Communication system, receiver, equalization signal processing circuit, method, and program

Abstract

The present invention can compensate for various types of distortion while suppressing an increase of the calculation amount. A first filter (23) performs compensation for first distortion included in reception signals which have been coherently received, on the reception signals and complex conjugate signals thereof, and outputs the reception signals and the complex conjugate signals thereof for which the compensation for the first distortion has been performed. A second filter (24) included in a filter group (25) receives, as input signals, the reception signals and the complex conjugate signals thereof for which the compensation for the first distortion has been performed, compensates for second distortion included in the reception signals, and outputs the reception signals for which the compensation for the second distortion has been performed. A coefficient updating means (26) adaptively controls a filter coefficient of the second filter (24) on the basis of a difference between an output signal outputted from the filter group (25) and a prescribed value of the output signal.

Description

[Technical Field]

[0001] The present disclosure relates to a communication system, a receiver, an equalization signal processing circuit, an equalization signal processing method, and a computer-readable medium. [Background technology]

[0002] In optical fiber communications, multi-level modulation, such as high-order quadrature amplitude modulation (QAM), is being adopted to achieve high spectral efficiency. The introduction of coherent receiving technology has enabled flexible equalization signal processing at the receiving end using digital signal processing, such as the collective compensation of chromatic dispersion accumulated in optical fiber transmission lines. However, high-order multi-level modulation signals are generally vulnerable to distortion. Therefore, distortion caused by imperfections in components within the transmitter and receiver is becoming a new bottleneck in advancing higher multi-level modulation.

[0003] As a related technique, Non-Patent Document 1 discloses a receiver-side equalization digital signal processing for equalizing a coherently received QAM signal. Fig. 8 shows an example of the receiver-side equalization digital signal processing described in Non-Patent Document 1. The equalization digital signal processing includes chromatic dispersion compensation 501, polarization separation 502, and carrier phase compensation 503. The received signals of X / Y polarized waves coherently received by the receiver are denoted by x1 and x2. The in-phase component (I) and quadrature component (Q) of each polarized wave are denoted by x1 and x2. jI , x jQ Then the received signal is x j =x jI +ix jQ It is expressed as:

[0004] The chromatic dispersion compensator 501 compensates for chromatic dispersion that occurs when an optical signal propagates through an optical fiber. The chromatic dispersion compensator 501 includes a static complex signal input complex coefficient filter that is independent for each polarization. The coefficients of the static filters included in the chromatic dispersion compensator 501 are determined so as to have the inverse characteristics of the chromatic dispersion that is determined from the amount of accumulated chromatic dispersion.

[0005] The polarization splitter 502 compensates for polarization state fluctuations and polarization mode dispersion that occur in an optical signal during propagation through an optical fiber. The polarization splitter 502 includes a 2×2 complex signal input complex coefficient multi-input multi-output (MIMO) filter with cross terms between polarizations. Figure 9 shows a 2×2 MIMO filter used in the polarization splitter 502. The MIMO filter 600 includes, for example, a 2×2 finite impulse response (FIR) filter 601. The coefficients of the FIR filter 601 are expressed as h 11 , h 12 , h 21 , and h 22 It is expressed as:

[0006] Fluctuations in the polarization state that occur in an optical signal while propagating through an optical fiber change over time depending on the external environment. The coefficient update unit 510 adaptively controls the coefficients of each FIR filter 601 to track fluctuations in the polarization state based on the input and output of the 2×2 MIMO filter (polarization splitter 502). The polarization splitter 502 uses algorithms such as the constant modulus algorithm (CMA), data-aided least mean square (DALMS) algorithm, and decision-directed least mean square (DDLMS) algorithm to update the coefficients. These algorithms update the coefficients so as to minimize the average magnitude of the difference between the filter output and the desired state. In these algorithms, the amount of coefficient update is calculated using the input and output of the filter.

[0007] Carrier phase compensation 503 compensates for the frequency offset and phase offset between the carrier frequency of the transmitted optical signal and the local oscillator light on the receiving side. Carrier phase compensation 503 includes a complex signal input complex coefficient filter that applies phase rotation to the received signal, independent of the polarization. Phase-locked loop (PLL) 520 determines the amount of phase rotation of carrier phase compensation 503. After carrier phase compensation, signals y1 and y2 of each polarization are obtained with various distortions compensated for.

[0008] The receiver-side equalization digital signal processing shown in Fig. 8 cannot compensate for IQ distortions that occur in the transmitter or receiver, such as a discrepancy in average signal strength between IQ components (IQ imbalance), a time difference between IQ components (IQ skew), and an orthogonality difference between IQ components (IQ phase difference). This is because a complex-signal-input complex-coefficient filter, such as the MIMO filter shown in Fig. 9, cannot impart an independent response to each IQ component. In this sense, a complex-signal-input complex-coefficient filter is called strictly linear (SL).

[0009] To compensate for IQ distortion that occurs in the transmitter or receiver, a filter that can handle IQ components independently is required. Such a filter is, for example, a real-coefficient MIMO filter that accepts real signals for each IQ component as input and output. For example, when applying such a filter to a signal of one polarization, a real-coefficient 2x2 MIMO filter is used, which accepts two real signals for the IQ components as input and output. This real-coefficient MIMO filter is equivalent to a filter that accepts a complex signal and its complex conjugate as input, convolves each with a complex coefficient response, and then outputs a complex signal obtained by adding the convolved signals. These filters are called widely linear (WL).

[0010] Generally, IQ distortion cannot be interchanged with other distortions such as chromatic dispersion, etc. Therefore, when attempting to provide IQ distortion compensation blocks for block-by-block distortion compensation, as in the configuration of Figure 8, the order becomes important.

[0011] Non-Patent Document 2 describes an example of receiver-side equalization digital signal processing for equalizing various types of distortion in optical fiber communications, including IQ distortion occurring in a transmitter or receiver. Fig. 10 shows an adaptive multilayer filter that performs equalization signal processing. The adaptive multilayer filter includes, in this order, receiver-internal distortion compensation 701, chromatic dispersion compensation 702, polarization separation 703, carrier phase compensation 704, and transmitter-internal distortion compensation 705. In this adaptive multilayer filter, various types of distortion contained in a received signal are compensated for in the reverse order of the order in which the distortion occurred.

[0012] The receiver distortion compensation 701 has a WL2×1 filter for each polarization, i.e., for each of the input signals x1 and x2. The chromatic dispersion compensation 702 has an SL filter for each polarization. The polarization separation 703 includes a 2×2 MIMO SL filter. The carrier phase compensation 704 has an SL filter for each polarization. The transmitter distortion compensation 705 has a WL2×1 filter for each polarization.

[0013] 11 shows a WL2×1 filter used in the receiver distortion compensation 701 and the transmitter distortion compensation 705. The WL2×1 filter 800 has a complex conjugate calculation unit 801. The complex conjugate calculation unit 801 calculates the complex conjugate of an input complex signal. In the WL2×1 filter 800, the complex signal is input to an FIR filter 802, and the complex conjugate signal is input to an FIR filter 803. The WL2×1 filter 800 outputs a signal obtained by adding the output of the FIR filter 802 and the output of the FIR filter 803. The receiver distortion compensation 701 and the transmitter distortion compensation 705 each have such a WL2×1 filter 800 for each polarization.

[0014] The characteristics of the distortion in the transmitter and the distortion in the receiver occurring in an optical communication system are usually unknown. Therefore, the filter coefficients of the distortion compensation in the receiver 701 and the distortion compensation in the transmitter 705 need to be adaptively controlled. However, in this case, it is difficult to control the coefficients based on the direct input and output of each filter block, as in the configuration of Fig. 8. This is because uncompensated distortion remains in the output of blocks other than the last distortion compensation in the transmitter 705. This makes it extremely difficult to design an appropriate loss function to be minimized for adaptive control.

[0015] 10 , the loss function calculation unit 730 calculates the difference between the filter output of the final layer, i.e., the output of the transmitter distortion compensation 705, and the desired state as a loss function. The coefficient update unit 710 calculates the gradient of the loss function for all coefficients of each filter block based on the fact that the outputs of all filter blocks can be expressed in a form that is differentiable with respect to their inputs and coefficients, and based on the backpropagation method. The coefficient update unit 710 adaptively controls the coefficients of each filter block using the calculated gradient to minimize the loss function.

[0016] The PLL 720 controls the amount of phase rotation of the carrier phase compensation 704 according to the output of the transmitter distortion compensation 705, which is the final layer of the filter block. By using the adaptive multilayer filter shown in Fig. 10, high-precision receiver-side equalization signal processing can be achieved even when multiple distortions, including IQ distortions in the transmitter and receiver, exist simultaneously. [Prior art documents] [Non-patent literature]

[0017] [Non-Patent Document 1] SJ Savory, “Digital filters for coherent optical receivers,” Opt. Express 16(2), 804 (2008). [Non-patent document 2] M. Arikawa and K. Hayashi, “Adaptive equalization of transmitter and receiver IQ skew by multi-layer linear and widely linear filters with deep unfolding,” Opt. Express 28(16), 23478 (2020). [Non-patent document 3] M. Arikawa and K. Hayashi, “Transmitter and receiver impairment monitoring using adaptive multi-layer linear and widely linear filter coefficients controlled by stochastic gradient descent,” Opt. Express 29(8), 11548 (2021). Summary of the Invention [Problem to be solved by the invention]

[0018] In the adaptive multilayer filter shown in Fig. 10 described in Non-Patent Document 2, various types of distortion are compensated for by multilayer FIR filters. In this configuration, due to the convolution relationship of the FIR filters, the time spread of the samples involved in the calculation increases as one goes back through the layers to obtain the final distortion-compensated sample output at one time point.

[0019] The following describes various distortion compensation processes and coefficient updates using a multilayer filter. The output signal vector and input signal vector of the lth layer related to obtaining a sample of the output signal at time k are respectively: TIFF0007772190000001.tif6141TIFF0007772190000002.tif6162. M l and M l-1are the lengths of the output signal vector and input signal vector of the lth layer, respectively. Due to the relationship of the multilayer filter, the input signal vector of the lth layer is equal to the output signal vector of the l-1th layer. i=1,2 represent the respective polarizations. When performing spatial mode compensation in the adaptive multilayer filter, i is expanded to values ​​greater than 2.

[0020] The filter coefficient h when the lth layer filter is an SL MIMO filter ij [l] of, TIFF0007772190000003.tif6150. The tap length of the lth layer filter is M [l] From the convolution relationship, The file is TIFF0007772190000004.tif6129.

[0021] When the lth layer filter is an SL MIMO filter, the forward propagation is as follows: TIFF0007772190000005.tif16146, where TIFF0007772190000006.tif29166, H ij [l] is size M l ×M l-1 The above formula 5 can be transformed into the following matrix: TIFF0007772190000007.tif14125TIFF0007772190000008.tif27162. U j [l-1] [k] is the size of M l ×M l-1 is a matrix of

[0022] Whether the first layer filter is an SL filter arranged for each polarization or a WL filter, the same calculation as above can be performed as described in Non-Patent Document 2. In the multilayer filter described in Non-Patent Document 2, all filter coefficients are adaptively controlled based on the final output of the multilayer filter, except for the chromatic dispersion compensation filter, whose coefficients are operated quasi-statically, and the carrier phase compensation filter, whose compensation amount is determined by a PLL.

[0023] For example, when the DALMS algorithm and the stochastic gradient descent method are used for coefficient update, the filter coefficients are updated to minimize the loss function φ[k]. The loss function φ[k] is defined as: i [k], training signal d i [k] is expressed by the following formula. TIFF0007772190000009.tif15141The coefficient update for the filter coefficient ξ is It is represented as TIFF0007772190000010.tif12125. α is the step size that determines the magnitude of the coefficient update. The gradient of the loss function is determined sequentially from the final layer using the backpropagation method. In the case of the DALMS algorithm, the gradient of the loss function for the output of the final layer is TIFF0007772190000011.tif12122TIFF0007772190000012.tif12121

[0024] If the l-th layer filter is an SL MIMO filter, when the gradient for the output vector is given, the gradient for the input vector and coefficients is obtained by backward propagation as follows: TIFF0007772190000013.tif13133TIFF0007772190000014.tif15137TIFF0007772190000015.tif15137. Also, the loss function to be minimized takes real values, so in that case, TIFF0007772190000016.tif16137. If the first layer filter is an SL filter for each polarization, the calculation can be done in the same way as if it were a WL filter. In this way, distortion compensation processing by the multilayer filter and adaptive updating of the filter coefficients based on the final output signal sample are performed.

[0025] In the backpropagation of multilayer filters, U j [l-1] [k], and H ijThe size of these matrices is related to the length of the input and output vectors of each layer. On the other hand, since Equation 4 holds for the length of the input and output vectors of each layer, in a multi-layer filter, the closer to the first layer, the smaller the M l and M l-1 tends to be large. This is because the tap length M [l] This is particularly noticeable when a large filter is present.

[0026] For example, in ultra-long distance single-mode fiber transmission such as 10,000 km, the accumulated chromatic dispersion reaches approximately 170 ns / nm. When performing chromatic dispersion compensation in the time domain with 2x oversampling for a general symbol rate signal of 32 Gbaud, the required tap length exceeds 5,500 taps. In this case, when various distortion compensations are performed with the configuration shown in Figure 10, the input and output vectors of the first and second layers, and ultimately the U j [l-1] [k] and H ij [l] As a result, the size of the matrix increases, and the amount of calculation required for error backpropagation increases. As such, when distortion compensation processing using a multilayer filter like the one shown in Figure 10 is applied to ultra-long distance single-mode fiber transmission, there is an issue in that the amount of calculation required for updating the coefficients becomes enormous.

[0027] In view of the above circumstances, one object of the present disclosure is to provide a communication system, a receiver, an equalization signal processing circuit, and a method that can compensate for various distortions while suppressing an increase in the amount of calculation. [Means for solving the problem]

[0028] To achieve the above object, the present disclosure provides, as a first aspect, an equalization signal processing circuit including: a first filter that compensates for a first distortion contained in a received signal obtained by coherently receiving a signal transmitted from a transmitter via a transmission line, for the received signal and a complex conjugate signal of the received signal, and outputs the received signal and the complex conjugate signal that have been compensated for the first distortion, a filter group including a second filter that receives the received signal and the complex conjugate signal that have been compensated for the first distortion as input signals, compensates for a second distortion contained in the received signal, and outputs the received signal that has been compensated for the second distortion, and coefficient update means that adaptively controls a filter coefficient of the second filter based on a difference between an output signal output from the filter group and a predetermined value of the output signal.

[0029] The present disclosure provides, as a second aspect, a receiver. The receiver includes a receiver circuit that coherently receives a signal transmitted from a transmitter via a transmission path, and an equalization signal processing circuit that performs equalization signal processing on the coherently received received signal. The equalization signal processing circuit includes a first filter that compensates for a first distortion contained in the received signal and a complex conjugate signal of the received signal, respectively, and outputs the received signal and the complex conjugate signal that have been compensated for the first distortion, a filter group including a second filter that receives the received signal and the complex conjugate signal that have been compensated for the first distortion as input signals, compensates for a second distortion contained in the received signal, and outputs the received signal that has been compensated for the second distortion, and coefficient update means that adaptively controls a filter coefficient of the second filter based on a difference between an output signal output from the filter group and a predetermined value of the output signal.

[0030] The present disclosure provides, as a third aspect, a communication system. The communication system includes a transmitter that transmits a signal via a transmission path and a receiver that receives the transmitted signal. The receiver includes a receiver circuit that coherently receives the signal transmitted from the transmitter and an equalization signal processing circuit that performs equalization signal processing on the coherently received received signal. The equalization signal processing circuit includes a first filter that compensates for a first distortion contained in the received signal and a complex conjugate signal of the received signal, respectively, and outputs the received signal and the complex conjugate signal that have been compensated for the first distortion, a filter group including a second filter that receives the received signal and the complex conjugate signal that have been compensated for the first distortion as input signals, compensates for a second distortion contained in the received signal, and outputs the received signal that has been compensated for the second distortion, and coefficient update means that adaptively controls a filter coefficient of the second filter based on a difference between an output signal output from the filter group and a predetermined value of the output signal.

[0031] The present disclosure provides, as a fourth aspect, an equalization signal processing method, which includes: using a first filter to compensate for a first distortion contained in a received signal obtained by coherently receiving a signal transmitted from a transmitter via a transmission path, the received signal and a complex conjugate signal of the received signal; inputting the received signal and the complex conjugate signal that have been compensated for the first distortion to a filter group including a second filter; compensating for a second distortion contained in the received signal using the second filter; and adaptively controlling a filter coefficient of the second filter based on a difference between an output signal output from the filter group and a predetermined value of the output signal.

[0032] In a fifth aspect, the present disclosure provides a computer-readable medium storing a program for causing a processor to execute a process including: using a first filter to compensate for a first distortion contained in a received signal obtained by coherently receiving a signal transmitted from a transmitter via a transmission line, the received signal and a complex conjugate signal of the received signal, respectively; inputting the received signal and the complex conjugate signal after the first distortion compensation to a filter group including a second filter; compensating for a second distortion contained in the received signal using the second filter; and adaptively controlling a filter coefficient of the second filter based on a difference between an output signal output from the filter group and a predetermined value of the output signal. [Effects of the Invention]

[0033] The communication system, receiver, equalization signal processing circuit, method, and computer-readable medium according to the present disclosure can compensate for various distortions while minimizing an increase in the amount of calculations. [Brief explanation of the drawings]

[0034] [Figure 1] 1 is a block diagram illustrating a schematic diagram of a communication system according to the present disclosure. [Figure 2] FIG. 2 is a block diagram showing a schematic configuration of a receiver. [Figure 3] FIG. 1 is a block diagram illustrating a signal transmission system according to an embodiment of the present disclosure. [Figure 4] FIG. 2 is a block diagram showing an example of digital signal processing in an equalization unit. [Figure 5] Block diagram showing a 2x1 SL MISO filter. [Figure 6] FIG. [Figure 7] FIG. 2 is a block diagram showing an example of the configuration of an equalization unit. [Figure 8] FIG. 1 is a block diagram showing an example of receiver-side equalization digital signal processing described in Non-Patent Document 1. [Figure 9] Block diagram showing a 2x2 MIMO filter. [Figure 10]FIG. 1 is a block diagram showing an adaptive multilayer filter for performing equalization signal processing. [Figure 11] Block diagram showing the WL2×1 filter. DETAILED DESCRIPTION OF THE INVENTION

[0035] Prior to describing embodiments of the present disclosure, an overview of the present disclosure will be described. Fig. 1 schematically shows a communication system according to the present disclosure. The communication system 10 includes a transmitter 11 and a receiver 15. The transmitter 11 and the receiver 15 are connected to each other via a transmission path 13. The transmitter 11 transmits a signal via the transmission path 13. The receiver 15 receives the signal transmitted from the transmitter 11 via the transmission path 13.

[0036] 2 shows a schematic configuration of the receiver 15. The receiver 15 has a receiving circuit 21 and an equalization signal processing circuit 22. The receiving circuit 21 coherently receives a signal transmitted from the transmitter 11. The equalization signal processing circuit 22 performs equalization signal processing on the coherently received received signal.

[0037] The equalization signal processing circuit 22 has a first filter 23, a filter group 25, and coefficient update means 26. The first filter 23 compensates for a first distortion contained in a coherently received received signal, for each of the received signal and a complex conjugate signal of the received signal, and outputs the received signal and the complex conjugate signal that have been compensated for the first distortion.

[0038] The filter group 25 includes a second filter 24. The second filter 24 receives as input signals the received signal that has been compensated for the first distortion and the complex conjugate signal, and compensates for the second distortion contained in the received signal. The filter group 25 may include one or more filters connected in cascade along the signal path of the received signal after the second filter 24. The coefficient update means 26 adaptively controls the filter coefficient of the second filter 24 based on the difference between the output signal output from the filter group 25 and a predetermined value of the output signal.

[0039] In the present disclosure, the first filter 23, which compensates for the first distortion, is arranged before the second filter 24, which compensates for the second distortion. The second distortion is assumed to be distortion that is usually compensated for using a WL filter. If the first filter 23 were arranged after the second filter 24 in the filter group 25, updating the filter coefficients of the second filter 24 would require calculating the gradient of the input vector and coefficients of the loss function for the first filter 23. In this case, if the tap length of the first filter 23 is long, the amount of calculation required for updating the coefficients increases. In the present disclosure, as described below, the first filter 23 can be arranged before the second filter 24 while still allowing the second filter 24 to compensate for the second distortion. Therefore, the equalization signal processing circuit 22 can compensate for various distortions while suppressing an increase in the amount of calculation required for updating the coefficients.

[0040] Hereinafter, embodiments of the present disclosure will be described in detail with reference to the drawings. FIG. 3 shows a signal transmission system according to an embodiment of the present disclosure. In this embodiment, it is assumed that the signal transmission system is an optical fiber communication system that employs a polarization multiplexed QAM method and performs coherent reception. The optical fiber communication system 100 includes an optical transmitter 110, a transmission line 130, and an optical receiver 150. The optical fiber communication system 100 constitutes, for example, an optical submarine cable system. The optical fiber communication system 100 corresponds to the communication system 10 shown in FIG. 1. The optical transmitter 110 corresponds to the transmitter 11 shown in FIG. 1. The transmission line 130 corresponds to the transmission line 13 shown in FIG. 1. The optical receiver 150 corresponds to the receiver 15 shown in FIG. 1.

[0041] The optical transmitter 110 converts transmission data into a polarization multiplexed signal. The optical transmitter 110 includes an encoder 111, a pre-equalizer 112, a DAC (Digital Analog Converter) 113, an optical modulator 114, and an LD (Laser Diode) 115. The encoder 111 encodes the transmission data and generates a signal sequence for optical modulation. In the case of a polarization multiplexed QAM system, the encoder 111 generates a total of four signal sequences, including an in-phase (I) component and a quadrature (Q) component of each of the X polarization (first polarization) and the Y polarization (second polarization). Note that in FIG. 3, for simplicity, the four encoded signal sequences are shown as a single solid line. Hereinafter, a single solid line shown in FIG. 3 represents a predetermined number of signal sequences collectively as a physical entity.

[0042] The pre-equalization unit 112 performs pre-equalization on the coded four-sequence signal to compensate for distortions of devices in the optical transmitter in advance. The DAC 113 converts each of the four-sequence signals that have undergone pre-equalization into an analog electrical signal.

[0043] The LD 115 outputs a CW (Continuous wave) light. The optical modulator 114 modulates the CW light output from the LD 115 in accordance with the four-series signals output from the DAC 113 to generate a polarization multiplexed QAM optical signal. The optical signal generated by the optical modulator 114 (polarization multiplexed optical signal) is output to the transmission path 130.

[0044] The transmission path 130 transmits the polarization multiplexed optical signal output from the optical transmitter 110 to the optical receiver 150. The transmission path 130 has an optical fiber 132 and an optical amplifier 133. The optical fiber 132 guides the optical signal transmitted from the optical transmitter 110. The optical amplifier 133 amplifies the optical signal and compensates for propagation loss in the optical fiber 132. The optical amplifier 133 is configured as, for example, an erbium-doped fiber amplifier (EDFA). The transmission path 130 may include multiple optical amplifiers 133.

[0045] The optical receiver 150 includes an LD 151, a coherent receiver 152, an ADC (Analog Digital Converter) 153, an equalization unit 154, and a decoding unit 155. In the optical receiver 150, circuits such as the equalization unit (equalizer) 154 and the decoding unit (decoder) 155 can be configured using a device such as a DSP (digital signal processor).

[0046] The LD 151 outputs CW light to be used as local oscillator light. In this embodiment, the coherent receiver 152 is configured as a polarization diversity coherent receiver. The coherent receiver 152 uses the CW light output from the LD 151 to perform coherent detection on the optical signal transmitted through the optical fiber 132. The coherent receiver 152 outputs four series of received signals (electrical signals) corresponding to the I and Q components of the coherently detected X and Y polarizations. The coherent receiver 152 corresponds to the receiving circuit 21 shown in FIG. 2.

[0047] The ADC 153 samples the received signal output from the coherent receiver 152 and converts the received signal into a digital signal. The equalizer 154 performs receiver-side equalization signal processing on the four series of received signals sampled by the ADC 153. The equalizer 154 compensates for various distortions in the optical fiber communication system by performing equalization signal processing on the received signals. In the following, it is assumed that the equalizer 154 performs receiver-internal distortion compensation, chromatic dispersion compensation, polarization demultiplexing, carrier phase compensation, and transmitter-internal distortion compensation, as in the example of FIG. 10. The equalizer 154 corresponds to the equalization signal processing circuit 22 shown in FIG. 2. The decoder 155 decodes the signal that has been subjected to equalization signal processing by the equalizer 154, thereby restoring the transmitted data. The decoder 155 outputs the restored data to another circuit (not shown).

[0048] 4 shows a specific example of digital signal processing (equalization signal processing) in the equalization unit 154. In the example shown in FIG. 4, the digital signal processing includes a chromatic dispersion compensation filter 171, a receiver-internal distortion compensation filter 172, a polarization separation filter 173, a carrier phase compensation filter 174, a transmitter-internal distortion compensation filter 175, a loss function calculation unit 176, a coefficient update unit 177, and a PLL 178. The digital signal processing constitutes an equalization signal processing circuit that implements the equalization signal processing method according to this embodiment. In this embodiment, the receiver-internal distortion compensation filter 172, the polarization separation filter 173, the carrier phase compensation filter 174, and the transmitter-internal distortion compensation filter 175 constitute a multilayer filter whose coefficients are adaptively controlled.

[0049] Two received complex signals (x1 and x2) corresponding to two polarized waves are input to the equalizer 154. The received complex signals input to the equalizer 154 may be signals that have been compensated for in advance for known device distortion. Alternatively, the received complex signals input to the equalizer 154 may be signals that have been subjected to a matched filter. The complex conjugate calculator 179 calculates the complex conjugates (x1 and x2) of the two received complex signals (x1 and x2) respectively. * and x2 * The wavelength dispersion compensation filter 171 receives two received complex signals (x1 and x2) and their complex conjugate signals (x1 * and x2 * ) is entered.

[0050] The wavelength dispersion compensation filter 171 is configured to compensate for the input signals (x1, x2, x1 * , and x2 * ) in the transmission path due to chromatic dispersion (first distortion). In other words, the chromatic dispersion compensation filter 171 compensates for the distortion (first distortion) that occurs in each of the input signals (x1, x2, x1 * , and x2 *) is subjected to filtering to compensate for chromatic dispersion. The chromatic dispersion compensation filter 171 includes a complex signal input complex coefficient filter with a predetermined tap length. Either a time domain filter or a frequency domain filter may be used for the chromatic dispersion compensation filter 171. The coefficients of the chromatic dispersion compensation filter 171 are determined so as to compensate for accumulated chromatic dispersion according to transmission path information such as the transmission fiber and transmission distance, as is commonly done in optical fiber communications. The coefficients of the chromatic dispersion compensation filter 171 are handled statically. The chromatic dispersion compensation filter 171 corresponds to the first filter 23 shown in FIG. 2.

[0051] The signals obtained by performing chromatic dispersion compensation on the received complex signals of each polarization and the signals obtained by performing chromatic dispersion compensation on the complex conjugates of the received complex signals of each polarization, which are output from the chromatic dispersion compensation filter 171, are input to the multilayer filter. The multilayer filter includes, in this order from the signal input side, a receiver-internal distortion compensation filter 172, a polarization separation filter 173, a carrier phase compensation filter 174, and a transmitter-internal distortion compensation filter 175. The multilayer filter corresponds to the filter group 25 shown in FIG. 2. The receiver-internal distortion compensation filter 172 corresponds to the second filter 24 shown in FIG. 2.

[0052] The receiver-internal distortion compensation filter 172 compensates for signal distortion (second distortion) occurring within the optical receiver 150 (FIG. 3). The polarization separation filter 173 compensates for signal distortion occurring due to polarization state fluctuations and polarization mode dispersion during optical fiber transmission. The carrier phase compensation filter 174 compensates for signal distortion occurring due to frequency offsets and phase offsets between the carrier of the transmitted optical signal and the local oscillator light on the receiving side. The transmitter-internal distortion compensation filter (third filter) 175 compensates for signal distortion (third distortion) occurring within the optical transmitter 110. The signals y1 and y2 output by the transmitter-internal distortion compensation filter 175 are signals in which various distortions contained in the received complex signals x1 and x2 have been compensated for.

[0053] In Fig. 4, the filter of each block is configured according to the characteristics of the distortion to be compensated for. The filter of each block is configured using, for example, an FIR filter. In the filter of each block, the tap length of the FIR filter is set to a tap length according to the characteristics of the distortion to be compensated for.

[0054] The receiver distortion compensation filter 172 includes two 2×1 SL MISO (Multi-input single-output) filters, one for each polarization. FIG. 5 shows a 2×1 SL MISO filter. In FIG. 5, the MISO filter 190 has two FIR filters 191 and 192. The FIR filter 191 convolves a complex coefficient (first complex coefficient) h1 with a complex signal that has been subjected to chromatic dispersion compensation. The FIR filter 192 convolves a complex coefficient (second complex coefficient) h1 with a complex conjugate signal that has been subjected to chromatic dispersion compensation. *1 The MISO filter 190 outputs a signal obtained by adding the output of the FIR filter 191 and the output of the FIR filter 192. The distortion compensation filter 172 in the receiver outputs a pair of the complex signal of the X polarization and its complex conjugate signal (x1, x1 * ), and a pair of Y-polarized complex signals and their complex conjugate signals (x2, x2 * 7. The receiver distortion compensation filter 172 outputs a signal obtained by adding the output of the FIR filter 191 and the output of the FIR filter 192 for each polarization.

[0055] Although the above description has been given of an example in which the receiver distortion compensation filter 172 has two 2×1 SL MISO filters arranged for each polarization, the present embodiment is not limited to this. For example, depending on the receiver configuration, there may be cases in which distortion caused by mixing of signals between polarizations appears significantly. In such cases, the receiver distortion compensation filter 172 may use a 4×2 SL MIMO filter instead of two 2×1 SL MISO filters.

[0056] The output signals corresponding to the two polarized waves output by the receiver distortion compensation filter 172 are input to the polarization separation filter 173. The polarization separation filter 173 includes a 2×2 MIMO SL filter. The output signals corresponding to the two polarized waves output by the polarization separation filter 173 are input to the carrier phase compensation filter 174. The carrier phase compensation filter 174 includes a one-tap SL filter arranged for each polarized wave. The output signals corresponding to the two polarized waves output by the carrier phase compensation filter 174 are input to the transmitter distortion compensation filter 175. The transmitter distortion compensation filter 175 includes a WL2×1 filter arranged for each polarized wave.

[0057] The coefficient of the carrier phase compensation filter 174, i.e., the compensation amount in carrier phase compensation, is controlled by a PLL 178. The PLL 178 determines the compensation amount in carrier phase compensation based on the output of the internal distortion compensation filter 175, which is the final output of the multi-layer filter.

[0058] The loss function calculation unit 176 calculates the difference between the output of the transmitter distortion compensation filter 175, which is the final stage of the multilayer filter, and the desired state as a loss function. The coefficient update unit 177 updates the coefficients of the receiver distortion compensation filter 172, the polarization separation filter 173, and the transmitter distortion compensation filter 175. The coefficient update unit 177 updates the coefficients of each filter, for example, for each sample or symbol at one time. The coefficient update unit 177 sequentially updates the coefficients of each filter so as to minimize the loss function, for example, using backpropagation and gradient descent. The coefficient update unit 177 updates the filter coefficients of each filter, for example, using the DALMS algorithm and stochastic gradient descent. The coefficient update unit 177 corresponds to the coefficient update means 26 shown in FIG. 2.

[0059] Next, we will explain the operating principle of the equalization signal processing shown in Fig. 4. Generally, when a signal is subjected to a WL filter and an SL filter, if the order is reversed, the results will be different before and after the reversal. Therefore, in the adaptive multilayer filter shown in Fig. 10, which compensates for each distortion in the reverse order from the order in which the distortions occurred, it is not possible to simply reverse the receiver distortion compensation 701 and chromatic dispersion compensation 702.

[0060] However, according to the distributive law of products, the following equivalence holds. Here, we consider the case where an input signal x is first filtered using a 2×1WL filter, and then chromatic dispersion compensation (SL filter) is applied. The output signal y(t) of the 2×1WL filter for the input signal x is expressed by the following equation: TIFF0007772190000017.tif10141. Furthermore, the output signal y(t) of the 2×1WL filter is filtered by the chromatic dispersion compensation filter h CD The output signal z(t) is The file name will be TIFF0007772190000018.tif12141. Using the distributive law of products, the above formula 18 can be rewritten as the following formula 19. TIFF0007772190000019.tif10166By rearranging the above equation 19, we obtain the following equation 20. TIFF0007772190000020.tif10166

[0061] As can be seen from Equation 20 above, applying a 2×1WL filter for distortion compensation within the receiver and an SL filter for chromatic dispersion compensation to the input signal in this order is equivalent to applying a 2×1 SL MISO filter to the input signal after chromatic dispersion compensation and the signal after chromatic dispersion compensation of the complex conjugate signal of the input signal. Therefore, in the digital signal processing shown in Figure 4, distortion compensation and chromatic dispersion compensation within the receiver can be performed appropriately. For the error backpropagation for coefficient update, the formula for the SL MIMO filter that has already been obtained can be used as is.

[0062] Chromatic dispersion spreads widely over time in ultra-long-distance transmission over single-mode fiber, and compensating for such chromatic dispersion requires a chromatic dispersion compensation filter with a huge number of taps. In the digital signal processing shown in FIG. 4, the chromatic dispersion compensation filter 171 is independent of the multilayer filter whose coefficients are adaptively controlled. The multilayer filter does not include a filter with a large number of taps, such as the chromatic dispersion compensation filter. Therefore, in this embodiment, it is possible to avoid the multiplication of large matrices required in the error backpropagation for coefficient update, and the amount of calculation required for coefficient update can be significantly reduced.

[0063] In the digital signal processing shown in Fig. 4, the coefficients h1 and h2 of the 2 × 1 SL MISO filter for distortion compensation in the receiver are *1 As previously shown, the coefficients h1, h2 of the 2×1WL filter for distortion compensation in the receiver in the equalization signal processing shown in FIG. *1 Therefore, the digital signal processing in this embodiment can be applied to the detection of the amount of distortion as described in Non-Patent Document 3 without modification.

[0064] The inventors conducted a simulation to verify the performance of distortion compensation in the configuration of this embodiment. In the simulation, a 32-Gbaud polarization-multiplexed probabilistic constellation-shaped 64QAM signal (entropy 2.8 bit / symbol / pol) was used, and this signal was subjected to an accumulation of chromatic dispersion equivalent to transmission over 10,000 km of single-mode fiber, and random polarization rotation. In the simulation, the transmit / receive laser phase noise was assumed to be 100 kHz, no nonlinear distortion was present, and distortion compensation was performed using the digital signal processing shown in Figure 4 under the conditions of a receive OSNR (Optical Signal-to-Noise Ratio) of 30 dB / 0.1 nm.

[0065] In the simulation, a 10 ps IQ skew was added to the X-polarized signal in the transmitter and receiver, and the distortion compensation performance was evaluated. Each filter in the multilayer filter was a T / 2-spaced FIR filter. Chromatic dispersion compensation was performed using a frequency domain filter. A known pilot signal with the same format as the transmitted signal was inserted into the transmitted signal every 15 symbols, and this was used to update the coefficients using DALMS.

[0066] Figure 6 shows the simulation results. Figure 7 shows the simulation results as constellation diagrams in which the demodulated signal from the multilayer filter is mapped onto the IQ plane at symbol timing. Figure 6 shows the compensated constellations without IQ skew at the transmitter (Tx) and receiver (Rx), the compensated constellations with IQ skew at the transmitter, and the compensated constellations with IQ skew at the receiver. Comparing the three constellations shown in Figure 6 reveals that similar reception characteristics are obtained with and without IQ skew at the transmitter and receiver. Therefore, the simulation confirmed that the distortion compensation in the transmitter and receiver functions properly even when there is accumulated chromatic dispersion equivalent to that of an ultra-long-distance 10,000 km single-mode fiber transmission.

[0067] In the above embodiment, the equalization unit 154 may be configured as any digital signal processing circuit. Fig. 7 shows an example configuration of the equalization unit 154. For example, the equalization unit 154 includes one or more processors 410 and one or more memories 420. The processor 410 reads out a program stored in the memory 420 to perform receiver-side equalization signal processing.

[0068] The program includes instructions (or software code) that, when loaded into a processor, cause the processor to perform one or more functions described in the embodiments. The program may be stored in a non-transitory computer-readable medium or a tangible storage medium. By way of example and not limitation, computer-readable media or tangible storage media include random-access memory (RAM), read-only memory (ROM), flash memory, solid-state drive (SSD) or other memory technology, compact disc (CD)-ROM, digital versatile disc (DVD), Blu-ray disc or other optical disk storage, magnetic cassette, magnetic tape, magnetic disk storage or other magnetic storage device. The program may also be transmitted on a transitory computer-readable medium or communication medium. By way of example and not limitation, transitory computer-readable media or communication media include electrical, optical, acoustic, or other forms of propagated signals.

[0069] The above describes the embodiments of the present disclosure in detail, but the present disclosure is not limited to the above-described embodiments, and changes and modifications to the above-described embodiments that do not deviate from the spirit of the present disclosure are also included in the present disclosure.

[0070] For example, some or all of the above embodiments can be described as, but are not limited to, the following supplementary notes.

[0071] [Appendix 1] a first filter that compensates for a first distortion contained in a received signal obtained by coherently receiving a signal transmitted from a transmitter via a transmission line, for the received signal and a complex conjugate signal of the received signal, and outputs the received signal and the complex conjugate signal that have been compensated for the first distortion; a filter group including a second filter that receives the received signal that has been compensated for the first distortion and a complex conjugate signal as input signals, compensates for the second distortion contained in the received signal, and outputs the received signal that has been compensated for the second distortion; an equalization signal processing circuit comprising: a coefficient update means for adaptively controlling the filter coefficient of the second filter based on the difference between the output signal output from the filter group and a predetermined value of the output signal;

[0072] [Appendix 2] 2. The equalization signal processing circuit according to claim 1, wherein the first distortion includes distortion caused by chromatic dispersion in the transmission path, and the first filter compensates for the chromatic dispersion.

[0073] [Appendix 3] 3. The equalization signal processing circuit according to claim 1, wherein the second distortion includes intra-receiver distortion caused within a receiver, and the second filter compensates for the intra-receiver distortion.

[0074] [Appendix 4] 4. The equalization signal processing circuit according to claim 1, wherein the first filter includes a complex signal input complex coefficient filter having a predetermined tap length, and the second filter includes a MISO (Multiple Input Single Output) filter.

[0075] [Appendix 5] the MISO filter convolves a first complex coefficient with the received signal that has been compensated for the first distortion, convolves a second complex coefficient with the complex conjugate signal that has been compensated for the first distortion, and adds together the received signal convolved with the first complex coefficient and the complex conjugate signal convolved with the second complex coefficient, and outputs the sum.

[0076] [Appendix 6] 6. The equalization signal processing circuit according to claim 1, wherein the signal transmitted from the transmitter is a polarization multiplexed signal, and the first filter and the second filter are arranged for each polarization.

[0077] [Appendix 7] the filter group includes one or more filters connected in cascade along a signal path of the received signal on a subsequent stage of the second filter; 7. The equalization signal processing circuit according to claim 1, wherein the coefficient update means adaptively controls the filter coefficients of the second filter using a backpropagation algorithm.

[0078] [Appendix 8] the one or more filters include a third filter that compensates for a third distortion included in the received signal; 8. The equalization signal processing circuit according to claim 7, wherein the coefficient update means further adaptively controls the filter coefficient of the third filter based on a difference between an output signal output from the filter group and a predetermined value of the output signal.

[0079] [Appendix 9] 9. The equalization signal processing circuit of claim 8, wherein the third distortion includes in-transmitter distortion caused in a transmitter, and the third filter compensates for the in-transmitter distortion.

[0080] [Appendix 10] a receiving circuit for coherently receiving a signal transmitted from a transmitter via a transmission line; an equalization signal processing circuit that performs equalization signal processing on the coherently received received signal, The equalization signal processing circuit a first filter that compensates for a first distortion contained in the received signal with respect to the received signal and a complex conjugate signal of the received signal, and outputs the received signal and the complex conjugate signal that have been compensated for the first distortion; a filter group including a second filter that receives the received signal that has been compensated for the first distortion and a complex conjugate signal as input signals, compensates for the second distortion contained in the received signal, and outputs the received signal that has been compensated for the second distortion; a coefficient update means for adaptively controlling the filter coefficient of the second filter based on a difference between an output signal output from the group of filters and a predetermined value of the output signal.

[0081] [Appendix 11] 11. The receiver of claim 10, wherein the first distortion includes distortion caused by chromatic dispersion in the transmission path, and the first filter compensates for the chromatic dispersion.

[0082] [Appendix 12] 12. The receiver of claim 10 or 11, wherein the second distortion includes intra-receiver distortion caused within a receiver, and the second filter compensates for the intra-receiver distortion.

[0083] [Appendix 13] 13. The receiver according to any one of appendixes 10 to 12, wherein the first filter includes a complex signal input complex coefficient filter of a predetermined tap length, and the second filter includes a MISO (Multiple Input Single Output) filter.

[0084] [Appendix 14] a transmitter for transmitting a signal via a transmission line; a receiver for receiving the transmitted signal; The receiver includes: a receiving circuit for coherently receiving a signal transmitted from the transmitter; an equalization signal processing circuit that performs equalization signal processing on the coherently received received signal, The equalization signal processing circuit a first filter that compensates for a first distortion contained in the received signal with respect to the received signal and a complex conjugate signal of the received signal, and outputs the received signal and the complex conjugate signal that have been compensated for the first distortion; a filter group including a second filter that receives the received signal that has been compensated for the first distortion and a complex conjugate signal as input signals, compensates for the second distortion contained in the received signal, and outputs the received signal that has been compensated for the second distortion; a coefficient update means for adaptively controlling the filter coefficient of the second filter based on the difference between the output signal output from the filter group and a predetermined value of the output signal.

[0085] [Appendix 15] 15. The communication system of claim 14, wherein the first distortion includes distortion caused by chromatic dispersion in the transmission path, and the first filter compensates for the chromatic dispersion.

[0086] [Appendix 16] 16. The communication system of claim 14, wherein the second distortion includes intra-receiver distortion caused within a receiver, and the second filter compensates for the intra-receiver distortion.

[0087] [Appendix 17] using a first filter, a signal transmitted from a transmitter via a transmission line is coherently received, and compensation for a first distortion contained in the received signal is performed on each of the received signal and a complex conjugate signal of the received signal; inputting the received signal and the complex conjugate signal that have been compensated for the first distortion into a filter group including a second filter, and compensating for a second distortion contained in the received signal using the second filter; an equalization signal processing method comprising adaptively controlling a filter coefficient of the second filter based on a difference between an output signal output from the filter group and a predetermined value of the output signal;

[0088] [Appendix 18] using a first filter, a signal transmitted from a transmitter via a transmission line is coherently received, and compensation for a first distortion contained in the received signal is performed on each of the received signal and a complex conjugate signal of the received signal; inputting the received signal and the complex conjugate signal that have been compensated for the first distortion into a filter group including a second filter, and compensating for a second distortion contained in the received signal using the second filter; A non-transitory computer-readable medium storing a program for causing a processor to execute a process including adaptively controlling the filter coefficients of the second filter based on a difference between an output signal output from the group of filters and a predetermined value of the output signal. [Explanation of symbols]

[0089] 10:Communication Systems 11:Transmitter 15: Receiver 13: Transmission path 21: Receiving circuit 22: Equalization signal processing circuit 23: First filter 24: Second filter 25: Filter group 26: Coefficient update means 100: Optical fiber communication system 110: Optical transmitter 130: Transmission line 150: Optical receiver 111: Encoding section 112: Pre-equalization section 113:DAC 114: Optical modulator 115:LD 132: Optical fiber 133: Optical amplifier 151:LD 152: Coherent receiver 153:ADC 154: Equalization section 155: Decryption unit 171: chromatic dispersion compensation filter 172: Distortion compensation filter in the receiver 173: Polarization separation filter 174: Carrier phase compensation filter 175: Transmitter internal distortion compensation filter 176: Loss function calculation part 177: Coefficient update unit 178:PLL 179: Complex conjugate calculation unit

Claims

1. a first filter that compensates for a first distortion contained in a received signal obtained by coherently receiving a signal transmitted from a transmitter via a transmission line, for the received signal and a complex conjugate signal of the received signal, and outputs the received signal and the complex conjugate signal that have been compensated for the first distortion; a filter group including a second filter that receives the received signal and the complex conjugate signal that have been compensated for the first distortion as input signals, compensates for the second distortion contained in the received signal, and outputs the received signal that has been compensated for the second distortion as an output signal; and and a coefficient update means for adaptively controlling the filter coefficient of the second filter based on the difference between the output signal output from the filter group and a predetermined value of the output signal.

2. 2. The equalization signal processing circuit according to claim 1, wherein the first distortion includes distortion caused by chromatic dispersion in the transmission path, and the first filter compensates for the chromatic dispersion.

3. 3. The equalization signal processing circuit according to claim 1, wherein the second distortion includes a receiver-intra-distortion occurring within a receiver, and the second filter compensates for the receiver-intra-distortion.

4. 2. The method according to claim 1, wherein the first filter includes a complex-signal-input complex-coefficient filter having a predetermined tap length, and the second filter includes a MISO (Multiple Input Single Output) filter.

4. An equalization signal processing circuit according to any one of claims 1 to 3.

5. 5. The equalization signal processing circuit according to claim 1, wherein the signal transmitted from the transmitter is a polarization multiplexed signal, and the first filter and the second filter are arranged for each polarization.

6. the filter group includes one or more filters connected in cascade along a signal path of the received signal on a subsequent stage side of the second filter, 6. The equalization signal processing circuit according to claim 1, wherein said coefficient updating means adaptively controls the filter coefficients of said second filter using an error backpropagation method.

7. a receiving circuit for coherently receiving a signal transmitted from a transmitter via a transmission line; an equalization signal processing circuit that performs equalization signal processing on the coherently received received signal, The equalization signal processing circuit a first filter that compensates for a first distortion contained in the received signal with respect to the received signal and a complex conjugate signal of the received signal, and outputs the received signal and the complex conjugate signal that have been compensated for the first distortion; a filter group including a second filter that receives the received signal and the complex conjugate signal that have been compensated for the first distortion as input signals, compensates for the second distortion contained in the received signal, and outputs the received signal that has been compensated for the second distortion as an output signal; and a coefficient update means for adaptively controlling the filter coefficient of the second filter based on a difference between an output signal output from the group of filters and a predetermined value of the output signal.

8. a transmitter for transmitting a signal via a transmission line; a receiver for receiving the transmitted signal; The receiver includes: a receiving circuit for coherently receiving a signal transmitted from the transmitter; an equalization signal processing circuit that performs equalization signal processing on the coherently received received signal, The equalization signal processing circuit a first filter that compensates for a first distortion contained in the received signal with respect to the received signal and a complex conjugate signal of the received signal, and outputs the received signal and the complex conjugate signal that have been compensated for the first distortion; a filter group including a second filter that receives the received signal and the complex conjugate signal that have been compensated for the first distortion as input signals, compensates for the second distortion contained in the received signal, and outputs the received signal that has been compensated for the second distortion as an output signal; and a coefficient update means for adaptively controlling the filter coefficient of the second filter based on the difference between the output signal output from the filter group and a predetermined value of the output signal.

9. using a first filter, a signal transmitted from a transmitter via a transmission line is coherently received, and compensation for a first distortion contained in the received signal is performed on each of the received signal and a complex conjugate signal of the received signal; inputting the received signal and the complex conjugate signal that have been compensated for the first distortion to a filter group including a second filter, and compensating for the second distortion contained in the received signal in the filter group using at least the second filter; and adaptively controlling a filter coefficient of the second filter based on a difference between a received signal, which is an output signal of the filter group and has been compensated for at least the second distortion, and a predetermined value of the output signal.

10. using a first filter, a signal transmitted from a transmitter via a transmission line is coherently received, and compensation for a first distortion contained in the received signal is performed on each of the received signal and a complex conjugate signal of the received signal; inputting the received signal and the complex conjugate signal that have been compensated for the first distortion to a filter group including a second filter, and compensating for the second distortion contained in the received signal in the filter group using at least the second filter; a program for causing a processor to execute processing including adaptively controlling a filter coefficient of the second filter based on a difference between a received signal, which is an output signal of the filter group and in which at least the second distortion has been compensated for, and a predetermined value of the output signal.

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