Source number estimation method and system based on capon space spectrum diagram and improved convolution network

Abstract

The application discloses a kind of based on Capon space spectrum and the signal source number estimation method and system of improved convolution network.It is guaranteed that the numerical stability of spectrum calculation under low snapshot low noise environment by diagonal loading technique correction covariance matrix.Using global fixed dB scale, one-dimensional Capon power spectrum is mapped into two-dimensional image, and the spatial structure and amplitude contrast information of spectrum peak are completely retained.The standard Stem initial convolution module and the ReLU activation function in each residual block are replaced by Mish activation function, which strengthens the negative gradient transmission and nonlinear feature expression of weak spectrum peaks.A coordinate attention module is embedded at the end of the four-stage residual stage to accurately model the spectrum peak position information and suppress background noise interference.Meanwhile, the model's generalization performance under high dynamic conditions is improved by combining MixStyle, label smoothing and Dropout strategies.The application significantly enhances the model's multi-scale perception and representation ability for weak spectrum peaks, greatly improving the accuracy and anti-interference robustness of signal source number estimation in low SNR and very low SNR scenarios.

Description

Technical Field

[0001] This invention belongs to the field of array signal processing technology, specifically relating to a source number estimation method and system based on Capon spatial spectrum and improved convolutional neural network. It specifically solves the technical problems of low signal-to-noise ratio, low source number estimation accuracy, easy loss of weak spectral peak features, and poor model generalization ability in scenarios with low signal-to-noise ratio and limited snapshots. It can be used for spatial signal source number detection in fields such as radar detection, sonar direction finding, wireless communication, and electronic countermeasures. Background Technology

[0002] As modern electromagnetic detection technology advances towards longer ranges, lower intercept rates, and higher interference resistance, radar and electronic reconnaissance systems operate for extended periods in complex environments characterized by low signal-to-noise ratios, limited snapshot times, and strong clutter interference. Source number estimation is a fundamental problem in array signal processing, aiming to determine the number of incident signals in space based on noisy array observation data. This problem is typically a preliminary step in angle-of-arrival (AOA) estimation, and its results directly impact subsequent direction-finding and positioning performance. Underestimation or overestimation directly leads to increased AOA estimation errors, multi-target confusion and loss, and severely degrades the overall performance of the detection system. Therefore, improving the accuracy of source number estimation under low SOA conditions has significant engineering application value for enhancing array detection capabilities in complex electromagnetic environments.

[0003] Traditional source number estimation methods are mainly based on information theory criteria and eigenvalue structure analysis, with typical examples being the Akaike Information Criterion (AIC), the Minimum Description Length Criterion (MDL), and the Gaussian Disk Estimation (GDE). These methods rely on the difference between signal and noise eigenvalues ​​in the sample covariance matrix to make the decision. Under ideal conditions of high signal-to-noise ratio (SNR) and sufficient snapshots, the separation between signal and noise eigenvalues ​​is high, resulting in stable and accurate estimation results. However, under conditions of low SNR or small snapshots, signal and noise eigenvalues ​​in the finite sample covariance matrix are prone to aliasing, leading to a significant performance degradation of traditional methods and often resulting in underestimation of the source number.

[0004] In recent years, deep learning technology has been gradually introduced into source number estimation tasks, demonstrating good adaptability under conditions of low signal-to-noise ratio and small snapshot number due to its powerful feature learning capabilities. Existing deep learning source number estimation schemes present different technical paths in input design: one type directly uses the complex signals received by the original array as network input. This method preserves complete observation information, but the input dimension dynamically changes with the number of snapshots, and complex data requires additional processing, resulting in poor deployment flexibility. Another type uses eigenvalue vectors arranged in descending order of the covariance matrix as input, transforming source number estimation into a classification or regression task. This type of method fixes the input dimension, resulting in a simpler model structure, but it essentially represents one-dimensional compressed statistical features. While it can reflect the overall feature changes of the covariance matrix, it is difficult to explicitly preserve the spatial spectral structure information related to source number discrimination. Under extremely low signal-to-noise ratio conditions, when eigenvalue distributions become aliased, networks relying solely on one-dimensional feature input are prone to performance degradation.

[0005] At the network architecture level, existing solutions mostly use standard ResNet and other general convolutional networks to process spectral or feature inputs directly, without making customized improvements for the source number estimation task. This results in three obvious defects: First, the networks generally use the ReLU activation function, which directly sets the negative half-axis features to zero. The gradient of the weak response features corresponding to weak spectral peaks under low signal-to-noise ratio is directly lost, resulting in insufficient perception of shallow and narrow weak peaks. Second, general convolutional networks only model channel-dimensional attention and cannot effectively utilize the clear physical meaning of the horizontal and vertical coordinates of the spatial spectrum. It is difficult to accurately distinguish between random noise fluctuations and true continuous spectral peaks, and misjudgments are prone to occur in weak signal scenarios. Third, the training process is not optimized for difficult samples with low signal-to-noise ratio. The training set has a high proportion of simple samples with high signal-to-noise ratio, and the model tends to learn the features of simple samples, resulting in insufficient recognition ability of difficult samples and limited generalization performance.

[0006] Currently, techniques such as Mish smoothing activation, coordinate attention, and MixStyle style perturbation are all independent and scattered improvement methods. There is no integrated source number estimation scheme that deeply integrates fixed dB scale spatial spectrum construction, lightweight attention enhancement network, and joint training strategy for difficult samples. Therefore, it cannot simultaneously solve the three core technical pain points of input representation information loss, insufficient weak feature extraction capability, and poor generalization ability under strong noise. Summary of the Invention

[0007] The purpose of this invention is to address the challenges in estimating the number of sources in a low signal-to-noise ratio uniform linear array, such as loss of spatial structure information, difficulty in extracting weak spectral peak features, and poor generalization under complex noise environments. This invention proposes a method for estimating the number of sources in a low signal-to-noise ratio uniform linear array based on Capon spatial spectrum and MCA-ResNet18.

[0008] This invention corrects the covariance matrix using an adaptive diagonal loading technique based on trace constraints, ensuring the numerical stability of spectral calculations in low-shot, low-noise environments. It maps the one-dimensional Capon power spectrum to a two-dimensional image input using a globally fixed dB scale, fully preserving the spatial structure and amplitude contrast information of spectral peaks. It replaces the ReLU activation function in the standard Stem initial convolution module and each residual block with the Mish activation function, enhancing the negative gradient propagation and nonlinear feature representation of weak spectral peaks. A coordinate attention (CA) module is embedded in series at the end of the fourth-level residual stage to accurately model spectral peak position information and suppress background noise interference. During the training phase, auxiliary training strategies are introduced, combining MixStyle, label smoothing, and Dropout to improve the model's generalization performance under high dynamic conditions, addressing the problem of the model's bias towards simple samples and weak recognition ability for difficult samples. These five improvements work synergistically to significantly enhance the model's multi-scale perception and representation ability of weak spectral peaks, greatly improving the accuracy and robustness against interference in source number estimation under low and extremely low signal-to-noise ratio scenarios.

[0009] The technical solution adopted in this invention is as follows: S1. Collect array observation data and construct a data set for estimating the number of information sources.

[0010] The signal source number estimation dataset used in this invention is the Signal-Set-36 dataset, which is independently constructed based on the simulation of a uniform linear array far-field narrowband receiver model. It is generated based on the classical theoretical assumptions of array signal processing and can accurately control experimental variables such as signal-to-noise ratio, incident angle, and number of snapshots.

[0011] Multiple snapshot array observation data of far-field narrowband signals were acquired using a uniform linear array. The minimum incident angle interval of the far-field narrowband signals was constrained to ensure spatial resolvability, generating multiple sets of samples covering a wide signal-to-noise ratio range. These samples were then cleaned to construct a source number estimation dataset. This dataset was divided into training, validation, and test sets. The training set was used for iterative training of the network model; the validation set was used for performance monitoring, hyperparameter tuning, and early stopping detection during training; and the test set included a balanced test subset binned by signal-to-noise ratio level, used to finally verify the model's estimation performance under different noise intensities.

[0012] S2. Capon spatial power spectrum preprocessing based on diagonal loading and fixed dB mapping.

[0013] Using array observation data from the Signal-Set-36 dataset as input, the sample covariance matrix for each sample is solved. An adaptive diagonal loading correction covariance matrix based on trace constraints is introduced to eliminate matrix ill-conditioning under low snapshot and low signal-to-noise ratio conditions. Within a set scanning angle range, the logarithmic form of the Capon spatial power spectrum is calculated for the corrected covariance matrix. A globally uniform dB interval is used to perform linear normalization mapping on all samples, removing coordinate axes, scales, and text labels, converting the one-dimensional Capon spatial power spectrum into a uniform-sized two-dimensional Capon grayscale spectrum, which serves as the input to the standardized network.

[0014] S3. Hierarchical feature extraction based on MCA-ResNet18 network.

[0015] The preprocessed 2D grayscale spectral image is fed into the initial convolutional module of Stem to complete the low-level texture feature encoding. Then, the four-stage hierarchical residual structure of the MCA-ResNet18 network is used to complete multi-scale feature extraction from shallow to deep, progressively improving the semantic abstraction capability of the features. The output feature map of the previous residual stage is used as the input of the next residual stage, and the four-level feature transfer is completed in sequence.

[0016] S4. Spatial location feature enhancement based on coordinate attention.

[0017] Independent coordinate attention modules are embedded at the output of each of the four residual stages. One-dimensional pooling encoding is performed along the two orthogonal dimensions of height and width to generate two channel attention weights carrying position information. The output feature map of this stage is multiplied element-wise with the channel attention weights in the two directions to complete feature recalibration, suppress redundant responses to noise background, and enhance the feature weights of the real spectral peak regions.

[0018] S5. Optimization of weak feature gradient preservation based on Mish activation.

[0019] All ReLU activation functions in the backbone of the MCA-ResNet18 network are uniformly replaced with the Mish smooth nonlinear activation function. Taking advantage of its differentiability across the entire range and gradient preservation for negative values, the weak response feature gradients corresponding to weak spectral peaks under low signal-to-noise ratio are fully preserved, thereby improving the model's ability to perceive shallow and narrow weak peaks.

[0020] The core formula for the Mish activation function:

[0021] in, Input feature values S6. Optimization of auxiliary training strategies and output of information source numbers.

[0022] During the training phase, MixStyle feature perturbation, label smoothing, Dropout regularization, and low signal-to-noise ratio sample weighted sampling strategies are integrated to optimize the model's generalization performance. During inference, the spectrum to be tested is input into the network, and after global average pooling and fully connected layers, the probability of the number of three types of information sources is output. The category corresponding to the highest probability value is taken as the final estimation result.

[0023] The beneficial effects of this invention are as follows: Existing technologies struggle to effectively address issues such as eigenvalue aliasing, loss of spatial structure information, and the easy masking of weak spectral peaks by noise when estimating the number of sources at low signal-to-noise ratios, leading to a significant decrease in recognition accuracy at extremely low signal-to-noise ratios.

[0024] This invention solves the problems of insufficient accuracy and poor robustness in estimating the number of signal sources in a uniform linear array under complex electromagnetic environments with low signal-to-noise ratios. This invention employs a diagonally loaded stable covariance matrix calculation combined with a globally fixed dB-scale two-dimensional Capon spectrum construction method. While preserving complete spatial structure information such as the number, position, and relative intensity of spectral peaks, it unifies the amplitude scale of all samples, avoiding the disruption of amplitude comparison between samples by single-sample adaptive normalization. This improves feature discriminability under low signal-to-noise ratio conditions from the input level. A modified MCA-ResNet18 network is used for deep feature extraction. Weak feature gradients are retained by replacing them with Mish activation across the entire network. Channel weights and spatial position relationships are synchronously modeled through four-level concatenated coordinate attention, enabling accurate differentiation between random noise fluctuations and true continuous spectral peaks. This method directionally enhances the feature response of weak spectral peaks, significantly improving recognition performance in weak signal scenarios with minimal parameter and computational overhead. A multi-strategy joint training optimization scheme is employed. Through the synergistic effects of MixStyle feature statistical perturbation, label smoothing regularization, Dropout random deactivation, and weighted sampling of low signal-to-noise ratio samples, the training weights of difficult and simple samples are balanced, reducing the risk of model overfitting and significantly improving generalization ability in complex noise environments.

[0025] The proposed source number estimation method based on Capon spatial spectrum and MCA-ResNet18 effectively addresses the insufficient recognition accuracy of traditional methods and existing deep learning methods under low signal-to-noise ratio (SNR) conditions. Simulation experiments verify that the overall Top-1 recognition accuracy reaches 94.74% across the full SNR range of -20dB to 15dB; even in the extremely low SNR range of -20dB to -15dB, the average recognition accuracy still reaches 69.28%, significantly outperforming traditional methods such as AIC, MDL, and GDE, as well as deep learning methods with one-dimensional feature input such as ERNet, and also significantly outperforming the standard ResNet18 baseline network. Furthermore, this method can adapt to both the [-60°, 60°] conventional scanning angle domain and the [-90°, 90°] wide-angle domain without modifying the network structure, demonstrating excellent generalization and adaptability, and can be directly integrated into various array detection systems. Attached Figure Description

[0026] Figure 1 This is a schematic diagram comparing the Capon spatial spectrum and the diagonal matrix image of sorted eigenvalues ​​for two source scenes at signal-to-noise ratios of 10dB and -10dB.

[0027] Figure 2 This is a schematic diagram comparing the Capon spatial spectrum and the diagonal matrix image of sorted eigenvalues ​​for a three-source scene at signal-to-noise ratios of 10dB and -10dB.

[0028] Figure 3 This is a schematic diagram of the overall process and network structure of the source number estimation algorithm based on MCA-ResNet18 in this invention.

[0029] Figure 4 This is a structural diagram of the Coordinate Attention (CA) module.

[0030] Figure 5 This is a curve comparing the accuracy of the method of this invention with various comparative algorithms across the full signal-to-noise ratio range of -20dB to 15dB.

[0031] Figure 6 This is a schematic diagram comparing the accuracy of standard ResNet18 and MCA-ResNet18 in the normal scanning angular domain of [-60°, 60°].

[0032] Figure 7 A schematic diagram showing the accuracy comparison between standard ResNet18 and MCA-ResNet18 in the extended scan angle domain of [-90°, 90°].

[0033] in, Figure 1The top left is the Capon spatial spectrum at 10dB, the top right is the diagonal matrix image of the ordered eigenvalues ​​at 10dB, the bottom left is the Capon spatial spectrum at -10dB, and the bottom right is the diagonal matrix image of the ordered eigenvalues ​​at -10dB.

[0034] Figure 2 The top left image shows the Capon spatial spectrum at 10dB, the top right image shows the diagonal matrix of ordered eigenvalues ​​at 10dB, the bottom left image shows the Capon spatial spectrum at -10dB, and the bottom right image shows the diagonal matrix of ordered eigenvalues ​​at -10dB.

[0035] Specific implementation methods The specific embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0036] S1. Experimental environment construction and dataset creation.

[0037] This embodiment uses simulation to construct the dataset and models the source number estimation as the number of categories. This is a three-class classification problem. In the simulation, a uniform linear array is used as the receiver array, with 16 array elements and a fixed number of snapshots of 200. The source direction angles are randomly generated within the range of [-60°, 60°]. To ensure spatial theoretical resolvability, the minimum spatial angular interval between any two sources is strictly constrained to [value missing]. The spatial spectrum scanning range is set to [-60°, 60°], and the scanning step is set to 0.5° (i.e., 241 angle sampling points per spectral line). During sample generation, array-received data is first simulated under given source number, angle of arrival, and signal-to-noise ratio conditions. The covariance matrix of the samples is constructed accordingly. To improve the numerical stability of the covariance matrix inversion process, an adaptive diagonal loading technique is introduced to calculate the one-dimensional Capon spatial power spectrum. Subsequently, the spatial spectrum is uniformly represented within a fixed dB display range and converted into a high-contrast two-dimensional grayscale spectrum of size 224×224, which serves as the direct input to the deep learning network.

[0038] The experimental signal-to-noise ratio (SNR) ranged from -20 dB to 15 dB, with 1 dB increments, totaling 36 discrete SNR points. The dataset was independently divided into training, validation, and test sets, with the specific numbers and distributions as follows: Training set: Random continuous sampling is performed across the entire signal-to-noise ratio range, generating 20,000 samples for each type of source, for a total of 60,000 samples.

[0039] Validation set: Sampled uniformly across the entire signal-to-noise ratio range, generating 2,000 samples for each type of source, for a total of 6,000 samples.

[0040] Test set: The test set is strictly distributed equally at each specific signal-to-noise ratio (SNR) point, with a fixed number of 200 samples per class of information source at each SNR point. The total number of samples in a single class test set is 7,200, for a total of 21,600 test samples.

[0041] Based on the above test set settings, this invention employs an accuracy statistics method based on SNR binning. The test set covers -20dB to 15dB in 1dB increments, containing a total of 36 SNR points. At each SNR point, there are 200 samples each for the three signal source classes K=1, K=2, and K=3, therefore each SNR bin contains 600 test samples. The accuracy within a given SNR bin is defined as the ratio of the number of correctly classified samples to the total number of samples in that bin under that SNR condition.

[0042] Obtain the necessary hardware and software environment parameters for the experiment: Table 1. List of Experimental Parameters

[0043] S2. Design a source number estimation method based on Capon spatial spectrum and MCA-ResNet18.

[0044] The method is generally divided into a preprocessing module and a network inference module: The preprocessing module independently completes the conversion of array data into a standardized two-dimensional Capon spectrum. This conversion process abandons single-sample adaptive normalization and uses a globally unified fixed dB range for linear mapping to generate a two-dimensional grayscale spectrum, providing a uniform scale input for the network.

[0045] The MCA-ResNet18 network module completes the layer-by-layer extraction of spectral features and the source number classification output. The network as a whole adopts a four-stage hierarchical residual architecture, with a coordinate attention module embedded at the end of each stage. The front end of the first two stages is configured with MixStyle feature perturbation units, and the entire network uses the Mish activation function instead of the original ReLU.

[0046] S2-1, Detailed implementation of diagonal loading and fixed dB scale Capon spectrum construction.

[0047] The preprocessing module sequentially completes five steps: covariance matrix solving, diagonal loading correction, Capon spatial spectrum calculation, fixed dB normalization, and two-dimensional grayscale spectrum generation. The specific implementation logic is as follows: Suppose a far-field narrowband signal is incident on... M A uniform linear array, from the perspective of direction (directional angle). Incident, at the At each snapshot, the array receive vector is: .

[0048] in, For array receiving data vectors, For the first The far-field narrowband signal vector at a snapshot moment For the first The noise vector at each snapshot moment, Let be an array manifold matrix, where For angle The corresponding guide vector.

[0049] For array element spacing is The uniform linear array, the guiding vector is expressed as: .

[0050] in, Indicates the signal wavelength.

[0051] This invention does not directly use the raw array observation data as network input, but instead first constructs the covariance matrix of the samples from multiple snapshot observations. The covariance matrix is ​​defined as: .

[0052] To improve the numerical stability of Capon spatial spectrum calculations, this invention introduces diagonal loading to enhance inversion stability, i.e. .

[0053] in, The covariance matrix after diagonal loading. Represents the matrix trace operation. for M An identity matrix of order 1.

[0054] Subsequently, in the scanning direction angle The spatial power spectrum was calculated in 0.5° increments within the range [-60°, 60°] and converted to logarithmic form. .

[0055] in The guide vector for the corresponding angle. To prevent the occurrence of extremely small positive numbers with negative infinity when taking the logarithm.

[0056] Instead of using single-sample adaptive normalization, a globally unified interval of [-40dB, 20dB] is adopted to linearly map the spatial spectrum of all samples, normalizing the spectral values ​​to the range [0, 1]. The lower bound of the display range is set as follows: Upper limit of display range Then the fixed-scale spatial spectrum The mapping can be represented as: .

[0057] This method preserves the relative contrast of spectral peak amplitudes between different samples, enabling the model to learn the correspondence between signal-to-noise ratio and spectral peak intensity, thereby improving recognition stability under low signal-to-noise ratio conditions.

[0058] The normalized one-dimensional spatial spectrum is plotted as a two-dimensional curve with a white background and black lines. All coordinate axes, scales, and text labels are removed, retaining only the spectral lines themselves. The final image size is adjusted to 224×224 pixels and used as the standardized input for the network. Comparisons between Capon spatial spectra and eigenvalue matrix images at different signal-to-noise ratios are shown below. Figure 1 , Figure 2 As shown.

[0059] S2-2, MCA-ResNet18 network structure and detailed implementation of each stage.

[0060] The MCA-ResNet18 network adopts a four-stage hierarchical feature extraction structure. The overall structure of the MCA-ResNet18 network is as follows: Figure 3 As shown.

[0061] Stage 1 stacks two Mish-Basic residual blocks while maintaining high resolution, focusing on extracting low-level texture features such as the edges and local undulations of spectral lines, thereby establishing a preliminary characterization of the spectral peak morphology; the front end of the stage is connected to the MixStyle1 unit, which simulates the changes in spectral style under different signal-to-noise ratios by using the mean and variance of random perturbation features.

[0062] Stage 2 continues to stack two Mish-Basic residual blocks after the downsampling operation, which expands the receptive field and enhances the modeling ability of relationships between local regions, improves the model's adaptability to spectral peaks of different widths and intensities, and effectively addresses feature shifts caused by cross signal-to-noise ratios; the stage front end is connected to the MixStyle2 unit.

[0063] Stage3 fully models the multi-peak distribution, inter-peak spacing, and overall spectral structure of the entire spectrum by stacking two Mish-Basic residual blocks. When the source angle distribution changes, it can stably capture global quantitative features and ensure recognition stability under different incident angles.

[0064] Stage 4 then stacks two Mish-Basic residual blocks on a lower spatial resolution basis to further integrate and optimize high-level semantic features, ultimately forming a source number feature representation with strong discriminative power and robustness.

[0065] The Mish-Basic residual block adopts a residual structure design, and by introducing the Mish activation function and coordinate attention module, it achieves a dual improvement in feature representation capability and positioning accuracy.

[0066] The two residual blocks within each residual stage are cascaded (the output of the previous one is the input of the next). The final output of this stage is recalibrated by the CA module before being used as the input of the next residual stage. After the fourth-level feature extraction is completed, a global average pooling layer is used to compress the two-dimensional feature map into a one-dimensional feature vector. Then, a Dropout layer and a three-class fully connected layer are used to finally output the probability values ​​corresponding to the number of information sources of classes 1, 2, and 3.

[0067] S2-3, Detailed implementation of the coordinate attention module.

[0068] The coordinate attention module described is a lightweight position-aware attention mechanism that can simultaneously model the weights of both the channel dimension and the spatial position dimension, making it particularly suitable for processing spatial spectra with explicit physical coordinate meaning. Its internal structure is as follows: Figure 4 As shown, the specific calculation process consists of four steps: Let the input feature tensor be ,in For the number of channels, For feature height, Let be the feature width. Global average pooling is performed along both the height and width orthogonal directions to obtain aggregated features in two directions: the aggregated feature size in the height direction is... 1. The value of the i-th height position in the c-th channel is: .

[0069] The aggregation feature size in the width direction is 1 The value at the j-th width position of the c-th channel is: .

[0070] in, This represents the original input features. Compared to traditional two-dimensional global pooling, bidirectional one-dimensional pooling can preserve positional information in both directions, avoiding the loss of spatial positional details.

[0071] The aggregated features in both height and width directions are concatenated spatially and fed into a shared 1×1 convolutional layer and the Mish activation function for a non-linear transformation, generating intermediate features that simultaneously contain channel and positional information. The shared convolutional design ensures efficient use of attention parameters and controls the increase in the number of parameters.

[0072] The fused intermediate features are re-split into height and width branches along the spatial dimension. After adjusting the number of channels by 1×1 convolution, bidirectional channel attention weights with values ​​in the range [0,1] are generated using the Sigmoid activation function. and .

[0073] The preprocessed two-dimensional grayscale spectrum (size 224×224×1) is multiplied element-wise with the attention weights in both directions to complete feature recalibration. Output of each channel Defined as:

[0074] Through recalibration, the model can automatically increase the feature weights at the positions corresponding to the true spectral peaks and reduce the weights in the random noise fluctuation regions, thereby achieving the effects of background noise suppression and target feature enhancement.

[0075] This invention embeds a coordinate attention module at the end of four residual stages to achieve progressive feature optimization from shallow to deep layers, enabling features at different scales to obtain positional awareness enhancement and comprehensively improving the ability to extract weak spectral peaks.

[0076] S2-4, Detailed implementation of Mish activation and multi-policy training optimization.

[0077] The standard ReLU activation function, i.e., the linear rectifier unit, is expressed as follows: .

[0078] in, For input feature values.

[0079] As shown in the above equation, ReLU directly sets the negative half-axis response to zero. While this characteristic is beneficial for introducing nonlinearity and sparse activation, it may cause the loss of some weak response information when the weak spectral peak characteristics are not obvious. To improve this problem, this invention replaces the ReLU activation function in the backbone network with the Mish activation function. Its expression is: .

[0080] Compared to ReLU, Mish exhibits smoother nonlinear mapping characteristics and can preserve non-zero gradients in the negative half-axis region, which helps enhance the network's feature transfer ability in weak response regions. For the fixed dB scale spatial spectrum used in this invention, this modification is beneficial for preserving subtle information in weak spectral peak edges, local fluctuations, and inter-peak transition regions, thereby improving the network's ability to represent complex spectral shapes. Subsequent ablation experiments show that the model's recognition performance in the low signal-to-noise ratio range is improved after introducing Mish, indicating that this modification has a positive effect on spatial spectrum feature learning.

[0081] To improve the model's generalization performance in complex noisy environments, this invention employs four optimization strategies simultaneously during the training phase. All strategies are automatically disabled during the inference phase, without increasing inference overhead: ① MixStyle Feature Statistical Perturbation: Deployed at the front end of Stage 1 and Stage 2, randomly perturbs the mean and variance of the feature maps during training, simulating spectral style changes under different signal-to-noise ratios and noise distributions. This enhances the model's robustness to style shifts and prevents overfitting to spectral features with specific signal-to-noise ratios. ② Label Smoothing Regularization: Softens the original hard 0 / 1 classification labels, setting the label smoothing coefficient to 0.05. This alleviates overfitting caused by blurred class boundaries, improving the model's classification generalization ability, especially suitable for scenarios with unclear sample feature boundaries under low signal-to-noise ratios. ③ Dropout Regularization: Set between the global average pooling layer and the fully connected classification layer, with a deactivation probability of 0.5. Randomly deactivates some neurons during training, preventing the model from over-relying on local high-response features and forcing the model to learn more robust global discriminative features, reducing the risk of overfitting. ④ Weighted sampling of low signal-to-noise ratio samples: Increase the sampling weight of difficult samples in the range of -20dB to -15dB, with the weight coefficient set to 1.8, to increase the frequency of difficult samples in the training batch, balance the training ratio of simple samples and difficult samples, and improve the model's ability to identify samples with extremely low signal-to-noise ratio.

[0082] S3, Model Training.

[0083] The training set was created using the Signal-Set-36 dataset, with the training and validation sets divided in a 4:1 ratio. Before training, the backbone network was initialized with ResNet18 weights pre-trained on ImageNet, while the coordinate attention module and classification head were randomly initialized. Automatic mixed precision calculation was enabled during training to accelerate the process. After each training round, the Top-1 recognition accuracy was calculated on the validation set, and the weights of the model with the highest validation accuracy were saved. If the validation set accuracy did not improve for 10 consecutive rounds, an early stopping mechanism was triggered to terminate training and prevent overfitting. A cosine annealing strategy was used throughout training to dynamically adjust the learning rate, allowing the model to converge more precisely to the optimal solution in the later stages of training.

[0084] S4. Use the algorithm of this invention to estimate the number of information sources and compare its performance with the comparison method. The algorithm of this invention is used to estimate and test the full signal-to-noise ratio test set and the extremely low signal-to-noise ratio test interval, and its performance is compared with traditional methods, Capon-Peak methods and deep learning methods. The recognition performance is evaluated by the Top 1 classification accuracy.

[0085] Figure 5The accuracy of our proposed method is compared with that of traditional source number estimation methods (AIC, MDL, GDE) and deep learning methods (ERNet, standard ResNet18) across the entire signal-to-noise ratio range. Overall, the accuracy of all methods improves with increasing signal-to-noise ratio, but the performance differences between different methods are more significant in the low signal-to-noise ratio range.

[0086] Depend on Figure 5 As can be seen, compared with traditional methods such as MDL, AIC, and GDE, the proposed method exhibits higher estimation accuracy in the negative signal-to-noise ratio (SNR) range. Traditional methods rely on the degree of separation between eigenvalues ​​of the sample covariance matrix, and are easily affected by eigenvalue aliasing under low SNR conditions, thus their accuracy drops rapidly in the extremely low SNR range. Among them, MDL shows the most significant performance degradation under low SNR conditions, while AIC and GDE, although relatively milder, still struggle to maintain stable recognition below -15 dB.

[0087] Furthermore, compared to the Capon-Peak method, which directly detects peaks in the Capon spatial spectrum, the optimal peak prominence threshold found by Capon-Peak on the validation set is 1.50 dB, with an overall accuracy of 82.72% on the test set and an average accuracy of 41.14% in the -20 dB to -15 dB range. In contrast, the proposed method achieves an overall accuracy of 94.74% and an average accuracy of 69.28% in the -20 dB to -15 dB range. This indicates that direct peak detection is easily affected by weak peak masking and noise fluctuations under strong noise conditions, while the proposed method can utilize information such as the number of peaks, relative intensity, and background morphology in the complete Capon spatial spectrum, thus exhibiting better adaptability to weak peak structures under strong noise conditions.

[0088] Compared to deep learning methods with one-dimensional feature input, such as ERNet, our proposed method also exhibits better recognition performance in the low signal-to-noise ratio (SNR) range. As the SNR increases, all deep learning methods gradually approach saturation, but the performance differences arising from different input representation methods are particularly pronounced in the -20 dB to -10 dB range. ERNet primarily classifies based on the eigenvalues ​​of the covariance matrix or its preprocessed statistics, while our proposed method uses a two-dimensional Capon spatial spectrum at a fixed dB scale as input, which can simultaneously preserve information such as peak positions, relative intensities, and spectral shape variations. Therefore, under extremely low SNR conditions, our proposed method demonstrates better robustness than one-dimensional feature input networks, and first approaches saturation at -12 dB.

[0089] The MCA-ResNet18 algorithm of this invention achieves the best Top-1 estimation performance on the full signal-to-noise ratio test set, reaching an accuracy of 94.74%; at the same time, it also maintains the best estimation performance in the extremely low signal-to-noise ratio test range, with an accuracy of 69.28%.

[0090] S5, verification of wide-angle domain generalization performance.

[0091] To verify the adaptability of the method of this invention under different scanning angle domains, comparative tests were conducted in the main experimental angle domain of [-60°, 60°] and the extended wide angle domain of [-90°, 90°]. The performance comparison between the standard ResNet18 and the MCA-ResNet18 of this invention is as follows: Figure 6 , Figure 7 As shown in the figure. Test results show that, under both angular domains, the accuracy of the method of this invention is higher than that of the standard ResNet18 throughout the entire process, and the performance improvement trend is consistent. When the scanning angular domain is expanded to [-90°, 90°], the overall accuracy of both models decreases slightly, but the decrease is similar, and the performance gain of this invention does not decrease with the expansion of the angular domain. This result proves that the improved scheme of this invention does not depend on a specific angular domain setting, has excellent scene generalization ability, and can adapt to the array detection requirements of different scanning ranges without modifying the network structure and hyperparameters.

[0092] S6, Ablation Experiment Verification To verify the effectiveness of each improved module, ablation experiments were conducted, and the results are shown in Table 2: Table 2. Ablation Experiment Results of MCA-ResNet18 Model

[0093] As shown in Table 2, introducing different improved modules into the original ResNet18 network improved the model performance to varying degrees. Mish activation improved the feature transfer efficiency of weak spectral peaks under low signal-to-noise ratio by preserving weak feature gradients on the negative half-axis; coordinate attention (CA) accurately enhanced spectral peak regions and suppressed noise interference through spatially aware feature recalibration, which was the main source of the model performance improvement; the auxiliary training strategy further improved the model's generalization ability through the synergistic effect of MixStyle feature statistical perturbation, label smoothing regularization, Dropout random deactivation, and low signal-to-noise ratio sample weighted sampling. The synergistic effect of each module enabled the model to more effectively capture the source number discrimination features under low signal-to-noise ratio, thereby improving the estimation accuracy and robustness.

[0094] Further verification of the input preprocessing method shows that the globally fixed dB normalization used in this invention has significant advantages at extremely low signal-to-noise ratios (SNRs). At the -20 dB level, it achieves an accuracy 8.33 percentage points higher than single-sample maximum-minimum normalization. The gain is more pronounced as the SNR decreases, verifying the effectiveness of the globally unified amplitude scale. Parameter and computational complexity statistics show that the complete network of this invention only increases the number of parameters by 0.037M, an increase of approximately 0.33%, and the computational complexity increases by approximately 0.03%, making the hardware overhead almost negligible and demonstrating excellent lightweight characteristics.

[0095] The above experimental data verifies the feasibility of the algorithm of this invention. The accuracy of source number estimation reaches 94.74% under full signal-to-noise ratio conditions and 69.28% under extremely low signal-to-noise ratio conditions, which is significantly better than existing methods, and the errors are all within an acceptable range.

[0096] This invention proposes a source number estimation method based on Capon spatial spectrum and MCA-ResNet18 under conditions of low signal-to-noise ratio and limited snapshots in complex electromagnetic environments. By utilizing fixed-scale spectrogram construction, lightweight attention enhancement, and multi-strategy training optimization, the method effectively improves the accuracy and robustness of source number estimation under low signal-to-noise ratio conditions, while maintaining low estimation error. Compared with the algorithm of this invention, other current algorithms show a significant decrease in estimation performance under low signal-to-noise ratio conditions, further demonstrating the effectiveness of the proposed method.

[0097] Table 3. Ablation experimental results using Capon spatial spectrum preprocessing method:

[0098] As shown in Table 3, different spatial spectrum preprocessing methods significantly affect the recognition performance under low signal-to-noise ratio (SNR) conditions. Within the -20 dB to -17 dB range, fixed dB scale representation achieved the highest accuracy at all test points, with even more pronounced advantages at -20 dB and -19 dB. Compared to robust normalization and max-min normalization, fixed dB scale representation retains more consistent amplitude scale information across different samples, while also better preserving the relative strength relationships between spectral peaks. Therefore, for the source number estimation task of this invention, fixed dB scale representation is more beneficial than intra-sample adaptive normalization for the network to extract stable multi-peak structure features and improves recognition performance under extremely low SNR conditions.

[0099] Table 4. Comparison of model complexity with different modifications

[0100] As shown in Table 4, replacing the ReLU activation function with the Mish activation function does not change the number of model parameters and computational cost. The additional overhead mainly comes from element-wise nonlinear operations such as exponential, logarithmic, and hyperbolic tangent. MixStyle, label smoothing, and Dropout mainly affect the training phase. MixStyle enhances the model's generalization ability by perturbing the mean and variance of features without introducing trainable parameters; label smoothing only changes the distribution of target labels in the loss function without changing the network structure; Dropout is turned off during the inference phase. Therefore, these three do not increase the number of parameters and computational cost during the inference phase. Finally, after introducing the coordinate attention module, the number of parameters in the MCA-ResNet18 of this invention increased from 11.178 M to 11.215 M, an increase of approximately 0.33%; the computational cost increased from 3.647 GFLOPs to 3.648 GFLOPs, an increase of approximately 0.03%. This shows that the improvement in this paper only introduces a small additional computational overhead while improving the low signal-to-noise ratio recognition performance.

[0101] To address the issue of decreased accuracy in source number estimation under low signal-to-noise ratio (SNR) conditions in uniform linear array scenarios, this invention proposes a source number estimation method based on Capon spatial spectrograms and MCA-ResNet18. This method enhances the preservation of spectral peak structure information by constructing a two-dimensional Capon spatial spectrogram input at a fixed dB scale. Furthermore, it improves the model's representation ability for low SNR spectrograms by combining the Mish activation function, coordinate attention module, and training enhancement strategies on top of ResNet18. Experimental results show that the proposed method exhibits good recognition performance under different SNR conditions and demonstrates good adaptability in low SNR scenarios. Overall, this invention improves source number estimation under low SNR conditions by addressing both input representation and network structure, providing a feasible method for source number estimation in complex noisy environments.

[0102] This application also provides an electronic device, including a processor and a memory.

[0103] The memory is used to store computer programs.

[0104] When the processor executes a program stored in the memory, it implements any of the methods described in this application.

[0105] In one possible implementation, the electronic device of this application embodiment further includes a communication interface and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus.

[0106] The communication bus mentioned in the above electronic devices can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. This communication bus can be divided into address bus, data bus, control bus, etc.

[0107] The communication interface is used for communication between the aforementioned electronic devices and other devices.

[0108] The memory may include random access memory (RAM) or non-volatile memory (NVM), such as at least one disk storage device. Optionally, the memory may also be at least one storage device located remotely from the aforementioned processor.

[0109] The processors mentioned above can be general-purpose processors, including central processing units (CPUs), network processors (NPs), etc.; they can also be digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0110] In another embodiment provided in this application, a computer-readable storage medium is also provided, which stores a computer program that, when executed by a processor, implements any of the methods described in this application.

[0111] In another embodiment provided in this application, a computer program product containing instructions is also provided, which, when run on a computer, causes the computer to perform any of the methods described in this application.

[0112] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid state disk (SSD)).

[0113] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0114] The various embodiments in this specification are described in a related manner. Each embodiment focuses on the differences from other embodiments, and the same or similar parts between the various embodiments can be referred to each other.

[0115] The above description is merely a preferred embodiment of this application and is not intended to limit the scope of protection of this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application are included within the scope of protection of this application.

Claims

1. A source number estimation method based on Capon spatial spectral graphs and improved convolutional networks, characterized in that, Includes the following steps: S1. Collect array observation data and construct a source number estimation dataset; S2. Capon spatial power spectrum preprocessing based on diagonal loading and fixed dB mapping; S3. Hierarchical feature extraction based on MCA-ResNet18 network; S4. Spatial location feature enhancement based on coordinate attention; S5. Optimization of weak feature gradient preservation based on Mish activation; S6, Optimization of auxiliary training strategy and output of information source number.

2. The source number estimation method based on Capon spatial spectral graph and improved convolutional network according to claim 1, characterized in that, Step 1 is implemented as follows: Multiple sets of samples were generated by using a multi-shot array observation data of far-field narrowband signals acquired by a uniform linear array and constraining the minimum incident angle interval of the far-field narrowband signals, covering a wide signal-to-noise ratio range. Multiple sets of samples were cleaned, and then a source number estimation dataset was constructed. The source number estimation dataset is divided into a training set, a validation set, and a test set.

3. The source number estimation method based on Capon spatial spectral graph and improved convolutional network according to claim 1, characterized in that, Step 2 is implemented as follows: Using array observation data as input to the MCA-ResNet18 network, the sample covariance matrix corresponding to each sample is solved, and an adaptive diagonal loading correction covariance matrix based on trace constraints is introduced; within a set scanning angle range, the logarithmic form of the Capon spatial power spectrum is calculated for the correction covariance matrix. A globally unified dB range is used to perform linear normalization mapping on all samples, removing coordinate axes, scales, and text labels, and converting the one-dimensional Capon space power spectrum into a two-dimensional grayscale spectrum of uniform size as the input to the standardized network. The MCA-ResNet18 network completes the layer-by-layer extraction of spectral features and the source number classification output. The MCA-ResNet18 network adopts a four-stage hierarchical residual architecture, with a coordinate attention module embedded at the end of each stage. The front end of the first two stages is configured with MixStyle feature perturbation units, and the entire network uses the Mish activation function instead of the original ReLU.

4. The source number estimation method based on Capon spatial spectral graph and improved convolutional network according to claim 1, characterized in that, Step 2, involving diagonal loading and fixed dB scale Capon spectrum construction, requires completing five steps sequentially: solving the covariance matrix, diagonal loading correction, Capon spatial spectrum calculation, fixed dB normalization, and generating the two-dimensional grayscale spectrum. The specific logic is as follows: Suppose a far-field narrowband signal is incident on... M A uniform linear array, from the perspective of direction and angle Incident, at the At each snapshot, the array receive vector is: ； in, For array receiving data vectors, For the first The far-field narrowband signal vector at a snapshot moment For the first The noise vector at each snapshot moment, Let be an array manifold matrix, where For angle The corresponding guide vector; For array element spacing is The uniform linear array, the guiding vector is expressed as: ； in, Indicates the signal wavelength; The covariance matrix is ​​used as input to the MCA-ResNet18 network. The covariance matrix is ​​defined as follows: ； Diagonal loading is introduced to improve the stability of inversion, i.e.: ； in, The covariance matrix after diagonal loading. Represents the matrix trace operation. for M An identity matrix of order 1; scanning direction angle The spatial power spectrum was calculated in 0.5° increments within the range [-60°, 60°] and converted to logarithmic form. ； in, The guide vector for the corresponding angle. To prevent the occurrence of extremely small positive constants with negative infinity when taking the logarithm; Perform a linear mapping on the spatial spectrum of all samples, normalizing the spectral values ​​to the range [0,1]. Let the lower bound of the display range be... Upper limit of display range Then the fixed-scale spatial spectrum The mapping can be represented as: ； The normalized one-dimensional spatial spectrum is plotted as a two-dimensional grayscale spectrum.

5. The source number estimation method based on Capon spatial spectral graph and improved convolutional network according to claim 1, characterized in that, The MCA-ResNet18 network employs a four-stage hierarchical feature extraction structure, as detailed below: The first stage involves stacking two Mish-Basic residual blocks to extract underlying texture features, which are used to establish a preliminary characterization of the spectral peak morphology. The front end of this stage is connected to the first MixStyle feature perturbation unit, which simulates the spectral style changes under different signal-to-noise ratios by using the mean and variance of the random perturbation features. Second stage: After the downsampling operation, two Mish-Basic residual blocks are stacked, and a second MixStyle feature perturbation unit is connected at the front end of this stage; Phase 3: By stacking two Mish-Basic residual blocks; Phase 4: Continue stacking two Mish-Basic residual blocks; The Mish-Basic residual block adopts a residual structure design, and by introducing the Mish activation function and coordinate attention module, it achieves a dual improvement in feature representation capability and localization accuracy. The two residual blocks within each stage are connected in series. The output of the previous residual block serves as the input of the next residual block. The final output of each stage is recalibrated by the coordinate attention module before serving as the input of the next stage. After the fourth-level feature extraction is completed, a global average pooling layer is used to compress the two-dimensional grayscale spectrum into a one-dimensional feature vector. Then, a Dropout layer and a three-class fully connected layer are used to finally output the probability values ​​corresponding to the number of information sources of the three classes 1, 2, and 3. At the end of each stage, a coordinate attention module is embedded.

6. The source number estimation method based on Capon spatial spectral graph and improved convolutional network according to claim 1, characterized in that, The outputs of the four residual stages each embed an independent coordinate attention module, which performs one-dimensional pooling encoding along the two orthogonal dimensions of height and width to generate two channel attention weights carrying position information. The output feature map of this stage is then multiplied element-wise with the channel attention weights in the two directions to complete feature recalibration.

7. The source number estimation method based on Capon spatial spectral graph and improved convolutional network according to claim 6, characterized in that, The specific implementation of the coordinate attention module is as follows: Let the input feature tensor be ,in For the number of channels, For feature height, The feature width; Global average pooling is performed along both the height and width orthogonal directions to obtain aggregated features in both directions: The height-direction aggregation feature size is 1. The value of the i-th height position in the c-th channel is: ； The width-direction aggregation feature size is 1 The value at the j-th width position of the c-th channel is: ； in, Represents the original input features; The height-oriented aggregated features and the width-oriented aggregated features are concatenated in the spatial dimension and fed into a shared convolutional layer and the Mish activation function for non-linear transformation to generate intermediate features that simultaneously contain channel information and positional information. The fused intermediate features are re-split into height and width branches along the spatial dimension. After adjusting the number of channels through convolution, bidirectional channel attention weights with values ​​in the range [0,1] are generated using the Sigmoid activation function. and ; The preprocessed two-dimensional grayscale spectrum is multiplied element-wise with the attention weights in both directions to complete feature recalibration. Output of each channel Defined as: 。 8. A source number estimation system based on Capon spatial spectral graphs and improved convolutional networks, characterized in that, The system is used to implement the method as described in claim 1, specifically including: Acquisition module: Acquires array observation data and constructs a source number estimation dataset; Preprocessing module: Capon spatial power spectrum preprocessing based on diagonal loading and fixed dB mapping; Feature extraction module: Hierarchical feature extraction is performed using the MCA-ResNet18 network; Enhancement module: Spatial location feature enhancement based on coordinate attention; Optimization module: Weak feature gradient preservation optimization based on Mish activation; Training and Output Module: Assists in optimizing training strategies and outputting the number of information sources.

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