Multi-user NOMA signal separation method based on VMD
Through the VMD-based signal separation method, the center frequency of the signal components is adaptively adjusted and the IMF decomposition results are optimized, which solves the problem of signal separation accuracy and anti-interference in multi-user NOMA signal separation, and improves the adaptability and feasibility of signal separation.
Patent Information
- Application Number
- CN202510410244.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-04-02
- Publication Date
- 2025-07-08
AI Technical Summary
The existing multi-user NOMA signal separation technology cannot take into account the accuracy and anti-interference of signal separation at the receiving end. Especially in the scenarios of large user scale and rapidly changing user count, the existing methods rely on accurate signal estimation and insufficient anti-noise capability.
Using VMD-based signal separation method, through signal model establishment, VMD decomposition parameter initialization, iterative optimization and signal component recognition, combined with Lagrangian multiplication method and ADMM iterative update, the center frequency of the signal component is adaptively adjusted, the IMF decomposition results are optimized, and the impact of modal aliasing and noise is reduced.
It realizes the accuracy and anti-interference of signal separation under large user scale and rapid changes, improves the adaptability and feasibility of signal separation, and reduces the requirements for accurate signal estimation.
Smart Images
Figure CN120281614A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of signal processing in the field of communications, and particularly relates to a multi-user NOMA signal separation method based on VMD. Background Art
[0002] Currently, in wireless communication systems, non-orthogonal multiple access (NOMA) technology is a multi-user access technology that is becoming increasingly common. This technology enables signals of different users to be multiplexed in non-orthogonal dimensions such as the power domain and the code domain, which can effectively improve the system spectrum efficiency. This multi-user NOMA technology is applicable to scenarios with a large number of users, tight spectrum resources, and high requirements for system capacity, such as large-scale Internet of Things applications in 5G and future communication systems, and has broad application potential. At the same time, with the increase in the number of users, multi-user scenarios have gradually become common.
[0003] Due to the limited nature of wireless communication resources, multi-user signals often transmit simultaneously in a wireless communication system. The signals of different users are intertwined and overlapped in space, forming a complex signal mixture. Therefore, in order to ensure smooth communication and ensure that the signals of each user can be received and processed accurately and without error, multi-user signal separation technology is particularly important.
[0004] The technology for separating multi-user signals obtained through NOMA technology is multi-user NOMA signal separation technology. The principle of this technology is: first, perform superposition coding on the signals at the sending end, and then adopt signal detection and interference cancellation technology at the receiving end to separate the signals of different users. Currently, the research content of this technology mainly focuses on the optimization of resource allocation such as the power at the sending end, ignoring the improvement of the method at the receiving end. The current technology at the receiving end cannot balance the accuracy and anti-interference ability of signal separation in a multi-user scenario, and a method that is adaptive to user signals, can better separate noise, and ensure the accuracy of signal separation is needed.
[0005] The existing signal separation technologies are as follows: based on signal detection algorithms, based on signal processing technologies, and based on machine learning algorithms.
[0006] The signal separation technology based on signal detection algorithms is based on detecting prior information such as the information of the transmitted signal, that is, the user signal, such as power. Specifically, there are serial interference cancellation (SIC) technology, maximum likelihood detection technology, etc. Among them, SIC technology has been widely applied and improved. For example, "An interleaved BCH coding and decoding method for NOMA" was proposed to use a special coding method to assist the error performance during SIC and improve the signal separation performance.
[0007] The signal separation technology based on signal processing methods is to automatically solve the separation scheme through calculations based on the characteristics of the signals themselves, that is, it has adaptability to the signals. Specifically, there are zero-forcing algorithms, singular value decomposition algorithms, etc. To reduce the interference between signals, methods based on the code domain are often used for assistance, that is, different code sequences are assigned to different users for specific encoding to improve the receiver's recognition of signals from different users.
[0008] The signal separation technology based on machine learning algorithms is to let the model directly learn the mapping relationship between the received signals and the transmitted signals. Specifically, there are methods such as deep neural networks.
[0009] However, these three signal separation technologies also have disadvantages:
[0010] The method based on signal detection: It highly depends on the accurate estimation of user signals or accurate channel characteristic information. Otherwise, it is easy to have the problem of error propagation, that is, the separation error of a single user continues to propagate under the iterative separation of subsequent user signals, thus affecting the separation effects of all subsequent users. This will have a large impact range in multi-user scenarios. This method depends on system configuration, such as increasing communication transmission equipment and other means to reduce the complexity of multi-user signals transmitted by a single device.
[0011] The method based on signal processing: It is sensitive to noise, that is, it has weak anti-interference ability. The noise existing in the channel will affect the calculation of each feature of the signal, and the influence of this noise will be amplified in the calculation. Although code domain technology can be used for assistance, the limited code domain resources make it impossible to improve in large user scales.
[0012] The method based on machine learning: It requires a large amount of training data and a long training time, and the interpretability of the model is poor. When the user information changes, it is very likely that the model needs to be retrained or adjusted, and the "black box" nature of the model itself will bring huge challenges.
[0013] Therefore, it is necessary to design a new multi-user NOMA signal separation method to solve the above problems. Summary of the Invention
[0014] An object of the present invention is to propose a multi-user NOMA signal separation method based on VMD to solve at least one of the technical problems existing in the above prior art.
[0015] To achieve the above object, the present invention adopts the following technical solutions:
[0016] A multi-user NOMA signal separation method based on VMD includes the following steps:
[0017] S1, Signal model establishment: Establish multi-user NOMA signals with noise in a real and complex environment, and simultaneously define the theoretical user signals of each one;
[0018] S2, VMD decomposition parameter definition: Initialize the settings for three key parameters, and the decomposition parameters are directly defined as default values;
[0019] S3, VMD decomposition: Obtain the VMD decomposition IMF components based on the method of iterative updating of the optimization objective and variables. During the decomposition process, the center frequencies of each user signal, that is, the signal components, will be roughly set, and the center frequency values of each signal component will be updated according to the characteristics of the multi-user signal itself;
[0020] S4, Optimization of VMD decomposition results: Check and locally optimize the IMF to ensure the separation effect of each IMF component. At the same time, check and locally optimize the signal components containing noise;
[0021] S5, Signal component identification: Determine which user each IMF component belongs to according to the signal characteristics of each IMF component;
[0022] S6, Signal reconstruction: Reconstruct the corresponding signals for different users according to the identification results of each IMF component.
[0023] Preferably, in the signal model construction in S1, let y(t) be the received signal superimposed by multi-user NOMA signals, and K be the number of users. Then the signal model is: Where P k is the user power allocation coefficient, h k is the channel response value, s k (t) is the signal symbol sent by the user at time t, and n(t) is additive white Gaussian noise;
[0024] The model parameters are obtained through actual measurements on the base station side or the user side.
[0025] Preferably, in the VMD decomposition parameter setting in S2, the key parameters are the decomposition layer number, the penalty factor, and the convergence threshold; the decomposition layer number is set to K, that is, the number of users, then the initial VMD decomposition result will have K IMF components; the penalty factor α is determined according to the signal frequency, and the convergence threshold ε is the VMD iteration termination condition.
[0026] Preferably, the VMD decomposition in S3 is an iterative decomposition, and the iterative optimization method is the alternating direction multiplier method, continuously iterating the IMF results until the iteration termination condition is met;
[0027] S31. Frequency band initialization, which is set according to the user power allocation situation. Specifically, the center frequencies of each mode are initialized to correspond to the frequency regions where the energies of different user signals are concentrated; the initial values of each IMF frequency band are denoted as w k, k = 1, 2, ..., K;
[0028] S32. Construct the VMD constrained variational problem, and at the same time require that the sum of all mode functions is equal to the original signal y(t); this constrained variational problem is expressed as:
[0029] At the same time, the constraint condition is where u k (t) represents the IMF, represents the derivative with respect to time t, δ(t) represents the unit impulse function, * represents the convolution calculation, and ||·||2 represents the L2 norm; for this constrained variational problem, by introducing the Lagrange multiplier λ(t), it is transformed into an unconstrained Lagrangian function for solution, and at this time the penalty factor α will be used;
[0030] S33. ADMM iteration. Combining with the Lagrangian function, ADMM iteratively solves the minimum value of the Lagrangian function by alternately updating u k (t), w k and λ(t). The specific steps are as follows: fix w k and λ(t), and let the Lagrangian function be differentiated with respect to u k (t) and set it to zero to obtain the update formula for u k (t); similarly, fix u k (t) and λ(t) to obtain the update formula for w k ; similarly, fix u k (t) and w k , and obtain the update formula for λ(t); thus, continuously update the three variables successively. When the change amount of the IMF between two adjacent iterations is less than the threshold ε, the iterative update process is terminated;
[0031] S34. Output the IMF. After the iteration is terminated, K IMFs will be obtained, that is, {u1(t), u2(t),..., u K (t)}, corresponding to the initial identification IDs of K users, that is, from 1 to K.
[0032] Preferably, in the optimization of the VMD decomposition result in S4, the IMFs with mode mixing and the IMFs with noise are detected; the Pearson correlation coefficient between every two IMFs is calculated by traversing. When the correlation coefficient is greater than 0.8, it is considered that there is mode mixing between the two; if there is mode mixing, compare the amplitudes of the two IMFs, and further separate the IMF with smaller power; when the correlation coefficient is less than 0.3, it is considered that there is noise between the two, and similarly, the IMF with smaller power will be further separated;
[0033] For the IMF that needs further separation, complementary ensemble empirical mode decomposition is used for decomposition; the specific decomposition process is as follows: positive and negative paired white noises are added to the IMF at the same time; denote this IMF as u i (t), then u1 i (t) = u i (t) + n i (t) and u2 i (t) = u i (t) - n i (t); perform empirical mode decomposition on u1 i (t) and u2 i (t) to obtain two sets of IMF component collections; perform ensemble averaging on the IMF components with the same serial number in the two collections to obtain a new IMF collection; the new IMF collection will replace the original small-amplitude IMF result; if the original small-amplitude IMF needs to be further separated because it is determined to contain, then the mean and variance of each IMF in the new IMF collection need to be calculated. If the mean is in [-0.1, 0.1] and the variance is less than then this IMF is determined to be noise and will be removed from the IMF collection.
[0034] Preferably, for the signal component identification in S5, it is determined which user each IMF belongs to by power correlation matching, calculate the power correlation with each IMF, and the IMF with the highest correlation with which user is determined to belong to that user; each IMF has a recalculated identification ID.
[0035] Preferably, for the signal reconstruction in S6: for different users, retrieve their corresponding IMF components and perform linear superposition to obtain the reconstructed signal of that user.
[0036] Compared with the prior art, a multi-user NOMA signal separation method based on VMD provided by the present invention has the following beneficial effects:
[0037] 1. The present invention combines the advantages of the two methods based on signal detection and signal processing, ensures the accuracy and adaptability of signal separation, increases its application feasibility under a large user scale, and can flexibly handle the situation where the number of users is large and changes rapidly.
[0038] 2. The adaptive characteristic of the VMD method can reduce the requirement for accurate signal estimation, lower the application requirement of the multi-user NOMA signal separation technical solution at the receiving end, and optimize the result at the same time to ensure the anti-interference performance of the signal separation result. BRIEF DESCRIPTION OF THE DRAWINGS
[0039] Figure 1 It is a flowchart of the multi-user NOMA signal separation method based on VMD described in the present invention. Detailed implementation manners
[0040] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part rather than all of the embodiments of the present invention.
[0041] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by the terms "upper", "lower", "front", "rear", "left", "right", "top", "bottom", "inner", "outer", etc. is based on the orientation or positional relationship shown in the accompanying drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation to the present invention.
[0042] First, the professional terms in this application are explained:
[0043] NOMA: Non-Orthogonal Multiple Access, is an advanced multiple access technology aiming to improve the spectral efficiency and connection density of wireless communication systems. Different from traditional orthogonal multiple access technologies (such as OFDMA, TDMA, CDMA), NOMA allows multiple users to share communication resources on the same time, frequency, and space resources.
[0044] VMD: Variational Mode Decomposition, is an adaptive signal processing method that decomposes a signal into modal components with finite bandwidth through a variational framework. Its core lies in minimizing the sum of the bandwidths of each mode and using the alternating direction method of multipliers to iteratively update the modes and central frequencies. This method is widely used in fields such as communication signal processing, but it needs to cope with challenges such as complexity and noise sensitivity.
[0045] IMF: Intrinsic Mode Function, in vibration analysis, a signal can be decomposed into multiple intrinsic mode functions (IMFs), and these IMFs represent the natural frequencies and vibration modes of the signal. Each IMF represents an independent vibration mode of the signal.
[0046] Please refer to the attached Figure 1 As shown, this embodiment provides a multi-user NOMA signal separation method based on VMD, including the following steps:
[0047] S1, signal model establishment: Establish a multi-user NOMA signal with noise in a real complex environment, and at the same time define each theoretical user signal;
[0048] S2, Definition of VMD decomposition parameters: Initialize the settings for three key parameters, and the decomposition parameters are directly defined as default values;
[0049] S3, VMD decomposition: Obtain the VMD decomposition IMF components based on the method of iterative update of the optimization objective and variables. During the decomposition process, the center frequencies of each user signal, i.e., signal components, will be roughly set, and the center frequency values of each signal component will be updated according to the characteristics of the multi-user signals;
[0050] S4, Optimization of VMD decomposition results: Check and locally optimize the IMF to ensure the separation effect of each IMF component. At the same time, check and locally optimize the signal components containing noise;
[0051] S5, Signal component identification: Determine which user each IMF component belongs to according to the signal characteristics of each IMF component;
[0052] S6, Signal reconstruction: Reconstruct the corresponding signals for different users according to the identification results of each IMF component.
[0053] In this embodiment, the specific technical process is signal model establishment, VMD decomposition parameter definition, VMD decomposition, VMD decomposition result optimization, signal component identification, signal reconstruction, and performance evaluation. Among them, VMD decomposition obtains the VMD decomposition IMF components based on the method of iterative update of the optimization objective and variables. During the decomposition process, the center frequencies of each user signal, i.e., signal components, will be roughly set to determine the general trend of signal separation. During the decomposition process, the center frequency values of each signal component will be updated according to the characteristics of the multi-user signals to achieve the effect of adaptive adjustment, so that the frequency range of each component is more in line with the actual situation, thereby reducing the workload of accurately estimating the user signals.
[0054] Regarding the optimization of the VMD decomposition results, since one of the key parameters, the penalty factor parameter, may be a non-optimal value, it may cause the problem of mode mixing between IMF components. Therefore, it is necessary to check and locally optimize to ensure the separation effect of each IMF component. At the same time, check and locally optimize the signal components containing noise. Reduce mode mixing and noise to ensure the anti-interference ability of the separation process. The present invention combines the advantages of two methods based on signal detection and signal processing to ensure the accuracy and adaptability of signal separation. The VMD method is widely used in the NOMA signal system, and at the same time, the results are optimized to ensure the anti-interference ability of the signal separation results.
[0055] In a specific embodiment, in the signal model construction in S1, let y(t) be the received signal of the superposition of multi-user NOMA signals, and K be the number of users. Then the signal model is where P k is the user power allocation coefficient, hk is the channel response value (including path loss, shadowing, and multipath fading), s k (t) is the signal symbol sent by the user at time t, and n(t) is the additive white Gaussian noise; here, by reflects the characteristics of power domain multiplexing, and the signals of different users are linearly superimposed to reflect the non-orthogonal characteristics of NOMA. The power allocation coefficient P k The corresponding theoretical user signal is This theoretical user signal is a rough estimate of the user signal.
[0056] The model parameters are obtained through actual measurements on the base station side or the user side. For example, P k can be read from the base station side, and h k can estimate the channel state information through pilot signals in this communication environment or be obtained through actual measurements.
[0057] In a specific embodiment, for the VMD decomposition parameter setting in S2, the key parameters are the decomposition layer number, penalty factor, and convergence threshold; the decomposition layer number is set to K, which is the number of users, so the initial VMD decomposition result will have K IMF components; the penalty factor α depends on the signal frequency, and the larger it is, the narrower the modal bandwidth decomposed. Since the signal is generally in the range of 100 Hz to 10,000 Hz, α can be set to 10 3 . The convergence threshold v is the VMD iteration termination condition, generally set to 10 -6 .
[0058] In a specific embodiment, the VMD decomposition in S3 is an iterative decomposition, and the iterative optimization method is the alternating direction multiplier method, continuously iterating the IMF result until the iteration termination condition is met;
[0059] S31. Frequency band initialization, which is roughly set according to the user power allocation situation. Specifically, the center frequency of each mode is initialized to correspond to the frequency region where the energy of different user signals is concentrated; for example, if the signal energy of user 1 is mainly concentrated in the frequency range from f1 to f2, then and so on. The initial values of each IMF frequency band are denoted as w k , k = 1, 2,..., K;
[0060] S32. Construct the VMD constrained variational problem, with the minimum sum of the bandwidths of each modal function as the optimal objective, and at the same time requiring the sum of all modal functions to be equal to the original signal y(t); this constrained variational problem is expressed as At the same time, the constraint condition is where, u k (t) represents the IMF, Denotes the derivative with respect to time \(t\), \(\delta(t)\) denotes the unit impulse function, \(*\) denotes the convolution operation, and \(\|\cdot\|_2\) denotes the \(L_2\) norm; for this constrained variational problem, by introducing the Lagrange multiplier \(\lambda(t)\), it is transformed into an unconstrained Lagrangian function for solution, and at this time the penalty factor \(\alpha\) will be used;
[0061] S33. ADMM iteration. Combining with the Lagrangian function, ADMM iteratively solves for the minimum value of the Lagrangian function by alternately updating \(u\) k (t), \(w\) k and \(\lambda(t)\). The specific steps are as follows: fixing \(w\) k and \(\lambda(t)\), taking the partial derivative of the Lagrangian function with respect to \(u\) k (t) and setting it to zero to obtain the update formula for \(u\) k (t); similarly, fixing \(u\) k (t) and \(\lambda(t)\) to obtain the update formula for \(w\) k ; similarly, fixing \(u\) k (t) and \(w\) k to obtain the update formula for \(\lambda(t)\); thus, continuously update the three variables successively. When the change amount of the IMF between two adjacent iterations is less than the threshold \(\varepsilon\), the iterative update process is terminated;
[0062] S34. Output the IMF. After terminating the iteration, \(K\) IMFs will be obtained, namely \(\{u_1(t), u_2(t), \cdots, u\) K (t)\}, corresponding to the initial identification IDs of \(K\) users, namely from 1 to \(K\).
[0063] In a specific embodiment, in the optimization of the VMD decomposition result in S4, the IMFs with mode mixing and the IMFs with noise are detected; calculate the Pearson correlation coefficient between every two IMFs traversally. When the correlation coefficient is greater than 0.8, it is considered that there is mode mixing between the two; if there is mode mixing, compare the amplitudes of the two IMFs. The IMF with the larger amplitude is considered to be the user signal with higher power and higher signal-to-noise ratio, and the IMF with smaller power is further separated; when the correlation coefficient is less than 0.3, it is considered that there is noise between the two, and similarly, the IMF with smaller power will be further separated;
[0064] For the IMFs that need to be further separated, complementary ensemble empirical mode decomposition is used for decomposition; the specific decomposition process is as follows: add positive and negative paired white noises to this IMF at the same time, noting that the energy of this white noise should be as small as possible and should not significantly affect this IMF component; denote this IMF as \(u\) i (t), then \(u_1\) i (t) = \(u\) i (t) + \(n\) i (t) and \(u_2\) i (t) = \(u\) i(t) - n i (t); for u1 i (t) and u2 i (t) is subjected to empirical mode decomposition to obtain two sets of IMF component collections; the IMF components with the same serial number in the two sets are averaged to obtain a new IMF set; the new IMF set will replace the original small - amplitude IMF results; if the original small - amplitude IMF needs to be further separated because it is determined to contain [noise], then the mean and variance of each IMF in the new IMF set need to be calculated. If the mean is in the range of [-0.1, 0.1] and the variance is less than then the IMF is determined to be noise and will be removed from the IMF set.
[0065] In a specific embodiment, for the signal component identification in S5, it is determined which user each IMF belongs to by power correlation matching. Here, power correlation matching means using the known power distribution coefficient P k corresponding theoretical user signal That is calculate the power correlation with each IMF. The IMF with the highest correlation with a certain user is determined to belong to that user. Therefore, each IMF, including the new IMF generated during the optimization process, will have a recalculated identification ID. If there is no corresponding IMF for a certain user in this calculation, then the results of the initial identification ID will be followed to match the IMF of that user, and the other users cannot be reconstructed through the IMF of that user (including its optimized IMF set).
[0066] In a specific embodiment, for the signal reconstruction in S6: for different users, retrieve their corresponding IMF components and perform linear superposition to obtain the reconstructed signal of that user.
[0067] The above is only the preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, according to the technical solution and inventive concept of the present invention, makes equivalent substitutions or changes, and all should be covered by the protection scope of the present invention.
Claims
1. A multi-user NOMA signal separation method based on VMD, characterized in that: It includes the following steps: S1, Signal model establishment: Establish a multi-user NOMA signal with noise in a real complex environment, and at the same time define the theoretical user signals of each user; S2, VMD decomposition parameter definition: Initialize the settings for three key parameters, and the decomposition parameters are directly defined as default values; S3, VMD decomposition: Obtain the VMD decomposition IMF components through an optimization objective and variable iterative update method. During the decomposition process, the center frequencies of each user signal, that is, the signal components, will be roughly set, and the center frequency values of each signal component will be updated according to the characteristics of the multi-user signal itself; S4, Optimization of VMD decomposition results: Check and locally optimize the IMF to ensure the separation effect of each IMF component, and at the same time check and locally optimize the signal components containing noise; S5, Signal component identification: Determine which user each IMF component belongs to according to the signal characteristics of each IMF component; S6, Signal reconstruction: Reconstruct the corresponding signals for different users according to the identification results of each IMF component.
2. The multi-user NOMA signal separation method based on VMD according to claim 1, wherein: In the signal model construction in S1, let y(t) be the received signal of the superimposed multi-user NOMA signal, and K be the number of users. Then the signal model is as follows: where P k is the user power allocation coefficient, h k is the channel response value, s k (t) is the signal symbol sent by the user at time t, and n(t) is the additive white Gaussian noise; The model parameters are obtained through on-site measurement on the base station side or the user side.
3. A multi-user NOMA signal separation method based on VMD according to claim 1, characterized in that: In S2, the VMD decomposition parameters are set as three key parameters, which are the decomposition layer number, the penalty factor, and the convergence threshold; the decomposition layer number is set to K, which is the number of users, so the initial VMD decomposition result will have K IMF components; the penalty factor α is determined according to the signal frequency, and the convergence threshold ε is the VMD iteration termination condition.
4. A multi-user NOMA signal separation method based on VMD according to claim 1, characterized in that: In S3, the VMD decomposition is an iterative decomposition, and the iterative optimization method is the alternating direction multiplier method. The IMF results are continuously iterated until the iteration termination condition is met; S31. Band initialization, which is set according to the user power distribution. Specifically, the center frequency of each mode is initialized to correspond to the frequency region where the energy of different user signals is concentrated; the initial value of each IMF band is denoted as w k , k = 1, 2,..., K; S32. Construct the VMD constrained variational problem, and at the same time require that the sum of all mode functions is equal to the original signal y(t); this constrained variational problem is expressed as: At the same time, the constraint condition is where u k (t) represents the IMF, represents the derivative with respect to time t, δ(t) represents the unit impulse function, * represents the convolution calculation, and ||·||2 represents the L2 norm; for this constrained variational problem, by introducing the Lagrange multiplier λ(t), it is transformed into an unconstrained Lagrangian function for solution, and at this time the penalty factor α will be used. S33. ADMM iteration. Combining with the Lagrangian function, ADMM iteratively solves for the minimum value of the Lagrangian function by alternately updating u k (t), w k and λ(t). The specific steps are as follows: Fix w k and λ(t), and take the partial derivative of the Lagrangian function with respect to u k (t) and set it to zero to obtain the update formula for u k (t); Similarly, fix u k (t) and λ(t) to obtain the update formula for w k ; Similarly, fix u k (t) and w k to obtain the update formula for λ(t); Thus, continuously update the three variables successively. When the change amount of the IMF between two adjacent iterations is less than the threshold ε, terminate the iterative update process; S34. Output the IMFs. After the iteration is terminated, K IMFs will be obtained, namely {u1(t), u2(t),..., u K (t)}, corresponding to the initial identification IDs of K users, namely from 1 to K respectively.
5. A multi-user NOMA signal separation method based on VMD according to claim 1, characterized in that: In S4, for the optimization of the VMD decomposition results, the IMFs with mode mixing and the IMFs with noise are detected; the Pearson correlation coefficient between every two IMFs is calculated traversally. When the correlation coefficient is greater than 0.8, it is considered that there is mode mixing between the two; if there is mode mixing, compare the amplitudes of the two IMFs, and further separate the IMF with smaller power; when the correlation coefficient is less than 0.3, it is considered that there is noise between the two, and similarly, the IMF with smaller power will be further separated; For the IMF that needs further separation, complementary ensemble empirical mode decomposition is used for decomposition; the specific decomposition process is as follows: positive and negative paired white noises are added to the IMF at the same time; denote the IMF as u i (t), then u1 i (t) = u i (t) + n i (t) and u2 i (t) = u i (t) - n i (t); perform empirical mode decomposition on u1 i (t) and u2 i (t) to obtain two sets of IMF component collections; perform ensemble averaging on the IMF components with the same serial number in the two sets to obtain a new IMF set; the new IMF set will replace the original small-amplitude IMF result; if the original small-amplitude IMF needs further separation because it is determined to contain [noise], then the mean and variance of each IMF in the new IMF set need to be calculated. If the mean is in [-0.1, 0.1] and the variance is less than then the IMF is determined to be noise and will be removed from the IMF set.
6. A multi - user NOMA signal separation method based on VMD according to claim 1, characterized in that: In S5, for signal component identification, it is judged which specific user each IMF belongs to through power correlation matching. Calculate the power correlation with each IMF, and the IMF is judged to belong to the user with which it has the highest correlation; each IMF has a recalculated identification ID.
7. A multi-user NOMA signal separation method based on VMD according to claim 1, characterized in that: In S6, for signal reconstruction: For different users, retrieve their corresponding IMF components and perform linear superposition to obtain the reconstructed signal of this user.