An end-to-end doa estimation method and system based on complex correlation entropy under pulse noise
By introducing a learnable complex correlation entropy layer and full-link complex domain processing into DOA estimation, the robustness and accuracy issues of DOA estimation under impulse noise are solved, and high-precision positioning is achieved in strong interference environments.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- TAIZHOU UNIV
- Filing Date
- 2026-04-10
- Publication Date
- 2026-07-24
AI Technical Summary
Existing technologies for direction of arrival (DOA) estimation in impulse noise environments suffer from poor robustness and low feature extraction accuracy, especially under strong impulse interference conditions, making it difficult to achieve high-precision positioning.
A learnable complex correlation entropy layer is used as the front-end noise suppression module. The coupling correlation between the amplitude and phase of the array signal is preserved through full-link complex domain processing. An end-to-end DOA estimation network is constructed to achieve joint optimization of noise suppression and feature extraction.
It significantly improves the robustness of the algorithm under strong impulse noise and the accuracy of DOA feature representation. It is suitable for complex scenarios such as radar, sonar and 5G/6G millimeter wave communication, and has higher anti-interference ability and angle estimation accuracy.
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Figure CN122449461A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of array signal processing and direction-of-arrival (DOA) estimation technology, specifically to an end-to-end DOA estimation method and system based on complex correlation entropy under impulse noise. Background Technology
[0002] In practical engineering scenarios such as radar detection, underwater sonar positioning, and 5G / 6G millimeter-wave communication, the signals received by array antennas are easily affected by atmospheric discharge, sea clutter, electromagnetic shock, and other factors, and are contaminated by non-Gaussian impulse noise. This type of noise typically follows an alpha-stable distribution and does not possess finite second moments, which is fundamentally different from traditional Gaussian noise models. Traditional direction-of-arrival (DOA) estimation algorithms based on the Gaussian noise assumption, such as the MUSIC algorithm and ESPRIT algorithm, mainly rely on the second-order statistics of the signal to achieve spatial spectrum estimation and target orientation calculation. In impulse noise environments, they experience problems such as a sharp degradation in estimation performance and algorithm failure, and cannot meet the high-precision positioning requirements under strong impulse interference conditions.
[0003] To improve the robustness of DOA estimation under impulse noise, existing techniques have focused on both traditional robust statistical methods and deep learning methods, but both have significant limitations. Traditional robust methods based on manually calculated statistical measures such as fractional-order low-order moments and correlation entropy use pre-defined, fixed robust statistical features to suppress noise. They are highly sensitive to parameters such as kernel length and order, have poor adaptability in time-varying and complex impulse noise scenarios, and can only be used as a front-end preprocessing tool, making it difficult to deeply integrate with the adaptive feature extraction mechanisms of deep learning.
[0004] While deep learning-based DOA estimation methods possess strong feature learning capabilities, existing schemes often separate the real and imaginary parts of the array covariance matrix into dual-channel input real-valued networks. This severs the inherent coupling between the real and imaginary parts of complex signals, resulting in the loss of the core information of inter-element phase differences upon which DOA estimation depends. Furthermore, these methods do not integrate a learnable noise suppression module at the network front end; noise suppression and DOA feature extraction are independent, preventing end-to-end joint optimization and leading to a significant decrease in feature extraction accuracy under strong impulse noise.
[0005] Complex correlation entropy can utilize the second-order and higher-order statistical properties of complex signals, and has a natural suppression effect on impulse noise. However, existing studies only use it as a fixed preprocessing operator and have not built a learnable layer structure that can be embedded in neural networks and backpropagated. Therefore, it cannot achieve parameter co-optimization with subsequent feature extraction networks, and its robust suppression potential has not been fully released. Summary of the Invention
[0006] The purpose of this invention is to propose an end-to-end DOA estimation method and system based on complex correlation entropy under impulse noise. The method adaptively suppresses impulse noise through a learnable complex correlation entropy layer and preserves phase and amplitude information through full-link complex domain processing, thereby achieving joint optimization of noise suppression and feature extraction.
[0007] According to a first aspect of the present disclosure, an end-to-end DOA estimation method based on complex correlation entropy under impulse noise is provided, comprising the following steps: Obtain the complex snapshot matrix received by the array antenna; The complex snapshot matrix is preprocessed using a complex correlation entropy layer to obtain the complex correlation entropy of the signals between array elements, and a complex correlation entropy matrix is constructed; wherein, the kernel length parameter of the complex Gaussian kernel function in the calculation of complex correlation entropy is a learnable parameter; The complex correlation entropy matrix is input into the complex-valued CNN module, and features are extracted through full-link complex domain convolution operation to output a complex feature map containing robust spatial features. The complex feature map is input into a fully connected regression module, which outputs the estimated direction of arrival (DOA). A loss function is constructed based on the difference between the DOA estimate and the true label, and end-to-end joint optimization is completed.
[0008] In one embodiment, the complex snapshot matrix is represented as follows: ,in The number of array elements. The number of snapshots; for any two array elements receiving signals. and The complex correlation entropy is obtained by the following formula: in, Nuclear length parameter Adaptive updates are achieved through backpropagation.
[0009] In one embodiment, the complex correlation entropy layer is constructed based on the calculation results of all array element pairs. Multidimensional correlation entropy matrix The feature maps are input into the complex-valued CNN module in the form of M×M×1 single-channel complex feature maps.
[0010] In one embodiment, the complex-valued CNN module is constructed by serially cascading three levels of complex-valued convolutional units. Each level of complex-valued convolutional unit sequentially includes a complex-valued two-dimensional convolutional layer, a complex-valued batch normalization layer, and a complex-valued CELU activation layer, and the feature extraction is completed entirely in the complex domain.
[0011] In one embodiment, the complex-valued CNN module outputs a 128-channel high-dimensional complex feature map, which is then flattened in the complex domain and input to the fully connected regression module.
[0012] In one embodiment, the fully connected regression module includes two complex fully connected layers and one real output layer. The complex fully connected layers operate according to the complex multiplication rule and finally output the DOA angle estimate in real form.
[0013] In one embodiment, the loss function is the mean squared error (MSE) loss, and the Adam optimizer is used to perform end-to-end joint optimization, synchronously updating the kernel length parameter of the complex correlation entropy layer, all weight parameters of the complex-valued CNN module, and the parameters of the complex fully connected layer.
[0014] According to a second aspect of the present disclosure, an end-to-end DOA estimation system based on complex correlation entropy under impulse noise is provided, comprising: The signal input module acquires the complex snapshot matrix received by the array antenna; The complex correlation entropy preprocessing module uses the complex correlation entropy layer to preprocess the complex snapshot matrix to obtain the complex correlation entropy of the signals between array elements and construct the complex correlation entropy matrix; wherein, the kernel length parameter of the complex Gaussian kernel function in the calculation of complex correlation entropy is a learnable parameter; The complex domain feature extraction module inputs the complex correlation entropy matrix into the complex-valued CNN module, performs feature extraction through full-link complex domain convolution operation, and outputs a complex feature map containing robust spatial features. The DOA regression output module inputs the complex feature map into the fully connected regression module and outputs the DOA estimate. The training module is optimized by constructing a loss function based on the difference between the DOA estimate and the true label, thus completing end-to-end joint optimization.
[0015] According to a third aspect of the present disclosure, an electronic device is provided, including a memory, a processor, and a computer program stored in the memory and running on the memory, wherein the processor executes the program to implement the described end-to-end DOA estimation method based on complex correlation entropy under impulse noise.
[0016] According to a fourth aspect of the present disclosure, a computer-readable storage medium is provided having a computer program stored thereon that, when executed by a processor, implements the described end-to-end DOA estimation method based on complex correlation entropy under impulse noise.
[0017] The advantages of the above technical solutions adopted in this invention compared with the prior art are as follows: 1. A learnable complex correlation entropy is used as the front-end noise suppression module. The kernel length parameter is adaptively optimized during network training without manual pre-setting. It can achieve adaptive noise suppression under strong impulse noise, significantly improving the robustness of the algorithm.
[0018] 2. Adopting a full-link complex domain processing architecture, the coupling relationship between the amplitude and phase of the array signal is fully preserved, avoiding the loss of phase difference information caused by traditional real-value processing, and effectively improving the accuracy of DOA feature expression.
[0019] 3. The noise suppression module and feature extraction module are integrated into the end-to-end network to achieve joint optimization and synchronous parameter updates, which greatly improves the estimation stability and generalization ability under low snapshot conditions.
[0020] 4. In non-Gaussian impulse noise environments, it can maintain higher angle estimation accuracy and stronger anti-interference capability, making it suitable for complex scenarios such as radar, sonar, and 5G / 6G millimeter-wave communication, and possessing higher practical value. Attached Figure Description
[0021] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments of this application and their descriptions are used to explain this application and do not constitute an undue limitation of this application.
[0022] Figure 1 This is an architecture diagram of an end-to-end DOA estimation method based on complex correlation entropy under impulse noise. Figure 2 This is a schematic diagram of the complex correlation entropy calculation process; Figure 3 This is a schematic diagram of the complex-valued CNN module structure; Figure 4 A schematic diagram illustrating the performance of DOA estimation under different characteristic indices; Figure 5 This diagram illustrates the performance of DOA estimation under different generalized signal-to-noise ratios. Detailed Implementation
[0023] The present disclosure will be further described below with reference to the accompanying drawings and embodiments.
[0024] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.
[0025] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.
[0026] It should be noted that the flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of methods and systems according to various embodiments of this disclosure. It should be noted that each block in a flowchart or block diagram may represent a module, segment, or portion of code, which may include one or more executable instructions for implementing the logical functions specified in the various embodiments. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than that shown in the drawings. For example, two consecutively represented blocks may actually be executed substantially in parallel, or they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the flowcharts and / or block diagrams, and combinations of blocks in the flowcharts and / or block diagrams, may be implemented using a dedicated hardware-based system that performs the specified functions or operations, or using a combination of dedicated hardware and computer instructions.
[0027] like Figure 1 As shown, the deep learning DOA estimation network constructed in this invention is sequentially connected in series: an input layer, a complex correlation entropy layer (CCL), a complex-valued CNN module, and a fully connected regression module. The network input is the complex snapshot matrix received by the array antenna, and it directly outputs the DOA estimate, realizing an end-to-end mapping from the original received signal to the DOA result.
[0028] Example 1: This embodiment provides an end-to-end DOA estimation method based on complex correlation entropy under impulse noise, including the following steps: S1. Obtain the complex snapshot matrix received by the array antenna; Specifically, the complex snapshot matrix received by the array ,in The number of array elements. This represents the number of snapshots.
[0029] S2. The complex snapshot matrix is preprocessed using a complex correlation entropy layer to obtain the complex correlation entropy of the signals between array elements, and a complex correlation entropy matrix is constructed; wherein, the kernel length parameter of the complex Gaussian kernel function in the calculation of complex correlation entropy is a learnable parameter; like Figure 2As shown, this invention reconstructs the complex correlation entropy into an independent network layer in the neural network that can be backpropagated and learned; as the core of noise suppression at the front end of the network, the specific implementation is as follows: Received signals for any two array elements and , The complex correlation entropy between the two is obtained as follows: in, Let be the complex Gaussian kernel function, with the expression: ; The kernel length parameter is set as a learnable parameter that can be adaptively updated through backpropagation, replacing the manual parameter tuning of the traditional approach.
[0030] Based on the complex correlation entropy of all array element pairs, construct dimensional complex correlation entropy matrix This serves as the input feature map for subsequent complex-valued CNN modules.
[0031] S3. Input the complex correlation entropy matrix into the complex-valued CNN module, perform feature extraction through full-link complex domain convolution operation, and output a complex feature map containing robust spatial features; like Figure 3 As shown, this module is the core unit for full-link feature extraction in the complex domain. It fully preserves the coupling correlation information between amplitude and phase in the complex correlation entropy matrix, fundamentally avoiding the loss of core phase information caused by the separation of real and imaginary parts in traditional real-valued CNNs. At the same time, it extracts robust spatial features that are strongly correlated with DOA and suppresses feature perturbations caused by impulse noise.
[0032] The complex-valued CNN module adopts a three-layer cascaded complex-valued convolutional unit serial structure. Each convolutional unit consists of a complex-valued two-dimensional convolutional layer (Conv2d), a complex-valued batch normalization layer (BatchNorm), and a complex-valued CELU activation layer cascaded in sequence. The structure is branchless, which ensures the simplicity of the feature extraction chain and the stability of training.
[0033] The input to the complex-valued CNN module is an M×M×1 dimensional single-channel complex feature map output from the complex correlation entropy layer, and the output is a 128-channel high-dimensional robust complex feature map, which is flattened in the complex domain and then input into the subsequent fully connected regression module.
[0034] S4. Input the complex feature map into the fully connected regression module and output the direction of arrival (DOA) estimate; Specifically, the fully connected regression module includes two complex fully connected layers and one real output layer, which maps the high-dimensional complex features output by the complex-valued CNN module to the final DOA angle estimate. The complex fully connected layers are also designed according to the complex multiplication rule to ensure the complete transmission of complex information.
[0035] S5. Construct a loss function based on the difference between the DOA estimate and the true label, and complete the end-to-end joint optimization.
[0036] Mean squared error (MSE) is used as the loss function to measure the difference between the DOA estimate and the true label. The Adam optimizer is used to simultaneously update the kernel length parameter of the complex correlation entropy layer, all weight parameters of the complex value CNN module, and the parameters of the fully connected layer, so as to achieve end-to-end joint optimization of noise suppression and feature extraction.
[0037] To verify the technical advantages of this invention, multiple simulation experiments were conducted, comparing the method of this invention with MUSIC, CRCO-MUSIC, PFLOM-MUSIC and FLOM-MUSIC algorithms, and using the direction-of-arrival estimation accuracy as the core indicator to complete the performance evaluation.
[0038] The simulation conditions were set as follows: two independent BPSK signals were incident on a uniform linear array with M=12 elements, with incident angles of 15 degrees and 35 degrees respectively; the received signal of the array was superimposed with impulse noise following a symmetrical alpha stable distribution. Since the signal-to-noise ratio (SNR) commonly used in Gaussian noise environments is not applicable to alpha stable distributed impulse noise without finite second moments, the generalized signal-to-noise ratio (GSNR) was used as the performance evaluation index.
[0039] Under impulse noise environments with different characteristic indices, Figure 4 The root mean square error (RMSE) of DOA estimation for the method of this invention was compared with that of five algorithms: MUSIC, CRCO-MUSIC, PFLOM-MUSIC, and FLOM-MUSIC. The results show that as the feature exponent increases from 1.0 to 2.0 (as the impulse noise intensity gradually decreases), the RMSE of each algorithm shows a significant decreasing trend. Among them, the MUSIC algorithm, which does not perform any robust processing for impulse noise, has the highest RMSE and worst performance across the entire feature exponent range. FLOM-MUSIC and PFLOM-MUSIC use fractional low-order statistics for noise suppression, resulting in significantly lower RMSEs than the MUSIC algorithm, with similar performance. The CRCO-MUSIC algorithm further outperforms the other three algorithms in DOA estimation. The method of this invention consistently maintains the lowest RMSE and stable estimation results across the entire feature exponent range. Only when the feature exponent is 2 does its performance approach that of traditional algorithms, fully demonstrating the superiority of this invention in complex impulse noise environments.
[0040] To further verify the performance in strong impulse scenes, symmetric alpha-stable distributed impulse noise with a characteristic exponent of 1.3 was used. The DOA estimation performance of the proposed method was compared with that of four algorithms: MUSIC, CRCO-MUSIC, PFLOM-MUSIC, and FLOM-MUSIC, under different generalized signal-to-noise ratios (GSNR). The results are as follows: Figure 5 As shown in the figure, as the GSNR increases from 0dB to 20dB, the root mean square error (RMSE) of each algorithm gradually decreases. Among them, FLOM-MUSIC and PFLOM-MUSIC outperform the MUSIC algorithm. CRCO-MUSIC, due to its use of correlation entropy weighting, exhibits better suppression of impulse noise than fractional low-order statistics, demonstrating superior performance. The MUSIC algorithm, lacking impulse noise suppression capability, has the largest RMSE. The method of this invention maintains the lowest RMSE across the entire generalized signal-to-noise ratio (SNR) range, achieving the best DOA estimation accuracy and robustness.
[0041] Example 2: This embodiment provides an end-to-end DOA estimation system based on complex correlation entropy under impulse noise, including: The signal input module acquires the complex snapshot matrix received by the array antenna; The complex correlation entropy preprocessing module uses the complex correlation entropy layer to preprocess the complex snapshot matrix to obtain the complex correlation entropy of the signals between array elements and construct the complex correlation entropy matrix; wherein, the kernel length parameter of the complex Gaussian kernel function in the calculation of complex correlation entropy is a learnable parameter; The complex domain feature extraction module inputs the complex correlation entropy matrix into the complex-valued CNN module, performs feature extraction through full-link complex domain convolution operation, and outputs a complex feature map containing robust spatial features. The DOA regression output module inputs the complex feature map into the fully connected regression module and outputs the DOA estimate. The training module is optimized by constructing a loss function based on the difference between the DOA estimate and the true label, thus completing end-to-end joint optimization.
[0042] The above modules can be deployed on the same device or distributed devices; the division of modules is only a functional logic description and does not limit the specific physical boundaries or implementation order.
[0043] Example 3: An electronic device is provided for running the aforementioned "End-to-End DOA Estimation Method Based on Complex Correlation Entropy under Impulse Noise". The electronic device includes: a processor, a memory, and optional communication interface / display device / input device, etc.; the memory stores a computer program that can run on the processor, and when the processor executes the program, it implements steps S1 to S5 of the method described in Embodiment 1, specifically including but not limited to: S1. Obtain the complex snapshot matrix received by the array antenna; S2. The complex snapshot matrix is preprocessed using a complex correlation entropy layer to obtain the complex correlation entropy of the signals between array elements, and a complex correlation entropy matrix is constructed; wherein, the kernel length parameter of the complex Gaussian kernel function in the calculation of complex correlation entropy is a learnable parameter; S3. Input the complex correlation entropy matrix into the complex-valued CNN module, perform feature extraction through full-link complex domain convolution operation, and output a complex feature map containing robust spatial features; S4. Input the complex feature map into the fully connected regression module and output the direction of arrival (DOA) estimate; S5. Construct a loss function based on the difference between the DOA estimate and the true label, and complete the end-to-end joint optimization.
[0044] The electronic device hardware can be one of a server, personal computer, workstation, industrial controller, edge computing device, or mobile terminal; the processor can be a general-purpose CPU, GPU, NPU, FPGA, or a combination thereof; the memory can be RAM, ROM, flash memory, or disk array. The device can interact with local / remote data storage (acquiring observation data and outputting inversion results) through a communication interface. The above hardware configuration does not constitute a limitation of the present invention.
[0045] Example 4: A computer-readable storage medium storing a computer program, which, when run on a processor of an electronic device, causes the program to execute the method steps S1 to S5 described in Embodiment 1; the storage medium may be a disk, optical disk, flash memory, solid-state drive, read-only memory, random access memory, or any combination of the above media.
[0046] Those skilled in the art will understand that the modules or steps described above can be implemented using general-purpose computer devices. Optionally, they can be implemented using computer-executable program code, which can then be stored in a storage device for execution by a computer device. Alternatively, they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. This disclosure is not limited to any particular combination of hardware and software.
[0047] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.
[0048] While the specific embodiments of this disclosure have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of this disclosure. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of this disclosure are still within the scope of protection of this disclosure.
Claims
1. An end-to-end DOA estimation method based on complex correlation entropy under impulse noise, characterized in that, Includes the following steps: Obtain the complex snapshot matrix received by the array antenna; The complex snapshot matrix is preprocessed using a complex correlation entropy layer to obtain the complex correlation entropy of the signals between array elements, and a complex correlation entropy matrix is constructed; wherein, the kernel length parameter of the complex Gaussian kernel function in the calculation of complex correlation entropy is a learnable parameter; The complex correlation entropy matrix is input into the complex-valued CNN module, and features are extracted through full-link complex domain convolution operation to output a complex feature map containing robust spatial features. The complex feature map is input into a fully connected regression module, which outputs the estimated direction of arrival (DOA). A loss function is constructed based on the difference between the DOA estimate and the true label, and end-to-end joint optimization is completed.
2. The end-to-end DOA estimation method based on complex correlation entropy under impulse noise according to claim 1, characterized in that, The complex snapshot matrix is represented as follows: ,in The number of array elements. The number of snapshots; for any two array elements receiving signals. and The complex correlation entropy is obtained by the following formula: in, Nuclear length parameter Adaptive updates are achieved through backpropagation.
3. The end-to-end DOA estimation method based on complex correlation entropy under impulse noise according to claim 2, characterized in that, The complex correlation entropy layer is constructed based on the calculation results of all matrix element pairs. Multidimensional correlation entropy matrix The feature maps are input into the complex-valued CNN module in the form of M×M×1 single-channel complex feature maps.
4. The end-to-end DOA estimation method based on complex correlation entropy under impulse noise according to claim 1, characterized in that, The complex-valued CNN module is composed of three levels of complex-valued convolutional units cascaded in series. Each level of complex-valued convolutional unit includes a complex-valued two-dimensional convolutional layer, a complex-valued batch normalization layer, and a complex-valued CELU activation layer, and the feature extraction is completed entirely in the complex domain.
5. The end-to-end DOA estimation method based on complex correlation entropy under impulse noise according to claim 1, characterized in that, The complex-valued CNN module outputs a 128-channel high-dimensional complex feature map, which is then flattened in the complex domain and input into the fully connected regression module.
6. The end-to-end DOA estimation method based on complex correlation entropy under impulse noise according to claim 1, characterized in that, The fully connected regression module includes two complex fully connected layers and one real output layer. The complex fully connected layers operate according to the complex multiplication rules and finally output the DOA angle estimate in real form.
7. The end-to-end DOA estimation method based on complex correlation entropy under impulse noise according to claim 6, characterized in that, The loss function is the mean squared error (MSE) loss. The Adam optimizer is used to perform end-to-end joint optimization, and the kernel length parameter of the complex correlation entropy layer, all weight parameters of the complex value CNN module, and parameters of the complex fully connected layer are updated synchronously.
8. An end-to-end DOA estimation system based on complex correlation entropy under impulse noise, characterized in that, include: The signal input module acquires the complex snapshot matrix received by the array antenna; The complex correlation entropy preprocessing module uses the complex correlation entropy layer to preprocess the complex snapshot matrix to obtain the complex correlation entropy of the signals between array elements and construct the complex correlation entropy matrix; wherein, the kernel length parameter of the complex Gaussian kernel function in the calculation of complex correlation entropy is a learnable parameter; The complex domain feature extraction module inputs the complex correlation entropy matrix into the complex-valued CNN module, performs feature extraction through full-link complex domain convolution operation, and outputs a complex feature map containing robust spatial features. The DOA regression output module inputs the complex feature map into the fully connected regression module and outputs the DOA estimate. The training module is optimized by constructing a loss function based on the difference between the DOA estimate and the true label, thus completing end-to-end joint optimization.
9. An electronic device, comprising a memory, a processor, and a computer program stored in the memory and running thereon, characterized in that, When the processor executes the program, it implements an end-to-end DOA estimation method based on complex correlation entropy under impulse noise as described in any one of claims 1-7.
10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements an end-to-end DOA estimation method based on complex correlation entropy under impulse noise as described in any one of claims 1-7.