Non-cooperative OFDM (Orthogonal Frequency Division Multiplexing) user number estimation method

Abstract

The invention discloses a non-cooperative OFDM user number estimation method, and belongs to the field of communication. According to the method, the orthogonality between OFDM subcarriers is utilized, the signal is decomposed into a plurality of subcarriers through FFT, the power feature, the high-order cumulant feature and the high-power spectrum line feature of the signal are calculated according to the characteristics of different signal modulation modes and power distribution between users, feature extraction is conducted on the signal, and blind recognition of the signal can be achieved without priori conditions. According to the method, OFDM user number estimation is carried out based on AP affinity propagation clustering, and the number of clusters does not need to be specified in advance. According to the method, the dimension reduction operation is utilized, and the high-dimension data is subjected to visualization processing. When the dimension of a classification result is relatively high, a principal component analysis (PCA) algorithm is utilized to carry out linear dimension reduction, original data is projected to a new coordinate system, a direction with the maximum variance is selected as a principal component, and an important component is selected to convert high-dimensional data into two-dimensional data or three-dimensional data, so that visualization is realized, and cluster targets in the data can be found.

Description

Technical Field

[0001] The present invention relates to a non-cooperative OFDM user number estimation method, in particular to OFDM subcarrier separation, signal feature extraction, feature clustering, and data dimension reduction, and belongs to the field of communications. Background Art

[0002] In OFDMA, the system divides the spectrum into multiple subcarriers, assigning each user a set of subcarriers to enable parallel transmission among multiple users. Traditional single-carrier modulation identification is simple, but due to the difficulty of subband division in OFDM, traditional single-carrier modulation identification methods are no longer applicable. This paper proposes a method for non-cooperative OFDM modulation identification and user number estimation by extracting signal features and performing cluster analysis on data information. This method only requires calculating the corresponding signal eigenvalues and performing clustering, and can blindly estimate the number of users without extensive prior knowledge.

[0003] Feature clustering and identification distinguishes and identifies individual user signals by clustering and analyzing the data characteristics of different users. This includes effectively classifying and identifying characteristics such as user modulation methods and power levels. Through multi-user feature clustering and identification, OFDMA systems can more effectively adapt to complex communication environments and provide reliable communication services.

[0004] Feature extraction algorithms can extract characteristic parameters that distinguish the signal's modulation pattern. Different modulation patterns produce different values for these characteristic parameters, enabling signal classification and discrimination. One of the key technologies is feature extraction. The more discriminative the extracted characteristic parameters, the better the algorithm's recognition performance.

[0005] Compared to feature extraction, clustering is a specialized technique for analyzing and classifying static data and information signals. The key concept behind the Affinity Propagation clustering algorithm (AP) is to use a similarity matrix to describe the similarities between sample data points. This similarity is used to determine a set of cluster centers. This clustering method eliminates the need to predefine the number of clusters and can effectively achieve blind detection. Summary of the Invention

[0006] Traditional user estimation methods typically rely on extensive prior knowledge and assumptions, such as signal propagation models and user behavior patterns, requiring complex data preprocessing and computation. The present invention aims to provide a method for non-cooperative OFDM user estimation. This method, based on feature clustering, eliminates reliance on prior knowledge and analyzes the signal's inherent characteristics. This method allows for simple and accurate non-cooperative OFDM user estimation, improving the efficiency of user estimation while reducing reliance on external information and enhancing its universality.

[0007] In order to achieve the above objectives, the present invention adopts the following technical solutions.

[0008] The present invention discloses a method for estimating the number of non-cooperative OFDM users, comprising the following steps:

[0009] Step 1: Based on the OFDM signal structure, perform an FFT on the OFDM signal, mapping the signal from the time domain to the frequency domain. After the FFT, the data of each user can be easily distinguished in the frequency domain. Multiple orthogonal subcarriers are separated to obtain individual subcarriers, facilitating subsequent classification of individual subcarriers and user number estimation.

[0010] OFDM symbol is the basic component of OFDM signal. An OFDM symbol is composed of multiple orthogonal subcarriers. The baseband signal at the transmitting end is expressed as:

[0011]

[0012] In the above formula, s t (t) is the time domain signal, S[k] is the discrete frequency domain representation of the signal, k is the index of the data point in the signal, N is the number of signal data points, and l represents the symbol corresponding to the signal. k represents the frequency of the discrete frequency component, T s is the duration of a complete OFDM symbol, T c is the duration of a single serial symbol, T s =NT c , j represents the imaginary unit. Its discrete-time OFDM symbol is represented as follows:

[0013]

[0014] s l [n] represents the time domain discrete component of an OFDM symbol indexed as n, S l [k] represents a frequency domain discrete component with symbol index k.

[0015] The discrete representation of an OFDM signal is similar to the result of the Inverse Discrete Fourier Transform (IDFT). When demodulating an OFDM signal, an FFT transform is performed. The FFT transform primarily maps the signal from the time domain to the frequency domain. After the FFT, the data of each user is distinguished in the frequency domain. The FFT value at point index n is represented as follows:

[0016]

[0017] Among them, s l is the symbol information, Y n is the FFT of the point indexed by n;

[0018] The purpose of subcarrier demapping is to separate the data of each user in the frequency domain, and each user obtains the frequency domain data of each user according to the current resource block allocation strategy.

[0019] Step 2: Preprocess the OFDM subcarrier signal obtained in step 1 and convert it into baseband IQ data. Perform feature extraction based on the IQ data. After separating different subcarriers, use feature extraction methods to identify the modulation of the subcarrier signal. For OFDM signals, feature identification is performed on the modulation methods of MPSK and MQAM subcarriers. The selected features are power features, high-order cumulative amount features, and high-order spectrum line features. For power features, different users may be at different distances or channel conditions in a wireless communication environment. Therefore, the power required for each user's signal is different, and the user's signals are distinguished based on different powers. For high-order cumulative amount features and high-order spectrum line features, both are distinguished based on the characteristics of the signal itself. Affected by the modulation method and modulation parameters, the high-order cumulative amount features and high-order spectrum line features of different signals are different. Signals are distinguished based on the above features.

[0020] Step 2.1: In the modulation recognition algorithm based on feature extraction, preprocessing is performed before signal data processing. After processing, it is converted into baseband IQ data, and then subsequent feature calculation is performed. The normalization processing method is as follows:

[0021] s l =|a l +jb l | (4)

[0022]

[0023] Among them, l represents the symbol corresponding to the signal, a l and b l are the real and imaginary parts respectively, z lRefers to the lth signal symbol data after normalization, s l Refers to the lth signal symbol data before normalization, s min is the minimum value of the signal data, s max is the maximum value of the signal data.

[0024] Step 2.2: After preprocessing the subcarrier data, feature extraction begins, extracting power features, high-order cumulants, and high-order spectrum line features. The specific method is as follows.

[0025] The power characteristics are specifically implemented as follows:

[0026] To maintain received signal quality, communication systems control the transmission power of each user. By adjusting the signal power for each user, the system ensures that the received signal quality for each user meets preset quality requirements, improving the reliability and performance of the entire communication system. Users are differentiated based on the power allocated to them.

[0027] Calculate the average power of the received subcarriers:

[0028]

[0029] P xx (e jw ) is the average power, N is the number of signal data points, and z(n) is the signal data after normalization of the discrete time domain signal.

[0030] The specific implementation method of the high-order cumulative amount feature is as follows:

[0031] The p-order q-order mixing moment M of the zero-mean random process X(k) pq As shown in formula (7).

[0032] M pq =E[X(k) (p-q) (X * (k)) q ] (7) Where X(k) refers to the value of the frequency domain discrete signal when the index is k, * represents conjugation, E[·] is the expectation operator, which refers to the statistical expectation, p is the order of the mixing matrix, which means the operation of the random process X(k) to the power of p, and q is another index in the mixing matrix, which means the operation of X * (k) Perform q-th power calculation, M pq is the p-order q-order mixing moment of the signal, indicating that X(k) and X * (k) The expected relationship between them.

[0033] The calculation formulas for the second-order, fourth-order, sixth-order, and eighth-order cumulants are shown in equations (8) to (15).

[0034]

[0035]

[0036] Where cum(·) represents the cumulative amount (Cumulant), C pq Represents the p-order cumulant between random processes or random variables. k is the symbol synchronous sampling sequence of the received signal at time k, where k is the time of the data point in the signal.

[0037] The characteristic parameters F1 and F2 are constructed using the eighth-order, fourth-order and second-order cumulants:

[0038]

[0039] The specific implementation method of the high-order spectrum line characteristics is as follows:

[0040] After performing nonlinear transformation operations on digital communication signals, discrete spectral line characteristics may appear in the frequency domain. The number of spectral lines and their positions and intensities are intrinsically related to the modulation mode and modulation parameters of the signal. The characteristics of the signal spectral lines can be used as identification parameters to effectively identify the modulation mode.

[0041] The quadratic spectrum characteristic is the power spectrum after the signal is squared, and the square spectrum reflects the power spectrum characteristics of the modulated signal after frequency doubling:

[0042]

[0043] The fourth power spectrum feature is the fourth power power spectrum of the signal:

[0044]

[0045] Where a n , b n represent the real and imaginary parts of the signal respectively, and E(·) represents the expectation of the contents in the brackets.

[0046] Step 3: AP (Affinity Propagation) clustering is performed on the features obtained in Step 2. The similarity matrix Sim is constructed by calculating the similarity between sample data points, where similarity is measured by the square of the negative Euclidean distance. Based on the similarity matrix, different sample points are selected to iteratively calculate the attraction matrix R and the attribution matrix A. These matrices are continuously updated. When the maximum number of iterations is exceeded or the change in the value of R(i,c)+A(i,c) falls below a predetermined threshold, the AP affinity propagation clustering algorithm is terminated, resulting in the decision matrix Q, which is the final classification result. Based on the classification results, an estimate of the number of users is obtained, thus achieving non-cooperative OFDM user number estimation.

[0047] Step 3.1: Use the square of the negative Euclidean distance to construct the similarity between sample data points and construct the similarity matrix Sim. The AP algorithm implements cluster analysis based on the similarity matrix between samples and does not require the symmetry of the similarity matrix generated by the dataset. Use the square of the negative Euclidean distance to construct the similarity between sample data points. There are y data points, and these data points form a y*y similarity matrix Sim. Sim(i,h) represents the similarity between data points and, as shown below:

[0048] Sim(i,h)=-||x i -x h || 2 And Sim(i,h)∈(-∞,0] (19)

[0049] x represents the sample, x i and x h It represents the i-th sample and the h-th sample in the sample space, where i and h represent the labels in the samples.

[0050] The cluster center is determined by the values of the elements on the diagonal of the similarity matrix, Sim(i,h). Sim(i,h), called the preference parameter, is a key parameter in the AP affinity propagation clustering algorithm. It indicates the suitability of data point i as a cluster representative. A larger value indicates a more suitable data point for being a cluster center. A higher preference indicates a greater tendency for data points to become class representatives, resulting in a greater number of clusters; conversely, a lower preference indicates a smaller number of clusters. This parameter not only affects the number of clustering results but also the subsequent message passing process. The preference value is often set to the median of the similarity matrix.

[0051] preference=median(Sim(i,h)) (20)

[0052] Therefore, the similarity matrix is expressed as:

[0053]

[0054] Step 3.2: Based on the similarity matrix obtained in step 3.1, select different sample points to iteratively calculate the attraction matrix R and the attribution matrix A. The attraction matrix R(i,c) is the information sent by sample point i to the candidate cluster center c, expressing the degree of support of sample point i for cluster center c. The larger its value, the more likely c is to become the actual class center; the attribution information A(i,c) is the information sent by the candidate cluster center c to the sample data i, expressing the suitability of the candidate cluster center c as the center of sample point i. The larger its value, the more likely i is to belong to the class centered on c. During the iteration process of the attraction matrix R(i,c) and the attribution information A(i,c), the two types of information influence each other through competition and are updated alternately. The calculation and update methods of R(i,c) and A(i,c) are as follows:

[0055] When i≠c,

[0056]

[0057] When i=c,

[0058]

[0059] When i≠c,

[0060]

[0061] When i=c,

[0062]

[0063] c′ is the point in the sample that is not equal to c, and i′ is the point in the sample that is not equal to the corresponding subscript condition in the formula. To prevent numerical oscillation during the iteration process, the damping coefficient λ is used for message updates. The function of the damping coefficient is to correct R(i,c) and A(i,c) before and after the iteration. The larger the value, the slower the matrix update speed, the smoother the iteration process, and the better the effect of eliminating oscillation. The value of λ is set based on experience. The current number of iterations is set to t, and the correction process is as follows:

[0064] R t (i,c)=R t (i,c)*(1-λ)+R t-1 (i,c)*λ (26)

[0065] A t (i,c)=A t (i,c)*(1-λ)+A t-1 (i,c)*λ (27)

[0066] Among them, λ∈(0,1), R t-1 (i,c) and A t-1(i, c) respectively represent the attractiveness and belonging degree in the (t - 1)-th iteration, R t (i, c) and A t (i, c) respectively represent the attractiveness and belonging degree in the t-th iteration.

[0067] Step 3.3: Calculate the decision matrix Q based on the obtained attractiveness matrix R and belonging degree matrix A. The AP affinity propagation clustering algorithm continuously updates the above two matrices. When the maximum number of iterations preset in advance is exceeded or the change amount of the value of R(i, c)+A(i, c) is lower than the predetermined threshold, the AP affinity propagation clustering algorithm will stop iterating. The clustering result is determined by the value of R(i, c)+A(i, c) at the termination. The class representative point of data point i is determined as c, and c satisfies:

[0068] c = argmax(R(i, c)+A(i, c)) (28)

[0069] Adding A(i, c) to both sides of the formula gives:

[0070]

[0071] c′ is the point in the sample that is not equal to c.

[0072] Let the decision matrix Q = R + R, AS = A + Sium, then there is:

[0073]

[0074] The final classification result can be obtained from Q. When Q(c, c)>0, that is, Q(c, j)<Q(c, c) holds, so the c-th point is the class representative point.

[0075] Step Four: Perform dimensionality reduction on the feature dimensions obtained in Step Three. When performing the visualization operation of the final result, when the features exceed 3 dimensions, it is very difficult to clearly explain the meaning of each dimension and their relationships by traditional visualization means (such as two-dimensional or three-dimensional graphs). Observing and understanding data in a high-dimensional space becomes more abstract. The present invention uses the principal component analysis algorithm PCA for dimensionality reduction operation to process the data and perform visualization operation on the processed data, so as to more intuitively and clearly display the classification result.

[0076] The principal component analysis algorithm PCA is a linear dimensionality reduction method. By calculating the covariance matrix and performing eigenvalue decomposition on it, eigenvectors are obtained. The eigenvalues reflect the importance of each component. Sort them according to the importance, select the dimension of the target low-dimensional space, map the high-dimensional data to the low-dimensional space, and expect the information amount (variance) of the data to be the largest on the projected dimension, so as to obtain the result after dimensionality reduction. Use fewer data dimensions to retain the characteristics of the original data points.

[0077] Step 4.1: Normalize the input sample data. Input sample set x={x1,x2,…,x y}, y is the number of sample points, and p′ is the number of principal components. Decentering (Z-score standardization) the data is performed, subtracting the mean from each variable and centering the data at zero, i.e., with a mean of zero.

[0078] Step 4.2: Calculate the normalized sample covariance matrix:

[0079]

[0080] Step 4.3: Calculate the eigenvalues and eigenvectors and arrange them in descending order. Perform eigenvalue decomposition on the covariance matrix to obtain the eigenvalues and corresponding eigenvectors. The eigenvectors are the principal component directions that need to be retained, and the eigenvalues λ reflect the importance of each principal component. The number of principal components p is calculated and arranged:

[0081] λ1≥λ2≥…≥λ p (32)

[0082] Step 4.4: Select the first p′ eigenvectors as principal components, where p′ is the dimension to be reduced, that is, the dimension of the target low-dimensional space:

[0083] W={W1,W2,…,W y} (33)

[0084] The original data set is projected onto a new low-dimensional space, and the resulting new dimension W is visualized after dimensionality reduction, overcoming the difficulty of analyzing high-dimensional data and obtaining the final user quantity classification result.

[0085] Implement non-cooperative OFDM user number estimation.

[0086] Beneficial effects:

[0087] 1. This invention discloses a non-cooperative OFDM user number estimation method that classifies OFDM user subcarriers based on feature extraction. Leveraging the orthogonality between OFDM subcarriers, the signal is decomposed into multiple subcarriers using FFT. Based on the different signal modulation schemes and power allocations between users, the signal's power characteristics, high-order cumulants, and high-order spectrum line characteristics are calculated to extract signal features. Compared to traditional signal recognition, this feature extraction method eliminates the need for prior conditions (such as user signal modulation scheme and power allocation), enabling blind signal recognition.

[0088] 2. The present invention discloses a non-cooperative OFDM user number estimation method, which uses AP neighbor propagation clustering to estimate the number of OFDM users. Clustering is performed using the AP neighbor propagation clustering algorithm, and the similarity between samples is used as the basis for clustering. By calculating the similarity between samples, a similarity matrix is formed. The attraction and membership of each sample are updated through an iterative message passing process, and the final classification result is finally calculated. Compared with the partition-based clustering method (K-Means) and the hierarchical clustering method, the clustering method of the present invention does not require the pre-specification of the number of clusters. Compared with the machine learning classification method, the present invention does not require a large data set for training, that is, it can achieve blind classification of user signals.

[0089] 3. The present invention discloses a method for estimating the number of non-cooperative OFDM users, which uses dimensionality reduction to visualize high-dimensional data. When the dimensionality of the classification results is high, traditional visualization methods (such as two-dimensional or three-dimensional graphs) cannot clearly explain the meaning of each dimension and the relationship between them. The present invention uses the PCA principal component analysis algorithm to perform linear dimensionality reduction. By projecting the original data into a new coordinate system, the direction with the largest variance is selected as the principal component, and the important components are selected to convert the high-dimensional data into two or three dimensions for visualization, which helps to discover clusters in the data. BRIEF DESCRIPTION OF THE DRAWINGS

[0090] Figure 1 This is a flowchart of the multi-user number estimation method based on signal feature clustering;

[0091] Figure 2 It is the frequency division structure diagram of OFDM signal;

[0092] Figure 3 It is the clustering result graph of two users;

[0093] Figure 4 This is the result graph of four-user dimensionality reduction. Specific implementation plan

[0094] In order to enable those skilled in the art to have a deeper understanding of the implementation ideas of the solutions of the present invention, the technical solutions in the embodiments of the present invention will be described in detail and clearly in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other implementation cases obtained by ordinary technicians in this field without making creative work should fall within the scope of protection of the present invention.

[0095] like Figure 1 The present embodiment discloses a method for estimating the number of non-cooperative OFDM users, and the specific implementation steps are as follows:

[0096] Example 1

[0097] In this example, the received OFDM signal has been precisely synchronized and CP removed for feature analysis and clustered user detection. The four user modulation schemes used in this example are BPSK, QPSK, 8PSK, and 16QAM. Each OFDM symbol contains 64 subcarriers, and the FFT size is 64.

[0098] Step 1: According to Figure 2 The OFDM signal's frequency division structure is used to map the OFDM signal from the time domain to the frequency domain. After the FFT, the data of each user can be easily distinguished in the frequency domain. Multiple orthogonal subcarriers are separated to obtain individual subcarriers, facilitating subsequent classification of individual subcarriers and user number estimation.

[0099] OFDM symbol is the basic component of OFDM signal. An OFDM symbol is composed of multiple orthogonal subcarriers. The baseband signal at the transmitting end is expressed as:

[0100]

[0101] In the above formula, s t (t) is the time domain signal, S[k] is the discrete frequency domain representation of the signal, k is the index of the data point in the signal, N is the number of signal data points, and l represents the symbol corresponding to the signal. k represents the frequency of the discrete frequency component, T s is the duration of a complete OFDM symbol, T c is the duration of a single serial symbol, T s =NT c , j represents the imaginary unit. Its discrete-time OFDM symbol is represented as follows:

[0102]

[0103] s l [n] represents the time domain discrete component of an OFDM symbol indexed as n, S l [k] represents a frequency domain discrete component with symbol index k.

[0104] The discrete representation of an OFDM signal is similar to the result of the Inverse Discrete Fourier Transform (IDFT). When demodulating an OFDM signal, an FFT transform is performed. The FFT transform primarily maps the signal from the time domain to the frequency domain. After the FFT, the data of each user is distinguished in the frequency domain. The FFT value at point index n is represented as follows:

[0105]

[0106] Among them, s l is the symbol information, Y n is the FFT of the point indexed by n;

[0107] The purpose of subcarrier demapping is to separate the data of each user in the frequency domain, and each user obtains the frequency domain data of each user according to the current resource block allocation strategy.

[0108] Step 2: Preprocess the OFDM subcarrier signal obtained in step 1 and convert it into baseband IQ data. Perform feature extraction based on the IQ data. After separating different subcarriers, use feature extraction methods to identify the modulation of the subcarrier signal. For OFDM signals, feature identification is performed on the modulation methods of MPSK and MQAM subcarriers. The selected features are power features, high-order cumulative amount features, and high-order spectrum line features. For power features, different users may be at different distances or channel conditions in a wireless communication environment. Therefore, the power required for each user's signal is different, and the user's signals are distinguished based on different powers. For high-order cumulative amount features and high-order spectrum line features, both are distinguished based on the characteristics of the signal itself. Affected by the modulation method and modulation parameters, the high-order cumulative amount features and high-order spectrum line features of different signals are different. Signals are distinguished based on the above features.

[0109] Step 2.1: In the modulation recognition algorithm based on feature extraction, preprocessing is performed before signal data processing. After processing, it is converted into baseband IQ data, and then subsequent feature calculation is performed. The normalization processing method is as follows:

[0110] s l =|a l +jb l | (4)

[0111]

[0112] Among them, l represents the symbol corresponding to the signal, a l and b l are the real and imaginary parts respectively, z l Refers to the lth signal symbol data after normalization, s l Refers to the lth signal symbol data before normalization, s min is the minimum value of the signal data, s max is the maximum value of the signal data.

[0113] Step 2.2: After preprocessing the subcarrier data, feature extraction begins, extracting power features, high-order cumulants, and high-order spectrum line features. The specific method is as follows.

[0114] The power characteristics are specifically implemented as follows:

[0115] To maintain received signal quality, communication systems control the transmission power of each user. By adjusting the signal power for each user, the system ensures that the received signal quality for each user meets preset quality requirements, improving the reliability and performance of the entire communication system. Users are differentiated based on the power allocated to them.

[0116] Calculate the average power of the received subcarriers:

[0117]

[0118] P xx (e jw ) is the average power, N is the number of signal data points, and z(n) is the signal data after normalization of the discrete time domain signal.

[0119] The specific implementation method of the high-order cumulative amount feature is as follows:

[0120] The p-order q-order mixing moment M of the zero-mean random process X(k) pq As shown in formula (7).

[0121] M pq =E[X(k) (p-q) (X * (k)) q ] (7)

[0122] Among them, X(k) refers to the value of the frequency domain discrete signal when the index is k, * represents conjugation, E[·] is the expectation operator, which refers to the statistical expectation, p is the order of the mixing matrix, which means the operation of the random process X(k) to the power of p, and q is another index in the mixing matrix, which means the operation of X * (k) Perform q-th power calculation, M pq is the p-order q-order mixing moment of the signal, indicating that X(k) and X * (k) The expected relationship between them.

[0123] The calculation formulas for the second-order, fourth-order, sixth-order, and eighth-order cumulants are shown in equations (8) to (15).

[0124]

[0125]

[0126] Where cum(·) represents the cumulative amount (Cumulant), C pq Represents the p-order cumulant between random processes or random variables. k is the symbol synchronous sampling sequence of the received signal at time k, where k is the time of the data point in the signal.

[0127] The characteristic parameters F1 and F2 are constructed using the eighth-order, fourth-order and second-order cumulants:

[0128]

[0129] The specific implementation method of the high-order spectrum line characteristics is as follows:

[0130] After performing nonlinear transformation operations on digital communication signals, discrete spectral line characteristics may appear in the frequency domain. The number of spectral lines and their positions and intensities are intrinsically related to the modulation mode and modulation parameters of the signal. The characteristics of the signal spectral lines can be used as identification parameters to effectively identify the modulation mode.

[0131] The quadratic spectrum characteristic is the power spectrum after the signal is squared, and the square spectrum reflects the power spectrum characteristics of the modulated signal after frequency doubling:

[0132]

[0133] The fourth power spectrum feature is the fourth power power spectrum of the signal:

[0134]

[0135] Where a n , b n represent the real and imaginary parts of the signal respectively, and E(·) represents the expectation of the contents in the brackets.

[0136] Step 3: AP (Affinity Propagation) clustering is performed on the features obtained in Step 2. The similarity matrix Sim is constructed by calculating the similarity between sample data points, where similarity is measured by the square of the negative Euclidean distance. Based on the similarity matrix, different sample points are selected to iteratively calculate the attraction matrix R and the attribution matrix A. These matrices are continuously updated. When the maximum number of iterations is exceeded or the change in the value of R(i,c)+A(i,c) falls below a predetermined threshold, the AP affinity propagation clustering algorithm is terminated, resulting in the decision matrix Q, which is the final classification result. Based on the classification results, an estimate of the number of users is obtained, thus achieving non-cooperative OFDM user number estimation.

[0137] Step 3.1: Use the square of the negative Euclidean distance to construct the similarity between sample data points and construct the similarity matrix Sim. The AP algorithm implements cluster analysis based on the similarity matrix between samples and does not require the symmetry of the similarity matrix generated by the dataset. Use the square of the negative Euclidean distance to construct the similarity between sample data points. There are y data points, and these data points form a y*y similarity matrix Sim. Sim(i,h) represents the similarity between data points and, as shown below:

[0138] Sim(i,h)=-||x i -x h || 2 And Sim(i,h)∈(-∞,0] (19)

[0139] x represents the sample, x i and x h It represents the i-th sample and the h-th sample in the sample space, where i and h represent the labels in the samples.

[0140] The cluster center is determined by the values of the elements on the diagonal of the similarity matrix, Sim(i,h). Sim(i,h), called the preference parameter, is a key parameter in the AP affinity propagation clustering algorithm. It indicates the suitability of data point i as a cluster representative. A larger value indicates a more suitable data point for being a cluster center. A higher preference indicates a greater tendency for data points to become class representatives, resulting in a greater number of clusters; conversely, a lower preference indicates a smaller number of clusters. This parameter not only affects the number of clustering results but also the subsequent message passing process. The preference value is often set to the median of the similarity matrix.

[0141] preference=median(Sim(i,h)) (20)

[0142] Therefore, the similarity matrix is expressed as:

[0143]

[0144] Step 3.2: Based on the similarity matrix obtained in step 3.1, select different sample points to iteratively calculate the attraction matrix R and the attribution matrix A. The attraction matrix R(i,c) is the information sent by sample point i to the candidate cluster center c, expressing the degree of support of sample point i for cluster center c. The larger its value, the more likely c is to become the actual class center; the attribution information A(i,c) is the information sent by the candidate cluster center c to the sample data i, expressing the suitability of the candidate cluster center c as the center of sample point i. The larger its value, the more likely i is to belong to the class centered on c. During the iteration process of the attraction matrix R(i,c) and the attribution information A(i,c), the two types of information influence each other through competition and are updated alternately. The calculation and update methods of R(i,c) and A(i,c) are as follows:

[0145] When i≠c,

[0146]

[0147] When i=c,

[0148]

[0149] When i≠c,

[0150]

[0151] When i=c,

[0152]

[0153] c′ is the point in the sample that is not equal to c, and i′ is the point in the sample that is not equal to the corresponding subscript condition in the formula. To prevent numerical oscillation during the iteration process, the damping coefficient λ is used for message updates. The function of the damping coefficient is to correct R(i,c) and A(i,c) before and after the iteration. The larger the value, the slower the matrix update speed, the smoother the iteration process, and the better the effect of eliminating oscillation. The value of λ is set based on experience. The current number of iterations is set to t, and the correction process is as follows:

[0154] R t (i,c)=R t (i,c)*(1-λ)+R t-1 (i,c)*λ (26)

[0155] A t (i,c)=A t (i,c)*(1-λ)+A t-1 (i,c)*λ (27)

[0156] Among them, λ∈(0,1), R t-1 (i,c) and A t-1(i, c) respectively represent the degree of attraction and the degree of belonging in the (t - 1)-th iteration, R t (i, c) and A t (i, c) respectively represent the degree of attraction and the degree of belonging in the t-th iteration.

[0157] Step 3.3: Calculate the decision matrix Q according to the obtained degree of attraction matrix r and degree of belonging matrix A. The AP affinity propagation clustering algorithm continuously updates the above two matrices. When the maximum number of iterations preset is exceeded or the change amount of the value of R(i, c)+A(i, c) is lower than the preset threshold, the AP affinity propagation clustering algorithm will stop iterating. Determine the clustering result through the value of R(i, c)+A(i, c) at termination. The class representative point of data point i is determined as c, and c satisfies:

[0158] c = argmax(R(i, c)+A(i, c)) (28)

[0159] Adding A(i, c) to both sides of the formula gives:

[0160]

[0161] c′ is the point in the sample that is not equal to c.

[0162] Let the decision matrix Q = R + A, AS = A + Sim, then there is:

[0163]

[0164] The final classification result can be obtained from Q. When Q(c, c)>0, that is, Q(c, j)<Q(c, c) holds, so the c-th point is the class representative point.

[0165] Step Four: Perform dimensionality reduction on the feature dimensions obtained in Step Three. When performing the visualization operation of the final result, when the features exceed 3 dimensions, it is difficult to clearly explain the meaning of each dimension and their relationships by traditional visualization means (such as two-dimensional or three-dimensional graphs). Observing and understanding data in a high-dimensional space becomes more abstract. The present invention uses the principal component analysis algorithm PCA for dimensionality reduction operation to process the data and perform visualization operation on the processed data, so as to more intuitively and clearly display the classification result.

[0166] The principal component analysis algorithm PCA is a linear dimensionality reduction method. By calculating the covariance matrix and performing eigenvalue decomposition on it, eigenvectors are obtained. The eigenvalues reflect the importance of each component. Sort them according to the importance, select the dimension of the target low-dimensional space, map the high-dimensional data to the low-dimensional space, and expect the information amount (variance) of the data to be the largest on the projected dimension, so as to obtain the result after dimensionality reduction. Use fewer data dimensions to retain the characteristics of the original data points.

[0167] Step 4.1: Normalize the input sample data and input the feature sample set x={P xx ,F1,F2,K2,K4}, where p′ is the specified number of principal components, p′=2, and the feature dataset is reduced from a high-dimensional space to two dimensions. The input data is decentralized (Z-score normalization) and normalized. Each variable is subtracted from its own mean, returning the center of the data to zero, i.e., the mean is zero.

[0168] Step 4.2: Calculate the normalized sample covariance matrix:

[0169]

[0170] There are y feature samples in total, x represents {P xx ,F1,F2,K2,K4} feature samples.

[0171] Step 4.3: Calculate the eigenvalues and eigenvectors and arrange them in descending order. Perform eigenvalue decomposition on the covariance matrix to obtain the eigenvalues and corresponding eigenvectors. The eigenvectors are the principal component directions that need to be retained, and the eigenvalues λ reflect the importance of each principal component. The number of principal components p is calculated and arranged:

[0172] λ1≥λ2≥...≥λ p (32)

[0173] Step 4.4: Select the first p′ eigenvectors as principal components, where p′ is the dimension to be reduced, that is, the dimension of the target low-dimensional space. Select the first two eigenvectors as principal components, p′ = 2, that is, reduce from high dimension to 2 dimension:

[0174] W={W1,W2} (33)

[0175] The original data set is projected onto a new low-dimensional space, and the resulting new dimension W is visualized after dimensionality reduction, overcoming the difficulty of analyzing high-dimensional data and obtaining the final user quantity classification result.

[0176] In this example, when performing two-dimensional user feature clustering, it is a binary classification problem. The feature samples used are small and no dimensionality reduction processing is required. The clustering results of the two user signals are as follows: Figure 3 As shown in the figure, there are two types of points, corresponding to the number of users 2; when performing four-user feature clustering, the feature samples used exceed three dimensions, and high-dimensional space visualization is difficult. PCA principal component analysis in step 4 is used to reduce the dimension and project the high-dimensional space into two dimensions. The signal clustering results after dimensionality reduction for four users are shown as follows Figure 4 As shown in the figure, there are four types of points, corresponding to the number of users 4.

[0177] The above specific description further illustrates the purpose and technical solution of the invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A non-cooperative OFDM user number estimation method, characterized by: The following steps are included: Step 1: Based on the structure of the OFDM signal, perform an FFT on the OFDM signal to map the signal from the time domain to the frequency domain. After the FFT, the data of each user can be easily distinguished in the frequency domain. Multiple orthogonal subcarriers are separated to obtain single subcarriers, which facilitates subsequent classification of single carriers and estimation of the number of users. Step 2: Before performing signal data processing on the subcarrier signal obtained in step 1, a preprocessing operation is performed. After processing, it is converted into baseband IQ data and normalized. After the subcarrier data is preprocessed, feature extraction is started to extract power features, high-order cumulant features, and high-order spectrum line features; Step 3: Perform proximity propagation clustering on the features obtained in Step 2, calculate the similarity between sample data points to construct a similarity matrix Sim, where similarity is measured by the square of the negative Euclidean distance. Based on the similarity matrix, select different sample points to iteratively calculate the attraction matrix R and the attribution matrix A. The attraction matrix R and the attribution matrix A are continuously updated. When the maximum number of iterations is exceeded or the change in the value of R(i,c)+A(i,c) falls below a predetermined threshold, stop iterating the AP proximity propagation clustering algorithm and obtain the decision matrix Q, which is the final classification result. Based on the classification result, the user number estimation result is obtained, thus realizing the estimation of the number of non-cooperative OFDM users.

2. The method for estimating the number of non-cooperative OFDM users according to claim 1, wherein: It also includes step four: performing a dimensionality reduction operation on the feature dimension obtained in step three. When visualizing the final result, if the feature exceeds 3 dimensions, the principal component analysis algorithm PCA dimensionality reduction operation is used to process the data, and the processed data is visualized to display the classification results more intuitively and clearly.

3. The method for estimating the number of non-cooperative OFDM users according to claim 1 or 2, wherein: The implementation method of step one is: OFDM symbol is the basic component of OFDM signal. An OFDM symbol is composed of multiple orthogonal subcarriers. The baseband signal at the transmitting end is expressed as: In the above formula, s t (t) is the time domain signal, S[k] is the discrete frequency domain representation of the signal, k is the index of the data point in the signal, N is the number of signal data points, and l is the number of symbols corresponding to the signal; f k represents the frequency of the discrete frequency component, T s is the duration of a complete OFDM symbol, T c is the duration of a single serial symbol, T s =NT c , j represents the imaginary unit; the discrete-time OFDM symbol is represented as follows: s l [n] represents the time domain discrete component of an OFDM symbol indexed as n, S l [k] represents a frequency domain discrete component with symbol index k; The discrete representation of an OFDM signal is similar to the result of the Inverse Discrete Fourier Transform (IDFT). When demodulating an OFDM signal, an FFT transform is performed. The FFT transform primarily maps the signal from the time domain to the frequency domain. After the FFT, the data of each user is distinguished in the frequency domain. The FFT value at the point indexed by n is expressed as follows: Among them, s l is the symbol information, Y n is the FFT of the point indexed by n; The purpose of subcarrier demapping is to separate the data of each user in the frequency domain, and each user obtains the frequency domain data of each user according to the current resource block allocation strategy.

4. The method for estimating the number of non-cooperative OFDM users according to claim 3, wherein: Before performing signal data processing on the subcarrier signal obtained in step 1, a preprocessing operation is performed. After processing, it is converted into baseband IQ data and normalized. After preprocessing the subcarrier data, feature extraction is started. The method for extracting power features, high-order cumulative amount features, and high-order spectrum line features is as follows: The normalization process is as follows: s l =|a l +jb l | (4) Among them, l represents the symbol corresponding to the signal, a l and b l are the real and imaginary parts respectively, z l Refers to the lth signal symbol data after normalization, s l Refers to the lth signal symbol data before normalization, s min is the minimum value of the signal data, s max is the maximum value of the signal data.

5. The method for estimating the number of non-cooperative OFDM users according to claim 3, wherein: The specific implementation method of extracting power characteristics in step 2 is as follows: To maintain the quality of received signals, the communication system controls the transmission power of each user. By adjusting the signal power of different users, the system ensures that the signal quality received by each user meets the preset quality requirements, thereby improving the reliability and performance of the entire communication system. Users are differentiated based on the power allocated to each user. Calculate the average power of the received subcarriers: P xx (e jw ) is the average power, N is the number of signal data points, and z(n) is the signal data after normalization of the discrete time domain signal.

6. The method for estimating the number of non-cooperative OFDM users according to claim 3, wherein: The specific implementation method of extracting high-order cumulative features in step 2 is as follows: The p-order q-order mixing moment M of the zero-mean random process X(k) pq As shown in formula (7); M pq =E[X(k) (p-q) (X * (k)) q ] (7) Where X(k) refers to the value of the frequency domain discrete signal when the index is k, * represents conjugation, E[·] is the expectation operator, which refers to the statistical expectation, p is the order of the mixing matrix, which means the operation of the random process X(k) to the power of p, and q is another index in the mixing matrix, which means the operation of X * (k) Perform q-th power calculation, M pq is the p-order q-order mixing moment of the signal, which represents the expected relationship between X(k) and X*(k); the calculation formulas for the second-order, fourth-order, sixth-order, and eighth-order cumulants are shown in equations (8) to (15); Where cum(·) represents the cumulative amount (Cumulant), C pq Represents the p-order cumulant between random processes or random variables; S k is the symbol synchronous sampling sequence of the received signal at time k, where k is the time of the data point in the signal; The characteristic parameters F1 and F2 are constructed using the eighth-order, fourth-order, and second-order cumulants:

7. The method for estimating the number of non-cooperative OFDM users according to claim 3, wherein: The specific implementation method of extracting high-order spectrum line features in step 2 is as follows: After a nonlinear transformation is performed on a digital communication signal, the signal may exhibit discrete spectral line features in the frequency domain. The number, position, and intensity of the spectral lines are intrinsically related to the modulation mode and modulation parameters of the signal. The characteristics of the signal spectral lines can be used as identification parameters to effectively identify the modulation mode. The quadratic spectrum characteristic is the power spectrum after the signal is squared, and the square spectrum reflects the power spectrum characteristics of the modulated signal after frequency doubling: The fourth power spectrum feature is the fourth power power spectrum of the signal: Where a n , b n represent the real and imaginary parts of the signal respectively, and E(·) represents the expectation of the contents in the brackets.

8. The method for estimating the number of non-cooperative OFDM users according to claim 7, wherein: The implementation method of step three to construct the similarity matrix is: The similarity between sample data points is constructed by the square of the negative Euclidean distance, and the similarity matrix Sim is constructed; The AP algorithm implements cluster analysis based on the similarity matrix between samples, and does not require the symmetry of the similarity matrix generated by the data set; it uses the square of the negative Euclidean distance to construct the similarity between sample data points; there are y data points, and the data points form a y*y similarity matrix Sim, where Sim(i,h) represents the similarity between the data points and, as shown below: Sim(i,h) = -||x i -x h || 2 and Sim(i,h) ∈ (-∞, 0] (19) x represents the sample, x i and x h It represents the i-th sample and the h-th sample in the sample space, where i and h represent the labels in the sample; The cluster center is determined by the element value Sim(i,h) on the diagonal of the similarity matrix. Sim(i,h) is called the preference parameter, which is an important parameter in the AP proximity propagation clustering algorithm. It indicates the suitability of data point i as a class representative point. The larger its value, the more suitable the data point is as a cluster center. The larger the preference, the more data points tend to become class representatives, and the more clusters there are. Conversely, the smaller the preference, the fewer clusters there are. This parameter not only affects the number of clustering results, but also affects the subsequent message passing process. The preference value is set to the median of the similarity matrix. preference=median(Sim(i,h)) (20) Therefore, the similarity matrix is expressed as: Step 3: The method to construct the attraction matrix and the belonging matrix is: According to the obtained similarity matrix, different sample points are selected to iteratively calculate the attraction matrix R and the attribution matrix A; The attraction matrix R(i, c) is the information sent by sample point i to candidate cluster center c, expressing the degree of support of sample point i for cluster center c. The larger its value, the more likely c is to become the actual class center; the membership information A(i, c) is the information sent by candidate cluster center c to sample data i, expressing the suitability of candidate cluster center c as the center of sample point i. The larger its value, the more likely i belongs to the class centered on c; in the iterative process of the attraction matrix R(i, c) and the membership information A(i, c), the two kinds of information affect each other through competition and are alternately updated; the calculation and update methods of R(i, c) and A(i, c) are as follows: When i ≠ c, When i = c, When i ≠ c, When i = c, Let c′ be the point in the sample that is not equal to c, and i′ be the point in the sample that does not satisfy the corresponding subscript condition in the formula. To avoid numerical oscillations in the iterative process, the damping coefficient λ is used for message update; the role of the damping coefficient is to correct R(i, c) and A(i, c) in the previous and subsequent iterations. The larger its value, the slower the matrix update speed, the smoother the iterative process, and the better the effect of eliminating oscillations. The value of λ is set according to experience; the current iteration number is set as t, and the correction process is as follows: R t (i,c)=R t (i,c)*(1-λ)+R t-1 (i,c)*λ (26) A t (i,c)=A t (i,c)*(1-λ)+A t-1 (i,c)*λ (27) Among them, λ∈(0,1), R t-1 (i,c) and A t-1 (i, c) represent the attraction and belonging degree of the t-1th iteration, R t (i,c) and A t (i,c) represent the attraction and belongingness of the tth iteration respectively.

9. The method for estimating the number of non-cooperative OFDM users according to claim 8, wherein: The implementation method of step three to construct the decision matrix to obtain the final result is Calculate the decision matrix Q according to the obtained attraction matrix R and membership matrix A; the AP affinity propagation clustering algorithm continuously updates the above two matrices. When the maximum number of iterations preset is exceeded or the change amount of the value of R(i, c) + A(i, c) is lower than the preset threshold, the AP affinity propagation clustering algorithm will stop iterating; determine the clustering result by the value of R(i, c) + A(i, c) at the end; the class representative point of data point i is determined as c, and c satisfies: c = argmax(R(i, c) + A(i, c)) (28) Adding A(i, c) to both sides of formula (28) gives: The decision matrix Q = R + A, AS = A + Sim, then there is: Obtain the final classification result from Q. When Q(c, c) > 0, that is, Q(c, j) < Q(c, c) holds, so the c-th point is the class representative point.

10. The non-cooperative OFDM user number estimation method according to claim 9, wherein: The implementation method of step four is Step 4.1: Normalize the input sample data. Input sample set x={x1,x2,…,x y }, y is the number of sample points, and the number of principal components p′ is specified; the data is decentralized and standardized, each variable is subtracted from its own mean, and the center of the data is returned to the zero point position, that is, the mean is zero; Step 4.2: Calculate the normalized sample covariance matrix: Step 4.3: Calculate the eigenvalues and eigenvectors, and arrange them in descending order; perform eigenvalue decomposition on the covariance matrix to obtain the eigenvalues and corresponding eigenvectors; the eigenvectors are the directions of the principal components to be retained, and the eigenvalue λ reflects the importance of each principal component; p is the number of principal components, and perform arrangement after calculation: λ1≥λ2≥…≥λ p (32) Step 4.4: Select the first p′ eigenvectors as the principal components, where p′ is the dimension to be reduced, that is, the dimension of the target low-dimensional space: W={W1,W2,…,W n } (33) Project the original data set onto the new low-dimensional space, obtain the new dimension W, and use the reduced dimension for visualization to obtain the final user quantity classification result.

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