An array super-resolution direction-of-arrival estimation method

Abstract

The present invention discloses an array super-resolution direction-of-arrival estimation method. Based on the information in the autocorrelation matrix of the received signal, a two-stage deep neural network structure is adopted. The first part determines the 1° interval where the signal angle is located, and the second part specifically estimates the signal angle on a grid with higher resolution. The combination of the two realizes the accurate estimation of the signal incident angle, including off-grid signals in the general sense, and can achieve a resolution level of 0.01°. The present invention innovatively uses a two-stage network architecture, which effectively avoids the problems of excessive neural network parameters and long training time while achieving ultra-high-resolution direction-of-arrival estimation, and has simple calculation and fast response, meeting the requirements of practical applications.

Description

Technical Field

[0001] The present invention belongs to the field of direction of arrival (DOA) estimation, and particularly relates to a super-resolution DOA estimation method based on deep learning. Background Art

[0002] Direction of Arrival (DOA) estimation is a research problem with a long history in the fields of radar and wireless communication, and is an important branch of array signal processing. The commonly used classical super-resolution DOA estimation algorithms include the Multiple Signal Classification (MUSIC) algorithm proposed by American scholar Schmidt in 1986. By separating the signal subspace and the noise subspace, a spatial pseudospectrum is constructed to achieve the leap from traditional estimation methods to super-resolution DOA estimation. Similarly successful is the Estimation of Signal Parameters via Rotational Invariance (ESPRIT) algorithm, which realizes super-resolution DOA estimation through the rotational invariance between different sub-arrays of the array. Many variants of these two algorithms have also emerged later and have been further studied and developed.

[0003] Deep learning is a popular non-linear algorithm. With the rapid development of computer technology in recent years, the powerful ability of deep learning to solve problems has become increasingly prominent, and its applications have also been extended to various fields, including DOA estimation of array signals. Since deep learning for DOA estimation has many unique advantages compared with traditional methods, it has become a very attractive research direction for researchers in recent years. First of all, the deep learning method is only time-consuming during network training. After training is completed and applied to DOA estimation, results can be obtained quickly. Its fast and efficient characteristics are of great significance for practical applications. Secondly, after the network training is completed, there is no need to perform complex operations on the input parameters, and the estimation results can be obtained through simple addition and subtraction, which better meets the needs of practical applications. Finally, the deep learning network can also extract data features well with lower signal-to-noise ratio and fewer snapshots, showing good robustness.

[0004] At present, there are some methods for DOA estimation based on deep learning. However, in previous studies on DOA estimation based on deep learning, grids with an interval of 1° were used for training. However, the actual signals are usually off-grid signals, that is, the target angle contains a decimal part. The angle of off-grid signals in the general sense is accurate to two decimal places, and the decimal part is ignored at this time. When the true angle of the signal is not exactly on the grid, a large estimation error will occur, and the performance of DOA estimation will also decrease, so a higher angular resolution needs to be considered. In addition, using grids with larger intervals for training will ignore a lot of information about the decimal part of the signal angle. Reducing the spacing of the grid, or increasing the angular resolution, is an effective way to improve the estimation accuracy, but in the deep learning method, this means increasing the length of the output vector, and the problem that the network parameters will increase greatly. Therefore, it is necessary to design a reasonable network model to improve the estimation accuracy while avoiding the problem of too many network parameters. Summary of the invention

[0005] Purpose of the invention: In view of the limitations of angular resolution encountered in existing deep learning-based DOA estimation methods, mainly off-grid signals in a general sense, a new two-stage neural network structure is proposed for direction of arrival estimation. After accurately estimating the target angle using a grid with an interval of 1°, the decimal part of the signal angle is further estimated, achieving a resolution of 0.01°.

[0006] Technical solution: A method for estimating the direction of arrival of an array signal with ultra-high resolution, comprising the following steps:

[0007] (1) Determine the number K of incident signals, the angle range, the angle space to be estimated, and the angle resolution;

[0008] (2) Determine the receiving array model, number of array elements N, wavelength λ, array element spacing d, and noise type;

[0009] (3) Determine the number of snapshots L of the received signal, randomly generate an incident signal according to the angle space to be estimated and the signal-to-noise ratio, and calculate the snapshots of the received signal;

[0010] (4) Estimate the autocorrelation matrix of the received signal from its snapshots, perform preprocessing, and obtain a real vector as the training input of the neural network;

[0011] (5) Preprocess the actual angle of the incident signal and perform vector encoding to obtain two vectors as training labels for the neural network;

[0012] (6) Integrate the input and labels into a dataset, divide it into a training set and a validation set, build a neural network and train it. Adjust the network parameters and structure according to the loss curves of the training set and the validation set during the training process to obtain a high-resolution direction-of-arrival estimation neural network model, reducing the estimation error to the level of 0.01°;

[0013] (7) Apply the direction-of-arrival estimation neural network model obtained in step (6) to perform DOA estimation. Randomly generate an incident signal at a certain angle within the angle range, repeat the data processing flow in step (4) to obtain the input of the neural network, use the trained neural network model to perform angle estimation, obtain the output vector and process it, calculate the estimated angle and output it.

[0014] In step (1), the number of incident signals K = 1, the signal is a Gaussian signal, and the angle search range is φ min to φ max , and the angle resolution is Δφ = 0.01°.

[0015] In step (2), the element spacing is half of the wavelength, i.e., d = λ / 2, and the noise is additive white Gaussian noise, which is uncorrelated with the signal.

[0016] In step (3), the received signal is y(t) = A(θ)s(t) + n(t), t = 1, …, L; s(t) is the incident signal, n(t) is the additive white Gaussian noise, A(θ) is the steering vector matrix, and y(t) represents the sampling of the received signal at time t.

[0017] In step (4), the estimated value of the autocorrelation matrix of the received signal is The preprocessing is to take the real values on the diagonal and the real and imaginary parts of the lower triangular part to form a real vector:

[0018]

[0019] where τ i,j , i, j ∈ {1, 2, …, N} represent the element in the i-th row and j-th column of the matrix R y , and represent the real part and the imaginary part respectively, and the obtained vector x is the input of the model, with a length of N 2 .

[0020] In step (5), the first label is a vector z1 with a length of φ max -φ min +1, representing a large grid with a resolution of Δφ = 1°. For the target angle θ j , the corresponding label is only at round(θ j) takes the value of 100 at the corresponding grid point and 0 at other positions, θ j Accurate to two decimal places; the second label is a vector z2 of length 100, representing a small grid range with a resolution of 0.01° centered on the grid point determined by the first part. Only at θ j -round(θ j ) takes the value of 100 at the corresponding grid point and 0 at other positions.

[0021] In the said step (6), the data set is The said neural network has a two-stage structure, including two parts. The first part contains five fully connected layers, and the second part contains six fully connected layers, with a total of eleven fully connected layers and two outputs.

[0022] In the said step (7), the processing of the output is to find the maximum value of the two vectors and add the corresponding integer angle and decimal angle.

[0023] Beneficial effects: Based on the previous DOA estimation method of deep learning, the present invention trains the integer and decimal parts of the off-grid signal separately with two parts of the network. The first part determines the position on the grid at 1° intervals of the angle, that is, the 1° interval range where the target angle is located. The second part combines the original input with the output of the first part to obtain a more accurate decimal part of the angle within the range determined by the first part. Thus, without increasing too many training parameters and the length of the output vector, useful information can be extracted from the data and a more accurate and ultra-high resolution DOA estimation can be achieved. The entire network consists of fully connected layers, with few model parameters, simple and fast calculations, and has good practical application prospects. Description of the Drawings

[0024] Figure 1 is a model diagram of a uniform linear array (ULA);

[0025] Figure 2 is a flow chart of the direction of arrival estimation of the neural network designed by the present invention;

[0026] Figure 3 is a schematic diagram of label setting;

[0027] Figure 4 is a model diagram of the neural network designed by the present invention;

[0028] Figure 5 is the loss decline curve during the training of the first part of the neural network of the present invention;

[0029] Figure 6 is the loss decline curve during the training of the second part of the neural network of the present invention;

[0030] Figures 7a - 7d The outputs after the signal data with incident angles of -27.43° and 13.29° at a signal-to-noise ratio of 5 dB pass through the network respectively, where Figure 7a and Figure 7c are the outputs of the first part of the network, Figure 7b and Figure 7d are the outputs of the second part of the network;

[0031] Figures 8a - 8d are the outputs after the signal data with incident angles of -27.43° and 13.29° at a signal-to-noise ratio of 20 dB pass through the network respectively, where Figure 8a and Figure 8c are the outputs of the first part of the network, Figure 8b and Figure 8d are the outputs of the second part of the network;

[0032] Figure 9 is the RMSE graph of the direction-of-arrival estimation of the neural network of the present invention under different signal-to-noise ratios. Detailed implementation manners

[0033] The present invention will be further explained below with reference to the accompanying drawings.

[0034] The following parameters and settings are adopted. The number of array elements N = 12, and a uniform linear array (ULA) with an element spacing of half a wavelength is used. The number of signal sources K = 1. According to the number of array elements, the length of the DNN input vector is 144. The DOA range is from -60° to 60°. Considering an angular resolution of 0.01°, there are a total of 12001 incident angle cases. At each signal-to-noise ratio, 12001×5 = 60005 data are randomly generated. The inputs for training and testing are real vectors obtained after preprocessing the estimated value of the autocorrelation matrix, and L = 100 snapshots of the received signal are used for calculation. To train the proposed model, we used the data at high signal-to-noise ratios {25, 26, 27, 28, 29, 30} dB, and the total number of samples is D = 6×60005 = 360030.

[0035] The DNN network of the present invention adopts an offline training method. The data set is divided into a training set (90%) and a validation set (10%). Adaptive moment estimation (Adam) is used to update / optimize the parameters. The initial learning rate is set to 0.0001, and the loss weights of the two parts of the network are 1 and 0.1 respectively. The training batch size is 1000, and 500 epochs are trained. The network is built with Keras. The operating system is Windows, the processor is Intel i7-9750H, and the GPU is NVIDIA GeForce RTX 2060.

[0036] Build a neural network model as shown in Figure 4 , and train it with a dataset. During the training process, the loss curves of the two outputs of the network are respectively as shown in Figure 5 and Figure 6 . After the training is completed, the output of the model at a fixed angle under different signal-to-noise ratio conditions is tested, and the outputs and functions of the two parts of the model are roughly observed. The two target angles used in the test are -27.43° and 13.29° respectively. Figure 7 shows the estimation results of the two angles when the signal-to-noise ratio is 5 dB and the number of snapshots is 100. Among them, Figure 7(a) and (c) are the output results of the first part of the model. It can be seen that the peaks of the outputs coincide exactly with the true labels, and the corresponding results are -27° and 13° respectively, determining a very accurate candidate region, and the angles to be estimated are respectively limited to the intervals [-27.5, -26.5) and [12.5, 13.5). Then, Figure 7(b) and (d) are the output results of the second part of the model, and more accurate angles are obtained within the intervals determined by the first part. The output result in (b) is -0.36°, and the output result in (d) is 0.19°. Therefore, the estimated angles are -27° + (-0.36°) = -27.36° and 13° + 0.19° = 13.19° respectively, with differences of 0.07° and 0.1° from the actual results respectively. Obviously, the error between the estimated result and the true value is already very small, reduced to the level of 0.1° or even lower.

[0037] Figure 8 shows the estimation results of the two angles when the signal-to-noise ratio is 20 dB and the number of snapshots is 100. Similarly, in Figure 8(a) and (c), the first part of the model accurately obtains the candidate region, and more accurate results are output in the second part. The output in Figure 8(b) is -0.44°, and the output in Figure 8(d) is 0.25°. Therefore, the results estimated by the DNN are -27.44° and 13.25° respectively, with differences of 0.01° and 0.04° from the true values respectively. Obviously, when the signal-to-noise ratio is increased, the performance of the DNN is also improved, and the estimated values of the model are more accurate.

[0038] As shown in Figure 9 , the RMSE of the DOA estimation of the neural network of the present invention under different signal-to-noise ratios can be seen. Even under low signal-to-noise ratio conditions, the estimation error is reduced to about 0.1°, and even under high signal-to-noise ratio conditions, the error is controlled within about 0.02 - 0.03°.

[0039] The present invention divides the DOA estimation into two steps and designs a two-stage network. The first part of the network can accurately estimate the target angle at the 1° level with an accuracy close to 100%. On this basis, the second part further estimates the target angle with a resolution of 0.01°, controls the error within a very limited range, and can achieve precise estimation of off-grid signals.

[0040] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. An array super-resolution direction-of-arrival estimation method, characterized in that, It includes the following steps: (1) Determine the number K of incident signals, the angle range, the angle space to be estimated, and the angle resolution; (2) Determine the receiving array model, the number N of array elements, the wavelength λ and the element spacing d, and the noise type; (3) Determine the number of snapshots L of the received signal, randomly generate incident signals according to the angle space to be estimated and the signal-to-noise ratio, and calculate the snapshots of the received signal; (4) Estimate the autocorrelation matrix of the received signal snapshots, perform preprocessing, and obtain a real vector as the training input of the neural network; (5) Preprocess the actual angles of the incident signals and perform vector encoding to obtain two vectors as the training labels of the neural network; (6) Integrate the input and labels into a data set, divide it into a training set and a validation set, build and train a neural network, adjust the network parameters and structure according to the loss curves of the training set and the validation set during the training process, and obtain a high-resolution direction-of-arrival estimation neural network model to reduce the estimation error to the 0.01° level; (7) Apply the direction-of-arrival estimation neural network model obtained in step (6) to perform DOA estimation, randomly generate an incident signal at an angle within the angle range, repeat the data processing process in step (4) to obtain the input of the neural network, use the trained neural network model to perform angle estimation, obtain the output vector and process it, calculate the estimated angle and output it; In step (1), the number of incident signals K = 1, the signal is a Gaussian signal, and the angle search range is φ min to φ max , and the angle resolution is Δφ = 0.01°; In step (5), the first label is a vector z1 of length φ max -φ min +1, representing a large grid with a resolution of Δφ = 1°, for the target angle θ j , and the corresponding label takes the value 100 only at the grid point corresponding to round(θ j ), and is 0 at other positions. θ j is accurate to two decimal places; the second label is a vector z2 of length 100, representing a small grid range with a resolution of 0.01° centered on the grid point determined in the first part, and takes the value 100 only at the grid point corresponding to θ j -round(θ j ), and is 0 at other positions.

2. The method for array super-resolution direction-of-arrival estimation according to claim 1, characterized in that: In step (2), the element spacing is half of the wavelength, i.e., d = λ / 2, and the noise is additive white Gaussian noise, which is uncorrelated with the signal.

3. The method for array super-resolution direction-of-arrival estimation according to claim 1, characterized in that: In step (3), the received signal is y(t) = A(θ)s(t) + n(t), t = 1,..., L; s(t) is the incident signal, n(t) is the additive white Gaussian noise, A(θ) is the steering vector matrix, and y(t) represents the sampling of the received signal at time t.

4. The method for estimating the direction of arrival of an array super-resolution according to claim 1, characterized in that: In step (4), the estimated value of the autocorrelation matrix of the received signal is The preprocessing is to take the real values of the diagonal and the real and imaginary parts of the lower triangular part to form a real vector: where τ i,j , i, j ∈ {1, 2, ..., N} represent the element at the i-th row and j-th column of the matrix R y , and the real and imaginary parts are represented by and respectively. The resulting vector x is the input of the model, with a length of N 2 .

5. The method for array super-resolution direction-of-arrival estimation according to claim 1, wherein: In step (6), the data set is The neural network has a two-stage structure, including two parts. The first part contains five fully connected layers, and the second part contains six fully connected layers, with a total of eleven fully connected layers and two outputs.

6. The method for array super-resolution direction-of-arrival estimation according to claim 1, wherein: In step (7), the processing of the output is to find the maximum value of the two vectors and add the corresponding integer angle and decimal angle.

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