JP7420238B2 - MIMO processing device, signal receiving device, signal transmission system, and filter coefficient update method - Google Patents

Description

The present disclosure relates to a MIMO processing device, a signal receiving device, a signal transmission system, and a filter coefficient updating method.

In optical fiber communications, capacity has been increased by introducing multiplexing techniques that utilize various physical degrees of freedom, such as time multiplexing, wavelength multiplexing, and polarization multiplexing. In recent years, in order to further increase capacity, studies have been conducted on spatial multiplexing transmission technology that utilizes the degree of freedom in space to multiplex signals.

In typical optical fiber communications, a single core single mode fiber with one core with one propagation mode in one cladding is used as the transmission medium. On the other hand, spatial multiplexing transmission technology uses transmission media for spatial multiplexing, such as a multicore fiber having multiple cores in one cladding or a multimode fiber in which each core has multiple propagation modes. When such a transmission medium is used, the number of propagation channels in a single fiber can be increased by the number of cores or modes, increasing the transmission capacity per fiber.

High space utilization efficiency is desired for the above-mentioned transmission medium for spatial multiplexing transmission. For example, in a multi-core fiber, the transmission capacity per fiber can be increased by reducing the distance between cores and arranging more cores with the same cladding diameter. In particular, a multicore fiber in which the distance between the cores is so close that strong crosstalk occurs between the cores is called a coupled multicore fiber. However, when crosstalk occurs between cores, mixing occurs between signals propagating through multiple propagation channels. Therefore, when signals are received individually for each propagation channel, the received signal quality deteriorates.

Multi-Input Multi-Output (MIMO) processing in the digital domain is known as one technique for compensating for crosstalk between propagation channels and separating respective signals. In optical fiber communications, MIMO processing is typically performed on multiple coherently received signals. For example, when polarization multiplexed signals are spatially multiplexed using a coupled three-core fiber, the receiving device performs 6-input, 6-output (6×6) MIMO processing on the signals propagated through each core. do. Polarization separation processing that performs polarization separation of a polarization multiplexed signal can also be regarded as 2×2 MIMO processing.

As a related technique, Patent Document 1 discloses an optical receiving device that receives a plurality of optical signals transmitted through different routes close to each other. For example, when a coupled multi-core fiber with N cores is used for signal transmission and polarization multiplexed signals are transmitted in each core, the number of multiplexed signals is 2N. In the optical receiver, the MIMO processing unit compensates for crosstalk between spatially multiplexed and polarization multiplexed signals and separates each signal. The MIMO processing unit has a 2N×2N matrix type filter (MIMO filter) for compensating for crosstalk between 2N signals. The MIMO filter compensates for time-spread effects such as polarization mode dispersion and propagation delay differences between cores that occur in coupled multi-core fiber transmission. Each filter is configured as a finite impulse response (FIR) filter, a frequency domain filter, or the like. For example, when an FIR filter is used for each filter, and the number of taps is M, the MIMO filter has 2N×2N×M coefficients as a whole.

FIG. 16 shows a configuration example of a MIMO filter. FIG. 16 shows a configuration example of a MIMO filter when the number of cores is N=2 and the number of multiplexed signals is 2N=4. As shown in FIG. 16, the MIMO filter 500 includes FIR filters 510 arranged in a 4×4 matrix. Coefficient update section 520 updates the coefficients of FIR filter 510. Note that although only one coefficient updating section 520 is shown in FIG. 16 to simplify the drawing, the coefficient updating section 520 is arranged corresponding to each FIR filter 510.

上記式において、「^＋」（ダガー）は、エルミート共役を表す。Let the input of the MIMO filter 500 be x _j (j=1, . . . , 2N), and the output be y _i (i=1, . . . , 2N). Further, it is assumed that the coefficient (coefficient vector) of the FIR filter 510 corresponding to x _j and y _i is H _ij . When the number of taps of each FIR filter 510 is M, the coefficient H _ij of each FIR filter 510 is expressed by the following formula.
H _ij = (h _ij [0], h _ij [1], ..., h _ij [M-1]) ^T
In the above formula, " ^T " represents transposition. For an integer k corresponding to a certain symbol time, the input (input vector) of the MIMO filter is expressed as X _j [k] = (x _j [k], x _j [k-1], ..., x _j [k- M+1]) ^T , the output y _i [k] of the MIMO filter is expressed by the following formula.

In the above formula, " ⁺ " (dagger) represents a Hermitian conjugate.

In the MIMO filter 500, a signal before crosstalk occurs can be separated by calculating an inverse characteristic of a characteristic such as crosstalk occurring in a transmission path with respect to X _j [k]. The state of the transmission path changes depending on the environmental temperature and the state of the force applied to the optical fiber. The coefficient update unit 520 adaptively updates the coefficients of the FIR filter 510 in accordance with the state of the transmission path. As algorithms for adaptive coefficient updating, algorithms such as CMA (Constant modulus algorithm) and DDLMS (Decision directed least mean square) are known.

FIG. 17 shows calculation of the coefficient update amount in the coefficient update unit 520. Here, it is assumed that the coefficient update unit 520 updates the coefficients of the MIMO filter using CMA. The filter coefficient update by CMA is expressed by the following formula.
H _ij →H _ij +με _i [k]y _i [k]X _j ^* [k]
In the above formula, " ^* " represents a complex conjugate. μ is a parameter called step size that determines the size of coefficient update for each step. ε _i [k] is expressed by the following formula, where r is the amplitude.
ε _i [k]=r ² −|y _i [k] | ²

As another related technology, Patent Document 2 discloses an adaptive array device. The adaptive array device described in Patent Document 2 includes an adaptive filter for receiving only a certain signal source as a target signal source from among a plurality of signal sources. The adaptive array device generates a first indication of a beamformer output signal amplitude that is more sensitive to the target signal source than to other signal sources. The adaptive array device also generates a second indicator regarding the output signal amplitude of the beamformer that is less sensitive to the target signal source than to other signal sources. The adaptive array device uses the first index and the second index to determine a step size of an adaptive algorithm in the adaptive filter.

International Publication No. 2015/052895 Japanese Patent Application Publication No. 11-052988

As mentioned above, the MIMO filter has 2N×2N×M coefficients as a whole. In adaptive coefficient control of a MIMO filter, each filter coefficient needs to be updated from an initial state and converged to a desired state that has the opposite characteristics of the transmission path. However, when the number of spatial multiplexing is large, N becomes large, and in the case of long-distance transmission, M is required, and the number of coefficients in the MIMO filter becomes enormous. In that case, it is necessary to update a huge number of coefficients, so it takes a long time for the coefficients to converge. Generally, when updating filter coefficients, the convergence speed can be increased by setting the step size to a large value. However, when the step size is set to a large value, the stability of adaptive control decreases.

The adaptive array device described in Patent Document 2 determines the step size using indicators related to the output signal amplitudes of two beamformers. However, the object of Patent Document 2 is to provide an adaptive array device that can quickly follow the movement of a disturbance signal source while reducing breathing noise and maintaining high output signal quality. In Patent Document 2, input to an adaptive filter is used to determine the step size. Even if the step size determination described in Patent Document 2 is applied to adaptive control of the coefficients of a MIMO filter, the time required for the coefficients to converge from an initial state to a desired state cannot be shortened.

In view of the above circumstances, the present disclosure provides a MIMO processing device, a signal receiving device, a signal transmission system, and a signal receiving device that can reduce the time required for coefficients to converge from an initial state to a desired state in adaptive MIMO signal processing. The purpose of this invention is to provide a method for updating filter coefficients.

To achieve the above object, the present disclosure provides a MIMO filter that includes a plurality of filters having adaptively controlled coefficients and compensates for crosstalk between a plurality of signals including crosstalk; gradient calculation means for calculating a gradient regarding the coefficient of a loss function that is a function; magnitude detection means for detecting the magnitude of the gradient; and use in adaptive control of the coefficient based on the magnitude of the detected gradient. step size adjusting means for adjusting the step size to be updated; update amount calculating means for calculating the update amount of the coefficient using the step size adjusted by the step size adjusting means; and coefficient updating means for updating the coefficients of the filter using the updated amount.

The present disclosure includes a receiving unit that receives a plurality of signals including crosstalk, a demodulator that separates and demodulates the plurality of signals, and a decoder that decodes transmission data from the plurality of demodulated signals. A signal receiving device is provided. In the signal receiving device, the demodulator includes a plurality of filters having coefficients that are adaptively controlled, a MIMO filter that compensates for crosstalk between the plurality of signals, and a loss function that is a function of the output of the MIMO filter. a gradient calculating means for calculating a gradient with respect to the coefficient, a magnitude detecting means for detecting the magnitude of the gradient, and a step size used in adaptive control of the coefficient based on the magnitude of the detected gradient. step size adjusting means for adjusting, update amount calculating means for calculating the update amount of the coefficient using the step size adjusted by the step size adjusting means, and using the update amount calculated by the update amount calculating means. and coefficient updating means for updating coefficients of the filter.

The present disclosure provides a signal transmission system including a signal transmitting device that multiplexes a plurality of signals and transmitting the multiplexed signals to a transmission path, and a signal receiving device that receives the plurality of signals via the transmission path. In the signal transmission system, the signal receiving device includes a receiving unit that receives the plurality of signals, a demodulator that separates and demodulates the plurality of signals, and a decoder that decodes transmission data from the plurality of demodulated signals. Equipped with a container. In the signal receiving device, the demodulator includes a plurality of filters having coefficients that are adaptively controlled, and a MIMO filter that compensates for crosstalk occurring between the plurality of signals between the signal transmitting device and the signal receiving device. a gradient calculating means for calculating a gradient regarding the coefficient of a loss function that is a function of the output of the MIMO filter; a magnitude detecting means for detecting the magnitude of the gradient; and a magnitude detecting means for detecting the magnitude of the gradient, based on the magnitude of the detected gradient. step size adjusting means for adjusting the step size used in the adaptive control of the coefficient; and update amount calculating means for calculating the update amount of the coefficient using the step size adjusted by the step size adjusting means. and coefficient updating means for updating coefficients of the filter using the update amount calculated by the update amount calculation means.

The present disclosure includes a plurality of filters having coefficients that are adaptively controlled, and a loss function that is a function of the output of a multi-input multi-output (MIMO) filter that compensates for crosstalk between a plurality of signals including crosstalk. calculating a gradient with respect to the coefficient of , detecting the magnitude of the gradient, adjusting a step size used in adaptive control of the coefficient based on the detected magnitude of the gradient, and determining the adjusted step size. A MIMO filter coefficient updating method is provided, in which an update amount of the coefficient is calculated using the above-described update amount, and a coefficient of the filter is updated using the calculated update amount.

A MIMO processing device, a signal receiving device, a signal transmission system, and a filter coefficient updating method according to the present disclosure can reduce the time required for coefficients to converge from an initial state to a desired state in adaptive MIMO signal processing. can.

FIG. 1 is a block diagram schematically showing a MIMO processing device according to the present disclosure. FIG. 1 is a block diagram showing a signal transmission system according to an embodiment of the present disclosure. FIG. 2 is a block diagram showing a configuration example of an optical transmitter. FIG. 2 is a block diagram showing a configuration example of an optical transmission line. FIG. 1 is a cross-sectional view showing a cross section of an optical fiber. FIG. 2 is a block diagram showing a configuration example of an optical receiver. FIG. 2 is a block diagram showing a configuration example of a demodulation section. FIG. 2 is a block diagram illustrating a configuration example of a MIMO processing unit. FIG. 3 is a block diagram showing a configuration example of an update amount calculation unit. FIG. 3 is a block diagram illustrating an example of calculation of a coefficient update amount in an update amount calculation unit. FIG. 7 is a block diagram showing another example of calculation of the coefficient update amount in the update amount calculation unit. 5 is a flowchart showing an operation procedure in a MIMO processing unit. A graph showing changes in loss over time. A graph showing changes in loss over time. A graph showing changes in loss over time. FIG. 2 is a block diagram showing a configuration example of a MIMO filter. FIG. 3 is a block diagram showing calculation of coefficient update amount in a coefficient update section.

Prior to describing the embodiments of the present disclosure, an overview of the present disclosure will be explained. FIG. 1 schematically shows a MIMO processing apparatus according to the present disclosure. The MIMO processing device 10 includes a MIMO filter 11, a gradient calculation means 12, a magnitude detection means 13, a step size adjustment means 14, an update amount calculation means 15, and a coefficient update means 16.

MIMO filter 11 includes a plurality of filters having adaptively controlled coefficients. MIMO filter 11 compensates for crosstalk between multiple signals including crosstalk. The gradient calculating means 12 calculates the gradient regarding the coefficient of the loss function which is a function of the output of the MIMO filter 11. The magnitude detection means 13 detects the magnitude of the gradient regarding the coefficients of the loss function.

The step size adjustment means 14 adjusts the step size used in adaptive control of the coefficients of the filter based on the magnitude of the detected gradient. The update amount calculation means 15 uses the step size adjusted by the step size adjustment means 14 to calculate the update amount of the coefficients of the filter. The coefficient updating means 16 uses the update amount calculated by the update amount calculation means 15 to update the coefficients of the MIMO filter.

In the present disclosure, the coefficient update unit 16 updates the coefficients of the MIMO filter 11 with the coefficient update amount calculated using the step size adjusted based on the magnitude of the gradient regarding the coefficients of the loss function. If the magnitude of the slope for the coefficients of the loss function is small, the coefficients may remain near a saddle point or local optimum, and the time required for the coefficients to converge to the desired state may be longer. In the present disclosure, by appropriately adjusting the step size according to the magnitude of the gradient, it is possible to avoid the coefficients from remaining at a saddle point or a local optimum value. Therefore, in the adaptive control of the coefficients of the MIMO filter 11, the present disclosure can shorten the time required for the coefficients to converge from an initial state to a desired state.

Embodiments of the present disclosure will be described in detail below. FIG. 2 shows a signal transmission system according to an embodiment of the present disclosure. In this embodiment, the signal transmission system is configured as an optical fiber communication system 100. The optical fiber communication system 100 includes an optical transmitter (optical transmitter) 110, an optical transmission line (transmission line) 130, and an optical receiver (optical receiver) 150. The optical fiber communication system 100 constitutes, for example, an optical submarine cable system.

The optical transmitter 110 converts a plurality of transmission data into a plurality of spatially multiplexed and/or polarization multiplexed optical signals. The optical transmitter 110 converts, for example, four pieces of transmission data into two polarization multiplexed optical signals. The optical transmitter 110 sends the two converted polarization multiplexed optical signals to the optical transmission line 130. In the optical transmission line 130, the two polarization multiplexed optical signals are spatially multiplexed. The optical transmission line 130 includes, for example, a coupled two-core fiber. The optical transmission line 130 transmits the two polarization multiplexed optical signals sent from the optical transmitter 110 to the optical receiver 150. The optical receiver 150 restores a plurality of transmission data from a plurality of optical signals received via the optical transmission line 130. The optical receiver 150 restores four pieces of transmission data from, for example, two polarization multiplexed optical signals.

FIG. 3 shows a configuration example of the optical transmitter 110. The optical transmitter 110 includes an encoding section 111, pre-equalization sections 112a and 112b, DACs (Digital analog converters) 113a and 113b, optical modulators 114a and 114b, and an LD (Laser diode) 115. Encoding section 111 encodes data. The encoding unit 111 encodes in-phase (I) components and quadrature (Q) components of X and Y polarization for each core of the coupled two-core fiber used in the optical transmission line 130 (see FIG. 2). Outputs four series of signals.

Pre-equalization units 112a and 112b each perform pre-equalization on the encoded four-series signals to compensate for distortion of devices within the optical transmitter in advance. The DACs 113a and 113b each convert the four series of pre-equalized signals into electrical signals.

The LD 115 outputs CW (continuous wave) light. The optical modulators 114a and 114b respectively modulate the CW light output from the LD 115 according to the four series of signals output from the DACs 113a and 113b, and generate polarization-multiplexed optical signals. The optical modulators 114a and 114b generate, for example, polarization multiplexed QPSK (Quadrature Phase Shift Keying) signals. The optical modulator 114a sends out a polarization-multiplexed optical signal to one core (core 1) of the coupled two-core fiber. The optical modulator 114b sends out a polarization-multiplexed optical signal to the other core (core 2) of the coupled two-core fiber.

FIG. 4 shows an example of the configuration of the optical transmission line 130. The optical transmission line 130 has fanouts 131 and 134, an optical fiber 132, and an optical amplifier 133. The optical fiber 132 is configured, for example, as a coupled two-core fiber. FIG. 5 shows a cross section of optical fiber 132. Optical fiber 132 has two cores 141 and 142 in one cladding. The cores 141 and 142 each guide, for example, a polarization multiplexed QPSK signal.

Fan-out 131 guides multiple optical signals to each core of optical fiber 132. The optical amplifier 133 amplifies the optical signal guided to each core. The optical amplifier 133 is configured, for example, as an erbium doped fiber amplifier (EDFA) with multiple cores. Optical amplifier 133 may include a fan-out and a conventional single-core EDFA. Fanout 134 outputs the optical signals guided through each core of optical fiber 132 to optical receiver 150 (see FIG. 2).

FIG. 6 shows a configuration example of the optical receiver 150. The optical receiver 150 includes an LD 151, coherent receivers 152a and 152b, ADCs (analog digital converters) 153a and 153b, a demodulator 154, and a decoder 155. In the optical receiver 150, circuits such as a demodulator 154 and a decoder 155 may be configured using a device such as a DSP (digital signal processor).

The LD 151 outputs CW light that becomes local oscillator light. The coherent receivers 152a and 152b each use the CW light output from the LD 151 to perform coherent detection on the optical signal transmitted through each core of the optical fiber. The coherent receivers 152a and 152b each output four series of received signals (electrical signals) corresponding to the I/Q components of the coherently detected X/Y polarized waves.

The ADCs 153a and 153b sample the received signals output from the coherent receivers 152a and 152b, respectively, and convert them into signals in the digital domain. The demodulator (demodulated signal processing circuit) 154 performs digital signal processing on a total of eight series of received signals sampled by the ADCs 153a and 153b, and demodulates the received signals. The decoding unit (decoded signal processing circuit) 155 decodes the demodulated signal and restores the transmitted data.

FIG. 7 shows an example of the configuration of the demodulator 154. The demodulation section 154 includes a complex number conversion section 161, a chromatic dispersion compensation section 162, a MIMO processing section 163, and a carrier phase compensation section 164. The complex number conversion unit 161 converts the received signal of the I/Q component of each polarized wave of each core into a complex number. The complex number conversion unit 161 outputs four series of signals of X/Y polarization of core 1/2 which have been converted into complex numbers.

The chromatic dispersion compensator 162 compensates for the chromatic dispersion accumulated in the optical transmission line 130 (see FIG. 2) for each of the four series of received signals converted into complex numbers. The MIMO processing unit 163 performs MIMO processing on the four series of signals whose chromatic dispersion has been compensated to compensate for crosstalk, and separates the X/Y polarized signals transmitted through each core. The MIMO processing unit 163 corresponds to the MIMO processing device 10 shown in FIG.

The carrier phase compensation unit 164 performs carrier phase compensation on each of the four separated signals. The carrier phase compensator 164 removes the frequency and phase offset between the carrier of the optical signal and the local oscillator light, and outputs four demodulated received signals. Note that depending on the algorithm used by the MIMO processing unit 163, carrier phase compensation and MIMO processing are integrated.

FIG. 8 shows a configuration example of the MIMO processing unit 163. The MIMO processing section 163 includes a plurality of filters 200, an update amount calculation section 210, and a coefficient updating section 220. The MIMO processing section 163 may further include a coefficient convergence determination section 230. In the MIMO processing unit 163, the plurality of filters 200 are arranged in a 4×4 matrix. Filter 200 corresponds to MIMO filter 11 shown in FIG. The input of the MIMO processing unit 163 is x _j (j=1,..., 4), the output is y _{i (} i=1,..., 4), _and the filter (h _ij ) Let the coefficient (coefficient vector) of 200 be H _ij . Each filter 200 is configured as, for example, an FIR filter with M taps. In that case, the coefficient H _ij of the filter 200 is expressed by the following equation (1).
H _ij = (h _ij [0], h _ij [1], ..., h _ij [M-1]) ^T (1)

It is assumed that for an integer k (hereinafter also referred to as time k) corresponding to a certain symbol time, the input (input vector) X _j [k] of the MIMO processing unit 163 is expressed by the following equation (2).
X _j [k] = (x _j [k], x _j [k-1], ..., x _j [k-M+1]) ^T (2)
The output y _i [k] of the MIMO processing unit 163 at time k is expressed by the following equation (3).

The update amount calculation unit 210 and the coefficient update unit 220 are arranged corresponding to each filter 200. The update amount calculation unit 210 and the coefficient update unit 220 adaptively control the coefficient H _ij of the filter 200. Below, an example in which the update amount calculation unit 210 and the coefficient update unit 220 sequentially control the coefficients of the filter 200 using CMA as an adaptive coefficient control algorithm will be mainly described.

あるフィルタ係数ξ^＊は、損失関数の係数ξに対する勾配を用いて、下記式（５）により更新される。

上記式（５）における微分項を計算すると、下記式（６）が得られる。
Ｈ_ｉｊ→Ｈ_ｉｊ＋μ_Ｓε_ｉ［ｋ］ｙ_ｉ［ｋ］Ｘ_ｊ ^＊［ｋ］ （６）
ここで、ε_ｉ［ｋ］＝ｒ^２－｜ｙ_ｉ［ｋ］｜^２である。
上記式（６）の右辺の第２項目が、係数更新量ΔＨ_ｉｊに対応する。Generally, in adaptive coefficient control, coefficients are controlled using a stochastic descent method so as to minimize a predetermined loss function. In the case of CMA, the loss function φ[k] is defined by the following equation (4) using the error between the output y _i [k] and the predetermined amplitude value r.

A certain filter coefficient ξ ^* is updated by the following equation (5) using the slope of the loss function with respect to the coefficient ξ.

When the differential term in the above equation (5) is calculated, the following equation (6) is obtained.
H _ij →H _ij +μ _S ε _i [k]y _i [k]X _j ^* [k] (6)
Here, ε _i [k]=r ² −|y _i [k]| ² .
The second item on the right side of the above equation (6) corresponds to the coefficient update amount ΔH _ij .

FIG. 9 shows a configuration example of the update amount calculation unit 210. The update amount calculation section 210 includes a gradient calculation section 211 , a magnitude detection section 212 , a step size adjustment section 213 , and an application section 214 . The gradient calculation unit 211 calculates the gradient regarding the coefficients of the loss function. The gradient calculation section 211 corresponds to the gradient calculation means 12 shown in FIG.

The magnitude detection unit 212 detects the magnitude of the gradient regarding the coefficient of the calculated loss function. The magnitude detection unit 212 detects, for example, the temporal average of the magnitude of the gradient regarding the coefficients of the loss function. The step size adjustment unit 213 adjusts the step size _μS based on the temporal average of the gradient magnitude detected by the magnitude detection unit 212. The application unit 214 calculates the coefficient update amount ΔH _ij using the adjusted step size μ _S. The size detection section 212 corresponds to the size detection means 13 shown in FIG. The step size adjustment section 213 corresponds to the step size adjustment means 14 shown in FIG. The application unit 214 corresponds to the update amount calculation means 15 shown in FIG.

For example, if the temporal average of the magnitude of the gradient for a certain coefficient is small around a certain time, it means that the coefficient does not change much around that time. The fact that the temporal average of the magnitude of the gradient is small at a certain stage from the initial state to the desired state in adaptive coefficient control suggests that the coefficient may remain at a saddle point or local optimum value. . In this embodiment, the step size adjustment unit 213 adjusts the step size to increase the step size when the temporal average of the magnitude of the gradient regarding the coefficient of the loss function is small. By doing so, it is possible to reduce the possibility that the coefficients remain at a saddle point or a local optimum value, and it is possible to shorten the time required for the coefficients to converge.

勾配算出部２１１は、入力されるｘ_ｊとｙ_ｉとに対して、上記式（７）で表される損失関数の係数に関する勾配を計算する。ここで、Ｘ_ｊ［ｋ］は、式（２）に表されるようにＭ個の要素を有しており、損失関数の係数に関する勾配は、Ｍ個の要素を持つベクトルである。大きさ検出部２１２は、損失関数の係数に関する勾配の各要素を２乗し、その移動平均を要素ごとに計算する。大きさ検出部２１２は、例えば、勾配の各要素の２乗に対し、時間が遡るほどに重みを減少させた指数移動平均（指数平滑平均）を計算する。大きさ検出部２１２は、移動平均の平方根を算出する。この値は、損失関数の係数に関する勾配の大きさの時間的な平均の指標となる。FIG. 10 shows an example of calculation of the coefficient update amount in the update amount calculation unit 210. Regarding the filter h _ij , the slope of the coefficient of the loss function at a certain symbol time k is expressed by the following equation (7).

The gradient calculation unit 211 calculates the gradient regarding the coefficient of the loss function expressed by the above equation (7) with respect to the input x _j and y _i . Here, X _j [k] has M elements as expressed in equation (2), and the gradient regarding the coefficient of the loss function is a vector with M elements. The magnitude detection unit 212 squares each element of the gradient regarding the coefficient of the loss function, and calculates the moving average for each element. The magnitude detection unit 212 calculates, for example, an exponential moving average (exponential smoothed average) with respect to the square of each element of the gradient, in which the weight decreases as time goes back. The size detection unit 212 calculates the square root of the moving average. This value provides an indication of the temporal average of the magnitude of the slope for the coefficients of the loss function.

ここで、大きさ検出部２１２は、損失関数の係数に関する勾配の大きさの時間的な平均の指標をＭ個の要素ごとに算出する。このため、ステップサイズμ_Ｓは、要素ごとに異なる値をとり得る。適用部２１４は、上記式（８）を用いて計算したステップサイズを用いて、式（６）の第２項に対応する係数更新量ΔＨ_ｉｊを計算する。係数更新部２２０（８を参照）は、係数更新量ΔＨ_ｉｊを用いて、係数Ｈ_ｉｊを更新する。係数更新部２２０は、図１に示される係数更新手段１６に対応する。The step size adjustment unit 213 adjusts the step size so that the step size becomes large when the index of the temporal average of the magnitude of the gradient regarding the coefficient of the loss function calculated by the size detection unit 212 is small. For example, the step size adjustment unit 213 determines the value (adjustment rate) by which the fixed value μ of the predetermined step size is multiplied based on the reciprocal of the index of the temporal average of the magnitude of the gradient regarding the coefficient of the loss function. decide. The step size adjustment unit 213 calculates a value obtained by multiplying the fixed value μ of the step size by the determined adjustment rate as the adjusted step size _μS . That is, the step size adjustment unit 213 calculates the adjusted step size _μS using the following formula.

Here, the magnitude detection unit 212 calculates an index of the temporal average of the magnitude of the gradient regarding the coefficient of the loss function for each of the M elements. Therefore, the step size _μS can take different values for each element. The application unit 214 uses the step size calculated using the above equation (8) to calculate the coefficient update amount ΔH _ij corresponding to the second term of equation (6). The coefficient update unit 220 (see 8) updates the coefficient H _ij using the coefficient update amount ΔH _ij . The coefficient update section 220 corresponds to the coefficient update means 16 shown in FIG.

Note that in the step size adjustment unit 213, if the adjusted step size _μS is set to the value obtained by multiplying the fixed step size μ by the reciprocal of the above-mentioned index, when updating the coefficient H _ij , if the step size is too large or the inverse The step size may be too small. In order to stabilize the process, the step size adjustment unit 213 may set an upper limit and a lower limit to the adjusted step size μ _S so that the value of the adjusted step size μ _S falls within a predetermined range. . Moreover, although an example has been described above in which the reciprocal of the index of the temporal average of the magnitude of the gradient regarding the coefficient of the loss function is used as the adjustment rate, the present disclosure is not limited thereto. The step size adjustment unit 213 uses, for example, a lookup table created in advance that defines the relationship between the temporal average of the magnitude of the slope regarding the coefficients of the loss function and the adjusted step size μ _s . You may adjust the size.

FIG. 11 shows another example of calculation of the coefficient update amount in the update amount calculation unit. In this example, the update amount calculation section 210 includes a moving average calculation section 215 in addition to a gradient calculation section 211, a magnitude detection section 212, a step size adjustment section 213, and an application section 214. The calculation of the gradient regarding the coefficient of the loss function in the slope calculation unit 211 and the calculation of the temporal average of the magnitude of the slope regarding the coefficient of the loss function in the magnitude detection unit 212 are similar to those in the example shown in FIG. good. Further, the step size adjustment in the step size adjustment section 213 may be similar to the step size adjustment in the example shown in FIG. 10 .

In the example of FIG. 11, the moving average calculation unit 215 calculates, for each element, the moving average of the gradient regarding the coefficients of the loss function calculated by the gradient calculation unit 211. The moving average calculation unit 215 calculates an exponential moving average for each element of the gradient, for example. The application unit 214 calculates the coefficient update amount ΔH _ij in the second term of Equation (6) using the moving average calculated by the moving average calculation unit 215 instead of the gradient itself regarding the coefficients of the loss function. In this way, when a moving average of the gradient is used, it is believed that the convergence of the coefficients can be stabilized or accelerated.

Returning to FIG. 8, the coefficient convergence determination unit (convergence determination means) 230 determines whether the coefficient H _ij has converged to a predetermined state. The coefficient convergence determination unit 230 monitors the convergence state of the coefficient H _ij . The coefficient convergence determination unit 230 monitors signal characteristics such as error vector magnitude (EVM) of the filter output, and determines whether the coefficients have converged to a predetermined state. The coefficient convergence determination unit 230 may determine whether the coefficients have converged to a predetermined state using an index such as the number of error corrections obtained in the decoding unit 155 (see FIG. 6) that is downstream of the demodulation unit. good. The coefficient convergence determination unit 230 compares an index such as a signal characteristic such as EVM or the number of error corrections with a predetermined threshold, and determines whether a convergence state has been reached based on the comparison result.

The operation of the update amount calculation unit 210 may include an initial acquisition mode and a tracking mode. The update amount calculation unit 210 operates in the initial acquisition mode, for example, from the initial state until the coefficient convergence determination unit 230 determines that the coefficients have converged to a predetermined state. In the initial acquisition mode, the update amount calculation unit 210 calculates the coefficient update amount using a step size that is adjusted according to the magnitude of the gradient regarding the coefficients of the loss function.

The update amount calculation unit 210 operates in the tracking mode after the coefficient convergence determination unit 230 determines that the coefficients have converged to a predetermined state. The updating of the coefficients in the tracking mode may be similar to the updating of the coefficients using the normal stochastic gradient descent method. In the tracking mode, the update amount calculation unit 210 calculates the coefficient update amount using a fixed step size. When a fixed step size is used to calculate the coefficient update amount, the step size adjustment unit 213 (see FIG. 10, for example) may output the step size μ to the application unit 214. In that case, the magnitude detection unit 212 may stop detecting the magnitude of the gradient.

Next, the operating procedure will be explained. FIG. 12 explains the operation procedure (filter coefficient updating method) in the MIMO processing unit 163. The coefficient update unit 220 initializes each coefficient of the MIMO filter (step S1). For example, as shown in equation (9) below, in the filter (h _ii ) located on the main diagonal, the coefficient updating unit 220 sets the coefficient of only the central tap to "1" and sets the coefficients of the other taps to "1". Initialize to 0. Further, the coefficient updating unit 220 initializes the coefficients of all taps to "0" in the off-diagonal filters (h _ij , i≠j), as shown in equation (10) below.
H _ii = (0,...,0,1,0,...,0) ^T (9)
H _ij = (0,...,0) ^T (i≠j) (10)
After that, adaptive control of the coefficients is started in the MIMO processing unit 163.

In the update amount calculation unit 210, the gradient calculation unit 211 (see FIG. 9, for example) calculates the slope regarding the coefficient of the loss function (step S2). The magnitude detection unit 212 detects the temporal average of the magnitude of the gradient regarding the coefficients of the loss function (step S3). The step size adjustment unit 213 adjusts the step size based on the detected temporal average of the magnitude of the gradient (step 4). The update amount calculation unit 210 calculates the coefficient update amount using the gradient calculated in step S2 and the step size adjusted in step S4. The coefficient update unit 220 updates the coefficients of the filter 200 using the coefficient update amount calculated using the adjusted step size (step S5).

The coefficient convergence determination unit 230 determines whether the coefficients have converged to a predetermined state (step S6). If it is determined in step S6 that the coefficients have not converged to a predetermined state, the process returns to step S1, and updating of the coefficients using the adjusted step size is continued. The operations from step S1 to step S6 correspond to the operations in the initial acquisition mode.

If it is determined in step S6 that the coefficients have converged to a predetermined state, the operation mode is switched to tracking mode. In the tracking mode, the step size adjustment unit 213 outputs, for example, a fixed step size μ to the application unit 214. The gradient calculation unit 211 calculates the gradient regarding the coefficients of the loss function (step S7). The update amount calculation unit 210 calculates the coefficient update amount using the gradient calculated in step S7 and the fixed step size. The coefficient update unit 220 updates the coefficients of the filter 200 using the coefficient update amount calculated using the fixed step size (step S8). Thereafter, steps S7 and S8 are repeatedly performed to adaptively control the coefficients of the MIMO filter. The operations in steps S7 and S8 correspond to the operations in the tracking mode.

The present inventor verified the effect of coefficient control of the MIMO filter in this embodiment. FIGS. 13 to 15 each show the change in loss calculated using the loss function over time. In the verification, a coupled four-core fiber with a length of 52 km was used, and polarization multiplexed QPSK signals with a symbol rate of 32 Gbaud were spatially multiplexed and transmitted. The signals transmitted through each core were received by respective coherent receivers and then sampled using a 16-channel oscilloscope. For each signal, intensity normalization was performed, resampling to 2x oversampling was performed, and then demodulated digital signal processing, including MIMO signal processing, was performed offline. In this verification, a coupled four-core fiber is used for spatial multiplexing and a polarization multiplexed signal is used, so MIMO signal processing is 8×8.

FIG. 13 shows a change in loss over time when coefficient control of an adaptive MIMO filter is performed using a normal stochastic gradient descent method. In the graph shown in FIG. 13, the horizontal axis represents time in units of the number of symbols, and the vertical axis represents time changes in the magnitude of the loss function φ _i for each output of the MIMO filter. In FIG. 13, the loss is calculated using the CMA loss function up to 8×10 ⁵ symbols, and is calculated using the DDLMS loss function from 8×10 ⁵ to 10×10 ⁵ symbols. A state in which the magnitude of the loss function is around 0.6 indicates a state in which the coefficients have not reached a converged state. A state in which the magnitude of the loss function is less than 0.2 can be regarded as a state in which the coefficients have reached a converged state.

As shown in FIG. 13, when coefficient updating using the normal stochastic gradient descent method using a fixed step size is used, one signal reaches a convergence state in about 1×10 ⁵ symbols. Moreover, six signals reach a convergence state by about 6×10 ⁵ symbols. If some signals can reach a convergence state, subsequent demodulation processing and decoding processing can be performed normally on the filter output. Therefore, it is important that the signal quickly and stably reach a convergence state.

FIG. 14 shows the change in loss over time when the average magnitude of the slope with respect to the coefficients of the loss function is detected and the step size is adjusted based on it. In the graph shown in FIG. 14, the horizontal axis represents time in units of the number of symbols, and the vertical axis represents time changes in the magnitude of the loss function φ _i for each output of the MIMO filter. In this example, the coefficient update amount ΔH _ij is expressed as the product of the slope regarding the coefficient of the loss function and the step size, similar to the example shown in FIG. The update amount calculation unit 210 detected the average magnitude of the gradient up to 8×10 ⁵ symbols, and adjusted the step size using the detected average magnitude of the gradient. Comparing the results shown in FIG. 14 and the results shown in FIG. 13, it can be confirmed that the time it takes for one signal to reach a convergence state is shorter.

FIG. 15 shows the change in loss over time when the average slope of the coefficients of the loss function is used to calculate the coefficient update amount. In the graph shown in FIG. 15, the horizontal axis represents time in units of the number of symbols, and the vertical axis represents time changes in the magnitude of the loss function φ _i for each output of the MIMO filter. In this example, similarly to the example shown in FIG. 11, the coefficient update amount ΔH _ij is expressed as the product of the average slope of the coefficients of the loss function and the step size. Similar to the example in FIG. 14, the update amount calculation unit 210 detects the average size of the gradient up to 8×10 ⁵ symbols, and adjusts the step size using the detected average size of the gradient. did. Comparing the results shown in FIG. 14 with the results shown in FIG. 13, it can be confirmed that the time it takes for a plurality of signals to reach a stable convergence state is shorter.

In this embodiment, the update amount calculation unit 210 detects the magnitude of the gradient regarding the coefficients of the loss function, and adjusts the step size for updating the coefficients according to the magnitude of the detected gradient. In this embodiment, by appropriately adjusting the step size according to the magnitude of the gradient, it is possible to avoid the coefficients from remaining at a saddle point or a local optimum value. Therefore, in the adaptive control of the coefficients of the MIMO filter, the present embodiment can particularly shorten the time required for the coefficients to converge from an initial state to a predetermined state.

In this embodiment, the MIMO processing section 163 may include a coefficient convergence determination section 230. In that case, the update amount calculation unit 210 calculates the average magnitude of the slope regarding the coefficients of the loss function from the start of adaptive control of the coefficients until the coefficient convergence determination unit 230 determines that the coefficients have converged to a predetermined state. The coefficient update amount may be calculated using a step size adjusted accordingly. After it is determined that the coefficients have converged to a predetermined state, the update amount calculation unit 210 may calculate the coefficient update amount using a fixed step size. In this case, after the coefficients have converged, tracking of the filter coefficients with respect to transmission path fluctuations is performed by the usual stochastic gradient descent method.

Here, in this embodiment, the update amount calculation unit 210 detects the temporal average of the magnitude of the gradient regarding the coefficient of the loss function. Therefore, the amount of calculation in the update amount calculation unit 210 increases compared to the amount of calculation in adaptive coefficient control using the normal stochastic gradient descent method. In this embodiment, after it is determined that the coefficients have converged to a predetermined state, the update amount calculation unit 210 adjusts the step size, such as by detecting the temporal average of the magnitude of the gradient regarding the coefficients of the loss function. The calculation for can be stopped. In this embodiment, when the calculation such as the detection of the temporal average of the gradient magnitude is stopped, the time required for the coefficients to converge from the initial state to the predetermined state can be shortened. , the amount of calculations after convergence can be reduced.

Note that in the above embodiment, an example in which the optical fiber communication system 100 (see FIG. 2) includes one optical transmitter 110 and one optical receiver 150 has been described, but the present disclosure is not limited thereto. The optical fiber communication system 100 may be configured as a wavelength multiplexing system, and may include an optical transmitter 110 and an optical receiver 150 for each of a plurality of mutually different wavelengths. In that case, each core of the coupled multi-core fiber used in the optical transmission line 130 may transmit wavelength-multiplexed optical signals to the optical receiver 150.

Further, in the above embodiment, an example in which the signal transmission system is configured as an optical fiber communication system (optical transmission system) has been described, but the present invention is not limited to this. The signals that are multiplexed and transmitted are not limited to optical signals, but may also be wireless signals. The MIMO processing unit 163 (see FIG. 8, for example) is used, for example, to separate each data stream in a wireless communication system that uses multiple antennas to receive wireless signals transmitted from multiple transmitting antennas. obtain.

Although the embodiments of the present disclosure have been described in detail above, the present disclosure is not limited to the embodiments described above, and changes and modifications may be made to the embodiments described above without departing from the spirit of the present disclosure. are also included in this disclosure.

For example, some or all of the above embodiments may be described as in the following additional notes, but are not limited to the following.

[Additional note 1]
a MIMO (Multi-Input Multi-Output) filter that includes a plurality of filters having adaptively controlled coefficients and compensates for crosstalk between a plurality of signals including crosstalk;
gradient calculating means for calculating a gradient with respect to the coefficients of a loss function that is a function of the output of the MIMO filter;
Size detection means for detecting the size of the gradient;
step size adjusting means for adjusting the step size used in the adaptive control of the coefficients based on the magnitude of the detected gradient;
update amount calculation means for calculating an update amount of the coefficient using the step size adjusted by the step size adjustment means;
A MIMO processing device comprising: coefficient updating means for updating coefficients of the filter using the update amount calculated by the update amount calculation means.

[Additional note 2]
The MIMO processing device according to supplementary note 1, wherein the magnitude detection means detects a temporal average of the magnitude of the gradient as the magnitude of the gradient.

[Additional note 3]
The MIMO processing device according to appendix 1 or 2, wherein the step size adjustment means adjusts the step size so that the step size becomes smaller as the magnitude of the detected gradient becomes larger.

[Additional note 4]
The step size adjustment means determines an adjustment rate based on the magnitude of the detected gradient, and sets the adjusted step size to a value obtained by multiplying the determined adjustment rate by a fixed value of a predetermined step size. The MIMO processing device according to any one of Supplementary Notes 1 to 3.

[Additional note 5]
The MIMO processing device according to appendix 4, wherein the step size adjustment means determines the adjustment rate according to a magnitude of a reciprocal of a magnitude of the detected gradient.

[Additional note 6]
The MIMO processing device according to any one of appendices 1 to 5, wherein each of the plurality of filters is configured as a finite impulse response filter having M taps.

[Additional note 7]
The MIMO processing device according to any one of Supplementary Notes 1 to 6, wherein the update amount calculation means calculates a value obtained by multiplying the gradient regarding the coefficient of the loss function by the adjusted step size as the update amount of the coefficient. .

[Additional note 8]
further comprising a moving average calculation means for calculating a moving average of the slope regarding the coefficients of the loss function,
From Supplementary Note 1, the update amount calculation means calculates, as the update amount of the coefficient, a value obtained by multiplying the moving average of the slope regarding the coefficients of the loss function calculated by the moving average calculation means by the adjusted step size. 6. The MIMO processing device according to any one of 6.

[Additional note 9]
The MIMO processing device according to any one of appendices 1 to 8, wherein the plurality of signals are signals generated by digitally coherently receiving optical signals received via a transmission path.

[Additional note 10]
The MIMO processing device according to appendix 9, wherein the plurality of signals are spatially multiplexed and/or polarization multiplexed on the transmission path.

[Additional note 11]
The MIMO processing device according to appendix 9 or 10, wherein the transmission path includes a coupled multi-core fiber.

[Additional note 12]
further comprising convergence determination means for determining whether the coefficients have converged to a predetermined state;
The update amount calculation means calculates the update amount of the coefficient using the adjusted step size from an initial state until the convergence determination means determines that the coefficient has converged to the predetermined state. , after the convergence determining means determines that the coefficients have converged to the predetermined state, the MIMO process according to any one of Supplementary Notes 1 to 11, wherein the update amount of the coefficients is calculated using a fixed step size. Device.

[Additional note 13]
The MIMO processing device according to appendix 12, wherein the magnitude detection means stops detecting the magnitude of the gradient after the convergence determination means determines that the coefficient has converged to the predetermined state.

[Additional note 14]
receiving means for receiving a plurality of signals including crosstalk;
a demodulator that separates and demodulates the plurality of signals;
a decoder that decodes transmission data from the plurality of demodulated signals,
The demodulator is
a MIMO (Multi-Input Multi-Output) filter that includes a plurality of filters having adaptively controlled coefficients and compensates for crosstalk between the plurality of signals;
gradient calculating means for calculating a gradient with respect to the coefficients of a loss function that is a function of the output of the MIMO filter;
Size detection means for detecting the size of the gradient;
step size adjusting means for adjusting the step size used in the adaptive control of the coefficients based on the magnitude of the detected gradient;
update amount calculation means for calculating an update amount of the coefficient using the step size adjusted by the step size adjustment means;
and coefficient updating means for updating coefficients of the filter using the update amount calculated by the update amount calculation means.

[Additional note 15]
The signal receiving device according to appendix 14, wherein the magnitude detection means detects a temporal average of the magnitude of the gradient as the magnitude of the gradient.

[Additional note 16]
16. The signal receiving device according to appendix 14 or 15, wherein the step size adjusting means adjusts the step size so that the step size becomes smaller as the magnitude of the detected gradient becomes larger.

[Additional note 17]
a signal transmitter that multiplexes multiple signals and sends them to a transmission path;
and a signal receiving device that receives a plurality of signals via the transmission path,
The signal receiving device includes:
Receiving means for receiving the plurality of signals;
a demodulator that separates and demodulates the plurality of signals;
a decoder that decodes transmission data from the plurality of demodulated signals,
The demodulator is
a MIMO (Multi-Input Multi-Output) filter that includes a plurality of filters having adaptively controlled coefficients and compensates for crosstalk occurring between a plurality of signals between the signal transmitting device and the signal receiving device;
gradient calculating means for calculating a gradient with respect to the coefficients of a loss function that is a function of the output of the MIMO filter;
Size detection means for detecting the size of the gradient;
step size adjusting means for adjusting the step size used in the adaptive control of the coefficients based on the magnitude of the detected gradient;
update amount calculation means for calculating an update amount of the coefficient using the step size adjusted by the step size adjustment means;
A signal transmission system comprising: coefficient updating means for updating coefficients of the filter using the update amount calculated by the update amount calculation means.

[Additional note 18]
18. The signal transmission system according to appendix 17, wherein the magnitude detection means detects a temporal average of the magnitude of the gradient as the magnitude of the gradient.

[Additional note 19]
19. The signal transmission system according to appendix 17 or 18, wherein the step size adjustment means adjusts the step size so that the step size becomes smaller as the magnitude of the detected gradient becomes larger.

[Additional note 20]
relating to said coefficients of a loss function that is a function of the output of a MIMO (Multi-Input Multi-Output) filter comprising a plurality of filters with adaptively controlled coefficients and compensating for crosstalk between a plurality of signals including crosstalk; Calculate the slope,
detecting the magnitude of the gradient;
adjusting a step size used in the adaptive control of the coefficients based on the magnitude of the detected gradient;
Calculating the update amount of the coefficient using the adjusted step size,
A MIMO filter coefficient updating method of updating coefficients of the filter using the calculated update amount.

10: MIMO processing device 11: MIMO filter 12: Gradient calculation means 13: Size detection means 14: Step size adjustment means 15: Update amount calculation means 16: Coefficient update means 100: Optical fiber communication system 110: Optical transmitter 111: Encoding units 112a, 112b: Pre-equalization units 113a, 113b: DAC
114a, 114b: Optical modulator 115: LD
130: Optical transmission line 131, 134: Fan-out 132: Optical fiber 133: Optical amplifier 141, 142: Core 150: Optical receiver 151: LD
152a, 152b: coherent receiver 153a, 153b: ADC
154: Demodulation section 155: Decoding section 161: Complex number conversion section 162: Chromatic dispersion compensation section 163: MIMO processing section 164: Carrier phase compensation section 200: Filter 210: Update amount calculation section 211: Gradient calculation section 212: Magnitude detection section 213: Step size adjustment unit 214: Application unit 220: Coefficient update unit 230: Coefficient convergence determination unit

Claims (10)

a MIMO (Multi-Input Multi-Output) filter that includes a plurality of filters having adaptively controlled coefficients and compensates for crosstalk between a plurality of signals including crosstalk;
gradient calculating means for calculating a gradient with respect to the coefficients of a loss function that is a function of the output of the MIMO filter;
Size detection means for detecting the size of the gradient;
step size adjusting means for adjusting the step size used in the adaptive control of the coefficients based on the magnitude of the detected gradient;
update amount calculation means for calculating an update amount of the coefficient using the step size adjusted by the step size adjustment means;
A MIMO processing device comprising: coefficient updating means for updating coefficients of the filter using the update amount calculated by the update amount calculation means. The MIMO processing device according to claim 1, wherein the magnitude detection means detects a temporal average of the magnitude of the gradient as the magnitude of the gradient. 3. The MIMO processing device according to claim 1, wherein the step size adjusting means adjusts the step size so that the step size becomes smaller as the magnitude of the detected gradient becomes larger. The step size adjustment means determines an adjustment rate based on the magnitude of the detected gradient, and sets the adjusted step size to a value obtained by multiplying the determined adjustment rate by a fixed value of a predetermined step size. The MIMO processing device according to any one of claims 1 to 3. 5. The MIMO processing apparatus according to claim 4, wherein the step size adjustment means determines the adjustment rate according to a magnitude of a reciprocal of the magnitude of the detected gradient. The MIMO processing according to any one of claims 1 to 5 , wherein the update amount calculation means calculates a value obtained by multiplying the adjusted step size by a gradient regarding the coefficient of the loss function as the update amount of the coefficient. Device. further comprising convergence determination means for determining whether the coefficients have converged to a predetermined state;
The update amount calculation means calculates the update amount of the coefficient using the adjusted step size from an initial state until the convergence determination means determines that the coefficient has converged to the predetermined state. MIMO according to any one of claims 1 to 6 , wherein, after the convergence determining means determines that the coefficients have converged to the predetermined state, the update amount of the coefficients is calculated using a fixed step size. Processing equipment. receiving means for receiving a plurality of signals including crosstalk;
a demodulator that separates and demodulates the plurality of signals;
a decoder that decodes transmission data from the plurality of demodulated signals,
The demodulator is
a MIMO (Multi-Input Multi-Output) filter that includes a plurality of filters having adaptively controlled coefficients and compensates for crosstalk between the plurality of signals;
gradient calculating means for calculating a gradient with respect to the coefficients of a loss function that is a function of the output of the MIMO filter;
Size detection means for detecting the size of the gradient;
step size adjusting means for adjusting the step size used in the adaptive control of the coefficients based on the magnitude of the detected gradient;
update amount calculation means for calculating an update amount of the coefficient using the step size adjusted by the step size adjustment means;
and coefficient updating means for updating coefficients of the filter using the update amount calculated by the update amount calculation means. a signal transmitter that multiplexes multiple signals and sends them to a transmission path;
and a signal receiving device that receives a plurality of signals via the transmission path,
The signal receiving device includes:
Receiving means for receiving the plurality of signals;
a demodulator that separates and demodulates the plurality of signals;
a decoder that decodes transmission data from the plurality of demodulated signals,
The demodulator is
a MIMO (Multi-Input Multi-Output) filter that includes a plurality of filters having adaptively controlled coefficients and compensates for crosstalk occurring between a plurality of signals between the signal transmitting device and the signal receiving device;
gradient calculating means for calculating a gradient with respect to the coefficients of a loss function that is a function of the output of the MIMO filter;
Size detection means for detecting the size of the gradient;
step size adjusting means for adjusting the step size used in the adaptive control of the coefficients based on the magnitude of the detected gradient;
update amount calculation means for calculating an update amount of the coefficient using the step size adjusted by the step size adjustment means;
A signal transmission system comprising: coefficient updating means for updating coefficients of the filter using the update amount calculated by the update amount calculation means. relating to said coefficients of a loss function that is a function of the output of a MIMO (Multi-Input Multi-Output) filter comprising a plurality of filters with adaptively controlled coefficients and compensating for crosstalk between a plurality of signals including crosstalk; Calculate the slope,
detecting the magnitude of the gradient;
adjusting a step size used in the adaptive control of the coefficients based on the magnitude of the detected gradient;
Calculating the update amount of the coefficient using the adjusted step size,
A MIMO filter coefficient updating method of updating coefficients of the filter using the calculated update amount.

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