Intelligent estimation method for the number of signal sources of time-frequency overlapping multi-signals under non-Gaussian interference

Abstract

The embodiments of the present application relate to the field of electromagnetic space signal processing technology, and in particular to a method for intelligently estimating the number of signal sources of time-frequency overlapping multi-signals under non-Gaussian interference, comprising: sparsely decomposing the acquired time-frequency overlapping signal into multiple matching signals through a matching pursuit algorithm, and using a nonlinear transformer to reduce the influence of alpha stable noise on the time-frequency overlapping signal, using multiple matching signals and the original signal to form a virtual multi-channel signal, and constructing a generalized correlation matrix; performing data preprocessing operations including eigenvalue decomposition and similarity transformation on the generalized correlation matrix to obtain a processed generalized correlation matrix; inputting the processed generalized correlation matrix into an improved U-Net network to obtain a segmentation result output by the improved U-Net network, and realizing intelligent estimation of the number of signal sources of time-frequency overlapping multi-signals under non-Gaussian interference based on the segmentation result. The method has high estimation accuracy, and the estimation performance is not affected by the modulation mode and the spectrum aliasing degree, and has high robustness.

Description

Technical Field

[0001] The embodiments of the present application relate to the technical field of electromagnetic space signal processing, and in particular to a method for intelligently estimating the number of signal sources of time-frequency overlapping multiple signals under non-Gaussian interference. Background Art

[0002] Estimating the number of signal sources originates in the field of array signal processing technology and is also a key research topic in electromagnetic space signal processing technology. Only after accurately determining the number of signal sources can further work be carried out. Common methods for estimating the number of signal sources are based on overdetermined or positive definite conditions, that is, when the number of receiving channels is greater than or equal to the number of signal sources. Examples include estimation methods based on the Akaike Information Criterion, estimation methods based on the Minimum Description Length Criterion, algorithms based on Gale Circle estimation, and singular value decomposition. Both the AIC and MDL criteria are well-suited for practical engineering applications. However, under small sample conditions, the AIC and MDL criteria can suffer from overestimation and underestimation, respectively. Furthermore, both the AIC and MDL criteria require Gaussian white noise and are only applicable to overdetermined or positive definite conditions. In underdetermined conditions, they cannot accurately estimate the number of signal sources.

[0003] In recent years, domestic and foreign teams have conducted research on the problem of estimating the number of signal sources in underdetermined conditions, especially in the special case of underdetermined single channels. A commonly used single-channel signal source number estimation idea is to perform dimensionality expansion operations on the time-frequency overlapping signal with the help of other auxiliary methods, convert the time-frequency overlapping signal into a virtual multi-channel signal, and then use the multi-channel signal source number estimation method to estimate the number of signal sources on the virtual multi-channel signal. Pan et al. decomposed the time-frequency overlapping signal through empirical mode decomposition to obtain the intrinsic mode function, and combined it with the IMF to form a multidimensional signal to achieve dimensionality expansion of the time-frequency overlapping signal. Then, the multi-channel source number estimation method was applied to the multidimensional signal to obtain the number of signal sources. However, this type of method is greatly affected by the spectrum overlap rate and has certain limitations.

[0004] With the development of deep learning technology, research on source number estimation has also been gradually introduced. Although still in its infancy, some research results have been achieved. Zhang et al. directly fed time signals as input features into the E2ECNN network, achieving end-to-end source number estimation. Andrei et al. designed a deep stacked convolutional network with a corresponding structure to address the problem of estimating the number of mixed speech signals. However, this method is only for estimating the number of speech signals, and its applicability to communication signals requires further verification. Shen et al. reconstructed the received complex signal into in-phase and quadrature data to adapt a CNN. They leveraged the CNN's powerful feature extraction capabilities to extract deep features of the mixed signal, thereby estimating the number of sources. Currently proposed deep learning-based source number estimation methods are all in their infancy. The neural network models they use are mostly classic shallow networks with relatively simple structures, and their performance does not meet practical requirements.

[0005] Through the above analysis, the current spectrum prediction method has the following defects.

[0006] First, the currently proposed methods for estimating the number of signal sources require certain prior information or target specific mixed signals to achieve good estimation performance, which has certain limitations.

[0007] Second, most of the currently proposed methods for estimating the number of signal sources consider the influence of Gaussian noise, and there has been no in-depth study on the number estimation under the conditions of coexistence of non-Gaussian interference and Gaussian noise.

[0008] Third, although the source number estimation method based on deep learning has improved performance compared with traditional methods, the models used are mostly shallow networks, and the extraction of input features is not sufficient. Summary of the Invention

[0009] To solve the above technical problems, an embodiment of the present application provides an intelligent estimation method for the number of signal sources of time-frequency overlapping multi-signals under non-Gaussian interference, which effectively solves the problem of estimating the number of signal sources of time-frequency overlapping multi-signals under the coexistence of Gaussian noise and alpha-stable noise, and the overall estimation effect is superior. The estimation performance is not affected by the modulation mode and spectrum aliasing degree, and has good robustness.

[0010] To achieve the above-mentioned purpose, an embodiment of the present application proposes a method for intelligently estimating the number of signal sources of time-frequency overlapping multiple signals under non-Gaussian interference, the method comprising the following steps: sparsely decomposing the acquired time-frequency overlapping signal into multiple matching signals through a matching pursuit algorithm, and using a nonlinear transformer to weaken the influence of alpha stable noise on the time-frequency overlapping signal, using multiple matching signals and the original signal to form a virtual multi-channel signal to construct a generalized correlation matrix; performing data preprocessing operations on the generalized correlation matrix, increasing the difference between the signal eigenvalue and the noise eigenvalue through eigenvalue decomposition operations and similarity transformation operations to obtain a processed generalized correlation matrix; inputting the processed generalized correlation matrix into an improved U-Net network, finding the boundary between the signal eigenvalue and the noise eigenvalue, obtaining the segmentation result output by the improved U-Net network, and realizing intelligent estimation of the number of signal sources of time-frequency overlapping multiple signals under non-Gaussian interference based on the segmentation result.

[0011] To achieve the above-mentioned purpose, an embodiment of the present application also proposes an intelligent estimation system for the number of sources of time-frequency overlapping multiple signals under non-Gaussian interference, wherein the system includes: a matrix construction module, which is used to sparsely decompose the acquired time-frequency overlapping signal into multiple matching signals through a matching pursuit algorithm, and use a nonlinear transformer to weaken the influence of alpha stable noise on the time-frequency overlapping signal, and use multiple matching signals and the original signal to form a virtual multi-channel signal to construct a generalized correlation matrix; a data preprocessing module, which is used to perform data preprocessing operations on the generalized correlation matrix, increase the difference between the signal eigenvalue and the noise eigenvalue through eigenvalue decomposition operations and similarity transformation operations, and obtain a processed generalized correlation matrix; a source number estimation module, which is used to input the processed generalized correlation matrix into an improved U-Net network, find the boundary between the signal eigenvalue and the noise eigenvalue, obtain the segmentation result output by the improved U-Net network, and realize intelligent estimation of the number of sources of time-frequency overlapping multiple signals under non-Gaussian interference based on the segmentation result.

[0012] To achieve the above-mentioned purpose, an embodiment of the present application also proposes an electronic device, comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the above-mentioned method for intelligently estimating the number of signal sources of time-frequency overlapping multiple signals under non-Gaussian interference.

[0013] To achieve the above-mentioned purpose, an embodiment of the present application also proposes a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it can implement the above-mentioned method for intelligently estimating the number of signal sources of time-frequency overlapping multiple signals under non-Gaussian interference.

[0014] The present invention proposes an intelligent method for estimating the number of sources in time-frequency overlapping multi-signals under non-Gaussian interference. The method uses a matching pursuit algorithm to sparsely decompose the time-frequency overlapping signals into multiple matching signals. A nonlinear transformer is then used to mitigate the influence of alpha-stable noise on the time-frequency overlapping signals, thereby constructing a generalized correlation matrix. Eigenvalue decomposition and similarity transformation operations are then performed on the generalized correlation matrix to increase the difference between the signal eigenvalues ​​and the noise eigenvalues, resulting in a processed generalized correlation matrix. The processed generalized correlation matrix is ​​then treated as a "two-dimensional image," with each signal eigenvalue in the matrix treated as an independent source target and the noise eigenvalues ​​as the background of the "two-dimensional image." Finally, an improved U-Net network is used to perform semantic segmentation between the source target and the noise background. The number of sources can be determined based on the segmentation output. This method effectively solves the problem of estimating the number of sources in time-frequency overlapping multi-signals under the coexistence of Gaussian noise and alpha-stable noise. The overall estimation is superior, and the estimation performance is unaffected by the modulation scheme and the degree of spectral aliasing, demonstrating excellent robustness.

[0015] Optionally, before sparsely decomposing the acquired time-frequency overlapping signal into a plurality of matching signals using a matching pursuit algorithm, the method further includes:

[0016] Obtain the time-frequency overlapping signal and establish a time-frequency overlapping signal reception model. The signal components in the time-frequency overlapping signal are independent of each other, and the signal components and noise are also independent of each other. The time-frequency overlapping signal reception model is expressed by the formula:

[0017]

[0018] Where M is the total number of signal components, s i (t) represents the i-th signal component, h i is a preset constant, w(t) represents Gaussian white noise, u(t) represents alpha stable distribution noise, A i For s i (t) signal amplitude, a i (c) represents the code element sequence sent, C is the total number of code elements sent, f i For s i (t) is the carrier frequency, is the initial phase, p i (t) is the shaped pulse function with a roll-off factor of α = 0.5, T si is the symbol period, and x(t) represents the time-frequency overlapping signal reception model.

[0019] Optionally, a symmetric alpha stable distribution is used in the time-frequency overlapping signal reception model to characterize non-Gaussian interference. The characteristic function expression of non-Gaussian interference is:

[0020] φ(w)=exp(jμw-γ|w| ζ );

[0021] Among them, φ(w) is the characteristic function of non-Gaussian interference, ζ is the characteristic factor used to control the tail thickness in the alpha-stable distribution, indicating the strength of the impulse, μ is the position parameter used to control the center position of the alpha-stable distribution, indicating the offset of the probability density function on the horizontal axis, and γ is the scale parameter used to measure the degree to which the alpha-stable distribution deviates from the mean.

[0022] Optionally, the acquired time-frequency overlapping signal is sparsely decomposed into multiple matching signals by a matching pursuit algorithm, and a nonlinear transformer is used to reduce the influence of alpha stable noise on the time-frequency overlapping signal. The multiple matching signals and the original signal are used to form a virtual multi-channel signal, including:

[0023] Based on the time-frequency overlapping signal reception model, the discrete expression of the single-channel reception signal is established. The discrete expression of the single-channel reception signal is:

[0024]

[0025] The matching pursuit algorithm is used to sparsely represent x(n). The sparse representation of x(n) is:

[0026]

[0027] Among them, K is the total number of iterations, r k (n) is the residual signal after the kth iteration, g k (n) is the same as r k (n) Gabor atom with the largest inner product, <·,·> indicates the inner product operation;

[0028] Save the projection of the best matching atom in each iteration, that is, save <r k (n),g k (n)>·g k (n), and use it as a dimension in the virtual multi-channel signal, and finally obtain multiple matching signals, which are expressed by the formula:

[0029]

[0030] Optionally, a generalized correlation matrix is ​​constructed using the following formula:

[0031]

[0032] Among them, f[y i (n)] represents the nonlinear transformation to suppress the interference of alpha noise, if |yi (n)|<λ i , then f[y i (n)]=1, if |y i (n)|≥λ i , then f[y i (n)]=|y i (n)|+|ξ|, |ξ| is the compression factor, and it is specified y i The median of (n)|, G ij Represents the element in row i and column j in G.

[0033] Optionally, a data preprocessing operation is performed on the generalized correlation matrix to increase the difference between the signal eigenvalue and the noise eigenvalue through an eigenvalue decomposition operation and a similarity transformation operation to obtain a processed generalized correlation matrix, including:

[0034] The generalized correlation matrix G is divided into blocks as follows:

[0035]

[0036] Among them, G1 is a square matrix consisting of the elements of the first K-1 rows and the first K-1 columns of G, g is a column vector consisting of the elements of the first K-1 rows of the Kth column of G, and g H is a row vector consisting of the elements of the first K-1 columns of the K-th row of G;

[0037] Perform eigenvalue decomposition on the square matrix G1. The eigenvalue decomposition is achieved by the following formula:

[0038]

[0039] T1=[t1,t2,…,t K-1 ];

[0040] ∑1=diag(τ1,τ2,…,τ K-1 );

[0041] Among them, T1 is the unitary matrix composed of the eigenvectors of G1, t K-1 represents the K-1th eigenvector of G1, ∑1 is the diagonal matrix of the eigenvalues ​​of G1, τ K-1 represents the K-1th eigenvalue of G1. The eigenvalues ​​of G and G1 satisfy the following relationship:

[0042] λ1≥τ1…≥λ M+1 ≥τ M+1 ≥…λ K-1 ≥τ K-1 ≥λ K ;

[0043] Among them, λ K represents the Kth eigenvalue of G;

[0044] make Based on T2, a unitary transformation is performed on G to obtain a unitary transformation matrix G2. The unitary transformation matrix G2 is expressed by the formula:

[0045]

[0046] Construct a diagonal matrix P based on ∑1. The diagonal matrix P is expressed by the formula:

[0047] P=diag(p1,p2,…,p K );

[0048]

[0049] k=1,2,…,K-1;

[0050]

[0051] The diagonal matrix P is used to perform a similarity transformation on the unitary transformation matrix G2 to obtain the similarity transformation matrix G3. The similarity transformation matrix G3 is the processed generalized correlation matrix. The similarity transformation matrix G3 is expressed by the formula:

[0052]

[0053] Optionally, the processed generalized correlation matrix is ​​input into the improved U-Net network, the boundary between the signal eigenvalue and the noise eigenvalue is found, and the segmentation result output by the improved U-Net network is obtained. According to the segmentation result, the number of signal sources of time-frequency overlapping multi-signals under non-Gaussian interference is intelligently estimated, including: reducing the four-layer structure of the U-Net network to two layers, and adding a batch normalization layer and a ReLU activation function layer after each convolution layer of the original encoding operation in the encoder of the U-Net network, and adding a shortcut connection outside the convolution layer to The output of the convolutional layer is added to the original input to obtain an improved U-Net network; the similarity transformation matrix G3 is input into the improved U-Net network, and the normalized probability of each pixel point in the similarity transformation matrix G3 belonging to signal or noise is output, the dividing line between the signal eigenvalue and the noise eigenvalue is determined, and the segmentation result output by the improved U-Net network is obtained; each row in the segmentation result is traversed in turn, all elements of the current row are accumulated to obtain a K-dimensional vector, and the number of elements in the K-dimensional vector with values ​​greater than K / 2 is counted to obtain the number of signal sources. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the related technologies, the following is a brief introduction to the drawings required for use in the embodiments of the present application or the description of the related technologies. Obviously, the following drawings are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work. The drawings described here are only used to explain the present application and are not used to limit the present application.

[0055] Figure 1 This is a flow chart of a method for intelligently estimating the number of signal sources of time-frequency overlapping multiple signals under non-Gaussian interference provided in one embodiment of the present application;

[0056] Figure 2 This is a performance diagram of a method for intelligently estimating the number of signal sources of time-frequency overlapping multiple signals under non-Gaussian interference provided in one embodiment of the present application;

[0057] Figure 3 1 is a structural diagram of an intelligent estimation system for the number of signal sources of time-frequency overlapping multiple signals under non-Gaussian interference, provided in another embodiment of the present application;

[0058] Figure 4 It is a structural diagram of an electronic device provided in another embodiment of the present application. DETAILED DESCRIPTION

[0059] In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, the embodiments of the present application will be described in detail below with reference to the accompanying drawings. In the various embodiments of the present application, many technical details are proposed to enable the reader to better understand the present application. However, even without these technical details and various changes and modifications based on the following embodiments, the technical solutions claimed in the present application can be implemented. The division of the following embodiments is only for the convenience of description and should not constitute any limitation on the specific implementation of the present application. The various embodiments can be combined with each other and referenced to each other under the premise of no contradiction.

[0060] An embodiment of the present application proposes a method for intelligently estimating the number of signal sources of time-frequency overlapping multiple signals under non-Gaussian interference, which is applied to an electronic device, wherein the electronic device can be a terminal or a server. In this embodiment and the following embodiments, the electronic device is explained using the server as an example. The implementation details of the method for intelligently estimating the number of signal sources of time-frequency overlapping multiple signals under non-Gaussian interference proposed in this embodiment are specifically described below. The following content is only the implementation details provided for the convenience of understanding and is not necessary for implementing this solution.

[0061] The specific process of the method for intelligently estimating the number of signal sources of time-frequency overlapping multi-signals under non-Gaussian interference proposed in this embodiment can be as follows: Figure 1 Shown, including:

[0062] S1, the obtained time-frequency overlapping signal is sparsely decomposed into multiple matching signals through the matching pursuit algorithm, and a nonlinear transformer is used to weaken the influence of alpha stable noise on the time-frequency overlapping signal. Multiple matching signals are combined with the original signal to form a virtual multi-channel signal to construct a generalized correlation matrix.

[0063] In the specific implementation, the server first needs to obtain the time-frequency overlapping signal, and then use the matching pursuit algorithm to sparsely decompose the obtained time-frequency overlapping signal into multiple matching signals, and use a nonlinear transformer to weaken the influence of alpha stable noise on the time-frequency overlapping signal. Then, multiple matching signals are used together with the original signal to form a virtual multi-channel signal to construct a generalized correlation matrix.

[0064] In one example, the server needs to acquire the time-frequency overlapping signal in real time and establish a time-frequency overlapping signal reception model. In the time-frequency overlapping signal reception model, each signal component is independent of each other, and each signal component is also independent of noise.

[0065] In one example, the modulation mode of the transmitted signal may be MPSK or 16QAM.

[0066] In one example, the time-frequency overlapping signal reception model can be expressed as:

[0067]

[0068] Where M is the total number of signal components, s i (t) represents the i-th signal component, h i is a preset constant, w(t) represents Gaussian white noise, u(t) represents alpha stable distribution noise, A i For s i (t) signal amplitude, a i (c) represents the code element sequence sent, C is the total number of code elements sent, f i For s i (t) is the carrier frequency, is the initial phase, p i (t) is the shaped pulse function with a roll-off coefficient of α = 0.5, t si is the symbol period, and x(t) represents the time-frequency overlapping signal reception model.

[0069] In one example, a symmetric alpha stable distribution is used in a time-frequency overlapping signal reception model to characterize non-Gaussian interference. The characteristic function expression of non-Gaussian interference is:

[0070] φ(w)=exp(jμw-γ|w| ζ);

[0071] Among them, φ(w) is the characteristic function of non-Gaussian interference, ζ is the characteristic factor used to control the tail thickness in the alpha-stable distribution, indicating the strength of the impulse, μ is the position parameter used to control the center position of the alpha-stable distribution, indicating the offset of the probability density function on the horizontal axis, and γ is the scale parameter used to measure the degree to which the alpha-stable distribution deviates from the mean.

[0072] In one example, the server first needs to establish a discrete expression for a single-channel received signal based on a time-frequency overlapping signal reception model. The discrete expression for a single-channel received signal is:

[0073]

[0074] Subsequently, the matching pursuit algorithm is used to sparsely represent x(n). The sparse representation of x(n) is:

[0075]

[0076] Among them, K is the total number of iterations, r k (n) is the residual signal after the kth iteration, g k (n) is the same as r k (n) The Gabor atom with the largest inner product, <·,·> indicates the inner product operation, n = 1, 2, …, N, where N is the total number of sampling points.

[0077] Finally, the server saves the projection of the best matching atom in each iteration, that is, saves the sparse representation of x(n) <r k (n),g k (n)>·g k (n), and use it as a dimension in the virtual multi-channel signal, and finally obtain multiple matching signals, which are expressed by the formula:

[0078]

[0079] For the convenience of representation, let y k+1 (n)= <r k (n),g k (n)>·g k (n).

[0080] In an example, the server constructs a generalized correlation matrix G based on Y. The generalized correlation matrix G can be expressed as follows:

[0081]

[0082] Among them, f[y i(n)] represents the nonlinear transformation to suppress the interference of alpha noise, if |y i (n)|<λ i , then f[y i (n)]=1, if |y i (n)|≥λ i , then f[y i (n)]=|y i (n)|+|ξ|, |ξ| is the compression factor, and it is specified y i The median of (n)|, G ij Represents the element in row i and column j in G.

[0083] S2, performing data preprocessing operations on the generalized correlation matrix, increasing the difference between the signal eigenvalue and the noise eigenvalue through eigenvalue decomposition operations and similarity transformation operations, and obtaining the processed generalized correlation matrix.

[0084] In a specific implementation, after obtaining the generalized correlation matrix G, the server needs to perform preprocessing operations on the generalized correlation matrix G, including eigenvalue decomposition operations and similarity transformation operations, to increase the difference between the signal eigenvalues ​​and the noise eigenvalues, and obtain the processed generalized correlation matrix.

[0085] In an example, the server performs a preprocessing operation on the generalized correlation matrix G. First, the generalized correlation matrix G needs to be divided into blocks as follows:

[0086]

[0087] Among them, G1 is a square matrix consisting of the elements of the first K-1 rows and the first K-1 columns of G, g is a column vector consisting of the elements of the first K-1 rows of the Kth column of G, and g H is a row vector consisting of the elements of the first K-1 columns of the Kth row of G.

[0088] Next, the server performs eigenvalue decomposition on the matrix G1. The eigenvalue decomposition is achieved by the following formula:

[0089]

[0090] T1=[t1,t2,…,t K-1 ];

[0091] ∑1=diag(τ1,τ2,…,τ K-1 );

[0092] Among them, T1 is the unitary matrix composed of the eigenvectors of G1, t K-1represents the K-1th eigenvector of G1, ∑1 is the diagonal matrix of the eigenvalues ​​of G1, τ K-1 represents the K-1th eigenvalue of G1. The eigenvalues ​​of G and G1 satisfy the following relationship:

[0093] λ1≥τ1…≥λ M+1 ≥τ M+1 ≥…λ K-1 ≥τ K-1 ≥λ K ;

[0094] Among them, λ K represents the Kth eigenvalue of G.

[0095] The server then needs to Based on T2, a unitary transformation is performed on G to obtain a unitary transformation matrix G2. The unitary transformation matrix G2 is expressed by the formula:

[0096]

[0097] After completing the unitary transformation and obtaining the unitary transformation matrix G2, the server constructs a diagonal matrix P based on ∑1. The diagonal matrix P is expressed by the formula:

[0098] P=diag(p1,p2,…,p K );

[0099]

[0100] k=1,2,…,K-1;

[0101]

[0102] Finally, the server uses the diagonal matrix P to perform a similarity transformation on the unitary transformation matrix G2 to obtain the similarity transformation matrix G3. The similarity transformation matrix G3 is the processed generalized correlation matrix. The similarity transformation matrix G3 is expressed by the formula:

[0103]

[0104] The similarity transformation matrix G3 and the unitary transformation matrix G2 are similar matrices. They have the same eigenvalues ​​and are proportional to different factors p1 / p K The original values ​​are compressed, which makes the boundary between the signal characteristic value and the noise characteristic value more obvious, which is more conducive to distinguishing between signals and noise.

[0105] S3, inputs the processed generalized correlation matrix into the improved U-Net network, finds the boundary between the signal eigenvalue and the noise eigenvalue, obtains the segmentation result output by the improved U-Net network, and realizes the intelligent estimation of the number of signal sources of time-frequency overlapping multi-signals under non-Gaussian interference based on the segmentation result.

[0106] In one example, after the server completes the data preprocessing operation and obtains the processed generalized correlation matrix G (i.e., the similarity transformation matrix G3), the processed generalized correlation matrix G can be input into the improved U-Net network to find the boundary between the signal eigenvalue and the noise eigenvalue, and obtain the segmentation result output by the improved U-Net network. Based on the segmentation result, intelligent estimation of the number of signal sources of time-frequency overlapping multiple signals under non-Gaussian interference is realized.

[0107] In one example, to enable the U-Net network to process similarity transformation matrices G3 of small dimensions, the server needed to improve the U-Net network by reducing its four-layer structure to two layers. A batch normalization layer and a ReLU activation function layer were added after each convolution layer in the original encoding operation in the U-Net encoder. A shortcut connection was added outside the convolution layer to add the convolution layer output to the original input, resulting in an improved U-Net network. This improved U-Net network helps preserve the original input information and avoids the loss of important features.

[0108] Next, the server inputs the similarity transformation matrix G3 into the improved U-Net network, outputs the normalized probability that each pixel in the similarity transformation matrix G3 belongs to signal or noise, determines the dividing line between the signal eigenvalue and the noise eigenvalue, and obtains the segmentation result output by the improved U-Net network.

[0109] Finally, the server traverses each row in the segmentation result in turn, accumulates all elements of the current row to obtain a K-dimensional vector, and counts the number of elements in the K-dimensional vector whose values ​​are greater than K / 2. The number of elements in the K-dimensional vector whose values ​​are greater than K / 2 is the number of information sources.

[0110] In this embodiment, a matching pursuit algorithm is used to perform sparse decomposition on time-frequency overlapping signals. A nonlinear transformer is then used to reduce the influence of alpha-stable noise on the time-frequency overlapping signals, thereby constructing a generalized correlation matrix. Eigenvalue decomposition and similarity transformation operations are then performed on the generalized correlation matrix to increase the difference between the signal eigenvalues ​​and the noise eigenvalues, resulting in a processed generalized correlation matrix. The processed generalized correlation matrix is ​​considered a "two-dimensional image," with each signal eigenvalue in the matrix considered an independent source target, and the noise eigenvalues ​​considered the background of the "two-dimensional image." Finally, an improved U-Net network is used to perform semantic segmentation between the source target and the noise background. The number of sources can be determined based on the output segmentation results. This approach effectively solves the problem of estimating the number of sources in time-frequency overlapping multi-signals under the coexistence of Gaussian noise and alpha-stable noise. The overall estimation effect is superior, and the estimation performance is unaffected by the modulation mode and the degree of spectral aliasing, demonstrating excellent robustness.

[0111] The steps of the various methods above are divided only for clarity of description. They can be combined into one step or some steps can be decomposed into multiple steps during implementation. As long as they include the same logical relationship, they are all within the scope of protection of this application. Adding insignificant modifications or introducing insignificant designs to the algorithm or process without changing the core design of the algorithm and process are all within the scope of protection of this application.

[0112] In an example, in order to evaluate the intelligent estimation method for the number of signal sources of time-frequency overlapping multiple signals under non-Gaussian interference proposed in this application, we conducted relevant simulation experiments. Through simulation experiments, we verified the estimation performance of the intelligent estimation method for the number of signal sources of time-frequency overlapping multiple signals under non-Gaussian interference proposed in this application under the coexistence conditions of Gaussian noise and alpha-stable noise. Specifically, the correct estimation probability under different signal-to-noise ratios was used as the performance evaluation criterion.

[0113] The parameters in the simulation experiment are set as follows: the modulation types of the independent signal sources in the time-frequency overlapping signal are BPSK, QPSK, 8PSK and 16QAM, and the symbol rate is f b =1000Baud, the carrier frequencies are set to f c0 =3800Hz, f c1 =4400Hz, f c2 =5000Hz, f c3 =5600Hz, the spectrum aliasing degree is 68.4%, the channel is a Gaussian noise channel, and the sampling rate is f s =16000 Hz, the length of each sample data is 12800, and the signal components are mixed with equal power.

[0114] The signal-to-noise ratio (SNR) range was set from -7dB to 7dB. 1,600 data samples were generated for each SNR, including 400 samples each for single, two, three, and four source mixtures, for a total of 24,000 samples. The network model was trained in PyTorch 1.11.0. The concepts of signal-to-noise ratio (SNR) and signal-to-interference ratio (SIR) were introduced, representing the power ratio of the signal to Gaussian noise and the power ratio of the signal to alpha-stable noise interference, respectively.

[0115] Figure 2 The relationship between the probability of correct estimation and the number of sources under different signal-to-noise ratios is demonstrated, demonstrating that the proposed method for intelligently estimating the number of sources for time-frequency overlapping multiple signals under non-Gaussian interference can effectively estimate the number of sources under the coexistence of Gaussian noise and alpha-stable noise. Furthermore, under the same signal-to-noise ratio, the probability of correct estimation gradually decreases as the number of sources increases. This is because, at the same signal-to-noise ratio, the more types of signals in the mixed signal, the lower the equivalent signal-to-noise ratio for each signal, resulting in a decrease in the estimation performance of the proposed method for intelligently estimating the number of sources for time-frequency overlapping multiple signals under non-Gaussian interference.

[0116] Another embodiment of the present application proposes an intelligent estimation system for the number of signal sources of time-frequency overlapping multiple signals under non-Gaussian interference. The implementation details of the intelligent estimation system for the number of signal sources of time-frequency overlapping multiple signals under non-Gaussian interference proposed in this embodiment are described in detail below. The following content is only the implementation details provided for the convenience of understanding and is not necessary for the implementation of this example.

[0117] Figure 3 This is a structural diagram of an intelligent estimation system for the number of signal sources of time-frequency overlapping multiple signals under non-Gaussian interference proposed in this embodiment. The system includes: a matrix construction module M1, a data preprocessing module M2 and a signal source number estimation module M3.

[0118] The matrix construction module M1 is used to sparsely decompose the acquired time-frequency overlapping signal into multiple matching signals through the matching pursuit algorithm, and use a nonlinear transformer to reduce the influence of alpha stable noise on the time-frequency overlapping signal. The multiple matching signals and the original signal are combined to form a virtual multi-channel signal to construct a generalized correlation matrix.

[0119] The data preprocessing module M2 is used to perform data preprocessing operations on the generalized correlation matrix, increase the difference between the signal eigenvalue and the noise eigenvalue through eigenvalue decomposition operations and similarity transformation operations, and obtain the processed generalized correlation matrix.

[0120] The signal source number estimation module M3 is used to input the processed generalized correlation matrix into the improved U-Net network, find the boundary between the signal eigenvalue and the noise eigenvalue, obtain the segmentation result output by the improved U-Net network, and realize the intelligent estimation of the number of signal sources of time-frequency overlapping multi-signals under non-Gaussian interference based on the segmentation result.

[0121] It is worth mentioning that all modules involved in this embodiment are logical modules. In actual applications, a logical unit can be a physical unit, a part of a physical unit, or a combination of multiple physical units. In addition, to highlight the innovation of this application, this embodiment does not include units that are not closely related to solving the technical problem proposed by this application. However, this does not mean that other units do not exist in this embodiment.

[0122] It is not difficult to find that this embodiment is a system embodiment corresponding to the above-mentioned method embodiments, and this embodiment can be implemented in conjunction with the above-mentioned method embodiments. The relevant technical details and technical effects mentioned in the above-mentioned method embodiments are still valid in this embodiment, and to reduce repetition, they are not repeated here. Accordingly, the relevant technical details mentioned in this embodiment can also be applied to the above-mentioned method embodiments.

[0123] Another embodiment of the present application provides an electronic device, the specific structure of which is as follows: Figure 4 As shown, it includes: at least one processor C1; and a memory C2 communicatively connected to the at least one processor C1; wherein the memory C2 stores instructions that can be executed by the at least one processor C1, and the instructions are executed by the at least one processor C1 so that the at least one processor C1 can execute a method for intelligently estimating the number of signal sources of time-frequency overlapping multiple signals under non-Gaussian interference as described in the above-mentioned method embodiments.

[0124] The memory and processor can be connected using a bus. The bus can include any number of interconnected buses and bridges, connecting various circuits within one or more processors and the memory. The bus can also connect various other circuits, such as peripherals, voltage regulators, and power management circuits. These are well known in the art and will not be described further herein. The bus interface is responsible for providing an interface between the bus and the transceiver. The transceiver can be a single component or multiple components, such as multiple receivers and transmitters, providing a unit for communicating with various other devices over a transmission medium.

[0125] The processor is responsible for managing the bus and general processing, and can also provide various functions, including timing, peripheral interfaces, voltage regulation, power management, and other control functions. Memory can be used to store data used by the processor when performing operations.

[0126] Another embodiment of the present application proposes a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it can implement a method for intelligently estimating the number of signal sources of time-frequency overlapping multiple signals under non-Gaussian interference as described in the above method embodiments.

[0127] That is, those skilled in the art will appreciate that all or part of the steps in the above-described method embodiments can be implemented by instructing related hardware through a program, wherein the program is stored in a storage medium and includes a number of instructions for causing a device (such as a single-chip microcomputer, chip, etc.) or a processor to execute all or part of the steps in the above-described method embodiments. The storage medium includes various media capable of storing program code, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0128] Those skilled in the art will appreciate that the above embodiments are specific embodiments for implementing the present application, and that in actual applications, various changes may be made thereto in form and detail without departing from the spirit and scope of the present application.

Claims

1. A method for intelligently estimating the number of signal sources of time-frequency overlapping multi-signals under non-Gaussian interference, characterized in that: The method comprises: The obtained time-frequency overlapping signal is sparsely decomposed into multiple matching signals through the matching pursuit algorithm, and the influence of alpha stable noise on the time-frequency overlapping signal is weakened by a nonlinear transformer. The multiple matching signals and the original signal are combined to form a virtual multi-channel signal to construct a generalized correlation matrix. Perform data preprocessing on the generalized correlation matrix, increase the difference between the signal eigenvalue and the noise eigenvalue through eigenvalue decomposition and similarity transformation, and obtain the processed generalized correlation matrix; The processed generalized correlation matrix is ​​input into the improved U-Net network to find the boundary between the signal eigenvalue and the noise eigenvalue, and the segmentation result output by the improved U-Net network is obtained. Based on the segmentation result, the number of signal sources of time-frequency overlapping multi-signals under non-Gaussian interference is intelligently estimated; The processed generalized correlation matrix is ​​input into the improved U-Net network to find the boundary between the signal eigenvalue and the noise eigenvalue. The segmentation result output by the improved U-Net network is obtained. Based on the segmentation result, the number of signal sources of time-frequency overlapping multi-signals under non-Gaussian interference is intelligently estimated, including: The four-layer structure of the U-Net network is reduced to two layers, and a batch normalization layer and a ReLU activation function layer are added after each convolution layer of the original encoding operation in the encoder of the U-Net network. A shortcut connection is added outside the convolution layer to add the output of the convolution layer to the original input, thereby obtaining an improved U-Net network; The similarity transformation matrix Input into the improved U-Net network and output the similarity transformation matrix The normalized probability of each pixel belonging to signal or noise is determined, the dividing line between the signal eigenvalue and the noise eigenvalue is determined, and the segmentation result output by the improved U-Net network is obtained; Traverse each row in the split result in turn, accumulate all elements of the current row, and get a dimensional vector, statistics The value of the element in the dimension vector is greater than The number of sources is obtained by .

2. The method for intelligently estimating the number of signal sources of time-frequency overlapping multi-signals under non-Gaussian interference according to claim 1, wherein: Before sparsely decomposing the acquired time-frequency overlapping signal into a plurality of matching signals by a matching pursuit algorithm, the method further includes: Obtain the time-frequency overlapping signal and establish a time-frequency overlapping signal reception model. The signal components in the time-frequency overlapping signal are independent of each other, and the signal components and noise are also independent of each other. The time-frequency overlapping signal reception model is expressed by the formula: ； ； ； in, is the total number of signal components, Indicates the signal components, is a preset constant, represents Gaussian white noise, represents alpha stable distributed noise, for The signal amplitude, represents the transmitted symbol sequence, is the total number of code elements sent, for The carrier frequency, is the initial phase, The roll-off coefficient is The shaped pulse function, is the symbol period, Represents the time-frequency overlapping signal reception model.

3. The method for intelligently estimating the number of signal sources of time-frequency overlapping multi-signals under non-Gaussian interference according to claim 2, characterized in that: In the time-frequency overlapping signal reception model, the symmetric alpha stable distribution is used to characterize non-Gaussian interference. The characteristic function expression of non-Gaussian interference is: ； in, is the characteristic function of non-Gaussian interference, is a characteristic factor used to control the tail thickness in the alpha stable distribution, indicating the strength of the pulse. is the location parameter used to control the center position of the alpha stable distribution and represents the offset of the probability density function on the horizontal axis. is a scale parameter that measures the degree to which the alpha stable distribution deviates from the mean.

4. The method for intelligently estimating the number of signal sources of time-frequency overlapping multiple signals under non-Gaussian interference according to claim 3, wherein: The obtained time-frequency overlapping signal is sparsely decomposed into multiple matching signals through the matching pursuit algorithm, and a nonlinear transformer is used to reduce the influence of alpha stable noise on the time-frequency overlapping signal. The multiple matching signals and the original signal are used to form a virtual multi-channel signal, including: Based on the time-frequency overlapping signal reception model, the discrete expression of the single-channel reception signal is established. The discrete expression of the single-channel reception signal is: ； Through the matching pursuit algorithm For sparse representation, The sparse representation of is: ； in, is the total number of iterations, For the The residual signal after iterations is For The Gabor atom with the largest inner product, Indicates inner product operation; Save the projection of the best matching atom in each iteration, that is, save , and use it as a dimension in the virtual multi-channel signal, and finally obtain multiple matching signals, which are expressed by the formula: 。 5. The method for intelligently estimating the number of signal sources of time-frequency overlapping multiple signals under non-Gaussian interference according to claim 4, wherein: The generalized correlation matrix is ​​constructed using the following formula: ； ； ； in, Indicates that the nonlinear transformation suppresses the interference of alpha noise. If ,but ,like ,but , is the compression factor, , for the median of express The Rank Elements of a column.

6. The method for intelligently estimating the number of signal sources of time-frequency overlapping multiple signals under non-Gaussian interference according to claim 5, characterized in that: The generalized correlation matrix is ​​preprocessed to increase the difference between the signal eigenvalue and the noise eigenvalue through eigenvalue decomposition and similarity transformation, and the processed generalized correlation matrix is ​​obtained, including: The generalized correlation matrix The blocks are divided as follows: ； in, is Before Line and front The square matrix of the elements of the column, is No. Front of column The column vector of the elements of the row, is No. Before the trip The row vector of the column elements; Opposing Phalanx Perform eigenvalue decomposition, which is achieved by the following formula: ； ； ； in, is The unitary matrix composed of the eigenvectors of express No. feature vectors, yes The diagonal matrix of the eigenvalues ​​of express No. eigenvalues, The eigenvalues ​​of The eigenvalues ​​of satisfy the following relationship: ； in, express No. eigenvalues; make ,based on right Perform unitary transformation to obtain the unitary transformation matrix , unitary transformation matrix It is expressed by the formula: ； exist Construct a diagonal matrix based on , a diagonal matrix It is expressed by the formula: ； ； ； ； Using diagonal matrices Unitary transformation matrix Perform similarity transformation to obtain similarity transformation matrix , similarity transformation matrix That is, the processed generalized correlation matrix, similarity transformation matrix It is expressed by the formula: 。 7. An intelligent estimation system for the number of signal sources of time-frequency overlapping multi-signals under non-Gaussian interference, characterized in that: The system comprises: The matrix construction module is used to sparsely decompose the acquired time-frequency overlapping signal into multiple matching signals through the matching pursuit algorithm, and use a nonlinear transformer to reduce the influence of alpha-stable noise on the time-frequency overlapping signal. The multiple matching signals and the original signal are combined to form a virtual multi-channel signal to construct a generalized correlation matrix. The data preprocessing module is used to perform data preprocessing operations on the generalized correlation matrix, increase the difference between the signal eigenvalue and the noise eigenvalue through eigenvalue decomposition operations and similarity transformation operations, and obtain the processed generalized correlation matrix; The source number estimation module is used to input the processed generalized correlation matrix into the improved U-Net network, find the boundary between the signal eigenvalue and the noise eigenvalue, obtain the segmentation result output by the improved U-Net network, and realize intelligent estimation of the number of sources of time-frequency overlapping multi-signals under non-Gaussian interference based on the segmentation result; The processed generalized correlation matrix is ​​input into the improved U-Net network to find the boundary between the signal eigenvalue and the noise eigenvalue. The segmentation result output by the improved U-Net network is obtained. Based on the segmentation result, the number of signal sources of time-frequency overlapping multi-signals under non-Gaussian interference is intelligently estimated, including: The four-layer structure of the U-Net network is reduced to two layers, and a batch normalization layer and a ReLU activation function layer are added after each convolution layer of the original encoding operation in the encoder of the U-Net network. A shortcut connection is added outside the convolution layer to add the output of the convolution layer to the original input, thereby obtaining an improved U-Net network; The similarity transformation matrix Input into the improved U-Net network and output the similarity transformation matrix The normalized probability of each pixel belonging to signal or noise is determined, the dividing line between the signal eigenvalue and the noise eigenvalue is determined, and the segmentation result output by the improved U-Net network is obtained; Traverse each row in the split result in turn, accumulate all elements of the current row, and get a dimensional vector, statistics The value of the element in the dimension vector is greater than The number of sources is obtained by .

8. An electronic device, characterized in that: include: at least one processor; and, a memory communicatively coupled to the at least one processor; In which, the memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute a method for intelligently estimating the number of signal sources of time-frequency overlapping multiple signals under non-Gaussian interference as described in any one of claims 1 to 6.

9. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, it can implement the method for intelligently estimating the number of signal sources of time-frequency overlapping multiple signals under non-Gaussian interference according to any one of claims 1 to 6.

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