Noise reduction method, system and device based on adaptive cascaded empirical mode decomposition

Abstract

The present invention discloses a noise reduction method, system and device based on adaptive cascaded empirical mode decomposition, which relates to the field of optical fiber communication. The method mainly includes determining the linear reconstruction coefficient of each signal component based on the signal components obtained through empirical mode decomposition and the adaptive multi-segment linear reconstruction coefficient function, thereby obtaining an initial noise reduction signal; determining the parameter update amount of the adaptive multi-segment linear reconstruction coefficient function based on the error value of the initial noise reduction signal; determining the linear reconstruction coefficient of each phase component based on the initial noise reduction signal and the adaptive phase linear reconstruction coefficient function, thereby obtaining complex-valued signals under different amplitude numbers; determining the parameter update amount of the adaptive phase linear reconstruction coefficient function based on the error of each complex-valued signal; when all parameter update amounts are less than a set threshold, combining and outputting the complex-valued signals under different amplitude numbers, otherwise returning to the initial step. The present invention can solve the noise problem faced by optical transmission signals at the receiving end.

Description

Technical Field

[0001] The present invention relates to the field of optical fiber communications, and in particular to a noise reduction method, system and device based on adaptive cascaded empirical mode decomposition. Background Art

[0002] With the advent of the information age, fiber-optic communication systems are continuously developing towards longer distances and higher capacity. However, fiber-optic communication systems are subject to various noises, including amplifier spontaneous emission (ASE), linewidth-induced phase noise, and nonlinear noise. This noise, in turn, significantly interferes with the sampling decision and subsequent digital signal processing at the receiver, potentially leading to severe bit errors. Therefore, noise reduction solutions for ASE, phase noise, and nonlinear noise are currently a hot topic of research. Currently, a common approach in fiber-optic communication systems is to perform a short-time Fourier transform on the signal and filter out some of the noise using a frequency-domain filter. However, this still leaves residual noise in the same frequency domain as the signal, and phase noise and nonlinear noise cannot be effectively reduced. Commonly used methods for phase noise include the Viterbi-Viterbi phase estimation (VVPE) algorithm and the blind phase estimation (BPS) algorithm. The VVPE algorithm is only applicable to the QPSK modulation format, while the BPS algorithm can be used for modulation formats of any order. However, its high computational complexity and large amount of computation make it unsuitable for fiber-optic communication systems sensitive to computational complexity. For nonlinear noise, various solutions have been proposed, including digital backpropagation (DBP) and nonlinear compensation based on Volterra series. However, their high complexity has hindered their practical deployment. Furthermore, noise reduction algorithms based on artificial intelligence (AI) deep learning have also been widely researched in recent years. While these algorithms offer excellent noise reduction and can simultaneously reduce multiple types of noise, they require significant time and sample training, making them unsuitable for fiber-optic communication systems, where the communication environment changes rapidly. Summary of the Invention

[0003] The purpose of the present invention is to provide a noise reduction method, system and device based on adaptive cascaded empirical mode decomposition to solve the noise problems faced by optical transmission signals at the receiving end, including: the noise reduction algorithm based on Fourier transform cannot take into account the processing of phase noise and nonlinear noise, and after processing, noise in the same frequency domain as the signal remains; the filtering or compensation algorithm for phase noise and nonlinear noise has a high complexity after cascading, and is not suitable for optical fiber communication systems that are sensitive to computational complexity; the noise reduction algorithm based on artificial intelligence deep learning requires a lot of time and samples to train it, and is not suitable for optical fiber communication systems with rapidly changing information environments.

[0004] To achieve the above object, the present invention provides the following solutions:

[0005] In a first aspect, the present invention provides a noise reduction method based on adaptive cascaded empirical mode decomposition, comprising:

[0006] Performing empirical mode decomposition on an initial target signal to obtain multiple signal components; wherein, in a first iteration, the initial target signal is a signal obtained by processing an original signal received at a receiving end in an optical fiber communication system after clock recovery, dispersion compensation, signal equalization, and frequency offset estimation;

[0007] Determining a linear reconstruction coefficient for each of the signal components according to an adaptive multi-segment linear reconstruction coefficient function, and determining an initial noise reduction signal according to each of the signal components and the corresponding linear reconstruction coefficient;

[0008] Determining an update amount of each slope of the adaptive multi-segment linear reconstruction coefficient function according to an error value of the initial noise reduction signal;

[0009] Classifying the initial noise reduction signal according to the signal amplitude to obtain signal phases under different amplitude numbers, and performing empirical mode decomposition on the signal phases under different amplitude numbers to obtain multiple phase components under each amplitude number; wherein one signal amplitude corresponds to one or more amplitude numbers;

[0010] Determining a linear reconstruction coefficient for each phase component according to an adaptive phase linear reconstruction coefficient function, and determining a reconstructed signal phase for each amplitude sequence number according to each phase component and the corresponding linear reconstruction coefficient;

[0011] Obtaining complex-valued signals under different amplitude numbers according to the reconstructed signal phase and the corresponding signal amplitude, and determining an update amount for each coefficient in the adaptive phase linear reconstruction coefficient function according to errors of the complex-valued signals under different amplitude numbers;

[0012] According to the amplitude sequence number, the complex-valued signals under different amplitude sequences are combined to obtain a combined complex-valued signal;

[0013] When a set condition is met, the combined complex-valued signal is determined as the final noise reduction signal; wherein the set condition is that the update amount of each slope is less than the corresponding set threshold and the update amount of each coefficient is less than the corresponding set threshold;

[0014] When the set conditions are not met, the combined complex-valued signal is determined as the initial target signal, the adaptive multi-segment linear reconstruction coefficient function is updated according to the update amount of each slope, the adaptive phase linear reconstruction coefficient function is updated according to the update amount of each coefficient, and the initial target signal is returned to perform empirical mode decomposition to obtain multiple signal components.

[0015] In a second aspect, the present invention provides a noise reduction system based on adaptive cascaded empirical mode decomposition, comprising:

[0016] a signal component determination module, configured to perform empirical mode decomposition on an initial target signal to obtain multiple signal components; wherein, in a first iteration, the initial target signal is a signal obtained by processing an original signal received at a receiving end in an optical fiber communication system through clock recovery, dispersion compensation, signal equalization, and frequency offset estimation;

[0017] an initial noise reduction signal determination module, configured to determine a linear reconstruction coefficient of each of the signal components according to an adaptive multi-segment linear reconstruction coefficient function, and determine an initial noise reduction signal according to each of the signal components and the corresponding linear reconstruction coefficient;

[0018] A slope update amount determination module, configured to determine an update amount of each slope in the adaptive multi-segment linear reconstruction coefficient function according to an error value of the initial noise reduction signal;

[0019] a phase component determination module, configured to classify the initial noise reduction signal according to the signal amplitude to obtain the signal phases under different amplitude sequence numbers, and perform empirical mode decomposition on the signal phases under different amplitude sequence numbers to obtain multiple phase components under each amplitude sequence number; wherein one signal amplitude corresponds to one or more amplitude sequence numbers;

[0020] A signal phase reconstruction module, configured to determine a linear reconstruction coefficient for each phase component according to an adaptive phase linear reconstruction coefficient function, and determine a reconstructed signal phase for each amplitude sequence number according to each phase component and the corresponding linear reconstruction coefficient;

[0021] A coefficient update amount determination module is used to obtain complex-valued signals under different amplitude sequence numbers based on the reconstructed signal phase and the corresponding signal amplitude, and determine the update amount of each coefficient in the adaptive phase linear reconstruction coefficient function based on the error of the complex-valued signals under different amplitude sequence numbers;

[0022] The complex-valued signal combination module is used to combine the complex-valued signals with different amplitude numbers according to the amplitude numbers to obtain the combined complex-valued signal;

[0023] a result determination module, configured to determine the combined complex-valued signal as a final noise reduction signal when a set condition is met; wherein the set condition is that the update amount of each slope segment is less than a corresponding set threshold and the update amount of each coefficient is less than a corresponding set threshold;

[0024] The jump module is used to determine the combined complex-valued signal as the initial target signal when the set conditions are not met, update the adaptive multi-segment linear reconstruction coefficient function according to the update amount of each slope, update the adaptive phase linear reconstruction coefficient function according to the update amount of each coefficient, and return to the signal component determination module.

[0025] In a third aspect, the present invention provides an electronic device comprising a memory and a processor, wherein the memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to perform the denoising method based on adaptive cascaded empirical mode decomposition according to the first aspect.

[0026] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0027] The present invention is based on the cascade of empirical mode decomposition and linear reconstruction (i.e., an adaptive multi-segment linear reconstruction coefficient function and a phase linear reconstruction coefficient function), thereby filtering out ASE noise, phase noise, and nonlinear noise from the signal. In addition, a feedback mechanism is introduced to adjust the key parameters of the adaptive multi-segment linear reconstruction coefficient function and the adaptive phase linear reconstruction coefficient function by monitoring the error changes, thereby further improving the filtering effect of the noise component and thus improving the system transmission performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0029] Figure 1 A schematic diagram of a process flow of a noise reduction method based on adaptive cascaded empirical mode decomposition provided by an embodiment of the present invention;

[0030] Figure 2 A flowchart of a receiving end provided in an embodiment of the present invention; wherein the noise reduction module is an implementation module based on the noise reduction method described in the present invention;

[0031] Figure 3 A flowchart of a noise reduction method based on adaptive cascaded empirical mode decomposition in an optical fiber communication system provided by an embodiment of the present invention;

[0032] Figure 4 A flowchart of the first linear reconstruction provided by an embodiment of the present invention;

[0033] Figure 5An image of an adaptive multi-segment linear reconstruction coefficient function for a standard square 64QAM signal provided by an embodiment of the present invention;

[0034] Figure 6 A flowchart of phase linear reconstruction provided by an embodiment of the present invention;

[0035] Figure 7 An image of an adaptive phase linear reconstruction coefficient function for a standard square 64QAM signal provided by an embodiment of the present invention;

[0036] Figure 8 A schematic structural diagram of a noise reduction system based on adaptive cascaded empirical mode decomposition provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0037] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0038] The present invention provides a noise reduction method, system, and device based on adaptive cascaded empirical mode decomposition, which are applied in optical fiber communication systems. The first-level noise reduction based on empirical mode decomposition uses a multi-segment linear reconstruction coefficient function, which is applicable to multi-level high-order modulation formats. While filtering out ASE noise with Gaussian distribution characteristics, it also takes into account the characteristic that nonlinear noise varies with signal energy, thus having the ability to filter out ASE noise and some nonlinear noise. The second-level noise reduction based on empirical mode decomposition on the signal phase can effectively filter out phase noise and some nonlinear noise contained in the signal. Furthermore, the present invention implements adaptive updating of the linear reconstruction coefficient function based on the signal error after noise reduction, which can effectively optimize the reconstruction ratio of each component after decomposition and improve the algorithm's noise filtering effect.

[0039] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0040] Example 1

[0041] like Figure 1 As shown, the denoising method based on adaptive cascaded empirical mode decomposition provided by the embodiment of the present invention includes:

[0042] Step 100: Perform empirical mode decomposition on the initial target signal to obtain multiple signal components; wherein, in the first iteration, the initial target signal is a signal obtained by processing the original signal received at the receiving end in the optical fiber communication system after clock recovery, dispersion compensation, signal equalization and frequency offset estimation.

[0043] Step 200: Determine the linear reconstruction coefficient of each signal component according to the adaptive multi-segment linear reconstruction coefficient function, and determine the initial noise reduction signal according to each signal component and the corresponding linear reconstruction coefficient.

[0044] Step 300: Determine the update amount of each slope of the adaptive multi-segment linear reconstruction coefficient function according to the error value of the initial noise reduction signal.

[0045] Step 400: Classify the initial noise reduction signal according to the signal amplitude to obtain signal phases under different amplitude numbers, and perform empirical mode decomposition on the signal phases under different amplitude numbers to obtain multiple phase components under each amplitude number; wherein one signal amplitude corresponds to one or more amplitude numbers.

[0046] Step 500: Determine the linear reconstruction coefficient of each phase component according to the adaptive phase linear reconstruction coefficient function, and determine the reconstructed signal phase under each amplitude sequence number according to each phase component and the corresponding linear reconstruction coefficient.

[0047] Step 600: Obtain complex-valued signals under different amplitude numbers according to the reconstructed signal phase and the corresponding signal amplitude, and determine the update amount of each coefficient in the adaptive phase linear reconstruction coefficient function according to the error of the complex-valued signals under different amplitude numbers.

[0048] Step 700: Combining complex-valued signals with different amplitude numbers according to the amplitude numbers to obtain a combined complex-valued signal.

[0049] Step 800: When a set condition is met, the combined complex-valued signal is determined as the final noise reduction signal; wherein the set condition is that the update amount of each slope segment is less than the corresponding set threshold and the update amount of each coefficient is less than the corresponding set threshold.

[0050] Step 900: When the set conditions are not met, the combined complex-valued signal is determined as the initial target signal, the adaptive multi-segment linear reconstruction coefficient function is updated according to the update amount of each slope, the adaptive phase linear reconstruction coefficient function is updated according to the update amount of each coefficient, and the process returns to step 100.

[0051] In this embodiment of the present invention, step 100 specifically includes:

[0052] The initial target signal is divided into I and Q paths and empirical mode decomposition is performed to obtain multiple signal components corresponding to each signal path.

[0053] An example: First, find all the extreme points of the signal to be decomposed (the original signal); second, fit the upper envelope through all the maximum points, and fit the lower envelope through all the minimum points; then calculate the mean envelope (the mean of the upper and lower envelopes); then subtract the mean envelope from the original signal to obtain an intermediate signal; if the intermediate signal meets the two constraints of the intrinsic mode function (IMF), it is used as an IMF component; if it does not meet the constraints, find the extreme points again and iterate repeatedly; when an IMF component is obtained, use the current mean envelope as the original signal to continue decomposing to obtain the next IMF component, and stop decomposing when the residual component is a monotonic function or a constant. Finally, multiple IMF components and a residual are obtained, and the calculation formula is as follows:

[0054]

[0055] Among them, X(t) is the original signal, IMF k (t) is the kth IMF component, M-1 is the total number of IMF components, M is the number of components, r(t) is the residual, and t represents different moments.

[0056] During the process, the two constraints of the intrinsic mode function (IMF) are as follows:

[0057] (1) The number of local extreme points and the number of zero crossing points of the function must be equal or differ by at most one in the entire time range;

[0058] (2) At any point in time, the average of the envelope of the local maximum (upper envelope) and the envelope of the local minimum (lower envelope) must be zero.

[0059] In this embodiment of the present invention, step 200 specifically includes:

[0060] The root mean square value of each signal component is calculated, and a linear reconstruction coefficient for each signal component is determined based on the root mean square value of the signal component and the adaptive multi-segment linear reconstruction coefficient function. Each signal component is then multiplied by the corresponding linear reconstruction coefficient, and then superimposed and normalized to obtain an initial noise reduction signal.

[0061] An example: The IMF components and residuals obtained after the empirical mode decomposition of the signal are regarded as signal components, and the root mean square of the time series of each signal component is calculated. The calculation formula is as follows:

[0062]

[0063] Among them, x i(n) is the i-th signal component, RMS i is the RMS value of the i-th signal component, n represents different sampling points, and N represents the total number of sampling points.

[0064] Substitute the root mean square of different signal components into the adaptive multi-segment linear reconstruction coefficient function to obtain the linear reconstruction coefficient A corresponding to each signal component i Wherein, the adaptive multi-segment linear reconstruction coefficient function is:

[0065]

[0066] f(RMS i ) represents the linear reconstruction coefficient of the i-th signal component, RMS i represents the root mean square value of the i-th signal component. Let k j (j=1,2,...,m) represents the slope of the adaptive multi-segment linear reconstruction coefficient function in different segments, k1 and k m The initial value of is set to 0, and the rest of the initial values ​​are set to l j (j=1,2,...,m) represents different level values, then I1, I2, I3, I4, I m-1 , I m Indicates different level values; m indicates the total number of levels, k1, k2, k3, k4, k m Indicates the slope of different segments.

[0067] In this embodiment of the present invention, step 300 specifically includes:

[0068] The mean square error of the initial noise reduction signal at different levels is calculated, and the update amount of each slope in the adaptive multi-segment linear reconstruction coefficient function is determined according to the mean square error of the initial noise reduction signal at different levels.

[0069] An example: Multiply the time series of each signal component by its linear reconstruction coefficient and superimpose them, then normalize them to obtain the reconstructed signal, that is, the initial noise reduction signal, which is expressed as follows:

[0070]

[0071] Among them, X rec (n) represents the reconstructed signal, |·| represents the absolute value, and mean(·) represents the mean.

[0072] The mean square error of the reconstructed signal at different levels is calculated according to the following formula:

[0073]

[0074] in, Indicates level is lj The mean square error of the reconstructed signal is Indicates that the level after judgment is l j The reconstructed signal.

[0075] The adaptive multi-segment linear reconstruction coefficient function is updated according to the mean square error of the reconstructed signal at different levels. The specific update formula is as follows:

[0076]

[0077]

[0078] Where Δq j Indicates the change in the slope of different segments of the adaptive multi-segment linear reconstruction coefficient function, represents the variable in the next iteration, · Represents the variable in the previous iteration, μ is the step size, and represents the influence of the error on the parameter change in each iteration.

[0079] In this embodiment of the present invention, step 400 specifically includes:

[0080] The initial noise reduction signals of the I and Q paths are synthesized to obtain a synthesized signal. The synthesized signal is classified according to the signal amplitude to obtain the signal phases under different amplitude numbers. The signal phases with different amplitude numbers are subjected to empirical mode decomposition. The IMF components and residuals obtained by the decomposition are regarded as signal phase components, and multiple phase components under each amplitude number are obtained.

[0081] In this embodiment of the present invention, step 500 specifically includes:

[0082] The root mean square value of each phase component is calculated, and the linear reconstruction coefficient of each phase component is calculated according to the root mean square value of the phase component and the adaptive phase linear reconstruction coefficient function; then, each phase component under the same amplitude sequence number is multiplied by the corresponding linear reconstruction coefficient, and then superimposed and normalized in sequence to obtain the reconstructed signal phase under each amplitude sequence number.

[0083] An example: Calculate the RMS of the time series of each phase component using the following formula:

[0084]

[0085] in, (c=1,2,...,N c ) represents the i-th phase component of the signal phase with amplitude number c, N c is the number of standard constellation point amplitudes under the transmission signal modulation format; Represents the RMS value of the i-th phase component of the signal phase with amplitude number c.

[0086] Substitute the RMS of different phase components into the adaptive phase linear reconstruction coefficient function to obtain the linear reconstruction coefficient corresponding to each phase component

[0087] The specific expression of the adaptive phase linear reconstruction coefficient function is as follows:

[0088]

[0089] Where, f(RMS i ) represents the linear reconstruction coefficient of the i-th phase component of the signal phase with amplitude number c; a c 、b c The coefficients of the adaptive phase linear reconstruction coefficient function corresponding to the signal phase with amplitude ordinal number c are also the parameters to be iteratively trained in the adaptive phase linear reconstruction coefficient function. The initial values ​​are set as 0.

[0090] The time series of each phase component is multiplied by its linear reconstruction coefficient and then superimposed, and then normalized to obtain the reconstructed signal phase, which is expressed as follows:

[0091]

[0092] in, Represents the phase of the reconstructed signal.

[0093] In the embodiment of the present invention, determining the update amount of each coefficient in the adaptive phase linear reconstruction coefficient function according to the error of the complex-valued signal under different amplitude sequence numbers in step 600 specifically includes:

[0094] The mean square error of the complex-valued signal under different amplitude numbers is calculated, and the update amount of each coefficient in the adaptive phase linear reconstruction coefficient function under different amplitude numbers is determined according to the mean square error of the complex-valued signal.

[0095] An example: Based on the original signal amplitude and the reconstructed signal phase, calculate the complex signal with amplitude order c after phase noise reduction

[0096] The mean square error of the complex-valued signal under different amplitude numbers is calculated according to the following formula:

[0097]

[0098] in, Represents a complex-valued signal The decision value, MSE cis a complex-valued signal with amplitude order c The mean square error of .

[0099] The adaptive phase linear reconstruction coefficient function is updated according to the mean square error of the complex-valued signal under different amplitude numbers. The update formula is as follows:

[0100]

[0101] Δa c =a c -μ a ×(MSE c - MSE c )×a c

[0102]

[0103] Δb c =b c -μ b ×(MSE c - MSE c )×b c

[0104] Where Δa c , Δb c For each iteration a c 、b c The change in μ a 、μ b is parameter a c 、b c The step size represents the influence of the error on the parameter change in each iteration.

[0105] Preferably, based on the receiving end module of the present invention, the signal processing module therein performs signal processing in the following order: coherent receiving module, clock recovery module, dispersion compensation module, channel equalization module and noise reduction module, wherein the noise reduction scheme used by the noise reduction module is a noise reduction algorithm based on adaptive cascaded empirical mode decomposition in an optical fiber communication system proposed by the present invention.

[0106] Example 2

[0107] In the standard square 64QAM system, the levels are set to ±7, ±5, ±3, and ±1, and the structure of the receiving module used is as follows: Figure 2 As shown, after coherent reception and signal clock recovery, dispersion compensation and channel equalization, the Figure 3 The process shown here performs noise reduction on the signal, including the following steps:

[0108] Step 1: Perform empirical mode decomposition on the signal after clock recovery, dispersion compensation, signal equalization, and frequency offset estimation, and obtain multiple intrinsic mode function components and a residual in the I and Q paths respectively, both of which are used as signal components x i (n), i is the ordinal number of the signal component, and n represents different sampling points;

[0109] Step 2: Based on Figure 4 As shown in the process, calculate the root mean square of multiple components obtained by signal decomposition in step 1 above and substitute them into Figure 5 The adaptive multi-segment reconstruction coefficient function shown determines the linear reconstruction coefficient A i , the specific expression of the function is as follows:

[0110]

[0111] Among them, RMS i is the root mean square value of the i-th component, k j (j=1,2,...,8) represents the slope of different segments of the adaptive multi-segment linear reconstruction coefficient function. The initial values ​​of k1 and k8 are set to 0, and the initial values ​​of the others are set to

[0112] According to the following formula, multiple components are linearly combined with different coefficients to reconstruct the initial noise reduction signal:

[0113]

[0114] Among them, M is the number of components, X rec (n) represents the reconstructed signal, |·| represents the absolute value,

[0115] mean(·) means taking the mean.

[0116] At this time, the change in the parameters in the multi-segment reconstruction coefficient function is calculated according to the following formula, and the multi-segment reconstruction coefficient function is updated:

[0117]

[0118]

[0119] in, Indicates level is l j The mean square error of the reconstructed signal, Indicates that the level after judgment is l j The reconstructed signal, Δq j Indicates the change in the slope of different segments of the adaptive multi-segment linear reconstruction coefficient function, represents the variable in the next iteration, ·Represents the variable in the previous iteration, μ is the step size, and represents the influence of the error on the parameter change in each iteration.

[0120] Step 3: The I / Q signals after the initial noise reduction in step 2 are synthesized into complex-valued signals. Then, all signals are classified with the amplitude of the standard square 64QAM as a reference. The signal phases at different amplitudes are extracted for empirical mode decomposition. The intrinsic mode function components and residuals at different amplitudes are obtained as signal phase components. (c=1,2,...,N c ), where c is the amplitude ordinal number, N c is the number of standard constellation point amplitudes under the transmission signal modulation format;

[0121] Step 4: Based on Figure 6 As shown in the process, first calculate the root mean square of the signal components under different amplitudes, and substitute the root mean square of the signal components under different amplitudes into Figure 7 The adaptive phase reconstruction coefficient function shown determines the linear reconstruction coefficient The specific expression of the phase reconstruction coefficient function is as follows:

[0122]

[0123] in, represents the root mean square value corresponding to the i-th component, a c 、b c are the parameters to be iteratively trained in the adaptive phase linear reconstruction coefficient function, and their initial values ​​are set as 0.

[0124] Multiple components of the same amplitude are linearly combined with different coefficients according to the following formula to reconstruct the signal phase under multiple amplitudes

[0125]

[0126] According to the original signal amplitude and the reconstructed signal phase, the complex signal with amplitude order c after phase noise reduction is calculated.

[0127] At this time, the change in the parameters in the phase reconstruction coefficient function is calculated according to the following formula, and the phase reconstruction coefficient function is updated:

[0128]

[0129] Δa c =a c -μ a ×(MSE c - MSE c )×a c

[0130]

[0131] Δb c =b c -μ b ×(MSE c - MSE c )×b c

[0132] in, is the mean square error of the signal with amplitude number c, express The decision value, Δa c , Δb c For each iteration a c 、b c The change in μ a 、μ b is parameter a c 、b c The step size represents the influence of the error on the parameter change in each iteration.

[0133] Step 5: Determine whether the absolute values ​​of the updated parameters in the adaptive multi-segment reconstruction coefficient function and the adaptive phase reconstruction coefficient function are both less than a set threshold. If so, output a noise reduction signal; if not, repeat steps 1 to 5.

[0134] Example 3

[0135] To achieve the above objectives, the embodiment of the present invention provides a noise reduction system based on adaptive cascaded empirical mode decomposition, such as Figure 8 Shown, including:

[0136] Signal component determination module 1 is configured to perform empirical mode decomposition on an initial target signal to obtain multiple signal components; wherein, in a first iteration, the initial target signal is a signal obtained by processing an original signal received at a receiving end in an optical fiber communication system after clock recovery, dispersion compensation, signal equalization, and frequency offset estimation;

[0137] an initial noise reduction signal determination module 2, configured to determine a linear reconstruction coefficient of each of the signal components according to an adaptive multi-segment linear reconstruction coefficient function, and determine an initial noise reduction signal according to each of the signal components and the corresponding linear reconstruction coefficient;

[0138] A slope update amount determination module 3 is used to determine the update amount of each slope in the adaptive multi-segment linear reconstruction coefficient function according to the error value of the initial noise reduction signal;

[0139] Phase component determination module 4, configured to classify the initial noise reduction signal according to the signal amplitude to obtain the signal phases under different amplitude numbers, and perform empirical mode decomposition on the signal phases under different amplitude numbers to obtain multiple phase components under each amplitude number; wherein one signal amplitude corresponds to one or more amplitude numbers;

[0140] A signal phase reconstruction module 5 is configured to determine a linear reconstruction coefficient for each phase component according to an adaptive phase linear reconstruction coefficient function, and determine a reconstructed signal phase for each amplitude sequence number according to each phase component and the corresponding linear reconstruction coefficient;

[0141] A coefficient update amount determination module 6 is used to obtain complex-valued signals under different amplitude sequence numbers based on the reconstructed signal phase and the corresponding signal amplitude, and determine the update amount of each coefficient in the adaptive phase linear reconstruction coefficient function based on the error of the complex-valued signals under different amplitude sequence numbers;

[0142] The complex-valued signal combining module 7 is used to combine the complex-valued signals with different amplitude numbers according to the amplitude numbers to obtain a combined complex-valued signal;

[0143] A result determination module 8 is configured to determine the combined complex-valued signal as a final noise reduction signal when a set condition is met; wherein the set condition is that the update amount of each slope segment is less than the corresponding set threshold and the update amount of each coefficient is less than the corresponding set threshold;

[0144] Jump module 9 is used to determine the combined complex-valued signal as the initial target signal when the set conditions are not met, update the adaptive multi-segment linear reconstruction coefficient function according to the update amount of each slope, update the adaptive phase linear reconstruction coefficient function according to the update amount of each coefficient, and return to the signal component determination module.

[0145] Example 4

[0146] An embodiment of the present invention provides an electronic device, including a memory and a processor, wherein the memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to perform the denoising method based on adaptive cascaded empirical mode decomposition according to the first embodiment.

[0147] After performing clock recovery, dispersion compensation, channel equalization, and frequency offset estimation on the signal obtained by photoelectric detection in the optical fiber communication system, the present invention first decomposes it into multiple eigenmode functions and a residual through empirical mode decomposition, calculates the root mean square of the above multiple components, and determines the reconstruction coefficients of different components based on the root mean square value of each component and the adaptive multi-segment reconstruction coefficient function, thereby performing linear reconstruction to obtain an initial denoised signal, and at the same time, updates the adaptive multi-segment reconstruction coefficient function based on the signal error after denoising; then, the initial denoised signal is divided according to the amplitude, and empirical mode decomposition is performed on the signal phase of different constellation circles respectively. The root mean square of different components is calculated again, and linear reconstruction is performed based on the reconstruction coefficient determined by the adaptive phase reconstruction coefficient function to obtain a denoised phase, which is synthesized with the signal amplitude to form a phase-denoised signal, and at the same time, the adaptive phase reconstruction coefficient function is updated based on the signal error after phase denoising; the above process is repeated many times until the parameters of the two reconstruction coefficient functions tend to be stable, thereby achieving the optimal noise reduction effect. The present invention realizes noise reduction processing of the signal in the time domain based on empirical mode decomposition, and designs and cascades the reconstruction coefficient function according to the actual signal modulation format, which can better highlight the effective signal part and filter out various types of noise in the signal including amplifier noise, phase noise, and nonlinear noise; in addition, the present invention realizes the adaptation of the reconstruction coefficient function according to the signal error after noise reduction, which can effectively optimize the reconstruction coefficient function and improve the noise reduction performance of the algorithm.

[0148] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0149] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only intended to help understand the method and core concept of the present invention. At the same time, those skilled in the art will find that the specific implementation methods and application scopes may vary based on the concept of the present invention. In summary, the contents of this specification should not be construed as limiting the present invention.

Claims

1. A noise reduction method based on adaptive cascaded empirical mode decomposition, characterized in that: include: Performing empirical mode decomposition on an initial target signal to obtain multiple signal components; wherein, in a first iteration, the initial target signal is a signal obtained by processing an original signal received at a receiving end in an optical fiber communication system after clock recovery, dispersion compensation, signal equalization, and frequency offset estimation; Determining a linear reconstruction coefficient for each of the signal components according to an adaptive multi-segment linear reconstruction coefficient function, and determining an initial noise reduction signal according to each of the signal components and the corresponding linear reconstruction coefficient; Determining an update amount of each slope of the adaptive multi-segment linear reconstruction coefficient function according to an error value of the initial noise reduction signal; Classifying the initial noise reduction signal according to the signal amplitude to obtain signal phases under different amplitude numbers, and performing empirical mode decomposition on the signal phases under different amplitude numbers to obtain multiple phase components under each amplitude number; wherein one signal amplitude corresponds to one or more amplitude numbers; Determining a linear reconstruction coefficient for each phase component according to an adaptive phase linear reconstruction coefficient function, and determining a reconstructed signal phase for each amplitude sequence number according to each phase component and the corresponding linear reconstruction coefficient; Obtaining complex-valued signals under different amplitude numbers according to the reconstructed signal phase and the corresponding signal amplitude, and determining an update amount for each coefficient in the adaptive phase linear reconstruction coefficient function according to errors of the complex-valued signals under different amplitude numbers; According to the amplitude sequence number, the complex-valued signals under different amplitude sequences are combined to obtain a combined complex-valued signal; When a set condition is met, the combined complex-valued signal is determined as the final noise reduction signal; wherein the set condition is that the update amount of each slope is less than the corresponding set threshold and the update amount of each coefficient is less than the corresponding set threshold; When the set conditions are not met, the combined complex-valued signal is determined as the initial target signal, the adaptive multi-segment linear reconstruction coefficient function is updated according to the update amount of each slope, the adaptive phase linear reconstruction coefficient function is updated according to the update amount of each coefficient, and the initial target signal is returned to perform empirical mode decomposition to obtain multiple signal components.

2. The noise reduction method based on adaptive cascaded empirical mode decomposition according to claim 1, characterized in that: Perform empirical mode decomposition on the initial target signal to obtain multiple signal components, including: The initial target signal is divided into I and Q paths and empirical mode decomposition is performed to obtain multiple signal components corresponding to each signal path.

3. The noise reduction method based on adaptive cascaded empirical mode decomposition according to claim 1, characterized in that: Determining a linear reconstruction coefficient for each of the signal components according to an adaptive multi-segment linear reconstruction coefficient function, and determining an initial noise reduction signal according to each of the signal components and the corresponding linear reconstruction coefficient, specifically including: Calculating a root mean square value of each of the signal components; Determining a linear reconstruction coefficient for each of the signal components based on a root mean square value of the signal component and an adaptive multi-segment linear reconstruction coefficient function; After multiplying each of the signal components with the corresponding linear reconstruction coefficient, superposition and normalization processing are performed in sequence to obtain an initial noise reduction signal.

4. The noise reduction method based on adaptive cascaded empirical mode decomposition according to claim 1 or 3, characterized in that: The adaptive multi-segment linear reconstruction coefficient function is: Among them, f(RMS i ) represents the linear reconstruction coefficient of the i-th signal component, RMS i Represents the root mean square value of the i-th signal component, I1, I2, I3, I4, I m-1 , I m Indicates different level values; m indicates the total number of levels, k1, k2, k3, k4, k m Indicates the slope of different segments.

5. The noise reduction method based on adaptive cascaded empirical mode decomposition according to claim 1, characterized in that: Determining an update amount of each slope of the adaptive multi-segment linear reconstruction coefficient function according to the error value of the initial noise reduction signal specifically includes: Calculate the mean square error of the initial noise reduction signal at different levels; The update amount of each slope of the adaptive multi-segment linear reconstruction coefficient function is determined according to the mean square error of the initial noise reduction signal at different levels.

6. The noise reduction method based on adaptive cascaded empirical mode decomposition according to claim 1, characterized in that: Determining a linear reconstruction coefficient for each phase component according to an adaptive phase linear reconstruction coefficient function, and determining a reconstructed signal phase for each amplitude sequence number according to each phase component and the corresponding linear reconstruction coefficient, specifically including: Calculating a root mean square value of each phase component; Calculating a linear reconstruction coefficient of each phase component according to the root mean square value of the phase component and an adaptive phase linear reconstruction coefficient function; After multiplying each phase component under the same amplitude sequence number by the corresponding linear reconstruction coefficient, superposition and normalization processing are performed in sequence to obtain the reconstructed signal phase under each amplitude sequence number.

7. The denoising method based on adaptive cascaded empirical mode decomposition according to claim 1 or 6, characterized in that: The adaptive phase linear reconstruction coefficient function specifically includes: Among them, f(RMS i ) represents the linear reconstruction coefficient of the i-th phase component of the signal phase with amplitude number c; a c 、b c Represents the coefficient of the adaptive phase linear reconstruction coefficient function corresponding to the signal phase with amplitude order number c; Represents the RMS value of the i-th phase component of the signal phase with amplitude number c.

8. The noise reduction method based on adaptive cascaded empirical mode decomposition according to claim 1, characterized in that: Determining the update amount of each coefficient in the adaptive phase linear reconstruction coefficient function according to the error of the complex-valued signal under different amplitude sequence numbers specifically includes: Calculate the mean square error of complex-valued signals under different amplitude numbers; According to the mean square error of the complex-valued signal, the update amount of each coefficient in the adaptive phase linear reconstruction coefficient function under different amplitude sequence numbers is determined.

9. A noise reduction system based on adaptive cascaded empirical mode decomposition, characterized in that: include: a signal component determination module, configured to perform empirical mode decomposition on an initial target signal to obtain multiple signal components; wherein, in a first iteration, the initial target signal is a signal obtained by processing an original signal received at a receiving end in an optical fiber communication system through clock recovery, dispersion compensation, signal equalization, and frequency offset estimation; an initial noise reduction signal determination module, configured to determine a linear reconstruction coefficient of each of the signal components according to an adaptive multi-segment linear reconstruction coefficient function, and determine an initial noise reduction signal according to each of the signal components and the corresponding linear reconstruction coefficient; A slope update amount determination module, configured to determine an update amount of each slope in the adaptive multi-segment linear reconstruction coefficient function according to an error value of the initial noise reduction signal; a phase component determination module, configured to classify the initial noise reduction signal according to the signal amplitude to obtain the signal phases under different amplitude sequence numbers, and perform empirical mode decomposition on the signal phases under different amplitude sequence numbers to obtain multiple phase components under each amplitude sequence number; wherein one signal amplitude corresponds to one or more amplitude sequence numbers; A signal phase reconstruction module, configured to determine a linear reconstruction coefficient for each phase component according to an adaptive phase linear reconstruction coefficient function, and determine a reconstructed signal phase for each amplitude sequence number according to each phase component and the corresponding linear reconstruction coefficient; A coefficient update amount determination module is used to obtain complex-valued signals under different amplitude sequence numbers based on the reconstructed signal phase and the corresponding signal amplitude, and determine the update amount of each coefficient in the adaptive phase linear reconstruction coefficient function based on the error of the complex-valued signals under different amplitude sequence numbers; The complex-valued signal combination module is used to combine the complex-valued signals with different amplitude numbers according to the amplitude numbers to obtain the combined complex-valued signal; a result determination module, configured to determine the combined complex-valued signal as a final noise reduction signal when a set condition is satisfied; wherein the set condition is that the update amount of each slope segment is less than a corresponding set threshold and the update amount of each coefficient is less than a corresponding set threshold; The jump module is used to determine the combined complex-valued signal as the initial target signal when the set conditions are not met, update the adaptive multi-segment linear reconstruction coefficient function according to the update amount of each slope, update the adaptive phase linear reconstruction coefficient function according to the update amount of each coefficient, and return to the signal component determination module.

10. An electronic device, characterized in that: The electronic device comprises a memory and a processor, wherein the memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to perform the denoising method based on adaptive cascaded empirical mode decomposition according to any one of claims 1 to 8.

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