End-to-end intelligent direction-of-arrival estimation method based on subarray sampling

Abstract

The invention discloses an end-to-end intelligent direction of arrival estimation method based on subarray sampling, and belongs to the technical field of wireless communication. A sub-array sampling technology is adopted to replace traditional full-array sampling, and signal processing is completed by using fewer radio frequency links, so that the hardware cost is reduced; an end-to-end learning framework is adopted, so that a network can automatically capture features and rules according to a data set, and excessive dependence on a model is avoided; data features are preliminarily captured through a deep neural network, a pre-estimated value is given, then an iteration process of a maximum likelihood estimation method is converted into a deep expansion network, initialization is performed by using output of the deep neural network, and the effect of the method is improved while convergence is accelerated; a large number of data sets are generated through a sub-array sampling signal mathematical model, the network is trained, and the problem that overfitting is prone to occurring under a small data set is avoided. The method is suitable for the technical field of wireless communication, and realizes direction of arrival estimation with lower complexity and higher accuracy in a low-snapshot scene.

Description

Technical Field

[0001] The invention belongs to the technical field of wireless communications and relates to an end-to-end intelligent direction of arrival estimation method based on subarray sampling. Background Art

[0002] Due to the open nature of wireless channels, wireless communication links are very susceptible to interference from illegal users, communication quality cannot be guaranteed, and privacy information may be leaked. To ensure the secure transmission of information, legitimate communication users can use direction of arrival estimation to obtain the position of illegal users, and on this basis, use beamforming technology to eliminate the impact of malicious interference on communication performance. In this context, using antenna arrays to achieve accurate direction of arrival estimation is of great significance to ensure the security of wireless communication links.

[0003] With the large-scale application of wireless communication technology, the electromagnetic environment in which antenna arrays are located is becoming increasingly complex, and small arrays can no longer meet the needs of direction finding. In order to enhance the direction finding capability in complex environments, antenna arrays are showing a large-scale development trend. Although the general multiple signal classification algorithm has the advantages of super-resolution capability and applicability to a variety of array structures, it requires the number of RF links to be equal to the number of antennas. Therefore, if subspace algorithms represented by multiple signal classification are continued to be used for wave direction estimation, the high hardware cost will limit the widespread application of large-scale arrays. This problem can be solved by subarray sampling technology, which divides the array, performs sequential sampling of the arrays between groups, and simultaneous sampling of the arrays within the group, so as to achieve the purpose of using fewer RF links to complete signal processing and reduce hardware costs.

[0004] In actual direction-finding environments, it is often impossible to know the number of signal sources in advance. Therefore, after applying subarray sampling technology, the quantitative relationship between the number of signal sources and the number of subarray antennas is difficult to determine. Existing direction-finding methods based on subarray sampling can only deal with situations where the number of signal sources is greater than the number of subarray antennas or the number of signal sources is less than the number of subarray antennas. They are also extremely dependent on the accuracy of model assumptions and are difficult to adapt to complex direction-finding environments and diverse direction-finding requirements. In addition, the data received by the subarray has inherent information loss compared to the full array itself. Therefore, when facing low snapshot scenarios, existing direction-finding schemes are difficult to achieve better estimation performance. Summary of the invention

[0005] In view of the problem that the existing subspace algorithms require the number of RF links to be equal to the number of antennas, resulting in a large-scale array and high hardware cost, the main purpose of the present invention is to propose an end-to-end intelligent DOA estimation method based on subarray sampling, which uses subarray sampling technology to replace traditional full array sampling to achieve signal processing using fewer RF links, thereby reducing hardware costs; an end-to-end learning framework is adopted to enable the network to automatically capture features and rules according to the data set, and get rid of excessive dependence on the model; in the learning framework, the data features are initially captured by the deep neural network to give a pre-estimated value. Based on this estimation, the iterative process of the maximum likelihood estimation method is converted into a deep unfolding network using the deep unfolding technology, and the output of the deep neural network is used for initialization, which accelerates convergence and improves the method effect; a large number of data sets are generated using a specific signal mathematical model, and the network is trained based on the data set, so that the trained network has excellent generalization performance and avoids the problem of overfitting that is very easy to occur in a small data set. In low-snapshot scenarios, DOA estimation with lower complexity and higher accuracy is achieved.

[0006] The object of the present invention is achieved through the following technical solutions:

[0007] The present invention discloses an end-to-end intelligent direction of arrival method based on subarray sampling, which specifically comprises the following steps:

[0008] Step 1: Construct a mathematical model of subarray sampling signals;

[0009] For far-field narrowband signal sources, when L far-field independent narrowband signals are simultaneously incident on an antenna array with M array elements, the corresponding full array signal model is:

[0010] y(t)=A(θ)s(t)+η(t) (1)

[0011] The signal vector is

[0012] The noise vector is

[0013] Manifold Matrix

[0014] In the subarray sampling system, the number of array elements in each independent subarray is equal to the number of RF links, and the number of antennas between subarrays is equal. The antennas in the subarray group are sampled simultaneously, and the subarrays are sampled sequentially, and the division of the subarrays does not require the antennas to be mutually exclusive. For an array consisting of M antennas, only W RF links are used to receive the signal, where W < M. The sampling process is as follows: at a certain moment, there is only one group of antennas in the subarray that are sampled simultaneously. Therefore, at any given sampling moment, each RF link is connected to only one antenna and the connection network has a total of K states.

[0015] For each group of subarrays, N snapshot data are sampled. According to the subarray model, the nth sampled data of the kth subarray is expressed as follows

[0016] y (k) (n) = G (k) (A(θ)s (k) (n)+η (k) (n)) (2)

[0017] Among them, the noise signal is a cyclically symmetric complex Gaussian distribution, that is, Select the network matrix G (k) ∈{0,1} W×M represents the connection relationship between the RF link and the antenna unit in the kth subarray; the specific form of the manifold matrix A(θ) is related to the array geometry; θ represents the direction of arrival of the source signal; the source signal satisfies the cyclically symmetric complex Gaussian distribution, that is, y (k) (n) is the received signal of the array.

[0018] Step 2: Generate a data set based on the signal mathematical model, train a deep neural network with adaptive signal-to-noise ratio, and directly give a reasonable estimate value from the network for initialization of step 3;

[0019] The data set required for deep neural network training is constructed as follows: According to the mathematical model of the signal sampled by the subarray, the snapshot data corresponding to the kth subarray is obtained as

[0020] Y k =G (k) (A(θ)S+η) (3)

[0021] Among them, G (k) is the selection matrix corresponding to the selection network; A(θ) is the manifold matrix, θ is the incident direction of the source signal, that is, the direction of arrival angle; S is the source signal, η is the noise, both of which satisfy the cyclic symmetric complex Gaussian distribution.

[0022] In order to make the trained network have good estimation results for any angle within the field of view, the angle θ of the training data should be uniformly sampled within the direction finding range, that is,

[0023] θ~U(0,β) (4)

[0024] Where, for a uniform linear array, β = π; for a uniform circular array, β = 2π.

[0025] The signal of the signal source satisfies the maximum likelihood model assumption and is a zero-mean cyclic symmetric complex Gaussian distribution. At the same time, in order to facilitate data generation and network training, the power of the signal source is set to The power of the noise is adjusted according to the signal-to-noise ratio. The corresponding formula is as follows:

[0026]

[0027] By using the above data generation method, new data samples can be provided to the network at any time, thereby preventing the model training from falling into overfitting and making the trained network more robust.

[0028] The full array is divided into several sub-arrays with an equal number of antennas to obtain K groups of received signal data. Directly using the data as network input will increase the parameter scale of the network and reduce the convergence speed. And if the signal sampling snapshot changes, the network input dimension needs to change accordingly, which will limit the network's scenario practicality. Therefore, it is necessary to preprocess the original data, which has three main functions: extract the characteristics of the original signal so that the network can more easily learn the mapping relationship between data and angles; dissociate the data dimension from the number of snapshots so that the network can be applied to DOA estimation in different snapshot scenarios; convert the complex signal data into the real data required by the network.

[0029] The covariance matrix of the data is used as the network input, and K covariance matrices are obtained by sampling data from K groups of subarrays:

[0030]

[0031] To perform dimension matching, the two-dimensional matrix data needs to be converted into one-dimensional vector data. It is observed that the covariance matrix of the received signal is a Hermite matrix, that is, the matrix can be represented by real numbers equal to the number of matrix elements. The real and imaginary parts of the diagonal elements and upper half-angle elements of K matrices are extracted and concatenated into a vector. This vector is used as the input of the deep neural network.

[0032] The dimension of the vector obtained after processing is KW 2 , which is independent of the number of snapshots, so the deep neural network has no special requirements for the number of snapshots of received data. When generating the data set, the direction of arrival angle corresponding to each sample data is known, and it is directly used as a label for network training.

[0033] The deep neural network is composed of a multi-layer perceptron and can process array signal data with different signal-to-noise ratios. The activation function in the network is the ReLU function, which gives the network the ability of nonlinear fitting while saving computing resources. The specific form is:

[0034] ReLU(x)=max(0,x) (7)

[0035] The loss function of the regression network is the mean square error:

[0036]

[0037] Where θ is the true direction of arrival angle, is the estimated direction of arrival angle.

[0038] Since the angle in DOA estimation is periodic, the periodic mean square error can be used as the loss function:

[0039]

[0040] In addition, the average cycle error can be expressed as

[0041]

[0042] When estimating multiple sources, the loss function used should be:

[0043]

[0044] Among them, Π is a set of permutation matrices that can represent all permutations of angles.

[0045] After convergence, the optimal permutation matrix is ​​constant, that is, the output of the network follows a fixed order. This indicates that during the training process, the mean of the sum of errors of all permutations can be used as the loss function.

[0046] After training is completed, the periodic mean square error is used to measure the distance between the estimated direction of arrival value and the true value, as follows:

[0047]

[0048] The hyperparameters of the neural network structure are mainly divided into network structure parameters and training parameters. The structural parameters of the deep neural network include the number of hidden layers and the number of neurons in the hidden layer; the training parameters include the batch sample size, learning rate, and the number of epochs of data set iterations. The structural parameters determine the data representation ability of the neural network and affect the fitting and generalization performance; the training parameters affect the convergence speed, stability, and performance of the given structural network.

[0049] With the help of small-scale random search methods, it is possible to determine a hyperparameter combination with better performance in a shorter time. The basic principle of this method is to randomly select hyperparameter combinations within the range of hyperparameter values ​​to train the network and record the model parameters with the best performance. Each parameter extraction is independent without any prior information reference, so the final model effect often depends on the set parameter range.

[0050] Deep neural networks compensate for information loss to a certain extent by learning from large amounts of data. However, since no prior knowledge of the model is introduced, the estimation accuracy is limited, so they are only used for initialization.

[0051] Step 3: Based on the mathematical model of the sub-array signal, the wave direction parameter estimation form is derived according to the maximum likelihood criterion and solved in combination with the gradient ascent method; the deep expansion technology is then used to improve the method, and an end-to-end learning framework is constructed based on step 2 to achieve the purpose of directly obtaining the final wave direction estimation by inputting the array receiving data.

[0052] The maximum likelihood criterion is to select the parameters that maximize the probability of the observed data. The source signal s(t) satisfies the cyclic symmetric complex Gaussian distribution, so that the received data depends only on the parameters and has nothing to do with the specific implementation of the signal.

[0053] s(t)~CN(0,R s ) (13)

[0054] Among them, R s is the covariance matrix of the signal, which is the power of the source signal in physical sense.

[0055] The second-order characteristics of the source signal are as follows

[0056]

[0057] E[y(t i )y H (t j )]=0 (15)

[0058] Among them, t i ,t j Represents different sampling times, R s is the Hermite matrix, δ ij is the Kronecker function, (·) H Represents a matrix conjugate transpose operation.

[0059] According to the signal model, a single observation x(t i The probability density function of ) is

[0060]

[0061] Among them, R y is the covariance matrix of the signal received by the array.

[0062] Since each snapshot data is independent of each other, the joint conditional probability of N snapshot data can be obtained, that is, the likelihood function

[0063]

[0064] Among them, y i represents the array receiving data at different times, θ represents the direction of arrival angle, R s represents the covariance matrix of the source signal, Represents the noise power.

[0065] Taking the negative logarithm of the likelihood function, we get

[0066]

[0067] N and M in the negative log-likelihood function are constants and not optimization parameters, so they can be ignored. After processing, the optimization target is obtained

[0068]

[0069] in, is the sampling covariance matrix, obtained from the observed data.

[0070] The above derivation is based on full array sampling. When sampling subarrays, since each subarray is independent of each other, the subarray is considered as a small full array, and the above optimization objective is modified as follows:

[0071]

[0072] in, is the sampling covariance matrix corresponding to the kth group of subarrays; y (k) (n) is obtained from the mathematical model of the sub-array signal described in step 1.

[0073] Due to the introduction of subarray sampling technology, the optimization objective analytical expression is in the form of and, so the signal covariance matrix R cannot be obtained when the angle θ is fixed s and noise power The closed-form solution of θ cannot be converted into a multidimensional search problem only about the angle θ. The gradient ascent method is used to solve the optimization objective. The iterative process of the optimization variables is as follows:

[0074]

[0075] Among them, c [t] is the set of optimization variables, α [t] represents the update step size, P c (·) represents a mapping to the set c.

[0076] According to the subarray sampling signal data model, optimize the variables θ, R s and Independent of each other, block coordinate ascent is used for iterative updates. At the same time, in order to accelerate the convergence process and improve performance, the update step size of the variable block is set independently. The complete iterative process is as follows:

[0077]

[0078] Here, t represents the number of iterations.

[0079] Combined with the mathematical model of subarray sampling signals, the specific form of the gradient in the iterative process is as follows:

[0080]

[0081] The result in step 2 is used as the initial value of the maximum likelihood method. However, the iterative process based entirely on the model cannot make the estimation method free from its dependence on accuracy, and it is also difficult to adapt to complex direction finding environments. Therefore, the deep unfolding technology is introduced to transform the iterative process into a deep unfolding network, and the network parameters are initialized according to the result of step 2, thereby forming an end-to-end learning framework.

[0082] Deep unfolding maps the iterative method into a deep learning framework. In this framework, each iteration becomes a layer in the network, and the operation of each layer simulates an iterative step of the original method, and the parameters are optimized in a data-driven way. The unfolded form of the network is the same as the update formula in step 2. Through this transformation, the iterative steps and parameter selections that originally required manual adjustment in the traditional method are automatically learned and adjusted by the network during the back-propagation training process. The parameters that need to be optimized are the direction of arrival angle θ, the source signal covariance matrix R s , Noise Power and update step size α. In this way, the unfolded deep network is able to exploit the powerful data processing capabilities of deep learning while maintaining the interpretability of the method.

[0083] After the introduction of deep unfolding technology, the deep neural network part and the iterative part form a complete end-to-end framework. From a data perspective, its input is the covariance matrix of each sub-array snapshot data or the IQ data of the array, and the output is the final direction of arrival estimation result. From the functional composition point of view, the deep neural network part completes the estimation initialization, and the deep unfolding network iteratively updates according to the initial value to obtain a more accurate direction of arrival estimate.

[0084] Beneficial effects:

[0085] 1. The present invention discloses an end-to-end intelligent direction of arrival estimation method based on subarray sampling, which reduces the use of radio frequency links by introducing subarray sampling technology to group array antennas and solve the problem of high hardware cost in large-scale array antennas.

[0086] 2. The present invention discloses an end-to-end intelligent DOA estimation method based on subarray sampling. In order to solve the problem that the model-based methods in this field are sensitive to signal assumptions and noise and have reduced estimation accuracy in low snapshot scenarios, a huge data set is constructed according to the signal mathematical model, and a deep neural network with a multi-layer perceptron as the main architecture is used. The optimal hyperparameters are determined through random search to achieve preliminary DOA estimation, give initial values ​​to the subsequent deep expansion network, and improve overall efficiency.

[0087] 3. The present invention discloses an end-to-end intelligent DOA estimation method based on subarray sampling. In order to further improve the estimation accuracy of the estimation method, the model prior knowledge is added by introducing the deep unfolding technology, that is, the iterative optimization process based on the model method is mapped to a deep unfolding network to achieve automatic update of optimization parameters and iterative process. The end-to-end learning framework obtained by combining the deep neural network enables the network to learn more feature information from the data to obtain a higher-precision estimation value, and avoids the grid mismatch problem while being interpretable.

[0088] 4. The present invention discloses an end-to-end intelligent DOA estimation method based on subarray sampling. After mapping the iterative part to a deep unfolding network, the entire model can be trained through the classic back-propagation algorithm. This end-to-end learning method can achieve global optimality and better performance through joint optimization compared to the model trained in stages. In addition, the end-to-end architecture is more flexible and can adapt to different types of data and tasks. When the usage scenario changes, it only needs to adjust the definition of input and output to handle various complex problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] Figure 1 It is a flow chart of an end-to-end intelligent direction of arrival estimation method based on subarray sampling disclosed in the present invention;

[0090] Figure 2 is a direction of arrival scene diagram of an end-to-end intelligent direction of arrival estimation method based on subarray sampling disclosed in this embodiment;

[0091] Figure 3 This is a schematic diagram of subarray sampling of an end-to-end intelligent direction of arrival estimation method based on subarray sampling disclosed in this embodiment. DETAILED DESCRIPTION

[0092] The present invention will be described in detail below with reference to the accompanying drawings and specific implementation methods. The technical problems solved by the technical solution of the present invention and the beneficial effects are also described. It should be noted that the described embodiments are only intended to facilitate the understanding of the present invention and do not have any limiting effect on it.

[0093] This embodiment discloses an end-to-end intelligent direction of arrival estimation method based on subarray sampling. Considering that there are three far-field independent narrowband signals from different directions incident on an array composed of nine antennas, the signal source and the array are in the same horizontal plane. According to the subarray sampling, the array is divided into four groups of subarrays, each of which consists of three antennas. The antenna array is a uniform circular array, the array radius is equal to the wavelength of the signal, and the direction finding range is 2π. As shown in the attached figure, Figure 1 As shown, it includes the following steps:

[0094] Step 1: Construct a mathematical model of subarray sampling signals;

[0095] For each group of subarrays, 10 snapshots are sampled. Figure 2 As shown, the nth sample data of the kth subarray is expressed as follows

[0096] y (k) (n) = G (k) (A(θ)s (k) (n)+η (k) (n))

[0097] in, Manifold matrix corresponding to uniform circular array The specific form is as follows:

[0098]

[0099] In the formula, β m =2π(m-1) / M(M=9),θ i (i=1,2,...,L) is the direction of arrival angle, r is the array radius and λ is the signal wavelength.

[0100] According to the attached Figure 3 , the subarrays are divided as follows:

[0101] Table 1: Division of subarrays

[0102]

[0103] The corresponding selection matrix is:

[0104]

[0105]

[0106] Step 2: Generate a data set based on the signal mathematical model, train a deep neural network with adaptive signal-to-noise ratio, and directly give a reasonable estimate value from the network for initialization of step 3;

[0107] For deep neural networks, it is a multi-layer perceptron architecture, which is divided into three parts: input layer, hidden layer and output layer. The number of neurons in the input layer should match the specific scene data, which is 36 in this scene; the number of neurons in the output layer is equal to the number of signal sources, which is 3 here; there are four layers in the middle hidden layer, and the number of neurons in each layer is equal.

[0108] Generate snapshot data according to the array signal model in step 1, obtain the covariance matrix corresponding to each subarray and vectorize it, and then obtain a training data set with 1.28 million samples, where the data set contains signal data under different signal-to-noise ratios, which enables the trained network to process data under different signal-to-noise ratios. Finally, construct a deep neural network for initialization based on the structural parameters.

[0109] The adjacent layers of the network are fully connected, and the calculation process is as follows:

[0110] s l =f(w l s l-1 +b l )

[0111] Among them, s l represents the output vector of the lth layer, w l represents the weight matrix of the lth layer, b l represents the bias vector of the lth layer, f() is the activation function, here is the ReLU function.

[0112] When performing a random search for hyperparameters, the corresponding search range is shown in the table:

[0113] Table 2. Search range of deep neural network hyperparameters

[0114]

[0115] According to random search, the optimal number of hidden layer neurons is 2048 and the learning rate is 10 -4 The optimizer used for parameter update is Adam. The training parameter settings of the deep neural network are shown in the table:

[0116] Table 3. Deep neural network training parameters

[0117]

[0118] The loss function used by deep neural networks is the cyclic mean square error, which is as follows:

[0119]

[0120] The output of this neural network gives the initial value of the direction of arrival angle to the deep expansion network in step 4.

[0121] Step 3: Based on the mathematical model of the sub-array signal, the wave direction parameter estimation form is derived according to the maximum likelihood criterion and solved in combination with the gradient ascent method; the deep expansion technology is then used to improve the method, and an end-to-end learning framework is constructed based on step 2 to achieve the purpose of directly obtaining the final wave direction estimation by inputting the array receiving data.

[0122] Four different selection matrices G divide the array containing 9 antennas into 4 independent sub-arrays. The sub-arrays are regarded as small full arrays, and the parameter estimation target is obtained according to the maximum likelihood criterion:

[0123]

[0124] in, is the sampling covariance matrix corresponding to the kth group of subarrays; y (k) (n) Generated based on the sub-array signal mathematical model.

[0125] The process of gradient ascent is as follows:

[0126]

[0127] Among them, the values ​​of the update step length are α θ =0.0005,α s =0.001,α σ =0.001.

[0128] During the parameter adjustment process, it was found that the step size used to update the arrival direction angle is the most critical and can directly affect the iteration result. This feature helps to initialize the step size of the subsequent deep expansion network. Experiments have shown that the estimation error of the simple model-based iteration result is large under low signal-to-noise ratio, which shows the necessity of deep expansion network.

[0129] The results of the deep neural network are directly input into the deep unfolding network for initialization. In the deep unfolding network, its structure is similar to the iterative likelihood part, and the core part is the gradient solution and parameter update. The formula used for the gradient solution is as follows:

[0130]

[0131] Where L is the likelihood function, is the received signal covariance matrix. According to the chain rule, we get

[0132]

[0133]

[0134] In the formula, θ, R s and is the network parameter.

[0135] The entire end-to-end learning architecture is shown in the attached Figure 1 As shown in the figure, in a complete training process, the parameters of the deep neural network and the deep unfolding network are updated simultaneously. The input of this learning architecture is the snapshot data received by the array or the corresponding covariance matrix, which is passed through the deep neural network to obtain a preliminary estimate of the direction of arrival angle, and then this value is used as the initial value of the deep unfolding network. After the network iteration, the final direction of arrival angle is directly obtained. Among them, if the number of iterations is too small, the network will not converge and the estimation error will be large; if the number of iterations is too large, more computing time will be consumed and efficiency will be reduced. After, the number of iterations is generally set to 8 to obtain better estimation performance while ensuring higher efficiency.

[0136] The specific direction finding scene parameter settings are as follows:

[0137] Table 4 Direction finding scenario parameters

[0138]

[0139] In the implementation process, RMSPE is used to measure the estimation accuracy to show the effect of this method. The form of this indicator in this scenario is as follows:

[0140]

[0141] In the experiment of the present invention, a data set generated according to the mathematical model of the subarray signal is used to verify the effectiveness of the present invention. The data in the data set is the covariance matrix of each subarray after vectorization, the label is the true direction of arrival angle, and the direction finding range is 2π. The data size in a single sample is 1×36, and the label is 1×3. The number of samples in the entire data set is 1.28 million, of which 1.08 million are used for network training and 200,000 are used for model testing.

[0142] All experiments were implemented using the Pytorch framework. The momentum of the Adam optimizer was 0.9, the weight decay was 0, the exponential decay rate of the first-order moment estimate was 0.9, and the exponential decay rate of the second-order moment estimate was 0.999.

[0143] The results of the method are as follows:

[0144] Table 5 Estimation error (unit: °)

[0145]

[0146] According to the experimental results, the accuracy of the estimation method in the present invention is much higher than that of the existing estimation method, and a high-precision estimation result can be achieved within the range of signal-to-noise ratio greater than 5dB. This shows that the end-to-end learning architecture can effectively improve the accuracy of wave direction estimation while ensuring interpretability.

[0147] In order to compare the complexity of different methods, the running time under different signal-to-noise ratios was measured. During the test, the software environment was Python, the hardware environment was Intel Core i7 9750H, and the number of samples was 1000.

[0148] Table 6 Comparison of running time of each method under different signal-to-noise ratios

[0149] method 0dB 20dB Generalized Least Squares 1495.57s 1259.45s Sparse Signal Representation 817.34s 727.56s The present invention 60.38s 59.87s

[0150] From the results, the calculation of the present invention consumes the least time, has the highest efficiency, and is not affected by the signal-to-noise ratio. However, the comparison algorithm requires more iterations at a lower signal-to-noise ratio, which leads to a decrease in efficiency.

[0151] The overall description of the method is as follows:

[0152]

[0153]

[0154] The specific description above further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. An end-to-end intelligent direction of arrival estimation method based on subarray sampling, characterized in that: The following steps are included: Step 1: Construct a mathematical model of subarray sampling signals; Step 2: Generate a data set based on the signal mathematical model, train a deep neural network with adaptive signal-to-noise ratio, and directly give a reasonable estimate value from the network for initialization of step 3; Step 3: Based on the mathematical model of the sub-array signal, the wave direction parameter estimation form is derived according to the maximum likelihood criterion and solved in combination with the gradient ascent method; the deep expansion technology is then used to improve the method, and an end-to-end learning framework is constructed based on step 2 to achieve the purpose of directly obtaining the final wave direction estimation by inputting the array receiving data.

2. The end-to-end intelligent direction of arrival estimation method based on subarray sampling according to claim 1, characterized in that: The implementation method of step one is: For far-field narrowband signal sources, when L far-field independent narrowband signals are simultaneously incident on an antenna array with M array elements, the corresponding full array signal model is: y(t)=A(θ)s(t)+η(t) (1) The signal vector is The noise vector is Manifold Matrix In the subarray sampling system, the number of array elements in each independent subarray is equal to the number of RF links, and the number of antennas between subarrays is equal; the antennas in the subarray group are sampled simultaneously, and the subarrays are sampled sequentially, and the division of the subarrays does not require the antennas to be mutually exclusive; for an array composed of M antennas, only W RF links are used to receive signals, where W < M; the sampling process is as follows: at a certain moment, there is only one group of antennas in the subarray that are sampled simultaneously; therefore, at any given sampling moment, each RF link is connected to only one antenna and the connection network has a total of K states; For each group of subarrays, N snapshot data are sampled; according to the subarray model, the nth sampled data of the kth subarray is expressed as follows y (k) (n)=G (k) (A(θ)s (k) (n)+η (k) (n)) (2) Among them, the noise signal is a cyclically symmetric complex Gaussian distribution, that is, Select the network matrix G (k) ∈{0,1} W×M represents the connection relationship between the RF link and the antenna unit in the kth subarray; the specific form of the manifold matrix A(θ) is related to the array geometry; θ represents the direction of arrival of the source signal; the source signal satisfies the cyclically symmetric complex Gaussian distribution, that is, y (k) (n) is the received signal of the array.

3. The end-to-end intelligent direction of arrival estimation method based on subarray sampling according to claim 2, characterized in that: The implementation method of step 2 is: The data set required for deep neural network training is constructed as follows: According to the mathematical model of the signal sampled by the subarray, the snapshot data corresponding to the kth subarray is obtained as Y k =G (k) (A(θ)S+η) (3) Among them, G (k) is the selection matrix corresponding to the selection network; A(θ) is the manifold matrix, θ is the incident direction of the source signal, that is, the wave arrival direction angle; S is the source signal, η is the noise, both of which satisfy the cyclic symmetric complex Gaussian distribution; In order to make the trained network have good estimation results for any angle within the field of view, the angle θ of the training data should be uniformly sampled within the direction finding range, that is, θ~U(0,β) (4) Where, for a uniform linear array, β = π; for a uniform circular array, β = 2π; The signal of the signal source satisfies the maximum likelihood model assumption and is a zero-mean cyclic symmetric complex Gaussian distribution. To facilitate data generation and network training, the power of the signal source is set to The power of the noise is adjusted according to the signal-to-noise ratio. The corresponding formula is as follows: By using the above data generation method, new data samples can be provided to the network at any time, so as to avoid overfitting in model training and make the trained network more robust. Divide the full array into several sub-arrays with the same number of antennas to obtain K groups of received signal data; directly using the data as network input will increase the parameter scale of the network and reduce the convergence speed; and if the signal sampling snapshot changes, the network input dimension needs to change accordingly, which will limit the network's scene practicality; therefore, it is necessary to preprocess the original data, which has three main functions: extract the characteristics of the original signal so that the network can more easily learn the mapping relationship between data and angles; decouple the data dimension from the number of snapshots so that the network can be applied to DOA estimation in different snapshot scenarios; convert the complex signal data into the real data required by the network; The covariance matrix of the data is used as the network input, and K covariance matrices are obtained by sampling data from K groups of subarrays: To perform dimension matching, the two-dimensional matrix data needs to be converted into one-dimensional vector data. The covariance matrix of the received signal is a Hermite matrix, that is, the matrix can be represented by real numbers equal to the number of matrix elements. The real and imaginary parts of the diagonal elements and upper half-angle elements of K matrices are extracted and concatenated into a vector. This vector is used as the input of the deep neural network. The dimension of the vector obtained after processing is KW 2 , this dimension is independent of the number of snapshots, so the deep neural network has no special requirements for the number of snapshots of received data; when generating the data set, the direction of arrival angle corresponding to each sample data is known, and it is directly used as a label for network training; The deep neural network is composed of a multi-layer perceptron and can process array signal data with different signal-to-noise ratios. The activation function in the network is the ReLU function, which gives the network the ability of nonlinear fitting while saving computing resources. The specific form is: ReLU(x)=max(0,x) (7) The loss function of the regression network is the mean square error: Where θ is the true direction of arrival angle, is the estimated direction of arrival angle; Since the angle in DOA estimation is periodic, the periodic mean square error can be used as the loss function: In addition, the average cycle error can be expressed as When estimating multiple sources, the loss function used should be: Among them, Π is a set of permutation matrices that can represent all permutations of angles; After convergence, the optimal permutation matrix is ​​constant, that is, the output of the network follows a fixed order; this indicates that during the training process, the mean of the sum of errors of all permutation orders can be used as the loss function; After training is completed, the periodic mean square error is used to measure the distance between the estimated value of the direction of arrival and the true value, as follows: The hyperparameters of the neural network structure are mainly divided into network structure parameters and training parameters; the structural parameters of the deep neural network include the number of hidden layers and the number of neurons in the hidden layer; the training parameters include the batch sample size, learning rate, and the number of epochs of data set iterations; the structural parameters determine the data representation ability of the neural network and affect the fitting and generalization performance; the training parameters affect the convergence speed, stability and performance of the given structural network; With the help of small-scale random search methods, it is possible to determine a hyperparameter combination with better performance in a shorter time. The basic principle of this method is to randomly select hyperparameter combinations within the range of hyperparameter values ​​to train the network and record the model parameters with the best performance. Each parameter extraction is independent without any prior information reference, so the final model effect often depends on the set parameter range. Deep neural networks compensate for information loss to a certain extent by learning from large amounts of data. However, since no prior knowledge of the model is introduced, the estimation accuracy is limited, so they are only used for initialization.

4. The end-to-end intelligent direction of arrival estimation method based on subarray sampling according to claim 3, characterized in that: The implementation method of step three is: The maximum likelihood criterion is to select the parameters that maximize the probability of the observed data; the source signal s(t) satisfies the cyclic symmetric complex Gaussian distribution, so that the received data depends only on the parameters and has nothing to do with the specific implementation of the signal; s(t)~CN(0,R s ) (13) Among them, R s is the covariance matrix of the signal, which is the power of the source signal in physical sense; The second-order characteristics of the source signal are as follows E[y(t i )y H (t j )]=0 (15) Among them, t i ,t j Represents different sampling times, R s is the Hermite matrix, δ ij is the Kronecker function, (·) H Represents the matrix conjugate transpose operation; According to the signal model, a single observation x(t i The probability density function of ) is Among them, R y is the covariance matrix of the array received signal; Since each snapshot data is independent of each other, the joint conditional probability of N snapshot data can be obtained, that is, the likelihood function Among them, y i represents the array receiving data at different times, θ represents the direction of arrival angle, R s represents the covariance matrix of the source signal, represents the noise power; Taking the negative logarithm of the likelihood function, we get N and M in the negative log-likelihood function are constants and not optimization parameters, so they can be ignored. After processing, the optimization target is obtained. in, is the sampling covariance matrix, obtained from the observed data; The above derivation is based on full array sampling. When sampling subarrays, since each subarray is independent of each other, the subarray is regarded as a small full array, and the above optimization objective form is modified as follows: in, is the sampling covariance matrix corresponding to the kth group of subarrays; y (k) (n) obtained by the subarray signal mathematical model described in step 1; Due to the introduction of subarray sampling technology, the optimization objective analytical expression is in the form of and, so the signal covariance matrix R cannot be obtained when the angle θ is fixed s and noise power The closed-form solution of θ cannot be transformed into a multidimensional search problem only about the angle θ. The gradient ascent method is used to solve the optimization target. The iterative process of the optimization variables is as follows: Among them, c [t] is the set of optimization variables, α [t] represents the update step size, P c (·) represents the mapping of set c; According to the subarray sampling signal data model, optimize the variables θ, R s and Independent of each other, block coordinate ascent is used for iterative update. At the same time, in order to accelerate the convergence process and improve performance, the update step size of the variable block is set independently; the complete iterative process is as follows: Where t represents the number of iterations; Combined with the mathematical model of subarray sampling signals, the specific form of the gradient in the iterative process is as follows: The result in step 2 is used as the initial value of the maximum likelihood method. However, the iterative process based entirely on the model cannot make the estimation method free from its dependence on accuracy, and it is also difficult to adapt to complex direction finding environments. Therefore, the deep unfolding technology is introduced to transform the iterative process into a deep unfolding network, and the network parameters are initialized according to the result of step 2, thereby forming an end-to-end learning framework. Deep unfolding maps the iterative method to the deep learning framework. In this framework, each iteration becomes a layer in the network. The operation of each layer simulates an iterative step of the original method, and the parameters are optimized in a data-driven way. The unfolding form of the network is the same as the update formula in step 2. Through this transformation, the iterative steps and parameter selections that originally required manual adjustment in the traditional method are automatically learned and adjusted by the network during the back-propagation training process. The parameters that need to be optimized are the direction of arrival angle θ, the source signal covariance matrix R s , Noise Power and update step size α; in this way, the unfolded deep network can take advantage of the powerful data processing capabilities of deep learning while maintaining the interpretability of the method; After the introduction of deep unfolding technology, the deep neural network part and the iterative part form a complete end-to-end framework. From a data perspective, its input is the covariance matrix of each sub-array snapshot data or the IQ data of the array, and the output is the final direction of arrival estimation result. From the functional composition point of view, the deep neural network part completes the estimation initialization, and the deep unfolding network iteratively updates according to the initial value to obtain a more accurate direction of arrival estimate.

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