High-precision two-dimensional DOA estimation method based on double-branch CNN

Abstract

The invention relates to the technical field of array signal processing, discloses a high-precision two-dimensional DOA estimation method based on a double-branch CNN, and aims to solve the problems of poor robustness, angle pairing confusion and the like in the prior art. The method comprises the following steps: receiving signals by using a uniform rectangular array and constructing an array covariance matrix as network input; a double-branch CNN containing a shared feature encoder and a double-angle prediction head is constructed, the shared feature encoder extracts common features of a pitch angle and an azimuth angle, and the double-angle prediction head decouples and estimates the two angles; a mixed loss function weighted by cross entropy loss and comparison loss is designed, and classification precision and multi-target angle pairing accuracy are guaranteed; and an AdamW optimizer and an OneCycle learning rate are adopted to schedule and train the network, and a signal source angle estimation result is finally output. The method still has high robustness and precision under the scenes of low signal-to-noise ratio, few snapshots, non-grid angles and the like, is high in operation efficiency, and is suitable for the fields of radar, communication and the like needing real-time two-dimensional DOA estimation.

Description

Technical Field

[0001] This invention belongs to the field of array signal processing technology, specifically relating to a high-precision two-dimensional DOA estimation method based on a dual-branch CNN. Background Technology

[0002] Direction of Arrival (DOA) estimation, a core technology in array signal processing, aims to retrieve the angular position of a source in space from the signal information acquired by the array. It plays an irreplaceable role in military and civilian fields such as radar target detection and tracking, sonar underwater positioning, intelligent beamforming for mobile communications, and UAV environmental perception. Compared to one-dimensional DOA estimation, which only acquires angle information in a single dimension, two-dimensional DOA estimation can simultaneously output the azimuth and elevation angles of the source, providing a more accurate description of the target's specific position in three-dimensional space. This effectively solves the positioning ambiguity problem in scenarios with overlapping multiple targets, thus becoming the mainstream research direction for DOA estimation in complex scenarios.

[0003] Traditional two-dimensional DOA estimation methods are model-driven, with two-dimensional multiple signal classification (2-DMUSIC) being a typical example. This method, based on the orthogonality principle between the signal and noise subspaces, can achieve approximately unbiased angle estimation, and under ideal conditions, its performance approaches the Cramer-Rao bound (CRB). However, its core drawback lies in the need to obtain angle values ​​through two-dimensional grid peak search, resulting in computational complexity that increases quadratically with increasing angle resolution, reaching a computational complexity of O(N). 3 +G 2 (where N is the number of array elements and G is the number of spectral peak search points). In radar and communication scenarios with high real-time requirements, it is difficult to meet the application needs, which greatly limits its use in high-speed dynamic target localization.

[0004] The 2-DESPRIT algorithm utilizes the rotation invariance of the signal subspace to directly solve for angles using a closed-form solution, eliminating the need for spectral peak search and reducing computational complexity to O(N). 3 This algorithm improves real-time performance to some extent. However, it is highly dependent on the structure of the receiving array and requires strict adherence to the assumptions of array symmetry and rotation invariance. When non-ideal conditions such as array element amplitude and phase errors or array element position perturbations exist in practical applications, the subspace orthogonality will be severely damaged, leading to a significant decrease in angle estimation accuracy. At the same time, its ability to process coherent sources is weak, requiring preprocessing methods such as spatial smoothing to sacrifice the array aperture to decoherence, further reducing estimation performance and applicability.

[0005] With the development of compressed sensing (CS) theory, two-dimensional DOA estimation methods based on sparse reconstruction have emerged as a new technical approach. These methods leverage the sparsity of the information source in space, transforming DOA estimation into a sparse vector reconstruction problem by constructing an overcomplete dictionary, thus achieving super-resolution estimation by overcoming the Rayleigh limit. However, the performance of this method is highly dependent on the accurate construction of the overcomplete dictionary: when array errors exist, the sparsity of the information source is disrupted, or the source angle exceeds the dictionary's preset grid, the matching degree between the dictionary and the actual signal decreases significantly, leading to a surge in reconstruction errors. Furthermore, the sparse reconstruction process requires solving a complex convex optimization problem, resulting in low computational efficiency and limiting its practicality in multi-target, dynamic scenarios.

[0006] In recent years, deep learning technology has provided a new data-driven approach for DOA estimation. Some studies have proposed DOA estimation methods based on deep neural networks (DNNs) and complex-valued convolutional neural networks (CV-CNNs), which demonstrate certain robustness under non-ideal conditions by learning the mapping relationship between "received signal and angle". However, existing deep learning methods still have significant shortcomings in the field of two-dimensional DOA estimation: on the one hand, most methods use a single predictor to estimate both azimuth and elevation angles simultaneously, which can easily lead to confusion between the two angle features and result in multi-target angle pairing errors; on the other hand, existing methods are mostly designed based on classification ideas, which can only estimate angles within a preset grid, and have limited accuracy in estimating non-grid angles. Furthermore, the loss function only focuses on the classification error of a single angle and does not show the correlation between constrained angle pairs, making it difficult to meet the needs of high-precision, continuous angle estimation in real-world scenarios. Summary of the Invention

[0007] The present invention aims to address the technical problems of insufficient robustness and high computational complexity of traditional model-driven two-dimensional DOA estimation methods (such as MUSIC and ESPRIT) under non-ideal conditions, as well as the technical problems of angle pairing confusion and limited accuracy of non-mesh angle estimation in existing deep learning methods.

[0008] To achieve the above objectives, the present invention provides the following technical solution:

[0009] A high-precision two-dimensional DOA estimation method based on a two-branch CNN includes:

[0010] Step 1: Use a uniform rectangular array (URA) to receive signals from K far-field narrowband signal sources in space, and construct the array covariance matrix based on the signals received by the uniform rectangular array. ,in This represents the sampling matrix of the array received signal. Represents the conjugate transpose of the sampling matrix. This represents the number of times the received signal from the array is sampled, i.e., the number of snapshots. The array covariance matrix is ​​used as the input to the two-branch CNN network.

[0011] Step 2: Construct a two-branch CNN network, which includes a shared feature encoder and a dual-angle prediction head. The shared feature encoder is used to extract the pitch angle from the array covariance matrix. and azimuth The common feature of dual-angle prediction heads is that they are used to achieve pitch angle. With azimuth Decoupling estimation;

[0012] Step 3: Design the hybrid loss function Hybrid loss function Cross-entropy loss Compared with loss Linear weighting is used to solve the multi-target angle pairing problem and ensure the accuracy of angle classification.

[0013] Step 4: Train the dual-branch CNN network using the AdamW optimizer and the OneCycle learning rate scheduling strategy;

[0014] Step 5: Apply the trained dual-branch CNN network to 2D DOA estimation, outputting the elevation angle of the source. With azimuth Estimation results.

[0015] By employing a dual-branch CNN network, a hybrid loss function, and optimization strategies, we achieve high-precision 2D DOA estimation, accurate pairing of multiple target angles, and efficient computation, making it suitable for complex application scenarios.

[0016] Preferably, the element spacing of the uniform rectangular array in step 1 satisfies... To avoid the grating lobe effect, where For the signal wavelength, the first The two-dimensional direction of arrival of each signal source is , ,in, Representing the The elevation angle of a signal source, Indicates the first The azimuth angle of each signal source is determined, the element spacing constraint is clearly defined to avoid grating lobe interference, and the angle parameters are clearly defined, laying the foundation for subsequent accurate signal reception and angle estimation.

[0017] Preferably, the array covariance matrix is ​​constructed in step 1. The specific process is as follows: the uniform rectangular array URA in axis, The number of elements of the axial array are respectively , ; axis, The direction vector of the axis source is:

[0018] ;

[0019] ;

[0020] exist On the axis The direction matrix corresponding to each array element is ;

[0021] exist On the axis The direction matrix corresponding to each array element is ;

[0022] The signal received by the entire uniform rectangular array is ,in For source vectors, , Represents the Khatri-Rao product.

[0023] through The received signal after the second sampling is represented as follows: ;

[0024] In the formula, The signal passes through Source vector after sampling ; Represents the matrix of the first A diagonal matrix formed by rows, To obtain the additive white Gaussian noise matrix in the received signal, the mathematical relationship between the array signal and the covariance matrix is ​​accurately derived, thus fully preserving the source angle information and providing high-quality feature data for network input.

[0025] Preferably, the shared feature encoder in step 2 includes a convolutional layer, two residual modules, and a channel attention module; the residual modules solve the gradient vanishing problem through cross-layer connections, and the gradient satisfies the gradient during backpropagation of the residual modules. ,in This represents the gradient of the loss function; the number 1 indicates the short-circuiting mechanism of the residual block.

[0026] The residual module contains two convolutional layers, two batch normalization layers, and a ReLU activation function. The expression for the ReLU activation function is: ;

[0027] The channel attention module obtains channel statistics through global average pooling, and then generates channel weights through two fully connected layers. The calculation process of the channel weights satisfies... ,in This is a global average pooling feature. and For learnable parameters, It is a ReLU activation function. Using the Sigmoid function, combined with convolution, residual modules, and channel attention mechanisms, it effectively extracts common features, solves the gradient vanishing problem, strengthens the weights of key features, and improves feature extraction capabilities and network training stability.

[0028] Preferably, in step 2, the dual-angle prediction head consists of two sub-networks with identical structures, completely independent networks, and no parameter sharing, which are used for estimating the pitch angle and azimuth angle respectively.

[0029] Each sub-network follows a three-stage processing flow of "feature refinement - spatial aggregation - angular label classification";

[0030] In the feature refinement stage, the common features output by the shared feature encoder are further purified and optimized through a stacked structure of "convolution-batch normalization-ReLU". After the first convolution, a channel attention module is introduced to enhance the perception of angle-related key features.

[0031] The spatial aggregation stage transforms the feature map into a fixed-length feature vector through a global average pooling layer. The computation process of global average pooling satisfies... ,in, The spatial dimension of the feature map;

[0032] In the angle label classification stage, pitch angles are estimated separately using independent fully connected layers. and azimuth ,satisfy:

[0033] ;

[0034] in, The weight vector to be learned. As a bias term, angle decoupling estimation is achieved through independent sub-networks and a three-stage process, refining features and accurately mapping angles, avoiding confusion of angle features, and improving the estimation accuracy of pitch and azimuth angles.

[0035] As a preferred option, the cross-entropy loss in step 3 The expression is ;

[0036] in, Indicates the first The probability of predicting the pitch angle of a target. Indicates the first The azimuth prediction probability of a target;

[0037] The pitch angle probability distribution output by the model;

[0038] This represents the azimuth probability distribution. This indicates the number of angle categories, with the actual label being... , By measuring the difference between the predicted probability distribution and the true label, the classification accuracy of the pitch and azimuth angles of a single target is ensured, providing a basic accuracy guarantee for angle estimation.

[0039] As a preferred option, the comparison loss function in step 3 The expression is ;

[0040] in, For positive sample loss, The negative sample loss is used to strengthen the correlation of the same target angle and weaken the interference of different targets by constraining the similarity of positive and negative sample angle pairs, thus solving the problem of multi-target angle pairing.

[0041] Preferably, the hybrid loss function in step 3 The expression is ;in The weighting coefficients are used to balance the cross-entropy loss and contrast loss, taking into account both the accuracy of angle classification and the accuracy of multi-target pairing, thereby optimizing the overall estimation performance of the model.

[0042] Preferably, the OneCycle learning rate scheduling strategy in step 4 includes a linear rising phase and a cosine falling phase. During the linear rising phase, the learning rate starts from the initial value... Linear growth to maximum value The duration accounts for 30% of the total training steps. During the cosine descent phase, the learning rate decays from its maximum value to its initial value according to the cosine function. By scheduling the learning rate to first increase and then decrease, the convergence speed in the early stage of the model and the stability in the later stage of training are taken into account, which helps the network to converge quickly and stably and improves its generalization ability.

[0043] As a preferred method, the root mean square error is used to measure the accuracy of the estimation. In the formula Indicates the number of Monte Carlo experiments performed. Indicates the number of information sources. and They represent the first time. During the Monte Carlo experiment, the first The angle estimates and true values ​​of each source are compared using multiple Monte Carlo experiments to calculate the error, thus objectively and accurately quantifying the angle estimation accuracy and providing a reliable and unified standard for evaluating the method's performance.

[0044] Compared with the prior art, the technical effects and advantages of the present invention are:

[0045] (1) Compared with traditional model-driven methods (such as MUSIC and ESPRIT) which rely heavily on array symmetry, high signal-to-noise ratio and high number of snapshots, this invention is based on the data-driven approach of dual-branch CNN. It does not require complex signal model assumptions. It extracts stable common features through a shared feature encoder and combines dual prediction heads to decouple angle estimation. Even in non-ideal scenarios such as low signal-to-noise ratio, low number of snapshots, and non-grid angles, it can still maintain high-precision estimation and effectively avoid the performance degradation caused by the mismatch between model assumptions and actual scenarios.

[0046] (2) To address the problem of confusion between pitch and azimuth pairings of multiple targets that is prone to occur in existing deep learning methods, this invention designs a hybrid loss function that integrates cross-entropy loss and contrastive loss. The contrastive loss explicitly constrains the correlation of angle pairs of the same target and weakens the interference of angle pairs of different targets. Combined with the decoupling design of dual independent prediction heads, it ensures the accuracy of multi-target angle pairing from both the perspectives of loss optimization and network structure, thus solving the defect of a single loss function that only focuses on the accuracy of angle classification and ignores the correlation.

[0047] (3) Traditional MUSIC algorithms require two-dimensional spectral peak search and ESPRIT algorithms require complex feature value decomposition, both of which have high computational complexity. However, this invention uses the efficient forward propagation computation of CNN to replace the time-consuming processes of subspace extraction and spectral peak search in traditional methods. At the same time, it ensures the rapid and stable convergence of the model through OneCycle learning rate scheduling and AdamW optimizer, which greatly reduces the computation time and is more suitable for scenarios with high real-time requirements such as radar and communication.

[0048] (4) Unlike existing classification-based deep learning methods that can only estimate angles within a preset grid, this invention adopts a regression-based estimation method to directly output continuous pitch and azimuth results, breaking through the grid limitation and adapting to the needs of arbitrary distribution of signal source angles in actual scenarios. At the same time, the selection of uniform rectangular array and the introduction of channel attention and residual modules further enhance the network's ability to extract spatial signal features and improve the applicability of the method in complex environments. Attached Figure Description

[0049] Figure 1 This is a diagram of a uniform rectangular array according to the present invention;

[0050] Figure 2 This is a network structure diagram of the present invention;

[0051] Figure 3 This is a structural diagram of the residual block of the present invention;

[0052] Figure 4(a) is a visualization of the two-dimensional DOA estimation results of the present invention in a general scene, comparing the real angle, 2-DESPRIT, 2-DMUSIC and the two-branch CNN method of the present invention;

[0053] Figure 4(b) is a visualization of the two-dimensional DOA estimation results of the present invention compared with the real angle, 2-DESPRIT, 2-DMUSIC and the two-branch CNN method of the present invention in a scene with small target angle interval;

[0054] Figure 4(c) is a visualization of the two-dimensional DOA estimation results of the present invention in low signal-to-noise ratio scenarios, comparing the real angle, 2-DESPRIT, 2-DMUSIC and the two-branch CNN method of the present invention.

[0055] Figure 4(d) is a visualization of the two-dimensional DOA estimation results of the present invention in a non-network angle scene, comparing the real angle, 2-DESPRIT, 2-DMUSIC and the two-branch CNN method of the present invention;

[0056] Figure 5 This is a comparison chart showing the RMSE of the pitch angle estimation accuracy of 2-DMUSIC, 2-DESPRIT, the dual-branch CNN of this invention, and ordinary CNN under different signal-to-noise ratios, with signal-to-noise ratio as the horizontal axis and pitch angle estimation RMSE as the vertical axis.

[0057] Figure 6 This is a comparison chart showing the RMSE of the azimuth estimation accuracy of 2-DMUSIC, 2-DESPRIT, the dual-branch CNN of this invention, and ordinary CNN at different signal-to-noise ratios, with signal-to-noise ratio as the horizontal axis and azimuth estimation RMSE as the vertical axis.

[0058] Figure 7 This is a comparison chart showing the RMSE of the two-dimensional DOA comprehensive estimation accuracy of 2-DMUSIC, 2-DESPRIT, the dual-branch CNN of this invention and ordinary CNN under different signal-to-noise ratios, with signal-to-noise ratio as the horizontal axis and the RMSE of the two-dimensional DOA total estimation as the vertical axis.

[0059] Figure 8 This is a comparison chart of the RMSE of the pitch angle estimation accuracy of 2-DMUSIC, 2-DESPRIT, the dual-branch CNN of this invention and ordinary CNN at different numbers of snapshots, with the number of snapshots as the horizontal axis and the pitch angle estimation RMSE as the vertical axis.

[0060] Figure 9 This is a comparison chart of the RMSE of the present invention's dual-branch CNN and ordinary CNN at different numbers of snapshots, with the number of snapshots as the horizontal axis and the RMSE of azimuth estimation as the vertical axis.

[0061] Figure 10This is a comparison chart showing the RMSE of the overall DOA estimation accuracy of 2-DMUSIC, 2-DESPRIT, the dual-branch CNN of this invention, and ordinary CNN under different snapshot counts, with the number of snapshots as the horizontal axis and the total RMSE of the two-dimensional DOA estimation as the vertical axis. Detailed Implementation

[0062] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0063] The following combination Figures 1 to 3 Figures 4(a) to 4(d) Figures 5 to 10 This application will be described in further detail;

[0064] To more clearly illustrate the technical details and practical application effects of the high-precision two-dimensional DOA estimation method based on a dual-branch CNN proposed in this invention, a detailed description is provided below in conjunction with specific hardware environments, parameter settings, and simulation scenarios. In this embodiment, the signal reception of the uniform rectangular array (URA), the construction of the array covariance matrix, the construction and training of the dual-branch CNN network, and the two-dimensional DOA estimation test are all implemented based on the Matlab2023a and PyTorch2.0 deep learning framework. The hardware platform configuration is CPU i7-11800H, GPU NVIDIA RTX3070 (8GB VRAM), and 64GB of memory, ensuring efficient operation of data generation, model training, and estimation testing. The signal source to be estimated is set as a far-field narrowband incoherent signal. The basic parameters of the array and the signal source, the network structure parameters, and the training optimization parameters all strictly follow the core limitations of the technical solution of this invention to verify the estimation accuracy, robustness, and computational efficiency of the method in different scenarios.

[0065] This invention proposes a dual-branch convolutional neural network. This network extracts the same features of pitch and azimuth angles through a shared feature encoder, and obtains the pitch and azimuth angles of different targets through two independent angle prediction heads with the same structure. In two-dimensional DOA estimation, the pairing effect of pitch and azimuth angles of different targets affects the network's fitting effect. To improve the fitting effect and accelerate model convergence, this invention proposes a hybrid loss function that combines cross-entropy loss and contrastive loss, based on the cross-entropy loss commonly used in label classification problems. The introduced contrastive loss function improves the correlation between pitch and azimuth angles of the same target by setting a threshold. The invention is described in detail below:

[0066] The performance of two-dimensional DOA estimation is closely related to the structure of the receiving array. Uniform rectangular arrays (URAs) are preferred array structures for two-dimensional angle estimation due to their advantages of balanced spatial resolution, strong decoupling capability between azimuth and elevation angles, and regular element layout. Therefore, this invention uses a URA as the receiving array. This array has a total of There are 10 array elements, which are evenly distributed on a plane, with a spacing of 1 / 2 Ω between adjacent elements. To avoid the grating lobe effect, ( (Where the wavelength is given). Suppose there are K far-field narrowband signal sources in space, then the th... The two-dimensional direction of arrival of each signal source is , .in, Representing the The elevation angle of a signal source, Indicates the first The azimuth angle of each signal source. Specific details are as follows: Figure 1 As shown.

[0067] At this time, The direction vector of the on-axis source can be represented as

[0068]

[0069] Therefore, in On the axis The direction matrix corresponding to each array element is .

[0070] Similarly, in The direction vector of the on-axis source can be represented as

[0071]

[0072] At this time, On the axis The direction matrix corresponding to each array element is .

[0073] Figure 1 The signal received by subarray 1 in the rectangular array shown can be represented as

[0074]

[0075] In the formula, Represents the direction matrix in subarray 1. For source vectors, This represents the additive white Gaussian noise in subarray 1.

[0076] The first in the array The signals received by each subarray can also be obtained through the direction matrix corresponding to subarray 1. It is expressed as follows

[0077]

[0078] in, , Representing the The additive white Gaussian noise of each subarray. Therefore, the signal received by the entire uniform rectangular array can be obtained as follows:

[0079]

[0080] The signal corresponding to equation (5) can also be expressed as

[0081]

[0082] In the formula, That is On the axis The direction matrix corresponding to each array element , This represents the Khatri-Rao product.

[0083] Assuming the signal is sampled L times, Direction vector on the axis and Direction vector on the axis They are all fixed and unchanging, defined. So after The received signal after the second sampling can be expressed as:

[0084]

[0085] In the formula, The signal passes through Source vector after sampling . Represents the matrix of the first A diagonal matrix formed by rows, This is the additive white Gaussian noise matrix in the received signal.

[0086] In classic DOA estimation algorithms, the array covariance matrix is ​​mainly used for estimation. From equation (7), the covariance matrix can be expressed as follows:

[0087]

[0088] In the deep learning network proposed in this invention, the array covariance matrix will also be used as the network input.

[0089] Convolutional neural networks (CNNs), as multi-layered nonlinear neural networks, have achieved great success in computer vision due to their powerful feature extraction capabilities (see reference [Zeiler MD, Fergus R. Visualizing and understanding convolutional networks (J). Lecture Notes in Computer Science, 2014, 8689: 818-833.]). In the field of DOA estimation, classification-based CNNs are generally used. However, classification-based DOA estimation networks are not ideal when estimating angles outside a preset grid set, while in practical applications, the angle of the signal source can be arbitrary. To address this issue, this invention proposes a regression-based DOA estimation algorithm. This method directly outputs the predicted DOA, rather than the confidence score of the class. This overcomes the limitations imposed by the grid set, thus obtaining more accurate and continuous DOA estimates. The network proposed in this invention employs an encoder-dual prediction head design, such as... Figure 2 As shown, the network takes the spatial covariance matrix as input, extracts high-level feature representations through a shared feature encoder, and then estimates the pitch and azimuth angles of two targets using two structurally identical but parameter-independent prediction heads. This structure ensures both the sufficiency of feature extraction and the decoupling of the two angles.

[0090] Figure 2 The first module shown is the shared feature encoder, which is mainly used to extract common features of pitch and azimuth angles from the array covariance matrix. This module includes a convolutional layer, two residual modules, and a channel attention module.

[0091] As the number of layers in a convolutional neural network increases, gradient vanishing and gradient exploding may occur, as described in [K. He and J. Sun, “Convolutional neural networks at constrained time cost,” in Proc. IEEE Conf. Comput. Vis. Pattern Recognit., 2015, pp. 5353–5360.], which significantly impacts the network's training performance. ResNet addresses the vanishing gradient problem through direct mapping. While ordinary networks are simply stacked layers, residual blocks contain cross-layer connections, offering advantages during backpropagation.

[0092]

[0093] In the formula, The number 1 represents the gradient of the loss function. The number 1 indicates the short-circuit mechanism of the residual block, which can propagate the gradient without loss. The other residual gradient is subject to weight constraints, so there is no gradient vanishing problem.

[0094] The structure of the residual block used in this invention is as follows: Figure 3 As shown, it includes two convolutional layers, two batch normalization layers, and corresponding activation functions. The activation function used is the Rectified Linear Unit (ReLU), which can be expressed as:

[0095]

[0096] The ReLU function is computationally efficient and less prone to gradient vanishing.

[0097] Additionally, this shared editor includes a channel attention module. The Channel Attention Mechanism (CAM) enhances model performance by learning different channels within a feature. The channel attention module obtains channel statistics through global average pooling and generates channel weights through two fully connected layers.

[0098]

[0099] in This is a global average pooling feature. and For learnable parameters, It is a ReLU activation function. This is the Sigmoid function.

[0100] Since two-dimensional DOA estimation requires simultaneous estimation of the azimuth and elevation angles of the source, using a single prediction head would require the network to learn both angles simultaneously, leading to feature representation confusion and performance degradation. To address this issue, this invention proposes a dual-decoupled prediction probe structure. This structure consists of two identical sub-networks that are completely independent and do not share parameters, focusing on elevation and azimuth angle estimation respectively. Both prediction heads follow a three-stage processing flow: feature refinement, spatial aggregation, and angle label classification.

[0101] Considering the sensitivity of DOA estimation to spatial information, we introduce a normalization layer after each convolutional layer to stabilize the training process. Simultaneously, an element-wise zeroing probability is introduced into each probe. The random dropout layer is a regularization technique that randomly sets a portion of neurons to zero during the training phase to prevent overfitting.

[0102] In the second stage, the spatial dimension is compressed through a Global Average Pooling layer, converting the feature map into a fixed-length feature vector.

[0103]

[0104] in, represents the spatial dimension of the feature map. Employing a global average pooling strategy can reduce the number of parameters while preserving the statistical properties of spatial information, thereby enhancing the model's robustness to input variations.

[0105] In the final angle label classification stage, the two prediction heads use independent fully connected layers to estimate the pitch angle separately. and azimuth

[0106]

[0107] in, The weight vector to be learned. This is the bias term. This design allows the network to learn the nonlinear mapping between angles while ensuring the independence of the two angle estimates. This structure can be represented as...

[0108]

[0109] in, and These represent the parameters of the two prediction heads, respectively. and These represent the loss terms of the two prediction heads, respectively. For regularization terms, This represents the trade-off parameter.

[0110] Dual predictors effectively avoid feature confusion issues that occur when a single predictor is used to process the pitch and azimuth angles of multiple targets. Their independent parameters allow the network to better adapt to different feature distributions.

[0111] The loss function is used to measure the difference between the model's predicted values ​​and the true values, and it is crucial to model performance. In the deep learning-based 2D DOA estimation task, the model needs to simultaneously optimize angle classification accuracy and the correlation between angle pairing for multiple targets. To address this problem, this invention proposes a hybrid loss function that integrates cross-entropy loss and contrastive loss. Cross-entropy loss is a commonly used loss function in label classification problems, which ensures the accuracy of angle classification. Contrastive loss reflects the correlation between pitch and azimuth angles in 2D DOA estimation, thereby solving the angle pairing problem in multi-target scenarios.

[0112] Cross-entropy loss is often used to measure the difference between the probability distribution of the model's output and the true label. Assuming the pitch angle probability distribution of the model's output is... The azimuth probability distribution is ,in This indicates the number of angle categories, with the actual label being... , The cross-entropy loss is defined as:

[0113]

[0114] in, Indicates the first The probability of predicting the pitch angle of a target. Indicates the first The loss function calculates the azimuth prediction probability for each target. It maximizes the prediction probability of the correct angle, ensuring optimal classification performance for a single angle.

[0115] The core objective of contrastive loss is to solve the angle pairing problem for multiple targets by explicitly constraining the similarity between angle pairs. Assume the feature vector output by the pitch angle branch network is... The feature vector output by the azimuth branch network is ,in This represents the feature dimension. Then the... The pitch angle characteristics of the first target and the second target The cosine similarity between the azimuth features of the targets is:

[0116]

[0117] in and They represent the first , The feature vectors of the pitch and azimuth angles of each target. The contrastive loss function is designed as follows:

[0118]

[0119] in, This is the positive sample loss, used to strengthen the correlation between pairs of angles representing the same target. The negative sample loss is used to weaken the correlation between different target angle pairs. These two losses, by setting corresponding similarity thresholds, aim to improve the correlation between the same target angle pairs.

[0120] The total loss function is obtained by linearly weighting the cross-entropy loss and the contrastive loss:

[0121]

[0122] in , where is the weighting coefficient, used to balance the contributions of the two losses. Experiments show that when At that time, the model achieves the best balance between angle classification and matching accuracy.

[0123] By introducing contrast loss, the similarity of angle pairs with the same target can be forced to be higher than the threshold, while the similarity of angle pairs with different targets can be lower than the threshold. This explicitly constrains the angle pairing relationship and avoids incorrect pairing caused by ignoring the angle correlation due to cross-entropy loss.

[0124] In deep neural networks, the optimization process is a key step to ensure model convergence. This invention designs corresponding optimization strategies for the characteristics of DOA estimation tasks, covering optimizer selection, learning rate scheduling and gradient management, to ensure that the model has good generalization ability while converging stably.

[0125] Regarding the selection of optimizer, this invention uses AdamW instead of the Adam optimizer. This optimizer decouples weight decay from gradient update, allowing weight decay to act as a regularization mechanism. This resolves the conflict between weight decay and adaptive learning rate in the Adam optimizer.

[0126] The learning rate scheduling strategy is also crucial for model convergence. This invention employs a OneCycle learning rate strategy. Under this strategy, the learning rate first increases and then decreases, ensuring both the initial convergence speed and the stability of later training. The OneCycle strategy consists of two phases: a linear increase phase and a cosine decrease phase. In the increase phase, the learning rate starts from the initial value... Linear growth to maximum value The rising phase lasts for 30% of the total training steps, and the learning rate decays from its maximum value to its initial value according to a cosine function during the decay phase.

[0127] In the simulation experiment proposed in this invention, the following is adopted: A uniform rectangular array with an element spacing of half a wavelength is used. The proposed two-dimensional DOA estimation network is implemented using the PyTorch framework. The computer used for training the neural network has an i7-11800 CPU, an NVIDIA RTX 3070 GPU, and 64GB of RAM. Unless otherwise stated, the simulation scene of this invention uses the default signal source. Quick shot number .

[0128] In the simulation experiment used in this invention, the range of the source azimuth angle to be estimated is: The pitch angle range is The present invention sets the resolution of discrete angles to... The azimuth label is The pitch angle is labeled as Each has 61 angle labels. Training data was generated through Matlab simulation and saved in HDF5 files. The input feature is the array covariance matrix. The training and validation sets are divided proportionally, and the input features are standardized by channel to accelerate model convergence.

[0129] The structure of the model is Figure 2As already described, this section mainly introduces the specific parameters of each layer. The input 2×16×16 array covariance matrix first passes through a convolutional layer with a 3×3 kernel, a stride of 1, and padding of 1, mapping the number of channels from 2 to 64. This convolutional layer is followed by batch normalization and a ReLU activation function to enhance the model's non-linear expressiveness and training stability. The backbone network consists of three stacked residual blocks (ResBlocks), with the number of channels increasing sequentially from 64 to 128, and then to 256. The stride of the first two residual blocks is set to 2, halving the feature map size from 16×16 to 8×8, and then halving it again to 4×4, gradually expanding the receptive field and reducing computation. The stride of the third residual block is 1, maintaining the feature map size at 4×4. Each residual block contains two 3×3 convolutional layers, and when the number or size of the input and output channels in the residual connections do not match, a 1×1 convolutional layer is used for adjustment. The residual connection mechanism effectively alleviates the gradient vanishing problem during deep network training. After each residual block, a ChannelAttention module is introduced. This module first compresses the feature map of each channel into a scalar using global average pooling. Then, it passes through a bottleneck structure containing two fully connected layers with a compression ratio of 8 (reducing dimensionality from 256 to 32 and then back to 256). This structure adaptively learns the importance weights of each channel and applies these weights to the original features, thereby enhancing the contribution of key feature channels and suppressing redundant information.

[0130] The 256×4×4 feature map output from the common feature extraction backbone network is fed into azimuth and elevation prediction branches with identical structures. Each branch first refines the features through a stack of three layers of "convolution-BN-ReLU". The first convolution reduces the 256 channels to 128 channels, the second reduces the 128 channels to 64 channels, and the third remains unchanged. All convolutional layers use 3×3 kernels with a stride of 1 and padding of 1 to maintain the feature map size. After the first convolution, a channel attention module with a compression ratio of 8 is introduced to further enhance the perception of specific angle information. After feature refinement, global average pooling (GAP) compresses the 64×4×4 feature map into a 64-dimensional feature vector. This vector is then fed into a fully connected layer (ReLU activation) with 256 neurons, and a dropout layer with a dropout rate of 0.4 is introduced to suppress overfitting. Finally, a fully connected layer with an output dimension of 61 is used to obtain the label of the angle category.

[0131] In the training hyperparameter settings, the batch size is set to 128, and the total number of training epochs is set to 200. The initial learning rate is set to... A cosine annealing scheduler is used for dynamic adjustment, with a minimum learning rate of This ensures the model's convergence speed and ability to escape local optima. The loss function adopted is the hybrid loss function proposed in this invention, with a weight of 0.8 for cross-entropy loss and a weight of 0.2 for contrastive loss.

[0132] To verify the estimation performance of the model, this invention analyzes the DOA estimation results under four different scenarios. Figure 4(a) shows the angle estimation results for a general scenario, with the angle set as the pitch angle. azimuth In this scenario, both traditional algorithms and the method proposed in this invention have good estimation results; in Figure 4(b), the target's pitch angle azimuth In this scenario, the interval between targets is small, and the MUSIC algorithm only obtains one spectral peak, thus the estimation result only shows one target. The ESPRIT algorithm's estimation result has some deviation, while the network proposed in this invention can still obtain the correct estimation result; in Figure 4(c), the signal-to-noise ratio... In this scenario, traditional methods perform poorly in estimation, with large errors, while the network estimation proposed in this invention deviates less from the true value; in Figure 4(d), the target's pitch angle azimuth Since the angle setting is not on the label grid of the network, in this scenario, the estimation results of the MUSIC algorithm and the network proposed in this invention are on the grid, so there is a grid error, but the error is small. Although the ESPRIT algorithm is not affected by the grid error, there is still a certain estimation error.

[0133] The computation time of the MUSIC algorithm, ESPRIT algorithm, and the network proposed in this invention are shown in Table 1. The MUSIC algorithm, which requires eigenvalue decomposition and spectral peak search, has a computational complexity of O(n log n). ,in Because the number of peaks searched is limited, the algorithm requires significant computation time, resulting in poor real-time performance. While the ESPRIT algorithm avoids the computational complexity of peak search, it still requires eigenvalue decomposition, leading to a computational complexity of O(log n). While the computational load is reduced compared to the MUSIC algorithm, the improvement in real-time performance is not significant. However, the method proposed in this invention significantly improves the computational speed of the proposed network by replacing the complex subspace extraction, spectral peak search, and optimization processes with efficient forward propagation computation.

[0134] Table 1. Calculation timelines for different methods

[0135] Method MUSIC ESPRIT Proposed methods Time(s) 1.6365 0.8459 0.0243

[0136] Regarding DOA estimation accuracy, this invention compares the proposed neural network with model-based DOA estimation methods (MUSIC, ESPRIT) and general convolutional neural networks. Considering that the MUSIC algorithm requires spectral peak search, and to avoid abnormally large errors caused by indistinguishable signals and to make the simulation results more representative, this invention defaults to the angular interval between the two targets. Meanwhile, to standardize error measurement, this invention uses root mean square error (RMSE) to measure the accuracy of angle estimation:

[0137]

[0138] In the formula Indicates the number of Monte Carlo experiments performed. Indicates the number of information sources. and They represent the first time. During the Monte Carlo experiment, the first The estimated and true values ​​of each information source.

[0139] The present invention has a signal-to-noise ratio range of [value missing]. Signal-to-noise ratio interval Different methods were compared in various scenarios. At each signal-to-noise ratio (SNR) level, 1000 Monte Carlo experiments were conducted, and the RMSE as a function of SNR was calculated as follows: Figures 5 to 7 As shown.

[0140] Figure 5 Using "Signal-to-noise ratio (SNR, unit: dB)" as the x-axis (range -10dB to 10dB, interval 5dB) and "Root mean square error of pitch angle estimation (RMSE, unit: °)" as the y-axis, the pitch angle estimation accuracy of four methods (2-DMUSIC, 2-DESPRIT, the dual-branch CNN method of this invention, and ordinary CNN method) under different signal-to-noise ratios is compared and shown. Figure 6 x-axis and Figure 5 Consistent (signal-to-noise ratio -10dB to 10dB), the vertical axis represents the "root mean square error of azimuth estimation (RMSE, unit: °)", which also compares the azimuth estimation accuracy of the four methods. Figure 7 The horizontal axis represents the signal-to-noise ratio (-10dB to 10dB), and the vertical axis represents the root mean square error (RMSE, unit: °) of the total two-dimensional DOA estimation error.

[0141] From the results chart ( Figures 5 to 7As can be seen from the data, under various signal-to-noise ratio conditions, the data-driven 2D DOA estimation method achieves higher estimation accuracy and smaller error compared to the model-driven estimation method. Compared to a typical CNN network, the network structure proposed in this invention significantly improves the estimation accuracy of the pitch angle because the branch networks estimate the azimuth and elevation angles separately, and the estimation accuracy of the azimuth angle is also somewhat improved. As the signal-to-noise ratio decreases, the model-driven DOA estimation method is more susceptible to noise, while the network-based DOA estimation method, although also affected by noise, has a smaller impact on accuracy.

[0142] To verify the impact of different methods on the accuracy of 2D DOA estimation under different snapshot numbers, this invention... In the case of, the number of quick shots respectively The Monte Carlo experiment was conducted in a scenario where the results were as follows: Figures 8 to 10 As shown.

[0143] Figure 8 Using "Number of Snapshots" as the x-axis (range 50-250, interval 50) and "Root Mean Square Error (RMSE, unit: °) of Pitch Angle Estimation" as the y-axis, the pitch angle estimation accuracy of 2-DMUSIC, 2-DESPRIT, the present invention's dual-branch CNN method, and ordinary CNN methods are compared and shown at different numbers of snapshots. When the number of snapshots decreases to 50 (in scenarios with few snapshots), the pitch angle RMSE of the MUSIC and ESPRIT methods increases significantly, while the present invention's method, due to extracting stable features through the covariance matrix and combining residual and attention mechanisms to enhance robustness, still maintains a low error, significantly outperforming traditional methods and ordinary CNNs.

[0144] Figure 9 x-axis and Figure 8 The graph shows the azimuth estimation accuracy of four methods, with the vertical axis representing the root mean square error (RMSE, unit: °) of the azimuth estimation (50~250 snapshots). This comparison reveals the dependence of each method on the number of snapshots in the azimuth dimension: traditional model-driven methods (MUSIC, ESPRIT) require a sufficient number of snapshots to construct a stable signal / noise subspace, resulting in significant fluctuations in azimuth RMSE as the number of snapshots decreases. In contrast, the dual-branch CNN of this invention, employing a "decoupled prediction head" to focus on azimuth feature learning and using a hybrid loss function to constrain angle pairing accuracy, achieves a lower azimuth RMSE than ordinary CNNs and traditional methods even with 50 snapshots, validating its advantage in azimuth estimation under conditions of fewer snapshots.

[0145] Figure 10The horizontal axis represents the number of snapshots (50~250), and the vertical axis represents the "root mean square error (RMSE, unit: °) of the total dimensionality error of 2D DOA". Here, "total dimensionality error" is the combined quantitative result of pitch angle error and azimuth angle error (matching the definition formula of RMSE). This figure is the core visualization result for measuring the overall two-dimensional DOA estimation performance of each method, and it can directly reflect the comprehensive advantages of the method of the present invention: regardless of the number of snapshots, its total RMSE is the lowest. Especially when the number of snapshots is 50, the difference in total error is significant, which fully verifies the robustness of the method of the present invention under the "non-ideal condition of few snapshots" and solves the core defect of traditional methods that rely on a large number of snapshots.

[0146] From the results chart ( Figures 8 to 10 As can be seen from the results, the network proposed in this invention achieves high DOA estimation accuracy across various snapshot counts, significantly outperforming model-based two-dimensional DOA estimation methods. Furthermore, compared to typical CNN networks, the network proposed in this invention also shows improved accuracy with fewer snapshots. In contrast, the angle estimation accuracy of the MUSIC and ESPRIT methods is significantly affected by the decrease in the number of snapshots, particularly when the number of snapshots is 50. The RMSE of the MUSIC algorithm is 17.63°, while the RMSE of the network proposed in this invention is 3.51°.

[0147] This invention proposes a two-dimensional DOA estimation method based on a dual-branch convolutional neural network. Using the covariance matrix of a uniform rectangular array as input, it extracts common features of pitch and azimuth angles through a shared feature encoder. Combined with two independent prediction heads, it achieves decoupled angle estimation, effectively avoiding feature confusion caused by a single prediction head. The designed hybrid loss function ensures angle classification accuracy through cross-entropy loss and explicitly constrains multi-target angle pairing relationships through contrastive loss, significantly improving the model's ability to learn angle correlations. Simulation experiments show that this method outperforms traditional MUSIC, ESPRIT algorithms, and ordinary CNN methods under different signal-to-noise ratios, snapshot counts, and angle intervals. It not only reduces the root mean square error but also improves computational efficiency and significantly enhances real-time performance. Furthermore, this method exhibits strong robustness in low signal-to-noise ratio, low snapshot count, and non-grid angle scenarios, providing an efficient solution for two-dimensional DOA estimation in complex real-world environments.

[0148] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A high-precision two-dimensional DOA estimation method based on a two-branch CNN, characterized in that, include: Step 1: Use a uniform rectangular array (URA) to receive signals from K far-field narrowband signal sources in space, and construct the array covariance matrix based on the signals received by the uniform rectangular array. ,in This represents the sampling matrix of the array received signal. Represents the conjugate transpose of the sampling matrix. This represents the number of times the received signal from the array is sampled, i.e., the number of snapshots. The array covariance matrix is ​​used as the input to the two-branch CNN network. Step 2: Construct a two-branch CNN network, which includes a shared feature encoder and a dual-angle prediction head; Step 3: Design the hybrid loss function Hybrid loss function Cross-entropy loss Compared with loss Linear weighting; Step 4: Train the dual-branch CNN network using the AdamW optimizer and the OneCycle learning rate scheduling strategy; Step 5: Apply the trained dual-branch CNN network to 2D DOA estimation, outputting the elevation angle of the source. With azimuth Estimation results.

2. The high-precision two-dimensional DOA estimation method based on a dual-branch CNN according to claim 1, characterized in that: The element spacing of the uniform rectangular array in step 1 satisfies To avoid the grating lobe effect, where For the signal wavelength, the first The two-dimensional direction of arrival of each signal source is , ,in, Representing the The elevation angle of a signal source, Indicates the first The azimuth angle of each signal source.

3. The high-precision two-dimensional DOA estimation method based on a dual-branch CNN according to claim 1, characterized in that: In step 1, construct the array covariance matrix. The specific process is as follows: the uniform rectangular array URA in axis, The number of elements in the axial array are respectively , ; axis, The direction vector of the axis source is: ； ； exist On the axis The direction matrix corresponding to each array element is ; exist On the axis The direction matrix corresponding to each array element is ; The signal received by the entire uniform rectangular array is ,in For source vectors, , Represents the Khatri-Rao product. through The received signal after the second sampling is represented as follows: ; In the formula, The signal passes through Source vector after sampling ; Represents the matrix of the first A diagonal matrix formed by rows, This is the additive white Gaussian noise matrix in the received signal.

4. The high-precision two-dimensional DOA estimation method based on a dual-branch CNN according to claim 1, characterized in that: The shared feature encoder in step 2 includes a convolutional layer, two residual modules, and a channel attention module; The residual module solves the vanishing gradient problem through cross-layer connections, and the gradient satisfies the following during backpropagation of the residual module. ,in This represents the gradient of the loss function; the number 1 indicates the short-circuiting mechanism of the residual block. The residual module contains two convolutional layers, two batch normalization layers, and a ReLU activation function. The expression for the ReLU activation function is: ; The channel attention module obtains channel statistics through global average pooling, and then generates channel weights through two fully connected layers. The calculation process of the channel weights satisfies... ,in This is a global average pooling feature. and For learnable parameters, It is a ReLU activation function. This is the Sigmoid function.

5. A high-precision two-dimensional DOA estimation method based on a dual-branch CNN according to claim 1, characterized in that: In step 2, the dual-angle prediction head consists of two sub-networks with identical structures, completely independent networks, and no parameter sharing, which are used for pitch and azimuth estimation, respectively. Each sub-network follows a three-stage processing flow of "feature refinement - spatial aggregation - angular label classification"; In the feature refinement stage, the common features output by the shared feature encoder are further purified and optimized through a stacked structure of "convolution-batch normalization-ReLU". A channel attention module is introduced after the first convolution to enhance the perception of angle-related key features. The spatial aggregation stage transforms the feature map into a fixed-length feature vector through a global average pooling layer. The computation process of global average pooling satisfies... ,in, The spatial dimension of the feature map; In the angle label classification stage, pitch angles are estimated separately using independent fully connected layers. and azimuth ,satisfy: ； in, The weight vector to be learned. This is a bias term.

6. The high-precision two-dimensional DOA estimation method based on a dual-branch CNN according to claim 1, characterized in that: Cross-entropy loss in step 3 The expression is ; in, Indicates the first The probability of predicting the pitch angle of a target. Indicates the first The azimuth prediction probability of a target; The pitch angle probability distribution output by the model; This represents the azimuth probability distribution. This indicates the number of angle categories, with the actual label being... , .

7. The high-precision two-dimensional DOA estimation method based on a dual-branch CNN according to claim 1, characterized in that: In step 3, compare the loss functions. The expression is ; in, For positive sample loss, The loss is negative.

8. The high-precision two-dimensional DOA estimation method based on a dual-branch CNN according to claim 1, characterized in that: Step 3 Mixed loss function The expression is ;in These are the weighting coefficients.

9. A high-precision two-dimensional DOA estimation method based on a dual-branch CNN according to claim 1, characterized in that: Step 4's OneCycle learning rate scheduling strategy includes a linear rising phase and a cosine falling phase. During the linear rising phase, the learning rate starts from the initial value... Linear growth to maximum value The duration accounts for 30% of the total training steps, and the learning rate decays from its maximum value to its initial value according to the cosine function during the cosine descent phase.

10. A high-precision two-dimensional DOA estimation method based on a dual-branch CNN according to claim 1, characterized in that: The root mean square error is used to measure the accuracy of the estimation. In the formula Indicates the number of Monte Carlo experiments performed. Indicates the number of information sources. and They represent the first time. During the Monte Carlo experiment, the first The estimated and true values ​​of each information source.

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