Non-sparse wideband signal reconstruction and detection method based on nuclear norm minimization

Abstract

The application discloses a kind of based on kernel norm minimization non-sparse wideband signal reconstruction and detection method, comprising the following steps: constructing reconstruction network: iterative algorithm is deepened into data-driven reconstruction network, and it is trained;Construct detection network: combine CNN module and Transformer module to construct and train detection network;Compressed signal sampling: based on the architecture of parallel sampling, utilize multiple channels to sample original signal simultaneously, obtain observation signal, and form observation matrix by column stacking;Signal reconstruction: according to the observation matrix obtained by parallel sampling and known measurement matrix, the spectral matrix is recovered using kernel norm minimization, to obtain reconstructed signal;Spectrum occupancy detection: according to reconstructed signal, the detection network is used to determine the spectrum occupancy. The method can improve the reconstruction accuracy and detection accuracy of the signal under low signal-to-noise ratio.

Description

Technical Field

[0001] This invention relates to the field of broadband spectrum sensing technology, and in particular to a method for reconstructing and detecting non-sparse broadband signals based on nuclear norm minimization. Background Technology

[0002] Compressed sensing (CS) is an efficient method for broadband spectral sensing using sampling rates lower than the Nyquist sampling rate. CS acquires discrete samples of the signal through random sampling and then reconstructs the spectral signal using a nonlinear reconstruction algorithm. However, traditional reconstruction methods often rely on empirically determined and optimized regularization coefficients and step sizes, significantly impacting reconstruction accuracy and algorithm convergence. Parameter setting is typically time-consuming and complex, and reconstruction accuracy is low at low signal-to-noise ratios. Furthermore, CS relies on signal sparsity, and reconstruction accuracy is insufficient in non-sparse scenarios. By transforming the signal sparsity constraint into a low-rank constraint, the signal reconstruction problem can be converted into a rank function minimization problem. However, the rank function of a matrix is ​​non-convex and discontinuous, leading to high computational complexity in signal reconstruction. Currently, several signal reconstruction methods based on deep neural networks (DNNs) have been proposed. These DNN models are trained as black boxes, allowing direct reconstruction of the original signal from CS measurement signals. The paper "Deep Learning Based Compressive Sensing for Image Reconstruction and Inference" (IEEE 7th International Conference for Convergence in Technology, 2022) designed a CS-based image reconstruction algorithm to reconstruct the original image from a compressed image. However, this type of method has poor interpretability. Therefore, there is an urgent need to design a reconstruction and detection method for non-sparse broadband signals with low computational complexity, high recovery accuracy, and good interpretability. Summary of the Invention

[0003] The technical problem to be solved by the present invention is how to provide a method for reconstructing and detecting non-sparse broadband signals with low computational complexity, high recovery accuracy and good interpretability, so as to improve the reconstruction accuracy and detection accuracy of signals under low signal-to-noise ratio.

[0004] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a method for reconstructing and detecting non-sparse broadband signals based on nuclear norm minimization, comprising the following steps:

[0005] S101, Constructing the Reconstruction Network: Deeply expand the iterative algorithm into a data-driven reconstruction network and train it;

[0006] S102, Constructing the detection network: Combine the CNN module and the Transformer module to construct and train the detection network;

[0007] S103, Compressed signal sampling: Based on a parallel sampling architecture, multiple channels are used to sample the original signal simultaneously to obtain the observed signal, which is then stacked in columns to form an observation matrix;

[0008] S104, Signal Reconstruction: Based on the observation matrix obtained from parallel sampling and the known measurement matrix, the reconstructed signal is obtained by minimizing the nuclear norm to recover the spectrum matrix;

[0009] S105, Spectrum Occupation Detection: Based on the reconstructed signal, a detection network is used to determine the spectrum occupancy status.

[0010] A further technical solution is that step S101 specifically includes the following steps:

[0011] S1011, Obtain the observation matrix and the perception matrix: Obtain the sample set of the observation matrix by sampling, and then construct a new perception matrix by block diagonalizing the perception matrix of each sampling channel;

[0012] S1012, Constructing the Reconstruction Network: An iterative algorithm based on the deep unfolding method is used to construct the reconstruction network;

[0013] S1013, Training the Reconstruction Network: Using the mean squared error of reconstruction as the loss function, the reconstruction network is trained using the observation matrix and the perception matrix to optimize the parameters of the iterative algorithm.

[0014] A further technical solution is that step S102 specifically includes the following steps:

[0015] S1021, Calculate the power spectral density of the reconstructed signal: Obtain the reconstructed signal from the reconstruction network and calculate its power spectrum;

[0016] S1022, Design the detection network: Build a detection network by combining the CNN module and the Transformer module. Use the CNN to extract features within the frequency band and use the Transformer's long-range capture capability to extract features between frequency bands.

[0017] S1023, Training the detection network: Using the detection mean square error as the loss function, the reconstruction network is trained using the power spectrum of the reconstructed signal.

[0018] A further technical solution is that S103 specifically includes the following steps:

[0019] S1031, Parallel Sampling: Simultaneous acquisition of the observed signal using multiple analog-to-digital converters;

[0020] S1032, Stack by column: Stack the obtained observation signals by column to form an observation matrix;

[0021] S1033, Block diagonalization: Multiple sub-sensory matrices form a new sensing basis matrix along the main diagonal;

[0022] S1034, Matrix Rank Minimization: Utilizing the low-rank property of the original spectral matrix, the reconstruction of non-sparse signals is expressed as a low-rank matrix recovery problem.

[0023] A further technical solution is that step S104 specifically includes the following steps:

[0024] S1041, Minimizing the nuclear norm: Relax the rank function to the nuclear norm, use the alternating direction multiplier method to solve the nuclear norm minimization problem, and obtain the reconstructed spectrum matrix to enhance interpretability;

[0025] S1042, Reconstructing the signal: The observation matrix and sensing matrix processed in step S103 are used as inputs to the reconstruction network. The trained detection network is used to reconstruct the spectrum matrix. The recovered spectrum matrix is ​​then averaged to obtain the reconstructed signal.

[0026] A further technical solution is that step S105 specifically includes the following steps:

[0027] S1051, Signal preprocessing: Calculate the power spectrum of the reconstructed signal;

[0028] S1052, Output spectrum occupancy status: Determine the frequency band occupancy status using a detection network.

[0029] The beneficial effects of adopting the above technical solution are as follows: The method described in this application automatically optimizes parameters by reconstructing the network instead of manually optimizing parameters, inherits the interpretability of iterative algorithms, and combines CNN and Transformer modules. In scenarios such as spectrum leakage and channel aggregation, it has the advantages of low computational complexity, high reconstruction accuracy, good interpretability, and high detection accuracy. Attached Figure Description

[0030] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0031] Figure 1 This is an overall flowchart of the method described in the embodiments of the present invention;

[0032] Figure 2 This is a flowchart of the network reconstruction method described in the embodiments of the present invention;

[0033] Figure 3This is a block diagram illustrating the principle of network reconstruction in the method described in this embodiment of the invention;

[0034] Figure 4 This is a flowchart of the detection network in the method described in the embodiments of the present invention;

[0035] Figure 5 This is a block diagram illustrating the principle of the detection network in the method described in this embodiment of the invention;

[0036] Figure 6 This is a flowchart of the compressed signal sampling process in the method described in the embodiments of the present invention;

[0037] Figure 7 This is a schematic diagram of the parallel sampling structure in the method described in the embodiments of the present invention;

[0038] Figure 8 This is a flowchart of the signal reconstruction process in the method described in the embodiments of the present invention;

[0039] Figure 9 This is a flowchart of spectrum occupancy detection in the method described in the embodiments of the present invention;

[0040] Figure 10 This is a comparison chart of reconstruction methods proposed by different algorithms under different signal-to-noise ratios;

[0041] Figure 11 This is a comparison chart of the proposed detection methods under different signal-to-noise ratios. Detailed Implementation

[0042] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0043] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0044] Overall, such as Figure 1 As shown in the figure, this invention discloses a method for reconstructing and detecting non-sparse broadband signals based on nuclear norm minimization. The method includes the following steps:

[0045] S101, Constructing the Reconstruction Network: The iterative algorithm is expanded through deep expansion to obtain an interpretable reconstruction network. The observation matrix and perception matrix are used as inputs to train the reconstruction network and optimize the parameters of the iterative algorithm.

[0046] S102, Construct the detection network: Combine CNN and Transformer modules to build a detection network. Use the power spectral density of the reconstructed signal obtained from the reconstruction network as input to train the detection network and predict the spectrum occupancy.

[0047] S103, Compressed signal sampling: Multiple observation signals are obtained using a parallel sampling architecture, the observation signals are stacked column by column into an observation matrix, the sub-sensing matrix blocks are diagonalized into a new sensing matrix, and the signal matrix is ​​reconstructed by minimizing the matrix rank by utilizing the low-rank property of the original signal matrix.

[0048] S104, Signal Reconstruction: Since the matrix rank function is non-convex and discontinuous, the matrix rank function is replaced with the matrix nuclear norm, and the spectrum matrix is ​​reconstructed by minimizing the matrix nuclear norm.

[0049] S105, Spectrum Occupancy Detection: Calculate the power spectral density of the reconstructed signal and use it as input to the detection network. Then, use the trained detection network to predict the spectrum occupancy.

[0050] The above steps will be explained in detail below:

[0051] Furthermore, such as Figure 2 As shown, step S101 specifically includes the following steps:

[0052] S1011: Obtain the observation matrix and the perception matrix: obtain the sample set of the observation matrix by sampling, and then construct a new perception matrix by block diagonalizing the perception matrix of each sampling channel;

[0053] The observation matrix is ​​composed of observation signal vectors sampled from each sampling channel, stacked column-wise. The sensing matrix is ​​a mathematical operator that uses linear projection to obtain low-dimensional observation values ​​from high-dimensional signals. The block diagonalization is constructed by multiple sub-sensing matrices along the main diagonal. The formula for diagonalization is:

[0054]

[0055] The column stacking method involves sequentially concatenating sub-measurement vectors into a composite measurement vector, with each sub-vector forming a column, and then stacking all columns from top to bottom to form a longer single-column vector. The column stacking formula is as follows:

[0056]

[0057] S1012: Constructing a signal reconstruction network: Using a traditional iterative algorithm based on a depth expansion method, a signal reconstruction network is constructed; this network is used to reconstruct a high-dimensional signal from a low-dimensional compressed signal; wherein... Figure 3 A schematic diagram of the structure of a reconstructed network constructed using a deep expansion method is presented;

[0058] S1013: Training the signal reconstruction network: Using the reconstruction mean square error as the loss function, the reconstruction network is trained using the observation matrix and the perception matrix, and the parameters of the iterative algorithm are optimized.

[0059] Furthermore, the construction of the reconstructed network in step S101 includes the following steps:

[0060] S1011, Obtain the observation matrix and the perception matrix: Obtain the sample set of the observation matrix by sampling, and then construct a new perception matrix by block diagonalizing the perception matrix of each sampling channel, where the observation matrix is ​​Y and the perception matrix is ​​A;

[0061] S1012, Constructing the signal reconstruction network: In the (k+1)th iteration of the reconstruction network, the first step of the algorithm is:

[0062]

[0063] Where I represents the identity matrix, ρ k+1 This represents the result of the first step of the algorithm in the (k+1)th iteration, where ρ is the learning parameter of the reconstructed network, and Z... k and U k Let represent the results of the third and fourth steps of the algorithm in the k-th iteration, respectively, where vec denotes matrix vectorization, and (·). T Represents the transpose of a matrix;

[0064] In the (k+1)th iteration of reconstructing the network, the second step of the algorithm is:

[0065] Λ k+1 =μ k+1 D k+1 X k+1 -(1-μ k+1 )Z k ;

[0066] Among them, Λ k+1 D represents the result of the second step of the algorithm in the (k+1)th iteration. k+1 Let μ represent the noise suppression matrix in the (k+1)th iteration. k+1 These are the learning parameters of a deep network.

[0067] In the (k+1)th iteration of reconstructing the network, the third step of the algorithm is:

[0068] Z k+1←U·diag(max(σ i -λ k+1 / ρ k+1 ,0))·V T ;

[0069] Among them, Z k+1 σ represents the result of the third step of the algorithm in the (k+1)th iteration. i λ is the i-th singular threshold, where U and V are the left and right singular vectors, respectively. k+1 and ρ k+1 These are all learning parameters for deep networks.

[0070] In the (k+1)th iteration of reconstructing the network, the fourth step of the algorithm is:

[0071] U k+1 ←U k +η k+1 (X k+1 -Z k+1 );

[0072] Among them, U k+1 η represents the result of the fourth step of the algorithm in the (k+1)th iteration. k+1 These are the learning parameters of a deep network.

[0073] The above four steps constitute the reconstructed network, such as Figure 3 As shown.

[0074] S1013, Training the Reconstructed Network: In the reconstruction network, the mean squared error (MSE) is used as the loss function, and the network parameters are optimized using the backpropagation algorithm and the stochastic gradient-based optimizer Adam. This invention aims to learn the following parameters, whose expressions are as follows:

[0075]

[0076] Furthermore, such as Figure 4 As shown, step S102 specifically includes the following steps:

[0077] S1021, Calculate the power spectral density of the reconstructed signal: Obtain the reconstructed signal from the reconstruction network and calculate its power spectrum.

[0078] S1022, Design a signal detection network: Build a monitoring network by combining a CNN module and a Transformer module. Use CNN to extract features within the frequency band and use the long-range acquisition capability of Transformer to extract features between frequency bands. The signal detection network is used to detect the occupancy of the spectrum.

[0079] S1023, Training the detection network: Using the detection mean square error as the loss function, the reconstruction network is trained using the power spectrum of the reconstructed signal.

[0080] Furthermore, the construction of the detection network in step S102 includes the following steps:

[0081] S1021: Calculate the power spectral density of the reconstructed signal: The power spectral density can be calculated using the following formula:

[0082]

[0083] Where p is the power spectral density. When performing a Fourier transform, Corr(·) is the autocorrelation function. It is a signal reconstructed through step S104.

[0084] S1022: Design a signal detection network: cascade a CNN module and a Transformer to build a CNN-Transformer network. Figure 5 A schematic diagram of the constructed detection network is given. The CNN is a one-dimensional convolutional layer of size 1×1×3, representing 1 input channel, 1 output channel, and a kernel size of 3. The Transformer module mainly includes an embedding layer, a position-encoding layer, and a multi-head attention layer.

[0085] S1023: Training the detection network: The network is trained using the mean squared error of the detection accuracy as the loss function.

[0086] Furthermore, such as Figure 6 As shown, step S103 specifically includes the following steps:

[0087] S1031: Parallel sampling: Utilizing multiple low-speed analog-to-digital converters to simultaneously acquire the observed signal. Among these, Figure 7 One possible parallel sampling structure is presented;

[0088] S1032: Stack by column: Stack the observation signals obtained through S1031 by column into an observation matrix.

[0089] S1033: Block diagonalization: Multiple sub-sensory matrices form a new sensing basis matrix along the main diagonal.

[0090] S1034: Utilizing the low-rank property of the original spectral matrix, the reconstruction of non-sparse signals is represented as a low-rank matrix recovery problem;

[0091] Furthermore, the compressed signal sampling in step S103 includes the following steps:

[0092] S1031: Parallel sampling: Measurement signal y of the i-th channel i It can be represented as:

[0093] y i =A i x f +n i i = 1, 2, ..., P;

[0094] Where P is the number of channels, n i and A i These are the measurement noise and sensing matrix of the i-th channel, respectively, x f It is the frequency domain signal to be reconstructed.

[0095] S1032: Stack by column: y i and A i Stacked as observation matrix Y = [y1; y2; ...; y P ] and the new perception matrix A = diag{A1,…,A P}. The original spectrum matrix X = [x f ,…,x f The low-rank property can be recovered. Therefore, the forward model achieved by P sampling is:

[0096] Y = Avec(X) + n;

[0097] Where n is the total compression measurement noise.

[0098] S1033: Matrix Rank Minimization: Utilize the low-rank property of matrix X to find the lowest-rank X from Y.

[0099]

[0100] Where δ is the tolerance for noise error, and rank(·) is the rank function of the matrix. It is a low-rank matrix to be recovered.

[0101] Furthermore, such as Figure 8 As shown, step S104 specifically includes the following steps:

[0102] S1041: Minimize the nuclear norm: Relax the rank function to the nuclear norm, and use the alternating direction multiplier algorithm to solve the problem of minimizing the nuclear norm. The nuclear norm is the minimum sum of the absolute values ​​of all singular values ​​of the matrix.

[0103] S1042: Reconstructed signal: The data processed in step S103 is used as the input of the reconstruction network. The reconstruction network trained in step S1022 is used to reconstruct the spectrum matrix. The reconstructed spectrum matrix is ​​then averaged to obtain the reconstructed signal.

[0104] Furthermore, the signal reconstruction in step S104 includes the following steps:

[0105] S1041: Minimizing the nuclear norm: Since rank(·) is non-convex and discontinuous, minimizing the rank function is an NP-hard problem, difficult to solve in a short time. Therefore, the matrix restoration problem is relaxed from minimizing the rank function to minimizing the nuclear norm:

[0106]

[0107] in, This is the spectrum matrix to be recovered. It can be represented in Lagrange form:

[0108]

[0109] Where λ is the regularization parameter.

[0110] S1042: Using the observation matrix and perception matrix generated in step S103 as input to the trained reconstruction network, the output is the reconstructed signal.

[0111] Furthermore, such as Figure 9 As shown, step S105 specifically includes the following steps:

[0112] S1051: Signal preprocessing: Calculate the power spectrum of the reconstructed signal according to step S103;

[0113] S1052: Output spectrum occupancy status: Determine the frequency band occupancy status using a detection network.

[0114] Based on the data obtained from the above examples, under different signal-to-noise ratios, the ADMM algorithm proposed in the literature "ADMM-Net for Communication Interference Removal in Stepped-Frequency Radar" (IEEE Transactions on Signal Processing, 2021, Vol. 6), the CNN algorithm proposed in the literature "Deep Learning-Based Compressed Sensing for Image and UWB Signal Reconstruction" (IEEE Sensors Journal, 2025, Vol. 25(12)), the SGD algorithm proposed in the literature "The Global Geometry of Centralized and Distributed Low-rank Matrix Recovery Without Regularization" (IEEE Signal Processing Letters), the SVT algorithm proposed in the literature "A Model-Agnostic Method for PMU Data Recovery Using Optimal Singular Value Thresholding" (IEEE Transactions on Power Delivery), and the reconstruction network of this application are compared as follows: Figure 10 As shown.

[0115] from Figure 10 It can be seen that the reconstruction algorithm proposed in this application has higher reconstruction accuracy than other methods under different signal-to-noise ratios.

[0116] Based on the data obtained from the above examples, under different signal-to-noise ratios, the CNN_WSS method proposed in the paper "Compressed Spectrum Sensing of Sparse Wideband Signals Based on Deep Learning" (IEEE Transactions on Vehicular Technology), the Transformer proposed in the paper "Spectrum Transformer: An Attention-based Wideband Spectrum Detector" (IEEE Transactions on Wireless Communications), and DeepSense in the paper "DeepSense: Fast wideband spectrum sensing through real-time in-the-loop deep learning" (40th IEEE Conference on Computer Communications, INFOCOM 2021) are compared with the proposed CNN_Transformer detection algorithm, as shown in the figure. Figure 11 As shown.

[0117] from Figure 11 It can be seen that the proposed CNN_Transformer detection performance is superior to other comparative algorithms.

[0118] In summary, the proposed method has advantages such as low computational complexity, high recovery accuracy, and good interpretability, and can improve reconstruction accuracy and detection accuracy under low signal-to-noise ratio conditions.

Claims

1. A method for reconstructing and detecting non-sparse broadband signals based on nuclear norm minimization, characterized in that... Includes the following steps: S101, Constructing the Reconstruction Network: Deeply expand the iterative algorithm into a data-driven reconstruction network and train it; S102, Constructing the detection network: Combine the CNN module and the Transformer module to construct and train the detection network; S103, Compressed signal sampling: Based on a parallel sampling architecture, multiple channels are used to sample the original signal simultaneously to obtain the observed signal, which is then stacked in columns to form an observation matrix; S104, Signal Reconstruction: Based on the observation matrix obtained from parallel sampling and the known measurement matrix, the reconstructed signal is obtained by minimizing the nuclear norm to recover the spectrum matrix; S105, Spectrum Occupation Detection: Based on the reconstructed signal, a detection network is used to determine the spectrum occupancy status.

2. The non-sparse broadband signal reconstruction and detection method based on nuclear norm minimization as described in claim 1, characterized in that, S101 specifically includes the following steps: S1011, Obtain the observation matrix and the perception matrix: Obtain the sample set of the observation matrix by sampling, and then construct a new perception matrix by block diagonalizing the perception matrix of each sampling channel; S1012, Constructing the Reconstruction Network: An iterative algorithm based on the deep unfolding method is used to construct the reconstruction network; S1013, Training the Reconstruction Network: Using the mean squared error of reconstruction as the loss function, the reconstruction network is trained using the observation matrix and the perception matrix to optimize the parameters of the iterative algorithm.

3. The method for reconstructing and detecting non-sparse broadband signals based on nuclear norm minimization as described in claim 1, characterized in that, S101 specifically includes the following steps: S1011, Obtain the observation matrix and the perception matrix: Obtain the sample set of the observation matrix by sampling, and then construct a new perception matrix by block diagonalizing the perception matrix of each sampling channel, where the observation matrix is ​​Y and the perception matrix is ​​A; S1012, Constructing the Reconstructed Network: In the (k+1)th iteration of the reconstructed network, the first step of the algorithm is: r k+1 ←(A T A+r k+1 I) -1 (A T Y+r k+1 (vec(Z k )-vec(U k ))); Where I represents the identity matrix, ρ k+1 This represents the result of the first step of the algorithm in the (k+1)th iteration, where ρ is the learning parameter of the reconstructed network, and Z... k and U k Let represent the results of the third and fourth steps of the algorithm in the k-th iteration, respectively, where vec denotes matrix vectorization, and (·). T Represents the transpose of a matrix; In the (k+1)th iteration of reconstructing the network, the second step of the algorithm is: L k+1 =μ k+1 D k+1 X k+1 -(1-m k+1 )Z k ; Among them, Λ k+1 D represents the result of the second step of the algorithm in the (k+1)th iteration. k+1 Let μ represent the noise suppression matrix in the (k+1)th iteration. k+1 These are the learning parameters of deep networks; In the (k+1)th iteration of reconstructing the network, the third step of the algorithm is: Z k+1 ←U·diag(max(σ i -l k+1 / r k+1 ,0))·V T Among them, Z k+1 σ represents the result of the third step of the algorithm in the (k+1)th iteration. i It is the i-th singular threshold, U and V are the left and right singular vectors respectively, and λ k+1 and ρ k+1 These are all learning parameters of deep networks; In the (k+1)th iteration of reconstructing the network, the fourth step of the algorithm is: U k+1 ←U k +η k+1 (X k+1 -Z k+1 ) Among them, U k+1 η represents the result of the fourth step of the algorithm in the (k+1)th iteration. k+1 These are the learning parameters of deep networks; The above four steps constitute the reconstruction of the network; S1013, Training the Reconstructed Network: In the reconstructed network, the mean squared error (MSE) is used as the loss function, and the network parameters are optimized using the backpropagation algorithm and the stochastic gradient-based optimizer Adam.

4. The non-sparse broadband signal reconstruction and detection method based on nuclear norm minimization as described in claim 1, characterized in that, S102 specifically includes the following steps: S1021, Calculate the power spectral density of the reconstructed signal: Obtain the reconstructed signal from the reconstruction network and calculate its power spectrum; S1022, Design the detection network: Build a detection network by combining the CNN module and the Transformer module. Use the CNN to extract features within the frequency band and use the Transformer's long-range capture capability to extract features between frequency bands. S1023, Training the detection network: Using the detection mean square error as the loss function, the reconstruction network is trained using the power spectrum of the reconstructed signal.

5. The non-sparse broadband signal reconstruction and detection method based on nuclear norm minimization as described in claim 1, characterized in that, S102 specifically includes the following steps: S1021, Calculate the power spectral density of the reconstructed signal. The power spectral density is calculated using the following formula: Where p is the power spectral density. When performing a Fourier transform, Corr(·) is the autocorrelation function. It is a signal reconstructed through step S104; S1022, Design the detection network: cascade the CNN module and the Transformer to build a CNN-Transformer detection network; S1023: Training the detection network: The detection network is trained using the mean square error of the detection accuracy as the loss function.

6. The method for reconstructing and detecting non-sparse broadband signals based on nuclear norm minimization as described in claim 1, characterized in that, S103 specifically includes the following steps: S1031, Parallel Sampling: Simultaneous acquisition of the observed signal using multiple analog-to-digital converters; S1032, Stack by column: Stack the obtained observation signals by column to form an observation matrix; S1033, Block diagonalization: Multiple sub-sensory matrices form a new sensing basis matrix along the main diagonal; S1034, Minimization of the Rank Function of a Matrix: By utilizing the low-rank property of the original spectral matrix, the matrix is ​​recovered by minimizing the rank function of the matrix, and the reconstruction of non-sparse signals is expressed as a low-rank matrix recovery problem.

7. The method for reconstructing and detecting non-sparse broadband signals based on nuclear norm minimization as described in claim 1, characterized in that, S103 includes the following steps: S1031, Parallel Sampling: The measurement signal y of the i-th channel i Represented as: y i =A i x f +n i ,i=1,2,…,P; Where P is the number of channels, n i and A i These are the measurement noise and sensing matrix of the i-th channel, respectively, x f It is the frequency domain signal to be reconstructed; S1032, Stack by column: y i and A i Stacked as observation matrix Y = [y1; y2; ...; y P ] and the new perception matrix A = diag{A1,…,A P };Original spectrum matrix X=[x f ,…,x f The recovered model carries low-rank characteristics; therefore, the forward model achieved by P samplings is: Y = Avec(X) + n; Where n is the total compression measurement noise; S1033, Block diagonalization: Divide A i Block diagonalization of the new perceptual matrix A = diag{A1,…,A P }; S1034, Minimizing the Rank Function of a Matrix: By utilizing the low-rank property of matrix X, we solve for the minimization of the rank function of the matrix and find the original spectrum matrix X with the lowest rank from the observation matrix Y; Where δ is the tolerance noise error, and rank(·) is the rank function of the matrix. It is a low-rank matrix to be recovered.

8. The method for reconstructing and detecting non-sparse broadband signals based on nuclear norm minimization as described in claim 1, characterized in that, S104 specifically includes the following steps: S1041, Minimizing the nuclear norm: Relax the rank function to the nuclear norm, that is, replace the rank function with the nuclear norm, and solve the problem of minimizing the nuclear norm by using the alternating direction multiplier method; S1042, Reconstructing the signal: The data processed in step S103 is used as the input to the signal network. The trained detection network is used to reconstruct the spectrum matrix. The reconstructed spectrum matrix is ​​then averaged to obtain the reconstructed signal.

9. The method for reconstructing and detecting non-sparse broadband signals based on nuclear norm minimization as described in claim 1, characterized in that, S104 specifically includes the following steps: S1041, Minimizing the nuclear norm: Relaxing the matrix recovery problem from minimizing the rank function to minimizing the nuclear norm: in, The spectrum matrix to be recovered is expressed in Lagrange form: Where λ is the regularization parameter; S1042: The generated observation matrix and perception matrix are used as inputs to the trained reconstruction network, and the output is the reconstructed signal.

10. The method for reconstructing and detecting non-sparse broadband signals based on nuclear norm minimization as described in claim 1, characterized in that, S105 specifically includes the following steps: S1051, Signal preprocessing: Calculate the power spectrum of the reconstructed signal; S1052, Output spectrum occupancy status: Determine the frequency band occupancy status using a detection network.

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