A deep learning-based non-ideal non-uniform array single-snapshot direction finding method

Abstract

The application relates to a non-ideal non-uniform array single-snapshot direction finding method based on deep learning, which comprises the following steps: collecting data in a darkroom and obtaining an array steering vector; calculating a covariance matrix of array output and a deep learning label; generating a deep learning network training data set; designing a deep learning network architecture and a loss function and training the network; reconstructing a toeplyz covariance matrix by using the trained deep learning network; and estimating a target number and a signal wave direction by using the reconstructed toeplyz covariance matrix. Compared with a traditional processing method, the method can obtain high-precision direction finding performance because the toeplyz property of the covariance matrix is maintained in the network training process. In addition, the method can reconstruct the covariance matrix of a uniform linear array by using a neural network model, and simultaneously complete the functions of denoising, rank restoration, array interpolation and array calibration, so that the difficulty of subsequent conventional array signal processing is reduced.

Description

TECHNICAL FIELD

[0001] The present application relates to a kind of non-ideal non-uniform array single snapshot direction finding method based on deep learning, and particularly relates to using deep learning method to process radar, sonar, communication etc.The signal processing problem of receiver non-ideal array belongs to electronic information technology field, especially array signal processing technical field. BACKGROUND

[0002] Array signal processing is widely used in military and civil technical field, and has important application in radar, communication, navigation and other technical fields.The working mode is to arrange several sensors in different positions in space to form sensor array, and the sensor received signal is detected and estimated.In ideal case, each sensor does not interfere with each other, response is same, and sensor position is accurate, at this time, array flow type is accurate known, and sensor received signal can be processed by relevant array signal processing algorithm.However, in actual working environment, due to non-ideal sensor design and manufacturing process, array installation error and sensor mutual coupling and other factors, there may be gain / phase error, position error and mutual coupling error in array system.The array containing error is called non-ideal array.

[0003] To avoid the above problems, the most commonly used is offline calibration method. The idea of offline calibration is to measure the array steering vector at different angles in a darkroom first, and then process the signal accordingly. There are currently three offline calibration methods, namely exhaustive search method, gain / phase compensation method and global array interpolation method (see Literature 1: Mats Viberg, Maria Lanne, Astrid Lundgren. Chapter 3: Calibration in Array Processing, Classical and Modern Direction-of-Arrival Estimation[M], Academic Press, 2009, Pages 93-124). The exhaustive search method is to traverse all measured array steering vectors and select the optimal value. This method needs to perform interpolation processing on off-grid point targets, and has high computational complexity and large storage data volume. The gain / phase compensation method measures and stores the steering vector at a certain angle, and compensates the amplitude and phase of the signal based on this. This method has low computational complexity and small storage data volume, but does not handle array errors at other angles. The global array interpolation method measures the steering vector at each angle, and calculates the calibration matrix based on this through the least squares method. This method has moderate computational complexity and storage data volume, and its performance is better than the gain / phase compensation method. However, due to the angle dependence of the array error, the least squares method still brings a large residual array error. To solve the above problems, researchers introduced deep learning methods to solve the error calibration problem (see Literature 2: Yujian Pan, Sreeraj Rajendran, Sofie Pollin. 2D angularly dependent array error calibration for 1D array via neural network with local manifold interpolation[J], Radioengineering, 2021, Pages 547-555). This method outputs the angle of arrival through a deep learning network to achieve array error calibration, and its performance is better than the traditional methods mentioned above, but this method is only suitable for single target scenarios.

[0004] Moreover, for many applications such as radar, only single snapshot data is available for array signal processing after range and velocity processing. Furthermore, to obtain as large array aperture as possible with limited number of channels, the array is usually configured as a non-uniform array for radar and other applications. In single snapshot case, the rank of array covariance matrix is one, so only one target can be estimated using subspace method. For multi-target case, spatial smoothing is needed to recover the rank of array covariance matrix. However, spatial smoothing cannot be applied to non-uniform array. Maximum likelihood estimation can be used to solve the non-uniform array single snapshot direction finding problem, but its computational complexity increases exponentially with the number of signal sources in the scene. SUMMARY

[0005] In order to overcome the shortcomings of the prior art, the present application provides a non-ideal non-uniform array single snapshot direction finding method based on deep learning.

[0006] The specific steps of a non-ideal non-uniform array single snapshot direction finding method based on deep learning are as follows:

[0007] Step one, darkroom data acquisition and array steering vector acquisition: place the array on the servo platform in the darkroom, and according to the active or passive working mode of the array, fix an angle reflector or radiation source in the far field of the array, and collect darkroom data; set the system parameters so that the signal-to-noise ratio of the array output baseband signal is as close as possible to the maximum value in the dynamic range; set the set composed of multiple angle grid points to be calibrated as , the number of angles in the set is . For each angle in the set, the following operations are performed: let , rotate the servo to make the angle of arrival of the incoming signal relative to the array normal be ; record the corresponding array output baseband signal , is a -dimensional complex vector, is the number of array elements; calculate the corresponding steering vector: , is the first element of . After the iteration is completed, a set composed of steering vectors is obtained. There is a one-to-one correspondence between the elements in ;

[0008] Step two, calculate the array output covariance matrix and deep learning label: randomly select the number of targets in the target number range , where is the maximum number of targets to be processed. Randomly select different angles in . , from , the corresponding angle of the steering vector constitute the array flow pattern . Construct the array output , where represents a random signal vector of dimension , represents a complex Gaussian distribution, the first parameter position represents the mean vector, and the second parameter position represents the covariance matrix; the calculation formula of the covariance matrix is as follows: , where represents generating a diagonal matrix with the corresponding elements as the diagonal elements, and the power ratio is randomly selected from the signal power ratio range , is the maximum signal power ratio to be processed for direction finding, with the unit of dB; represents a noise vector of dimension , represents the noise power , represents a unit matrix of dimension , where the calculation formula of is as follows: , and are the minimum and maximum signal-to-noise ratios, respectively, with the unit of dB.

[0009] Calculate the array output covariance matrix , represents the conjugate transpose. Then generate the covariance matrix for the deep learning label: take a part of the sub-array of the array, fill the holes in the missing array elements, and obtain a virtual uniform linear array with array elements. The covariance matrix output by the uniform linear array is calculated as , where represents the array flow pattern matrix of the virtual uniform linear array, , the steering vector , where, represents the transpose, represents the element spacing, represents the signal wavelength, represents the imaginary unit. is the deep learning label;

[0010] Step three, generate the deep learning network training data set: set , , , numerical values, and perform step two The Monte Carlo experiment yielded... Covariance matrix of array output and deep learning tags For each Take the real and imaginary parts of the upper triangular elements and the diagonal elements to form the eigenvector. ,but Total The training dataset contains n real elements; finally, the training dataset has a total of n real elements. There are 10 samples, each sample consisting of a feature vector. and tags constitute;

[0011] Step 4: Design the deep learning network architecture and loss function, and train the network: Input layer dimension of the neural network. The output layer dimension is ,contain There are 1 hidden layer, and each hidden layer contains 1 hidden layer. There are neurons, and each hidden layer has an activation function; the neural network is represented as The output of the neural network is represented as The loss function for training the neural network is set to ,in This indicates finding the Frobenius norm of a vector. For the reason The reconstructed Topelitz covariance matrix, The construction includes the following sub-steps: obtaining the network output The 2nd to Value For vectors Get network output The arrive Value For vectors Construct auxiliary vectors ,in for The anti-diagonal identity matrix of order 1; the auxiliary vector Convert to Toplitz matrix ,Right now:

[0012]

[0013] in, express The One element, and so on for the rest. At this point, It possesses both Toplitzian and Hermitian properties;

[0014] The training of the neural network adopts a back propagation algorithm. ;

[0015] Step five, reconstructing the Toeplitz covariance matrix by using the trained deep learning network: constructing a new vector from the test data and inputting it into the neural network to obtain the network output ; and then reconstructing the Toeplitz covariance matrix , by ; the construction is as described in step four;

[0016] Step six, estimating the target number and the signal direction of wave arrival by using the reconstructed Toeplitz covariance matrix;

[0017] performing eigenvalue decomposition on the reconstructed covariance matrix to obtain eigenvalues arranged in ascending order ; calculating the difference , of the eigenvalues, and calculating the variance of the sequence : , ; finally, estimating the number of signal sources , , wherein represents , the intermediate parameter ; taking the eigenvectors corresponding to the smallest eigenvalues to constitute the noise subspace ; constructing a spectral function , and the peak value of the spectral function corresponds to the direction of wave arrival, wherein is the search angle, is the search steering vector, and is expressed as .

[0018] The deep learning network architecture in step four can be set as a full connection network, a residual network or a convolutional neural network; and the activation function can adopt a ReLu function.

[0019] The direction finding method in step six can be replaced by a beam forming method, which has the characteristics of low calculation amount and can reduce the sidelobe level of the spatial spectrum when applied to a uniform linear array.

[0020] Compared with the prior art, the present application has the beneficial effects that:

[0021] This invention proposes a deep learning-based single-shot direction finding method for non-ideal, non-uniform arrays. The covariance matrix used for direction-of-arrival estimation is constructed from an auxiliary matrix output by the network. Compared to methods that directly construct the covariance matrix using network output, this method ensures the Tolliterates property of the constructed covariance matrix. This Tolliterates property better conforms to the signal model of a general uniform array, enabling high-precision direction finding results. The method considers multiple signal sources and can effectively estimate multiple directions of arrival, making it more widely applicable than single-target non-ideal array direction finding methods. Furthermore, the method reconstructs the covariance matrix of a uniform linear array using a deep learning network model, simultaneously performing denoising, rank recovery, array interpolation, and array calibration functions, reducing the difficulty of subsequent conventional array signal processing. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0023] Figure 1 This is a flowchart of the overall process of the non-ideal non-uniform array single-shot direction finding method based on deep learning of the present invention;

[0024] Figure 2 This is a diagram showing the overall structure of the neural network of this invention;

[0025] Figure 3 The diagram shows the direction-of-arrival estimation results of this invention under different signal-to-noise ratios. Detailed Implementation

[0026] 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.

[0027] like Figure 1 As shown, the present invention includes the following:

[0028] Step one, collecting data in darkroom and obtaining array steering vectors: place the array on the servo platform in the darkroom, and according to the active or passive working mode of the array, fix an angle reflector or a radiation source in the far field of the array to collect the data in the darkroom; set the system parameters to make the signal-to-noise ratio of the array output baseband signal as close as possible to the maximum value in the dynamic range; set the set composed of multiple angle grid points to be calibrated as , the number of angles in the set is . For each angle in the set, the following operations are performed: let , rotate the servo to make the angle of arrival of the incoming wave signal relative to the array normal be ; record the corresponding array output baseband signal , is a -dimensional complex vector, is the number of array elements; calculate the corresponding steering vector: , is the first element of . After the traversal is completed, a set of steering vectors is obtained . There is a one-to-one correspondence between the elements in .

[0029] Step two, calculating the covariance matrix of the array output and the deep learning label: randomly select the target number in the target number range , wherein is the maximum target number to be processed. Randomly select different angles from , and select the steering vector corresponding to the angle from to form the array flow pattern . Construct the array output , wherein represents a -dimensional random signal vector, represents a complex Gaussian distribution, and the first parameter position represents the mean vector and the second parameter position represents the covariance matrix; the calculation formula of the covariance matrix is: , wherein represents generating a diagonal matrix with the corresponding elements as the diagonal elements, and the power ratio is randomly selected from the signal power ratio range , wherein is the maximum signal power ratio to be processed, and the unit is dB; represents a -dimensional noise vector, represents the noise power, express A 3D identity matrix, where The calculation formula is: , For signal-to-noise ratio (SNR), it needs to be determined from the SNR range. Randomly selected from, and These are the minimum and maximum signal-to-noise ratios, respectively, in dB.

[0030] Calculate the array output covariance matrix , This represents the conjugate transpose. Then, the covariance matrix for deep learning labels is generated: a partial subarray of the array is taken, and the holes where the elements are missing are filled to obtain a virtual uniform linear array with the number of elements being... The covariance matrix of the uniform linear array output is calculated as follows: ,in The array manifold matrix represents the virtual uniform linear array. ,guide vector ,in, Indicates transpose. Indicates the spacing between array elements. Indicates the signal wavelength. It represents the imaginary unit. This invention utilizes deep learning to reconstruct the covariance matrix of a uniform linear array using a deep learning network model, and leverages the powerful fitting capabilities of deep learning to interpolate non-uniform arrays. The covariance matrix used for deep learning labels in this invention does not contain added noise, enabling the invention to correct array errors through the deep learning neural network while simultaneously denoising the array output.

[0031] Step 3: Generate the deep learning network training dataset: Setting , , , Numerical values, for step two The Monte Carlo experiment yielded... Covariance matrix of array output and deep learning tags For each Take the real and imaginary parts of the upper triangular elements and the diagonal elements to form the eigenvector. ,but Total The training dataset contains n real elements; finally, the training dataset has a total of n real elements. There are 10 samples, each sample consisting of a feature vector. and tags Composition. Due to It is a conjugate symmetric matrix, that is Middle element, with properties , Indicates taking conjugate, so for Only need to take the real part and imaginary part of the diagonal elements and upper triangular elements to include all information of the covariance matrix This way simplifies the sample data, reduces network complexity, and speeds up network training.

[0032] Step four, design deep learning network architecture and loss function and train the network: the input layer dimension of the neural network , the output layer dimension is , contains hidden layers, each hidden layer contains neurons, and there is an activation function between each hidden layer; the neural network is represented as , the output of the neural network is represented as , and the loss function for training the neural network is set as , where represents the Frobenius norm of the vector, is the Toeplitz covariance matrix reconstructed by , and the construction of includes the following sub-steps: taking the 2th to values of the network output as the vector , taking the th to values of the network output as the vector , constructing the auxiliary vector , where is the th anti-diagonal unit matrix; convert the auxiliary vector into the Toeplitz matrix , that is:

[0033]

[0034] where, represents the th element of , and the rest are similar. At this time, has both Toeplitz and Hermitian properties;

[0035] The training of the neural network uses the back propagation algorithm. The trained neural network is represented as .

[0036] ​​The covariance matrix of the uniform linear array is a Hermitian matrix and has the property of Toeplitz. If the upper triangular part of the network output matrix is directly output to reconstruct the whole covariance matrix, only the matrix with the Hermitian property can be obtained, but not the Toeplitz property. Therefore, the method adopts the network output to construct an auxiliary vector first, and then converts it into a covariance matrix to ensure that the covariance matrix has both properties. The covariance matrix constructed by the method is more in line with the characteristics of the real covariance matrix, which is beneficial to subsequent signal processing.

[0037] Step five, reconstructing the Toeplitz covariance matrix by using the trained deep learning network: constructing a new vector from the test data , inputting the vector into the neural network , obtaining the network output ; and reconstructing the Toeplitz covariance matrix , The construction is as described in step four.

[0038] Step six, estimating the target number and the signal direction of arrival by using the reconstructed Toeplitz covariance matrix;

[0039] Performing eigenvalue decomposition on the reconstructed covariance matrix to obtain eigenvalues arranged in ascending order ; calculating the difference , of the eigenvalues, and calculating the variance of the sequence : , ; finally, estimating the number of signal sources , , wherein represents , the intermediate parameter ; taking the eigenvectors corresponding to the smallest eigenvalues to form the noise subspace ; constructing the spectral function , and the peak value of the spectral function corresponds to the direction of arrival angle, wherein is the search angle, is the search steering vector, and is represented as .

[0040] In order to verify the performance of the present application, the following simulation examples are used for verification, and the experimental results are compared with the gain / phase compensation method and the global array interpolation method in the background literature.

[0041] ​We place an 8-element non-uniform linear array in a microwave anechoic chamber, and place a radiation source at the far-field position of the array. A uniform angular grid is scanned at intervals of 1° in [-40°, 40°], and the array output baseband signal is collected. In the step of constructing training data, the signal-to-noise ratio is set to 15 dB, the target number range is 1 to 2, and in the case of 2 targets, the signal power ratio is set to 0 dB. Then, select the first 4 elements from the above 8-element array, and fill them into a 7-element uniform linear array. A total of 332100 training data are generated using the foregoing method. Select [-10.5°, 20.5°] as the signal incidence angle of the test data set, and generate test data by adding noise at a signal-to-noise ratio of 5 dB to 50 dB, a total of 500 test data for testing the direction of arrival estimation performance. The specific network structure of the deep learning network is set as shown in Figure 2 The input layer dimension of the deep learning network is 64, the output layer dimension is 13, it contains 6 hidden layers, each hidden layer contains 2048 neurons, there is an activation function between each hidden layer, the activation function uses the ReLu function, and the last 3 hidden layers of the network constitute a residual block. The optimizer is Adam, the maximum epoch number is set to 500, the Batch size is set to 1024, and the initial learning rate is 0.0001.

[0042] The simulation results of the method of the application and the gain / phase compensation method and the global array interpolation method are compared, and the last two methods perform spatial smoothing on two same sub-arrays in the 8-element array to estimate two signal sources. The root mean square error (RMSE) of the direction finding result is used as the comparison index. The comparison results are shown in Figure 3 As can be seen, the direction finding performance of the method of the application is obviously better than that of the two traditional methods, and the method has good generalization ability at high signal-to-noise ratio.

[0043] The embodiments of the application are described in detail above with reference to the drawings, but the application is not limited to the described embodiments. For those skilled in the art, various changes, modifications, replacements and variations can be made to the embodiments without departing from the principles and spirits of the application, and still fall within the protection scope of the application.

Claims

1. A method for non-ideal non-uniform array single-shot direction finding based on deep learning, characterized in that: Comprising the following steps: Step one, collecting data in the darkroom and obtaining array steering vector: placing the array on the servo platform in the darkroom, fixing a corner reflector or radiation source in the far field of the array according to the active or passive working mode of the array, and collecting darkroom data; The step one specifically comprises: setting system parameters to make the signal-to-noise ratio of the array output baseband signal as close as possible to the maximum value in the dynamic range; setting a set composed of a plurality of angle grid points to be calibrated as , the number of angles in the set is , for each angle in the set, the following operations are performed: setting , rotating the servo to make the angle of arrival of the incoming signal relative to the array normal as ; recording the corresponding array output baseband signal , is a -dimensional complex vector, is the number of array elements; calculating the corresponding steering vector: , is the first element of , after the traversal, a set composed of steering vectors is obtained , and the elements in have a one-to-one correspondence relationship; Step two: Calculate the covariance matrix of the array output and the deep learning label: In the target number range The target number is randomly selected in the target number range Wherein is the maximum target number to be processed for direction finding, In randomly selected different angles , from the guide vector corresponding to the angle is selected to form an array flow pattern ， Constructing array outputs wherein denotes a random signal vector, denotes a complex Gaussian distribution with the first argument position denoting the mean vector and the second argument position denoting the covariance matrix; covariance matrix The formula for calculating the covariance matrix is: wherein denotes generating a diagonal matrix with the corresponding elements as the diagonal elements, and the power ratio is randomly selected from the signal power ratio range , is the maximum signal power ratio to be processed for direction finding, in dB; denotes a noise vector of dimension denotes the noise power, denotes an identity matrix of dimension , wherein , is randomly selected from the signal-to-noise ratio range , and are the minimum and maximum signal-to-noise ratios, respectively, in dB; Computing array output covariance matrix , denotes the conjugate transpose, generating the covariance matrix for the deep learning label: taking the partial sub-array of the array, filling the holes in the missing array elements, a virtual uniform linear array with array element number , The covariance matrix output by the virtual uniform linear array is calculated as wherein represents an array flow pattern matrix of a virtual uniform linear array, , steering vector wherein, denotes the transpose, denotes the array element spacing, denotes the signal wavelength, denotes the imaginary unit, is the deep learning label; Step three: generate the training dataset for the deep learning network: set , , , the number of values, perform Monte Carlo experiments on step two to obtain the covariance matrix of the array output and the deep learning label , take the real and imaginary parts of the upper triangular elements and the diagonal elements for each , and construct the feature vector , then there are real elements in total; finally, the training dataset has a total of samples, each sample is composed of a feature vector and a label ; Step four: design deep learning network architecture and loss function and train the network: the input layer dimension of the neural network is , the output layer dimension is , contains hidden layers, each hidden layer contains neurons, and there is an activation function between each hidden layer; the neural network is represented as , and the output of the neural network is represented as The loss function for training the neural network is set to ,in This indicates finding the Frobenius norm of a vector. For the reason The reconstructed Topelitz covariance matrix, The construction includes the following sub-steps: obtaining the network output The 2nd to Value For vectors Get network output The arrive Value For vectors Construct auxiliary vectors ,in for The anti-diagonal identity matrix of order 1; the auxiliary vector Convert to Toplitz matrix ,Right now: wherein denotes the first element of the vector while having both Toeplitz and Hankel properties; The trained neural network is represented as ; Step 5: Reconstruct the Toplitz covariance matrix using the trained deep learning network: construct a new vector from the test data. Input into the neural network In the middle, the network output is obtained. Then by Reconstructing the Topletz covariance matrix , The construction is as described in step four; Step six: estimating the target number and signal direction of arrival by using the reconstructed Toeplitz covariance matrix. reconstructed covariance matrix performing eigen decomposition to obtain eigenvalues arranged from small to large ; calculating the difference of eigenvalues , , compute the variance of the sequence : , ;​ Estimating the number of signal sources , representing taking the minimum , intermediate parameters ; taking the eigenvectors corresponding to the smallest eigenvalues to form the noise subspace ; constructing a spectral function​​ The angle corresponding to the peak of the spectrum function is the direction of arrival, wherein is the search angle, is the search steering vector, denoted as 。 2. The non-ideal non-uniform array single snapshot direction finding method based on deep learning according to claim 1, characterized in that: The deep learning network architecture in the step four is set as a full connection network, a residual network or a convolutional neural network; and the activation function can adopt a ReLu function.

3. The non-ideal non-uniform array single snapshot direction finding method based on deep learning according to claim 1, characterized in that: The direction finding method in the step six is replaced by a beam forming method.

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