Single-bit direction of arrival estimation method and system with signal amplitude recovery function, terminal and storage medium

Abstract

The invention discloses a single-bit direction of arrival estimation method and system with signal amplitude recovery, a terminal and a storage medium, and the method comprises the steps: obtaining each snapshot time signal from a signal source of a uniform linear array receiver, introducing a non-zero threshold value to carry out the single-bit quantization of each snapshot time signal, and obtaining a signal model; reconstructing the signal model, replacing a sign function of the reconstructed signal model with a smooth hyperbolic tangent function, and performing reconstruction to obtain a target signal model; based on the target signal model, constructing a single-bit DOA estimation optimization problem by using a truncated Frobenius norm and an L2, 0 norm, and converting the optimization problem into a target optimization problem by using a semi-quadratic technology; and solving a target optimization problem by using a near-end alternating minimization algorithm and a forward-backward splitting algorithm to obtain a signal source estimation direction, a signal source estimation number and a signal estimation amplitude. According to the method, the amplitude of the signal source is accurately estimated while the prior dependence on the number of the signal source is eliminated.

Description

Technical Field

[0001] The present invention relates to the field of radar signal processing, and in particular to a single-bit arrival direction estimation method, system, terminal and computer-readable storage medium with signal amplitude recovery. Background Art

[0002] Single-bit DOA (Direction Of Arrival) estimation is a technology that uses a single-bit analog-to-digital converter to retain only the symbol information of the received signal and estimate the signal direction based on it. A single-bit analog-to-digital converter (ADC) can be regarded as the simplest ADC converter, which significantly reduces the burden of data storage, transmission and processing by abandoning high-precision quantization and data bit number.

[0003] Source DOA estimation methods can be roughly divided into two categories: subspace methods and sparse recovery-based algorithms. The subspace method uses a known single-bit covariance matrix to estimate the signal subspace, and then searches for the direction of arrival through algorithms such as multi-signal classification. Compared with the subspace method, the sparse recovery-based method shows better performance in scenarios with low snapshot counts, low signal-to-noise ratios, and even strong coherent signals.

[0004] However, the existing single-bit DOA method based on sparse regularization still needs to rely on grid search to determine the appropriate regularization parameters to determine the number of target signal sources, and the existing method cannot estimate the signal amplitude, which limits the dynamic range of the radar system and affects the radar system's ability to detect and distinguish signals within a wide power range.

[0005] Therefore, the prior art still needs to be improved and developed. Summary of the invention

[0006] The main purpose of the present invention is to provide a single-bit direction of arrival estimation method, system, terminal and computer-readable storage medium with signal amplitude recovery, aiming to solve the problem that the single-bit DOA method based on sparse regularization in the prior art still needs to rely on grid search to determine the number of target signal sources and cannot estimate the signal amplitude, resulting in limited dynamic range of the radar system and low DOA estimation accuracy.

[0007] To achieve the above object, the present invention provides a single-bit direction of arrival estimation method with signal amplitude recovery, the single-bit direction of arrival estimation method with signal amplitude recovery comprising the following steps: Acquire each snapshot moment signal from a signal source of a uniform linear array receiver, introduce a non-zero threshold to perform single-bit quantization on each snapshot moment signal, and obtain a signal model; Reconstructing the signal model, replacing the sign function of the reconstructed signal model with a smooth hyperbolic tangent function to obtain a replaced model, and reconstructing the replaced model to obtain a target signal model; Based on the target signal model, the truncated Frobenius norm and L 2,0 The single-bit DOA estimation optimization problem is constructed by using a semi-quadratic technique, and the optimization problem is converted into a target optimization problem; The target optimization problem is solved using a proximal alternating minimization algorithm and a forward-backward splitting algorithm to obtain a signal source estimation direction, a signal source estimation number, and a signal estimation amplitude.

[0008] Optionally, the single-bit arrival direction estimation method with signal amplitude recovery, wherein the step of acquiring each snapshot moment signal from a signal source of a uniform linear array receiver, introducing a non-zero threshold to perform single-bit quantization on each snapshot moment signal, and obtaining a signal model, specifically includes: Acquire each snapshot time signal from the signal source of the uniform linear array receiver, the uniform linear array receiver is an array manifold matrix : ; ; in, is the steering vector corresponding to the direction of arrival angle of the first narrowband signal, is the steering vector corresponding to the direction of arrival angle of the second narrowband signal, For the The steering vector corresponding to the direction of arrival angle of a narrowband signal, For the The steering vector corresponding to the direction of arrival angle of a narrowband signal, is a natural constant, is an imaginary unit, For the The direction of arrival angle of a narrowband signal, is the adjacent array element spacing of the uniform linear array receiver, is the wavelength of the incident signal, is the total number of array elements of the uniform linear array receiver, represents transpose; Introduce a non-zero threshold to perform single-bit quantization on the snapshot signals to obtain a signal model : ; ; ; ; in, is the sign function of complex numbers, is the signal source matrix to be estimated, is the noise vector, is the quantization threshold matrix, is the symbolic function, and are the real and imaginary parts of the complex number, is the total number of snapshots, are the signals of each signal source in the first snapshot, are the signals of each signal source in the second snapshot, For the The signal of each signal source in the snapshot, For the The signal of each signal source in the snapshot, For the The noise vector when the sensor receives the signal in the snapshot, For the The noise vector when the sensor receives the signal in the snapshot, For the The noise vector when the sensor receives the signal in the snapshot, For the The noise vector when the sensor receives the signal in each snapshot.

[0009] Optionally, the single-bit arrival direction estimation method with signal amplitude recovery, wherein the signal model is reconstructed, a sign function of the reconstructed signal model is replaced with a smooth hyperbolic tangent function to obtain a replaced model, and the replaced model is reconstructed to obtain a target signal model, specifically comprising: The signal model Reconstruct the signal and transfer the noise from the inside to the outside of the symbol function to obtain the reconstructed signal model. : ; in, is a noise matrix, wherein the real part and the imaginary part of each element in the noise matrix are respectively between -2, 0 and 2; The reconstructed signal model is replaced by a smooth hyperbolic tangent function The symbol function of the replaced signal model is obtained : ; ; in, is the approximate error term, is the complex hyperbolic tangent function, is the hyperbolic tangent function; The replaced model Reconstruct and obtain the target signal model : ; ; ; in, is the target manifold matrix, is the target signal source matrix, is the real-valued identity matrix, To transform the array manifold matrix With the quantization threshold matrix Perform a merge operation. To transform the signal source matrix The transpose of the real-valued identity matrix Perform a merge operation.

[0010] Optionally, the single-bit arrival direction estimation method with signal amplitude recovery, wherein the truncated Frobenius norm and L are used based on the target signal model. 2,0 The single-bit DOA estimation optimization problem is constructed by using the semi-quadratic technique, and the optimization problem is converted into a target optimization problem, which specifically includes: Based on the target signal model , using the truncated Frobenius norm and L 2,0 The norm constructs the single-bit DOA estimation optimization problem: ; Make ; in, is the truncated Frobenius norm, is the penalty parameter, For L 2,0 norm, represents the number of matrix rows, is the target signal source matrix Before OK; The optimization problem is transformed into a tractable target optimization problem using semi-quadratic techniques: ; Make ; in, is the Frobenius norm, is a function that acts on the real and imaginary parts separately.

[0011] Optionally, the single-bit arrival direction estimation method with signal amplitude recovery, wherein the use of a proximal alternating minimization algorithm and a forward-backward splitting algorithm to solve the target optimization problem to obtain a signal source estimated direction, a signal source estimated number and a signal estimated amplitude, specifically includes: Use a proximal alternating minimization algorithm to obtain a first iterative process in complex form and a second iterative process in complex form for the target optimization problem, use a forward-backward splitting algorithm to solve the first iterative process in complex form, solve the second iterative process in complex form element by element, and calculate the estimated direction of the signal source and the estimated number of the signal source according to the solution results; From the array manifold matrix Extract the corresponding columns, construct a column matrix, extract the corresponding rows from the signal source matrix, construct a row matrix, perform signal modeling and rewrite according to the column matrix and the row matrix to obtain a real-valued signal model, and obtain an amplitude estimation problem according to the real-valued signal model; A proximal alternating minimization algorithm is used to obtain the first iterative process and the second iterative process in real form of the amplitude estimation problem, the first iterative process in real form is solved using a forward-backward splitting algorithm, and the second iterative process in real form is solved using an element-by-element solution method, and the signal estimation amplitude is calculated based on the solution results.

[0012] Optionally, the single-bit arrival direction estimation method with signal amplitude recovery, wherein the use of the proximal alternating minimization algorithm to obtain the complex form of the first iterative process and the complex form of the second iterative process of the target optimization problem, the use of the forward-backward splitting algorithm to solve the complex form of the first iterative process, the element-by-element solution of the complex form of the second iterative process, and the calculation of the signal source estimation direction and the signal source estimation number according to the solution results, specifically includes: The first iteration process of the complex form of the target optimization problem is obtained using the proximal alternating minimization algorithm and the second iteration of the plural form : ; ; ; in, is the number of iterations in the proximal alternating minimization algorithm, is a minimum value greater than zero, In the second iteration, the plural form The previous iteration of iteration, The first iteration of the plural form The previous iteration of iteration, To calculate the intermediate quantity; The first iteration process of the complex form of the target optimization problem is obtained using the proximal alternating minimization algorithm and the second iteration of the plural form : ; ; ; in, is the number of iterations in the proximal alternating minimization algorithm, is a minimum value greater than zero, In the second iteration, the plural form The previous iteration of iteration, The first iteration of the plural form The previous iteration of iteration, To calculate the intermediate quantity; The first iteration process of the complex form is to use the forward-backward splitting algorithm Solve and get the first iterative update formula , the second iteration update formula And the third iteration update formula : ; ; ; in, is the number of iterations in the forward-backward splitting algorithm, is the stride control parameter, which is used to control the stride of the update process. yes Relative to The gradient of For the The next proximal alternating minimization algorithm and The iterative process of the forward-backward splitting algorithm, for In the previous iteration of the forward-backward splitting algorithm, is the i-th row, For storage space, is the array manifold matrix The number of columns, The quantization threshold matrix The number of columns, is the L2 norm; The second iteration process for the plural form Solve element by element to obtain a solution result, and according to the solution result, the first iterative update formula, the second iterative update formula and the third iterative update formula, Iterations, calculate the first target solution ; According to the first target solution, the estimated direction and number of signal sources are calculated: ; ; in, The first to S lines are the first target solution The corresponding matrix solution is, for No. L2 norm of row vector; right The peak value in the signal is identified to determine the estimated direction and number of signal sources.

[0013] Optionally, the single-bit arrival direction estimation method with signal amplitude recovery, wherein the array manifold matrix Extract the corresponding columns, construct a column matrix, extract the corresponding rows from the signal source matrix, construct a row matrix, perform signal modeling and rewrite according to the column matrix and the row matrix to obtain a real-valued signal model, and obtain an amplitude estimation problem according to the real-valued signal model, specifically including: Assume that the estimated The far-field and uncorrelated signals are ,in, For the The direction of arrival angle of a narrowband signal, For the The direction of arrival angle of a narrowband signal, For the The direction of arrival angle of a narrowband signal, For the The direction of arrival angle of a narrowband signal; From the array manifold matrix Extracted from Corresponding columns, construct column matrix , from the signal source matrix Extracted from Corresponding rows, construct row matrix , according to the column matrix and the row matrix Get the signal amplitude model : ; The signal amplitude model The real-valued signal model rewritten in real-valued form : ; in, , , and They are , , and The real-valued form of ; According to the real-valued signal model , we get the amplitude estimation problem: ; in, is a convex set.

[0014] In addition, to achieve the above object, the present invention further provides a single-bit direction of arrival estimation system with signal amplitude recovery, wherein the single-bit direction of arrival estimation system with signal amplitude recovery comprises: A signal model generation module, used to obtain each snapshot moment signal from a signal source of a uniform linear array receiver, introduce a non-zero threshold to perform single-bit quantization on each snapshot moment signal, and obtain a signal model; A signal model reconstruction module is used to reconstruct the signal model, replace the sign function of the reconstructed signal model with a smooth hyperbolic tangent function to obtain a replaced model, and reconstruct the replaced model to obtain a target signal model; The optimization problem building module is used to use the truncated Frobenius norm and L based on the target signal model. 2,0 The single-bit DOA estimation optimization problem is constructed by using a semi-quadratic technique, and the optimization problem is converted into a target optimization problem; The optimization problem solving module is used to solve the target optimization problem by using the proximal alternating minimization algorithm and the forward-backward splitting algorithm to obtain the signal source estimation direction, the signal source estimation number and the signal estimation amplitude.

[0015] In addition, to achieve the above-mentioned purpose, the present invention also provides a terminal, wherein the terminal includes: a memory, a processor, and a single-bit arrival direction estimation program with signal amplitude recovery stored in the memory and run on the processor, and when the single-bit arrival direction estimation program with signal amplitude recovery is executed by the processor, the steps of the single-bit arrival direction estimation method with signal amplitude recovery as described above are implemented.

[0016] In addition, to achieve the above-mentioned purpose, the present invention also provides a computer-readable storage medium, wherein the computer-readable storage medium stores a single-bit arrival direction estimation program with signal amplitude recovery, and when the single-bit arrival direction estimation program with signal amplitude recovery is executed by a processor, the steps of the single-bit arrival direction estimation method with signal amplitude recovery as described above are implemented.

[0017] In the present invention, each snapshot signal from the signal source of the uniform linear array receiver is obtained, and a non-zero threshold is introduced to perform single-bit quantization on each snapshot signal to obtain a signal model; the signal model is reconstructed, and the sign function of the reconstructed signal model is replaced by a smooth hyperbolic tangent function and reconstructed to obtain a target signal model; based on the target signal model, the truncated Frobenius norm and L 2,0 The single-bit DOA estimation optimization problem is constructed by using the norm, and the optimization problem is converted into a target optimization problem by using the semi-quadratic technique; the target optimization problem is solved by using the proximal alternating minimization algorithm and the forward-backward splitting algorithm to obtain the signal source estimation direction, the signal source estimation number and the signal estimation amplitude. The present invention eliminates the prior dependence on the number of signal sources and makes an accurate estimation of the signal source amplitude, thereby improving the accuracy of DOA estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 It is a flow chart of a preferred embodiment of a single-bit arrival direction estimation method with signal amplitude recovery of the present invention; Figure 2 It is a schematic diagram of a uniform linear array receiver with a single-bit arrival direction estimation method with signal amplitude recovery according to the present invention; Figure 3 It is a performance comparison diagram under different fast signal-to-noise ratios in the single-bit arrival direction estimation method with signal amplitude recovery of the present invention; Figure 4 It is a performance comparison diagram under different target numbers in the single-bit arrival direction estimation method with signal amplitude recovery of the present invention; Figure 5 It is a performance comparison diagram under different snapshot numbers in the single-bit arrival direction estimation method with signal amplitude recovery of the present invention; Figure 6 It is a performance comparison diagram of the single-bit arrival direction estimation method with signal amplitude recovery under different numbers of antennas in the present invention; Figure 7 It is a structural diagram of a preferred embodiment of the single-bit arrival direction estimation system with signal amplitude recovery of the present invention; Figure 8 It is a structural diagram of a preferred embodiment of the terminal of the present invention. DETAILED DESCRIPTION

[0019] The present application provides a single-bit direction of arrival estimation method, system and terminal with signal amplitude recovery. In order to make the purpose, technical solution and effect of the present application clearer and more specific, the present application is further described in detail with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0020] It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as those generally understood by those skilled in the art to which this application belongs. It should also be understood that terms such as those defined in general dictionaries should be understood to have meanings consistent with those in the context of the prior art, and will not be interpreted with idealized or overly formal meanings unless specifically defined as here.

[0021] In addition, if there are descriptions involving "first", "second", etc. in the embodiments of the present invention, the descriptions of "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or suggesting their relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features. In addition, the technical solutions between the various embodiments can be combined with each other, but they must be based on the ability of ordinary technicians in the field to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such a combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0022] The single-bit arrival direction estimation method with signal amplitude recovery described in the preferred embodiment of the present invention is as follows: Figure 1 As shown, the single-bit arrival direction estimation method with signal amplitude recovery includes the following steps: Step S10: acquiring each snapshot moment signal from a signal source of a uniform linear array receiver, introducing a non-zero threshold to perform single-bit quantization on each snapshot moment signal, and obtaining a signal model.

[0023] Specifically, consider a Uniform Linear Array (ULA) composed of array elements, with a spacing of adjacent array elements Need to meet , is the wavelength of the incident signal. Assume that the total number is If the far-field and uncorrelated narrowband signals are incident on the array from different directions, the uniform linear array receiver will be Figure 2 As shown (where is an arbitrary direction of arrival angle).

[0024] Acquire each snapshot time signal from the signal source of the uniform linear array receiver, the uniform linear array receiver is an array manifold matrix , the array manifold matrix It refers to the matrix of the phase relationship of S narrowband signals received from different directions by M antennas in the antenna array, which can be expressed as: ; ; in, is the steering vector corresponding to the direction of arrival angle of the first narrowband signal, is the steering vector corresponding to the direction of arrival angle of the 2-th narrowband signal, For the The steering vector corresponding to the direction of arrival angle of a narrowband signal, For the The steering vector corresponding to the direction of arrival angle of a narrowband signal, is a natural constant, is an imaginary unit, The number of narrowband signals is The direction of arrival angle of the signal, is the adjacent array element spacing of the uniform linear array receiver, is the wavelength of the incident signal, is the total number of array elements of the uniform linear array receiver, Indicates transpose.

[0025] Furthermore, a non-zero threshold is introduced to perform single-bit quantization on the snapshot signals to obtain a signal model : ; ; ; ; in, is the sign function of complex numbers, is the signal source matrix to be estimated, is the noise vector, is the quantization threshold matrix, is a sign function (returns 1, 0, or -1 depending on the sign of the input value. When the input value is positive, it returns 1; when the input value is negative, it returns -1; when the input value is zero, it returns 0). and are the real and imaginary parts of the complex number, is the total number of snapshots, are the signals of each signal source in the first snapshot, are the signals of each signal source in the second snapshot, For the The signal of each signal source in the snapshot, For the The signal of each signal source in the snapshot, For the The noise vector when the sensor receives the signal in the snapshot, is the noise vector when the sensor receives the signal in the second snapshot, For the The noise vector when the sensor receives the signal in the snapshot, For the The noise vector when the sensor receives the signal in each snapshot.

[0026] Step S20, reconstructing the signal model, using a smooth hyperbolic tangent function to replace the sign function of the reconstructed signal model to obtain a replaced model, and reconstructing the replaced model to obtain a target signal model.

[0027] Specifically, single-bit quantization blurs the noise distribution. In order to select a suitable loss function in the optimization problem modeling stage to ensure reliable estimation performance, the signal model is Reconstruct the signal and transfer the noise from the inside to the outside of the symbol function to obtain the reconstructed signal model. : ; in, is a noise matrix, and the real part and the imaginary part of each element in the noise matrix take values ​​between -2, 0 and 2 respectively.

[0028] It is understandable that the signal model The noise component in is transferred from the inside of the sign function to the outside, and the different distribution or intensity of the noise only affects The number of nonzero elements in .

[0029] Further, the reconstructed signal model is replaced by a smooth hyperbolic tangent function The symbol function of the replaced signal model is obtained : ; ; in, is the approximate error term, is the complex hyperbolic tangent function, is the hyperbolic tangent function; Furthermore, the non-zero threshold provides information about The prior information of the amplitude, this embodiment is for the replaced model Reconstruct and obtain the target signal model : ; ; ; in, is the target manifold matrix, is the target signal source matrix, is the real-valued identity matrix, To transform the array manifold matrix With the quantization threshold matrix Perform a merge operation. To transform the signal source matrix The transpose of the real-valued identity matrix Perform a merge operation.

[0030] Step S30: Based on the target signal model, use the truncated Frobenius norm and L 2,0 The single-bit DOA estimation optimization problem is constructed using the semi-quadratic technique, which is converted into a target optimization problem.

[0031] It is understandable that when As When the prior information The amplitude information can be estimated, so according to the target signal model , this embodiment can use the truncated Frobenius norm and L 2,0 The norm constructs the single-bit DOA estimation optimization problem: ; Make ; in, is the truncated Frobenius norm, is the penalty parameter, For L 2,0 norm, The transformation term is used to eliminate the reliance on prior information. represents the number of matrix rows, is the target signal source matrix Before OK.

[0032] Suppose there is a matrix , the truncated Frobenius norm can be expressed as: ; in, represents the number of rows of the matrix, represents the number of columns of the matrix, Expressed as Middle 'Line, 'The elements of the column, , As an auxiliary parameter, it reduces impact.

[0033] Furthermore, since the truncated Frobenius norm is non-convex and non-smooth, this embodiment uses a semi-quadratic technique to transform the optimization problem into a tractable target optimization problem: ; Make ; in, is the Frobenius norm, defined as the square root of the sum of the squares of all elements in the matrix, is a function that acts on the real and imaginary parts separately. Assume that there exists any real number ,but Defined as: ; in, is the absolute value symbol.

[0034] It can be seen that this application uses the truncated Frobenius norm and L 2,0 The single-bit DOA estimation problem is modeled using the norm, which enables it to adaptively estimate the number of target signal sources without the need for prior information.

[0035] Step S40: Use the proximal alternating minimization algorithm and the forward-backward splitting algorithm to solve the target optimization problem, and obtain the signal source estimation direction, the signal source estimation number and the signal estimation amplitude.

[0036] In this embodiment, a two-stage optimization strategy is proposed to solve the problem. In the first stage, the problem is solved directly in complex form; in the second stage, the target variable is reduced in dimension and then converted into a real number optimization problem for solution.

[0037] Specifically, a proximal alternating minimization algorithm is used to obtain a first iterative process in complex form and a second iterative process in complex form of the target optimization problem, a forward-backward splitting algorithm is used to solve the first iterative process in complex form, and the second iterative process in complex form is solved element by element, and the estimated direction and number of signal sources are calculated according to the solution results.

[0038] The first iterative process of obtaining the complex form of the target optimization problem using the proximal alternating minimization algorithm and the second iteration of the plural form : ; ; ; in, is the number of iterations in the proximal alternating minimization algorithm, is a minimum value greater than zero, which is used to ensure the convergence of the algorithm. In the second iteration, the plural form The previous iteration of iteration, The first iteration of the plural form The previous iteration of iteration, To calculate the intermediate quantity.

[0039] Since it is impossible to obtain the iterative process The present embodiment further adopts the forward-backward splitting algorithm to perform the first iterative process of the complex form Solve and get the first iterative update formula , the second iteration update formula And the third iteration update formula : ; ; ; in, is the number of iterations in the forward-backward splitting algorithm, is the stride control parameter, which is used to control the stride of the update process. yes Relative to The gradient of For the The next proximal alternating minimization algorithm and The iterative process of the forward-backward splitting algorithm, for In the previous iteration of the forward-backward splitting algorithm, is the i-th row, For storage space, is the array manifold matrix The number of columns, is the quantization threshold matrix The number of columns, is the L2 norm.

[0040] The second iteration process for the plural form Perform an element-by-element solution: ; in, is the complex angle.

[0041] Divide the element-by-element formula into the first subproblem And the second sub-problem : ; ; According to the first sub-question And the second sub-problem Get the solution result, that is, the optimal solution of the real part The optimal solution of the imaginary part : ; .

[0042] According to the solution result, the first iterative update formula, the second iterative update formula and the third iterative update formula, by Iterations, calculate the first target solution ; According to the first target solution, the estimated direction and number of signal sources are calculated: ; ; in, The first to S lines are the first target solution The corresponding matrix solution is, for No. L2 norm of row vector; right The peak value in is identified to determine the estimated direction and number of signal sources. It can be understood that by identifying The peaks in the can be used to determine the DOA of the source signal. The positions of these peaks indicate the direction of the signal source, and the number of peaks corresponds to the estimated number of signal sources.

[0043] Further, from the array manifold matrix The corresponding columns are extracted to construct a column matrix, the corresponding rows are extracted from the signal source matrix to construct a row matrix, signal modeling and rewriting are performed according to the column matrix and the row matrix to obtain a real-valued signal model, and the amplitude estimation problem is obtained according to the real-valued signal model.

[0044] In this embodiment, it can be assumed that the estimated The far-field and uncorrelated signals are ,in, For the The direction of arrival angle of a narrowband signal, is the direction of arrival angle of the second narrowband signal, For the The direction of arrival angle of a narrowband signal, For the The direction of arrival angle of a narrowband signal; From the array manifold matrix Extracted from Corresponding columns, construct column matrix , from the signal source matrix Extracted from Corresponding rows, construct row matrix , according to the column matrix and the row matrix Get the signal amplitude model : ; The signal amplitude model The real-valued signal model rewritten in real-valued form : ; ; ; ; ; in, , , and They are , , and The real-valued form of .

[0045] According to the real-valued signal model , we get the amplitude estimation problem: ; in, is a convex set, indicating is a diagonal matrix, express In arrive OK.

[0046] Furthermore, a proximal alternating minimization algorithm is used to obtain a first iterative process in real form and a second iterative process in real form of the amplitude estimation problem, the first iterative process in real form is solved using a forward-backward splitting algorithm, and the second iterative process in real form is solved using an element-by-element solution method, and the signal estimation amplitude is calculated based on the solution results.

[0047] It can be understood that the amplitude estimation problem is solved using the proximal alternating minimization algorithm and the forward-backward splitting algorithm to obtain The process is similar to the process of solving the target optimization problem using the proximal alternating minimization algorithm and the forward-backward splitting algorithm mentioned above, and will not be repeated here.

[0048] Get the solution result After that, In The part is normalized to form a unit matrix, so that the amplitude can be estimated. Furthermore, the complex signal can be reconstructed in the following way: ; in express The front OK, express In arrive OK.

[0049] It can be understood that the present application can effectively enhance the radar system's ability to detect and distinguish signals within a wide power range, and is widely used in miniaturized platforms, such as drones, microsatellites, and smart cars; for example, when a car is driving intelligently, the radar processes the signal source using the method of the present application, and after obtaining the estimated direction of the signal source, the estimated number of signal sources, and the estimated signal amplitude, the signal source, the estimated direction of the signal source, the estimated number of signal sources, and the estimated signal amplitude can be used as a basis for judging physical obstacles for intelligent driving.

[0050] Furthermore, a simulation experiment is carried out on the method proposed in this application.

[0051] The uniform linear array consists of M=60 sensors with an element spacing of =0.5 The number of snapshots is =64, the directions of arrival (DOA) of the three signals are , the corresponding amplitudes are 1.0, 1.4 and 1.8 respectively. Set the penalty parameter =5.5, auxiliary parameters =1.9. Adding zero-mean white Gaussian noise to the pure signal, the signal-to-noise ratio Defined as: ; in, is the noise variance.

[0052] The performance is evaluated by the mean square error (MSE) (in decibels), and the proposed method is compared with the following six manifold algorithms: 1-bit multiple signal classification (1-bit MUSIC), 1-bit spatial smoothed multiple signal classification (1-bit SS-MUSIC), complex-valued binary iterative hard threshold algorithm based on L2 norm (CBIHT-L2), 1-bit maximum likelihood (1-bit ML), 1-bit offline iterative weighting (1-bit OGIR), and 1-bit accelerated approximate gradient algorithm (1-bit APG). Due to the correlation of the signal source, the spatial smoothed multiple signal classification (SS-MUSIC) algorithm based on the unquantized received signal is additionally tested as a baseline method, and the test results are as follows: like Figure 3 As shown in the figure, the performance comparison under different signal-to-noise ratios (SNRs) is first studied. SS-MUSIC achieves the minimum mean square error (MSE) at all SNR levels because the received signal has no quantization error. The proposed method shows comparable estimation performance to 1-bit ML and 1-bit OGIR at high SNRs; ​​however, in low SNR scenarios, the proposed method significantly outperforms other algorithms and shows stronger robustness. In general, the method of this application always has the best performance among all single-bit quantization algorithms.

[0053] like Figure 4 As shown, Figure 4 The estimation accuracy of the six methods under different target numbers is shown, where the directions of arrival (DOA) of the fourth and fifth signals are , SS-MUSIC based on unquantized data still performs best, and its advantage becomes more significant as the number of targets increases. Under low target number conditions, the mean square error (MSE) of the proposed method is comparable to that of SS-MUSIC, significantly outperforming other competing methods. However, as the number of targets increases, the performance of the proposed method gradually approaches that of 1-bit SS-MUSIC, 1-bit APG, CBHTT-L2, 1-bit ML, and 1-bit OGIR. Overall, the method of the present application remains highly competitive under different target numbers.

[0054] like Figure 5 As shown in the figure, all the methods are compared under different numbers of snapshots. With the increase of the number of snapshots, except for the MSE of 1-bit MUSIC which tends to be stable, the estimation accuracy of other methods is improved. The performance of the proposed method increases significantly, and its performance gradually approaches that of SS-MUSIC.

[0055] like Figure 6 As shown, Figure 6 The estimation performance of six methods under different numbers of antennas is demonstrated. As the number of antennas increases, the advantage of SS-MUSIC over algorithms based on single-bit quantization data becomes more and more obvious, but the performance of the proposed method is always ranked first among all single-bit quantization algorithms.

[0056] Furthermore, if Figure 7 As shown, based on the above-mentioned single-bit arrival direction estimation method with signal amplitude recovery, the present invention also provides a single-bit arrival direction estimation system with signal amplitude recovery, wherein the single-bit arrival direction estimation system with signal amplitude recovery includes: The signal model generation module 51 is used to obtain each snapshot moment signal from the signal source of the uniform linear array receiver, introduce a non-zero threshold to perform single-bit quantization on each snapshot moment signal, and obtain a signal model; A signal model reconstruction module 52 is used to reconstruct the signal model, replace the sign function of the reconstructed signal model with a smooth hyperbolic tangent function to obtain a replaced model, and reconstruct the replaced model to obtain a target signal model; The optimization problem construction module 53 is used to optimize the target signal model using the truncated Frobenius norm and L 2,0 The single-bit DOA estimation optimization problem is constructed by using a semi-quadratic technique, and the optimization problem is converted into a target optimization problem; The optimization problem solving module 54 is used to solve the target optimization problem using a proximal alternating minimization algorithm and a forward-backward splitting algorithm to obtain a signal source estimation direction, a signal source estimation number and a signal estimation amplitude.

[0057] Furthermore, if Figure 8 As shown, based on the above-mentioned single-bit arrival direction estimation method and system with signal amplitude recovery, the present invention also provides a terminal accordingly, and the terminal includes a processor 10, a memory 20 and a display 30. Figure 8 Only some components of the terminal are shown, but it should be understood that it is not required to implement all of the components shown, and more or fewer components may be implemented instead.

[0058] In some embodiments, the memory 20 may be an internal storage unit of the terminal, such as a hard disk or memory of the terminal. In other embodiments, the memory 20 may also be an external storage device of the terminal, such as a plug-in hard disk, a smart memory card (Smart Media Card, SMC), a secure digital (SecureDigital, SD) card, a flash card (Flash Card), etc. equipped on the terminal. Further, the memory 20 may also include both an internal storage unit of the terminal and an external storage device. The memory 20 is used to store application software and various types of data installed on the terminal, such as the program code of the installation terminal. The memory 20 may also be used to temporarily store data that has been output or is to be output. In one embodiment, a single-bit arrival direction estimation program 40 with signal amplitude recovery is stored on the memory 20, and the single-bit arrival direction estimation program 40 with signal amplitude recovery can be executed by the processor 10, thereby realizing the single-bit arrival direction estimation method with signal amplitude recovery in the present application.

[0059] In some embodiments, the processor 10 may be a central processing unit (CPU), a microprocessor or other data processing chip, used to run the program code or process data stored in the memory 20, such as executing the single-bit arrival direction estimation method with signal amplitude recovery.

[0060] In some embodiments, the display 30 may be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, an OLED (Organic Light-Emitting Diode) touch device, etc. The display 30 is used to display information on the terminal and to display a visual user interface. The components of the terminal communicate with each other via a system bus.

[0061] In one embodiment, when the processor 10 executes the single-bit direction of arrival estimation program 40 with signal amplitude recovery in the memory 20, the following steps are implemented: Acquire each snapshot moment signal from a signal source of a uniform linear array receiver, introduce a non-zero threshold to perform single-bit quantization on each snapshot moment signal, and obtain a signal model; Reconstructing the signal model, replacing the sign function of the reconstructed signal model with a smooth hyperbolic tangent function to obtain a replaced model, and reconstructing the replaced model to obtain a target signal model; Based on the target signal model, the truncated Frobenius norm and L 2,0The single-bit DOA estimation optimization problem is constructed by using a semi-quadratic technique, and the optimization problem is converted into a target optimization problem; The target optimization problem is solved using a proximal alternating minimization algorithm and a forward-backward splitting algorithm to obtain a signal source estimation direction, a signal source estimation number, and a signal estimation amplitude.

[0062] The step of acquiring each snapshot moment signal from a signal source of a uniform linear array receiver, introducing a non-zero threshold to perform single-bit quantization on each snapshot moment signal, and obtaining a signal model specifically includes: Acquire each snapshot time signal from the signal source of the uniform linear array receiver, the uniform linear array receiver is an array manifold matrix : ; ; in, is the steering vector corresponding to the direction of arrival angle of the first narrowband signal, is the steering vector corresponding to the direction of arrival angle of the second narrowband signal, For the The steering vector corresponding to the direction of arrival angle of a narrowband signal, For the The steering vector corresponding to the direction of arrival angle of a narrowband signal, is a natural constant, is an imaginary unit, The number of narrowband signals is The direction of arrival angle of the signal, is the adjacent array element spacing of the uniform linear array receiver, is the wavelength of the incident signal, is the total number of array elements of the uniform linear array receiver, represents transpose; Introduce a non-zero threshold to perform single-bit quantization on the snapshot signals to obtain a signal model : ; ; ; ; in, is the sign function of complex numbers, is the signal source matrix to be estimated, is the noise vector, is the quantization threshold matrix, is the symbolic function, and are the real and imaginary parts of the complex number, is the total number of snapshots, are the signals of each signal source in the first snapshot, are the signals of each signal source in the second snapshot, For the The signal of each signal source in the snapshot, For the The signal of each signal source in the snapshot, For the The noise vector when the sensor receives the signal in the snapshot, is the noise vector when the sensor receives the signal in the second snapshot, For the The noise vector when the sensor receives the signal in the snapshot, For the The noise vector when the sensor receives the signal in each snapshot.

[0063] The signal model is reconstructed, a sign function of the reconstructed signal model is replaced with a smooth hyperbolic tangent function to obtain a replaced model, and the replaced model is reconstructed to obtain a target signal model, specifically including: The signal model Reconstruct the signal and transfer the noise from the inside to the outside of the symbol function to obtain the reconstructed signal model. : ; in, is a noise matrix, wherein the real part and the imaginary part of each element in the noise matrix are respectively between -2, 0 and 2; The reconstructed signal model is replaced by a smooth hyperbolic tangent function The symbol function of the replaced signal model is obtained : ; ; in, is the approximate error term, is the complex hyperbolic tangent function, is the hyperbolic tangent function; The replaced model Reconstruct and obtain the target signal model : ; ; ; in, is the target manifold matrix, is the target signal source matrix, is the real-valued identity matrix, To transform the array manifold matrix With the quantization threshold matrix Perform a merge operation. To transform the signal source matrix The transpose of the real-valued identity matrix Perform a merge operation.

[0064] Wherein, based on the target signal model, the truncated Frobenius norm and L 2,0 The single-bit DOA estimation optimization problem is constructed by using the semi-quadratic technique, and the optimization problem is converted into a target optimization problem, which specifically includes: Based on the target signal model , using the truncated Frobenius norm and L 2,0 The norm constructs the single-bit DOA estimation optimization problem: ; Make ; in, is the truncated Frobenius norm, is the penalty parameter, For L 2,0 norm, represents the number of matrix rows, is the target signal source matrix Before OK; The optimization problem is transformed into a tractable target optimization problem using semi-quadratic techniques: ; Make ; in, is the Frobenius norm, is a function that acts on the real and imaginary parts separately.

[0065] The method of using the proximal alternating minimization algorithm and the forward-backward splitting algorithm to solve the target optimization problem and obtain the signal source estimation direction, the signal source estimation number and the signal estimation amplitude specifically includes: Use a proximal alternating minimization algorithm to obtain a first iterative process in complex form and a second iterative process in complex form for the target optimization problem, use a forward-backward splitting algorithm to solve the first iterative process in complex form, solve the second iterative process in complex form element by element, and calculate the estimated direction of the signal source and the estimated number of the signal source according to the solution results; From the array manifold matrix Extract the corresponding columns, construct a column matrix, extract the corresponding rows from the signal source matrix, construct a row matrix, perform signal modeling and rewrite according to the column matrix and the row matrix to obtain a real-valued signal model, and obtain an amplitude estimation problem according to the real-valued signal model; A proximal alternating minimization algorithm is used to obtain the first iterative process and the second iterative process in real form of the amplitude estimation problem, the first iterative process in real form is solved using a forward-backward splitting algorithm, and the second iterative process in real form is solved using an element-by-element solution method, and the signal estimation amplitude is calculated based on the solution results.

[0066] The method of using the proximal alternating minimization algorithm to obtain a first iterative process in complex form and a second iterative process in complex form for the target optimization problem, using a forward-backward splitting algorithm to solve the first iterative process in complex form, solving the second iterative process in complex form element by element, and calculating the estimated direction and number of signal sources according to the solution results, specifically includes: The first iteration process of the complex form of the target optimization problem is obtained using the proximal alternating minimization algorithm and the second iteration of the plural form : ; ; ; in, is the number of iterations in the proximal alternating minimization algorithm, is a minimum value greater than zero, In the second iteration, the plural form The previous iteration of the iteration, The first iteration of the plural form The previous iteration of iteration, To calculate the intermediate quantity; The first iteration process of the complex form is to use the forward-backward splitting algorithm Solve and get the first iterative update formula , the second iteration update formula And the third iteration update formula : ; ; ; in, is the number of iterations in the forward-backward splitting algorithm, is the stride control parameter, which is used to control the stride of the update process. yes Relative to The gradient of For the The next proximal alternating minimization algorithm and The iterative process of the forward-backward splitting algorithm, for In the previous iteration of the forward-backward splitting algorithm, is the i-th row, For storage space, is the array manifold matrix The number of columns, is the quantization threshold matrix The number of columns, is the L2 norm; The second iteration process for the plural form Solve element by element to obtain a solution result, and according to the solution result, the first iterative update formula, the second iterative update formula and the third iterative update formula, Iterations, calculate the first target solution ; According to the first target solution, the estimated direction and number of signal sources are calculated: ; ; in, The first to S lines are the first target solution The corresponding matrix solution is, for No. L2 norm of row vector; right The peak value in the signal is identified to determine the estimated direction and number of signal sources.

[0067] Wherein, the matrix from the array manifold Extract the corresponding columns, construct a column matrix, extract the corresponding rows from the signal source matrix, construct a row matrix, perform signal modeling and rewrite according to the column matrix and the row matrix to obtain a real-valued signal model, and obtain an amplitude estimation problem according to the real-valued signal model, specifically including: Assume that the estimated The far-field and uncorrelated signals are ,in, For the The direction of arrival angle of a narrowband signal, is the direction of arrival angle of the second narrowband signal, For the The direction of arrival angle of a narrowband signal, For the The direction of arrival angle of a narrowband signal; From the array manifold matrix Extracted from Corresponding columns, construct column matrix , from the signal source matrix Extracted from Corresponding rows, construct row matrix , according to the column matrix and the row matrix Get the signal amplitude model : ; The signal amplitude model The real-valued signal model rewritten in real-valued form : ; in, , , and They are , , and The real-valued form of ; According to the real-valued signal model , we get the amplitude estimation problem: ; in, is a convex set.

[0068] The present invention also provides a computer-readable storage medium, wherein the computer-readable storage medium stores a single-bit arrival direction estimation program with signal amplitude recovery, and when the single-bit arrival direction estimation program with signal amplitude recovery is executed by a processor, the steps of the single-bit arrival direction estimation method with signal amplitude recovery as described above are implemented.

[0069] In summary, the present application provides a single-bit arrival direction estimation method, system, terminal and storage medium with signal amplitude recovery, the method comprising: obtaining each snapshot signal from a signal source of a uniform linear array receiver, introducing a non-zero threshold to perform single-bit quantization on each snapshot signal to obtain a signal model; reconstructing the signal model, replacing the sign function of the reconstructed signal model with a smooth hyperbolic tangent function and reconstructing to obtain a target signal model; based on the target signal model, using the truncated Frobenius norm and L 2,0 The single-bit DOA estimation optimization problem is constructed by using the norm, and the optimization problem is converted into a target optimization problem by using the semi-quadratic technique; the target optimization problem is solved by using the proximal alternating minimization algorithm and the forward-backward splitting algorithm to obtain the signal source estimation direction, the signal source estimation number and the signal estimation amplitude. The present invention eliminates the prior dependence on the number of signal sources and makes an accurate estimation of the signal source amplitude, thereby improving the accuracy of DOA estimation.

[0070] It should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or terminal including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or terminal. In the absence of further restrictions, an element defined by the sentence "comprises a ..." does not exclude the presence of other identical elements in the process, method, article or terminal including the element.

[0071] Of course, those skilled in the art can understand that all or part of the processes in the above-mentioned embodiments can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided by the present invention can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. As an illustration and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).

[0072] It should be understood that the application of the present invention is not limited to the above examples. For ordinary technicians in this field, improvements or changes can be made based on the above description. All these improvements and changes should fall within the scope of protection of the claims attached to the present invention.

Claims

1. A single-bit direction of arrival estimation method with signal amplitude recovery, characterized in that: The single-bit arrival direction estimation method with signal amplitude recovery includes: Acquire each snapshot moment signal from a signal source of a uniform linear array receiver, introduce a non-zero threshold to perform single-bit quantization on each snapshot moment signal, and obtain a signal model; Reconstructing the signal model, replacing the sign function of the reconstructed signal model with a smooth hyperbolic tangent function to obtain a replaced model, and reconstructing the replaced model to obtain a target signal model; Based on the target signal model, the truncated Frobenius norm and L 2,0 The single-bit DOA estimation optimization problem is constructed by using a semi-quadratic technique, and the optimization problem is converted into a target optimization problem; The target optimization problem is solved using a proximal alternating minimization algorithm and a forward-backward splitting algorithm to obtain a signal source estimation direction, a signal source estimation number, and a signal estimation amplitude.

2. The single-bit direction of arrival estimation method with signal amplitude recovery according to claim 1, characterized in that: The step of acquiring each snapshot moment signal from a signal source of a uniform linear array receiver, introducing a non-zero threshold to perform single-bit quantization on each snapshot moment signal, and obtaining a signal model specifically includes: Acquire each snapshot time signal from the signal source of the uniform linear array receiver, the uniform linear array receiver is an array manifold matrix : ； ； in, is the steering vector corresponding to the direction of arrival angle of the first narrowband signal, is the steering vector corresponding to the direction of arrival angle of the second narrowband signal, For the The steering vector corresponding to the direction of arrival angle of a narrowband signal, For the The steering vector corresponding to the direction of arrival angle of a narrowband signal, is a natural constant, is an imaginary unit, The number of narrowband signals is The direction of arrival angle of the signal, is the adjacent array element spacing of the uniform linear array receiver, is the wavelength of the incident signal, is the total number of array elements of the uniform linear array receiver, represents transpose; Introduce a non-zero threshold to perform single-bit quantization on the snapshot signals to obtain a signal model : ； ； ； ； in, is the sign function of complex numbers, is the signal source matrix to be estimated, is the noise vector, is the quantization threshold matrix, is the symbolic function, and are the real and imaginary parts of the complex number, is the total number of snapshots, are the signals of each signal source in the first snapshot, are the signals of each signal source in the second snapshot, is the signal of each signal source in the b-th snapshot, For the The signal of each signal source in the snapshot, is the noise vector when the sensor receives the signal in the first snapshot, is the noise vector when the sensor receives the signal in the second snapshot, For the The noise vector when the sensor receives the signal in the snapshot, For the The noise vector when the sensor receives the signal in each snapshot.

3. The single-bit direction of arrival estimation method with signal amplitude recovery according to claim 2, characterized in that: The signal model is reconstructed, a sign function of the reconstructed signal model is replaced with a smooth hyperbolic tangent function to obtain a replaced model, and the replaced model is reconstructed to obtain a target signal model, specifically comprising: The signal model Reconstruct the signal and transfer the noise from the inside to the outside of the symbol function to obtain the reconstructed signal model. : ； in, is a noise matrix, wherein the real part and the imaginary part of each element in the noise matrix are respectively between -2, 0 and 2; The reconstructed signal model is replaced by a smooth hyperbolic tangent function The symbol function of the replaced signal model is obtained : ； ； in, is the approximate error term, is the complex hyperbolic tangent function, is the hyperbolic tangent function; The replaced model Reconstruct and obtain the target signal model : ； ； ； in, is the target manifold matrix, is the target signal source matrix, is the real-valued identity matrix, To transform the array manifold matrix With the quantization threshold matrix Perform a merge operation. To transform the signal source matrix The transpose of the real-valued identity matrix Perform a merge operation.

4. The single-bit direction of arrival estimation method with signal amplitude recovery according to claim 3, characterized in that: Based on the target signal model, the truncated Frobenius norm and L 2,0 The single-bit DOA estimation optimization problem is constructed by using the semi-quadratic technique, and the optimization problem is converted into a target optimization problem, which specifically includes: Based on the target signal model , using the truncated Frobenius norm and L 2,0 The norm constructs the single-bit DOA estimation optimization problem: ； Make ; in, is the truncated Frobenius norm, is the penalty parameter, For L 2,0 norm, represents the number of matrix rows, is the target signal source matrix Before OK; The optimization problem is transformed into a tractable target optimization problem using semi-quadratic techniques: ； Make ; in, is the Frobenius norm, is a function that acts on the real and imaginary parts separately.

5. The single-bit direction of arrival estimation method with signal amplitude recovery according to claim 4, characterized in that: The method of using the proximal alternating minimization algorithm and the forward-backward splitting algorithm to solve the target optimization problem and obtain the signal source estimation direction, the signal source estimation number and the signal estimation amplitude specifically includes: Use a proximal alternating minimization algorithm to obtain a first iterative process in complex form and a second iterative process in complex form for the target optimization problem, use a forward-backward splitting algorithm to solve the first iterative process in complex form, solve the second iterative process in complex form element by element, and calculate the estimated direction of the signal source and the estimated number of the signal source according to the solution results; From the array manifold matrix Extract the corresponding columns, construct a column matrix, extract the corresponding rows from the signal source matrix, construct a row matrix, perform signal modeling and rewrite according to the column matrix and the row matrix to obtain a real-valued signal model, and obtain an amplitude estimation problem according to the real-valued signal model; A proximal alternating minimization algorithm is used to obtain the first iterative process and the second iterative process in real form of the amplitude estimation problem, the first iterative process in real form is solved using a forward-backward splitting algorithm, and the second iterative process in real form is solved using an element-by-element solution method, and the signal estimation amplitude is calculated based on the solution results.

6. The single-bit direction of arrival estimation method with signal amplitude recovery according to claim 5, characterized in that: The method uses the proximal alternating minimization algorithm to obtain a first iterative process in complex form and a second iterative process in complex form for the target optimization problem, uses a forward-backward splitting algorithm to solve the first iterative process in complex form, solves the second iterative process in complex form element by element, and calculates the estimated direction of the signal source and the estimated number of the signal source according to the solution results, specifically including: The first iteration process of the complex form of the target optimization problem is obtained using the proximal alternating minimization algorithm and the second iteration of the plural form : ； ； ； in, is the number of iterations in the proximal alternating minimization algorithm, is a minimum value greater than zero, In the second iteration, the plural form The previous iteration of the iteration, The first iteration of the plural form The previous iteration of the iteration, To calculate the intermediate quantity; The first iteration process of the complex form is to use the forward-backward splitting algorithm Solve and get the first iterative update formula , the second iteration update formula And the third iteration update formula : ； ； ； in, is the number of iterations in the forward-backward splitting algorithm, is the stride control parameter, which is used to control the stride of the update process. yes Relative to The gradient of For the The next proximal alternating minimization algorithm and The iterative process of the forward-backward splitting algorithm, for In the previous iteration of the forward-backward splitting algorithm, is the i-th row, For storage space, is the array manifold matrix The number of columns, is the quantization threshold matrix The number of columns, is the L2 norm; The second iteration process for the plural form Solve element by element to obtain a solution result, and according to the solution result, the first iterative update formula, the second iterative update formula and the third iterative update formula, Iterations, calculate the first target solution ; According to the first target solution, the estimated direction and number of signal sources are calculated: ； ； in, The first to S lines are the first target solution The corresponding matrix solution is, for No. L2 norm of row vector; right The peak value in the signal is identified to determine the estimated direction and number of signal sources.

7. The single-bit direction of arrival estimation method with signal amplitude recovery according to claim 5, characterized in that: From the array manifold matrix Extract the corresponding columns, construct a column matrix, extract the corresponding rows from the signal source matrix, construct a row matrix, perform signal modeling and rewrite according to the column matrix and the row matrix to obtain a real-valued signal model, and obtain an amplitude estimation problem according to the real-valued signal model, specifically including: Assume that the estimated The far-field and uncorrelated signals are ,in, is the direction of arrival angle of the first narrowband signal, is the direction of arrival angle of the second narrowband signal, For the The direction of arrival angle of a narrowband signal, For the The direction of arrival angle of a narrowband signal; From the array manifold matrix Extracted from Corresponding columns, construct column matrix , from the signal source matrix Extracted from Corresponding rows, construct row matrix , according to the column matrix and the row matrix Get the signal amplitude model : ； The signal amplitude model The real-valued signal model rewritten in real-valued form : ； in, , , and They are , , and The real-valued form of ; According to the real-valued signal model , we get the amplitude estimation problem: ； in, is a convex set.

8. A single-bit direction of arrival estimation system with signal amplitude recovery, characterized in that: The single-bit direction of arrival estimation system with signal amplitude recovery comprises: A signal model generation module, used for acquiring each snapshot moment signal from a signal source of a uniform linear array receiver, introducing a non-zero threshold to perform single-bit quantization on each snapshot moment signal, and obtaining a signal model; A signal model reconstruction module is used to reconstruct the signal model, replace the sign function of the reconstructed signal model with a smooth hyperbolic tangent function to obtain a replaced model, and reconstruct the replaced model to obtain a target signal model; The optimization problem building module is used to use the truncated Frobenius norm and L based on the target signal model. 2,0 The single-bit DOA estimation optimization problem is constructed by using a semi-quadratic technique, and the optimization problem is converted into a target optimization problem; The optimization problem solving module is used to solve the target optimization problem by using the proximal alternating minimization algorithm and the forward-backward splitting algorithm to obtain the signal source estimation direction, the signal source estimation number and the signal estimation amplitude.

9. A terminal, characterized in that: The terminal includes: a memory, a processor, and a single-bit arrival direction estimation program with signal amplitude recovery stored in the memory and executable on the processor. When the single-bit arrival direction estimation program with signal amplitude recovery is executed by the processor, the steps of the single-bit arrival direction estimation method with signal amplitude recovery as described in any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a single-bit arrival direction estimation program with signal amplitude recovery, and when the single-bit arrival direction estimation program with signal amplitude recovery is executed by a processor, the steps of the single-bit arrival direction estimation method with signal amplitude recovery as described in any one of claims 1-7 are implemented.

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