Single-bit Direction-of-Arrival Estimation Method, System, Terminal and Storage Medium with Signal Amplitude Recovery

Abstract

The present invention discloses a single-bit direction-of-arrival estimation method, system, terminal and storage medium with signal amplitude recovery. The method includes: obtaining signals of each snapshot moment of a signal source from a uniform linear array receiver, introducing a non-zero threshold to perform single-bit quantization on the signals of each snapshot moment to obtain a signal model; reconstructing the signal model, using a smooth hyperbolic tangent function to replace the sign function of the reconstructed signal model and performing reconstruction to obtain a target signal model; based on the target signal model, using the truncated Frobenius norm and the L 2,0 norm to construct a single-bit DOA estimation optimization problem, and using the semi-quadratic technique to convert the optimization problem into a target optimization problem; using the proximal alternating minimization algorithm and the forward-backward splitting algorithm to solve the target optimization problem to obtain the estimated direction of the signal source, the estimated number of signal sources and the estimated amplitude of the signal. The present invention eliminates the prior dependence on the number of signal sources and accurately estimates the amplitude of the signal source.

Description

Technical Field

[0001] The present invention relates to the field of radar signal processing, and particularly to a single-bit direction-of-arrival 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 technique that uses a single-bit analog-to-digital converter to retain only the sign information of the received signal and estimates the signal direction based on this. The single-bit analog-to-digital converter (ADC) can be regarded as the simplest ADC converter, which significantly reduces the data storage, transmission, and processing burden by discarding high-precision quantization and the number of data bits.

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

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

[0005] Therefore, the existing technology still needs to be improved and developed. Summary of the Invention

[0006] The main objective 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 existing single-bit DOA method based on sparse regularization still relies on grid search to determine the number of target signal sources and cannot estimate the signal amplitude, resulting in a limited dynamic range of the radar system and low DOA estimation accuracy.

[0007] To achieve the above objective, the present invention provides a single-bit direction-of-arrival estimation method with signal amplitude recovery, and the single-bit direction-of-arrival estimation method with signal amplitude recovery includes the following steps:

[0008] Obtain the signals at each snapshot moment of the signal source from a uniform linear array receiver, introduce a non-zero threshold to perform single-bit quantization on the signals at each snapshot moment, and obtain a signal model;

[0009] 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;

[0010] Based on the target signal model, use the truncated Frobenius norm and the L 2,0 norm to construct a single-bit DOA estimation optimization problem, and use the semi-quadratic technique to convert the optimization problem into a target optimization problem;

[0011] Use the proximal alternating minimization algorithm and the forward-backward splitting algorithm to solve the target optimization problem to obtain the estimated direction of the signal source, the estimated number of signal sources, and the estimated amplitude of the signal.

[0012] Optionally, in the single-bit direction-of-arrival estimation method with signal amplitude recovery, where the signals at each snapshot moment of the signal source from a uniform linear array receiver are obtained, and a non-zero threshold is introduced to perform single-bit quantization on the signals at each snapshot moment to obtain a signal model, specifically including:

[0013] Obtain the signals at each snapshot moment of the signal source from a uniform linear array receiver, and the uniform linear array receiver is an array manifold matrix :

[0014] ;

[0015] ;

[0016] where is the steering vector corresponding to the angle of arrival of the first narrowband signal, is the steering vector corresponding to the angle of arrival of the second narrowband signal, is the steering vector corresponding to the angle of arrival of the th narrowband signal, is the steering vector corresponding to the angle of arrival of the th narrowband signal, is the natural constant, is the imaginary unit, is the angle of arrival of the th narrowband signal, is the adjacent element spacing of the uniform linear array receiver, is the wavelength of the incident signal, is the total number of elements of the uniform linear array receiver, represents the transpose;

[0017] Introduce a non-zero threshold to perform single-bit quantization on the signals at each snapshot moment to obtain a signal model :

[0018] ;

[0019] ;

[0020] ;

[0021] ;

[0022] wherein, is the sign function of a complex number, is the signal source matrix to be estimated, is the noise vector, is the quantization threshold matrix, is the sign function, and are the real part and the imaginary part of the complex number respectively, is the total number of snapshots, is the signal of each signal source in the first snapshot, is the signal of each signal source in the second snapshot, is the th snapshot of the signal of each signal source, is the th snapshot of the signal of each signal source, is the th snapshot of the noise vector when the sensor receives the signal, is the th snapshot of the noise vector when the sensor receives the signal, is the th snapshot of the noise vector when the sensor receives the signal, is the th snapshot of the noise vector when the sensor receives the signal.

[0023] Optionally, in the single-bit direction-of-arrival estimation method with signal amplitude recovery, wherein the reconstruction of the signal model is performed by replacing the sign function of the reconstructed signal model with a smooth hyperbolic tangent function to obtain a replaced model, and the reconstruction of the replaced model is performed to obtain a target signal model, which specifically includes:

[0024] Reconstruct the signal model to transfer the noise from inside the sign function to the outside, and obtain the reconstructed signal model :

[0025] ;

[0026] wherein, is a noise matrix, and the real and imaginary parts of each element in the noise matrix take values between -2, 0, and 2 respectively;

[0027] Replace the sign function in the reconstructed signal model with a smooth hyperbolic tangent function to obtain a replaced signal model : :

[0028] ;

[0029] ;

[0030] where, is an approximation error term, is a complex hyperbolic tangent function, is a hyperbolic tangent function;

[0031] Reconstruct the replaced model to obtain a target signal model :

[0032] ;

[0033] ;

[0034] ;

[0035] where, is a target manifold matrix, is a target signal source matrix, is a real-valued identity matrix, is an operation of combining the array manifold matrix with the quantization threshold matrix , is an operation of combining the transpose of the signal source matrix with the real-valued identity matrix .

[0036] Optionally, in the single-bit direction-of-arrival estimation method with signal amplitude recovery, based on the target signal model, a single-bit DOA estimation optimization problem is constructed using the truncated Frobenius norm and the L 2,0 norm, and the optimization problem is converted into a target optimization problem using the semi-quadratic technique, specifically including:

[0037] Based on the target signal model , use the truncated Frobenius norm and the L 2,0 norm to construct a single-bit DOA estimation optimization problem:

[0038] ;

[0039] such that ;

[0040] wherein, is the truncated Frobenius norm, is the penalty parameter, is the L 2,0 norm, represents the number of rows of the matrix, is the target signal source matrix of the first rows;

[0041] Adopt the semi - quadratic technique to transform the form of the optimization problem to obtain a tractable target optimization problem:

[0042] ;

[0043] such that ;

[0044] wherein, is the Frobenius norm, is a function acting separately on the real and imaginary parts.

[0045] Optionally, for the single - bit direction - of - arrival estimation method with signal amplitude recovery, wherein, using the proximal alternating minimization algorithm and the forward - backward splitting algorithm to solve the target optimization problem to obtain the estimated direction of the signal source, the estimated number of signal sources, and the estimated amplitude of the signal, specifically including:

[0046] Use the proximal alternating minimization algorithm to obtain the first iterative process in complex form and the second iterative process in complex form of the target optimization problem, use the 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 signal sources according to the solution results;

[0047] Extract the corresponding columns from the array manifold matrix to construct a column matrix, extract the corresponding rows from the signal source matrix to construct a row matrix, perform signal modeling and rewriting 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;

[0048] 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.

[0049] 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:

[0050] 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 :

[0051] ;

[0052] ;

[0053] ;

[0054] 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;

[0055] 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 :

[0056] ;

[0057] ;

[0058] ;

[0059] in, is the number of iterations in the proximal alternating minimization algorithm, is a minimum value greater than zero, is the previous iteration of the th iteration in the second iterative process of the complex form, is the previous iteration of the th iteration in the first iterative process of the complex form, is the calculated intermediate quantity;

[0060] Solve the first iterative process of the complex form using the forward-backward splitting algorithm to obtain the first iterative update formula , the second iterative update formula and the third iterative update formula :

[0061] ;

[0062] ;

[0063] ;

[0064] where, is the number of iterations in the forward-backward splitting algorithm process, is the step size control parameter used to control the step size of the update process, is with respect to gradient, is at the th proximal alternating minimization algorithm and the th forward-backward splitting algorithm iteration process, is in the previous forward-backward splitting algorithm iteration process, is the i-th row, is the storage space, is the array manifold matrix number of columns, the quantization threshold matrix number of columns, is L 2 norm;

[0065] Solve the second iterative process of the complex form element by element to obtain the solution result. According to the solution result, the first iterative update formula, the second iterative update formula, and the third iterative update formula, through iterations, calculate the first target solution ; ;

[0066] Calculate the signal source estimation direction and the signal source estimation quantity based on the first target solution:

[0067] ;

[0068] ;

[0069] Among them, The first to S rows of are the solutions of the corresponding matrix, is of the row vector of 2 norm;

[0070] Identify the peaks in to determine the signal source estimation direction and the number of signal sources estimated.

[0071] Optionally, in the single-bit direction-of-arrival estimation method with signal amplitude recovery, among them, extracting the corresponding columns from the array manifold matrix to construct a column matrix, extracting the corresponding rows from the signal source matrix to construct a row matrix, performing signal modeling and rewriting according to the column matrix and the row matrix to obtain a real-valued signal model, and obtaining an amplitude estimation problem according to the real-valued signal model, specifically including:

[0072] Suppose the estimated far-field and uncorrelated signals are , among them, is the direction-of-arrival angle of the th narrowband signal, is the direction-of-arrival angle of the th narrowband signal, is the direction-of-arrival angle of the th narrowband signal, is the direction-of-arrival angle of the th narrowband signal;

[0073] Extract the corresponding columns from the array manifold matrix to construct a column matrix , extract the corresponding rows from the signal source matrix to construct a row matrix , and obtain a signal amplitude model according to the column matrix and the row matrix :

[0074] ;

[0075] Regarding the signal amplitude model Real-valued signal model rewritten in real-valued form :

[0076] ;

[0077] wherein 、 、 and are respectively 、 、 and in real-valued form;

[0078] According to the real-valued signal model , an amplitude estimation problem is obtained:

[0079] ;

[0080] wherein is a convex set.

[0081] In addition, to achieve the above object, the present invention also 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 includes:

[0082] A signal model generation module, configured to obtain signals of each snapshot moment of a signal source from a uniform linear array receiver, introduce a non-zero threshold to perform single-bit quantization on the signals of each snapshot moment, and obtain a signal model;

[0083] A signal model reconstruction module, configured 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;

[0084] An optimization problem construction module, configured to construct a single-bit DOA estimation optimization problem based on the target signal model by using a truncated Frobenius norm and an L 2,0 norm, and convert the optimization problem into a target optimization problem by using a semi-quadratic technique;

[0085] An optimization problem solving module, configured to solve the target optimization problem by using a proximal alternating minimization algorithm and a forward-backward splitting algorithm to obtain an estimated direction of the signal source, an estimated number of signal sources, and an estimated amplitude of the signal.

[0086] In addition, to achieve the above object, the present invention further provides a terminal, wherein the terminal includes: a memory, a processor, and a single-bit direction-of-arrival estimation program with signal amplitude recovery stored on the memory and executable on the processor. When the single-bit direction-of-arrival estimation program with signal amplitude recovery is executed by the processor, the steps of the single-bit direction-of-arrival estimation method with signal amplitude recovery as described above are implemented.

[0087] In addition, to achieve the above object, the present invention further provides a computer-readable storage medium, wherein the computer-readable storage medium stores a single-bit direction-of-arrival estimation program with signal amplitude recovery. When the single-bit direction-of-arrival estimation program with signal amplitude recovery is executed by a processor, the steps of the single-bit direction-of-arrival estimation method with signal amplitude recovery as described above are implemented.

[0088] In the present invention, signals of each snapshot moment of a signal source from a uniform linear array receiver are acquired, a non-zero threshold is introduced to perform single-bit quantization on the signals of each snapshot moment to obtain a signal model; the signal model is reconstructed, the sign function of the reconstructed signal model is replaced with a smooth hyperbolic tangent function and then reconstructed to obtain a target signal model; based on the target signal model, a truncated Frobenius norm and an L 2,0 norm are used to construct a single-bit DOA estimation optimization problem, and a semi-quadratic technique is used to convert the optimization problem into a target optimization problem; a proximal alternating minimization algorithm and a forward-backward splitting algorithm are used to solve the target optimization problem to obtain the estimated direction of the signal source, the estimated number of signal sources, and the estimated amplitude of the signal. The present invention eliminates the prior dependence on the number of signal sources and accurately estimates the amplitude of the signal source, improving the accuracy of DOA estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] Figure 1 is a flowchart of a preferred embodiment of the single-bit direction-of-arrival estimation method with signal amplitude recovery of the present invention;

[0090] Figure 2 is a schematic diagram of a uniform linear array receiver of the single-bit direction-of-arrival estimation method with signal amplitude recovery of the present invention;

[0091] Figure 3 is a performance comparison diagram at different fast signal-to-noise ratios of the single-bit direction-of-arrival estimation method with signal amplitude recovery of the present invention;

[0092] Figure 4 is a performance comparison diagram at different numbers of targets of the single-bit direction-of-arrival estimation method with signal amplitude recovery of the present invention;

[0093] Figure 5It is a performance comparison diagram under different snapshot numbers in the single-bit direction-of-arrival estimation method with signal amplitude recovery according to the present invention;

[0094] Figure 6 It is a performance comparison diagram under different numbers of antennas in the single-bit direction-of-arrival estimation method with signal amplitude recovery according to the present invention;

[0095] Figure 7 It is a structural diagram of a preferred embodiment of the single-bit direction-of-arrival estimation system with signal amplitude recovery according to the present invention;

[0096] Figure 8 It is a structural diagram of a preferred embodiment of the terminal according to the present invention. Detailed implementation manners

[0097] The present application provides a single-bit direction-of-arrival estimation method, system and terminal with signal amplitude recovery. To make the purpose, technical solutions and effects of the present application clearer and more definite, the following further elaborates on the present application with reference to the accompanying drawings and by way of examples. It should be understood that the specific examples described herein are only used to explain the present application and are not used to limit the present application.

[0098] Those skilled in the art of this technology can understand that, unless otherwise defined, all terms (including technical terms and scientific terms) used herein have the same meaning as the general understanding of those of ordinary skill in the field to which the present application belongs. It should also be understood that terms such as those defined in a general dictionary should be understood to have a meaning consistent with the meaning in the context of the prior art, and will not be interpreted with an idealized or overly formal meaning unless specifically defined as here.

[0099] In addition, if there is a description involving "first", "second", etc. in the embodiments of the present invention, such descriptions of "first", "second", etc. are only for descriptive purposes and cannot be understood as indicating or implying their relative importance or implicitly indicating the quantity of the indicated technical features. Thus, features defined with "first", "second" may explicitly or implicitly include at least one such feature. In addition, the technical solutions between various embodiments can be combined with each other, but it must be based on the fact that those of ordinary skill in the art can implement them. When the combination of technical solutions results in contradictions or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the protection scope required by the present invention.

[0100] The single-bit direction-of-arrival estimation method with signal amplitude recovery described in the preferred embodiment of the present invention, as Figure 1 shown, the single-bit direction-of-arrival estimation method with signal amplitude recovery includes the following steps:

[0101] Step S10: Obtain the signals of each snapshot moment of the signal source from the uniform linear array receiver, and introduce a non-zero threshold to perform single-bit quantization on the signals of each snapshot moment to obtain a signal model.

[0102] Specifically, consider a uniform linear array (ULA) composed of array elements, and the adjacent element spacing needs to satisfy , being the wavelength of the incident signal. Assume that a total of far-field and uncorrelated narrowband signals are incident on the array from different directions. Then, the uniform linear array receiver is as Figure 2 shown (where is an arbitrary angle of arrival).

[0103] Obtain the signals of each snapshot moment of the signal source from the uniform linear array receiver. The uniform linear array receiver is the array manifold matrix , and the array manifold matrix refers to the matrix of the phase relationships of the S narrowband signals received by the M antennas in the antenna array from different directions, and can be expressed as:

[0104] ;

[0105] ;

[0106] where is the steering vector corresponding to the angle of arrival of the first narrowband signal, is the steering vector corresponding to the angle of arrival of the signal with the narrowband signal number 2, is the th steering vector corresponding to the angle of arrival of the narrowband signal, is the th steering vector corresponding to the angle of arrival of the narrowband signal, is the natural constant, is the imaginary unit, is the angle of arrival of the signal with the narrowband signal number , is the adjacent element spacing of the uniform linear array receiver, is the wavelength of the incident signal, is the total number of elements of the uniform linear array receiver, represents the transpose.

[0107] Furthermore, introduce a non-zero threshold to perform single-bit quantization on the signals of each snapshot moment to obtain a signal model :

[0108] ;

[0109] ;

[0110] ;

[0111] ;

[0112] wherein, is the sign function of a complex number, is the signal source matrix to be estimated, is the noise vector, is the quantization threshold matrix, is the sign function (returns 1, 0, or -1 according to the sign of the input value, returns 1 when the input value is positive; returns -1 when the input value is negative; returns 0 when the input value is zero), and are the real and imaginary parts of the complex number respectively, is the total number of snapshots, is the signal of each signal source in the first snapshot, is the signal of each signal source in the second snapshot, is the th signal of each signal source in the th snapshot, is the th signal of each signal source in the th snapshot, is the noise vector when the sensor receives the signal in the second snapshot, is the th noise vector when the sensor receives the signal in the th snapshot, is the

[0113] Step S20, 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.

[0114] Specifically, single-bit quantization blurs the noise distribution. To select a suitable loss function in the optimization problem modeling stage to ensure reliable estimation performance, therefore, in this embodiment, the signal model is reconstructed to transfer the noise from inside the sign function to the outside to obtain the reconstructed signal model :

[0115] ;

[0116] Among them, is a noise matrix, and the real and imaginary parts of each element in the noise matrix take values between -2, 0, and 2 respectively.

[0117] It can be understood that the noise component in the signal model is transferred from inside the sign function to the outside, and different distributions or intensities of the noise only affect the number of non-zero elements.

[0118] Furthermore, the sign function of the reconstructed signal model is replaced with a smooth hyperbolic tangent function to obtain a replaced signal model :

[0119] ;

[0120] ;

[0121] Among them, is an approximation error term, is a complex hyperbolic tangent function, is a hyperbolic tangent function;

[0122] Even further, the non-zero threshold provides prior information about the amplitude. In this embodiment, the replaced model is reconstructed to obtain a target signal model :

[0123] ;

[0124] ;

[0125] ;

[0126] Among them, is a target manifold matrix, is a target signal source matrix, is a real-valued identity matrix, is an operation of combining the array manifold matrix with the quantization threshold matrix , is an operation of combining the transpose of the signal source matrix with the real-valued identity matrix .

[0127] Step S30, based on the target signal model, use the truncated Frobenius norm and L 2,0The norm constructs a single-bit DOA estimation optimization problem, and the semi-quadratic technique is used to transform the optimization problem into a target optimization problem.

[0128] It can be understood that when as the prior information of, the amplitude information of can be estimated. Therefore, according to the target signal model , this embodiment can use the truncated Frobenius norm and the L 2,0 norm to construct a single-bit DOA estimation optimization problem:

[0129] ;

[0130] such that ;

[0131] where is the truncated Frobenius norm, is the penalty parameter, is the L 2,0 norm, the regularization term is used to eliminate the dependence on the prior information, represents the number of rows of the matrix, is the target signal source matrix of the first rows.

[0132] Assume there is a matrix , the truncated Frobenius norm can be expressed as:

[0133] ;

[0134] where represents the number of rows of the matrix, represents the number of columns of the matrix, is expressed as in the 'th row, the 'th column element, , is an auxiliary parameter, reducing the influence.

[0135] Furthermore, since the truncated Frobenius norm is non-convex and non-smooth, this embodiment uses the semi-quadratic technique to transform the form of the optimization problem to obtain a tractable target optimization problem:

[0136] ;

[0137] such that ;

[0138] 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:

[0139] ;

[0140] in, is the absolute value symbol.

[0141] 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.

[0142] 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.

[0143] 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.

[0144] 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.

[0145] 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 :

[0146] ;

[0147] ;

[0148] ;

[0149] 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 the current iteration For the previous iteration of the th iteration in the first iterative process in complex form

[0150] Since the solution of the iterative process cannot be obtained, in this embodiment, the forward-backward splitting algorithm is further used to solve the first iterative process in complex form to obtain the first iterative update formula , the second iterative update formula and the third iterative update formula :

[0151] ;

[0152] ;

[0153] ;

[0154] Wherein, is the number of iterations in the forward-backward splitting algorithm process, is the step size control parameter, used to control the step size of the update process, is with respect to gradient, is at the th proximal alternating minimization algorithm and the th iteration process of the forward-backward splitting algorithm, is in the previous iteration process of the forward-backward splitting algorithm, is the i-th row, is the storage space, is the array manifold matrix number of columns of, is the quantization threshold matrix number of columns of, is L 2 norm.

[0155] Perform element-by-element solution on the second iterative process in complex form : ;

[0156] Wherein, is the complex argument.

[0157] Divide the formula for element-by-element solution into the first sub-problem and the second sub-problem :

[0158] ;

[0159] ;

[0160] According to the first sub - problem and the second sub - problem obtain a solution result, that is, the real - part optimal solution and the imaginary - part optimal solution :

[0161] ;

[0162] .

[0163] According to the solution result, the first iterative update formula, the second iterative update formula and the third iterative update formula, through iterations, calculate the first target solution ;

[0164] Calculate the estimated direction and the estimated number of signal sources according to the first target solution:

[0165] ;

[0166] ;

[0167] wherein, the first to S rows of are the solutions of the matrix corresponding to the first target solution is the L - norm of the 2 row vector of

[0168] Identify the peaks in to determine the estimated direction and the estimated number of signal sources. It can be understood that by identifying the peaks in the DOA of the source signal can be determined, the positions of these peaks represent the directions of the signal sources, and the number of peaks corresponds to the estimated number of signal sources.

[0169] Furthermore, extract the corresponding columns from the array manifold matrix to construct a column matrix, extract the corresponding rows from the signal source matrix to construct a row matrix, perform signal modeling and rewriting 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.

[0170] In this embodiment, it can be assumed that the estimated far - field and uncorrelated signals are , where is the direction of arrival angle of the th narrowband signal, is the direction of arrival angle of the 2nd narrowband signal, is the direction of arrival angle of the th narrowband signal, is the direction of arrival angle of the th narrowband signal;

[0171] Extract the corresponding column from the array manifold matrix to construct a column matrix , extract the corresponding row from the signal source matrix to construct a row matrix , and obtain the signal amplitude model according to the column matrix and the row matrix :

[0172] ;

[0173] Rewrite the signal amplitude model into a real-valued signal model in real-valued form:

[0174] ;

[0175] ;

[0176] ;

[0177] ;

[0178] ;

[0179] where , , and are the real-valued forms of , , and respectively.

[0180] According to the real-valued signal model , obtain the amplitude estimation problem:

[0181] ;

[0182] where is a convex set, indicating that is a diagonal matrix, Indicate in to rows

[0183] Furthermore, the proximal alternating minimization algorithm is used to obtain the first iterative process and the second iterative process in the real number form of the amplitude estimation problem. The forward-backward splitting algorithm is used to solve the first iterative process in the real number form, and the element-by-element solution method is used to solve the second iterative process in the real number form. The signal estimation amplitude is calculated according to the solution results.

[0184] It can be understood that using the proximal alternating minimization algorithm and the forward-backward splitting algorithm to solve the amplitude estimation problem gives , and its process is similar to the process of using the proximal alternating minimization algorithm and the forward-backward splitting algorithm to solve the target optimization problem in the above text, which will not be elaborated here.

[0185] Obtain the solution results After that, in part is normalized to form an identity matrix, so that amplitude estimation can be performed. Further, the complex signal can also be reconstructed in the following way:

[0186] ;

[0187] where indicates the first rows in indicates in to rows

[0188] It can be understood that this application can effectively improve the ability of the radar system to detect and distinguish signals within a wide power range, and is widely applied to miniaturized platforms, such as unmanned aerial vehicles, microsatellites and intelligent vehicles; for example, when an intelligent vehicle is driving, the radar processes the signal source through the method of this application. After obtaining the estimated direction of the signal source, the estimated number of signal sources and the estimated amplitude of the signal, the signal source, the estimated direction of the signal source, the estimated number of signal sources and the estimated amplitude of the signal can be used as the basis for obstacle judgment in intelligent driving.

[0189] Furthermore, a simulation experiment is conducted on the method proposed in this application.

[0190] The uniform linear array is composed of M = 60 sensors, and the element spacing = 0.5 . The number of snapshots is = 64, and the directions of arrival (DOA) of the three signals are respectively , with corresponding amplitudes of 1.0, 1.4, and 1.8 respectively. Set the penalty parameter = 5.5, and the auxiliary parameter = 1.9. Add white Gaussian noise with zero mean to the pure signal, and the signal-to-noise ratio is defined as:

[0191] ;

[0192] where is the noise variance.

[0193] Evaluate the performance through the mean square error MSE (in decibels dB), and compare the proposed method with the following six manifold algorithms: single-bit multi-signal classification (1-bit MUSIC), single-bit spatial smoothing multi-signal classification (1-bit SS-MUSIC), complex-valued binary iterative hard thresholding algorithm based on the L 2 norm (CBIHT-L 2 ), single-bit maximum likelihood (1-bit ML), single-bit offline iterative weighting (1-bit OGIR), and single-bit accelerated proximal gradient algorithm (1-bit APG). Due to the correlation of the signal sources, the spatial smoothing multi-signal classification (SS-MUSIC) algorithm based on the unquantized received signals was additionally tested as a benchmark method, and the test results are as follows:

[0194] As Figure 3 shown, first study the performance comparison under different signal-to-noise ratios (SNR). Since SS-MUSIC has no quantization error in the received signals, it achieves the minimum mean square error (MSE) at all SNR levels. The proposed method shows comparable estimation performance with 1-bit ML and 1-bit OGIR at high SNR; however, in the low SNR scenario, the proposed method is significantly better than other algorithms, demonstrating stronger robustness. Generally speaking, the method of this application always has the optimal performance among all single-bit quantization algorithms.

[0195] As Figure 4 shown, Figure 4 shows the estimation accuracy of the six methods under different numbers of targets. The directions of arrival (DOA) of the fourth and fifth signals are respectively. SS-MUSIC based on unquantized data still performs the best, and its advantage becomes more significant as the number of targets increases. Under the condition of a low number of targets, the mean square error (MSE) of the proposed method is comparable to that of SS-MUSIC and is significantly better than 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-L 2, 1-bit ML and 1-bit OGIR. Generally speaking, the method of this application remains highly competitive under different numbers of targets.

[0196] As Figure 5 shown, all methods are compared under different numbers of snapshots. As the number of snapshots increases, the MSE of 1-bit MUSIC tends to be stable, and the estimation accuracy of other methods has improved. The performance improvement of the proposed method is particularly significant, and the performance gradually approaches that of SS-MUSIC.

[0197] As Figure 6 shown, Figure 6 shows the estimation performance of six methods under different numbers of antennas. As the number of antennas increases, the advantage of SS-MUSIC over the algorithms based on single-bit quantized data becomes more obvious, but the performance of the proposed method always ranks first among all single-bit quantization algorithms.

[0198] Furthermore, as Figure 7 shown, based on the above single-bit direction-of-arrival estimation method with signal amplitude recovery, the present invention also correspondingly 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 includes:

[0199] A signal model generation module 51, configured to obtain the signals at each snapshot moment of the signal source from a uniform linear array receiver, introduce a non-zero threshold to perform single-bit quantization on the signals at each snapshot moment, and obtain a signal model;

[0200] A signal model reconstruction module 52, configured 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;

[0201] An optimization problem construction module 53, configured to construct a single-bit DOA estimation optimization problem based on the target signal model using the truncated Frobenius norm and the L 2,0 norm, and convert the optimization problem into a target optimization problem using the semi-quadratic technique;

[0202] An optimization problem solving module 54, configured to solve the target optimization problem using the proximal alternating minimization algorithm and the forward-backward splitting algorithm to obtain the estimated direction of the signal source, the estimated number of signal sources, and the estimated amplitude of the signal.

[0203] Furthermore, as Figure 8 shown, based on the above single-bit direction-of-arrival estimation method and system with signal amplitude recovery, the present invention also correspondingly provides a terminal, which 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 the shown components, and more or fewer components can be alternatively implemented.

[0204] The memory 20 may be an internal storage unit of the terminal in some embodiments, such as a hard disk or memory of the terminal. The memory 20 may also be an external storage device of the terminal in other embodiments, such as a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) card, a Flash Card, etc. equipped on the terminal. Further, the memory 20 may also include both the internal storage unit and the external storage device of the terminal. The memory 20 is used to store application software installed on the terminal and various types of data, such as program codes for installing the terminal. The memory 20 may also be used to temporarily store data that has been output or will be output. In one embodiment, a single-bit direction-of-arrival estimation program 40 with signal amplitude recovery is stored on the memory 20, and the single-bit direction-of-arrival estimation program 40 with signal amplitude recovery can be executed by the processor 10 to implement the single-bit direction-of-arrival estimation method with signal amplitude recovery in this application.

[0205] The processor 10 may be a central processing unit (CPU), a microprocessor, or other data processing chips in some embodiments, and is used to run the program codes stored in the memory 20 or process data, such as executing the single-bit direction-of-arrival estimation method with signal amplitude recovery.

[0206] The display 30 may be an LED display, a liquid crystal display, a touch liquid crystal display, and an OLED (Organic Light-Emitting Diode) toucher, etc. in some embodiments. 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 through a system bus.

[0207] 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:

[0208] Obtain signals of each snapshot moment of the signal source from a uniform linear array receiver, introduce a non-zero threshold to perform single-bit quantization on the signals of each snapshot moment, and obtain a signal model;

[0209] 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;

[0210] Based on the target signal model, use the truncated Frobenius norm and the L 2,0 norm to construct a single-bit DOA estimation optimization problem, and use the semi-quadratic technique to transform the optimization problem into a target optimization problem;

[0211] Use the proximal alternating minimization algorithm and the forward-backward splitting algorithm to solve the target optimization problem to obtain the estimated direction of the signal source, the estimated number of signal sources, and the estimated amplitude of the signal.

[0212] Among them, obtaining the signals at each snapshot moment of the signal source from a uniform linear array receiver, and introducing a non-zero threshold to perform single-bit quantization on the signals at each snapshot moment to obtain a signal model, specifically including:

[0213] Obtain the signals at each snapshot moment of the signal source from a uniform linear array receiver, and the uniform linear array receiver is an array manifold matrix :

[0214] ;

[0215] ;

[0216] Among them, is the steering vector corresponding to the direction angle of arrival of the first narrowband signal, is the steering vector corresponding to the direction angle of arrival of the second narrowband signal, is the th steering vector corresponding to the direction angle of arrival of the narrowband signal, is the th steering vector corresponding to the direction angle of arrival of the narrowband signal, is the natural constant, is the imaginary unit, is the number of narrowband signals as of the direction angle of arrival of the signal, is the adjacent element spacing of the uniform linear array receiver, is the wavelength of the incident signal, is the total number of elements of the uniform linear array receiver, represents the transpose;

[0217] Introduce a non-zero threshold to perform single-bit quantization on the signals at each snapshot moment to obtain a signal model :

[0218] ;

[0219] ;

[0220] ;

[0221] ;

[0222] wherein, 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 sign function, and are the real and imaginary parts of the complex number respectively, is the total number of snapshots, is the signal of each signal source in the first snapshot, is the signal of each signal source in the second snapshot, is the -th signal of each signal source in the snapshot, is the -th signal of each signal source in the snapshot, is the -th 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, is the -th noise vector when the sensor receives the signal in the snapshot, is the -th noise vector when the sensor receives the signal in the snapshot.

[0223] Among them, reconstructing the signal model, using the smooth hyperbolic tangent function to replace the sign function of the reconstructed signal model to obtain the replaced model, and reconstructing the replaced model to obtain the target signal model specifically includes:

[0224] Reconstructing the signal model to transfer the noise from inside the sign function to the outside to obtain the reconstructed signal model :

[0225] ;

[0226] wherein, is the noise matrix, and the real and imaginary parts of each element in the noise matrix take values between -2, 0, and 2 respectively;

[0227] Using the smooth hyperbolic tangent function to replace the reconstructed signal model The sign function is used to obtain the replaced signal model :

[0228] ;

[0229] ;

[0230] Among them, is the approximation error term, is the complex hyperbolic tangent function, is the hyperbolic tangent function;

[0231] The replaced model is reconstructed to obtain the target signal model :

[0232] ;

[0233] ;

[0234] ;

[0235] Among them, is the target manifold matrix, is the target signal source matrix, is the real-valued identity matrix, is to perform a merging operation on the array manifold matrix and the quantization threshold matrix , is to perform a merging operation on the transpose of the signal source matrix and the real-valued identity matrix .

[0236] Among them, based on the target signal model, a single-bit DOA estimation optimization problem is constructed using the truncated Frobenius norm and the L 2,0 norm, and the optimization problem is converted into a target optimization problem using the semi-quadratic technique, specifically including:

[0237] Based on the target signal model , a single-bit DOA estimation optimization problem is constructed using the truncated Frobenius norm and the L 2,0 norm:

[0238] ;

[0239] such that ;

[0240] Among them, is the truncated Frobenius norm, is the penalty parameter, is the L 2,0 norm, represents the number of rows of the matrix, is the target signal source matrix 's first rows;

[0241] The semi - quadratic technique is used to transform the form of the optimization problem to obtain a tractable target optimization problem:

[0242] ;

[0243] such that ;

[0244] where, is the Frobenius norm, is a function acting separately on the real and imaginary parts.

[0245] Among them, the proximal alternating minimization algorithm and the forward - backward splitting algorithm are used to solve the target optimization problem, and the signal source estimation direction, the signal source estimation number, and the signal estimation amplitude are obtained. Specifically, it includes:

[0246] The proximal alternating minimization algorithm is used to obtain the first iterative process in complex form and the second iterative process in complex form of the target optimization problem. The 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. According to the solution results, the signal source estimation direction and the signal source estimation number are calculated;

[0247] Extract the corresponding columns from the array manifold matrix to construct a column matrix, extract the corresponding rows 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 an amplitude estimation problem is obtained according to the real - valued signal model;

[0248] The proximal alternating minimization algorithm is used to obtain the first iterative process in real form and the second iterative process in real form of the amplitude estimation problem. The forward - backward splitting algorithm is used to solve the first iterative process in real form, and the element - by - element solution method is used to solve the second iterative process in real form. According to the solution results, the signal estimation amplitude is calculated.

[0249] 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:

[0250] 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 :

[0251] ;

[0252] ;

[0253] ;

[0254] 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;

[0255] 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 :

[0256] ;

[0257] ;

[0258] ;

[0259] 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 Iterative process of the previous forward-backward splitting algorithm is in the iterative process of the previous forward-backward splitting algorithm is the i-th row is the storage space is the array manifold matrix is the number of columns is the quantization threshold matrix is the number of columns is L 2 norm

[0260] Perform element-by-element solution on the complex second iterative process to obtain the solution result. According to the solution result, the first iterative update formula, the second iterative update formula, and the third iterative update formula, through iterations, calculate the first target solution ;

[0261] Calculate the estimated direction and number of signal sources according to the first target solution:

[0262] ;

[0263] ;

[0264] where The first to S rows of are the solutions of the matrix corresponding to the first target solution is is the row vector of 2 norm

[0265] For Identify the peaks in to determine the estimated direction and number of signal sources

[0266] where, extracting the corresponding columns from the array manifold matrix to construct a column matrix, extracting the corresponding rows from the signal source matrix to construct a row matrix, performing signal modeling and rewriting according to the column matrix and the row matrix to obtain a real-valued signal model, and obtaining an amplitude estimation problem according to the real-valued signal model, specifically including:

[0267] Suppose the estimated far-field and uncorrelated signals are where is the direction angle of arrival of the th narrowband signal is the direction angle of arrival of the second narrowband signal is the The direction of arrival angle of a narrowband signal is the direction of arrival angle of the -th narrowband signal;

[0268] Extract the corresponding column from the array manifold matrix to construct a column matrix , extract the corresponding row from the signal source matrix to construct a row matrix , and obtain a signal amplitude model according to the column matrix and the row matrix :

[0269] ;

[0270] Rewrite the signal amplitude model into a real-valued signal model in real-valued form:

[0271] ;

[0272] wherein, , , and are respectively the real-valued forms of , , and ;

[0273] According to the real-valued signal model , obtain an amplitude estimation problem:

[0274] ;

[0275] wherein, is a convex set.

[0276] The present invention also provides a computer-readable storage medium, wherein the computer-readable storage medium stores a single-bit direction-of-arrival estimation program with signal amplitude recovery, and when the single-bit direction-of-arrival estimation program with signal amplitude recovery is executed by a processor, the steps of the single-bit direction-of-arrival estimation method with signal amplitude recovery as described above are implemented.

[0277] In summary, the present application provides a single-bit direction-of-arrival estimation method, system, terminal, and storage medium with signal amplitude recovery. The method includes: obtaining signals of each snapshot moment of a signal source from a uniform linear array receiver, introducing a non-zero threshold to perform single-bit quantization on the signals of each snapshot moment to obtain a signal model; reconstructing the signal model, using a smooth hyperbolic tangent function to replace the sign function of the reconstructed signal model and performing reconstruction to obtain a target signal model; based on the target signal model, using the truncated Frobenius norm and the L 2,0 norm to construct a single-bit DOA estimation optimization problem, and using the semi-quadratic technique to convert the optimization problem into a target optimization problem; using the proximal alternating minimization algorithm and the forward-backward splitting algorithm to solve the target optimization problem to obtain the estimated direction of the signal source, the estimated number of signal sources, and the estimated amplitude of the signal. The present invention eliminates the prior dependence on the number of signal sources and accurately estimates the amplitude of the signal source, improving the accuracy of DOA estimation.

[0278] It should be noted that in this article, the term "including", "comprising", or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article, or terminal including a series of elements not only includes those elements but also includes other elements not explicitly listed, or further includes elements inherent to such a process, method, article, or terminal. Without further limitation, an element defined by the statement "including one..." does not exclude the existence of another identical element in the process, method, article, or terminal including that element.

[0279] Of course, those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. 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 methods. Among them, any reference to a memory, storage, database, or other medium used in the embodiments provided by the present invention can include non-volatile and / or volatile memories. Non-volatile memories can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memories can include random access memory (RAM) or external cache memory. By way of 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 (DDR SDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and Rambus dynamic RAM (RDRAM), etc.

[0280] It should be understood that the application of the present invention is not limited to the above examples. For those of ordinary skill in the art, improvements or transformations can be made according to the above description. All such improvements and transformations should fall within the protection scope of the appended claims of 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; Signal Model Reconstruct the signal by transferring the noise from the inside of the symbol function to the outside and obtain the reconstructed signal model. : ； in, is a noise matrix, the real part and imaginary part of each element in the noise matrix are respectively between -2, 0 and 2, is the sign function of complex numbers; 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, and are the real and imaginary parts of the complex number respectively; 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 and 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; Based on the target signal model, a single-bit DOA estimation optimization problem is constructed using the truncated Frobenius norm and the L2,0 norm, and the optimization problem is converted into a target optimization problem using a semi-quadratic technique; 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 signal source matrix to be estimated, is the noise vector, is the quantization threshold matrix, is the symbolic function, 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: Based on the target signal model, a single-bit DOA estimation optimization problem is constructed using the truncated Frobenius norm and the L2,0 norm, and the optimization problem is converted into a target optimization problem using a semi-quadratic technique, specifically including: Based on the target signal model , the single-bit DOA estimation optimization problem is constructed using the truncated Frobenius norm and L2,0 norm: ； Make ; in, is the truncated Frobenius norm, is the penalty parameter, is the L2,0 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.

4. The single-bit direction of arrival estimation method with signal amplitude recovery according to claim 3, 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.

5. The single-bit direction of arrival estimation method with signal amplitude recovery according to claim 4, 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 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.

6. The single-bit direction of arrival estimation method with signal amplitude recovery according to claim 4, 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.

7. 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; 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, the real part and imaginary part of each element in the noise matrix are respectively between -2, 0 and 2, is the sign function of complex numbers; 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, and are the real and imaginary parts of the complex number respectively; 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 and 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; An optimization problem construction module, for constructing a single-bit DOA estimation optimization problem based on the target signal model using a truncated Frobenius norm and an L2,0 norm, and converting the optimization problem into a target optimization problem using a semi-quadratic technique; 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.

8. 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 6 are implemented.

9. 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 1-6 are implemented.

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