾ is calculated and estimated. Similar to the second-order compensation operation 512_1, the first-order compensation operations 512_2, 512_3, and 512_4 have the estimated waveforms E _T1 ⁽²⁾ , E _T2 ⁽²⁾ , E _T2 ⁽³⁾ , and E _T4 ^(4). From the second formula, the third formula, and the fourth formula of the above-described formula (6), the second-order distortion fluctuation amounts ΔE ₂ ⁽²⁾ , ΔE ₃ ⁽²⁾ , ΔE ₄ ⁽²⁾ are respectively Calculate and estimate.

Then, the subtracter 514_1 is (5) based on the first equation of equation subtracts the estimated variation Delta] E ₁ ⁽²⁾ from the received waveform _{E R1,} calculates _E ^{T1 (2).} Subtractor 514_2 is (5) based on the second equation of Formula subtracts the estimated variation Delta] E ₂ ⁽²⁾ from the received waveform _{E R2,} computes _E ^{T2 (2).} Subtractor 514_3 is (5) based on the third expression of equation subtracts the estimated variation Delta] E ₃ ⁽²⁾ from the received waveform _{E R3,} calculated _E ^{T3 (2),} subtractor 514-4 is Based on the fourth equation of Equation (5), the variation ΔE ₄ ⁽²⁾ estimated from the received waveform E _R4 is subtracted to calculate E _T4 ⁽²⁾ .

Hereinafter, the processing based on the above-described equations (5) and (6) is repeated up to the nth order, and the final transmission waveforms _T1 ⁽ⁿ⁾ , E _T2 ⁽ⁿ⁾ , E _T2 ⁽ⁿ⁾ , E _T4 ^{(n )} Is estimated.

(Explanation of optical phase between carriers in nonlinear compensation calculation based on distortion variation)
Here, an example of symbol phase synchronization processing performed using the above-described phase synchronization unit 503 (see, for example, FIG. 3) will be described.

In the above formulas (5) and (6), φ1, φ2, φ3, and φ4 represent the optical phases of the light sources of the carriers 1, 2, 3, and 4, and φD _lmn represents the optical phase rotation due to wavelength dispersion.

  First, since the optical phase of the local light generation unit and the optical phase of the transmission light source carrier are in an asynchronous state, it is necessary to compensate for the phase rotation between them. In general, in information transmission, information is mapped to the amplitude and phase of a carrier wave and transmitted. Amplitude and phase mapping can be represented by points on a complex plane and is called a constellation map.

  As shown in FIG. 9A, the digital signal of each carrier after carrier separation is different from the phase mapping at the receiving end (for example, FIG. 9C) as shown in FIG. A) is rotating as a whole. Here, since FIG. 9A is an example in the case of quaternary phase modulation (QPSK), there are also four displacement directions. This is because the phases of the local light and the transmitted light are asynchronous. Further, this rotation angle varies with time.

  This is compensated to obtain the state shown in FIG. In general, the optical phase φk of each phase carrier fluctuates with time, but it is a fluctuation several orders of magnitude slower than the modulation speed in optical communication, and is extracted by separating it from the data phase fluctuation by averaging over time. (See, for example, Reference 2).

  [Reference 2] D. N. Godard, “Self-Recovering equalization and carrier tracking in two dimensional data communication systems,” IEEE Trans. Communication, Vol. Com-28, No. 11, 1980, p. 1867.

  For example, if the spectral line width of the light source is several kHz, the phase φk is stable for a time of about 1 ms, so φk can be estimated by nonlinearly averaging the optical phase of the received signal at time intervals shorter than this. It is.

  In addition, φk is subject to time variation even when the sub-carrier, the optical path length difference before multiplexing the carrier, and the wavelength dependence (wavelength dispersion) of the optical path length difference of the transmission path change with time. Since the speed is several orders of magnitude slower than the phase fluctuation caused by data modulation, it can be obtained separately by time averaging.

  FIG. 10 shows the configuration of an arithmetic circuit diagram for carrier estimation and phase synchronization. The phase rotation θ due to local light is removed from the received sampling value as shown in FIG. 9A, and FIG. The compensation method is shown as follows.

  As shown in FIG. 10, there is a method in which the complex optical electric field is raised to the fourth power and an average is taken between a plurality of bits (see the above-mentioned Reference 2).

In the example shown in FIG. 10, each channel received signal is sampled and converted into a digital complex value, which is sequentially input in time series, and a fourth power calculation unit 521, a moving average unit 522, a phase rotation angle extraction unit (Arg ( )) 523, and the phase rotation processing unit (Exp (−jθ)) 524 and the adder 525 output a digital complex value from which the local light phase rotation θ is removed. Thus, by further performing a nonlinear compensation calculation, the term relating to φ _{k in} the above equation is compensated and can be made zero.

  Secondly, the crosstalk fluctuation is expressed by a complex number, and it is necessary to estimate the phase rotation on the complex plane for nonlinear distortion compensation. This corresponds to the optical phase rotation φDlmn due to the chromatic dispersion of the above equation, but the phase angle of the fluctuation amount is chromatic dispersion, the optical path length difference between carriers at the transmitting end, the relative phase variation between each carrier at the transmitting end, etc. Depends on.

  Explaining this reason, for example, FWM crosstalk depends on the optical phase of the carrier that is the source, and in order to compensate for crosstalk, a relative phase relationship between the carriers is required. In particular, when each carrier and subcarrier are phase-modulated, the phase of the optical field of FWM crosstalk depends on the modulation phase depending on the transmission data of the adjacent channel and the relative phase of the light sources of the carrier and subcarrier. When the optical field of the FWM crosstalk is superimposed on the optical field of the main signal, waveform distortion occurs depending on the relative phase between the optical phase of the main signal and the optical phase of the FWM crosstalk.

  On the constellation map in which the received waveform is time-sampled and the values are plotted on a complex number plane, the position of the plot is displaced by FWM crosstalk as shown in FIG. 9B. The optical phase of FWM crosstalk changes depending on the phase modulation by the transmission data of each carrier and subcarrier that is the source of FWM crosstalk.

As a method of estimating this angle, as shown in FIG. 7, there is a method of turning off a certain channel and detecting an FWM crosstalk optical field generated in that channel. In the example shown in the figure, the amplitude and phase of the FWM crosstalk can be detected by performing coherent detection on Ch-4. Moreover, since the phase in each bit of Ch-1, Ch-2, and Ch-3 that causes it can also be estimated, φD _lmn of the above equation can be estimated from the correlation thereof.

Also, blind estimation that estimates φD _lmn is possible so that the dispersion of the distribution of the compensated plot becomes small so that the compensated constellation as shown in FIG. (See Reference 2 above).

(Explanation of estimation of parameters such as nonlinear coupling constants indicating transmission path conditions necessary for compensation calculation)
The nonlinear coupling coefficient κ in the above equation is also necessary for the compensation calculation. This value determines the FWM crosstalk efficiency.

  As a method of estimating this value, as shown in FIG. 7, there is a method of turning off a certain channel and detecting an FWM crosstalk optical field generated in that channel. In the example shown in FIG. 7, the amplitude of the FWM crosstalk can be detected by performing coherent detection on Ch-4. Therefore, since the amplitude / phase mapping of the other channels Ch-1, Ch-2, and Ch-3 can be estimated, the nonlinear coupling constant κ can be estimated from the relationship between the amplitude of the FWM and the amplitude of the channel that causes it.

  Further, blind estimation for estimating the nonlinear coupling constant κ is also possible so that the constellation after compensation as shown in FIG. 9C is placed in the same circle and the distribution of the plot distribution after compensation is reduced. is there. Further, in the equation, the same nonlinear coupling constant κ is used for all the FWM crosstalk fluctuation amount terms, but the compensation accuracy can be improved by estimating each of the FWM crosstalk fluctuation terms individually.

Further, the nonlinear coupling coefficient kappa, dispersed phase rotation phi _D is the nonlinear coefficient of the transmission path, the polarization state is a parameter that depends on the wavelength dispersion. Since these values have typical values determined to some extent depending on the type of optical fiber, these values can also be used.

  Also, assuming that these values depend on the manufacturing method and manufacturer of the optical fiber transmission line, and that the transmission line changes over time due to environmental fluctuations, estimate or monitor these values. A configuration that feeds back to the calculation unit of the nonlinear compensation is required. It is also necessary to estimate the loss coefficient α, the second-order propagation constant β2 that depends on the chromatic dispersion, the third-order propagation constant β3 that depends on the chromatic dispersion slope, and the like. Details are described in the compensation parameter estimation method.

(Explanation of model description formula for nonlinear waveform degradation in optical transmission line)
In this case, the optical signal waveform at the input end is estimated from the optical signal waveform at the output end of the optical fiber transmission line. In general, a change in waveform due to propagation in an optical fiber transmission line is described by being modeled by a nonlinear Schrodinger equation (see the following Reference 3).
[Reference 3] Agrawal, Nonlinear Fiber Optics, third edition, p.39-45

  The amplitude / phase waveform at the fiber output end in the nonlinear Schroedinger equation, or the time waveform of two components (in-phase component / orthogonal phase component) that are in phase orthogonal in the complex plane display, propagation axis z = L (L: transmission fiber length) The waveform at the input end z = 0 can be obtained by giving as a boundary condition in FIG. At that time, it is necessary to give a loss coefficient: α, dispersion β2, dispersion slope β3, and nonlinear coefficient γ as propagation constants.

(Modeling with FWM nonlinear waveform degradation, explanation of simultaneous equations)
Generation of FWM due to non-linearity in an optical fiber transmission line is described by a simple mathematical expression (see the above-mentioned Reference 1).

(Explanation of non-linear compensation including XPM and SPM)
In the combination of l, m, and n, when degenerate to l = n, a phenomenon called cross-phase modulation is described, which is proportional to the strength of the nth carrier and subcarrier, and the kth carrier. Phase rotation occurs. Further, the degeneracy of l = m = n = k corresponds to self phase modulation (SPM). In the model using FWM crosstalk, not only the nonlinear phenomenon interpreted as FWM crosstalk as described above but also XPM and SPM can be described.

  The optical phase of FWM crosstalk is completely random with its own optical phase, whereas cross-phase light (XPM) with l = n and self-phase modulation (SPM) with l = m = n Since the optical phase is orthogonal to the main signal, waveform deterioration due to crosstalk is small. Therefore, fluctuations due to XPM and SPM may be ignored, and only FWM crosstalk whose relative phase with respect to the main signal is random may be specialized in order to reduce the amount of calculation.

(Example for 4 carriers)
For example, transmission waveforms E _T1 , E _T2 , E _T3 , E _T4 and reception waveforms E _R1 , E _R2 , E _R3 including phase modulation by transmission data for signal light of four different frequency carriers and subcarriers. , _ER4 can be modeled by the following equation (7). Here, φ1, φ2, φ3, and φ4 represent the optical phase of the light source of each carrier, κ represents the nonlinear coupling coefficient, and φD _lmn represents the optical phase rotation due to wavelength dispersion.

(Explanation of approximate solution of FWM crosstalk model)
The received signal waveform is represented by the product of the values of each channel of the transmitted signal waveform. Therefore, when obtaining the symbol of the transmission signal from the reception signal, the nonlinear simultaneous equations are solved. In many cases, it is difficult to solve analytically, and a method of approximately solving a nonlinear equation by numerical calculation is used. Various methods have been proposed for numerical calculation. Generally, an approximate solution is obtained by giving an appropriate initial value and converting it to a simple equation that can be obtained analytically, for example, a linear equation. Further, using the approximate solution, an approximate solution with high accuracy is obtained by the same procedure. In this method, a value close to the true solution is gradually obtained by repeatedly calculating this operation.

(Multiple Newton method)
Waveform distortion due to the FWM crosstalk model is expressed by adding the crosstalk optical waveform to the optical waveform of the main signal at the transmitting end. Here, since the optical waveform of the added crosstalk is represented by the product of three optical electric field waveforms including not only its own carrier (subcarrier) but also surrounding carriers and subcarriers, the relationship between the transmission waveform and the reception waveform Becomes a multiple simultaneous nonlinear equation. Here, as a method for obtaining this solution approximately, there is a multiple Newton method (see Reference 5).

  [Reference 5] L. K. Schubert, “Modification of a Quasi-Newton Method for Nonlinear Equations with a Sparse Jacobian,” Mathematics of Computation, Vol. 24, No. 109 (Jan., 1970), pp. 27-30

  In addition, there are methods such as dichotomy, sequential substitution, and Steffensen's method (see Reference Document 6 below).

  [Reference 6] Noda, “General Steffensen Iterative Method for Simultaneous Nonlinear Equations (Nonlinear Programming (2)),” Abstracts of Autumn Meeting of the Japan Operations Research Society Autumn Meeting, 2-A-5, p.128-129

  In this case, as shown in FIG. 11A, a linear solution is obtained by simplifying, for example, converting a nonlinear equation into a linear equation using a certain appropriate initial value. Using this primary solution, the nonlinear equation is simplified again to obtain a quadratic solution. Similarly, by repeating the operation (steps S11 to S13) for obtaining the (n + 1) th order solution using the nth order solution, a more accurate solution of the nonlinear equation is obtained by numerical calculation. FIG. 11B shows an nth-order approximate solution and an n + 1-order approximate solution (steps S21 and S22) and then an n + second-order solution (step S23). This is a method using the following approximate solution.

(Explanation of sequential method using received waveform as initial value)
Waveform distortion due to the FWM crosstalk model is expressed by adding the crosstalk optical waveform to the optical waveform of the main signal at the transmitting end. Accordingly, the crosstalk optical waveform is obtained and the value is subtracted from the received optical waveform to obtain the transmission optical waveform. This method is shown in FIG.

When this method is used, it is necessary to obtain a crosstalk optical waveform from the received waveform. As a simple method, in the relational expression between the transmission waveform and the reception waveform by FWM crosstalk, and the FWM crosstalk terms in the second and subsequent terms in the equations (8) to (8), the transmission waveform is replaced with the reception waveform and crossed. There is a method of using a talk waveform. By subtracting this from the received waveform, the first transmission waveform estimated value ETK (1) can be estimated. Next, the first transmission waveform E _TK ⁽¹⁾ is substituted as a transmission waveform into an equation for obtaining the FWM crosstalk, and the FWM crosstalk waveform is obtained again and subtracted from the reception waveform _ERK to obtain the second transmission. The estimated waveform value E _TK ⁽²⁾ can be obtained. By repeating this, a transmission waveform with higher accuracy is estimated. This is expressed by the following equation.

  The calculation circuit diagram in this case is the same as the calculation circuit diagram shown in FIG.

In addition, as an improved version of the above method, in the relational expression between the transmission waveform and the reception waveform due to FWM crosstalk, and the FWM crosstalk terms in the second and subsequent terms of equations (2) to (8), transmission is performed except for the own channel. While replacing the waveform _{E Tm} received waveform _{E Rm} or by sequentially calculated estimates _E ^{Tm (p),,} as a transmit waveform _{E Tk} for its channel, the _{E Tk} is converted to multiple linear equations There is a way to ask.

  Since the transmission waveform is not approximated by the reception waveform for its own channel, a highly accurate FWM crosstalk waveform can be obtained accordingly. The received waveform is a waveform obtained by adding the FWM crosstalk waveform to the transmitted waveform. If the transmitted waveform other than its own channel is replaced with the received waveform of that channel in the FWM crosstalk term of this model formula, the received waveform is known. Therefore, a linear equation representing the relationship between the reception waveform and the transmission waveform of its own channel is obtained. This can be solved easily and the estimated value of the first transmission waveform can be obtained. Since the waveform obtained by subtracting the reception waveform from this waveform becomes the FWM crosstalk waveform, it can be understood as a method for obtaining the distortion fluctuation amount.

FIG. 12 shows an example of an arithmetic circuit that approximately solves a multi-dimensional nonlinear equation. Here, in the first arithmetic step shown in step S31, the received waveforms E _R1 , E _R2 , E _R3 , E _{R4 are shown.} From these, the first estimated transmission waveforms E ₁ ⁽¹⁾ , E ₂ ⁽¹⁾ , E ₃ ⁽¹⁾ , E ₄ ⁽¹⁾ are estimated. Subsequently, in the second calculation step shown in step S32, for example, for the waveform of E ₁ ⁽²⁾ , the received waveform E _R1 and the first estimated transmission waveforms E ₁ ⁽¹⁾ , E ₂ ⁽¹⁾ , E ₃ ⁽¹⁾ and E ₄ ⁽¹⁾ are used to estimate the second estimated waveform E ₁ ⁽²⁾ . The same applies to the other second estimated waveforms E ₂ ⁽²⁾ , E ₃ ⁽²⁾ , and E ₄ ⁽²⁾ .

(Description of compensation parameter estimation method by compensation parameter learning unit 505)
The nonlinear coupling constant of the transmission line, chromatic dispersion, or the FWM generation efficiency determined by them, and the relative phase difference between the FWM and the main signal are necessary for the compensation calculation. In addition, the relative phase between the carrier of the transmitting end light source and the subcarrier, or the FWM crosstalk determined by the carrier and the relative phase of the main signal is also necessary for the compensation calculation.

  Further, the bit phase delay difference between the carrier and the subcarrier at the position where the transmission / reception bit phase and the nonlinearity occur is also necessary as a compensation parameter.

  These values can be measured for transmission path parameters such as nonlinear coupling coefficient and chromatic dispersion by sending a known transmission signal from the transmission end and analyzing the distortion of the transmission pattern at the reception end. In addition, a blind estimation method is also possible in which a compensation parameter is estimated so as to maximize the compensation calculation effect while receiving an unknown actual traffic signal (see Reference Document 2 described above).

  Further, since the signal flowing through the optical transmission system has a frame structure, there is a method for estimating a compensation parameter by using a characteristic signal pattern of the frame as a known signal. Here, two independent polarizations in polarization multiplexing are also expressed in terms of carrier and subcarrier. That is, for example, when signals of two different polarizations are multiplexed, it is assumed that the signal is generated by two carriers and subcarriers. Further, when signal light in which two carriers and subcarriers are multiplexed for each polarization is further polarization multiplexed, it is considered that this signal is synthesized by a total of four carriers and subcarriers.

  In the nonlinear compensation calculation unit, the input position to the nonlinear compensation calculation unit and the signal bit phase delay difference of each carrier and subcarrier at the optical fiber output end, or the input position to the nonlinear compensation calculation unit, and the nonlinear waveform distortion are mainly used. The signal bit phase delay difference of each carrier and subcarrier at the generated position is corrected. Further, the nonlinear coupling constant, the optical phase difference between the FWM and the main signal is estimated and input to the compensation calculation unit. The nonlinear compensation calculation unit performs nonlinear compensation calculation using these values.

  FIG. 13 shows a configuration example of the compensation parameter estimation unit and the compensation arithmetic circuit. In the configuration example shown in FIG. 13, the skew monitor unit 532 that monitors the skew between each carrier and subcarrier based on the pilot signal transmitted from the transmission side, and the skew detection result in the skew monitor unit 532 Based on this, a skew correction unit 531 that corrects the skew between each carrier and subcarrier, a nonlinear coupling constant estimation unit 533 that estimates a nonlinear coupling constant of a simultaneous nonlinear equation representing the relationship between a transmission signal and a reception signal, and a transmission signal A phase estimation unit 534 that estimates the phase of the received signal, and a nonlinear compensation calculation processing unit 535 that performs nonlinear compensation calculation of the skew-corrected signal based on the parameters obtained by the nonlinear coupling constant estimation unit 533 and the phase estimation unit 534. It consists of.

  Note that the skew monitor unit 532, the skew correction unit 531, the nonlinear coupling constant estimation unit 533, and the phase estimation unit 534 are equivalent to the above-described compensation parameter learning unit. This compensation parameter learning unit learns chromatic dispersion, chromatic dispersion slope, transmission parameters including nonlinear constants of optical fiber transmission lines used for nonlinear compensation calculations, and compensation parameters that depend on the relative phase between carriers of multiplexed signal light. These values are input to the compensation arithmetic circuit.

  When performing nonlinear compensation calculation in this way, first, a circuit for adjusting the bit time phase delay (skew) between each carrier and subcarrier from the output end of the optical fiber transmission line to the digital calculation unit is required. . To compensate for the nonlinear waveform distortion, it is necessary to use the time waveform of each carrier and subcarrier at the transmission line position where the nonlinear waveform distortion occurs. When there is a chromatic dispersion compensation calculation, it is possible to trace back from the optical fiber output end to the propagation position where the nonlinear waveform distortion has occurred, and it is only necessary to estimate the time delay difference from the optical fiber output end to the digital calculation unit. On the other hand, when there is no dispersion compensation calculation, the nonlinear calculation unit needs to take into account the skew.

  It is assumed that the distance from the output end of the optical fiber transmission line to the compensation calculation unit varies depending on the carrier and subcarrier. Also, the propagation position where major nonlinear waveform degradation occurs and the distance to the output end of the optical fiber transmission line may differ between carriers and subcarriers due to the effects of chromatic dispersion and the demultiplexing / multiplexing of relay nodes. is assumed. In this way, when there is a carrier and subcarrier-dependent skew, the phase of the signal bit of each adjacent carrier and subcarrier is estimated at the position where nonlinear waveform degradation has occurred, and nonlinear compensation calculation is performed between the bits. carry out. Therefore, it is necessary to estimate which signal bit phase of the received signal of each carrier or subcarrier is generated by the FWM crosstalk received at the receiving end with respect to a certain carrier or subcarrier.

  As a method of monitoring this, there is a method of sending a pilot signal and estimating it from the received waveform. The simplest basic pattern is to output a single bit pulse for each carrier and subcarrier, and the FWM crosstalk generation position of the channel where FWM crosstalk occurs and the optical phase by coherent reception. To detect. The position of a single pulse is shifted bit by bit, and the FWM crosstalk generation pattern, amplitude and phase are observed.

  FIG. 14 shows an example of a transmission pilot signal for estimating a compensation parameter. The generation position of the FWM crosstalk generated in the channel Ch-4 by the channels Ch-1, Ch-2, and Ch-3, and its optical phase. And find the amplitude. Thereby, the nonlinear coupling constant and the phase term of the simultaneous nonlinear equations representing the relationship between the transmission signal and the reception signal can also be estimated.

  Further, even if it is not a single pulse, for example, if it is a known signal sequence such as a pseudo-random binary sequence (PRBS), the amount of skew between the carrier and the subcarrier that matches the generated FWM crosstalk pattern is searched for. It is possible. Assuming a bit phase delay between the carrier and the subcarrier, an occurrence pattern of FWM crosstalk can be predicted. The bit phase delay amount is swept to find a skew that matches the predicted FWM crosstalk pattern with the actually observed FWM crosstalk pattern.

(Explanation of experiment / simulation results showing the effect of the invention)
Each of three different frequency carriers was individually modulated with a PRBS NRZ pattern and transmitted through a 20 km dispersion-shifted fiber. At this time, the input power to the optical fiber is increased and the nonlinear waveform distortion is set to be large. In particular, in the channel 2 at the center of the three channels, the nonlinear waveform distortion is large. FIG. 15 shows a probability distribution of photocurrent values observed for channel 2 after separating three channels at the receiving end. In the originally expected probability distribution, two peaks corresponding to digital data 0 and 1 should be seen. However, in the probability distribution before distribution compensation shown in FIG. 15A, three peaks are seen in the probability distribution, and it can be seen that interference from other channels occurs. At this time, when the digital discrimination threshold was set as shown in the figure, the error rate was minimized and was 4.7 × 10 −3. On the other hand, when a compensation calculation was performed, a distribution having two peaks as shown in FIG. 15B was shown. Therefore, it is similar to the ideal probability distribution without waveform distortion. At this time, the error rate is reduced by about an order of magnitude to 5.0 × 10 −4, and the compensation effect is noticeable.

[Second Embodiment]
As a second embodiment of the present invention, an example of performing polarization separation (for example, an example of 2 carriers + polarized waves) will be described. FIG. 16 shows a configuration example of a receiving apparatus to which a polarization separator is added.

  When receiving polarization multiplexed signal light, it is separated into two independent polarizations by a polarization separator (PBS: optical beam splitter) 21. Then, the signal light of each polarization and the local light are input to the optical 90-degree hybrids 101 and 102, and are separated into the same phase component and the orthogonal phase component as the local light for each polarization. The signal light is input to the photoelectric converters 201 to 204, converted into electric signals, and further converted into digital signals by analog / digital converters (ADC) 301 to 304.

  Furthermore, as shown in the first embodiment, the signals in each carrier can be separated by using the FFT in the demultiplexing filters (digital filter or the like) 341-344. In this state, a digital signal separated for each carrier and each polarization is obtained.

  However, in general, the polarization of the received signal after transmission through the optical fiber transmission line is random, and the two polarization axes of the polarization beam splitter (PBS) 21 and the two polarization axes multiplexed with the received signal light are Not there. For this reason, two polarization multiplexed signal lights are mixed in each output port separated into two by the optical beam splitter (PBS) 21.

  For this reason, the polarization separation calculation units 601 to 604 perform polarization separation calculation. In this case, the polarization separation method for signal light of a single carrier is a conventional technique, and can be implemented using digital signal processing as described in “Reference Document 2” described above. The signal light after carrier separation can be separated into respective polarization signals by a similar algorithm. At the same time, PMD compensation is also possible. The polarization separated signal light and the carrier / subcarrier separated digital signal are input to the nonlinear compensation calculation unit 501.

  In nonlinear compensation calculation of subcarrier multiplexed and polarization multiplexed signal light, nonlinear waveform distortion is described by FWM crosstalk generation model between N carriers / subcarriers and between two polarized waves, a total of 2N carriers. Compensate for that distortion. FIG. 17 shows an FWM crosstalk generation pattern in polarization multiplexed signal light having two subcarriers.

  FIG. 17 shows an FWM crosstalk generation pattern that is superimposed on an E_Lx carrier, and occurs in a symmetric relationship with respect to other carriers. Here, FWM crosstalk is defined such that the relationship between the phase of its own main signal and the phase of the crosstalk is not orthogonal and changes randomly. A comparison of the magnitude of the nonlinear coefficient χ for each pattern is shown in the lower table of FIG. Here, the value is based on the magnitude 3 of the nonlinear coefficient χ with respect to the signal light having the same polarization (see the following Reference 4).

  [Reference 4] Agrawal, Nonlinear Fiber Optics, third edition, p.207.

  Considering these three patterns, a received signal subjected to waveform distortion due to FWM crosstalk is expressed. By solving this, the transmission waveform can be estimated from the reception waveform. The arithmetic circuit is described as an approximate solution of the FWM crosstalk model.

  This simultaneous nonlinear equation can be calculated by the arithmetic circuit configuration shown in the first embodiment.

  In FIG. 16, polarization separators (light beam splitters (PBS)) 21 and 22 correspond to the above-described polarization separation device. In addition, the portion constituted by the optical 90-degree hybrids 101 and 102, the photoelectric converters 201 and 202, the analog / digital converters (ADC) 301, 302, 303, and 304 and the demultiplexing filters 341, 342, 343, and 344 is described above. The polarization separation calculation units 601, 602, 603, and 604 correspond to the above-described polarization separation calculation unit. Further, the nonlinear compensation calculation unit 501 includes a phase synchronization unit 503, a compensation calculation 504, and a compensation parameter learning unit 505 (not shown in FIG. 16) shown in FIG.

  Then, the polarization multiplexed signal light is separated into two by a polarization separation device, and after the interference between the two polarizations for each carrier frequency is removed by the polarization separation calculation unit, the plurality of carrier waves are separated. In order to compensate for the non-linear waveform distortion, a phase synchronization unit performs pre-processing of phase synchronization between carrier waves. Then, the non-linear waveform distortion is approximated by a waveform degradation model such as four-wave mixed light crosstalk by the compensation calculation unit, and the nonlinear equation of this waveform degradation model is simplified by linearizing it by a successive approximation method or the like. Compensates for waveform distortion using the waveform distortion model. As a result, the nonlinear compensation calculation can be realized with a simple electric calculation circuit. The compensation parameter learning unit 505 is a compensation parameter that depends on the chromatic dispersion of the optical fiber transmission line used for the nonlinear compensation calculation, the chromatic dispersion slope, the transmission parameter including the nonlinear constant, and the relative phase between the carriers of the multiplexed signal light. This compensation parameter is used when performing compensation computation of nonlinear waveform distortion in the compensation computation unit.

[Third Embodiment]
(Example of 3-carrier direct reception)
Since coherent detection is assumed at the receiving end, information on the optical waveform including the optical phase can be obtained, and the received waveforms ER1, ER2, ER3, and ER4 are given as complex numbers in the mathematical expression describing the relationship between the transmitted waveform and the received waveform. be able to. On the other hand, the conventional intensity modulation signal generally uses a direct reception instead of a coherent reception. In the case of an intensity-modulated signal, even if the relative phase between FWM crosstalk and the main signal is unknown, nonlinear compensation calculation can be performed if the relative phase difference between individual carriers and subcarriers can be estimated.

The photocurrent value Ik of the channel k is interfered by the FWM crosstalk electric field generated from the channel l, the channel m, and the channel n. However, l + m = n + k. This photocurrent value Ik is calculated by the following analytical expression using input powers P _k (t), P _l (t), P _m (t), and P _n (t) to the optical fiber transmission line of each channel. expressed.

Here, η _{l, m, n} exp (iΔθ _{l, m, n} ), degeneracy factor D _{l, m, n} , loss factor α, The optical phase of the channel was set to φ _k , φ _l , φ _m , and φ _n . It should be noted that, to define _{"Δφ l, m, n = φ} l + φ m -φ n -φ k + θ l, m, n ," it said.

  Since this equation is prepared for all channels and it is difficult to analytically solve the simultaneous multiple equations, the optical power Pn (t at the input end to the optical fiber transmission line after the second item, that is, the transmission end ) Is replaced with the received photocurrent value In (t) to obtain the optical power estimated value of the first transmitting end. This time, this value is used as the transmission end optical power for the second and subsequent items to obtain an optical power estimation value for the second transmission end. By repeating this operation, more accurate transmission end optical power is obtained. However, since the photocurrent and the optical power are handled in the same dimension, it is necessary to normalize or redefine the nonlinear coupling constants η′1, m, and n. There, it is standardized or redefined including the loss of the optical fiber transmission line and the conversion efficiency of the photoelectric converter. Actually, since it is implemented by digital signal processing, a value obtained by sampling the photocurrent value is used. Here, an expression for sequentially obtaining the optical power sampling value at the transmission end using the normalized nonlinear coupling constant η so that the transmission end optical power and the reception photocurrent value can be handled with the same amplitude scale is shown below. .

  S (0) k, i represents the p-th estimated value obtained sequentially with the transmission end optical power of the sampling time number i-th channel k. However, the nonlinear coupling constant η is defined as a value including optical fiber loss.

Here, in the case of 3 channels, the degeneracy coefficient is given by “D _2,2,3 = D _2,2,1 = 3” and “D _1,3,2 = 6”. It is done. Also, the phase term Δφ due to the phase matching condition can be described using a single value.

  By solving this recurrence formula, the waveform at the transmitting end can be calculated from the waveform at the receiving end.

[Fourth Embodiment]
(Description of an example using a self-phase modulation (SPM) phase rotation model)
By changing the light intensity waveform of the signal light of a certain carrier or subcarrier and measuring the phase rotation experienced by other carriers, it is also possible to estimate a calculation parameter such as a nonlinear constant from the measured value. It is also possible to measure with higher accuracy by changing the slope of the change in the light intensity waveform. It is also possible to measure chromatic dispersion by measuring the beat signal observed at the receiving end by changing the frequency interval of the carrier and subcarrier.

Various other methods have been proposed for measuring transmission path parameters. Measurement methods have also been proposed for nonlinear propagation constants, which can be measured using these principles. However, in general, a method of inputting measurement light from the fiber input end and analyzing the light output from the output end at the time of measurement is common, but in an actual system, the input end and the output end are separated by several tens of kilometers or more. In many cases, it is not possible to apply these principles as they are.
Therefore, it is necessary to include pilot light for measuring the propagation constant in the signal light. As the pilot light, one according to each propagation constant measurement method is prepared. Furthermore, the exchange of information necessary for the propagation constant measurement can be transferred using the upstream and downstream paths of the transponder, OSC (Optical Supervisory channel), and the like.

  Ideally, a method of calculating the back propagation by numerically solving the Schrödinger equation is desirable, but the calculation amount becomes enormous. Therefore, a method for approximating the input end waveform from the output end waveform of the optical fiber transmission line is required. A group velocity difference between channels is caused by chromatic dispersion, and a walk-off phenomenon occurs in which the bits of adjacent channels are shifted by about 1 bit.

As an index of the distance at which the walk-off occurs, there is a dispersion length “L _D = c / (λ ² R ² D)”. However, c: speed of light, λ: wavelength, R: bit rate, D: chromatic dispersion. In this case, there is a method of using an approximate model in which linear waveform degradation and nonlinear waveform degradation occur sequentially rather than simultaneously by dividing into sections of a distance where the influence due to the occurrence of the walk-off phenomenon is sufficiently small. Further, in the transmission line fiber, the signal light power gradually attenuates as it propagates due to its loss factor. Since the optical non-linear effect is greatly generated when the optical power is high, the non-linear effect generally occurring up to several kilometers from the input end of the transmission line fiber is dominant. Therefore, it can approximate to linear propagation in the subsequent part. As the distance index, there is an effective fiber length “Leff = (1−e− ^αL ) / α” determined by the loss coefficient α and the fiber length L. If this method is used, the distance for the reverse propagation calculation using the Schrodinger equation describing the non-linear propagation can be shortened, so that the amount of calculation can be reduced.

[Fifth embodiment]
Next, a split step method will be described as a fifth embodiment of the present invention. Nonlinear waveform degradation in the optical fiber transmission line can be captured as optical phase rotation proportional to the optical electric field strength. However, the optical electric field strength changes during propagation due to chromatic dispersion (a phenomenon in which the light speed varies slightly depending on the wavelength of the light, so that the arrival time is slightly shifted between light having a short wavelength and light having a long wavelength). Nonlinear phase rotation and chromatic dispersion are intricately intertwined because chromatic dispersion causes a change in the light intensity waveform.

  The non-linear Schrodinger equation is a model equation describing this waveform change. Conventionally, a method of solving this model formula by numerical calculation has been proposed. A split-step Fourier method is a promising method (see the following Reference 7).

  [Reference 7] Govind P. Agrawal, Nonliear Fiber Optics, Third Edition, p.51

  This is a method in which an optical fiber transmission line is divided into fine sections, and a linear calculation representing a waveform change and loss due to chromatic dispersion in each section and a non-linear calculation representing a non-linear phase rotation proportional to the intensity of the optical electric field are repeatedly calculated. In general, it has been used for the purpose of predicting a change in a transmission waveform due to optical fiber propagation and a reception waveform.

  Here, on the contrary, it is used for the purpose of estimating the transmission waveform from the reception waveform. Instead of predicting the waveform at “z = L” by giving the waveform at “z = 0” as the initial value at the propagation distance z, giving the waveform at “z = L” as the initial value, The waveform at “z = 0” is estimated.

  The time waveform A (z + h, T) after the time waveform A (z, T) at the propagation distance z has propagated to z + h is

  A (z + h, T) = exp (hD) exp (hN) A (z, T).

  However, D and N represent a linear calculation and a non-linear calculation, respectively, N is calculated in the time domain, and D is calculated in the frequency domain. In other words, A (z, T) is subjected to a nonlinear operation, and then converted to a frequency domain function by exp (hD) by exp (hD), a linear operation D is performed, and converted to a time domain function by inverse Fourier transform. Returned.

  As shown in FIGS. 18A and 18B, the step of linear back propagation (step S41), the step of IFF (step S42), the step of nonlinear reverse rotation (step S43), and the step of FFT (step) The process of S44) is repeatedly performed.

  In this case, in order to give “z = L” as an initial condition and propagate it in reverse, the reception is performed by repeating the calculation of obtaining the waveform at zh from the waveform at the z point with h as −h. The waveform at the transmitting end can be calculated from the waveform at the end.

  Other methods for implementing back propagation include loss factor α, second-order propagation constant β2 proportional to chromatic dispersion D [ps / nm / km], third-order propagation constant β3 proportional to chromatic dispersion slope, nonlinear coefficient Back propagation calculation is possible by inverting the sign of a propagation constant such as γ. Further, as the inverse operation of the N nonlinear operation, there are an operation using the FWM crosstalk model and an operation using the self-phase rotation model (fourth embodiment). It is as follows.

  If the section is finely divided, the calculation can be performed with higher accuracy, but the load on the calculation increases. Here, in order to reduce the calculation load, it is important to lengthen the section and reduce the calculation steps. In that case, as the values of propagation constants such as α, β2, β3, and γ used for the calculation, effective values that increase the compensation effect are used instead of actual values. When the compensation parameter is learned from the training pattern, its value is close to the effective value. In the case of blind estimation, feedback control is performed so that the waveform distortion after compensation is minimized. By applying the conventional training method and blind estimation method to the present invention, it is possible to perform estimation with a higher system.

(Supplementary explanation about FWM occurrence)
In general, FWM is a phenomenon in which light of three different frequencies (ω1, ω2, ω3) is mixed to generate light of a new frequency ω, for example, “ω = ω1 + ω2 + ω3”. This is called non-degenerate FWM, but two of the three frequencies may be degenerated. In WDM transmission, FWM induces inter-channel crosstalk in which FWM light generated by signal light of three or two channels is superimposed on another channel.

  The generation efficiency of FWM greatly depends on the dispersion characteristics of the optical fiber transmission line, and since the phase matching condition is satisfied in the vicinity of the zero dispersion wavelength band, the amount of crosstalk between WDM channels caused by FWM increases, resulting in waveform degradation. There is a problem that is large.

  For example, a specific example will be described in the case where the crosstalk amount is set as the deterioration factor parameter. When the zero dispersion wavelength of a certain optical fiber transmission line section is given, the FWM crosstalk amount generated in the channel -n (n = i + j-k) by the channels -i, -j, and -k in the section is as follows. It is represented by an analytical model equation (see references 1 and 3).

  "Reference 1" P.O. Hill, "cw-three wave mixin GIn single mode optical fibers," J. Appl. Phys., 5098

  Reference 3 by Agrawal, Nonlinear Fiber Optics, third edition, p.39-45

  Here, Ei, Ej, Ek, and En are optical field amplitudes of channels i, j, k, and n, respectively, a is a loss coefficient, χ is a nonlinear coefficient, and L is a fiber length.

  Δκ represents the amount of phase mismatch and depends on the channel frequency interval Δf, the zero dispersion wavelength λ0, and the chromatic dispersion slope ∂D / ∂λ.

  However, n0 is a value representing the wavelength position of the zero dispersion wavelength by a channel number, and is expressed as “n0 = c / (λch1−λ0) / Δf−1” by the signal light wavelengths of the zero dispersion wavelength λ0 and Ch−1. The

  In practice, FWM crosstalk is generated in channel n by various channel combinations i, j, k. By obtaining these sums, the amount of crosstalk generated in channel n can be obtained. At this time, since the electric field crosstalk amount generated by each combination is a two-dimensional vector amount expressed by amplitude and phase, it is originally the sum of the optical electric field vectors. However, in a general WDM system, since individual laser light sources are prepared as the light sources of the respective channels, the phase relationship between them is uncorrelated and changes every moment. Therefore, in order to sum the electric field FWM crosstalk generated in each channel combination with a vector, the optical phase needs to be known and is generally difficult. By uniquely fixing the relative phase between the carriers, it becomes easy to compensate for nonlinear waveform deterioration.

[Sixth Embodiment]
Next, a configuration example of a receiving apparatus according to the sixth embodiment of the present invention will be described.
(Description of basic configuration)
If the transmission line is non-linear, even if the channels are independent on the frequency axis and do not interfere with each other, interference (crosstalk) occurs between the non-linearities of the optical fiber transmission line. Although this interference depends on the characteristics of the optical fiber transmission line, the waveform distortion is predictable mainly from the transmission waveform of the adjacent channel and is deterministic. Therefore, if there is a model describing the transmission characteristics of the optical fiber transmission line, the relationship between the transmission waveform of the main adjacent channel and the reception waveform subjected to nonlinear waveform distortion can be described. Therefore, by solving this relationship in reverse, the transmission waveform can be obtained from the reception waveform of the adjacent channel.

  In order to compensate for nonlinear waveform distortion at the receiving end using the above method, the received waveforms of adjacent channels are observed, the received waveforms of each channel are captured in parallel, and the description of the optical fiber transmission line model is solved in reverse. Input to a compensation circuit that equalizes the waveform.

(Description of optical 90-degree hybrid, optical demultiplexing configuration)
In the sixth embodiment, phase-synchronized multimode local light is used as the local light generation unit at the receiving end. As a local light generator at the receiving end, when using a multimode light source in which the relative phase between each carrier and subcarrier does not change in time and is uniquely fixed, the signal light of any carrier or subcarrier is received coherently. Since the reference phase for this is made common, the mutual offset phase and offset frequency excluding the phase change due to transmission data modulation can be known.

  Therefore, the relative phase relationship between each carrier and subcarrier at the transmission position where the FWM crosstalk has occurred can be known, and compensation thereof can be made. Even if the relative phase between the carrier and subcarrier is fixed, the initial value of the phase relationship between each carrier of local light, subcarrier, and phase rotation due to chromatic dispersion of the optical fiber transmission line, due to nonlinear effects There are various factors of phase rotation, such as average phase rotation. Therefore, it is also effective to send a known signal such as a training pattern or a pilot signal to once learn the relative phase of the local light generation unit between each carrier and subcarrier.

  There is also a method of monitoring the waveform after compensation, introducing a parameter indicating the magnitude of the compensation effect, monitoring the value, and maintaining a state where the compensation effect is high by blind estimation. An example is CMA (Constant Modulus Algorism). Even in that case, since the phase relationship between each carrier and subcarrier of the local light is fixed, the relative relationship between the offset phase and the offset frequency at the output end of the optical fiber transmission line and the FWM crosstalk occurrence position, It can be estimated using the phase relationship once learned. That is, if learning is performed at a certain time, the value can be applied to the subsequent time. Even with a phase-synchronized light source, fluctuations can occur with time, so it is necessary to occasionally update the values of the phase offset and frequency offset used in the compensation calculation.

(Explanation about 90-degree optical hybrid)
When a phase-locked multimode light source is used as local light, it is desirable to detect signal light using each carrier and subcarrier as a phase reference while maintaining the relative phase relationship between the carrier and subcarrier.

  In this case, there is a method of comparing the phase of local light and signal light using an optical 90-degree hybrid. The 90-degree optical hybrid is one in which optical signals input from two ports are separated into optical components of the same phase and optical components of quadrature and output from different ports.

  As a conventional technique of optical 90-degree hybrid, there is a method using a 3-port optical multiplexer in the case of single carrier coherent reception (see Reference 8). In this example, components of the same phase and quadrature phase are output from 2 ports out of 3 ports.

  When a 2-port optical multiplexer is used, there is a method using a 2 × 2-port optical multiplexer and a differential optical receiver for local light and signal light as described in Reference 9 below. is there.

  [Reference 8] Seb J. Savory, et al., “Electronic compensation of chromatic dispersion using a diGItal coherent receiver,” Optics Express, Vol. 15, No. 5, 2120.

  [Reference 9] Keang-Po Ho, “Phase-modulated optical communication systems,” Springer, p.7

  In the former case, as shown in FIG. 19, the received signal light and the multimode local light output from the multimode local light generator 12 are input to an optical hybrid 121 (for example, an optical 90-degree hybrid) 121, The optical phase relationship is compared and decomposed into the same phase component and the orthogonal phase component, and output from different output ports.

  This is input to the optical separators 131 and 132 which are separated according to the wavelength using the wavelength dispersion medium, is separated for each carrier, and is converted into a photocurrent by the photoelectric converters 201 to 208. This photocurrent is converted into digital signals by analog-digital converters (ADC) 301 to 308, and digital signals for each carrier and subcarrier are input to the nonlinear compensation calculation unit 501. In this configuration, in the optical 90-degree hybrid, each carrier component is separated into the same phase component and quadrature phase component, and then the carrier and subcarrier are demultiplexed. Therefore, the reference phase of the phase detection of each carrier and subcarrier is It is common.

  In other words, since the optical phase of the signal light of each carrier and subcarrier is detected based on the local light of each carrier and subcarrier in a fixed relative phase relationship, the phase relationship between each carrier and subcarrier of the signal light Also turns out. This property has an advantage in a situation where the aspect of waveform degradation of FWM crosstalk changes depending on the phase relationship between the carrier and the subcarrier, and in a situation where it is compensated.

  On the other hand, when the latter 2 × 2 port multiplexer is used, 2 ports are set for each of the same phase component and the orthogonal phase component. After this is separated into a carrier and a subcarrier for each wavelength by an optical demultiplexer, it is necessary to input it to a differential photodetector.

  In the configuration shown in FIG. 19, the optical separators 131 and 132 correspond to the optical separators using the above-described wavelength dispersion medium, the optical hybrid 121 corresponds to the optical 90-degree hybrid, and multimode local light emission occurs. The unit 12 corresponds to the above-described multimode local light generation unit. Then, by the multimode local light generation unit and the optical 90-degree hybrid, it is separated into a component orthogonal to the component having the same optical phase for each carrier frequency and output to a different port, and the output light from the optical 90-degree hybrid Are separated for each frequency (wavelength) by an optical separator using a wavelength dispersion medium. Thereby, a carrier wave can be separated in an optical system without using an electric filter (digital filter or the like).

  FIG. 20 is a configuration example of a receiving apparatus when detecting either one of the same phase components (orthogonal phase components). At this time, for each carrier and subcarrier, the difference in distance from the two branch points of the multiplexer 141 to the two input points of the differential PDs 211A to 211D is a sufficiently small value with respect to the time length of 1 bit. It is necessary to keep it down.

FIG. 21 is a configuration example of a receiving apparatus for detecting both phase components of in-phase and quadrature phases. Compared with FIG. 21, the multiplexer 142, the optical separators 133 and 134, and the operation PD 211E. To 211H, analog / digital converters (ADC) 305, 308, and the like are added.
In the example shown in FIG. 21, the demultiplexer 31 separates the received light into the in-phase component and the quadrature phase component, inputs the in-phase component to the multiplexer 141, and the quadrature phase component to the multiplexer 142. input. The local light output from the multimode local light generation unit 12 is also demultiplexed by the demultiplexer 32, and the same phase component of the local light is input to the multiplexer 142 and the optical separator 134. Is shifted by π / 2 by the phase shifter 41 and input to the multiplexer 141 and the optical separator 131.

  On the other hand, there is a configuration in which phase comparison is performed by optical 90-degree hybrid after demultiplexing for each carrier and subcarrier. Both signal light and local light are separated into carriers and subcarriers for each wavelength by an optical demultiplexer, and then the optical phases of both are compared by an optical 90-degree hybrid. An example of this configuration is shown in FIG.

  In the receiving apparatus illustrated in FIG. 22, the optical separator 131 demultiplexes each carrier and subcarrier, and then performs phase comparison using the optical 90-degree hybrids 101 to 104. In this case, local light from the multimode local light generation unit 12 is also separated by the optical separator 132 and input to each of the light 90-degree hybrids 101 to 104.

  As a conventional technique of the optical 90-degree hybrid, there is a method of using a three-port optical multiplexer as described in Reference Document 8 in the case of single carrier coherent reception. When a 2-port optical multiplexer is used, a method of using local light and signal light as described in the above-mentioned Reference 9 using a 2 × 2-port optical multiplexer and a differential photodetector There is.

  In FIG. 22, an optical separator 131 corresponds to an optical separator for signal light using the aforementioned wavelength dispersion medium, and an optical separator 132 is an optical separator for local light emission using the aforementioned wavelength dispersion medium. The multi-mode local light generator 12 corresponds to the aforementioned multi-mode local light generator.

  Then, the input signal light is separated for each wavelength by the signal light separator and output to different ports, and the output light from the multimode local light generator is separated for each wavelength by the local light separator. Output to a different port. In addition, the output light from each port of the signal light optical separator and the output light from each port of the local light optical separator are input, and the components are orthogonal to the components whose optical phases match. An optical 90 degree hybrid of each carrier wave that is output separately to different ports is provided. Thereby, a carrier wave can be separated in an optical system without using an electric filter (digital filter or the like).

  FIG. 23 illustrates an example in which the multimode local light generation unit 12 and the optical separator 132 illustrated in FIG. 22 are replaced with individual local light generation units 11A to 11D.

  As shown in FIG. 23, even when individual local light generation units are used for each carrier and subcarrier, the relative phase between the local light generation units using a training pattern or blind estimation, The frequency interval difference can be estimated. For this reason, it is also possible to estimate the optical phase relationship between each carrier and subcarrier at the output end of the optical fiber transmission line in consideration of the phase offset and the frequency offset. In this case, it is necessary to update the phase offset and the frequency offset so as to follow the temporal variation speed of the optical phase predicted from the line width of the laser.

  In FIG. 23, an optical separator 131 corresponds to the optical separator of signal light using the above-described wavelength dispersion medium, and the local light generation units 11A, 11B, 11C, and 11D generate the above-mentioned plural local light generations. It corresponds to the part.

  Then, the output light from each port of the signal light optical separator and the output light from each local light generation unit are input and separated into a component orthogonal to a component in which both optical phases coincide with each other. And a plurality of light 90-degree hybrids output to the port. Thereby, a carrier wave can be separated in an optical system without using an electric filter (digital filter or the like).

(Description of configuration example of direct reception device)
When receiving signal light in which each carrier and subcarrier are directly modulated, the conventional reception method does not require coherent reception. However, in a signal that has undergone FWM crosstalk, the displacement of the time sampling value of the received waveform in the complex plane depends on the relative phase of the FWM crosstalk and the main signal. Depends on its relative phase.

  FIG. 24 is a diagram illustrating a configuration example of a direct reception apparatus. As illustrated in FIG. 24, the received signal light is separated into each carrier and subcarrier by an optical separator (demultiplexer) 131. The intensity is detected by the photoelectric converters 201 to 204 by direct reception. This is input to analog / digital converters (ADC) 301 to 304, converted into a digital signal, and then input to the nonlinear compensation calculation unit 501.

(Description of configuration example of photoelectric conversion / electrical stage separation receiver)
A homodyne receiver that separates carriers using an electric filter will be described. In this receiving apparatus, a light source that oscillates at a single wavelength is used as local light, and signal light and local light are mixed by a 90-degree optical hybrid and converted into a photocurrent by a photoelectric converter. Thereafter, each carrier and subcarrier are separated using a frequency separation filter in the electrical domain.

  Here, it is often used in the case of homodyne reception where the optical frequency of local light coincides around the center frequency of signal light. In this case, a wide frequency band of about half of the signal light is required for the optical receiver and the electric filter. For this reason, there is also a configuration in which demultiplexing by an optical filter and demultiplexing by an electric filter are used in combination.

  FIG. 25 is a diagram illustrating a configuration example of a homodyne reception device that performs carrier separation by an electric filter. In FIG. 25, the light source of the local light generation unit 11 that oscillates at a single wavelength is used as the local light, and the signal light and the local light are mixed by the optical 90-degree hybrid 101, and the in-phase component and the quadrature phase of the local light are mixed. The components are converted into photocurrents by photoelectric converters 201 and 202, respectively, and separated into carriers and subcarriers by electric filters 611 and 612.

  These are converted into digital signals by analog / digital converters (ADCs) 301 to 308, and then digital signals of adjacent carriers and subcarriers are input to the nonlinear compensation calculation unit 501 to compensate for nonlinear waveform distortion.

  As the electric filters 611 and 612, in order to demultiplex each carrier and subcarrier, an absolute value of a high frequency is required. Therefore, a temperature adjustment circuit for holding the temperature at a constant value may be necessary. is there. Also, depending on the band characteristics of the electrical components such as the photoelectric converters 201 and 202, the frequency domain equalization filter may be connected to the input side of the electrical filter so as to compensate for a decrease in the transmittance of the frequency characteristics on the high frequency side and ripple in the frequency characteristics. It may be used for In some cases, a gain adjuster or a frequency response equalizer that compensates the band characteristics of the electrical components is used for each carrier and subcarrier after demultiplexing. FIG. 26 shows an example in which equalizers 421 and 422 are used.

  In FIGS. 25 and 26, the electric filters 611 and 612 correspond to the above-described electric filters. Then, the output light from the optical 90-degree hybrid is converted into an electric signal by a photoelectric converter, and the output signal from the photoelectric converter is separated into a plurality of electric signals by frequency using an electric filter. Thereby, a carrier wave can be separated for each frequency using an electric filter.

  Next, a heterodyne receiving apparatus that separates a carrier wave by an electric filter will be described. As in the receiver shown in FIG. 26, this type of receiver uses a light source that oscillates at this single wavelength as local light, mixes signal light and local light with a 90-degree optical hybrid, and produces a photoelectric converter. To convert to photocurrent.

  Alternatively, as illustrated in FIG. 27A, there is a configuration in which either the in-phase component or the in-phase component or the quadrature component is received using the multiplexer 141 and the differential photodetector 211. Here, after that, each carrier and subcarrier are separated using an electrical filter 611 as a frequency separation filter in the electrical domain. It is often used in the case of heterodyne reception in which the optical frequency of the local light is matched with a frequency having a sufficiently low spectral intensity at one end of the optical frequency band of the signal light.

  Therefore, as shown in FIG. 27B, a signal on a carrier wave in the electric frequency region of the difference frequency between each carrier, subcarrier and local light is input to the ADC. This may be down-converted by digital signal processing and dropped to a baseband signal.

  Also, before the analog-digital converter (ADC), it mixes with the LO (local signal) in the electric frequency domain of each carrier and subcarrier frequency, drops to the baseband, and then the analog-digital converter ( ADC). At this time, signals having in-phase and quadrature components with respect to LO (local signal) are obtained and input to an analog / digital converter (ADC). In this case, since the frequency band of the signal input to the analog / digital converter (ADC) is reduced to a frequency region of about baseband, the frequency characteristics required for the analog / digital converter (ADC) are alleviated. .

  In addition, there is a method of separating carriers and subcarriers by mixing with LO (local signal) in the electric frequency domain. The carrier / subcarrier separation electric filter 611 shown in FIG. 27A is deleted, mixed with LO, down-converted to a baseband signal, and then transmitted at a low frequency so that only baseband signal light is transmitted. This is a configuration using a filter. Thereafter, the signal is input to an analog / digital converter (ADC).

  With the above configuration, each carrier and subcarrier adjacent to each other are demultiplexed, converted into a digital signal, and input to the nonlinear compensation calculation unit 501. Also, depending on the band characteristics of electric components such as photoelectric converters, a frequency domain equalization filter may be used on the input side of the electric filter so as to compensate for a decrease in transmittance of frequency characteristics on the high frequency side and frequency ripple. . In some cases, a gain adjuster or a frequency response equalizer that compensates the band characteristics of the electrical components is used for each carrier and subcarrier after demultiplexing.

(Description of an example of a receiving apparatus that performs separation (FFT separation) using a digital filter)
Using a light source that oscillates at a single wavelength as local light, signal light and local light are mixed by an optical 90-degree hybrid and converted into a photocurrent by a photoelectric converter. Alternatively, as shown in FIG. 28, there is a configuration in which either the in-phase component or the in-phase component or the quadrature component is received using the multiplexer and the differential photodetector.

  Here, each carrier and subcarrier are separated using a digital filter 621 that performs frequency separation in the electrical domain. It is often used in the case of heterodyne reception in which the optical frequency of the local light is matched with a frequency having a sufficiently low spectral intensity at one end of the optical frequency band of the signal light.

  Accordingly, as shown in FIG. 27A, a signal on a carrier wave in the electric frequency region of the difference frequency between each carrier, subcarrier and local light is input to the ADC. After being converted into a digital signal, the carrier and subcarrier are separated by digital signal processing, and nonlinear compensation calculation is performed.

  In FIG. 28, the multiplexer 141 corresponds to the aforementioned optical 90-degree hybrid, the differential photodetector 211 corresponds to the photoelectric converter, and the digital filter 621 corresponds to the aforementioned digital filter. Then, the output light from the 90-degree optical hybrid is converted into an electrical signal by a photoelectric converter, and the output signal from the photoelectric converter is separated into a plurality of electrical signals by frequency using a digital filter. Thereby, a carrier wave can be separated for each frequency using a digital filter.

(Explanation of digital carrier separation method)
As a method for separating carrier and subcarrier by digital signal processing, as shown in FIG. 29, a down conversion unit 631 and a low pass filter (LPF) 632 are used, which corresponds to the optical frequency difference between each carrier, subcarrier and local light. Down-conversion is performed at the LO frequency (local frequency) in the electrical frequency domain, and DSP processing (signal processing by a digital signal processor) corresponding to a bandpass filter is performed to obtain a digital signal for each carrier.

  Further, as a method of separating the carrier and subcarrier by digital signal processing, as shown in FIG. 30, the time function is serial / parallel converted by the serial / parallel converter 641, and then input to the fast Fourier transform (FFT) unit 642. There is a configuration to do. In FFT, since a time function is converted into a frequency function, this is equivalent to separation for each carrier and subcarrier. This method is often used in an orthogonal frequency division demultiplexing system. In this case, the frequency multiplexing density is high up to f0 / 1 / ΔT to the extent that the reciprocal of the subcarrier frequency interval f0 and the symbol time length ΔT of each subcarrier are substantially equal.

  In orthogonal frequency division multiplexing (OFDM), serial / parallel conversion is performed for each frame time length and input to each port of the FFT. The OFDM frame length Ts is equal to the reciprocal of the subcarrier frequency interval f0. Also, a guard interval is often used to reduce the influence of chromatic dispersion on the transmission line, waveform spread due to polarization dispersion, and multipath. In this case, the OFDM frame length Ts is expressed as “Ts = 1 / f0 + Tg” using the subcarrier frequency interval f0 and the guard interval length Tg. In this way, the digital signal separated from the carrier and the subcarrier is input to the nonlinear compensation calculation.

(Description of receiver that performs digital separation by homodyne / intradyne system)
A receiving apparatus that performs digital separation of a carrier and a subcarrier by a homodyne / intradyne method can be configured. In this case, a light source that oscillates at a single wavelength is used as local light, signal light and local light are input to a multiplexer, the two outputs are mixed by a 90-degree optical hybrid, and a photoelectric current is output by a photoelectric converter. Convert to

  In this case, as shown in FIG. 31, the output from the optical 90-degree hybrid 101 and the photoelectric converters 201 and 202 may have a DC component in addition to the signal light and the local light mixing signal. By using the DC blocker to be removed, only the mixing signal can be taken out.

  Alternatively, as shown in FIG. 32, the received signal light is branched into at least two paths by the demultiplexer 31, and the local light is also branched into at least two paths by the demultiplexer 32 and the π / 2 phase shift unit 41. Then, the signals are input to the input ports of the multiplexers 141 and 142, respectively. At this time, the in-phase component and the quadrature component can be detected separately by shifting the relative phase difference between the received signal light and the local light by π / 2 in one of the two optical paths. The two outputs of the multiplexers 141 and 142 are input to the differential photodetectors 211 and 212 and converted into digital signals by the ADCs 301 and 302.

  Thereafter, each carrier and subcarrier are separated using a frequency separation filter (digital filters 621 and 622) in the electrical domain. It is often used in the case of heterodyne reception in which the optical frequency of the local light is matched with a frequency having a sufficiently low spectral intensity at one end of the optical frequency band of the signal light.

  Therefore, as shown in FIG. 27B, a signal on a carrier wave in the electric frequency region of the difference frequency between each carrier, subcarrier and local light is input to the ADC. After being converted into a digital signal, the carrier and subcarrier are separated by digital signal processing, and nonlinear compensation calculation is performed.

(Description of additional configuration example of chromatic dispersion compensation)
In an optical fiber transmission line, signal waveform distortion occurs due to chromatic dispersion. There is a typical value of chromatic dispersion depending on the type of optical fiber, and it is expressed as a linear frequency-dependent transfer function. Therefore, an impulse time response function is predicted by the Fourier transform, and chromatic dispersion can be compensated by applying a digital FIR filter that compensates for the waveform spread of the impulse response. For details, a compensation method using digital signal processing of chromatic dispersion in the case of a single carrier is described in Reference Document 8 described above.

  Here, after compensating for the chromatic dispersion, the nonlinear compensation calculation is performed. Due to the loss of the optical fiber transmission line, the optical power of the signal light decreases as it approaches the receiving end, so that the main nonlinear waveform degradation occurs in the portion close to the transmitting end. Therefore, after undergoing nonlinear waveform degradation in a portion near the transmission end, a waveform subjected to waveform distortion due to chromatic dispersion is received in the latter half of the transmission path.

  For this reason, in non-linear compensation, a configuration in which non-linear distortion compensation is performed after removing waveform distortion due to chromatic dispersion and returning to the signal light waveform at the position of the transmission path where the waveform distortion actually occurred is a compensation effect. May increase. Also, when polarization separation is performed by digital signal processing, there is a configuration in which intersymbol interference (ISI) due to wavelength dispersion is removed before polarization separation calculation.

  Waveform distortion due to chromatic dispersion has a small temporal variation and can be handled semi-fixed, so it can be removed by a semi-fixed FIR filter. On the other hand, the waveform distortion due to polarization demultiplexing crosstalk and PMD changes depending on time. Furthermore, the time range in which ISI due to chromatic dispersion occurs is wider than ISI due to polarization crosstalk and polarization mode dispersion. For this reason, it is desirable to perform dynamic polarization separation calculation and PMD compensation after compensating for chromatic dispersion with an FIR filter having a fixed tap coefficient.

  FIG. 33 illustrates a first configuration example of a receiving apparatus that performs chromatic dispersion compensation, and FIG. 34 illustrates a second configuration example of a receiving apparatus that performs chromatic dispersion compensation.

  The receiving apparatus shown in FIG. 33 has chromatic dispersion compensation calculation units 651 and 652 added to the receiving apparatus shown in FIG. 31, and the other configuration is the same as that of the receiving apparatus shown in FIG. The example shown in FIG. 34 has a configuration in which chromatic dispersion compensation calculation units 651, 652, 653, and 654 are added to the configuration of the receiving apparatus using the polarization separator shown in FIG.

  Although the embodiment of the present invention has been described above, the receiving apparatus and the compensation arithmetic circuit (nonlinear compensation arithmetic unit) of the present invention are not limited to the above-described illustrated examples, and depart from the gist of the present invention. Of course, various modifications can be made within the range not to be performed.

It is a figure which shows the form of the signal light applied to the receiver of this invention. It is a figure which shows the example of FWM crosstalk (four-wave mixing crosstalk). It is a figure which shows the structural example of the receiver of this invention. It is a figure which shows the structural example of light 90 degree | times hybrid and a photoelectric converter. It is a figure which shows the structural example of a digital filter. It is a figure which shows the structural example of the receiver which performs a carrier separation using a dispersion medium. It is a figure which shows the example of the transmission pattern and detection pattern for detecting a skew. It is a figure which shows the example of a calculation structure which solves a nonlinear equation sequentially. It is a figure which shows the constellation of a received signal. It is a figure which shows the structural example of the arithmetic circuit of a carrier phase estimation and a phase synchronization. It is a figure which shows the structural example of the calculation circuit which solves simultaneous nonlinear equations sequentially. It is a figure which shows the 2nd structural example of the calculation circuit which solves simultaneous nonlinear equations sequentially. It is a figure which shows the structural example of a compensation parameter and a nonlinear compensation arithmetic circuit. It is a figure which shows the example of the transmission pilot signal for compensation parameter estimation. It is a figure which shows the experimental result of a nonlinear distortion effect. It is a figure which shows the structural example of the receiver which performs polarization | polarized-light separation. It is a figure which shows the example of the FWM crosstalk generation pattern in the case of 2 carriers and polarization multiplexing. It is a figure which shows the circuit structure which repeatedly calculates nonlinear distortion compensation and linear compensation. It is a figure which shows the structural example of the receiver using an optical separator. It is a figure which shows the structural example of the receiver which detects one side of an in-phase component (quadrature phase component). It is a figure which shows the structural example of the receiver which detects both an in-phase component and a quadrature phase component. It is a figure which shows the structural example of the receiver which performs a phase comparison by optical 90 degree | times hybrid after isolation | separation by an optical separator. It is a figure which shows the structural example of the receiver which used the individual local light generation part in FIG. It is a figure which shows the structural example of the receiver which detects an intensity | strength by direct reception. It is a figure which shows the structural example of the receiver which isolate | separates into a carrier and a subcarrier with an electric filter. It is a figure which shows the structural example of the receiver which added the equalizer to FIG. It is a figure which shows the structural example of the receiver of the heterodyne system using an electrical filter. It is a figure which shows the structural example of the receiver of the heterodyne system using a digital filter. It is a figure which shows the structural example of the receiver using a down conversion part and a low-pass filter. It is a figure which shows the structural example of the receiver which isolate | separates a carrier and a subcarrier using a serial parallel conversion part and FFT. It is a figure which shows the structural example of the receiving device of a homodyne intradyne system. It is a figure which shows the structural example of the receiver of the homodyne / intradyne system which detects the same phase component and a quadrature phase component separately. It is a figure which shows the 1st structural example of the receiver which performs a chromatic dispersion compensation calculation. It is a figure which shows the 2nd structural example of the receiver which performs a chromatic dispersion compensation calculation.

Explanation of symbols

11, 11A, 11B, 11C, 11D... Local light generation unit, 12... Multimode local light generation unit, 21, 22, 31, 32... Duplexer (PBS: optical beam splitter), 41 ... π / 2 phase shift unit, 101, 102, 103, 104 ... optical 90-degree hybrid, 110 ... multiplexer, 121 ... optical hybrid, 131, 132, 133, 134 ... Optical separators, 141, 142 ... multiplexers, 201-208 ... photoelectric converters, 211, 211A-211H ... differential photo detectors (differential PD), 301, ... 308 ... Analog-to-digital converter (ADC) 401, 402 ... digital filter, 411 ... serial / parallel converter, 412 ... FFT, 501, 502 ... non-linear compensation calculator, 503 ... phase synchronization Part 504: Compensation calculation unit 505 ... Compensation parameter learning unit 531 ... Skew correction unit 532 ... Skew monitor unit 533 ... Non-linear coupling constant estimation unit 534 ... Phase estimation , 535... Nonlinear compensation calculation processing unit, 601, 602, 603, 604... Polarization separation calculation unit, 611, 612... Electric filter, 621, 622. Down conversion unit, 632... Low pass filter, 641... Serial / parallel conversion unit, 651, 652... Chromatic dispersion compensation operation unit, 661, 662, 663, 664. ..Polarization separation calculation unit

Claims (19)

In the optical transmission system using an optical fiber transmission path, a receiver for receiving the signal light polarization multiplexing encoded by the transmission information,
A separation device for separating a signal for each individual carrier wave according to the polarization of the signal light;
A phase synchronization unit that performs synchronization processing of a symbol phase between a plurality of carrier waves output from the separation device;
Based on a carrier wave signal that has been subjected to synchronization processing by the phase synchronization unit, non-linear waveform distortion of the multiplexed signal light in the optical fiber transmission line is modeled and calculated by a predetermined model including four-wave mixing crosstalk. And a compensation calculation unit for performing a calculation to compensate for the nonlinear waveform distortion,
With
A compensation arithmetic circuit that constitutes the compensation arithmetic unit in the receiving device configured to execute arithmetic processing in the phase synchronization unit and the compensation arithmetic unit by an electric arithmetic circuit,
Nonlinear waveform distortion generated before Kihen Shigeru Hata signal light in the optical fiber transmission path propagation, modeled by the waveform distortion due to four-wave mixing crosstalk caused between the different polarization of the signal light, transmitted and received signals An electrical operation circuit for calculating a transmission signal from a received signal by associating a signal waveform relationship with a multi-dimensional nonlinear equation and solving the multi-dimensional nonlinear equation,
When sequentially estimating the transmission waveform from the reception waveform based on the multi-dimensional nonlinear equation,
The n-th transmission waveform estimation value output from the n-th transmission waveform estimation step is temporarily used as a transmission waveform of a part of the multi-dimensional nonlinear equation, and the multi-dimensional nonlinear equation is linearized. A transmission waveform estimation step of the (n + 1) th stage for estimating the transmission waveform of
A compensation arithmetic circuit comprising an arithmetic circuit for sequentially estimating a compensation waveform. In an optical transmission system using an optical fiber transmission line, a receiving device that receives frequency-multiplexed and polarization- multiplexed signal light encoded by transmission information,
A polarization separation device that separates the frequency multiplexed and polarization multiplexed signal light into two by polarization;
A separation device for separation into each individual carrier by a frequency the signal light output from the polarization separating device,
Two polarization reception signals for each frequency carrier wave output from the separation device are input, and interference between the input two polarization reception signals is removed and polarization separation is performed into two independent signals. A polarization separation calculation unit,
A phase synchronization unit that performs a phase synchronization process between a plurality of carriers output from the polarization separation calculation unit;
Based on a carrier wave signal that has been subjected to synchronization processing by the phase synchronization unit, non-linear waveform distortion of the multiplexed signal light in the optical fiber transmission line is modeled and calculated by a predetermined model including four-wave mixing crosstalk. And a compensation calculation unit for performing a calculation to compensate for the nonlinear waveform distortion,
With
A compensation arithmetic circuit that constitutes the compensation arithmetic unit in a receiving device configured to execute arithmetic processing in the polarization separation arithmetic unit, the phase synchronization unit, and the compensation arithmetic unit by an electric arithmetic circuit,
The frequency-multiplexed and polarization multiplexed signal light nonlinear waveform distortion occurs in the optical fiber transmission path propagation, four-wave mixing crosstalk by the waveform occurring between a plurality of frequencies of the signal light Contact and different polarizations of the signal light Modeling by distortion, correlating the relationship between the waveform of the received signal and the transmitted signal with a multi-dimensional nonlinear equation, and comprising an electric arithmetic circuit for calculating the transmitted signal from the received signal by solving the multi-dimensional nonlinear equation,
When sequentially estimating the transmission waveform from the reception waveform based on the multi-dimensional nonlinear equation,
The n-th transmission waveform estimation value output from the n-th transmission waveform estimation step is temporarily used as a transmission waveform of a part of the multi-dimensional nonlinear equation, and the multi-dimensional nonlinear equation is linearized. A transmission waveform estimation step of the (n + 1) th stage for estimating the transmission waveform of
A compensation arithmetic circuit comprising an arithmetic circuit for sequentially estimating a compensation waveform. The compensation arithmetic circuit according to claim 1 or 2,
A compensation calculation circuit comprising: an arithmetic circuit that uses a reception waveform before compensation as a transmission waveform that is a part of the multi-dimensional nonlinear equation as an initial value in the first-stage transmission waveform estimation step. The compensation arithmetic circuit according to claim 1 or 2,
A compensation arithmetic circuit comprising: an arithmetic circuit that uses a predetermined arbitrary waveform as an initial value as a partial transmission waveform of the multi-dimensional nonlinear equation in the first-stage transmission waveform estimation step. In the optical transmission system using an optical fiber transmission path, a receiver for receiving the signal light polarization multiplexing encoded by the transmission information,
A separation device for separating a signal for each individual carrier wave according to the polarization of the signal light;
A phase synchronization unit that performs synchronization processing of a symbol phase between a plurality of carrier waves output from the separation device;
Based on a carrier wave signal that has been subjected to synchronization processing by the phase synchronization unit, non-linear waveform distortion of the multiplexed signal light in the optical fiber transmission line is modeled and calculated by a predetermined model including four-wave mixing crosstalk. And a compensation calculation unit for performing a calculation to compensate for the nonlinear waveform distortion,
With
A compensation arithmetic circuit that constitutes the compensation arithmetic unit in the receiving device configured to execute arithmetic processing in the phase synchronization unit and the compensation arithmetic unit by an electric arithmetic circuit,
Nonlinear waveform distortion generated before Kihen Shigeru Hata signal light in the optical fiber transmission path propagation, modeled by the waveform distortion due to four-wave mixing crosstalk caused between the different polarization of the signal light, transmission and reception waveform An electrical operation circuit for calculating a transmission signal from a received signal by associating a relationship of a nonlinear distortion fluctuation amount of a waveform with a multi-dimensional nonlinear equation and solving the multi-dimensional nonlinear equation,
When sequentially estimating the nonlinear distortion fluctuation amount,
The nth stage compensation waveform output from the nth fluctuation amount estimation step is temporarily used as a partial transmission waveform of the multiway nonlinear equation to linearize the multiway nonlinear equation, so that the (n + 1) th stage A fluctuation amount estimation step of the (n + 1) th stage for estimating the nonlinear distortion fluctuation amount of the received waveform of the eye;
Subtracting the output value from the (n + 1) th fluctuation amount estimation step from the received data, and outputting the waveform after the (n + 1) th stage nonlinear distortion compensation, the (n + 1) th stage fluctuation amount compensation step;
Have
A compensation arithmetic circuit comprising an arithmetic circuit for sequentially estimating a compensation waveform. In an optical transmission system using an optical fiber transmission line, a receiving device that receives frequency-multiplexed and polarization- multiplexed signal light encoded by transmission information,
A polarization separation device that separates the frequency multiplexed and polarization multiplexed signal light into two by polarization;
A separation device for separation into each individual carrier by a frequency the signal light output from the polarization separating device,
Two polarization reception signals for each frequency carrier wave output from the separation device are input, and interference between the input two polarization reception signals is removed and polarization separation is performed into two independent signals. A polarization separation calculation unit,
A phase synchronization unit that performs a phase synchronization process between a plurality of carriers output from the polarization separation calculation unit;
Based on a carrier wave signal that has been subjected to synchronization processing by the phase synchronization unit, non-linear waveform distortion of the multiplexed signal light in the optical fiber transmission line is modeled and calculated by a predetermined model including four-wave mixing crosstalk. And a compensation calculation unit for performing a calculation to compensate for the nonlinear waveform distortion,
With
A compensation arithmetic circuit that constitutes the compensation arithmetic unit in a receiving device configured to execute arithmetic processing in the polarization separation arithmetic unit, the phase synchronization unit, and the compensation arithmetic unit by an electric arithmetic circuit,
The frequency-multiplexed and polarization multiplexed signal light nonlinear waveform distortion occurs in the optical fiber transmission path propagation, four-wave mixing crosstalk by the waveform occurring between a plurality of frequencies of the signal light Contact and different polarizations of the signal light Modeled by distortion, correlated with the relationship between the nonlinear distortion fluctuation amount of the received waveform and the transmitted waveform by a multi-dimensional nonlinear equation, and comprises an electric arithmetic circuit for calculating the transmitted signal from the received signal by solving the multi-dimensional nonlinear equation,
When sequentially estimating the nonlinear distortion fluctuation amount,
The nth stage compensation waveform output from the nth fluctuation amount estimation step is temporarily used as a partial transmission waveform of the multiway nonlinear equation to linearize the multiway nonlinear equation, so that the (n + 1) th stage A fluctuation amount estimation step of the (n + 1) th stage for estimating the nonlinear distortion fluctuation amount of the received waveform of the eye;
Subtracting the output value from the (n + 1) th fluctuation amount estimation step from the received data, and outputting the waveform after the (n + 1) th stage nonlinear distortion compensation, the (n + 1) th stage fluctuation amount compensation step;
Have
A compensation arithmetic circuit comprising an arithmetic circuit for sequentially estimating a compensation waveform. The compensation arithmetic circuit according to claim 5 or 6,
In the first-stage fluctuation amount estimation step, the reception waveform before compensation is temporarily configured with an arithmetic circuit that uses it as a partial transmission waveform of the multi-dimensional nonlinear equation;
Compensation arithmetic circuit characterized by the above. The compensation arithmetic circuit according to claim 5 or 6,
In the first stage fluctuation amount estimation step, an arithmetic circuit that uses a predetermined arbitrary waveform as an initial value as a partial transmission waveform of the multi-dimensional nonlinear equation,
Compensation operation circuit characterized by comprising. The compensation arithmetic circuit according to claim 5 or 6,
In the first stage fluctuation amount estimation step, an arithmetic circuit that detects a value that can obtain a correction effect by changing a value used as an initial value,
Compensation operation circuit characterized by comprising. Learning the chromatic dispersion of the optical fiber transmission line used in the calculation for compensating the nonlinear waveform distortion, the chromatic dispersion slope, the transmission parameter including the nonlinear constant, and the compensation parameter depending on the relative phase between the carriers of the multiplexed signal light, A compensation parameter learning unit for inputting the compensation parameter value to the compensation calculation circuit;
The compensation arithmetic circuit according to claim 1, wherein: A receiving device comprising the compensation arithmetic circuit according to any one of claims 1 to 10,
A multi-mode local light generator that outputs continuous light of multiple frequencies;
An optical 90-degree hybrid that inputs the local light of the plurality of frequencies and the input signal light, separates them into a component orthogonal to a component in which both optical phases match, and outputs them to different ports,
Respective optical separators for inputting output light from the light 90-degree hybrid and separating each wavelength by a wavelength dispersion medium;
A photoelectric converter that inputs output light from each of the light separators and converts each of the light into an electrical signal;
Each analog-to-digital converter that converts the electrical signal of each of the photoelectric converters into a digital signal;
A receiving apparatus comprising: A receiving device comprising the compensation arithmetic circuit according to any one of claims 1 to 10,
A multi-mode local light generator that outputs continuous light of multiple frequencies as local light;
An optical separator for signal light that receives input signal light, separates it for each wavelength by a chromatic dispersion medium, and outputs it to different ports;
The local light output from the multi-mode local light generation unit is input, and the local light separator that separates the wavelength by the wavelength dispersion medium and outputs it to different ports,
The output light from each port of the signal light optical separator and the output light from each port of the local light optical separator are input, and the component is orthogonal to the component in which both optical phases match. An optical 90 degree hybrid of each carrier that is output separately to different ports;
Respective photoelectric converters that convert output light from the respective light 90-degree hybrids into electrical signals;
Each analog-to-digital converter that converts the electrical signal of each of the photoelectric converters into a digital signal;
A receiving apparatus comprising: A receiving device comprising the compensation arithmetic circuit according to any one of claims 1 to 10,
An optical separator for signal light that receives input signal light, separates it for each wavelength by a chromatic dispersion medium, and outputs it to different ports;
A plurality of local light generators that output continuous light of different frequencies;
The output light from each port of the optical separator of the signal light and the output light from each local light generator are input and separated into components orthogonal to the components in which both optical phases coincide with each other. A 90 degree optical hybrid output to the port,
Each photoelectric converter that converts output light from each of the wavelength separators into an electrical signal;
Each analog-to-digital converter that converts the electrical signal of each of the photoelectric converters into a digital signal;
A receiving apparatus comprising: A receiving device comprising the compensation arithmetic circuit according to any one of claims 1 to 10,
A local light generator that outputs continuous light having one frequency component;
An optical 90-degree hybrid that inputs the local light and the input signal light, and separates and outputs a component orthogonal to a component in which both optical phases match,
Each photoelectric converter that converts the output light from the light 90-degree hybrid into an electrical signal;
An electrical filter that separates an output signal from the photoelectric converter into a plurality of electrical signals according to frequency;
Respective analog-to-digital converters for converting electrical signals output from the respective electrical filters into digital signals;
A receiving apparatus comprising: A receiving device comprising the compensation arithmetic circuit according to any one of claims 1 to 10,
A local light generator for outputting continuous light having a component of one frequency;
An optical 90-degree hybrid that inputs the local light and the input signal light, and separates and outputs a component orthogonal to a component in which both optical phases match,
A photoelectric converter that converts output light from the light 90-degree hybrid into an electrical signal;
An analog / digital converter that converts an electrical signal of the photoelectric converter into a digital signal;
A digital filter that separates an output signal from each of the analog-digital converters into a plurality of channels according to frequency;
A receiving apparatus comprising: In the optical transmission system using an optical fiber transmission line, a receiving method of the signal light in the reception apparatus for receiving a signal light polarization multiplexing encoded by the transmission information,
A separation procedure for separating a signal for each individual carrier wave according to the polarization of the signal light;
A phase synchronization procedure for performing symbol phase synchronization processing between a plurality of carriers output by the separation procedure;
Based on the carrier wave signal that has been synchronized by the phase synchronization procedure, the nonlinear waveform distortion of the multiplexed signal light in the optical fiber transmission line is modeled and calculated by a predetermined model including four-wave mixing crosstalk. A compensation calculation procedure for performing a calculation to compensate for the nonlinear waveform distortion,
Including
In the compensation calculation procedure,
Nonlinear waveform distortion generated before Kihen Shigeru Hata signal light in the optical fiber transmission path propagation, modeled by the waveform distortion due to four-wave mixing crosstalk caused between the different polarization of the signal light, transmitted and received signals By correlating the signal waveform relationship with a multi-dimensional nonlinear equation, solving the multi-dimensional nonlinear equation to calculate a transmission signal from the received signal,
When sequentially estimating the transmission waveform from the reception waveform based on the multi-dimensional nonlinear equation,
The n-th transmission waveform estimation value output from the n-th transmission waveform estimation step is temporarily used as a transmission waveform of a part of the multi-dimensional nonlinear equation, and the multi-dimensional nonlinear equation is linearized. A transmission waveform estimation step of the (n + 1) th stage for estimating the transmission waveform of
A receiving method characterized by sequentially estimating a compensation waveform. In the optical transmission system using the optical fiber transmission line, the signal light receiving method in the receiving device that receives the frequency multiplexed and polarization multiplexed signal light encoded by the transmission information,
A polarization separation procedure for separating the frequency multiplexed and polarization multiplexed signal light into two by polarization;
A separation procedure for separation for each individual carrier by a frequency output signal light from the polarization separating device,
Two polarization reception signals for each frequency carrier wave output from the separation device are input, and interference between the input two polarization reception signals is removed and polarization separation is performed into two independent signals. Polarization separation calculation procedure to
A phase synchronization procedure for performing phase synchronization processing between a plurality of carriers output from the polarization separation calculation unit;
Based on a carrier wave signal that has been subjected to synchronization processing by the phase synchronization unit, non-linear waveform distortion of the multiplexed signal light in the optical fiber transmission line is modeled and calculated by a predetermined model including four-wave mixing crosstalk. A compensation calculation procedure for performing a calculation to compensate for the nonlinear waveform distortion,
Including
In the compensation calculation procedure,
The frequency-multiplexed and polarization multiplexed signal light nonlinear waveform distortion occurs in the optical fiber transmission path propagation, four-wave mixing crosstalk by the waveform occurring between a plurality of frequencies of the signal light Contact and different polarizations of the signal light Modeling by distortion, correlating the relationship between the waveform of the received signal and the transmitted signal with a multi-dimensional nonlinear equation, calculating the transmitted signal from the received signal by solving the multi-dimensional nonlinear equation,
When sequentially estimating the transmission waveform from the reception waveform based on the multi-dimensional nonlinear equation,
The n-th transmission waveform estimation value output from the n-th transmission waveform estimation step is temporarily used as a transmission waveform of a part of the multi-dimensional nonlinear equation, and the multi-dimensional nonlinear equation is linearized. A transmission waveform estimation step of the (n + 1) th stage for estimating the transmission waveform of
A receiving method characterized by sequentially estimating a compensation waveform. In the optical transmission system using an optical fiber transmission line, a receiving method of the signal light in the reception apparatus for receiving a signal light polarization multiplexing encoded by the transmission information,
A separation procedure for separating a signal for each individual carrier wave according to the polarization of the signal light;
A phase synchronization procedure for performing symbol phase synchronization processing between a plurality of carriers output by the separation procedure;
Based on the carrier wave signal that has been synchronized by the phase synchronization procedure, the nonlinear waveform distortion of the multiplexed signal light in the optical fiber transmission line is modeled and calculated by a predetermined model including four-wave mixing crosstalk. A compensation calculation procedure for performing a calculation to compensate for the nonlinear waveform distortion,
Including
In the compensation calculation procedure,
Nonlinear waveform distortion generated before Kihen Shigeru Hata signal light in the optical fiber transmission path propagation, modeled by the waveform distortion due to four-wave mixing crosstalk caused between the different polarization of the signal light, transmission and reception waveform By correlating the relationship of the nonlinear distortion fluctuation amount of the waveform with a multi-dimensional nonlinear equation, calculating the transmission signal from the received signal by solving the multi-dimensional nonlinear equation,
When sequentially estimating the nonlinear distortion fluctuation amount,
The nth stage compensation waveform output from the nth fluctuation amount estimation step is temporarily used as a partial transmission waveform of the multiway nonlinear equation to linearize the multiway nonlinear equation, so that the (n + 1) th stage A fluctuation amount estimation step of the (n + 1) th stage for estimating the nonlinear distortion fluctuation amount of the received waveform of the eye;
Subtracting the output value from the (n + 1) th fluctuation amount estimation step from the received data, and outputting the waveform after the (n + 1) th stage nonlinear distortion compensation, the (n + 1) th stage fluctuation amount compensation step;
Have
A receiving method characterized by sequentially estimating a compensation waveform. In the optical transmission system using the optical fiber transmission line, the signal light receiving method in the receiving device that receives the frequency multiplexed and polarization multiplexed signal light encoded by the transmission information,
A polarization separation procedure for separating the frequency multiplexed and polarization multiplexed signal light into two by polarization;
A separation procedure for separation for each individual carrier by a frequency output signal light from the polarization separating device,
Two polarization reception signals for each frequency carrier wave output from the separation device are input, and interference between the input two polarization reception signals is removed and polarization separation is performed into two independent signals. Polarization separation calculation procedure to
A phase synchronization procedure for performing phase synchronization processing between a plurality of carriers output from the polarization separation calculation unit;
Based on a carrier wave signal that has been subjected to synchronization processing by the phase synchronization unit, non-linear waveform distortion of the multiplexed signal light in the optical fiber transmission line is modeled and calculated by a predetermined model including four-wave mixing crosstalk. A compensation calculation procedure for performing a calculation to compensate for the nonlinear waveform distortion,
Including
In the compensation calculation procedure,
The frequency-multiplexed and polarization multiplexed signal light nonlinear waveform distortion occurs in the optical fiber transmission path propagation, four-wave mixing crosstalk by the waveform occurring between a plurality of frequencies of the signal light Contact and different polarizations of the signal light Modeling by distortion, associating the relationship between the amount of nonlinear distortion fluctuation of the received waveform and the transmitted waveform with a multi-dimensional nonlinear equation, calculating the transmitted signal from the received signal by solving the multi-dimensional nonlinear equation,
When sequentially estimating the nonlinear distortion fluctuation amount,
The nth stage compensation waveform output from the nth fluctuation amount estimation step is temporarily used as a partial transmission waveform of the multiway nonlinear equation to linearize the multiway nonlinear equation, so that the (n + 1) th stage A fluctuation amount estimation step of the (n + 1) th stage for estimating the nonlinear distortion fluctuation amount of the received waveform of the eye;
Subtracting the output value from the (n + 1) th fluctuation amount estimation step from the received data, and outputting the waveform after the (n + 1) th stage nonlinear distortion compensation, the (n + 1) th stage fluctuation amount compensation step;
Have
A receiving method characterized by sequentially estimating a compensation waveform.

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