Sensitivity-integrated multi-target direction-of-arrival estimation method

Abstract

The invention discloses a communication and sensing integrated multi-target direction of arrival estimation method, which comprises the following steps of: constructing a communication and sensing integrated system for describing a communication and sensing collaborative architecture between a first base station and a second base station, and constructing a reconfigurable intelligent reflecting surface signal receiving model and a second base station signal receiving model under the system; carrying out optimization processing on the second base station signal receiving model, constructing a positive semidefinite programming problem model based on atom norm minimization, and taking a minimization signal reconstruction error as an optimization target; carrying out decomposition solving on the matrix by adopting an alternating direction multiplier method of a dual-path self-adaptive penalty mechanism based on residual driving so as to output a Hermitian Toeplitz matrix; and constructing a reconstructed space covariance matrix based on the optimized Hermitian Toeplitz matrix, and performing spectrum peak search by adopting a multiple signal classification algorithm to finally obtain a multi-target direction of arrival estimation value. According to the method, a synergistic effect is formed in three aspects of interference suppression, robust estimation and low-complexity optimization, an efficient and feasible technical scheme is provided for high-precision and low-delay moving target positioning in a 6G sensing integrated system, and meanwhile, a lightweight sensing solution is provided for the Internet of Things with limited resources.

Description

Technical Field

[0001] This invention relates to the field of next-generation information technology, and in particular to a multi-target direction-of-arrival estimation method integrating sensing and communication. Background Technology

[0002] With the rapid development of 6G, Integrated Sensing and Communication (ISAC) technology has become a key driving force for achieving high-precision mobile target positioning and reliable wireless communication, making it possible to achieve environmental awareness without additional dedicated sensing hardware. Direction of Arrival (DOA) estimation is one of the key technologies for achieving positioning and environmental awareness. However, existing DOA estimation methods have significant limitations. Delay-based methods rely on synchronization reference signals, requiring additional synchronization links to ensure time consistency. Traditional array signal processing methods, while not relying on synchronization mechanisms, depend on multiple radio frequency channels and antenna arrays, resulting in complex system hardware, high deployment costs, and high sensitivity to interference. Reconfigurable Intelligent Surfaces (RIS) offer an innovative solution to the aforementioned challenges by dynamically manipulating signal reflection through programmable electromagnetic units. RIS assists signal propagation by reducing the number of RF links while enhancing received signal quality, significantly reducing system hardware complexity, and demonstrating great potential in passive sensing scenarios. However, existing RIS-assisted direction-of-arrival estimation methods still face key challenges in practical integrated sensing deployments. First, in dense scenarios, co-channel interference between the direct path signal of the wireless access point and the target reflected signal reduces angle resolution accuracy and parameter estimation accuracy. Second, signal crosstalk and mechanical vibration in integrated sensing systems introduce anomalous perturbations and outliers during sparse recovery, violating the grid-independent property of Atomic Norm Minimization (ANM). Finally, traditional ANM minimization methods using semidefinite programming have high computational complexity when dealing with large-scale RIS arrays, making it difficult to meet the real-time positioning requirements of moving targets. Therefore, there is an urgent need to develop a more efficient direction-of-arrival estimation method for reconfigurable intelligent reflector-assisted sensing systems to meet the practical application requirements of 6G sensing integration. Summary of the Invention

[0003] This invention provides a multi-target direction-of-arrival estimation method integrating sensing and communication to overcome the above-mentioned technical problems.

[0004] To achieve the above objectives, the technical solution of the present invention is as follows: A multi-target direction-of-arrival estimation method integrating sensing and communication, comprising the following steps: S1. Construct a sensor-integrated system for describing the communication and sensing collaborative architecture between the first base station and the second base station. The sensor-integrated system also includes a reconfigurable smart reflector, multiple moving targets, and interference scatterers. A multipath channel model is constructed based on the aforementioned integrated sensing system. This model includes a reconfigurable intelligent reflector signal receiving model and a second base station signal receiving model. The signal transmission relationships within the integrated sensing system are described using these two models. The reconfigurable smart reflector signal receiving model is used to describe the signal transmission process of the signal transmitted by the first base station to the reconfigurable smart reflector through the main path and the interference path. The second base station signal receiving model is constructed based on the reconfigurable intelligent reflector signal receiving model and is used to describe the multipath signals received by the second base station; S2. Optimize the signal receiving model of the second base station, construct a semidefinite programming problem model based on the minimization of the atomic norm based on the optimized signal receiving model of the second base station, and take minimizing the signal reconstruction error as its optimization objective. S3. The alternating direction multiplier method based on the residual-driven dual-path adaptive penalty mechanism is used to decompose and solve the semidefinite programming problem model based on atomic norm minimization, so as to output the Hermitian Toeplitz matrix. S4. Perform structural repair and outlier removal on the Hermitian Toeplitz matrix to obtain the optimized Hermitian Toeplitz matrix. S5. Construct a reconstructed spatial covariance matrix based on the optimized Hermitian Toeplitz matrix; S6. Based on the reconstructed spatial covariance matrix, a multi-signal classification algorithm is used to perform spectral peak search to obtain the estimated direction of arrival (DOA) values ​​for multiple targets.

[0005] Furthermore, the specific steps for constructing the reconfigurable smart reflector signal receiving model include: Define the signal transmitted by the first base station The expression is as follows: (1) In the formula: This indicates the transmission power of the first base station; Indicates the modulation symbols that carry communication data; Represents an integer; Indicates the baseband shaping pulse; Indicates the symbol period; Setting the first The positions of the moving targets are It will then be transmitted by the first base station and pass through the second... The signal of a moving target arriving at the reconfigurable smart reflector is defined as: (2) In the formula: This represents the summation of signals over all moving targets, where For moving target index, ; Indicates the first Complex scattering coefficients of a moving target; Indicates the distance from the first base station to the... Distance to a moving target; Indicates the first The distance from a moving target to the reconfigurable smart reflective surface; This indicates that the signal transmitted by the first base station passes through the [missing information]. Propagation delay from a moving target to a reconfigurable smart reflective surface; Indicates the propagation delay The original signal; Indicates the signal wavelength; Indicates the first The azimuth angle of the incident signal from a moving target to a reconfigurable smart reflector; It will be transmitted from the first base station and pass through the [missing information]. The signal of an interfering scatterer reaching the reconfigurable smart reflector is defined as: (3) In the formula: This represents the summation of the signals over the interfering scatterers, where Index for interfering scatterers, ; Indicates the first Complex scattering coefficients of individual interfering scatterers; Indicates the distance from the first base station to the... The distance between the interfering scatterers; Indicates the first The distance from each interfering scatterer to the reconfigurable smart reflector; This indicates that the signal transmitted by the first base station passes through the [missing information]. The propagation delay from an interfering scatterer to the reconfigurable smart reflector; Indicates the propagation delay The original signal; Indicates the first The azimuth angle of the incident signal from the interfering scatterer to the reconfigurable smart reflector; The signal transmitted by the first base station and arriving at the reconfigurable smart reflector is defined as: (4) In the formula: This represents the complex attenuation coefficient from the first base station to the reconfigurable smart reflector; This represents the distance from the first base station to the reconfigurable smart reflector; This represents the propagation delay of the signal transmitted from the first base station to the reconfigurable smart reflector; Indicates the propagation delay The original signal; This represents the azimuth angle of the incident signal from the first base station to the reconfigurable smart reflector; Based on equations (2)-(4), a reconfigurable smart reflector signal receiving model is constructed, which is expressed as follows: (5) In the formula: For the reconfigurable smart reflective surface The total signal received by each electromagnetic unit; Indicates the index of the electromagnetic unit of the reconfigurable smart reflector. .

[0006] Furthermore, the specific steps for constructing the second base station signal reception model include: Define the first reconfigurable smart reflective surface The electromagnetic unit in the first... The complex reflection coefficient of the time slot is: (6) In the formula: Indicates the time slot index. ; The first reconfigurable smart reflector The electromagnetic unit in the first... The reflection amplitude of the time slot; The first reconfigurable smart reflector The electromagnetic unit in the first... The reflection phase of the time slot; Then the reconfigurable intelligent reflective surface The electromagnetic unit in the first... The reflected signal of the time slot is: (7) Based on equation (7), it will be transmitted by the first base station, after passing through the... The signal of a moving target arriving at the reconfigurable smart reflector and being reflected by the reconfigurable smart reflector to the second base station is defined as: (8) In the formula: This represents the joint complex attenuation coefficient of the path; This indicates the distance from the reconfigurable smart reflector to the second base station; This indicates that the signal transmitted by the first base station passes through the [missing information]. The propagation delay of a mobile target from the reconfigurable smart reflector to the second base station; Indicates the propagation delay The The electromagnetic unit in the first... The reflected signal of the time slot; This indicates that the reconfigurable smart reflective surface reflects and carries the first... The signal azimuth angle of the signal scattered by a moving target and incident on the second base station; It will be transmitted from the first base station, after passing through the... The signal that arrives at the reconfigurable smart reflector from an interfering scatterer and is reflected by the reconfigurable smart reflector to the second base station is defined as: (9) In the formula: This represents the joint complex attenuation coefficient of the path; This indicates the distance from the reconfigurable smart reflector to the second base station; This indicates that the signal transmitted by the first base station passes through the [missing information]. The propagation delay of an interfering scatterer from the reconfigurable smart reflector to the second base station; Indicates the propagation delay The The electromagnetic unit in the first... The reflected signal of the time slot; This indicates that the reconfigurable smart reflective surface reflects and carries the first... The signal azimuth angle of the signal incident on the second base station is the signal scattered by an interfering scatterer. The signal transmitted from the first base station to the reconfigurable smart reflector and reflected by the reconfigurable smart reflector to the second base station is defined as: (10) In the formula: This represents the joint complex attenuation coefficient of the path; This indicates the distance between the reconfigurable smart reflector and the second base station; This indicates the propagation delay of the signal from the reconfigurable smart reflector to the second base station; Indicates the propagation delay The The electromagnetic unit in the first... The reflected signal of the time slot; This represents the azimuth angle of the signal incident on the second base station, which is reflected by the reconfigurable smart reflector and has no intermediate scattering source. The signal transmitted from the first base station and directly reaching the second base station is defined as: (11) In the formula: This represents the complex attenuation coefficient of the path from the first base station to the second base station; This indicates the distance between the first base station and the second base station; This indicates the propagation delay of the signal transmitted from the first base station to the second base station; The second base station signal reception model is constructed based on equations (8)-(11), and is expressed as follows: (12) In the formula: It is Gaussian white noise.

[0007] Furthermore, in S2, the second base station signal reception model is optimized. The specific steps for constructing a semidefinite programming problem model based on atomic norm minimization based on the optimized second base station signal reception model include: After eliminating multiple redundant signal paths at the second base station receiver, the received signal of the second base station is optimized as follows: (13) Furthermore, the signal received by the second base station is rewritten as The vector of each time slot is obtained by integrating the intermediate expression of the received signal: (14) In the formula: Indicates transpose; Represents the array manifold vector. ; Indicating reconfigurable smart reflective surfaces in The reflection state matrix within the nth time slot, its nth time slot Line number Column elements represent the first The electromagnetic unit in the first... The reflection coefficient corresponding to the time slot; It represents the Hadamardi (or Hadama) stack; This is a Gaussian white noise vector that has been integrated synchronously with the received signal; in, (15) (16) In the formula: Represents the set of complex numbers; Based on the reconfigurable smart reflector reflection state matrix Array manifold vector Based on the definition, we can further obtain the vector form of the signal received at the second base station, which is the optimized signal reception model of the second base station, expressed as: (17) In the formula: This represents the array response matrix of the moving target in the main path; This represents the array response matrix of the interfering scatterers in the interference path; This represents the complex envelope vector of the moving target in the main path signal; This represents the complex envelope vector of the interfering scatterer in the interference path signal; in, (18) (19) Based on the optimized second base station signal reception model, a semidefinite programming problem model based on atomic norm minimization is constructed, which is expressed as: (20) In the formula: This represents the vector of observation signals received by the second base station in multiple time slots; for The corresponding equivalent measurement matrix; The vector is the sparse representation of the angle domain to be estimated. Indicates conjugate transpose; This represents the signal reconstruction error term; For regularization parameters; Represents the atomic norm; It is a Hermitian Toeplitz matrix; To and Associated constant scalars; This represents the set of Hermitian Toeplitz matrices.

[0008] Furthermore, in S3, the specific steps of using the alternating direction multiplier method with a residual-driven dual-path adaptive penalty mechanism to decompose and solve the semidefinite programming problem model based on atomic norm minimization to output the Hermitian Toeplitz matrix include: S31, the sparse representation vector of the angle domain in equation (20) Perform path-level splitting to transform the original optimization problem into a bivariate optimization problem under consistency constraints, resulting in: (twenty one) In the formula: The sparse variables representing the main path are... Obtained through array response matrix mapping; The sparse variables representing the interference paths are... Obtained through array response matrix mapping; in: (twenty two) (twenty three) S32. An iterative solution is performed using the alternating direction multiplier method based on a residual-driven dual-path adaptive penalty mechanism. Each iteration includes the following update steps: S321, Calculate the first The original residual at the next iteration is given by the formula: (twenty four) In the formula: and They represent the first Main path variables and interference path variables in the next iteration; Calculate the penalty factor based on the interference path. The dual residual at the next iteration is given by the formula: (25) in, Indicates the first The penalty factor corresponding to the interference path in the next iteration; S322. Update the first residual based on the original residual and the dual residual. The consistency weighting matrix constructed in the next iteration, driven by the residual, is given by the following formula: (26) In the formula: Represents an identity matrix with dimensions consistent with those of the main path variables and interference path variables; Indicates the first scalar weight coefficients obtained by adaptive calculation of residuals in the next iteration; Representing vectors Norm; This represents a preset positive constant used to prevent the denominator from being zero; S323, The penalty factor for updating the main path is: (27) In the formula: The initial value of the main path penalty factor; The main path penalty enhancement coefficient; This indicates an indicator function that takes the value 1 if the condition is true and 0 otherwise. Indicates the residual driving term in the th The output at the next iteration; The threshold for interference detection; The penalty factor for updating the interference path is: (28) In the formula: This is the initial value for the interference path penalty factor; This is the interference path penalty enhancement coefficient; Indicates the residual driving term in the th The output at the next iteration; The threshold for interference detection; S324. The Hermitian Toeplitz positive semidefinite matrix is ​​updated based on the penalty factor of the main path as follows: (29) In the formula: The characteristic function of the Hermitian Toeplitz cone is used to maintain the structural consistency and low-rank property of the matrix; This represents the mapping operator that constructs the Hermitian Toeplitz matrix from the sparse variables of the main path; Represents the standard Frobenius norm; S325. Update the original variable for the joint weighting of the main path and interfering paths: (30) In the formula: This represents the augmented Lagrangian function after introducing the two-path penalty factor; As dual variables; Indicates the first The consistency weighting matrix constructed in the next iteration is driven by the residual; Indicates the first In the next iteration, a residual-driven weighted second penalty is applied to the difference between the main path variable and the interference path variable in the angle domain; The update formula for the dual variable among the original variables is: (31) S326. Determine whether both the original residual and the dual residual are less than the preset threshold. If so, it means that the current iteration result has satisfied the consistency constraint and the KKT optimality condition. The algorithm has converged and terminates the iteration, and outputs the final solution. That is, the Hermitian Toeplitz matrix; otherwise, repeat S321-S325 until the final solution is output.

[0009] Furthermore, in S4, the specific steps for performing structural repair and outlier removal on the Hermitian Toeplitz matrix to obtain the optimized Hermitian Toeplitz matrix include: Determine the Hermitian Toeplitz matrix Does it simultaneously satisfy the Toeplitz structural constraints? If so, then the preliminarily optimized Hermitian Toeplitz matrix is ​​obtained. ,and Otherwise, the least squares projection method is used to transform the matrix. Projected onto the Hermitian Toeplitz matrix set The Hermitian Toeplitz matrix was obtained after preliminary optimization. Specifically, it is expressed as: (32) The Hermitian Toeplitz matrix after initial optimization Eigenvalue decomposition is performed to obtain the signal subspace and noise subspace. Utilizing the principle that these two subspaces are statistically orthogonal, subspace projection is performed, and outliers deviating from the main signal subspace are identified and suppressed to obtain the final optimized Hermitian Toeplitz matrix. And the final optimized Hermitian Toeplitz matrix Includes an optimized signal vector sequence obtained from the main path recovery. .

[0010] Furthermore, in S5, the specific steps for constructing the reconstructed spatial covariance matrix based on the optimized Hermitian Toeplitz matrix include: Optimized signal vector sequence based on the optimized Hermitian Toeplitz matrix Construct the reconstructed spatial covariance matrix, expressed as: (33) In the formula: For the number of snapshots; Indicates the snapshot index. ; The robust statistical computer based on Huber loss is defined as follows: (34) In the formula, For threshold parameters; Represents a symbolic function.

[0011] Furthermore, in S6, the specific steps of using a multiple signal classification algorithm to perform spectral peak search based on the reconstructed spatial covariance matrix to obtain multi-target direction-of-arrival estimates include: S61, Subspace Decomposition: For the reconstructed spatial covariance matrix Eigenvalue decomposition is performed, which is expressed as: (35) In the formula: Let be a unitary matrix, and its column vectors be . eigenvectors; It is a diagonal matrix composed of eigenvalues; For the signal subspace, by the previous eigenvalues The corresponding feature vectors are composed of; For the noise subspace, by the remaining eigenvalues The corresponding feature vectors are composed of each other, and the two satisfy an orthogonal relationship; S62. Spatial spectrum construction and search in multiple signal classification algorithms: Based on the reconstructed spatial covariance matrix after eigenvalue decomposition, the spatial spectral function of the multi-signal classification algorithm is defined as follows: (36) In the formula: This represents the array manifold vector corresponding to the candidate angle; Within the candidate angle search range, i.e. Within the range, calculate the spatial spectral function values, sort the spatial spectral function values ​​in descending order, and select the top values. Angles corresponding to each function value As the estimated direction of arrival.

[0012] Beneficial Effects: This invention constructs a multipath channel model to describe the signal transmission relationships within the integrated sensing system; optimizes the signal reception model based on reconfigurable smart reflectors and second base stations, and constructs a semidefinite programming problem model based on atomic norm minimization; employs an alternating direction multiplier method with a residual-driven dual-path adaptive penalty mechanism to decompose and solve the semidefinite programming problem model based on atomic norm minimization, reducing the solution complexity of the semidefinite programming problem in large-scale reconfigurable smart reflector scenarios and improving convergence efficiency and robustness under non-stationary interference environments, thereby obtaining the Hermitian Toeplitz matrix for direction-of-arrival estimation; finally, the direction-of-arrival estimation value for multiple targets is obtained based on the Hermitian Toeplitz matrix. This invention achieves a synergistic effect in interference suppression, robust estimation, and low-complexity optimization, providing an efficient and feasible technical solution for high-precision, low-latency mobile target positioning and communication beam control in 6G integrated sensing systems, while also providing a lightweight sensing solution for resource-constrained IoT. Attached Figure Description To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0013] Figure 1 This is a flowchart of a multi-target direction-of-arrival estimation method integrating sensing and communication in this invention; Figure 2 This is a schematic diagram of the signal transmission and reflection path based on the multipath channel model in an embodiment of the present invention; Figure 3 This is a schematic diagram of the angle modeling of the reconfigurable smart reflective surface in an embodiment of the present invention. Detailed Implementation

[0014] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0015] This embodiment provides a multi-target direction-of-arrival estimation method integrating sensing and communication, such as... Figure 1 As shown, the specific steps include: S1. Construct a sensor-integrated system for describing the communication and sensing collaborative architecture between the first base station and the second base station. The sensor-integrated system also includes a reconfigurable smart reflector, multiple moving targets, and interference scatterers. A multipath channel model is constructed based on the aforementioned integrated sensing system. This model includes a reconfigurable intelligent reflector signal receiving model and a second base station signal receiving model. The signal transmission relationships within the integrated sensing system are described using these two models, wherein: The reconfigurable smart reflector signal receiving model is used to describe the signal transmission process of the signal transmitted by the first base station to the reconfigurable smart reflector through the main path and the interference path. The second base station signal receiving model is constructed based on the reconfigurable intelligent reflector signal receiving model and is used to describe the multipath signals received by the second base station; S2. Optimize the signal receiving model of the second base station, construct a semi-definite programming problem model based on the minimization of the atomic norm based on the optimized signal receiving model of the second base station, and take minimizing the signal reconstruction error as its optimization objective. S3. The alternating direction multiplier method based on the residual-driven dual-path adaptive penalty mechanism is used to decompose and solve the semidefinite programming problem model based on atomic norm minimization, so as to output the Hermitian Toeplitz matrix. S4. Perform structural repair and outlier removal on the Hermitian Toeplitz matrix to obtain the optimized Hermitian Toeplitz matrix. S5. Construct a reconstructed spatial covariance matrix based on the optimized Hermitian Toeplitz matrix; S6. Based on the reconstructed spatial covariance matrix, a multi-signal classification algorithm is used to perform spectral peak search to obtain the estimated direction of arrival (DOA) values ​​for multiple targets. As shown in Figure 2, this embodiment constructs an integrated sensing system comprising a first base station, a reconfigurable smart reflector, a second base station, a moving target, and an interference scatterer. The first base station transmits baseband signals to different target areas, propagating via three main paths: the first base station-moving target-reconfigurable smart reflector path (main path); the first base station-interference scatterer-reconfigurable smart reflector path (interference path); and the first base station-reconfigurable smart reflector direct path (interference path). The reconfigurable smart reflector reflects the received signal to the second base station after applying programmable modulation. Furthermore, by controlling the amplitude and phase of the array elements, the reconfigurable smart reflector can flexibly adjust the direction, shape, and energy distribution of the reflected beam, thus achieving both efficient communication and high-precision sensing performance in complex environments.

[0016] Specifically, since both non-moving targets and complex scattering structures may exist simultaneously within the target area, the resulting occlusion effects and multipath propagation can interfere with the main path corresponding to the moving target, thus increasing the direction estimation error. Therefore, this embodiment considers the superposition of signals from reconfigurable smart reflectors and combines them with... Figure 2 Based on the signal transmission path shown, a multipath channel model including direct and interference paths is established.

[0017] In a specific embodiment, the specific steps for constructing the reconfigurable smart reflector signal receiving model include: Define the signal transmitted by the first base station The expression is as follows: (1) In the formula: This indicates the transmission power of the first base station. Indicates the modulation symbols that carry communication data; Represents an integer; Indicates the baseband shaping pulse; Indicates the symbol period; Setting the first The positions of the moving targets are It will then be transmitted by the first base station and pass through the second... The signal of a moving target arriving at the reconfigurable smart reflector is defined as: (2) In the formula: This represents the summation of signals over all moving targets, where For moving target index, ; Indicates the first Complex scattering coefficients of a moving target; Indicates the distance from the first base station to the... Distance to a moving target; Indicates the first The distance from a moving target to the reconfigurable smart reflective surface; This indicates that the signal transmitted by the first base station passes through the [missing information]. Propagation delay from a moving target to a reconfigurable smart reflective surface; Indicates the propagation delay The original signal; Indicates the signal wavelength; Indicates the first The azimuth angle of the incident signal from a moving target to a reconfigurable smart reflector.

[0018] It will be transmitted from the first base station and pass through the [missing information]. The signal of an interfering scatterer reaching the reconfigurable smart reflector is defined as: (3) In the formula: This represents the summation of the signals over the interfering scatterers, where Index for interfering scatterers, ; Indicates the first Complex scattering coefficients of individual interfering scatterers; Indicates the distance from the first base station to the... The distance between the interfering scatterers; Indicates the first The distance from each interfering scatterer to the reconfigurable smart reflector; This indicates that the signal transmitted by the first base station passes through an interfering scatterer. The propagation delay to the reconfigurable smart reflective surface; Indicates the propagation delay The original signal; Indicates the first The azimuth angle of the incident signal from the interfering scatterer to the reconfigurable smart reflector.

[0019] The signal transmitted by the first base station and arriving at the reconfigurable smart reflector is defined as: (4) In the formula: This represents the complex attenuation coefficient of the direct path from the first base station to the reconfigurable smart reflector. This represents the distance from the first base station to the reconfigurable smart reflector; This represents the propagation delay of the signal transmitted from the first base station to the reconfigurable smart reflector; Indicates the propagation delay The original signal; This represents the azimuth angle of the incident signal from the first base station to the reconfigurable smart reflector.

[0020] Based on equations (2)-(4), a reconfigurable smart reflector signal receiving model is constructed, which is expressed as follows: (5) In the formula: For the reconfigurable smart reflective surface The total signal received by each electromagnetic unit; Indicates the index of the electromagnetic unit of the reconfigurable smart reflector. .

[0021] In a specific embodiment, such as Figure 3 The diagram shown is a geometrical schematic of the angular structure of the reconfigurable smart reflector (the reconfigurable smart reflector has a total of...). One electromagnetic unit Figure 3 Only a portion of the electromagnetic units of the reconfigurable smart reflector are listed to illustrate the incident and reflection mechanisms at different angles. Each electromagnetic unit is... The signals are arranged at equal intervals. The incident signal is a plane wave, and the incident angle is... It is incident on the reconfigurable smart reflective surface array. After reflection, it reaches a reflection angle of... Ejected. The path difference in propagation between adjacent electromagnetic units caused by the incident wave is... The corresponding phase difference is The path difference of the reflected wave between adjacent electromagnetic units is: The corresponding phase difference is Therefore, the array manifold vector can be represented as (Incident direction) (Reflection direction) Furthermore, the reflection characteristics of the array manifold vector are dynamically controlled by the complex reflection coefficients of each element of the reconfigurable intelligent reflector. Based on this, the specific steps for constructing the second base station signal reception model include: Define the first reconfigurable smart reflective surface The electromagnetic unit in the first... The complex reflection coefficient of the time slot is: (6) In the formula: Indicates the time slot index. ; The first reconfigurable smart reflector The electromagnetic unit in the first... The reflection amplitude of the time slot determines the intensity of the reflected signal of the electromagnetic unit; The first reconfigurable smart reflector The electromagnetic unit in the first... The reflection phase of the time slot determines the phase shift of the reflected signal of the electromagnetic unit.

[0022] Then the reconfigurable intelligent reflective surface The electromagnetic unit in the first... The reflected signal of the time slot is: (7) Specifically, this embodiment constructs the received signal of the second base station in multiple dimensions: the signal transmitted by the first base station, reaching the reconfigurable smart reflector via the moving target and reflected to the second base station (corresponding to the main path), and the signal reaching the reconfigurable smart reflector via the interference scatterer and reflected to the second base station (corresponding to the interference path) are integrated and transmitted. By separating the moving target signal and the interference scatterer signal, while ensuring the stability of the communication link signal transmission quality, the angular domain sparsity of the moving target signal is used to improve its direction of arrival estimation accuracy. At the same time, covariance matrix modeling is used to suppress coherent interference of the interference scatterer signal, ultimately achieving synergistic optimization of communication transmission and target perception performance.

[0023] Specifically, based on equation (7), it will be transmitted by the first base station, and after passing through the... The signal of a moving target arriving at the reconfigurable smart reflector and being reflected by the reconfigurable smart reflector to the second base station is defined as: (8) In the formula: This represents the joint complex attenuation coefficient of the path; This indicates the distance from the reconfigurable smart reflector to the second base station; This indicates that the signal transmitted by the first base station passes through the [missing information]. The propagation delay of a mobile target from the reconfigurable smart reflector to the second base station; Indicates the propagation delay The The electromagnetic unit in the first... The reflected signal of the time slot; This indicates that the reconfigurable smart reflective surface reflects and carries the first... The signal scattering information of a moving target is incident on the signal azimuth angle of the second base station.

[0024] It will be transmitted from the first base station, after passing through the... The signal that arrives at the reconfigurable smart reflector from an interfering scatterer and is reflected by the reconfigurable smart reflector to the second base station is defined as: (9) In the formula: This represents the joint complex attenuation coefficient of the path; This indicates the distance from the reconfigurable smart reflector to the second base station; This indicates that the signal transmitted by the first base station passes through the [missing information]. The propagation delay of an interfering scatterer from the reconfigurable smart reflector to the second base station; Indicates the propagation delay The The electromagnetic unit in the first... The reflected signal of the time slot; This indicates that the reconfigurable smart reflective surface reflects and carries the first... The signal azimuth angle of the signal scattered by the interfering scatterer is incident on the second base station. The signal transmitted from the first base station to the reconfigurable smart reflector and reflected by the reconfigurable smart reflector to the second base station is defined as: (10) In the formula: This represents the joint complex attenuation coefficient of the path; This indicates the distance between the reconfigurable smart reflector and the second base station; This indicates the propagation delay of the signal from the reconfigurable smart reflector to the second base station; Indicates the propagation delay The The electromagnetic unit in the first... The reflected signal of the time slot; This represents the azimuth angle of the signal incident on the second base station, which is reflected by the reconfigurable smart reflector and has no intermediate scattering source.

[0025] The signal transmitted from the first base station directly to the second base station is defined as: (11) In the formula: This represents the direct path loss coefficient from the first base station to the second base station; This indicates the distance between the first base station and the second base station; This indicates the propagation delay of the signal transmitted from the first base station to the second base station.

[0026] The second base station signal reception model is constructed based on equations (8)-(11), and is expressed as follows: (12) In the formula: It is Gaussian white noise.

[0027] In a specific embodiment, S2 involves optimizing the second base station signal reception model and constructing a semidefinite programming problem model based on atomic norm minimization using the optimized second base station signal reception model. The specific steps include: Specifically, in this embodiment, the second base station is equipped with a multi-RF channel receiver to capture the reflected signals and environmental interference from the reconfigurable smart reflector electromagnetic unit. Since the signal received by the second base station consists of signals of varying power, firstly, the multiple reflected signals received by the second base station are ignored. These signals, after multi-path loss, have power far weaker than the main link, and their contribution to target analysis is negligible. Simultaneously, since the signal enhanced by the reconfigurable smart reflector dominates at the receiving end, the signal from the first base station directly to the second base station without passing through the reconfigurable smart reflector has no gain enhancement, and its power is significantly lower than the enhanced link of the reconfigurable smart reflector; therefore, this path is eliminated. Furthermore, the path from the first base station directly to the second base station via the reconfigurable smart reflector does not carry scattering information of the moving target and is a non-target link. To focus on the signal characteristic analysis of the moving target, even if its power is higher than the main moving target path, this path is eliminated to avoid interference from non-target signals on angle estimation. Therefore, by eliminating multiple redundant signal paths at the receiving end of the second base station, the received signal of the second base station is optimized as follows: (13) Furthermore, the signal received by the second base station is rewritten as The vector of each time slot is obtained by integrating the intermediate expression of the received signal: (14) In the formula: Indicates transpose; Represents the array manifold vector. ; Indicating reconfigurable smart reflective surfaces in The reflection state matrix within the nth time slot, its nth time slot Line number Column elements represent the first The electromagnetic unit in the first... The reflection coefficient corresponding to the time slot; The Hadamard product is used to fuse the phase shift characteristics of the target angle with the reflection control characteristics of the electromagnetic unit of the reconfigurable smart reflector, so as to accurately characterize the target spatial signal features enhanced by the reconfigurable smart reflector. This is a Gaussian white noise vector (already integrated synchronously with the received signal). Among them, (15) (16) In the formula: It represents the set of complex numbers.

[0028] Based on the reconfigurable smart reflector reflection state matrix Array manifold vector Based on the definition, we can further obtain the vector form of the signal received at the second base station, which is the optimized signal reception model of the second base station, expressed as: (17) In the formula: This represents the array response matrix of the moving target in the main path; This represents the array response matrix of the interfering scatterers in the interference path; This represents the complex envelope vector of the moving target in the main path signal; This represents the complex envelope vector of the interfering scatterer in the interference path signal.

[0029] in, (18) (19) Specifically, in this embodiment, the received signal in the form of Equation (17) provides an observation model for sparse recovery based on atomic norm minimization that includes rotational features such as path delay and angle.

[0030] Based on the form of the signal vector received at the second base station, a semi-positive definite programming problem based on minimizing the atomic norm is constructed to recover the target signal representation with angular sparsity under noise and interference environment.

[0031] In a specific embodiment, the semidefinite programming problem model based on atomic norm minimization constructed based on the optimized second base station signal reception model is expressed as follows: (20) In the formula, This represents the vector of observation signals received by the second base station in multiple time slots; for The corresponding equivalent measurement matrix; The vector is the sparse representation of the angle domain to be estimated. This represents the signal reconstruction error term, used to characterize the consistency constraints of the signal model in the form of soft constraints, i.e., by minimizing the difference between the received signal and the equivalent measurement model. The deviation between the two is used to constrain the estimation results to match the actual received signal. This reconstruction error term equivalently serves as a constraint on the signal model during the optimization process, without the need to explicitly introduce an equality constraint form. This is a regularization parameter used to balance reconstruction accuracy with angular domain sparsity; Represents the atomic norm; This represents the conjugate transpose operation; This is the Hermitian Toeplitz matrix, used to characterize the structured priors of array manifolds; To and Associated constant scalars; This represents the set of Hermitian Toeplitz matrices.

[0032] Specifically, through the above modeling, under the constraints of positive semidefiniteness and signal model, it is possible to achieve a sparse representation vector corresponding to the target angle. The optimized estimation is used to recover the target angular features under noise and interference conditions, thus forming an angular domain sparse recovery optimization framework based on atomic norm minimization.

[0033] To reduce the solution complexity of the aforementioned semidefinite programming problem in the scenario of large-scale reconfigurable intelligent reflective surfaces, and to improve the convergence efficiency and robustness under non-stationary disturbance environments, this embodiment proposes a residual-driven dual-path adaptive penalty alternating direction multiplier method by introducing variable splitting and path differentiation mechanisms, based on the traditional alternating direction multiplier method.

[0034] In a specific embodiment, S3, the steps of using the alternating direction multiplier method based on a residual-driven dual-path adaptive penalty mechanism to decompose and solve the semidefinite programming problem model based on atomic norm minimization to output the Hermitian Toeplitz matrix include: S31. Considering the significant differences in statistical characteristics and interference intensity between the main path and the interference path in a multipath channel, the sparse representation vector in the angle domain of equation (20) is modified accordingly. Path-level splitting is performed to obtain the original principal path variables and interference path variables, transforming the original optimization problem into a bivariate optimization problem under consistency constraints, thus providing a foundation for subsequent solutions. The split results in: (twenty one) In the formula, The sparse variables representing the main path are... Obtained through array response matrix mapping; The sparse variables representing the interference paths are... Obtained through array response matrix mapping.

[0035] in: (twenty two) (twenty three) S32. An iterative solution is performed using the alternating direction multiplier method based on a residual-driven dual-path adaptive penalty mechanism. Each iteration includes the following update steps: S321. In this embodiment, within the framework of the alternating direction multiplier method based on a residual-driven dual-path adaptive penalty mechanism, the original residual and dual residual are introduced to measure the degree to which the current iterative solution satisfies the consistency constraint and the Karush–Kuhn–Tucker (KKT) optimality condition, and the calculation of the... The original residual at the next iteration is given by the formula: (twenty four) In the formula: and They represent the first Main path variables and interference path variables in the next iteration; Calculate the penalty factor based on the interference path. The dual residual at the next iteration is given by the formula: (25) in, Indicates the first The penalty factor corresponding to the interference path in the next iteration.

[0036] Specifically, in order to achieve differentiated constraints and dynamic adjustment between the main path and the interference path, this embodiment sets a main path penalty factor and an interference path penalty factor for the main path and the interference path in the multipath channel model, respectively, and dynamically and adaptively updates the value of the penalty factor based on the original residual and the dual residual of the current iteration.

[0037] S322. Update the first residual based on the original residual and the dual residual. The consistency weighting matrix constructed in the next iteration, driven by the residual, is given by the following formula: (26) In the formula, Represents an identity matrix with dimensions consistent with the main path variable and interference path variable, used to apply uniformly weighted consistency constraints to each component in the angle domain without introducing additional direction or angle bias. Indicates the first The scalar weight coefficients obtained by adaptive calculation of residuals in the next iteration are used to adjust the strength of the consistency penalty term in the update of the original variables. Representing vectors Norms are used to quantify key physical quantities such as signal error and vector magnitude, ensuring the rigor of the derivation logic and the clarity of the physical meaning. This represents a preset positive constant used to prevent the denominator from being zero.

[0038] S323, The penalty factor for updating the main path is: (27) In the formula: The initial value of the main path penalty factor; The main path penalty enhancement coefficient; This indicates an indicator function that takes the value 1 if the condition is true and 0 otherwise. Indicates the residual driving term in the th The output at each iteration is used to characterize the changes in the reconstruction residual of the main signal; As the interference detection threshold, when the residual corresponding to the main path Exceeding the threshold At that time, the regularization strength of the main path is adaptively enhanced to accelerate convergence and improve reconstruction stability.

[0039] The penalty factor for updating the interference path is: (28) In the formula: This is the initial value for the interference path penalty factor; This is the interference path penalty enhancement coefficient; Indicates the residual driving term in the th The output at the next iteration is used to characterize the changes in the residuals of the interference path reconstruction. The interference detection threshold is the residual value corresponding to the interference path. Exceeding the threshold At the same time, the regularization strength of the interference path is adaptively enhanced to significantly suppress abnormal interference energy.

[0040] S324. The Hermitian Toeplitz positive semidefinite matrix is ​​updated based on the penalty factor of the main path as follows: (29) In the formula, The characteristic function of the Hermitian Toeplitz cone is used to maintain the structural consistency and low-rank property of the matrix; This represents the mapping operator that constructs the Hermitian Toeplitz matrix from the sparse variables of the main path; The standard Frobenius norm is used to quantify the element-wise deviation between the Hermitian Toeplitz matrix to be updated and the main path reference matrix, combined with the main path penalty factor. This enables precise constraints on matrix updates.

[0041] S325. Update the original variable for the joint weighting of the main path and interfering paths: (30) In the formula, This represents the augmented Lagrangian function after introducing the two-path penalty factor; As dual variables; Indicates the first The consistency weighting matrix constructed by residual driving in the next iteration is used to adaptively adjust the consistency constraint strength between the main and interference path variables; Indicates the first In the next iteration, a residual-driven weighted secondary penalty is applied to the difference between the main path variable and the interference path variable in the angular domain, which is used to adaptively adjust the consistency constraint strength between the two paths.

[0042] The update formula for the dual variable among the original variables is: (31) S326. Determine whether both the original residual and the dual residual are less than the preset threshold. If so, it means that the current iteration result has satisfied the consistency constraint and the KKT optimality condition. The algorithm has converged and terminates the iteration, and outputs the final solution, i.e., the Hermitian Toeplitz matrix. Otherwise, repeat S321-S325 until the final solution is output.

[0043] Specifically, after the above-mentioned residual-driven dual-path adaptive penalty alternating direction multiplier method converges iteratively, an optimized solution that satisfies the KKT optimality conditions can be obtained. The KKT optimality conditions are a set of first-order optimality conditions that must be satisfied when a constrained optimization problem obtains the optimal solution. They are used to determine whether the solution has reached the global optimum or the local optimum.

[0044] Specifically, the matrix obtained in this embodiment is a Hermitian Toeplitz matrix that satisfies the positive semidefinite constraint. , The Hermitian Toeplitz matrix is ​​0, and its diagonal elements maintain constant consistency. Furthermore, this matrix is ​​induced by sparse variables along the main path and serves as a structured carrier for sparse representation in the angular domain. Its low-rank characteristic and Toeplitz structural consistency directly determine the accuracy of subsequent spatial covariance matrix reconstruction and subspace decomposition. Therefore, it is necessary to perform structural consistency checks and outlier suppression on the Hermitian Toeplitz matrix to obtain an optimized Hermitian Toeplitz matrix.

[0045] In a specific embodiment, S4 involves performing structural repair and outlier removal on the Hermitian Toeplitz matrix to obtain an optimized Hermitian Toeplitz matrix. The specific steps include: Because augmented Lagrange updates may introduce numerical perturbations under conditions of strong disturbance or rapid iteration, leading to slight structural distortions in the matrix, including but not limited to non-strict Toeplitz forms or effective rank expansion, it is necessary to modify the Hermitian Toeplitz matrix. Structural analysis is performed to determine whether it simultaneously satisfies the strict Toeplitz structure and low-rank property. If so, the preliminarily optimized Hermitian Toeplitz matrix is ​​obtained. ,and Otherwise, the least squares projection method is used to transform the matrix. Projected onto the Hermitian Toeplitz matrix set The Hermitian Toeplitz matrix was obtained after preliminary optimization. Specifically, it is expressed as: (32) Specifically, this embodiment ensures that the Hermitian Toeplitz matrix recovers strict mathematical structure consistency through the above-described structural repair process, providing reliable low-rank prior constraints for high-resolution angle estimation. The Hermitian Toeplitz matrix after initial optimization Eigenvalue decomposition is performed to obtain the signal subspace and noise subspace. Utilizing the principle that these two subspaces are statistically orthogonal, subspace projection is performed, and outliers deviating from the main signal subspace are identified and suppressed to obtain the final optimized Hermitian Toeplitz matrix. .

[0046] Specifically, this process is equivalent to projectively removing outlier features in the subspace, thereby reducing the damage to the angular domain structure caused by anomalous observations and residual interference, and further enhancing the sparse representation capability of the target signal in the angular space. The final optimized Hermitian Toeplitz matrix... It simultaneously satisfies the requirements of low-rank properties, Toeplitz structure consistency, and angular domain sparsity, and implicitly includes the optimized signal vector sequence recovered from the main path. This is then used as the final output of high-resolution signal recovery.

[0047] In a specific embodiment, the purpose of constructing the reconstructed spatial covariance matrix is ​​to recover the optimized signal vector based on the Hermitian-Toeplitz structure. It is further elevated from the instantaneous observation level to a second-order statistic in a statistical sense, thus providing a stable and reliable input for subsequent subspace-based direction-of-arrival estimation.

[0048] In a specific embodiment, S5, the specific steps for constructing the reconstructed spatial covariance matrix based on the optimized Hermitian Toeplitz matrix include: Optimized signal vector sequence based on the optimized Hermitian Toeplitz matrix Construct the reconstructed spatial covariance matrix, expressed as: (33) In the formula, For the number of snapshots; Indicates the snapshot index. ; The robust statistical computer based on Huber loss is defined as follows: (34) In the formula, For threshold parameters; Represents a symbolic function.

[0049] Specifically, by introducing a robust statistical operator, the influence of residual impulse noise and outlier samples on the covariance matrix estimation can be further suppressed. The resulting reconstructed spatial covariance matrix... It inherits the angular domain structural information preserved during the Hermitian Toeplitz structure restoration process, and also possesses good statistical stability.

[0050] In a specific embodiment, S6, the specific steps of using a multiple signal classification algorithm to perform spectral peak search based on the reconstructed spatial covariance matrix to obtain multi-target direction-of-arrival estimates include: S61, Subspace Decomposition: For the reconstructed spatial covariance matrix Eigenvalue decomposition is performed, which is expressed as: (35) In the formula: Let be a unitary matrix, and its column vectors be . eigenvectors; It is a diagonal matrix composed of eigenvalues; For the signal subspace, by the previous eigenvalues The corresponding feature vectors are composed of; For the noise subspace, by the remaining eigenvalues The corresponding feature vectors are composed of each other, and the two satisfy an orthogonal relationship.

[0051] S62. Spatial spectrum construction and search in multiple signal classification algorithms: Based on the reconstructed spatial covariance matrix after eigenvalue decomposition, the spatial spectral function of the multi-signal classification algorithm is defined as follows: (36) In the formula: This represents the array manifold vector corresponding to the candidate angle.

[0052] Within the candidate angle search range, i.e. Within the range, calculate the spatial spectral function values, sort the spatial spectral function values ​​in descending order, and select the top values. Angles corresponding to each function value As the estimated direction of arrival.

[0053] Beneficial effects: This embodiment addresses the problems of low angular resolution, outlier interference, and high computational complexity in traditional direction-of-arrival (DOA) estimation methods for reconfigurable intelligent reflector-assisted sensing systems. It proposes a residual-driven dual-path adaptive penalty alternating direction multiplier optimization framework. By introducing a dynamic residual adjustment mechanism and independent penalty factors for the main and auxiliary paths, adaptive separation of direct and interfering signals is achieved, significantly improving angular resolution. Combined with Huber robust loss and a dual residual constraint mechanism, the impact of noise and outliers on sparse reconstruction is effectively suppressed, ensuring the grid independence and robustness of atomic norm estimation. Simultaneously, the Toeplitz structure least-squares projection and low-rank subspace correction strategy avoid the dimensionality explosion problem in large-scale positive definite programming solutions, significantly reducing computational complexity and enabling DOA estimation of moving targets.

[0054] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A multi-target direction-of-arrival estimation method integrating sensing and communication, characterized in that, The specific steps include: S1. Construct a sensor-integrated system for describing the communication and sensing collaborative architecture between the first base station and the second base station. The sensor-integrated system also includes a reconfigurable smart reflector, multiple moving targets, and interference scatterers. A multipath channel model is constructed based on the aforementioned integrated sensing system. This model includes a reconfigurable intelligent reflector signal receiving model and a second base station signal receiving model. The signal transmission relationships within the integrated sensing system are described using these two models. The reconfigurable smart reflector signal receiving model is used to describe the signal transmission process of the signal transmitted by the first base station to the reconfigurable smart reflector through the main path and the interference path. The second base station signal receiving model is constructed based on the reconfigurable intelligent reflector signal receiving model and is used to describe the multipath signals received by the second base station; S2. Optimize the signal receiving model of the second base station, construct a semidefinite programming problem model based on the minimization of the atomic norm based on the optimized signal receiving model of the second base station, and take minimizing the signal reconstruction error as its optimization objective. S3. The alternating direction multiplier method based on the residual-driven dual-path adaptive penalty mechanism is used to decompose and solve the semidefinite programming problem model based on atomic norm minimization, so as to output the Hermitian Toeplitz matrix. S4. Perform structural repair and outlier removal on the Hermitian Toeplitz matrix to obtain the optimized Hermitian Toeplitz matrix. S5. Construct a reconstructed spatial covariance matrix based on the optimized Hermitian Toeplitz matrix; S6. Based on the reconstructed spatial covariance matrix, a multi-signal classification algorithm is used to perform spectral peak search to obtain the estimated direction of arrival (DOA) values ​​for multiple targets.

2. The multi-target direction-of-arrival estimation method integrating induction and communication as described in claim 1, characterized in that, The specific steps for constructing the reconfigurable smart reflector signal receiving model include: Define the signal transmitted by the first base station The expression is as follows: (1) In the formula: This indicates the transmission power of the first base station; Indicates the modulation symbols that carry communication data; Represents an integer; Indicates the baseband shaping pulse; Indicates the symbol period; Setting the first The positions of the moving targets are It will then be transmitted by the first base station and pass through the second... The signal of a moving target arriving at the reconfigurable smart reflector is defined as: (2) In the formula: This represents the summation of signals over all moving targets, where For moving target index, ; Indicates the first Complex scattering coefficients of a moving target; Indicates the distance from the first base station to the... Distance to a moving target; Indicates the first The distance from a moving target to the reconfigurable smart reflective surface; This indicates that the signal transmitted by the first base station passes through the [missing information]. Propagation delay from a moving target to a reconfigurable smart reflective surface; Indicates the propagation delay The original signal; Indicates the signal wavelength; Indicates the first The azimuth angle of the incident signal from a moving target to a reconfigurable smart reflector; It will be transmitted from the first base station and pass through the [missing information]. The signal of an interfering scatterer reaching the reconfigurable smart reflector is defined as: (3) In the formula: This represents the summation of the signals over the interfering scatterers, where Index for interfering scatterers, ; Indicates the first Complex scattering coefficients of individual interfering scatterers; Indicates the distance from the first base station to the... The distance between the interfering scatterers; Indicates the first The distance from each interfering scatterer to the reconfigurable smart reflector; This indicates that the signal transmitted by the first base station passes through the [missing information]. The propagation delay from an interfering scatterer to the reconfigurable smart reflector; Indicates the propagation delay The original signal; Indicates the first The azimuth angle of the incident signal from the interfering scatterer to the reconfigurable smart reflector; The signal transmitted by the first base station and arriving at the reconfigurable smart reflector is defined as: (4) In the formula: This represents the complex attenuation coefficient from the first base station to the reconfigurable smart reflector; This represents the distance from the first base station to the reconfigurable smart reflector; This represents the propagation delay of the signal transmitted from the first base station to the reconfigurable smart reflector; Indicates the propagation delay The original signal; This represents the azimuth angle of the incident signal from the first base station to the reconfigurable smart reflector; Based on equations (2)-(4), a reconfigurable smart reflector signal receiving model is constructed, which is expressed as follows: (5) In the formula: For the reconfigurable smart reflective surface The total signal received by each electromagnetic unit; Indicates the index of the electromagnetic unit of the reconfigurable smart reflector. .

3. The multi-target direction-of-arrival estimation method integrating induction and communication as described in claim 2, characterized in that, The specific steps for constructing the second base station signal reception model include: Define the first reconfigurable smart reflective surface The electromagnetic unit in the first... The complex reflection coefficient of the time slot is: (6) In the formula: Indicates the time slot index. ; The first reconfigurable smart reflector The electromagnetic unit in the first... The reflection amplitude of the time slot; The first reconfigurable smart reflector The electromagnetic unit in the first... The reflection phase of the time slot; Then the reconfigurable intelligent reflective surface The electromagnetic unit in the first... The reflected signal of the time slot is: (7) Based on equation (7), it will be transmitted by the first base station, after passing through the... The signal of a moving target arriving at the reconfigurable smart reflector and being reflected by the reconfigurable smart reflector to the second base station is defined as: (8) In the formula: This represents the joint complex attenuation coefficient of the path; This indicates the distance from the reconfigurable smart reflector to the second base station; This indicates that the signal transmitted by the first base station passes through the [missing information]. The propagation delay of a mobile target from the reconfigurable smart reflector to the second base station; Indicates the propagation delay The The electromagnetic unit in the first... The reflected signal of the time slot; This indicates that the reconfigurable smart reflective surface reflects and carries the first... The signal azimuth angle of the signal scattered by a moving target and incident on the second base station; It will be transmitted from the first base station, after passing through the... The signal that arrives at the reconfigurable smart reflector from an interfering scatterer and is reflected by the reconfigurable smart reflector to the second base station is defined as: (9) In the formula: This represents the joint complex attenuation coefficient of the path; This indicates the distance from the reconfigurable smart reflector to the second base station; This indicates that the signal transmitted by the first base station passes through the [missing information]. The propagation delay of an interfering scatterer from the reconfigurable smart reflector to the second base station; Indicates the propagation delay The The electromagnetic unit in the first... The reflected signal of the time slot; This indicates that the reconfigurable smart reflective surface reflects and carries the first... The signal azimuth angle of the signal incident on the second base station is the signal scattered by an interfering scatterer. The signal transmitted from the first base station to the reconfigurable smart reflector and reflected by the reconfigurable smart reflector to the second base station is defined as: (10) In the formula: This represents the joint complex attenuation coefficient of the path; This indicates the distance between the reconfigurable smart reflector and the second base station; This indicates the propagation delay of the signal from the reconfigurable smart reflector to the second base station; Indicates the propagation delay The The electromagnetic unit in the first... The reflected signal of the time slot; This represents the azimuth angle of the signal incident on the second base station, which is reflected by the reconfigurable smart reflector and has no intermediate scattering source. The signal transmitted from the first base station and directly reaching the second base station is defined as: (11) In the formula: This represents the complex attenuation coefficient of the path from the first base station to the second base station; This indicates the distance between the first base station and the second base station; This indicates the propagation delay of the signal transmitted from the first base station to the second base station; The second base station signal reception model is constructed based on equations (8)-(11), and is expressed as follows: (12) In the formula: It is Gaussian white noise.

4. The multi-target direction-of-arrival estimation method integrating induction and communication as described in claim 3, characterized in that, In S2, the second base station signal reception model is optimized. The specific steps for constructing a semidefinite programming problem model based on atomic norm minimization based on the optimized second base station signal reception model include: After eliminating multiple redundant signal paths at the second base station receiver, the received signal of the second base station is optimized as follows: (13) Furthermore, the signal received by the second base station is rewritten as The vector of each time slot is obtained by integrating the intermediate expression of the received signal: (14) In the formula: Indicates transpose; Represents the array manifold vector. ; Indicating reconfigurable smart reflective surfaces in The reflection state matrix within the nth time slot, its nth time slot Line number Column elements represent the first The electromagnetic unit in the first... The reflection coefficient corresponding to the time slot; It represents the Hadamardi (or Hadama) stack; This is a Gaussian white noise vector that has been integrated synchronously with the received signal; in, (15) (16) In the formula: Represents the set of complex numbers; Based on the reconfigurable smart reflector reflection state matrix Array manifold vector Based on the definition, we can further obtain the vector form of the signal received at the second base station, which is the optimized signal reception model of the second base station, expressed as: (17) In the formula: This represents the array response matrix of the moving target in the main path; This represents the array response matrix of the interfering scatterers in the interference path; This represents the complex envelope vector of the moving target in the main path signal; This represents the complex envelope vector of the interfering scatterer in the interference path signal; in, (18) (19) Based on the optimized second base station signal reception model, a semidefinite programming problem model based on atomic norm minimization is constructed, which is expressed as: (20) In the formula: This represents the vector of observation signals received by the second base station in multiple time slots; for The corresponding equivalent measurement matrix; The vector is the sparse representation of the angle domain to be estimated. Indicates conjugate transpose; This represents the signal reconstruction error term; For regularization parameters; Represents the atomic norm; It is a Hermitian Toeplitz matrix; To and Associated constant scalars; This represents the set of Hermitian Toeplitz matrices.

5. The multi-target direction-of-arrival estimation method integrating induction and communication as described in claim 4, characterized in that, In S3, the specific steps of using the alternating direction multiplier method based on the residual-driven dual-path adaptive penalty mechanism to decompose and solve the semidefinite programming problem model based on atomic norm minimization to output the Hermitian Toeplitz matrix include: S31, the sparse representation vector of the angle domain in equation (20) Perform path-level splitting to transform the original optimization problem into a bivariate optimization problem under consistency constraints, resulting in: (21) In the formula: The sparse variables representing the main path are... Obtained through array response matrix mapping; The sparse variables representing the interference paths are... Obtained through array response matrix mapping; in: (22) (23) S32. An iterative solution is performed using the alternating direction multiplier method based on a residual-driven dual-path adaptive penalty mechanism. Each iteration includes the following update steps: S321, Calculate the first The original residual at the next iteration is given by the formula: (24) In the formula: and They represent the first Main path variables and interference path variables in the next iteration; Calculate the penalty factor based on the interference path. The dual residual at the next iteration is given by the formula: (25) in, Indicates the first The penalty factor corresponding to the interference path in the next iteration; S322. Update the first residual based on the original residual and the dual residual. The consistency weighting matrix constructed in the next iteration, driven by the residual, is given by the following formula: (26) In the formula: Represents an identity matrix with dimensions consistent with those of the main path variables and interference path variables; Indicates the first scalar weight coefficients obtained by adaptive calculation of residuals in the next iteration; Representing vectors Norm; This represents a preset positive constant used to prevent the denominator from being zero; S323, The penalty factor for updating the main path is: (27) In the formula: The initial value of the main path penalty factor; The main path penalty enhancement coefficient; This indicates an indicator function that takes the value 1 if the condition is true and 0 otherwise. Indicates the residual driving term in the th The output at the next iteration; The threshold for interference detection; The penalty factor for updating the interference path is: (28) In the formula: This is the initial value for the interference path penalty factor; This is the interference path penalty enhancement coefficient; Indicates the residual driving term in the th The output at the next iteration; The threshold for interference detection; S324. The Hermitian Toeplitz positive semidefinite matrix is ​​updated based on the penalty factor of the main path as follows: (29) In the formula: The characteristic function of the Hermitian Toeplitz cone is used to maintain the structural consistency and low-rank property of the matrix; This represents the mapping operator that constructs the Hermitian Toeplitz matrix from the sparse variables of the main path; Represents the standard Frobenius norm; S325. Update the original variable for the joint weighting of the main path and interfering paths: (30) In the formula: This represents the augmented Lagrangian function after introducing the two-path penalty factor; As dual variables; Indicates the first The consistency weighting matrix constructed in the next iteration is driven by the residual; Indicates the first In the next iteration, a residual-driven weighted second penalty is applied to the difference between the main path variable and the interference path variable in the angle domain; The update formula for the dual variable among the original variables is: (31) S326. Determine whether both the original residual and the dual residual are less than the preset threshold. If so, it means that the current iteration result has satisfied the consistency constraint and the KKT optimality condition. The algorithm has converged and terminates the iteration, and outputs the final solution. That is, the Hermitian Toeplitz matrix; otherwise, repeat S321-S325 until the final solution is output.

6. The multi-target direction-of-arrival estimation method integrating induction and communication as described in claim 5, characterized in that, In S4, the specific steps for performing structural repair and outlier removal on the Hermitian Toeplitz matrix to obtain the optimized Hermitian Toeplitz matrix include: Determine the Hermitian Toeplitz matrix Does it simultaneously satisfy the Toeplitz structural constraints? If so, then the preliminarily optimized Hermitian Toeplitz matrix is ​​obtained. ,and Otherwise, the least squares projection method is used to transform the matrix. Projected onto the Hermitian Toeplitz matrix set The Hermitian Toeplitz matrix was obtained after preliminary optimization. Specifically, it is expressed as: (32) The Hermitian Toeplitz matrix after initial optimization Eigenvalue decomposition is performed to obtain the signal subspace and noise subspace. Utilizing the principle that these two subspaces are statistically orthogonal, subspace projection is performed, and outliers deviating from the main signal subspace are identified and suppressed to obtain the final optimized Hermitian Toeplitz matrix. And the final optimized Hermitian Toeplitz matrix Includes an optimized signal vector sequence obtained from the main path recovery. .

7. The multi-target direction-of-arrival estimation method integrating induction and communication as described in claim 6, characterized in that, In S5, the specific steps for constructing the reconstructed spatial covariance matrix based on the optimized Hermitian Toeplitz matrix include: Optimized signal vector sequence based on the optimized Hermitian Toeplitz matrix Construct the reconstructed spatial covariance matrix, expressed as: (33) In the formula: For the number of snapshots; Indicates the snapshot index. ; The robust statistical computer based on Huber loss is defined as follows: (34) In the formula, For threshold parameters; Represents a symbolic function.

8. The multi-target direction-of-arrival estimation method integrating induction and communication as described in claim 7, characterized in that, In S6, the specific steps for obtaining multi-target direction-of-arrival estimates by performing spectral peak search using a multiple signal classification algorithm based on the reconstructed spatial covariance matrix include: S61, Subspace Decomposition: For the reconstructed spatial covariance matrix Eigenvalue decomposition is performed, which is expressed as: (35) In the formula: Let be a unitary matrix, and its column vectors be . eigenvectors; It is a diagonal matrix composed of eigenvalues; For the signal subspace, by the previous eigenvalues The corresponding feature vectors are composed of; For the noise subspace, by the remaining eigenvalues The corresponding feature vectors are composed of each other, and the two satisfy an orthogonal relationship; S62. Spatial spectrum construction and search in multiple signal classification algorithms: Based on the reconstructed spatial covariance matrix after eigenvalue decomposition, the spatial spectral function of the multi-signal classification algorithm is defined as follows: (36) In the formula: This represents the array manifold vector corresponding to the candidate angle; Within the candidate angle search range, i.e. Within the range, calculate the spatial spectral function values, sort the spatial spectral function values ​​in descending order, and select the top values. Angles corresponding to each function value As the estimated direction of arrival.

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