Coherent optical receiver

Abstract

Provided is a coherent optical receiver for reproducing an optical complex signal used when generating an optical signal in a coherent optical transmitter without using local carrier light. The coherent optical receiver is provided with: an optical convolutional circuit for optical signal processing of an optical signal received via an optical transmission path; an optical detector for converting the optical signal-processed optical signal into an electrical signal having the intensity waveform of the optical signal-processed optical signal; and a demodulation algorithm for performing digital signal processing on the electrical signal to estimate a complex time series signal, where the estimated complex time series signal is taken as a result of having reproduced a complex time series signal that was used to generate the optical signal.

Description

Technical Field

[0001] The present disclosure relates to coherent communication, and more specifically to a coherent optical receiver that regenerates an optical complex signal without using a local carrier light.

Background Art

[0002] With the explosive increase in communication traffic accompanying the spread of smartphones and the Internet, further increases in the capacity of optical communication are progressing. To meet such requirements, in optical communication, coherent transmission and reception technologies based on wavelength, polarization, and spatial multiplexing technologies that utilize the parallelism of light and multilevel modulation technologies that utilize complex spaces have attracted attention.

[0003] FIG. 1(a) is a schematic diagram of a general wavelength division multiplexing (WDM) coherent communication system. In a general WDM coherent communication system, optical signals of a plurality of wavelengths respectively modulated by I / Q (In-phase / Quadrature) modulators that constitute coherent optical transmitters (Transmitter: TX) 101-1 to 101-N are multiplexed (wavelength multiplexed) by an optical multiplexer (multiplexer: MUX) circuit 102 (for example, an arrayed waveguide grating (AWG), etc.) and sent to the receiving side via an optical transmission line 103. The integer N is the number of wavelengths to be wavelength multiplexed. On the receiving side, each wavelength signal is demultiplexed (wavelength separated) by an optical demultiplexer (demultiplexer: DEMUX) circuit 104 (for example, an AWG, etc.), and a plurality of optical signals demultiplexed for each wavelength are respectively demodulated by coherent optical receivers 105-1 to 105-N. The signals demodulated by the coherent optical receivers 105-1 to 105-N are processed by digital signal processing (Digital Signal Processing: DSP) devices 106-1 to 106-N.

[0004] FIG. 1(b) is a configuration diagram of a general coherent optical receiver (RX) 105. In coherent optical receivers (RX) 105-1 to 105-N, in order to interfere and reproduce the optical signals 107-1 to 107-N modulated in the complex space, high-precision optical interference systems 109-1 to 109-N called 90° hybrids, laser light sources 108-1 to 108-N that generate narrow linewidth and highly stable local carrier light, and balanced photodetectors (Photodetector: PD) 110-1 to 110-N are required. Typically, the balanced photodetector 110 connected to one optical interference system 109 is composed of a set of a plurality of PDs. Therefore, compared with direct detection using intensity modulation, the device configuration of the coherent optical receiver 105 becomes complicated. Also, digital signal processing devices 106-1 to 106-N corresponding to each of the coherent optical receivers 105-1 to 105-N are required for distortion compensation and determination of each signal.

[0005] As an optical recovery method that does not use local carrier light, a method of diffusing an optical signal using a multimode fiber or the like is known (see, for example, Non-Patent Document 1). By using a two-dimensional PD array, the signals diffused in the time and space directions are oversampled to demodulate the signals.

Prior Art Documents

Non-Patent Documents

[0006]

Non-Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0007] However, in the conventional optical restoration method that does not use local carrier light, since the diffusion coefficient is treated as a known value, it is necessary to separately measure or set a plurality of hyperparameters. Further, in a configuration using a multimode fiber, the diffusion coefficient is not stable over time due to the bending or vibration of the optical fiber, and it is necessary to measure the diffusion coefficient many times.

[0008] The present disclosure has been made in view of such problems, and an object thereof is to provide a coherent optical receiver that reproduces an optical complex signal used when generating an optical signal in a coherent optical transmitter without using local carrier light.

Means for Solving the Problems

[0009] In order to achieve such an object, an embodiment of the present invention is a coherent optical receiver that reproduces a complex time series signal used for generating the received optical signal from the optical signal received via an optical transmission line, and includes an optical convolution circuit that optically processes the received optical signal, a photodetector that converts the optically processed optical signal into an electrical signal of the intensity waveform of the optically processed optical signal, and a demodulation algorithm that digitally processes the electrical signal to estimate a complex time series signal, and the estimated complex time series signal is used as a result of reproducing the complex time series signal used for generating the optical signal.

[0010] According to the coherent optical receiver of an embodiment of the present invention, it is possible to reproduce the optical complex signal used when generating an optical signal in an optical transmitter by using an optical operation on an optical signal in an optical circuit and a digital operation based on the intensity of the optically operated optical signal.

[0011] According to the present disclosure, since it is possible to diffuse an optical signal using a highly stable optical waveguide, it has an excellent feature that once the diffusion coefficient (corresponding to the impulse response h in the following description) is determined, it is not necessary to update it. Further, according to the digital operation algorithm of the present disclosure, it is possible to determine the diffusion count without prior knowledge.

Brief Description of the Drawings

[0012]

Figure 1

Figure 2

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Figure 7

Figure 8

Embodiments for Carrying Out the Invention

[0013] Hereinafter, embodiments of the present invention will be described with reference to the drawings. The same or similar reference numerals in the drawings indicate the same or similar elements, and redundant descriptions may be omitted. In the following description, the coherent optical transmitter may be referred to as TX, and the coherent optical receiver may be referred to as RX.

[0014] (First Embodiment) Referring to FIG. 2, a coherent optical receiver according to the first embodiment 1 will be described. FIG. 2 is a schematic diagram of a WDM coherent optical communication system including the coherent optical receiver according to this embodiment. In this embodiment, a method is provided for estimating the complex signal of a single coherent optical transmitter (TX) 210 from the intensity waveform of a single PD234 of a coherent optical receiver (RX) 230. The I / Q modulator 211 of the TX210 on the transmission side modulates light of a predetermined wavelength based on the complex time-series signal u(t) to generate an optical signal. The optical signals of a plurality of wavelengths modulated from a plurality of TX210s are wavelength multiplexed by an optical MUX (not shown) and sent to the RX230 on the reception side via the optical transmission line 220. The RX230 receives an optical signal of a specific wavelength separated by wavelength by an optical demultiplexer (not shown). The optical signal transmitted and received between the TX210 and the RX230 via the optical transmission line 220 may or may not be wavelength multiplexed. The coherent optical receiver of this embodiment may be used in a coherent optical communication system that does not include an optical MUX and an optical demultiplexer.

[0015] The RX230 includes an optical convolution circuit 233 that optically processes an optical signal of a specific wavelength separated by wavelength, a photodetector (PD) 234 that detects the optical signal from the optical convolution circuit 233, and a demodulation algorithm 235 that digitally processes the electrical signal converted from the optical signal by the PD234. The demodulation algorithm 235 executes the operations described later.

[0016] In the RX230, the complex time-series signal u(t) introduced into the received optical signal undergoes a conversion corresponding to Equation (1) via the optical convolution circuit 233.

Equation

[0017] Here, h represents the impulse response of the optical convolution circuit 233. θ represents the delay time difference imparted by the delay line of the optical convolution circuit 233, which is equal to the sampling time of PD234 or a time shorter than the sampling time. i represents the number of the branch section of the optical convolution circuit 233. * represents the symbol of the convolution operation. Equation (1) is equivalent to the input signal u being convolved by a one-dimensional kernel filter with impulse response h.

[0018] The optical convolution circuit 233 includes an optical waveguide made of a light-transmitting material such as quartz glass or silicon as a component. The optical convolution circuit 233 includes at least one optical branching section, an optical delay line connected to the output of the optical branching section, at least one optical combining section connected to the optical delay line, and a phase shifter disposed in part or all of the optical delay line. The optical convolution circuit 233 may include a variable attenuator disposed in part or all of the optical delay line. The optical delay line imparts a delay difference corresponding to the sampling time θ to the optical signal branched at the branching section. The impulse response h is determined by the branching ratio of each branching section that is a component of the optical convolution circuit 233, the length of the optical delay line, the phase imparted to the optical signal by the phase shifter, or the attenuation amount imparted by the variable attenuator. It is also possible to adjust the branching ratio and phase by arranging a Mach-Zehnder interferometer (MZI) or the like in each of the branching section, the delay line, and the combining section, and make the impulse response h variable. The impulse response h may be a random number sequence. The impulse response h of the random number sequence can be realized by designing or setting the phase difference between the arms of the MZI constituting the optical convolution circuit 233 (that is, the phase difference imparted by the phase shifter 303 disposed in the optical delay line 302), the attenuation amount in the variable attenuator 304, and the branching ratio of the branching section 301 according to random numbers.

[0019] With reference to FIGS. 3 and 4, a more specific and preferable configuration of the optical convolution circuit 233 will be described.

[0020] Fig. 3(a) shows the functional configuration of an optical circuit that can be used as the optical convolution circuit 233, which is an optical circuit that functions as a finite impulse response (FIR) filter. The optical circuit shown in Fig. 3(a) has a configuration in which M stages of branching sections that split light are connected. A phase shifter 303 and a variable attenuator 304 are arranged on an optical delay line 302 connected to one of the two outputs of the branching section 301. The other delay line where the phase shifter 303 and the variable attenuator 304 are not arranged is connected to the next branching section 301. For the M-th stage branching section 301, phase shifters 303 and variable attenuators 304 are arranged on both of the two outputs. The two optical delay lines 302 are configured such that the delay difference applied between the lights guiding them is θ. The lights branched by the M branching sections 301 are given a total delay difference of Mθ and are output from the combining section 305. The delay differences of the lights sequentially output from the combining section 305 are such that the delay difference between the first output light and the second output light is the minimum value (θ), and the delay difference between the first output light and the last output light is the maximum value (Mθ). The lights branched by the M branching sections 301 are sequentially output from the combining section 305 without overlapping each other.

[0021] Fig. 3(b) shows an example of an optical circuit with a functional configuration equivalent to an FIR filter, which is an optical circuit that functions as a transversal filter. In the optical circuit shown in Fig. 3(b), phase shifters 303 and variable attenuators 304 are arranged on all of the M optical delay lines 302 connected to the M outputs of the branching section 301 that splits light into M branches. The two adjacent optical delay lines 302 are configured such that the delay difference applied between the lights guiding them is θ. The delay difference applied between the lights guiding the two most distant optical delay lines 302 is Mθ. The lights that have propagated through the M optical delay lines 302 are output from the combining section 305. The delay differences of the lights sequentially output from the combining section 305 are such that the delay difference between the first output light and the second output light is the minimum value (θ), and the delay difference between the first output light and the last output light is the maximum value (Mθ). The lights branched into M branches by the branching section 301 are sequentially output from the combining section 305 without overlapping each other.

[0022] FIG. 3(c) is an optical circuit that can be used as the optical convolution circuit 233 and functions as an M-stage lattice filter. In the optical circuit shown in FIG. 3(c), phase shifters 303 and variable attenuators 304 are arranged on both of two optical delay lines 302 connected to two outputs of a branching section 301 that branches light. The two optical delay lines 302 are configured such that the delay difference imparted between the guided lights is θ. The lights that have propagated through the two optical delay lines 302 are sequentially output from a combining section 305 and input to the branching section 301 of the next stage. The minimum delay difference of the lights output from the combining section 305 at the M-th stage is θ, and the maximum delay difference is Mθ. The delay differences of the lights sequentially output from the combining section 305 at the M-th stage are such that the delay difference between the light output first and the light output second is the minimum value (θ), and the delay difference between the light output first and the light output last is the maximum value (Mθ). The lights branched by the M branching sections 301 do not overlap with each other and are sequentially output from the combining section 305 at the M-th stage.

[0023] The optical circuit that can be used as the optical convolution circuit 233 can also be implemented using an MZI and a delay line.

[0024] Figure 4(a) shows an implementation example (when M = 4) of an optical circuit having the function of a transversal filter. The optical circuit is a planar Lightwave Circuit (PLC), and each component includes an optical waveguide formed on a substrate. As shown in Figure 4(a), the optical circuit is configured with an optical splitter 301a as a branching section 301 that branches the input light into four, and an optical coupler 305a as a combining section 305. The optical splitter 301a, the optical coupler 305a, and the four optical waveguides between the output of the optical splitter 301a and the input of the optical coupler 305a form an MZI, and the arm waveguides of the MZI form an optical delay line 302. A phase shifter 303 and a variable attenuator 304 are arranged in the optical delay line 302. Each of the four optical delay lines 302 imparts different delays (0, θ, 2θ, Mθ) to the guided light. Therefore, the delay differences between the light propagating through the topmost arm waveguide and the light propagating through the second to Mth arm waveguides from the top are different from each other. The light branched into four by the optical splitter 301a constituting the branching section 301 is sequentially output from the optical coupler 305a constituting the combining section 305 without overlapping each other. In the optical coupler 305a shown in Figure 4(a), the light that has been phase-shifted by the phase shifter 303 and attenuated by the variable attenuator 304 is emitted from the lower output.

[0025] Also, when an attenuator is used in the optical circuit, optical power is lost, leading to deterioration of the signal-to-noise ratio (S / N ratio). Therefore, the branching section 301 of the optical circuits shown in Figures 3(a), 3(b), and 3(c) may be configured with a variable optical splitter to eliminate the variable attenuator 304. This brings out the excellent advantage that optical signals can be convolved without loss of principle.

[0026] Figure 4(b) is an optical circuit that can be used as the optical convolution circuit 233, and is a modified example of an optical circuit having the function of the transverse filter of Figure 4(a). In the optical circuit of Figure 4(b), the optical splitter 301a that constitutes the branching section 301 for branching the input optical signal shown in Figure 4(a) into four is replaced with a variable optical splitter 301b, making the branching ratio variable. Also, in the optical circuit of Figure 4(b), the optical coupler 305a that constitutes the combining section 305 shown in Figure 4(a) is replaced with a variable optical coupler 305b, making the combining ratio variable. The variable optical splitter 301b, the variable optical coupler 305b, and the four optical waveguides between the output of the variable optical splitter 301b and the input of the variable optical coupler 305b form an MZI, and the arm waveguides of the MZI form the optical delay line 302. A phase shifter 303 is arranged in the optical delay line 302. In the optical circuit of Figure 4(b), the variable attenuator 304 of Figure 4(a) is eliminated. Each of the four optical delay lines 302 imparts different delays (0, θ, 2θ, Mθ) to the guided light. Therefore, the delay differences between the light propagating in the top arm waveguide and the light propagating in the second to Mth arm waveguides from the top are different from each other. The light branched into four by the variable optical splitter 301b that constitutes the branching section 301 is sequentially output from the variable optical coupler 305b that constitutes the combining section 305 without overlapping each other.

[0027] Referring again to Figure 2, since the optical signal s(t) converted by the optical convolution circuit 233 is square-law detected by the PD 234, it undergoes the conversion as shown in Equation (3) and becomes the intensity signal I(t). This intensity signal I(t) has lost the intensity information due to the square-law detection.

Equation

[0028] Based on I(t) from the optical convolution circuit 233, the demodulation algorithm 235 estimates the complex time-series signal u(t) used when generating the optical signal by the I / Q modulator 211 on the input side, and the demodulated complex time-series signal u estObtain \(u(t)\). By minimizing the cost function \(L\) described by the following equation (3), a plausibly estimated demodulated complex signal can be obtained. The smaller the difference between the intensity signal \(I(t)\) of the optical signal received in the optical convolution circuit 233, which is the measurement result of PD234, and the intensity signal of the estimated demodulated complex signal, the more plausibly estimated \(u(t)\) is, and thus it can be said that the complex time series signal \(u(t)\) has been restored. est \(u(t)\) can be said to be more plausibly estimated, and thus it can be said that the complex time series signal \(u(t)\) has been restored.

Number

[0029] To minimize \(L\), it is preferable to obtain the gradient in the direction in which \(L\) decreases and use a gradient descent algorithm such as the steepest descent method. However, since \(L\) includes an operation to obtain the absolute value of a complex number, the derivative of equation (3) cannot be calculated to obtain the gradient in the direction in which \(L\) decreases. Therefore, a method (Wirtinger-flow) of calculating the Wirtinger derivative of \(L\) and minimizing \(L\) is considered. This method obtains a plausibly estimated \(u(t)\) asymptotically by repeating the following equation (4) \(n\) times. est \(u(t)\) is obtained.

Number

[0030] Here, the integer \(n\) is the number of repetitions, \(h^H\) is the Hermitian conjugate of \(h\), and \(\lambda(n)\) is a variable representing how much to update in the gradient direction at each step. By updating the demodulated complex time series signal \(u(t)\) based on equation (4), \(L\) can be minimized and restored to the original complex time series signal \(u(t)\). On the other hand, since the dimension of \(u(t)\) is higher than that of \(I\), there are multiple candidate solutions for \(L\). To solve the above problem, a pilot tone is given, and \(u(t)\) obtained at each step * is \(h^H\), and \(\lambda(n)\) is a variable representing how much to update in the gradient direction at each step. By updating the demodulated complex time series signal \(u(t)\) based on equation (4), \(L\) can be minimized and restored to the original complex time series signal \(u(t)\). On the other hand, since the dimension of \(u(t)\) is higher than that of \(I\), there are multiple candidate solutions for \(L\). To solve the above problem, a pilot tone is given, and \(u(t)\) obtained at each step est can minimize \(L\) and be restored to the original complex time series signal \(u(t)\). On the other hand, since the dimension of \(u(t)\) is higher than that of \(I\), there are multiple candidate solutions for \(L\). To solve the above problem, a pilot tone is given, and \(u(t)\) obtained at each step est has a higher dimension than \(I\), so there are multiple candidate solutions for the solution of \(L\). To solve the above problem, a pilot tone is given, and \(u(t)\) obtained at each step estIt may also be substituted. The pilot tone may transmit a known signal from TX210 to RX230 and use this as the pilot tone. As a result, excellent effects such as obtaining u closer to u are exhibited. Also, when measuring the intensity signal I at PD234, sampling may be performed at a rate higher than the symbol rate of the complex time-series signal u used on the input side (for example, θ / 2, θ / 4). As a result, the dimension of the intensity signal I can be made larger than the dimension of the complex time-series signal u, so excellent effects such as obtaining a demodulated complex time-series signal u closer to u are exhibited. est est est As a result, excellent effects such as obtaining u closer to u are exhibited.

[0031] The above algorithm uses the Hermitian conjugate h of the impulse response h of the optical convolution circuit 233 and the variable λ(n) representing the degree of update in the gradient direction in Equation (4) as parameters. Therefore, it is necessary to measure h with high precision in advance to obtain h and determine λ(n) empirically. Here, by regarding Equation (4) as a unit of the neural network and regarding the number of steps n as the number of layers, h and λ(n) can be optimized from the learning data. * * * *

[0032] Figure 5 is a diagram showing the configuration of the demodulation algorithm 235. The demodulation algorithm 235 is composed of, for example, a computer having a processor and a memory storing a program. By causing the processor to execute the program, the operation of a neural network with Equation (4) as a unit is executed.

[0033] The demodulation algorithm 235 is configured such that the intensity signal I(t), which is the result of square-law detection by PD234, is input. The intensity signal I(t) is supplied to the learnable phase recovery model together with the initial value u of the demodulated complex time-series signal u. The initial values of h and λ are also the initial value u. est est 0 est est 0 estand is supplied to a learnable phase recovery model. Each layer in the learnable phase recovery model is a layer in a Wirtinger-flow based network and performs the operation of Equation (4). The Tanh operation may be omitted in each layer. The estimated demodulated complex time series signal u, which is the operation result of the learnable phase recovery model est is compared with the teacher data d, and the difference (Loss(d, u est )) is calculated. The teacher data d can be the original complex time series signal u. Information δ corresponding to the difference (Loss(d, u est )) is fed back and used as the initial value in the next operation. The information δ is the updated h and λ. The smaller the difference (Loss(d, u est )) is, the more it can be said that h is sufficiently optimized. The optimized h is used in the operation of the subsequent demodulated complex time series signal u est .

[0034] As a result, excellent features such as being able to estimate the original complex time series signal u by obtaining a plausible demodulated complex time series signal u est without the need for prior knowledge of h and λ(n) in advance are exhibited. Here, in order to reduce the calculation and the number of learning data, it is preferable that the parameters of each layer of the neural network are common to all layers. Although Figure 5 describes in the time domain, the input signal may be Fourier-transformed and described in the frequency domain.

[0035] (Second Embodiment) In the first embodiment, the optical convolution circuit 233 has one input port for inputting one optical signal of a specific wavelength among a plurality of optical signals wavelength-separated by the optical DEMUX, and one output port for outputting the intensity signal I supplied to the PD234. The optical convolution circuit may have a plurality of input ports and a plurality of output ports.

[0036] Referring to Fig. 6, a coherent optical receiver according to the second embodiment will be described. Fig. 6 shows a configuration example of an N×K optical convolution circuit 500 having N input ports and K output ports as a modification of the optical convolution circuit 233. The optical convolution circuit of this embodiment includes an N-input J-output N×J optical cross-connect 501, a J-input K-output J×K optical cross-connect 502, J optical delay lines 302 connecting the J output ports of the N×J optical cross-connect 501 and the J input ports of the J×K optical cross-connect 502, and phase shifters 303 and variable attenuators 304 arranged in each optical delay line 302. The integer N is the number of wavelengths multiplexed in the WDM coherent communication system. J and K are integers equal to or greater than N.

[0037] The J optical delay lines 302 are configured such that the delay difference between adjacent optical delay lines is θ. The delay difference imparted between the lights guided by the two most distant optical delay lines 302 is Jθ.

[0038] The N×J optical cross-connect 501 distributes the N optical signals wavelength-separated from the WDM signal by the optical DEMUX respectively input from the N input ports to the J output ports.

[0039] The optical signals distributed to the J output ports are each given a delay difference by the optical delay line 302, given a phase by the phase shifter 303, attenuated by the variable attenuator 304, and input to the J×K optical cross-connect 502.

[0040] The J×K optical cross-connect 502 distributes the input optical signals to the K output ports.

[0041] The N×K optical convolution circuit 500 functions as a transversal filter.

[0042] K PDs 234-1 to 234-K (not shown) are connected to the K output ports of the J×K optical cross-connect 502. The demodulation algorithm 235 executes the following operations on the signals from the K PDs 234-1 to 234-K (not shown).

[0043] The vector s(t) of the optical signals output to each output port of the N×K optical convolution circuit 500 in FIG. 6 is described by the following equation.

Equation

[0044] The vector u(t) is the vector of the complex time-series signals introduced into the optical signals input from each input port of the N×K optical convolution circuit 500. The matrix h is the matrix in which the impulse responses from each input port to each output port of the N×K optical convolution circuit 500 are stored. To realize such a matrix h, for example, the configuration of the transversal filter such as the N×K optical convolution circuit 500 in FIG. 6 may be changed. As described above, by making the distribution ratio from N input ports to J output ports variable in the N×J optical cross-connect 501, the variable attenuator 304 can be eliminated.

[0045] Since the optical signals output from the N×K optical convolution circuit 500 are square-law detected by PD234-1 to 234-K (not shown), they undergo the conversion as in Equation (6) and become intensity signals.

Equation

[0046] This vector signal I(t) has lost the intensity information due to the square-law detection. Based on the vector I(t), the vector u(t) of the complex time-series signals is estimated using the demodulation algorithm 235. This is to read I(t), L, and u in Equation (3) above as vectors and obtain a plausible value by minimizing the cost function L. For the demodulation of this signal, the same configuration as in the first embodiment can be used. That is, the operation of the demodulation algorithm 235 described above may be extended to the operations of vectors and matrices. est By replacing them with vectors and minimizing the cost function L, a plausible value can be obtained. For the demodulation of this signal, the same configuration as in the first embodiment can be used. That is, the operation of the demodulation algorithm 235 described above may be extended to the operations of vectors and matrices.

[0047] (Learning Example) As an example of learning in the demodulation algorithm 235, a simulation was performed for the estimation of a 16QAM signal. The simulation was calculated in the baseband band, ignoring the effects of bandwidth narrowing and group delay by the optical filter in the optical transmission line 220. The Baud-rate of the I / Q modulator 211 of the coherent optical transmitter 210 was set to 32G-Baud. The optical convolution circuit 233 was based on the 32-stage lattice filter configuration shown in Fig. 3(c). The branching section 301 was configured using a variable optical splitter 301b, the merging section 305 was configured using a variable optical coupler 305b, and the variable attenuator 304 was excluded. The optical path length difference (delay difference θ applied to the optical signal) of the two optical delay lines 302 connecting the variable optical splitter 301b and the variable optical coupler 305b was set to half a bit length, and the branching ratio of the variable optical splitter 301b, the merging ratio with the variable optical coupler 305b, and the phase difference applied by the phase shifter 303 were generated using uniform random numbers. PD234 was assumed to oversample the optical signal from the optical convolution circuit 233 at 6 times the Baud-rate of the I / Q modulator 211. 20% of the optical signal transmitted from TX210 was known to RX230, and this known optical signal was used as a pilot tone.

[0048] Fig. 7(a) shows the estimation results when the Wirtnger-flow is used in the demodulation algorithm. The horizontal axis is the number of repetitions per trial, and the vertical axis is the demodulated complex time-series signal u obtained by overwriting 100 trials est and the complex time-series signal u of the original signal, which is the mean square error. The impulse response of the lattice filter in this case was assumed to have been measured in advance, and h and h * were assumed to be known. λ(n) was set from the following empirically obtained equation.

Equation

[0049] However, it was set such that a = 0.5 and T = 100. a and T are hyperparameters.

[0050] Fig. 7(a) shows the demodulated complex time-series signal u at each number of repetitionsest shows the error from the original signal's complex time - series signal u, and Fig. 7(b) shows the estimated demodulated complex time - series signal u with 500 repetitions. est The constellation of is shown. A plurality of combinations of a and T were used to construct λ(n). In any of the λ(n), when the number of repetitions is 500, the mean - square error becomes small, and a more plausible demodulated complex time - series signal u est can be obtained. As can be seen from Fig. 7, by applying this embodiment, an optical signal in the complex space can be demodulated from the intensity signal.

[0051] Next, the case of estimation using the demodulation algorithm 235 that performs the above - described neural network operations with reference to Fig. 5 will be described. The number of layers in the network was set to 300, and to reduce the computational load, the parameters H and λ for each layer were made common throughout the layers. In this case, prior knowledge about h and λ is not required. As described above with reference to Fig. 5, first, h and λ are learned through training, and then the optimized h is used to calculate the demodulated complex time - series signal u est .

[0052] Fig. 8 is a graph showing the mean - square error between the complex time - series signal u and the predicted demodulated complex time - series signal u when learning is performed with the same calculation parameters as above using the demodulation algorithm 235 shown in Fig. 5. Fig. 8 also shows the constellation before learning and the constellation after learning. As can be seen from Fig. 8, the error decreases as learning progresses, indicating that the signal can be restored without prior knowledge in this configuration. est

Industrial Applicability

Industrial Applicability

[0053] It is possible to provide a coherent optical receiver that regenerates the optical complex signal used when generating an optical signal in a coherent optical transmitter without using local - carrier light.

Explanation of Signs

[0054] 101 Coherent optical transmitter 102 Optical MUX Circuit 103 Optical Transmission Line 104 Optical DEMUX Circuit 105 Coherent Optical Receiver 106 Digital Signal Processing Device 107 Optical Signal 108 Laser Light Source 109 Optical Interference System 210 Coherent Optical Transmitter 211 I / Q Modulator 220 Optical Transmission Line 230 Coherent Optical Receiver 233 Optical Convolution Circuit 234 Optical Detector 235 Demodulation Algorithm 301 Branching Section 302 Optical Delay Line 303 Phase Shifter 304 Variable Attenuator 305 Combining Section 301a Optical Splitter 301b Variable Optical Splitter 305a Optical Coupler 305b Variable Optical Coupler 500 Optical Convolution Circuit 501 N×J Optical Cross-Connect 502 J×K Optical Cross-Connect

Claims

1. A coherent optical receiver that regenerates a complex time-series signal used for generating the optical signal from the optical signal received via an optical transmission line, a plurality of optical convolution circuits that optically process the received optical signal, a photodetector that converts the optically processed optical signal into an electrical signal of the intensity waveform of the optically processed optical signal, a demodulation algorithm that digitally processes the electrical signal to estimate the complex time-series signal, and the estimated complex time-series signal is used as a result of regenerating the complex time-series signal used for generating the optical signal and comprising, each of the plurality of optical convolution circuits has a branching section that branches the received optical signal, an optical delay line that imparts different delay differences to the branched optical signals, a phase shifter that imparts a phase to the branched optical signals and is arranged in the optical delay line, an attenuator that imparts attenuation to the branched optical signals and is arranged in the optical delay line, and a merging section connected to the optical delay line and the plurality of optical convolution circuits are connected in cascade. A coherent optical receiver.

2. The coherent optical receiver according to claim 1, wherein the demodulation algorithm is configured to estimate the complex time-series signal by calculating a learning model that takes the electrical signal and the impulse response in the optical convolution circuit as inputs.

3. The coherent optical receiver according to claim 2, wherein the demodulation algorithm is configured to learn the impulse response by calculating the learning model.

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