A neural network-assisted modulation format recognition method, system and device based on Fourier series characteristics

Abstract

The invention discloses a neural network-assisted modulation format recognition method, system and device based on Fourier series features, belonging to the field of communication technology. The key points of the technical solution are as follows: S1, modulation format-insensitive digital signal processing; S2, histogram statistics of the amplitude of a historical signal set; S3, Fourier series decomposition of a historical amplitude distribution set; S4, training a neural network according to a historical amplitude feature set and a historical label set; S5, generating an actual signal to be recognized; S6, histogram statistics of the amplitude of the actual signal to be recognized to obtain a signal amplitude distribution; S7, Fourier series decomposition of the signal amplitude distribution; S8, inputting the amplitude distribution features into the trained neural network to obtain a corresponding modulation format label, thereby realizing modulation format recognition; the invention can recognize the signal modulation format at the receiving end of an optical fiber communication system within a large signal-to-noise ratio range with low computational complexity, thereby improving the flexibility of the receiver.

Description

Technical Field

[0001] The present invention relates to the field of communication technology, and in particular to a neural network-assisted modulation format recognition method, system and device based on Fourier series features. Background Art

[0002] With the rapid growth of global IP traffic and the increasing demand for diversified data services such as the Internet of Things, big data, cloud computing and streaming media, communication networks urgently need to adaptively adjust bandwidth, modulation format and transmission rate according to the real-time status of communication links and the dynamic needs of user traffic, so as to improve spectrum utilization while meeting users' expectations for service quality at a lower cost. In this context, signal modulation format recognition technology has gradually become a key research direction. The receiver of modern communication systems usually needs to obtain the modulation format of the signal as prior information to ensure that the digital signal processing algorithm can correctly demodulate and restore the transmission sequence. However, due to the dynamic characteristics of communication networks and the requirements for efficient processing, the receiver algorithm must have low complexity characteristics in design. In addition, with the continuous optimization of channel coding and error correction algorithms, the range of communicable signal-to-noise ratios under different modulation formats has further increased, making the modulation format recognition method must be robust to a larger signal-to-noise ratio range. Therefore, a low-complexity modulation format recognition method with high accuracy and a large signal-to-noise ratio range is indispensable.

[0003] At present, researchers have proposed a variety of implementation schemes to meet the needs of modulation format recognition. Non-data-assisted methods identify modulation formats by extracting statistical features such as the cumulative amplitude distribution of the signal, signal power characteristics, and peak-to-average power ratio (PAPR). However, with the continuous optimization of channel coding and error correction technology, the requirements of communication systems for signal-to-noise ratio have gradually decreased, making it difficult for non-data-assisted schemes to meet the actual application needs in low signal-to-noise ratio environments. In addition, machine learning-based schemes such as clustering and convolutional neural networks can improve the accuracy of modulation format recognition to a certain extent, but these schemes usually use the original data or constellation diagram of the signal as input, process a large amount of data, and have high computational complexity, making it difficult to adapt to the requirements of real-time communication scenarios. Another study proposed a shaping signal recognition scheme based on frequency offset loading technology. This method assists recognition by introducing pilot signals, but the loading of pilot signals not only increases the complexity of system implementation, but also occupies a certain amount of spectrum resources, which makes its deployment in actual communication systems have certain limitations.

[0004] In general, there is a contradiction between recognition performance and system complexity in the current modulation format recognition schemes. The non-data-assisted scheme has insufficient performance in a low signal-to-noise ratio environment, the recognition method based on machine learning has a high computational complexity, and the pilot loading technology scheme increases the difficulty of system implementation and spectrum utilization. Therefore, there is an urgent need for a modulation format recognition scheme that can balance high performance and low complexity in a low signal-to-noise ratio environment to meet the needs of actual communication systems. To solve the above problems, we propose a neural network-assisted modulation format recognition method, system and device based on Fourier series features. Summary of the invention

[0005] In view of the deficiencies in the prior art, the present invention provides a method, system and device for neural network-assisted modulation format recognition based on Fourier series features to solve the problems raised in the background technology.

[0006] The above technical objectives of the present invention are achieved through the following technical solutions:

[0007] A neural network-assisted modulation format recognition method based on Fourier series features comprises the following steps:

[0008] S1. Perform modulation format-insensitive digital signal processing on historical signals of various modulation formats and signal-to-noise ratios to generate a historical signal set and a historical label set for modulation format identification;

[0009] S2. Perform histogram statistics on the amplitude of the historical signal set to obtain a historical amplitude distribution set;

[0010] S3, performing Fourier series decomposition on the historical amplitude distribution set, and using the coefficients of each order obtained by the decomposition as the historical amplitude distribution feature set;

[0011] S4, training a neural network based on the historical amplitude feature set and the historical label set;

[0012] S5, performing modulation format-insensitive digital signal processing on the received signal to generate an actual signal to be identified;

[0013] S6. Performing histogram statistics on the amplitude of the actual signal to be identified to obtain signal amplitude distribution;

[0014] S7, performing Fourier series decomposition on the signal amplitude distribution, and using each order coefficient obtained by the decomposition as an amplitude distribution feature;

[0015] S8. Input the amplitude distribution characteristics into the trained neural network to obtain the corresponding modulation format label to realize modulation format recognition.

[0016] Optionally, the amplitude of the historical signal set is histogrammed to obtain a historical amplitude distribution set, which specifically includes:

[0017] For the historical signal set S = {s1(t),s2(t),…,s N (t)}, first for each signal s i (t) Extract the amplitude point by point to obtain the amplitude sequence A i ={|s i (t)||t=1,2,…,T i}, where T i is the number of sampling points of the signal;

[0018] Then, the statistical interval [a min ,a max ], and divide the amplitude range into B equal-width intervals [a k ,a k+1 ), the frequency of occurrence of the statistical amplitude in each interval h i,k , the histogram reflects the distribution trend of the signal amplitude and normalizes it to the probability distribution p i,k :

[0019]

[0020] Finally, the amplitude distribution P of each signal is obtained i ={p i,1 ,p i,2 ,…,p i,B}, used to describe the statistical characteristics of the signal, and the amplitude distribution of all signals is aggregated into the historical amplitude distribution set P set = {P1,P2,…,P N}, avoiding the impact of phase damage on the modulation format recognition performance and providing an input basis for subsequent feature extraction.

[0021] Optionally, the historical amplitude distribution set is decomposed using Fourier series, and the coefficients of each order obtained by the decomposition are used as the historical amplitude distribution feature set, specifically including:

[0022] For the historical amplitude distribution set P set = {P1,P2,…,P N Each amplitude distribution P in i ={p i,1 ,p i,2 ,…,p i,B}, perform Fourier series decomposition one by one. First, calculate the DC component a i,0 , reflecting the overall mean of the amplitude distribution:

[0023]

[0024] Next, calculate the nth order cosine component a i,n and the sine component bi,n , used to capture the periodic nature of the amplitude distribution:

[0025]

[0026] in, represents discrete frequency points, and M is the order of Fourier series truncation. Through these components, we can effectively capture the subtle fluctuations in the signal distribution, and accurately extract the high-dimensional information of the signal amplitude distribution under low signal-to-noise ratio;

[0027] Finally, the Fourier coefficients of each signal are combined into a feature set F i ={a i,0 ,a i,1 ,…,a i,M ,b i,1 ,…,b i,M}, the Fourier feature set of all signals is combined into the historical amplitude distribution feature set F set ={F1,F2,…,F N}, providing feature input for subsequent model training.

[0028] Optionally, a neural network is trained based on the historical amplitude feature set and the historical label set, specifically including:

[0029] Based on the historical amplitude feature set F set ={F1,F2,…,F N} and the corresponding historical label set Y set ={y1,y2,…,y N} as input, train the neural network model, establish the mapping relationship between Fourier features and modulation format labels, and input F i Describes the historical signal amplitude distribution characteristics of the signal, label y i Indicates the modulation format type of the signal;

[0030] First, design the neural network structure, including the input layer, several hidden layers and the output layer. The input layer receives the Fourier feature F i , whose dimension is determined by the order M of the Fourier series, and its magnitude is much smaller than the number of signals, so the scale of the model is very small. The hidden layer extracts the complex relationship between features through nonlinear activation functions, and the output layer generates prediction results according to the number of modulation format categories c;

[0031] During the training phase, the predicted value is calculated using the cross entropy loss function L(Θ) and the true label y i,c The error:

[0032]

[0033] in, is the probability of the c-th modulation format output by the network, is the unique hot encoding representation of the label, and the network weights and biases are iteratively updated through the back propagation algorithm to optimize the network parameters Θ;

[0034] After training, the network can accurately map Fourier features to corresponding modulation format categories, achieving high-precision and low-complexity classification of features over a large signal-to-noise ratio range.

[0035] Optionally, a histogram is performed on the amplitude of the actual signal to be identified to obtain a signal amplitude distribution, specifically including:

[0036] For the actual signal to be identified s real (t), first extract and normalize its amplitude to form the amplitude sequence A real ={|s real (t)||t=1,2,…,T real}, where T real is the number of sampling points of the signal. Amplitude extraction can effectively avoid the influence of phase damage on the modulation format recognition performance.

[0037] Then, the interval boundaries are set according to the amplitude range of the signal [a real,min ,a real,max ] and the number of intervals B real , the interval division usually needs to consider the dynamic range and sampling resolution of the signal to ensure the accuracy of statistics. The amplitude range is divided into B real equal width intervals, and count the frequency of occurrence of the amplitude in each interval h real,k , the formula is:

[0038] h real,k = count(A real ∈[a k ,a k+1 ))

[0039] To convert the frequency distribution to a probability distribution, the frequencies are normalized:

[0040]

[0041] Finally, the amplitude distribution of the signal is obtained It provides the input basis for the subsequent Fourier decomposition step.

[0042] Optionally, Fourier series decomposition is performed on the signal amplitude distribution, and each order coefficient obtained by the decomposition is used as an amplitude distribution feature, specifically including:

[0043] Amplitude distribution of actual signal Perform Fourier series decomposition to extract DC components and high-order components. The DC component areal,0 The calculation is as follows:

[0044]

[0045] The higher-order components include the cosine component a real,n and the sine component b real,n , respectively represent the characteristics of the amplitude distribution in the high-frequency part:

[0046]

[0047] in, The calculation is usually truncated to a specific order M real , to balance the computational complexity and the effectiveness of feature extraction;

[0048] Finally, the calculated coefficients of each order are combined into the amplitude distribution characteristics These features can effectively capture subtle fluctuations in signal distribution and accurately extract high-dimensional information of signal amplitude distribution even under low signal-to-noise ratio.

[0049] Optionally, the amplitude distribution feature is input into the trained neural network to obtain a corresponding modulation format label to implement modulation format recognition, specifically including:

[0050] The amplitude distribution feature F of the actual signal to be identified real Input the trained neural network model, which has learned the mapping relationship between amplitude distribution characteristics and modulation format categories from historical data and has the ability to identify different modulation formats. Since the amplitude distribution characteristics obtained by Fourier series decomposition have a low dimension, the neural network scale is small and the actual processing complexity is very low.

[0051] Input feature F real First, the input layer is processed and mapped to the hidden layer. The hidden layer gradually extracts the key patterns in the features through nonlinear activation functions (such as ReLU, tanh, etc.) and converts them into information related to the classification task. After multi-layer processing, the network output layer generates the predicted probability of each modulation format category. The formula is as follows:

[0052]

[0053] Among them, z real It is the feature representation of the final output of the hidden layer;

[0054] The multi-layer structure of the network is realized through the following recursive relationship:

[0055] h (l) =φ(W (l) ·h (l-1)+b (l) )

[0056] Among them, h (l-1) is the output of the l-1th layer, h (l) is the output of the lth layer; φ is the activation function, which is used to introduce nonlinear characteristics; W (l) and b (l) are the weight matrix and bias vector of the lth layer respectively. The output layer uses the softmax function to convert the output of the network into a probability distribution and predict the probability of each modulation format;

[0057] According to the category label y corresponding to the maximum probability real , and ultimately achieves high-precision and low-complexity modulation format recognition of features under a large signal-to-noise ratio range. This process can run efficiently in real-time communication systems, adapt to dynamic signal environments, and provide guarantees for accurate recognition of modulation formats.

[0058] A neural network-assisted modulation format recognition system based on Fourier series features comprises the following steps:

[0059] Signal receiving module;

[0060] Modulation format insensitive digital signal module;

[0061] Modulation format identification module;

[0062] Modulation format related digital signal processing module;

[0063] Signal output module.

[0064] An electronic device includes 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 execute the above-mentioned neural network-assisted modulation format recognition method based on Fourier series features.

[0065] Optionally, the memory is a non-transitory computer-readable storage medium, and the non-transitory computer-readable storage medium stores a computer program, and when the computer program is executed by the processor, the above-mentioned neural network-assisted modulation format recognition method based on Fourier series features is implemented.

[0066] In summary, the present invention mainly has the following beneficial effects:

[0067] 1. The embodiment of the present invention extracts the amplitude distribution of historical signals of the communication system under different modulation formats and signal-to-noise ratio conditions and generates a historical amplitude distribution feature set through Fourier series decomposition to train a neural network model. Based on the actual signal to be identified, the actual amplitude distribution features are extracted through amplitude distribution histogram statistics and Fourier series decomposition, and the features are input into the trained neural network model to identify the modulation format of the actual signal.

[0068] 2. The present invention captures subtle amplitude distribution fluctuation characteristics through the low-dimensional and high-characterization capability characteristics of the Fourier decomposition coefficients of the amplitude histogram distribution, thereby performing high-precision identification of different modulation formats, and has robustness to noise environments and insensitivity to phase damage.

[0069] 3. Compared with traditional high-complexity algorithms based on machine learning, the present invention is based on an ultra-lightweight network scale, which can significantly reduce computing costs while ensuring recognition accuracy. Through efficient recognition of modulation formats, it can significantly improve the flexibility and adaptability of the communication system to meet dynamic communication needs. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 A flow chart of the neural network-assisted modulation format recognition method based on Fourier series features provided by the present invention;

[0071] Figure 2 A schematic diagram of a receiving end of the communication system provided by the present invention;

[0072] Figure 3 A neural network structure diagram provided by Example 1 of the present invention;

[0073] Figure 4 This is a recognition performance diagram of a neural network-assisted modulation format recognition method based on Fourier series features provided in Example 1 of the present invention. DETAILED DESCRIPTION

[0074] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution of the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings of the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all the embodiments. Based on the described embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work belong to the scope of protection of the present invention.

[0075] The following examples are used to illustrate the present invention, but they cannot be used to limit the scope of protection of the present invention. The conditions in the examples can be further adjusted according to specific conditions. Simple improvements to the method of the present invention under the premise of the concept of the present invention belong to the scope of protection claimed in the present invention.

[0076] Example 1

[0077] like Figure 1 As shown, a neural network-assisted modulation format recognition method based on Fourier series features includes:

[0078] Step S1: In an optical fiber communication system, Figure 2 The receiving end of the communication system shown,

[0079] The receiving end performs modulation format-insensitive digital signal processing on the received signals of 4QAM, 8QAM, 16QAM, 32QAM and 64QAM modulation formats at 4-25dB, 8-25dB, 10-25dB, 13-25dB and 16-25dB respectively. There are 500 groups of each signal, and the corresponding label is the entropy value H of the signal, to generate the historical signal set and historical label set for modulation format identification; Figure 2 The system includes a modulation format transparent digital signal processing module, a probability shaping orthogonal amplitude modulation signal modulation format identification module and a modulation format related digital signal processing module.

[0080] Step S2: Perform histogram statistics on the amplitude of the historical signal set to obtain a historical amplitude distribution set.

[0081] In practical applications, the step S2 specifically includes: for the historical signal set S = {s1(t), s2(t), ..., s N (t)}, first for each signal s i (t) Extract the amplitude point by point to obtain the amplitude sequence A i ={|s i (t)||t=1,2,…,T i}, where T i is the number of sampling points of the signal. Then, the statistical interval [0, 20] is set according to the range of the normalized signal amplitude, and the amplitude range is divided into 20 equal-width intervals [a k ,a k+1 ), the frequency of occurrence of the statistical amplitude in each interval h i,k , the histogram reflects the distribution trend of the signal amplitude and normalizes it to the probability distribution p i,k :

[0082]

[0083] Finally, the amplitude distribution P of each signal is obtained i ={p i,1 ,p i,2 ,…,p i,B}, used to describe the statistical characteristics of the signal, and the amplitude distribution of all signals is aggregated into the historical amplitude distribution set P set = {P1,P2,…,P N}, avoiding the impact of phase damage on the modulation format recognition performance and providing an input basis for subsequent feature extraction.

[0084] Step S3: Perform Fourier series decomposition on the historical amplitude distribution set, and use the coefficients of each order obtained by the decomposition as the historical amplitude distribution feature set.

[0085] In practical applications, the step S2 specifically includes: set = {P1,P2,…,P N Each amplitude distribution P in i ={p i,1 ,p i,2 ,…,p i,b}, perform Fourier series decomposition one by one. First, calculate the DC component a i,0 , reflecting the overall mean of the amplitude distribution:

[0086]

[0087] Next, calculate the nth order cosine component a i,n and the sine component b i,n , used to capture the periodic nature of the amplitude distribution:

[0088]

[0089] in, represents discrete frequency points, M is the order of Fourier series truncation (value is 4). Through these components, we can effectively capture the subtle fluctuations in the signal distribution, and accurately extract the high-dimensional information of the signal amplitude distribution under low signal-to-noise ratio;

[0090] Finally, the Fourier coefficients of each signal are combined into a feature set F i ={a i,0 ,a i,1 ,…,a i,M ,b i,1 ,…,b i,M}, the Fourier feature set of all signals is combined into the historical amplitude distribution feature set F set ={F1,F2,…,F N}, providing feature input for subsequent model training.

[0091] Step S4: Train the neural network based on the historical amplitude feature set and the historical label set.

[0092] In practical applications, the step S4 specifically includes: using the historical amplitude feature set F set ={F1,F2,…,F N} and the corresponding historical label set Y set ={y1,y2,…,y N} as input, train the neural network model, establish the mapping relationship between Fourier features and modulation format labels, and input F i Describes the historical signal amplitude distribution characteristics of the signal, label y i Indicates the modulation format type of the signal;

[0093] First, design the neural network structure, including the input layer, several hidden layers and the output layer. The specific structure is as follows Figure 3 As shown, the input layer receives the Fourier feature F i , the dimension is 9, which is much smaller than the number of signals, so the scale of the model is very small. The hidden layer is divided into two layers, containing 16 and 8 neurons respectively. The complex relationship between features is extracted through nonlinear activation functions. The output layer generates prediction results according to the number of modulation format categories c. The output layer contains 5 neurons, representing five modulation formats;

[0094] During the training phase, the predicted value is calculated using the cross entropy loss function L(Θ) and the true label y i,c The error:

[0095]

[0096] in, is the probability of the c-th modulation format output by the network, is the unique hot encoding representation of the label, and the network weights and biases are iteratively updated through the back propagation algorithm to optimize the network parameters Θ;

[0097] After training, the network can accurately map Fourier features to corresponding modulation format categories, achieving high-precision and low-complexity classification of features over a large signal-to-noise ratio range.

[0098] Step S5: performing modulation format-insensitive digital signal processing on the received signal to generate an actual signal to be identified.

[0099] Step S6: Perform histogram statistics on the amplitude of the actual signal to be identified to obtain signal amplitude distribution.

[0100] In practical applications, the step S6 specifically includes: for the actual signal to be identified s real (t), first extract and normalize its amplitude to form the amplitude sequence A real ={|s real (t)||t=

[0101] 1,2,…,T real}, where T real is the number of sampling points of the signal. Amplitude extraction can effectively avoid the influence of phase damage on the modulation format recognition performance.

[0102] Then, the interval boundaries [0, 2] and the number of intervals 20 are set according to the amplitude range of the signal, and the

[0103] The frequency of occurrence of the amplitude value in each interval h real,k , the formula is:

[0104] h real,k = count(A real ∈[a k ,a k+1 ))

[0105] To convert the frequency distribution to a probability distribution, the frequencies are normalized:

[0106]

[0107] Finally, the amplitude distribution of the signal is obtained It provides the input basis for the subsequent Fourier decomposition step.

[0108] Step S7: Perform Fourier series decomposition on the signal amplitude distribution, and use the coefficients of each order obtained by the decomposition as amplitude distribution features.

[0109] In practical applications, the step S7 specifically includes:

[0110] Perform Fourier series decomposition to extract DC components and high-order components. The DC component a real,0 The calculation is as follows:

[0111]

[0112] The higher-order components include the cosine component a real,n and the sine component b real,n , respectively, indicating that the amplitude is distributed in

[0113] Characteristics of the high frequency part:

[0114]

[0115] in, Finally, the calculated coefficients of each order are combined into the amplitude distribution characteristics These features can effectively capture subtle fluctuations in signal distribution and accurately extract high-dimensional information of signal amplitude distribution even under low signal-to-noise ratio.

[0116] Step S8: Input the amplitude distribution feature into the trained neural network to obtain the corresponding modulation format label to realize modulation format recognition.

[0117] Example 2

[0118] In practical applications, the step S8 specifically includes: realInput the trained neural network model, which has learned the mapping relationship between amplitude distribution characteristics and modulation format categories from historical data and has the ability to identify different modulation formats.

[0119] Input feature F real First, the input layer processes it and maps it to the hidden layer. The hidden layer gradually extracts the key patterns in the features through nonlinear activation functions and converts them into information related to the classification task. After multiple layers of processing, the network output layer generates predictions for each modulation format category.

[0120] Probability The formula is as follows:

[0121]

[0122] Among them, z real It is the feature representation of the final output of the hidden layer;

[0123] The multi-layer structure of the network is realized through the following recursive relationship:

[0124] h (l) =φ(W (l) ·h (l-1) +b (l) )

[0125] Among them, h (l-1) is the output of the l-1th layer, h (l) is the output of the lth layer; φ is the activation function, which is used to introduce nonlinear characteristics; W (l) and b (l) are the weight matrix and bias vector of the lth layer respectively. The output layer uses the softmax function to convert the output of the network into a probability distribution and predict the probability of each modulation format.

[0126] According to the category label y corresponding to the maximum probability real , ultimately achieving high-precision and low-complexity modulation format recognition of features in a large signal-to-noise ratio range, with recognition performance such as Figure 4 As shown, this process can operate efficiently in real-time communication systems, adapt to dynamic signal environments, and provide guarantees for accurate identification of modulation formats.

[0127] Although the embodiments of the present invention have been shown and described, it is understood by those skilled in the art that, unless otherwise defined, the technical terms or scientific terms used in the present invention should have the usual meanings understood by persons with ordinary skills in the field to which the present invention belongs, and the words "include" or "comprise" and the like used in the present invention mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents.

[0128] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A neural network-assisted modulation format recognition method based on Fourier series features, characterized in that: The following steps are involved: S1. Perform modulation format-insensitive digital signal processing on historical signals of various modulation formats and signal-to-noise ratios to generate a historical signal set and a historical label set for modulation format identification; S2. Perform histogram statistics on the amplitude of the historical signal set to obtain a historical amplitude distribution set; S3, performing Fourier series decomposition on the historical amplitude distribution set, and using the coefficients of each order obtained by the decomposition as the historical amplitude distribution feature set; S4, training a neural network based on the historical amplitude feature set and the historical label set; S5, performing modulation format-insensitive digital signal processing on the received signal to generate an actual signal to be identified; S6. Performing histogram statistics on the amplitude of the actual signal to be identified to obtain signal amplitude distribution; S7, performing Fourier series decomposition on the signal amplitude distribution, and using each order coefficient obtained by the decomposition as an amplitude distribution feature; S8. Input the amplitude distribution characteristics into the trained neural network to obtain the corresponding modulation format label to realize modulation format recognition.

2. The method for neural network-assisted modulation format recognition based on Fourier series features according to claim 1, characterized in that: Step S2 specifically includes: For the historical signal set S = {s1(t), s2(t), ..., s N (t)}, first for each signal s i (t) Extract the amplitude point by point to obtain the amplitude sequence A i ={|s i (t)||t=1,2,...,T i }, where T i is the number of sampling points of the signal; Then, the statistical interval [a min , a max ], and divide the amplitude range into B equal-width intervals [a k , a k+1 ), the frequency of occurrence of the statistical amplitude in each interval h i，k , the histogram reflects the distribution trend of the signal amplitude and normalizes it to the probability distribution p i，k : Finally, the amplitude distribution P of each signal is obtained i ={p i，1 , p i，2 , ..., p i，B }, used to describe the statistical characteristics of the signal, and the amplitude distribution of all signals is aggregated into the historical amplitude distribution set P set = {P1, P2, ..., P N }, avoiding the impact of phase damage on the modulation format recognition performance and providing an input basis for subsequent feature extraction.

3. The method for neural network-assisted modulation format recognition based on Fourier series features according to claim 2, characterized in that: Step S3 specifically includes: For the historical amplitude distribution set P set = {P1, P2, ..., P N Each amplitude distribution P in i ={p i，1， p i，2 , ..., p i，B }, perform Fourier series decomposition one by one; First, calculate the DC component a i，0 , reflecting the overall mean of the amplitude distribution: Next, calculate the nth order cosine component a i，n and the sine component b i，n , which is used to capture the periodic nature of the amplitude distribution: in, represents discrete frequency points, M is the order of Fourier series truncation; Finally, the Fourier coefficients of each signal are combined into a feature set: F i ={a i，0 ,a i，1 ,...,a i，M ,b i，1 ,...,b i，M } The Fourier feature sets of all signals are combined into a historical amplitude distribution feature set: F set ={F1, F2, ..., F N }, providing feature input for subsequent model training.

4. According to the neural network-assisted modulation format recognition method based on Fourier series features of claim 1, the step S4 specifically comprises: Based on the historical amplitude feature set F set ={F1, F2, ..., F N } and the corresponding historical label set Y set ={y1, y2, ..., y N } as input, train the neural network model, establish the mapping relationship between Fourier features and modulation format labels, and input F i Describes the historical signal amplitude distribution characteristics of the signal, label y i Indicates the modulation format type of the signal.

5. According to the neural network-assisted modulation format recognition method based on Fourier series features of claim 1, the step S6 specifically comprises: Based on the historical amplitude feature set F set ={F1, F2, ..., F N } and the corresponding historical label set Y set ={y1, y2, ..., y N } as input, train the neural network model, establish the mapping relationship between Fourier features and modulation format labels, and input F i Describes the historical signal amplitude distribution characteristics of the signal, label y i Indicates the modulation format type of the signal.

6. The method for neural network-assisted modulation format recognition based on Fourier series features according to claim 1, characterized in that: The signal amplitude distribution is decomposed by Fourier series, and the coefficients of each order obtained by decomposition are used as the amplitude distribution characteristics, including: Amplitude distribution of actual signal Perform Fourier series decomposition to extract DC components and high-order components. The DC component a real，0 The calculation is as follows: The higher-order components include the cosine component a real，n and the sine component b real，n , respectively represent the characteristics of the amplitude distribution in the high-frequency part: in, The calculation is truncated to a specific order M real , to balance the computational complexity and the effectiveness of feature extraction; Finally, the calculated coefficients of each order are combined into the amplitude distribution characteristics These features can effectively capture subtle fluctuations in signal distribution and accurately extract high-dimensional information of signal amplitude distribution even under low signal-to-noise ratio.

7. The method for neural network-assisted modulation format recognition based on Fourier series features according to claim 1, characterized in that: The amplitude distribution features are input into the trained neural network to obtain the corresponding modulation format labels, including: The amplitude distribution feature F of the actual signal to be identified real Input the trained neural network model, which has learned the mapping relationship between amplitude distribution characteristics and modulation format categories from historical data and has the ability to identify different modulation formats; Input feature F real First, the input layer processes it and maps it to the hidden layer. The hidden layer gradually extracts the key patterns in the features through nonlinear activation functions and converts them into information related to the classification task. After multiple layers of processing, the network output layer generates the predicted probability of each modulation format category. According to the category label y corresponding to the maximum probability real , and ultimately achieves high-precision and low-complexity modulation format recognition of features under a large signal-to-noise ratio range. This process can run efficiently in real-time communication systems, adapt to dynamic signal environments, and provide guarantees for accurate recognition of modulation formats.

8. The method for neural network-assisted modulation format recognition based on Fourier series features according to claim 1, characterized in that: The neural network includes an input layer, several hidden layers and an output layer, and adopts a deep network design based on Fourier series feature input and multi-layer structure. The input layer is used to receive the amplitude distribution feature F of the actual signal. real , whose dimensions are determined by the order M of the Fourier decomposition real Decide.

9. An electronic device, characterized in that: It includes a memory and a processor, the memory is used to store a computer program, the processor runs the computer program to enable the electronic device to perform a neural network-assisted modulation format recognition method based on Fourier series features as described in any one of claims 1-7, and the memory is a non-transitory computer-readable storage medium.

Images