Equalization signal processing circuit, receiver, communication system, and equalization signal processing method

Abstract

To mitigate complexity of circuit design.SOLUTION: An equalization signal processing circuit includes: a signal division section which divides an input signal of oversampling which is M / L times in rational numbers into M pieces of signals; a first frequency domain filter which operates a first filter coefficient with respect to the M pieces of frequency domain signals; a second frequency domain filter which operates a second filter coefficient with respect to the M pieces of signals for which the first filter coefficient is operated for each of L groups; a time domain conversion section which converts signals which are added for each group into time domain signals; a switch circuit which successively selects the signals converted into the time domain signals for each group; and a coefficient update section which updates the first filter coefficient and the second filter coefficient.SELECTED DRAWING: Figure 2

Description

[Technical Field]

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

[0002] Since the introduction of so-called digital coherent technology, which combines coherent reception and digital signal processing, in optical fiber communications, flexible receiver-side equalization signal processing has become possible using digital signal processing. In receiver-side equalization signal processing, for example, chromatic dispersion accumulated in the optical fiber transmission line is compensated for collectively in the receiving device.

[0003] Optical fiber communications generally handle high-speed, large-capacity signals. For this reason, high throughput is also required for the digital signal processing used in optical fiber communications. Therefore, the large amount of calculation required for digital signal processing often becomes an issue. Adaptive equalization filters adaptively control their response according to the state of the transmission path. Adaptive equalization filters are one of the important elements of receiver-side equalization signal processing in optical fiber communications, and there is a demand for more efficient calculation of these adaptive equalization filters as well.

[0004] When an adaptive equalization filter compensates for effects with a large time spread, a large filter capable of representing a response with a large time spread is used in the adaptive equalization filter, which increases the amount of calculation required for compensation. One method for efficiently compensating for effects with a large time spread is to use a frequency domain filter. In the frequency domain, the convolution of the filter response with the time domain input signal can be treated as a simple multiplication. Furthermore, the conversion of a time domain signal to the frequency domain can be efficiently performed using a fast Fourier transform (FFT). Therefore, when the time spread of the response is large, a frequency domain filter requires less calculation than a time domain filter.

[0005] As a related technique, Non-Patent Document 1 discloses an adaptive frequency domain filter in which the response of the frequency domain filter is adaptively controlled. FIG. 8 is a block diagram showing an example of the adaptive frequency domain filter described in Non-Patent Document 1. This adaptive frequency domain filter is a linear adaptive filter. Normally, due to the Nyquist criterion, a linear adaptive filter operates on a signal with two samples per symbol, that is, an input signal that is 2x oversampled.

[0006] In the adaptive frequency domain filter 600 shown in FIG. 8, the block transform unit 601 transforms a 2x oversampled time domain input signal into a block signal of a certain length for conversion to the frequency domain. That is, the block transform unit 601 performs a serial-to-block transform on the time domain input signal. When converting to the frequency domain, the periodicity of the blocked signal is assumed. However, the assumption of signal periodicity does not generally hold for signals handled in optical communications. For this reason, the overlap-save method is used. That is, when serial-to-block transforming the input signal, a certain percentage of overlap, for example 50%, is provided between blocks.

[0007] The FFT 602 converts the blocked input signal into a frequency domain signal. The frequency domain filter 603 multiplies the input signal by a filter coefficient for each frequency. The inverse FFT (IFFT) 604 converts the output signal of the frequency domain filter 603 from a frequency domain signal to a time domain signal. The serial conversion unit 605 converts the blocked signal converted into a time domain signal by the IFFT 604 into a serial signal. That is, the serial conversion unit 605 performs block-to-serial conversion on the output signal of the IFFT 604. In converting to a serial signal, the serial conversion unit 605 retains only the region of the output signal of the IFFT 604 that is not affected by the periodicity assumption and removes the other region. The downsampling unit 606 performs 1 / 2 downsampling on the output signal of the serial conversion unit 605. The coefficients of the frequency domain filter 603 are adaptively controlled using the input signal of the frequency domain filter 603 and the output signal of the serial conversion unit 605.

[0008] Here, the input signal vector blocked by the block conversion unit 601 is denoted by x. Also, the size of the 1x oversampling time domain serial signal for one block of the input signal is denoted by N. When the overlap rate is 50%, the length of x is 4N. x is a 2x oversampling signal and is expressed by the following equation 1. TIFF2025174462000002.tif8134In Equation 1, T represents transposition. If the signal vector obtained by transforming the input signal vector x into the frequency domain is X, the input signal vector X in the frequency domain is expressed by the following Equation 2. TIFF2025174462000003.tif8139k, where n=0, 1, ..., 4N-1, the following equations 3 and 4 hold. TIFF2025174462000004.tif19129TIFF2025174462000005.tif18114

[0009] Let H be the filter coefficient vector of the frequency domain filter 603, and let Y be the output vector of the frequency domain filter 603. +The calculation of the filter coefficients in the frequency domain is expressed as the Hadamard product of the filter coefficient vector H and the input signal vector X, as shown in the following equation 5. TIFF2025174462000006.tif11156 Output signal vector Y of frequency domain filter 603 + The signal vector transformed into the time domain by IFFT 604 is expressed as y + Let the time domain output signal vector y + As shown in the following formula 6, the periodicity assumption does not affect the region y and the periodicity assumption can affect the region y. ~ Includes: TIFF2025174462000007.tif21134Assuming 50% overlap, y and y ~ The length of each of these is 2N.

[0010] The serial conversion unit 605 converts the output signal vector y + The region y that can be affected by the periodicity assumption ~ The downsampling unit 606 performs 1 / 2 downsampling on the y output from the serial conversion unit 605, and converts the downsampled signal y ↓2 Outputs y ↓2 The length of the downsampled output signal y ↓2 The filter coefficients may be updated by performing phase rotation for carrier phase compensation and frequency offset compensation on the signal.

[0011] When the least mean square (LMS) algorithm is used to update the filter coefficients, the coefficients of the frequency domain filter 603 are updated as follows: ↓2Let d be the desired signal for y. If a data-aided LMS algorithm is used, d is a known training signal. If a decision-directed LMS algorithm is used, d is the desired signal for y. ↓2 The update of the frequency domain filter coefficients using the LMS algorithm is expressed by the following equation 7. TIFF2025174462000008.tif17123In the above equation 7, D is a Discrete Fourier Transform (DFT) matrix, and α is an update step size. The second term on the right side of the above equation 7 represents the amount of update of the coefficients.

[0012] The error calculation unit 611 calculates the downsampled output signal y 2↓ The error e between the desired signal d and the received signal d is calculated using the following equation 8. TIFF2025174462000009.tif11149 The error calculation unit 611 calculates the signal e by upsampling the error e by a factor of two. ↑2 Output.

[0013] The zero insertion unit 612 inserts the 2x upsampled error e ↑2 That is, the zero insertion unit 612 connects the vector (e ↑2, 0) T Generate a vector (e ↑2, 0) T The zero part of the vector in is the y ~ This corresponds to the vector (e ↑2, 0) T is multiplied by the DFT matrix D to convert the error signal vector into a frequency domain signal. ↑2, 0) T Multiplying by the DFT matrix D is equivalent to performing an FFT on the error signal vector.

[0014] A complex conjugate calculation unit 614 calculates the complex conjugate of the input frequency domain signal X output by the FFT 602. A Hadamard product calculation unit 615 calculates the Hadamard product of the complex conjugate of the input frequency domain signal X and the error signal vector converted into a frequency domain signal by the FFT 613. The result obtained by multiplying the calculation result of the Hadamard product calculation unit 615 by the step size α corresponds to the coefficient update amount shown in the second term on the right side of the above equation 7.

[0015] The IFFT 616 converts the calculation result of the Hadamard product calculation unit 615, which corresponds to the coefficient update amount in the frequency domain, into a time domain signal. The zero substitution unit 617 substitutes zeros for coefficients in the region corresponding to the overlap of the signal converted into the time domain signal by the IFFT 616. The FFT 618 converts the signal after the zero substitution into a frequency domain signal, i.e., the frequency domain coefficient update amount. If the time spread of the response of the frequency domain filter 603 exceeds the time length of the overlap, the influence of loop interference at both ends of the block of the input signal, which is assumed to be periodic, cannot be eliminated even if only y is left in the serial conversion unit 605. The IFFT 616, the zero substitution unit 617, and the FFT 618 are necessary to avoid the influence of loop interference at both ends of the block, which is caused by the assumption of periodicity in the frequency domain filter, and to achieve operation equivalent to that of a time domain filter. This operation is called a time domain constraint. Omitting this constraint may have little impact on performance.

[0016] The coefficient update unit 619 multiplies the output of the FFT 618 by a step size α. The coefficient update unit 619 outputs the coefficient update amount multiplied by the step size α to the frequency domain filter 603, and updates the filter coefficients of the frequency domain filter 603. The above equation 7 is a vector c=(1,0) for appropriate coefficient 0 substitution. T Using the above, it can be transformed into the following equation 9. By performing such operations, adaptive control of the frequency domain filter coefficients is performed. Note that the above example describes a case where the input and output signals are one-dimensional signals. However, the above coefficient update operation can be easily extended to cases where the filter is a multi-input multi-output (MIMO) filter.

[0017] As another related technique, Non-Patent Document 2 discloses an even-odd 2x oversampling adaptive frequency domain filter. FIG. 9 is a block diagram showing the configuration of a general even-odd 2x oversampling adaptive frequency domain filter. In adaptive frequency domain filter 700 shown in FIG. 9, block transform unit 701 transforms a 2x oversampled input signal into blocks by providing overlap between previous and next blocks. Delay circuit 702 delays the signal output from block transform unit 701 by one sample.

[0018] Downsampling unit 703 downsamples the signal output from block conversion unit 701 by a factor of 1 / 2. Downsampling unit 706 downsamples the signal delayed by delay circuit 702 by a factor of 1 / 2. The signal downsampled by downsampling unit 703 by a factor of 1 / 2 contains even-numbered samples. On the other hand, the signal downsampled by downsampling unit 706 by a factor of 1 / 2 contains odd-numbered samples.

[0019] The FFT 704 converts the block containing the even-numbered samples output from the downsampling unit 703 into a frequency domain signal. The FFT 707 converts the block containing the odd-numbered samples output from the downsampling unit 706 into a frequency domain signal. The frequency domain filter 705 calculates a filter coefficient He for the frequency domain signal output from the FFT 704. The frequency domain filter 708 calculates a filter coefficient Ho for the frequency domain signal output from the FFT 707.

[0020] An adder 709 adds the output of the frequency domain filter 705 and the output of the frequency domain filter 708. An IFFT 710 performs an inverse Fourier transform on the output signal of the adder 709, converting the frequency domain signal into a time domain signal. A serial conversion unit 711 performs overlap-save block-to-serial conversion on the time domain signal converted by the IFFT 710. The filter coefficients of the frequency domain filters 705 and 708 can be updated using a method similar to that used to update the filter coefficients in the adaptive frequency domain filter 600 shown in FIG. 8.

[0021] As mentioned above, existing adaptive filters operate on input signals that are oversampled by two times. In response to this, there have been attempts to reduce the amount of calculation by reducing the sampling rate of the input signal of the adaptive filter to less than two times. For example, Non-Patent Document 3 discloses an example of an adaptive filter that operates in the time domain on an input signal with an oversampling rate that is less than two times and is not an integer multiple of the symbol rate.

[0022] Furthermore, Non-Patent Document 4 discloses an example of an adaptive filter that operates in the frequency domain for an input signal with an oversampling rate that is less than twice the symbol rate and is not an integer multiple of the symbol rate. The adaptive filter described in Non-Patent Document 4 converts the input signal into a frequency domain signal, inserts appropriate zeros into the frequency domain signal, and operates in the frequency domain with 2x oversampling. As described above, a frequency domain filter multiplies coefficients for each frequency. Therefore, the adaptive filter described in Non-Patent Document 3 only needs to perform calculations on non-zero frequency components, even for frequency domain signals equivalent to 2x oversampling, thereby streamlining the amount of calculation required for the frequency domain filter.

[0023] However, in the adaptive filter described in Non-Patent Document 4, adaptive coefficient update requires calculation of update amounts for 2x oversampling frequency domain filter coefficients. As mentioned above, calculation of update amounts for frequency domain filter coefficients requires an FFT of the error with appropriate zero insertion, as well as an IFFT and an FFT for constraining the coefficient update amount in the time domain. The amount of calculation depends on the size of the error and coefficient update amount to be handled, and the larger the size, the greater the amount of calculation. Furthermore, the higher the oversampling rate handled, the smaller the time width per sample. Therefore, assuming a constant filter time width, the frequency domain with 2x oversampling must handle larger filter coefficients, errors, and coefficient update amounts than an oversampling rate smaller than 2x. This results in an increase in the amount of calculation.

[0024] Non-Patent Document 5 discloses a frequency domain filter that operates in the frequency domain for a signal oversampled by a rational multiple less than twice the symbol rate, and its adaptive filter coefficient control. In Non-Patent Document 5, a frequency domain filter that operates with M / L multiple oversampling (M and L are integers) less than twice the symbol rate, and its adaptive filter coefficient control are directly realized. [Prior art documents] [Non-patent literature]

[0025] [Non-Patent Document 1] S. Haykin, “adaptive filter theory 4th edition”, Prentice Hall, 2002, chap. 7. [Non-patent document 2] Md. S. Faruk and K. Kikuchi, “Adaptive frequency-domain equalization in digital coherent optical receivers”, Opt. Express 19(13), 12789 (2011). [Non-patent document 3] C. Li et al., “Advanced DSP for single-carrier 400-Gb / s PDM-16QAM,” OFC 2016,W4A.4. [Non-patent document 4] M. Paskov et al., “A fully-blind fractionally-oversampled frequency domain adaptive equalizer”, OFC 2016, Th2A.33. [Non-patent document 5] M. Arikawa and K. Hayashi, “Frequency-domain adaptive MIMO filter with fractional oversampling using stochastic gradient descent for long-haul transmission over coupled 4-core fibers”, Opt. Express 31(8), 13104 (2023). Summary of the Invention [Problem to be solved by the invention]

[0026] In the frequency domain filter described in Non-Patent Document 5, the input signal is oversampled by a rational number and the output signal is sampled by 1. This places a significant constraint on the sizes of the FFT and IFFT included in the frequency domain filter. It is generally known that efficient calculations can be performed for FFTs and IFFTs when their sizes are a power of two. However, in the frequency domain filter described in Non-Patent Document 5, it is not possible to always select the sizes of both the FFT and IFFT as a power of two for any values ​​of M and L. This complicates the circuit design and calculations.

[0027] An exemplary objective of the present disclosure is to provide an equalization signal processing circuit, a receiver, a communication system, and an equalization signal processing method that can reduce the complexity of circuit design. [Means for solving the problem]

[0028] The equalization signal processing circuit according to the first aspect of the present disclosure includes a signal splitting unit that splits an input signal oversampled by a rational number M / L into M signals, where M and L are natural numbers satisfying 1 < M / L < 2; a frequency domain conversion unit that converts each of the M split signals into a signal in the frequency domain; a first frequency domain filter that calculates a first filter coefficient for the M signals converted into the signals in the frequency domain; a second frequency domain filter that calculates a second filter coefficient for the M signals for which the first filter coefficient has been calculated for each L group; an adder that adds the M signals for which the second filter coefficient has been calculated for each group; a time domain conversion unit that converts the output signal of the adder into a signal in the time domain for each group; a switch circuit that sequentially selects the signals converted into the signals in the time domain for each group; and a coefficient update unit that calculates gradients of the loss function with respect to the first filter coefficient and the second filter coefficient of the loss function using the error backpropagation method, where the loss function is the magnitude of the difference between the signal output from the switch circuit and a predetermined value, and updates the first filter coefficient and the second filter coefficient.

[0029] The receiver according to the second aspect of the present disclosure includes a detector that coherently receives a signal transmitted from a transmitter via a transmission line, and an equalization signal processing circuit that performs equalization signal processing on the coherently received signal. The equalization signal processing circuit divides an input signal of rational oversampling of M / L times, where M and L are natural numbers satisfying 1 < M / L < 2, into M signals, a signal dividing unit; a frequency domain conversion unit that converts each of the divided M signals into a signal in the frequency domain; a first frequency domain filter that calculates a first filter coefficient for the M signals converted into the signals in the frequency domain; a second frequency domain filter that calculates a second filter coefficient for the M signals for which the first filter coefficient has been calculated for each L group; an adder that adds the M signals for which the second filter coefficient has been calculated for each group; a time domain conversion unit that converts the output signal of the adder into a signal in the time domain for each group; a switch circuit that sequentially selects the signals converted into the signals in the time domain for each group; a coefficient update unit that calculates gradients of the first filter coefficient and the second filter coefficient of the loss function using the error backpropagation method with the magnitude of the difference between the signal output from the switch circuit and a predetermined value as the loss function, and updates the first filter coefficient and the second filter coefficient.

[0030] The communication system according to the third aspect of the present disclosure includes a transmitter that transmits a signal via a transmission line and the above receiver.

[0031] The equalization signal processing circuit according to the fourth aspect of the present disclosure divides an input signal oversampled by a rational number M / L into M signals, where M and L are natural numbers satisfying 1 < M / L < 2, converts each of the divided M signals into a signal in the frequency domain, calculates a first filter coefficient for the M signals converted into the signals in the frequency domain, calculates a second filter coefficient for the M signals for which the first filter coefficient has been calculated for each L groups, adds the M signals for which the second filter coefficient has been calculated for each group, converts the output signal of the adder into a signal in the time domain for each group, sequentially selects the signals converted into the signals in the time domain for each group to concatenate the signals of each group, uses the magnitude of the difference between the preselected concatenated signal and a predetermined value as a loss function, and calculates the gradient of the loss function with respect to the first filter coefficient and the gradient of the loss function with respect to the second filter coefficient using the error backpropagation method, and updates the first filter coefficient and the second filter coefficient.

Effects of the Invention

[0032] The equalization signal processing circuit, receiver, communication system, and equalization signal processing method according to the present disclosure can alleviate the complexity of circuit design.

Brief Description of the Drawings

[0033] [Figure 1] It is a block diagram schematically showing a configuration example of a communication system according to the present disclosure. [Figure 2] It is a block diagram showing a schematic configuration example of a receiver. [Figure 3] It is a block diagram showing a configuration example of a signal transmission system according to the present disclosure. [Figure 4] It is a block diagram showing an example of digital signal processing in an equalization unit. [Figure 5] It is a block diagram showing a configuration example of polarization separation / carrier phase compensation. [Figure 6] It is a schematic diagram showing the process of gradient calculation by error backpropagation for coefficient update in a coefficient update unit. [Figure 7]This is a diagram showing the constellation of the output signal of the adaptive frequency domain filter. [Figure 8] This is a block diagram showing an example of an adaptive frequency domain filter described in Non-Patent Document 1. [Figure 9] This is a block diagram showing the configuration of a general even-odd type 2-fold oversampling adaptive frequency domain filter.

Embodiments for Carrying Out the Invention

[0034] Prior to the description of the embodiments of the present disclosure, an overview of the present disclosure will be described. FIG. 1 is a block diagram schematically showing a configuration example of 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 interconnected via a transmission line 13. The transmitter 11 transmits a signal via the transmission line 13. The receiver 15 receives the signal transmitted from the transmitter 11 via the transmission line 13.

[0035] FIG. 2 is a block diagram showing a schematic configuration example of the receiver 15. The receiver 15 includes a detector 21 and an equalization signal processing circuit 22. The detector 21 coherently receives the signal transmitted from the transmitter 11. The equalization signal processing circuit 22 performs equalization signal processing on the coherently received input signal of rational number M / L-fold oversampling. Here, M and L are natural numbers satisfying 1 < M / L < 2.

[0036] The equalization signal processing circuit 22 includes a signal splitting unit 23, a frequency domain conversion unit 24, a first frequency domain filter 25, a second frequency domain filter 26, an adder 27, a time domain conversion unit 28, a switch circuit 29, and a coefficient update unit 30. The signal splitting unit 23 splits the input signal of M / L-fold oversampling into M signals. The frequency domain conversion unit 24 converts each of the M split signals into a signal in the frequency domain.

[0037] First frequency domain filter 25 calculates first filter coefficients for the M signals converted into frequency domain signals. Second frequency domain filter 26 calculates second filter coefficients for the M signals for which the first filter coefficients have been calculated, for each of L groups. Adder 27 adds the M signals for which the second filter coefficients have been calculated, for each group. Time domain transform unit 28 transforms the output signal of adder 27 into a time domain signal, for each group.

[0038] Switch circuit 29 sequentially selects the signals converted into time-domain signals for each group. Coefficient update unit 30 uses the magnitude of the difference between the signal output from switch circuit 29 and a predetermined value as a loss function and calculates the gradient of the loss function for the first filter coefficient and the gradient of the loss function for the second filter coefficient using the backpropagation algorithm. Coefficient update unit 30 updates the first filter coefficient and the second filter coefficient using the calculated gradients.

[0039] In the present disclosure, frequency domain transform unit 24 transforms the M divided signals into frequency domain signals. Furthermore, time domain transform unit 28 transforms the signal output from adder 27, for each of L groups, into a time domain signal. In the present disclosure, by appropriately selecting M and L, frequency domain transform unit 24 can transform signals whose size is a power of two into frequency domain signals. Furthermore, time domain transform unit 28 can transform signals whose size is a power of two into time domain signals. Therefore, in the present disclosure, circuits whose size is a power of two can be used for frequency domain transform unit 24 and time domain transform unit 28, respectively, thereby reducing the complexity of circuit design.

[0040] Hereinafter, embodiments of the present disclosure will be described with reference to the drawings. Note that the following description and drawings have been omitted and simplified as appropriate for clarity of explanation. In addition, in the following drawings, the same or similar elements are designated by the same reference numerals, and duplicate explanations are omitted as necessary.

[0041] 3 is a block diagram showing an example configuration of a signal transmission system according to the present disclosure. In one embodiment, the signal transmission system is assumed to be an optical fiber communication system that employs a polarization multiplexed QAM system and performs coherent reception. The receiver-side adaptive equalization signal processing method in this embodiment is also applicable to spatial multiplexing transmission using a multi-core optical fiber, but the following describes an example of single-mode optical fiber transmission. Wavelength multiplexing technology is often applied to optical fiber communication systems, but a description of this technology will be omitted.

[0042] 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.

[0043] The optical transmitter 110 converts transmission data into a polarization multiplexed optical 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 may represent a predetermined number of signal sequences collectively as a physical entity.

[0044] The pre-equalization unit 112 performs pre-equalization on the encoded four-channel signal to compensate in advance for known distortions of devices within the optical transmitter. The DAC 113 converts each of the four channels of pre-equalized signals into an analog electrical signal. The LD 115 outputs CW (Continuous Wave) light. The optical modulator 114 modulates the CW light output from the LD 115 according to the four channels of 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.

[0045] 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 a plurality of optical amplifiers 133.

[0046] The optical receiver 150 receives an optical signal from the transmission path 130. The optical receiver 150 includes an LD 151, a coherent receiver 152, an analog digital converter (ADC) 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 digital signal processor (DSP).

[0047] The LD 151 outputs CW light to be used as local oscillator light to the coherent receiver 152. 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 detector 21 shown in FIG. 2.

[0048] The ADC 153 samples the received signal output from the coherent receiver 152 and converts the received signal into a signal in the digital domain. The equalizer 154 performs receiving-side equalization signal processing on the four series of received signals sampled by the ADC 153. The equalizer 154 performs equalization signal processing on the received signals to compensate for various distortions that occur in the optical transmitter 110, the transmission path 130, and the optical receiver 150. The decoder 155 decodes the signal that has been equalized by the equalizer 154, restoring the transmitted data. The decoder 155 outputs the restored data to another circuit (not shown).

[0049] 4 is a block diagram showing an example of digital signal processing in the equalization unit 154. The equalization unit 154 has a chromatic dispersion compensation unit 161 and a polarization separation / carrier phase compensation unit 162. The equalization unit 154 receives two sequences of complex signals obtained by converting four sequences of sampled received signals into complex phasor representations for each polarization. The chromatic dispersion compensation unit 161 performs chromatic dispersion compensation for each polarization. The chromatic dispersion compensation unit 161 includes a fixed or quasi-static filter whose filter coefficients are determined to compensate for chromatic dispersion accumulated in the optical transmission path.

[0050] Two series of complex signals corresponding to each polarization, which have been subjected to chromatic dispersion compensation by the chromatic dispersion compensation 161, are input to the polarization separation / carrier phase compensation 162. The polarization separation / carrier phase compensation 162 performs polarization separation and carrier phase compensation on the two series of complex signals input. Changes in the polarization state that occur in the optical transmission path fluctuate over time due to minute pressure on the optical fiber and temperature changes. For this reason, the filter that compensates for changes in the polarization state needs to be adaptively controlled. The equalization signal processing circuit according to this embodiment is used in the polarization separation / carrier phase compensation 162.

[0051] Fig. 5 is a block diagram showing an example configuration of polarization separation / carrier phase compensation 162. Polarization separation / carrier phase compensation 162 corresponds to the equalization signal processing circuit 22 shown in Fig. 2. The operation of polarization separation / carrier phase compensation 162 is also called an equalization signal processing method. Each of the elements of polarization separation / carrier phase compensation 162 shown in Fig. 5 can be configured using a hardware circuit.

[0052] In Fig. 5, the compensation in polarization demultiplexing / carrier phase compensation 162 is performed using a 2x2 adaptive MIMO filter. However, for simplicity, Fig. 5 illustrates an example in which the input and output are a single series of complex signals. In polarization demultiplexing / carrier phase compensation 162, time domain constraints are omitted when updating the frequency domain filter coefficients. The operation described below can be easily extended to an adaptive MIMO filter. The configuration shown in Fig. 5 as a whole is an overlap-save adaptive frequency domain filter.

[0053] The input signal is a signal of oversampling by a predetermined multiple. In the present embodiment, it is assumed that the input signal is a signal of non-integer and rational multiple oversampling. In this case, the input signal is a complex signal sequence of oversampling M / L. That is, if the symbol interval of the input signal is T, the input signal is a complex signal sequence with a sampling interval of LT / M. Here, M and L are integers satisfying 1 < M / L < 2. In the following, the case of M = L + 1 will be described. FIG. 5 shows a configuration example of the polarization separation / carrier phase compensation 162 in the case of M = 3 and L = 2.

[0054] The block conversion unit 171 performs serial / block conversion on the input complex signal sequence while providing a certain overlap between blocks. Here, the overlap rate is set to 50%. Let the input signal vector block-converted by the block conversion unit 171 be x. The input signal (vector) x is represented by the following equation 10. TIFF2025174462000011.tif7127N x represents the size of the block-converted input signal x, and N x = 2MN / L.

[0055] The downsampling unit 174-0 downsamples the input signal block-converted by the block conversion unit 171 by a factor of 1 / 2. The delay circuit 172 delays the signal output from the block conversion unit 171 by one sample. The downsampling unit 174-1 downsamples the signal delayed by the delay circuit 172 by a factor of 1 / 2. The delay circuit 173 further delays the signal output from the delay circuit 172 by one sample. The downsampling unit 174-2 downsamples the signal delayed by the delay circuit 173 by a factor of 1 / 2.

[0056] The input signal x block-converted by the block conversion unit 171 is divided into M signals (vectors) by sample delay and downsampling by a factor of 1 / M. When the divided signals are x m (m = 0, 1,..., M - 1), x m is represented by the following equation 11. TIFF2025174462000012.tif8157 The output signal of the downsampling unit 174-0 corresponds to x0. The output signal of the downsampling unit 174-1 corresponds to x1. The output signal of the downsampling unit 174-2 corresponds to x2. The divided signal x m The size of the delay circuit 172 is 2N / L. The delay circuits 172 and 173 and the downsampling units 174-0 to 174-2 correspond to the signal dividing unit 23 shown in FIG.

[0057] The polarization separation / carrier phase compensation 162 includes M FFTs 175 and M first frequency domain filters 176. The FFTs 175-0 to 175-2 filter the divided signals x m the frequency domain signal X m More specifically, FFT 175-0 converts signal x0 output from downsampling unit 174-0 into frequency domain signal X0. FFT 175-1 converts signal x1 output from downsampling unit 174-1 into frequency domain signal X1. FFT 175-2 converts signal x2 output from downsampling unit 174-2 into frequency domain signal X2. FFT 175 corresponds to frequency domain transform unit 24 shown in FIG. 2.

[0058] The first frequency domain filters 176-0 to 176-2 filter the output signals X m , the filter coefficient G m More specifically, first frequency domain filter 176-0 calculates a filter coefficient G0 on signal X0 output from FFT 175-0. First frequency domain filter 176-1 calculates a filter coefficient G1 on signal X1 output from FFT 175-1. First frequency domain filter 176-2 calculates a filter coefficient G2 on signal X2 output from FFT 175-2. Output signals Y of first frequency domain filters 176-0 to 176-2 are calculated as follows: m is expressed by the following formula 12. TIFF2025174462000013.tif7117 The first frequency domain filter 176 corresponds to the first frequency domain filter 25 shown in FIG.

[0059] Polarization separation / carrier phase compensation 162 has M second frequency domain filters 180 and 181 for each of L groups. In Fig. 5, second frequency domain filters 180-0 to 180-2 are frequency domain filters corresponding to group 0. Second frequency domain filters 181-0 to 181-2 are frequency domain filters corresponding to group 1.

[0060] The second frequency domain filter 180-0 applies a filter coefficient H to the signal Y0 output from the first frequency domain filter 176-0. 00 The second frequency domain filter 180-1 applies a filter coefficient H 01 The second frequency domain filter 180-2 applies a filter coefficient H 00 Calculate the following.

[0061] Order permutation unit 177 cyclically shifts the order of signals Ym output from first frequency domain filters 176-0 to 176-2 by l (l=0, 1, ..., L-1) corresponding to group l. In the example of FIG. 5, order permutation unit 177 outputs signal Y2 output from first frequency domain filter 176-2 to second frequency domain filter 180-0. Order permutation unit 177 outputs signal Y0 output from first frequency domain filter 176-0 to second frequency domain filter 180-1. Order permutation unit 177 outputs signal Y1 output from first frequency domain filter 176-1 to second frequency domain filter 180-1.

[0062] The second frequency domain filter 181-0 applies a filter coefficient H 10 The second frequency domain filter 181-1 applies a filter coefficient H 11The second frequency domain filter 181-2 applies a filter coefficient H 12 Calculate the following.

[0063] Here, for convenience, Y m The signal whose order is circularly shifted by l is U lm Let's say. U lm is expressed by the following formula 13. TIFF2025174462000014.tif8117 The second frequency domain filters 180-0 to 180-2 and 181-0 to 181-2 are lm H lm The output signals Y of the second frequency domain filters 180-0 to 180-2 and 181-0 to 181-2 are calculated. lm is expressed by the following formula 14. TIFF2025174462000015.tif8145 The output signal of the second frequency domain filter 180-0 to 180-2 is Y 00 From Y 02 The output signals of the second frequency domain filters 181-0 to 181-2 correspond to Y 10 From Y 12 The second frequency domain filters 180 and 181 correspond to the second frequency domain filter 26 shown in FIG.

[0064] The adders 182 to 185 add the output signal Y of the second frequency domain filter for each l, i.e., for each group. lm That is, adders 182 and 183 add the output signals of second frequency domain filters 180-0 to 180-2 corresponding to group 0. Adders 184 and 185 add the output signals of second frequency domain filters 181-0 to 181-2 corresponding to group 1. The output signals of adders 182 and 183 and the output signals of adders 184 and 185 are added together to obtain Y l In this case, Y l is expressed by the following formula 15. TIFF2025174462000016.tif26122 Adders 182 to 185 correspond to the adder 27 shown in FIG.

[0065] The polarization separation / carrier phase compensation 162 has an IFFT 186 for each group. The IFFT 186-0 converts the signal Y0 output by the adder 183 into a time domain signal. The IFFT 186-1 converts the signal Y1 output by the adder 185 into a time domain signal. The signal converted into the time domain signal by the IFFTs 186-0 and 186-1 is expressed as y +l Let y +l The size of is 2N / L. The IFFT 186 corresponds to the time domain transform unit 28 shown in FIG.

[0066] The switch circuit 187 switches the connection destination of the serial conversion unit 188 between IFFT 186-0 and IFFT 186-1. For example, the switch circuit 187 switches the connection destination of the serial conversion unit 188 between IFFT 186-0 and IFFT 186-1 for each sample. In other words, the switch circuit 187 switches l for each sample, and outputs the output signals y of IFFT 186-0 and IFFT 186-1. +l The signal output from the switch circuit 187 to the serial conversion unit 188 is y + If so, y + is expressed by the following equation 16. TIFF2025174462000017.tif8128In Equation 16, TIFF2025174462000018.tif1226 is the floor function. y + The size of is 2N. The switch circuit 187 corresponds to the switch circuit 29 shown in FIG.

[0067] The serial conversion unit 188 converts the signal input from the switch circuit 187 into a serial signal in the time domain. In the conversion to a serial signal, the serial conversion unit 188 leaves only the region of the 1x oversampled time domain block signal that is not affected by the assumption of periodicity when converting to the frequency domain, and removes the rest. Based on the concept of the overlap-save method, y + can be expressed by the following equation 17. TIFF2025174462000019.tif22132 serial conversion unit 188 is y + From y ~ is removed, leaving only y. The size of y is N. The serial conversion unit 188 performs block-to-serial conversion on y. y is a time domain signal with 1x sampling.

[0068] Carrier phase compensation filter 189 is a time domain filter that performs phase rotation to remove carrier phase and frequency offset on the 1x oversampled time domain serial signal converted by serial conversion unit 188. Carrier phase compensation filter 189 performs phase rotation, which is determined separately by, for example, a phase-locked loop (PLL) method, on time domain signal y. The output signal of carrier phase compensation filter 189 is denoted by z. If the amount of phase rotation is θ, z is expressed by the following equation 18. The 1x oversampled time-domain serial signal output by the carrier phase compensation filter 189 is the output for one block. The above operation is performed for each overlapping block, and the output signals are connected together to obtain the final output of the overlap-save adaptive frequency domain filter shown in Figure 5.

[0069] The first frequency domain filters 176-0 to 176-2 mainly play a role in distortion compensation. In contrast, the second frequency domain filters 180-0 to 180-2 and 181-0 to 181-2 mainly play a role as decimation filters accompanying the sampling rate conversion from M / L times oversampling to 1 times sampling. From the polyphase representation of the filters and the polyphase equivalence in multirate signal processing, the filter coefficients H of the second frequency domain filters 180-0 to 180-2 and 181-0 to 181-2 are lm The initial value of is selected as follows:

[0070] First, prepare a decimation filter H with an appropriate passband of size 2MN, and decompose it into L polyphase coefficients. This is equivalent to shifting the time domain filter coefficients by l (l=0, 1, ...L-1) and extracting every L coefficients. Therefore, in the frequency domain, the polyphase decomposed frequency domain filter H l teeth, TIFF2025174462000021.tif7141TIFF2025174462000022.tif18115. Here, f M [k] is the frequency normalized by the symbol rate corresponding to index k in M-times oversampling. This is further decomposed into M polyphases to obtain H lm That is, TIFF2025174462000023.tif7157TIFF2025174462000024.tif18141 where f x [k] is the frequency normalized by the symbol rate corresponding to index k in M / L-times oversampling.

[0071] Furthermore, based on the equivalence of the sampling rate conversion from M / L times oversampling to 1 times sampling using the polyphase representation, H lm For m'=0, ...,l-1, it gives a one sample time delay in the 1 / L times oversampling domain. This means that The result is TIFF2025174462000025.tif8147. f 1 / L [k] is the frequency normalized by the symbol rate corresponding to index k with 1 / L times oversampling.

[0072] When extending to a MIMO filter, the filter coefficients G of the first frequency domain filters 176-0 to 176-2 are m is extended to a MIMO filter. That is, let the number of input and output dimensions be K, and let i,j=1,...K. TIFF2025174462000026.tif19118. Frequency domain filter Hlm The processing of Y mi By performing this process for each pixel, MIMO filtering is performed as a whole.

[0073] The coefficient update unit 190 updates the filter coefficients Gm of the first frequency domain filters 176-0 to 176-2 and the filter coefficients H lm The coefficient update unit 190 adaptively updates the filter coefficient G based on backpropagation and stochastic gradient descent so as to minimize the magnitude of the loss function determined according to the time-domain signal z, which is the final output. m and H lm The coefficient update unit 190 corresponds to the coefficient update unit 30 shown in FIG.

[0074] The coefficient update will be explained. The magnitude of the difference between the filter output signal z and the desired signal is set as the loss function φ to be minimized. Based on the concept of Wirtinger differentiation, φ is calculated by dividing ξ and ξ by the difference between ξ and ξ for a given filter coefficient ξ. * The filter coefficients ξ are calculated by the stochastic gradient descent method as follows: TIFF2025174462000027.tif21143, where α is the step size. Since the loss function to be minimized is a real number, the following equation (26) holds. TIFF2025174462000028.tif24150

[0075] When the LMS algorithm is used to construct the loss function, the loss function (its instantaneous value for each block) can be defined by the following equation 27 using the magnitude of the difference between the 1x oversampled time domain signal z and the desired signal d. TIFF2025174462000029.tif26144When the data-aided LMS algorithm is used, d is a known training signal.When the decision-directed LMS algorithm is used, d is the symbol decision result of z.There are several known methods for constructing a loss function to be minimized from a 1x oversampled time-domain signal, including the Constant Modulus Algorithm (CMA) and Radius Directed Equalization (RDE).

[0076] Fig. 6 is a schematic diagram showing the process of gradient calculation by error backpropagation for coefficient update in the coefficient update unit 190. In the following explanation, an example will be described in which a data-aided LMS algorithm is used. The coefficient update unit 190 uses the error backpropagation method, i.e., the chain rule of differentiation, to sequentially calculate the gradient of the loss function for each signal and filter coefficient, as shown in Fig. 6.

[0077] The gradient of the loss function φ of the LMS algorithm with respect to the time domain signal z with 1x oversampling of the output is expressed by the following Equation 28. TIFF2025174462000030.tif20130Here, e = dz. The gradient of the loss function with respect to y is calculated from the gradient with respect to z as shown in Equation 29 below. TIFF2025174462000031.tif15115

[0078] Loss function y + The gradient with respect to is TIFF2025174462000032.tif28146. The loss function y +l The gradient with respect to y +l and y + Based on the relationship between + The gradient component for Y is obtained by distributing it every L samples by the switch circuit 187. l The gradient with respect to is TIFF2025174462000033.tif25168. The loss function Y lm The gradient with respect to is The result is TIFF2025174462000034.tif21145.

[0079] Loss function H lm The gradient with respect to is TIFF2025174462000035.tif20145. In the case of MIMO filters, the loss function H lm The gradient with respect to is TIFF2025174462000036.tif24164. The coefficient update unit 190 updates the coefficient H lm The coefficients are updated as shown in Equation 35 below. TIFF2025174462000037.tif14116

[0080] Loss function U lm The gradient with respect to is TIFF2025174462000038.tif14117. The loss function Y m The gradient with respect to U lm Y m Reflecting the circular shift of the order of TIFF2025174462000039.tif19132. The loss function G m The gradient with respect to is TIFF2025174462000040.tif23168. In the case of MIMO filters, the loss function G mij The gradient with respect to is TIFF2025174462000041.tif15124. The coefficient update unit 190 updates the coefficient G m is updated as shown in the following equation 40. TIFF2025174462000042.tif14124

[0081] In this way, a frequency domain filter operating in the frequency domain with oversampling at a rational multiple less than twice the symbol rate and its adaptive filter coefficient control are obtained. The coefficient G of the first frequency domain filter is m and the coefficients of the second frequency domain filter H lm The coefficient update unit 190 does not necessarily need to update the coefficients for every block, but may update the coefficients once every few blocks. Also, the coefficient update unit 190 updates the coefficients G of the first frequency domain filter m and the coefficients of the second frequency domain filter H ml and may be updated at different update frequencies.

[0082] As explained above, in a frequency domain filter that operates in the frequency domain with oversampling at a rational multiple less than twice the symbol rate, and in its adaptive filter coefficient control, an FFT of size 2N / L and an IFFT of the same size 2N / L are used. If N is a power of 2 and L is a small power of 2, the sizes of the FFT and IFFT will be a power of 2. Therefore, this embodiment does not require an FFT / IFFT with a size that is not a power of 2. Therefore, this embodiment can reduce the complexity of circuit design related to the FFT / IFFT.

[0083] The inventors verified the operation of the receiver-side adaptive equalization signal processing method according to this embodiment through simulation. In the simulation, a 32-Gbaud polarization-multiplexed Quadrature Phase Shift Keying (QPSK) signal was transmitted over 6,000 km of single-mode fiber (SMF). In the simulation, the QPSK signal was given chromatic dispersion equivalent to 6,000 km of SMF and a 30° polarization rotation. The optical signal-to-noise ratio (OSNR) was set to 30 dB / 0.1 nm. The receiver coherently received the QPSK signal and sampled it with 2x oversampling. The chromatic dispersion compensation was performed for each polarization on the signal sampled with 2x oversampling, and the chromatic dispersion-compensated signal was resampled with M / L oversampling. Here, L=2 and M=3 were used.

[0084] In the simulation, two series of X- and Y-polarized signals, resampled with M / L-fold oversampling, were used as input to an adaptive frequency domain filter operating in the frequency domain with M / L-fold oversampling. For adaptive coefficient control, the loss function of the data-aided LMS algorithm was first used, and after the filter coefficients had roughly converged, the loss function was switched to that of the decision-directed LMS algorithm to adaptively control the filter coefficients. The overlap rate was set to 50%, and the size of the output after overlap removal was set to 64. A PLL method was used for carrier phase compensation.

[0085] In the simulation, resampling to M / L-fold oversampling is performed to focus on the adaptive frequency domain filter that operates in the frequency domain with M / L-fold oversampling. Instead of oversampling the coherently received signal by 2 times, the coherently received signal may be sampled by M / L-fold oversampling. In that case, chromatic dispersion compensation is also performed by oversampling less than 2 times. This also reduces the amount of calculation required for chromatic dispersion compensation.

[0086] Figure 7 shows the constellation of the adaptive frequency domain filter output signal obtained by the above simulation. After switching the loss function used for adaptive coefficient control to that of the decision-directed LMS algorithm, we evaluated the constellation of the adaptive frequency domain filter output signal after the filter coefficients had sufficiently converged. Figure 7 shows the constellation of the X-polarized signal.

[0087] As shown in Figure 7, the simulation results show that a good QPSK signal constellation is obtained. Therefore, it was confirmed that the frequency domain filter operating in the frequency domain with oversampling by a rational number multiple smaller than 2 according to this embodiment and its adaptive coefficient control function properly.

[0088] Although the present disclosure has been described above with reference to the embodiments, the present disclosure is not limited to the above-described embodiments. Various modifications that can be understood by those skilled in the art can be made to the configuration and details of the present disclosure within the scope of the present disclosure. Furthermore, each embodiment can be combined with other embodiments as appropriate.

[0089] Each drawing is merely an example for describing one or more embodiments. Each drawing may relate not only to one particular embodiment, but also to one or more other embodiments. As will be understood by those skilled in the art, various features or steps described with reference to any one drawing can be combined with features or steps shown in one or more other drawings to create, for example, an embodiment not explicitly shown or described. Not all features or steps shown in any one drawing are necessary to describe an exemplary embodiment, and some features or steps may be omitted. The order of steps described in any drawing may be changed as appropriate.

[0090] Some or all of the above embodiments may also be described as follows in the appended claims, but are not limited thereto.

[0091] [Appendix 1] Let M and L be natural numbers satisfying 1 < M / L < 2. A signal splitting unit that splits an input signal of oversampling by a rational number M / L into M signals, A frequency domain conversion unit that converts each of the M split signals into a signal in the frequency domain, A first frequency domain filter that calculates a first filter coefficient for the M signals converted into the signals in the frequency domain, A second frequency domain filter that calculates a second filter coefficient for the M signals for which the first filter coefficient has been calculated for each of the L groups, An adder that adds the M signals for which the second filter coefficient has been calculated for each group, A time domain conversion unit that converts the output signal of the adder into a signal in the time domain for each group, A switch circuit that sequentially selects the signals converted into the signals in the time domain for each group, Using the magnitude of the difference between the signal output from the switch circuit and a predetermined value as a loss function, calculating the gradient of the loss function with respect to the first filter coefficient and the gradient of the loss function with respect to the second filter coefficient using the error backpropagation method, and a coefficient update unit that updates the first filter coefficient and the second filter coefficient. An equalization signal processing circuit.

[0092] [Appendix 2] The equalization signal processing circuit is configured as a circuit that inputs a plurality of signals and outputs a plurality of signals, and the first frequency domain filter is configured as a multi-input multi-output (MIMO) filter. The equalization signal processing circuit according to Appendix 1.

[0093] [Appendix 3] 3. The equalization signal processing circuit according to claim 1, wherein the coefficient update unit updates the first filter coefficient based on a gradient of the loss function for the first filter coefficient by a stochastic gradient descent method, and updates the second filter coefficient based on a gradient of the loss function for the second filter coefficient by a stochastic gradient descent method.

[0094] [Appendix 4] 4. The equalization signal processing circuit according to any one of claims 1 to 3, wherein the input signal is a signal transmitted via a transmission line and coherently received by a receiver.

[0095] [Appendix 5] a time domain filter that performs time domain filtering on the signal output from the switch circuit; 5. The equalization signal processing circuit according to claim 1, wherein the coefficient update unit calculates the magnitude of a difference between the output signal of the time domain filter and the predetermined value as a loss function.

[0096] [Appendix 6] 6. The equalization signal processing circuit according to any one of appendices 1 to 5, wherein the switch circuit switches the group to be selected for each sample.

[0097] [Appendix 7] a block conversion unit that converts the input signal from a serial signal to a block signal while providing a certain overlap between blocks, and inputs the converted block signal to the signal division unit; and a serial conversion unit that converts the signal output from the front switch circuit from a block signal to a serial signal while leaving a region that is not affected by the periodicity assumption included in the signal output from the switch circuit and excluding a region that may be affected by the periodicity assumption included in the signal output from the switch circuit.

[0098] [Appendix 8] a detector that coherently receives a signal transmitted from a transmitter via a transmission line; An equalization signal processing circuit that performs equalization signal processing on the coherently received signal, The equalization signal processing circuit, Let M and L be natural numbers satisfying 1 < M / L < 2. A signal splitting unit that splits an input signal of rational number M / L times oversampling into M signals, A frequency domain conversion unit that converts each of the M split signals into a signal in the frequency domain, A first frequency domain filter that calculates a first filter coefficient for the M signals converted into the signals in the frequency domain, For each of the L groups, a second frequency domain filter that calculates a second filter coefficient for the M signals for which the first filter coefficient has been calculated, For each group, an adder that adds the M signals for which the second filter coefficient has been calculated, For each group, a time domain conversion unit that converts the output signal of the adder into a signal in the time domain, A switch circuit that sequentially selects the signals converted into the signals in the time domain for each group, Using the magnitude of the difference between the signal output from the switch circuit and a predetermined value as a loss function, calculating gradients of the first filter coefficient and the second filter coefficient of the loss function using the error backpropagation method, and a coefficient update unit that updates the first filter coefficient and the second filter coefficient. A receiver.

[0099] [Appendix 9] The equalization signal processing circuit is configured as a circuit that receives a plurality of signals and outputs a plurality of signals, and the first frequency domain filter is configured as a multi-input multi-output (MIMO) filter. The receiver according to Appendix 8.

[0100] [Appendix 10] The coefficient update unit updates the first filter coefficient based on the gradient of the loss function with respect to the first filter coefficient by stochastic gradient descent, and updates the second filter coefficient based on the gradient of the loss function with respect to the second filter coefficient by stochastic gradient descent, the receiver according to Appendix 8 or 9.

[0101] [Appendix 11] It further has a time-domain filter that performs filter processing in the time domain on the signal output from the switch circuit, The coefficient update unit calculates, as a loss function, the magnitude of the difference between the output signal of the time-domain filter and the predetermined value, the receiver according to any one of Appendices 8 to 10.

[0102] [Appendix 12] The switch circuit switches the selected group every sample, the receiver according to any one of Appendices 8 to 11.

[0103] [Appendix 13] A block conversion unit that converts the input signal from a serial signal to a block signal while providing a certain overlap between blocks, and inputs the converted block signal to the signal splitting unit, It further has a serial conversion unit that leaves a region not affected by the periodicity assumption included in the signal output from the switch circuit, and converts the signal output from the switch circuit from a block signal to a serial signal while excluding a region that may be affected by the periodicity assumption included in the signal output from the switch circuit, the receiver according to any one of Appendices 8 to 12.

[0104] [Appendix 14] A transmitter that transmits a signal via a transmission line, A communication system comprising the receiver according to any one of Appendices 7 to 13.

[0105] [Appendix 15] Let M and L be natural numbers satisfying 1 < M / L < 2, and divide an input signal of rational M / L - fold oversampling into M signals, Each of the M divided signals is converted into a frequency domain signal, calculating first filter coefficients for the M signals converted into frequency domain signals; calculating, for each of the L groups, second filter coefficients for the M signals on which the first filter coefficients have been calculated; Adding the M signals for which the second filter coefficients have been calculated for each group; converting the summed output signals for each group into time domain signals; sequentially selecting the signals converted into the time domain signals for each group and concatenating the signals of each group; a loss function representing the magnitude of a difference between a pre-selected signal and a predetermined value, a gradient of the loss function for the first filter coefficient and a gradient of the loss function for the second filter coefficient using an error backpropagation method, and updating the first filter coefficient and the second filter coefficient.

[0106] Some or all of the elements (e.g., configurations and functions) described in Supplementary Notes 2 to 7 that are dependent on Supplementary Note 1 may also be dependent on Supplementary Note 15 in the same dependency relationship as Supplementary Notes 2 to 7. Some or all of the elements described in any Supplementary Note may be applied to various hardware, software, recording means for recording software, systems, and methods. [Explanation of symbols]

[0107] 10:Communication Systems 11:Transmitter 13: Transmission path 15: Receiver 21: Detector 22: Equalization signal processing circuit 23: Signal division section 24: Frequency domain transform unit 25: First frequency domain filter 26: Second frequency domain filter 27: Adder 28: Time domain transform unit 29: Switch circuit 30: Coefficient update unit 100: Optical fiber communication systems 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 161: Chromatic dispersion compensation 162: Polarization separation / carrier phase compensation 171: Block conversion unit 172, 173: Delay circuit 174-0 to 174-2: Downsampling section 175-0~175-2:FFT 176-0 to 176-2: First frequency domain filter 180-0 to 180-2, 181-0 to 181-2: Second frequency domain filter 182~185: Adder 186-0~186-1:IFFT 187: Switch circuit 188: Serial conversion unit 189: Carrier phase compensation filter 190: Coefficient update unit

Claims

1. a signal dividing unit that divides an input signal oversampled by a rational number M / L into M signals, where M and L are natural numbers satisfying 1<M / L<2; a frequency domain transform unit that transforms each of the M divided signals into a frequency domain signal; a first frequency domain filter that calculates first filter coefficients for the M signals converted into frequency domain signals; a second frequency domain filter for calculating second filter coefficients for the M signals on which the first filter coefficients have been calculated, for each of the L groups; an adder that adds, for each group, the M signals on which the second filter coefficients have been calculated; a time domain conversion unit that converts the output signal of the adder into a time domain signal for each group; a switch circuit for sequentially selecting the signals converted into the time domain signals for each group; and a coefficient update unit that calculates a gradient of the loss function for the first filter coefficient and a gradient of the loss function for the second filter coefficient using a backpropagation algorithm, with the magnitude of the difference between the signal output from the switch circuit and a predetermined value as a loss function, and updates the first filter coefficient and the second filter coefficient.

2. 2. The equalization signal processing circuit according to claim 1, wherein the equalization signal processing circuit is configured as a circuit that receives a plurality of signals as input and outputs a plurality of signals, and the first frequency domain filter is configured as a multi-input multi-output (MIMO) filter.

3. 3. The equalization signal processing circuit according to claim 1, wherein the coefficient update unit updates the first filter coefficient based on a gradient of the loss function for the first filter coefficient by a stochastic gradient descent method, and updates the second filter coefficient based on a gradient of the loss function for the second filter coefficient by a stochastic gradient descent method.

4. 3. The equalization signal processing circuit according to claim 1, wherein the input signal is a signal transmitted via a transmission line and coherently received by a receiver.

5. a time domain filter that performs time domain filtering on the signal output from the switch circuit; 3. The equalization signal processing circuit according to claim 1, wherein the coefficient update unit calculates the magnitude of the difference between the output signal of the time domain filter and the predetermined value as a loss function.

6. 3. The equalization signal processing circuit according to claim 1, wherein the switch circuit switches the group to be selected for each sample.

7. a block conversion unit that converts the input signal from a serial signal to a block signal while providing a certain overlap between blocks, and inputs the converted block signal to the signal division unit; 3. The equalization signal processing circuit according to claim 1, further comprising a serial conversion unit that converts the signal output from the pre-transmission switch circuit from a block signal to a serial signal while leaving a region that is not affected by the periodicity assumption contained in the signal output from the switch circuit and excluding a region that may be affected by the periodicity assumption contained in the signal output from the switch circuit.

8. a detector that coherently receives a signal transmitted from a transmitter via a transmission line; an equalization signal processing circuit that performs equalization signal processing on the coherently received signal, The equalization signal processing circuit a signal dividing unit that divides an input signal oversampled by a rational number M / L into M signals, where M and L are natural numbers satisfying 1<M / L<2; a frequency domain transform unit that transforms each of the M divided signals into a frequency domain signal; a first frequency domain filter that calculates first filter coefficients for the M signals converted into frequency domain signals; a second frequency domain filter for calculating second filter coefficients for the M signals on which the first filter coefficients have been calculated, for each of the L groups; an adder that adds, for each group, the M signals on which the second filter coefficients have been calculated; a time domain conversion unit that converts the output signal of the adder into a time domain signal for each group; a switch circuit for sequentially selecting the signals converted into the time domain signals for each group; a coefficient update unit that calculates a gradient of the loss function for the first filter coefficient and a gradient of the loss function for the second filter coefficient using a backpropagation algorithm, with the magnitude of a difference between the signal output from the switch circuit and a predetermined value as a loss function, and updates the first filter coefficient and the second filter coefficient.

9. a transmitter for transmitting a signal via a transmission line; A communication system comprising the receiver according to claim 8.

10. Dividing an input signal oversampled by a rational number M / L into M signals, where M and L are natural numbers satisfying 1<M / L<2; Transforming each of the M divided signals into a frequency domain signal; Calculating first filter coefficients for the M signals converted into the frequency domain signals; calculating, for each of the L groups, second filter coefficients for the M signals on which the first filter coefficients have been calculated; adding, for each group, the M signals for which the second filter coefficients have been calculated; converting the summed output signals for each group into time domain signals; sequentially selecting the signals converted into the time domain signals for each group and concatenating the signals of each group; a loss function representing the magnitude of a difference between a pre-selected signal and a predetermined value, a gradient of the loss function for the first filter coefficient and a gradient of the loss function for the second filter coefficient using an error backpropagation method, and updating the first filter coefficient and the second filter coefficient.

Images