Robust doa estimation method based on generative denoising diffusion model

Abstract

The application discloses a kind of robust direction of arrival estimation method based on generative denoising diffusion model, mainly solve the problem that the direction of arrival estimation method based on discriminative neural network in prior art is strongly dependent on training scene, it is difficult to generalize to variable number of sources, different signal-to-noise ratio scene, its implementation steps are: array received signal modeling;Diffusion process and state transition forward distribution modeling;Based on the denoising of generative diffusion model iteration guided by received signal condition;The direction of arrival estimation is carried out using the noiseless signal estimation value obtained by the denoising of generative diffusion model iteration.The application converts the direction of arrival estimation problem into a denoising process guided by the received signal condition, can realize the generalization to different source number scenes under the condition of fixed source number training, and has good robustness and estimation performance in low signal-to-noise ratio, few snapshot scenes, etc.Provide support for new generation wireless communication system, low-altitude infrastructure construction and passive positioning, target detection and other applications.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, and in particular relates to a general direction-of-arrival estimation method for array-received signals in scenarios with a variable number of signal sources. Specifically, it is a robust direction-of-arrival estimation method based on a generative denoising diffusion model, which can be used for applications such as passive localization and target detection. Background Technology

[0002] Direction-of-arrival (DOA) estimation is a fundamental problem in array signal processing. It involves receiving spatial signals using an array antenna and processing the received signals through statistical signal processing techniques and various optimization methods to recover the DOA information contained in the signals. It has wide applications in radar, sonar, speech, radio astronomy, seismology, wireless communication, and medical imaging.

[0003] Traditional model-based methods, such as the MUSIC and ESPRIT algorithms, typically estimate direction-of-arrival (DOA) based on signal statistical properties and array manifold structure. However, as electromagnetic propagation environments become increasingly complex in practical applications, the performance of existing model-based methods degrades significantly due to model mismatch when systems face non-ideal scenarios such as low signal-to-noise ratio (SNR) and limited snapshots. To improve the robustness of ODA in complex scenarios, ODA methods based on discriminative neural networks such as multilayer perceptrons and convolutional neural networks have been proposed in recent years. These methods can directly learn the nonlinear mapping relationship between the array's received signal and the ODA, exhibiting good adaptability in handling problems such as low SNR, coherent sources, and grid mismatch, and have therefore received widespread attention in the field of robust ODA.

[0004] However, the effectiveness of existing discriminative neural network methods typically relies on the assumption that training and testing data conform to the same prior signal parameter configuration. In practical applications, key parameters in the array's received signals, especially the number of signal sources, often exceed the preset range of the training set. When there is a mismatch between the test samples and the training scenario, the performance of existing discriminative neural network-based methods will significantly decrease, or even fail. Improving generalization ability by increasing the size of the training dataset or training different networks for different scenarios would lead to a significant increase in data size and training costs, resulting in a heavy computational burden and hindering practical application deployment. This is because discriminative neural networks primarily learn the direct mapping relationship between the received signal and the direction of arrival (DOA), which is essentially an implicit probabilistic representation strongly correlated with specific scenario parameters. Therefore, when the training and testing scenarios change, this implicit mapping is difficult to maintain stability, leading to insufficient network generalization ability.

[0005] Unlike discriminative neural networks, generative diffusion models use the distribution of noiseless signals as their learning target and generate noiseless samples that conform to the target distribution through a progressive iterative denoising process starting from pure Gaussian noise. Therefore, they have stronger generalization potential when faced with scene-mismatched samples. However, the generation process of traditional generative diffusion models essentially involves randomly generating samples from the learned overall signal distribution. Their goal is to generate noiseless signals that satisfy specific distribution constraints, rather than recovering noiseless signals corresponding to the received signals of a specific array. This causes the random generation process of conventional diffusion models to eliminate the direction-of-arrival (DOA) information contained in the received signal during progressive denoising, making them unsuitable for direct DOA estimation tasks. Therefore, how to effectively transfer the generalization ability of diffusion models to the DOA estimation problem and further improve robust estimation performance in scenarios with variable number of sources and low signal-to-noise ratios is a crucial problem that urgently needs to be solved. Summary of the Invention

[0006] The purpose of this invention is to address the shortcomings of existing technologies by proposing a robust direction-of-arrival (DOA) estimation method based on a generative denoising diffusion model. This method models the array received signal, the diffusion process, and the forward distribution of state transitions, providing a foundation for subsequent noiseless signal recovery and robust ODA. Furthermore, it proposes introducing the array received signal as a conditional signal into the reverse diffusion process, using iterative denoising through the diffusion model to obtain an estimate of the noiseless signal. Finally, the obtained noiseless signal estimate is used for the final ODA. This invention can be extended from a fixed number of signal sources to a variable number of signal sources, and exhibits superior estimation performance and robustness compared to traditional model-based methods and discriminative neural network methods in scenarios with low signal-to-noise ratios and few snapshots. This provides technical support for its application in next-generation wireless communication systems, low-altitude infrastructure, passive positioning, and target detection.

[0007] To achieve the above objectives, the present invention may adopt the following specific technical solutions: The robust direction-of-arrival estimation method based on a generative denoising diffusion model includes the following steps: (1) Modeling the array received signal. Assume there are... One from A far-field narrowband incoherent signal source in the angular direction is used at the receiver to include... Antenna array receiving of individual elements Each signal sampling snapshot, the array received signal matrix is ​​modeled as follows: , in, Represents the array guidance matrix, express One source The signal matrix captured by a sampling snapshot Indicates the first The signal waveform vector of each source. This represents additive complex white Gaussian noise. Indicates noise power. This indicates the transpose operation. and These represent the zero vector and the unit vector, respectively.

[0008] (2) Forward distribution modeling of diffusion process and state transition. The array receives the signal. The expected signal element in Power normalization is performed to obtain a noise-free signal. : , in, Indicates the first The power of each signal source; in a multi-source direction-of-arrival estimation scenario. The probability distribution of can be approximated as a zero-mean multivariate complex Gaussian distribution, i.e. ,and Covariance matrix of the distribution With source number Irrelevant; therefore, in the subsequent diffusion model training phase, signal samples from scenarios with a fixed number of sources can be used to learn the noiseless signal distribution in scenarios with a variable number of sources. This property forms the basis of the training set construction strategy of this invention; it is worth noting that here... This information is used only as the ground truth label during the subsequent training phase of the diffusion model. During the inference phase, it needs to be obtained through iterative denoising using the diffusion model. The estimated value.

[0009] Will As the initial state, construct the... A noisy complex Gaussian state variable The diffusion process consists of states whose state variables satisfy the following: , in, It is a set of random Decreasing preset hyperparameters, This represents complex Gaussian noise. When... As it gradually increases, the state variable The proportion of noise gradually increases; when At that time, the final state It can be considered as pure Gaussian noise.

[0010] Based on the above definition of state variables, we can obtain the following: Transfer to The conditional probability distribution is: , in, , ,and This is called the forward distribution of state transition.

[0011] (3) Iterative denoising based on a generative diffusion model guided by received signal conditions. The purpose of iterative denoising is to denoise pure Gaussian noise. Starting from this point, through multiple iterations of the reverse diffusion process in the generative diffusion model, the signal received by the array is gradually recovered. Corresponding noiseless signal estimate In this process, each iteration of the reverse diffusion is performed using the current state variable. Generate its previous state variable and in accordance with The process is iterated sequentially until a noise-free signal estimate is obtained. In order to preserve the direction-of-arrival information contained in the original received signal during the back-diffusion process, this invention introduces an array of received signals during the back-diffusion process. As a conditional signal, it guides each step of the denoising process; therefore, the state transition probability of the reverse diffusion process can be expressed as: Furthermore, it is expressed as a complex Gaussian distribution using Bayes' rule: , in, and They represent The mean and covariance matrices, their specific values ​​and , and Related. Due to The target state for the reverse diffusion process cannot be directly obtained here. and Therefore, the exact expression for the state transition probability of the reverse diffusion process is approximated by the following complex Gaussian distribution: , in, It is the mean An estimated value, calculated by the following formula: , in, Indicates a For input, with Noise item in A neural network function is used to estimate the target. The array receives signals. The guiding effect of iterative denoising depends entirely on the training effect of this neural network; therefore, the neural network... It is called a denoising conditional diffusion network, and its training set consists of... structure.

[0012] Based on the above approximation of the state transition probability of the reverse diffusion process, in the first... In the next iteration, firstly , as well as Input the denoising conditional diffusion network to obtain the desired result. estimation results Then, the mean term is calculated based on the estimation result. And based on this, determine the approximate reverse transition probability. And sample from this approximate distribution to generate the previous state variable. Repeat the above process until... Iterate to Finally, the signal received by the array is obtained. Corresponding noiseless signal estimate .

[0013] (4) The direction of arrival is estimated by using the noiseless signal estimate obtained by iterative denoising through the generative diffusion model.

[0014] Furthermore, the antenna array in step (1) is deployed using a uniform rectangular array: the array along... Axis direction setting Each array element, along Axis direction setting There are array elements, and the total number of array elements is [number]. The element spacing is half the wavelength of the incident narrowband signal, corresponding to the first... Array guidance vectors of several sources It can be represented as: , in, ; ; ; .

[0015] Furthermore, in step (3), the denoising conditional diffusion network adopts a U-Net structure with parallel paths, including a main path and an auxiliary path; wherein the main path is used to process the current state variable. The auxiliary path is used to process the array received signal. The network structure of the main path and auxiliary paths remains consistent; in order to index the iteration steps Introducing the network, we first perform sinusoidal position encoding on it, and then compare the encoding result with... The input to the auxiliary path is concatenated according to the channel dimension; the auxiliary path is fused with the main path element-wise after each sampling layer; the U-Net structure includes an input convolutional layer, an output convolutional layer, two convolutional downsampling layers, and two transposed convolutional upsampling layers, and the network output is the output of the noise term. The estimation results.

[0016] Furthermore, in step (3), the denoising conditional diffusion network constructs a training set using signal sample pairs under a fixed number of sources: each training sample consists of the received signal... and its corresponding noiseless signal Composition. For any training sample, randomly select... Then from the complex Gaussian distribution Random sampling And using the diffusion state variables defined in step (2) to generate When constructing the training set, a fixed number of information sources are selected. Training samples are generated, and the noise-free signal after power normalization is used. The probability distribution is independent of the number of sources, and the trained denoising diffusion model can be used for direction-of-arrival estimation in scenarios with a variable number of sources; the goal of network training is to minimize the true noise term. The mean squared error between the network output and the loss function is expressed as: , in, Represents the mathematical expectation. This represents the Euclidean norm.

[0017] Furthermore, in step (4), the direction of arrival estimation can be achieved by the following method: First, based on the noiseless signal estimation value Calculate the sample covariance matrix: ,in, This represents the conjugate transpose operation; Then, calculate the following spatial spectral function: , , , in, Operations are used to collect the maximum value of the corresponding matrix. Eigenvectors corresponding to all eigenvalues ​​other than the given eigenvalue; finding the spatial spectral function. All local maxima are determined according to their response values. Sort the responses by size and select the one with the largest response value. The angle values ​​corresponding to each maximum point This is the direction of arrival estimation result.

[0018] Compared with the prior art, the present invention has the following advantages: (1) This invention introduces the denoising diffusion probability model into the field of direction of arrival estimation. By reconstructing the direction of arrival estimation problem into a conditional signal denoising task, the invention utilizes the back diffusion process to gradually recover the noiseless signal from the original noisy received signal, providing a new technical path and framework for robust direction of arrival estimation. (2) This invention utilizes the characteristic that the probability distribution of power-normalized noiseless signals is independent of the number of sources, so that the proposed method can be generalized to scenarios with a variable number of sources by training only on a dataset with a fixed number of sources, thus solving the generalization problem caused by scenario mismatch in traditional discriminative neural network methods. (3) The present invention designs a parallel dual-path conditional denoising diffusion network. The received signal is fused with the time embedding as conditional information through the auxiliary path and added to the main path features after each sampling layer, thereby achieving precise guidance of the back diffusion process and effectively avoiding the randomness problem in the diffusion model generation process. Attached Figure Description

[0019] Figure 1 This is the overall flowchart of the present invention; Figure 2 This is a schematic diagram of the reverse diffusion process and the noise-reducing conditional diffusion network structure proposed in this invention; Figure 3 This is a schematic diagram showing the performance comparison of the root mean square error of the method proposed in this invention as a function of signal-to-noise ratio. Figure 4 This is a schematic diagram showing the performance comparison of the root mean square error of the method proposed in this invention as a function of the number of snapshots. Figure 5 This is a schematic diagram comparing the performance of the root mean square error of the method proposed in this invention as the number of information sources changes. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0021] Existing direction-of-arrival (DOA) estimation methods based on discriminative neural networks face challenges in practical applications such as robust direction finding in complex environments and passive localization, including strong training scenario dependence and difficulty in generalizing to scenarios with different numbers of signal sources. To address these challenges, this invention reconstructs the ODA problem as a conditional signal denoising task and designs a back-diffusion process to gradually recover the noise-free signal from the original noisy received signal. A robust ODA method based on a generative denoising diffusion model is proposed, such as... Figure 1As shown, the implementation steps of this invention are as follows: Step 1: Modeling the array received signal.

[0022] Assume there is One from A far-field narrowband incoherent signal source in the angular direction is used at the receiver to include... Antenna array receiving of individual elements Each signal sampling snapshot, the array received signal matrix is ​​modeled as follows: , in, Represents the array guidance matrix, express One source The signal matrix captured by a sampling snapshot Indicates the first The signal waveform vector of each source. This represents additive complex white Gaussian noise. Indicates noise power. This indicates the transpose operation. and These represent the zero vector and the unit vector, respectively.

[0023] The antenna array is deployed using a uniform rectangular array: the array along... Axis direction setting Each array element, along Axis direction setting There are array elements, and the total number of array elements is [number]. The element spacing is half the wavelength of the incident narrowband signal, corresponding to the first... Array guidance vectors of several sources It can be represented as: , in, ; ; ; .

[0024] Step 2: Modeling the diffusion process and forward distribution of state transitions.

[0025] Array receives signals The expected signal element in Power normalization is performed to obtain a noise-free signal. : , in, Indicates the first The power of each signal source. In a multi-source direction-of-arrival estimation scenario. The probability distribution of can be approximated as a zero-mean multivariate complex Gaussian distribution, that is: ,and Covariance matrix of the distribution With source number Irrelevant; therefore, in the subsequent diffusion model training phase, signal samples from scenarios with a fixed number of sources can be used to learn the noiseless signal distribution in scenarios with a variable number of sources. This property forms the basis of the training set construction strategy of this invention; it is worth noting that here... This information is used only as the ground truth label during the subsequent training phase of the diffusion model. During the inference phase, it needs to be obtained through iterative denoising using the diffusion model. The estimated value.

[0026] Will As the initial state, construct the... A noisy complex Gaussian state variable The diffusion process consists of states whose state variables satisfy the following: , in, It is a set of random Decreasing preset hyperparameters, This represents complex Gaussian noise. When... As it gradually increases, the state variable The proportion of noise gradually increases; when At that time, the final state It can be considered as pure Gaussian noise. Based on the above definition of state variables, we can obtain... Transfer to The conditional probability distribution is: , in, , ,and This is called the forward distribution of state transition.

[0027] Step 3: Iterative denoising using a generative diffusion model guided by received signal conditions.

[0028] The purpose of iterative denoising is to remove pure Gaussian noise. Starting from this point, through multiple iterations of the reverse diffusion process in the generative diffusion model, the signal received by the array is gradually recovered. Corresponding noiseless signal estimate In this process, each iteration of the reverse diffusion is performed using the current state variable. Generate its previous state variable and in accordance with The process is iterated sequentially until a noise-free signal estimate is obtained. In order to preserve the direction-of-arrival information contained in the original received signal during the back-diffusion process, this invention introduces an array of received signals during the back-diffusion process. As a conditional signal, it guides each step of the denoising process; therefore, the state transition probability of the reverse diffusion process can be expressed as: Furthermore, it is expressed as a complex Gaussian distribution using Bayes' rule: , in, and They represent The mean and covariance matrices, their specific values ​​and , and Related. Due to The target state for the reverse diffusion process cannot be directly obtained here. and Therefore, the exact expression for the state transition probability of the reverse diffusion process is approximated by the following complex Gaussian distribution: , in, It is the mean An estimated value, calculated by the following formula: , in, Indicates a For input, with Noise item in A neural network function is used to estimate the target. The array receives signals. The guiding effect of iterative denoising depends entirely on the training effect of this neural network; therefore, the neural network... It is called a denoising conditional diffusion network, and its training set consists of... structure.

[0029] like Figure 2 As shown, based on the above approximation of the state transition probability of the reverse diffusion process, in the first... In the next iteration, firstly , as well as Input the denoising conditional diffusion network to obtain the desired result. estimation results Then, the mean term is calculated based on the estimation result. And based on this, determine the approximate reverse transition probability. And sample from this approximate distribution to generate the previous state variable. Repeat the above process until... Iterate to Finally, the signal received by the array is obtained. Corresponding noiseless signal estimate .

[0030] For the denoising conditional diffusion network, a U-Net structure with parallel paths is adopted, including a main path and an auxiliary path; the main path is used to process the current state variable. The auxiliary path is used to process the array received signal. The network structure of the main path and auxiliary paths remains consistent; in order to index the iteration steps Introducing the network, we first perform sinusoidal position encoding on it, and then compare the encoding result with... The input to the auxiliary path is concatenated according to the channel dimension; the auxiliary path is fused with the main path element-wise after each sampling layer; the U-Net structure includes an input convolutional layer, an output convolutional layer, two convolutional downsampling layers, and two transposed convolutional upsampling layers, and the network output is the output of the noise term. The estimation results.

[0031] The denoising conditional diffusion network constructs a training set using signal sample pairs from a scenario with a fixed number of sources: each training sample consists of the received signal... and its corresponding noiseless signal Composition. For any training sample, randomly select... Then from the complex Gaussian distribution Random sampling And using the diffusion state variables defined in step (2) to generate When constructing the training set, a fixed number of information sources are selected. Training samples are generated, and the noise-free signal after power normalization is used. The probability distribution is independent of the number of sources, and the trained denoising diffusion model can be used for direction-of-arrival estimation in scenarios with a variable number of sources; the goal of network training is to minimize the true noise term. The mean squared error between the network output and the loss function is expressed as: , in, Represents the mathematical expectation. This represents the Euclidean norm.

[0032] Step 4: Use the noiseless signal estimate obtained by iterative denoising using the generative diffusion model to estimate the direction of arrival.

[0033] Based on noiseless signal estimation Calculate the sample covariance matrix: , in, This represents the conjugate transpose operation. Next, the following spatial spectral function is calculated: , , , in, Operations are used to collect the maximum value of the corresponding matrix. The eigenvectors corresponding to all eigenvalues ​​other than the given eigenvalue. Finding the spatial spectral function. All local maxima are determined according to their response values. Sort the responses by size and select the one with the largest response value. The angle values ​​corresponding to each maximum point This is the direction of arrival estimation result.

[0034] This invention introduces a denoising diffusion probability model into the field of direction-of-arrival (DOA) estimation. By reconstructing the estimation problem into a conditional signal denoising task, it provides a novel technical path and framework for robust ODA. Furthermore, this invention leverages the property that the probability distribution of power-normalized noiseless signals is independent of the number of sources. This allows the proposed method to generalize to scenarios with a variable number of sources by training only on datasets with a fixed number of sources, effectively avoiding the performance degradation or failure of traditional discriminative networks due to scenario mismatch.

[0035] The effects of the method proposed in this invention will be further described below with reference to simulation examples.

[0036] use The uniform rectangular array, with azimuth and elevation angles randomly selected in each Monte Carlo experiment, all satisfy a uniform distribution. Unless otherwise specified, the number of sources is set to . Set the number of quick shots to Signal-to-noise ratio set to The method proposed in this invention uses only a single training set for training, with 200,000 training samples, and all samples use a fixed number of information sources. The model is generated. The model training epochs are 200, the batch size is 64, the learning rate is 0.0001, and the number of state variables in the backdivergence process is fixed. 1000 Monte Carlo experiments were conducted, with root mean square error (RMSE) used as the performance metric. The results were compared with typical subspace-based methods like ESPRIT and typical end-to-end discriminative neural network methods like CNN. Furthermore, the Cramer-Rao performance lower bound (CRB) was plotted in the simulation graphs for reference.

[0037] Simulation Example 1: In , Under the given conditions, the performance comparison diagram of the root mean square error of the proposed method with ESPRIT and CNN methods as a function of signal-to-noise ratio is shown in Figure 1. Figure 3 As shown. The results show that the method proposed in this invention outperforms the end-to-end CNN method across the entire test signal-to-noise ratio range; when the signal-to-noise ratio is lower than... In this case, the method proposed in this invention outperforms the ESPRIT method. This demonstrates that the method proposed in this invention utilizes the learning ability of the diffusion model on the prior distribution of noiseless signals and is more robust in low signal-to-noise ratio scenarios.

[0038] Simulation Example 2: In , Under the given conditions, the performance comparison diagram of the root mean square error of the proposed method with ESPRIT and CNN methods as a function of the number of snapshots is shown in the figure below. Figure 4 As shown. The results show that the root mean square error of the method proposed in this invention gradually decreases with the increase of the number of snapshots; when In this case, the proposed method outperforms the ESPRIT method. This demonstrates that the proposed method maintains robust estimation performance even in scenarios with few snapshots.

[0039] Simulation Example 3: In , Under the given conditions, the performance comparison diagram of the root mean square error of the proposed method with the number of sources is shown in Figure 1. Figure 5 As shown, the results indicate that the performance of the end-to-end CNN method degrades with the increase of the number of information sources and fails when the number of information sources exceeds its predefined output capacity (i.e., K>2). In contrast, the method proposed in this invention, although trained using only a dataset with two information sources (K=2), maintains relatively stable and superior root mean square error performance across the entire range of test information source numbers, verifying its generalization ability under different information source number scenarios.

[0040] In summary, the robust direction-of-arrival estimation method based on a generative denoising diffusion model proposed in this invention transforms direction-of-arrival estimation into a conditional signal denoising task. It can generalize to different scenarios with different numbers of signal sources under a fixed number of signal sources training condition, and exhibits good estimation performance and robustness in scenarios with low signal-to-noise ratio and few snapshots.

[0041] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A robust direction-of-arrival estimation method based on a generative denoising diffusion model, characterized in that, Includes the following steps: (1) Array received signal modeling: Assume there is One from A far-field narrowband incoherent signal source in the angular direction is used at the receiver to include... Antenna array receiving of individual elements Each signal sampling snapshot, the array received signal matrix is ​​modeled as follows: ， in, Represents the array guidance matrix, express One source A signal matrix captured by a sampling snapshot Indicates the first The signal waveform vector of each source. This represents additive complex white Gaussian noise. Indicates noise power. This indicates the transpose operation. and These represent the zero vector and the unit vector, respectively. (2) Forward distribution modeling of diffusion process and state transition: the array receives the signal The expected signal element in Power normalization is performed to obtain a noise-free signal. : ， in, Indicates the first The power of each signal source in a multi-source direction-of-arrival estimation scenario. The probability distribution of can be approximated as a zero-mean multivariate complex Gaussian distribution, i.e. ,and Covariance matrix of the distribution With source number Irrelevant; will As the initial state, construct the... A noisy complex Gaussian state variable The diffusion process consists of state variables that satisfy: ， in, It is a set of random Decreasing preset hyperparameters, Represents complex Gaussian noise, when As it gradually increases, the state variable The proportion of noise in the middle gradually increases; when At that time, the final state Treating it as pure Gaussian noise; according to the above definition of state variables, we obtain... Transfer to The conditional probability distribution is: ， in, , ,and This is called the forward distribution of state transitions; (3) Iterative denoising based on a generative diffusion model guided by received signal conditions: The purpose of iterative denoising is to remove pure Gaussian noise. Starting from this point, through multiple iterations of the reverse diffusion process in the generative diffusion model, the signal received by the array is gradually recovered. Corresponding noiseless signal estimate In this process, each iteration of the reverse diffusion is performed using the current state variable. Generate its previous state variable and in accordance with The process is iterated sequentially until a noise-free signal estimate is obtained. ; An array receiving signal was introduced during the reverse diffusion process. As a conditional signal, it guides each step of the denoising process; therefore, the state transition probability of the reverse diffusion process can be expressed as: Furthermore, it is expressed as a complex Gaussian distribution using Bayes' rule: ， in, and They represent The mean and covariance matrices, with specific values ​​related to , and The following complex Gaussian distribution is used to approximate the state transition probability of the reverse diffusion process: ， in, It is the mean An estimated value, calculated by the following formula: ， in, Indicates a For input, with Noise item in A neural network function is used to estimate the target; the array receives signals. The guiding effect of iterative denoising depends entirely on the training effect of this neural network; therefore, the neural network... It is called a denoising conditional diffusion network, and its training set consists of structure; Based on the above approximation of the state transition probability of the reverse diffusion process, in the first... In the next iteration, firstly , as well as Input the denoising conditional diffusion network to obtain the desired result. estimation results Then, the mean term is calculated based on the estimation result. And based on this, determine the approximate reverse transition probability. And sample from this approximate distribution to generate the previous state variable. Repeat the above process until... Iterate to Finally, the signal received by the array is obtained. Corresponding noiseless signal estimate ; (4) The direction of arrival is estimated by using the noiseless signal estimate obtained by iterative denoising through the generative diffusion model.

2. The robust direction-of-arrival estimation method based on a generative denoising diffusion model according to claim 1, characterized in that, The antenna array in step (1) is deployed using a uniform rectangular array: the array along... Axis direction setting Each array element, along Axis direction setting There are array elements, and the total number of array elements is [number]. The element spacing is half the wavelength of the incident narrowband signal, corresponding to the first... Array guidance vectors of one source Represented as: ， in, ; ; ; .

3. The robust direction-of-arrival estimation method based on a generative denoising diffusion model according to claim 1, characterized in that, The denoising conditional diffusion network in step (3) adopts a U-Net structure with parallel paths, including a main path and an auxiliary path; wherein the main path is used to process the current state variable. The auxiliary path is used to process the array received signal. The network structure of the main path and auxiliary paths remains consistent; in order to index the iteration steps Introducing the network, we first perform sinusoidal position encoding on it, and then compare the encoding result with... The input to the auxiliary path is concatenated according to the channel dimension; the auxiliary path is fused with the main path element-wise after each sampling layer; the U-Net structure includes an input convolutional layer, an output convolutional layer, two convolutional downsampling layers, and two transposed convolutional upsampling layers, and the network output is the output of the noise term. The estimation results.

4. The robust direction-of-arrival estimation method based on a generative denoising diffusion model according to claim 1, characterized in that, The denoising conditional diffusion network in step (3) constructs a training set using signal sample pairs under a fixed number of sources: each training sample consists of the received signal and its corresponding noiseless signal Composition: For any training sample, randomly select Then from the complex Gaussian distribution Random sampling And using the diffusion state variables defined in step (2) to generate When constructing the training set, a fixed number of information sources are selected. Training samples are generated. Since the probability distribution of the noiseless signal after power normalization is independent of the number of sources, the trained denoising and diffusion model can be used for direction-of-arrival estimation in scenarios with a variable number of sources. The goal of network training is to minimize the true noise term. The mean squared error between the network output and the loss function is expressed as: ， in, Represents the mathematical expectation. This represents the Euclidean norm.

5. The robust direction-of-arrival estimation method based on a generative denoising diffusion model according to claim 1, characterized in that, In step (4), the direction of arrival estimation is achieved through the following method: First, based on the noiseless signal estimation value Calculate the sample covariance matrix: ,in, This represents the conjugate transpose operation; Then, calculate the following spatial spectral function: ， ， ， in, Operations are used to collect the maximum value of the corresponding matrix. Eigenvectors corresponding to all eigenvalues ​​other than the given eigenvalue; finding the spatial spectral function. All local maxima are determined according to their response values. Sort the responses by size and select the one with the largest response value. The angle values ​​corresponding to each maximum point This is the result of the direction of arrival estimation.

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