Asynchronous spatiotemporal coding metasurface direction finding method and apparatus, computer device and medium

Abstract

The application relates to an asynchronous space-time coding metasurface direction finding method, device, computer equipment and medium. The method comprises the following steps: receiving an incident signal through a linear array metasurface, representing the time domain characteristics of the incident signal based on an asynchronous space-time coding metasurface array model, configuring an independent binary phase coding sequence and a unique modulation frequency for each unit to complete asynchronous periodic space-time modulation, collecting superimposed signals through a single receiving antenna and performing discrete Fourier transform, extracting multi-order harmonic components to construct an observation vector, combining a coded harmonic transform matrix and a path response vector to construct an over-complete dictionary, establishing a sparse representation model, constructing a probability model based on structural sparse Bayesian learning and iteratively optimizing parameters, and finally determining the incident signal wave direction through spectral peak search and matching of angle grid points. The method can simplify the hardware architecture, suppress direction finding ambiguity, strengthen the low signal-to-noise ratio anti-interference ability, and improve the multi-same-frequency signal resolution accuracy and passive direction finding robustness.

Description

Technical Field

[0001] This application relates to the field of metasurface signal processing technology, and in particular to an asynchronous spatiotemporal coded metasurface orientation finding method, apparatus, computer equipment, and medium. Background Technology

[0002] Direction of Arrival (DOA) estimation, a key technology in signal processing, has wide applications in various civilian fields such as communications, seismic exploration, radio astronomy, and the Internet of Things. It is a core support for signal source localization, signal identification, and tracking, and is of great significance for improving the performance of related systems. Among existing technologies, time-modulated array-based DOA estimation methods offer high DOA estimation accuracy and can meet the precise positioning requirements in some scenarios. However, this method requires the configuration of multiple antenna array receiving channels, resulting in complex hardware structures and high costs, making it difficult to widely promote and apply in cost-sensitive civilian scenarios.

[0003] In recent years, reconfigurable smart metasurfaces have attracted widespread attention in the industry due to their outstanding advantages such as low cost, high flexibility, and simple design. Reconfigurable smart metasurfaces can achieve precise control over the amplitude and phase of electromagnetic waves. Based on this characteristic, they have been applied in the field of array signal processing to achieve Direction of Analysis (DOA) estimation. Among related technologies, reconfigurable smart metasurfaces can achieve direction finding through a single channel, significantly reducing hardware costs compared to multi-channel solutions and showing promising application prospects. However, this type of method has significant limitations. In environments with low signal-to-noise ratios, the DOA estimation error is large, and when the metasurface cell spacing is greater than half a wavelength, severe direction finding ambiguity occurs, leading to algorithm failure and failing to meet the needs of complex scenarios.

[0004] To improve the accuracy of the aforementioned reconfigurable smart metasurface related DOA estimation method, spatiotemporal coding is used for optimization in related technologies. Although this can effectively improve the accuracy of DOA estimation and solve the error problem under low signal-to-noise ratio, this optimization method has functional limitations. It cannot perform DOA estimation for multiple signals of the same frequency, making it difficult to adapt to actual application scenarios where multiple signals coexist.

[0005] In summary, all existing DOA estimation methods have varying degrees of shortcomings, such as excessively high hardware costs, insufficient estimation accuracy, or limited applicability. They are unable to balance cost, accuracy, and applicability, and thus cannot fully meet the actual needs of civilian applications for DOA estimation technology. Therefore, there is an urgent need for a DOA estimation scheme that can solve the above-mentioned technical shortcomings. Summary of the Invention

[0006] Therefore, it is necessary to provide an asynchronous spatiotemporally coded metasurface direction finding method, apparatus, computer equipment, and medium that can balance cost and accuracy, solve the problems of low signal-to-noise ratio error and direction finding ambiguity, and support the estimation of multiple co-frequency signals, in order to address the above-mentioned technical problems.

[0007] An asynchronous spatiotemporally coded metasurface orientation finding method, the method comprising:

[0008] An incident signal is received by a metasurface consisting of a linear array of multiple units, and the temporal characteristics of the incident signal are characterized by an asynchronous spatiotemporally coded metasurface array model. By configuring each unit of the metasurface with an independent binary phase coding sequence and a unique modulation frequency, the corresponding incident signal is asynchronously and periodically timed to obtain the modulated signal; The superimposed signal of multiple modulated signals is received by a single receiving antenna, and the superimposed signal is sampled and subjected to discrete Fourier transform to extract the multi-order positive and negative harmonic components centered on the carrier frequency to form an observation vector. The angle space to be estimated is uniformly discretized to generate angle grid points. Based on the encoded harmonic transformation matrix that characterizes the asynchronous modulation characteristics of the metasurface, an overcomplete dictionary matrix is ​​constructed in combination with the path response vector of the metasurface unit array. A linear mapping relationship between the observation vector and the array space response is established, and the direction finding problem is transformed into a sparse signal recovery problem, resulting in a sparse representation model for metasurface direction finding estimation. Based on the structurally sparse Bayesian learning framework, a probabilistic model with a complex Gaussian distribution is established for the sparse representation model. The hyperparameters and noise power are iteratively updated through the expectation-maximization algorithm until the convergence condition is met and the iteration is terminated. A spectral peak search is performed on the posterior mean of the sparse vector after iterative convergence, and the direction of arrival of the incident signal is determined based on the angle grid points corresponding to the peak values.

[0009] In one embodiment, the asynchronous spatiotemporal coded metasurface array model is constructed based on the structural parameters of the metasurface linear array and the mathematical model for receiving multiple incident signals in the time domain. The time-domain receiving mathematical model characterizes the time-domain carrier characteristics, spatial phase difference, and additive white Gaussian noise distribution of the incident signal received by each unit of the metasurface.

[0010] In one embodiment, the binary phase coding sequence of each unit of the metasurface is configured in a one-to-one correspondence with the modulation frequency, the modulation frequencies of each unit are different, and each unit periodically generates a timing control function based on its own modulation frequency to generate the binary phase coding sequence.

[0011] In one embodiment, the construction of an overcomplete dictionary matrix based on the coded harmonic transform matrix characterizing the asynchronous modulation properties of the metasurface, combined with the path response vector of the metasurface unit array, includes: The spatial array response is constructed based on the ideal spatial response corresponding to each grid point in the angle grid and the path response vector, thereby constructing the overcomplete dictionary matrix.

[0012] In one embodiment, in the probabilistic model of the sparse representation model established by the structural sparse Bayesian learning framework, the prior distribution of the sparse vector is set as a complex Gaussian distribution with independent Gaussian components, the hyperparameter vector controls the precision of each component of the sparse vector, and the hyperparameter and noise power are jointly iteratively updated through the expectation-maximization algorithm.

[0013] In one embodiment, the peak search is performed by searching for the peak value of the posterior mean of the sparse vector after iterative convergence, and the direction of arrival of the incident signal is determined based on the angle grid points corresponding to the peak values.

[0014] This application also provides an asynchronous spatiotemporally coded metasurface orientation finding device, the device comprising: An incident signal receiving module is used to receive incident signals through a metasurface consisting of a linear array structure of multiple units, wherein the time-domain characteristics of the incident signals are characterized by an asynchronous spatiotemporally coded metasurface array model. An incident signal modulation module is used to asynchronously and periodically modulate the corresponding incident signal by configuring an independent binary phase coding sequence and a unique modulation frequency for each unit of the metasurface, so as to obtain a modulated signal. The observation vector construction module is used to receive the superimposed signal of multiple modulated signals through a single receiving antenna, sample the superimposed signal and perform discrete Fourier transform to extract the multi-order positive and negative harmonic components centered on the carrier frequency to form the observation vector. The sparse representation model construction module is used to uniformly discretize the angle space to be estimated to generate angle grid points. Based on the encoded harmonic transformation matrix that characterizes the asynchronous modulation characteristics of the metasurface, an overcomplete dictionary matrix is ​​constructed in combination with the path response vector of the metasurface unit array. The linear mapping relationship between the observation vector and the array space response is established, and the direction finding problem is transformed into a sparse signal recovery problem, thus obtaining a sparse representation model for metasurface direction finding estimation. The probability model iterative solution module is used to establish a complex Gaussian distribution probability model for the sparse representation model based on the structural sparse Bayesian learning framework. It iteratively updates the hyperparameters and noise power through the expectation-maximization algorithm until the convergence condition is met and the iteration is terminated. The direction-of-arrival (DOA) module is used to perform spectral peak search on the posterior mean of the sparse vector after iterative convergence, and determine the DOA of the incident signal based on the angle grid points corresponding to the peak values.

[0015] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the steps in the above-described asynchronous spatiotemporal coded metasurface orientation method.

[0016] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in the above-described asynchronous spatiotemporally encoded metasurface orientation finding method.

[0017] The aforementioned asynchronous spatiotemporal coded metasurface direction finding method, apparatus, computer equipment, and medium receive incident signals via a metasurface consisting of a linear array of multiple units. The temporal characteristics of the incident signals are characterized by an asynchronous spatiotemporal coded metasurface array model. By configuring each unit of the metasurface with an independent binary phase coding sequence and a unique modulation frequency, the corresponding incident signals are asynchronously and periodically temporally coded to obtain modulated signals. The superposition of multiple modulated signals is received through a single receiving antenna, and the superposition signal is sampled and subjected to discrete Fourier transform. The multi-order positive and negative harmonic components centered on the carrier frequency are extracted to form an observation vector. The angle to be estimated is then uniformly discretized to generate the angle. Based on the encoded harmonic transform matrix characterizing the asynchronous modulation properties of the metasurface, an overcomplete dictionary matrix is ​​constructed using the path response vector of the metasurface unit array. A linear mapping relationship between the observation vector and the array spatial response is established, transforming the direction finding problem into a sparse signal recovery problem. This yields a sparse representation model for metasurface direction finding estimation. A complex Gaussian distribution probability model is established for the sparse representation model based on the structural sparse Bayesian learning framework. The hyperparameters and noise power are iteratively updated using the expectation-maximization algorithm until the convergence condition is met, at which point the iteration terminates. The spectral peaks of the posterior mean of the sparse vectors after iterative convergence are searched, and the direction of arrival of the incident signal is determined based on the angle grid points corresponding to the peaks.

[0018] Beneficial effects: This method relies on an asynchronous spatiotemporally coded metasurface array model to accurately characterize the temporal features of the incident signal. By configuring each metasurface unit with an independent binary phase coding sequence and a unique modulation frequency, asynchronous periodic spatiotemporal modulation is achieved, effectively eliminating the direction-finding ambiguity defect that easily occurs in traditional synchronous modulation. It is well-suited for analytical scenarios involving multiple incident signals at the same frequency. Simultaneously, a single antenna is used to receive the modulated superimposed signal, and multiple harmonic components are extracted through discrete Fourier transform to construct the observation vector, greatly simplifying the system hardware architecture and reducing equipment setup costs and deployment complexity. Furthermore, the coded harmonic transform matrix, which characterizes the asynchronous modulation properties, maps the spatial array response to the harmonic domain and combines it with the path response vector to construct the harmonic transformation vector. A complete dictionary matrix enables precise linear matching between the observation vector and the array spatial response, ensuring the scientific validity and fit of the sparse representation model. Combined with a complex Gaussian probability model built based on structural sparse Bayesian learning and through joint iterative optimization of hyperparameters and noise power using the expectation-maximization algorithm, it significantly improves the anti-interference performance and sparse signal reconstruction accuracy under low signal-to-noise ratio and limited snapshot conditions. Finally, relying on spectral peak search, it accurately locks the angle grid points corresponding to the effective peaks, enhancing the resolution capability of multiple signals with small angle intervals and the accuracy of direction of arrival estimation. Overall, it achieves efficient passive direction finding of metasurfaces with lightweight hardware, strong anti-interference capability, high direction finding accuracy, and compatibility with multiple targets of the same frequency. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating an asynchronous spatiotemporal coded metasurface orientation finding method in one embodiment; Figure 2 This is a schematic diagram of a structure for DOA estimation based on an asynchronous time-controlled metasurface in one embodiment. Figure 3 This is a schematic diagram of an asynchronous spatiotemporal coded modulation sequence of a metasurface in one embodiment; Figure 4 This is a schematic diagram of the convergence curve of hyperparameters as a function of the number of iterations when Bayesian iterative calculation is performed using this method in one embodiment; Figure 5 This is a schematic diagram of the direction-of-arrival spatial spectrum obtained after Bayesian iterative calculation using this method when the incident angles are -20° and 10° in an experiment. Figure 6 This is a schematic diagram of the direction-of-arrival spatial spectrum obtained after Bayesian iterative calculation using this method when the incident angles are -5.2° and 8.7° in an experiment. Figure 7 The diagram shows the direction-of-arrival spatial spectrum calculated by our method with 600 iterations and the ISTA algorithm when the signal-to-noise ratio is 0dB and the incident angle is -30° and 10°, respectively, in an experiment. Figure 8The diagram shows the direction-of-arrival spatial spectrum calculated by our method and the ISTA method with 600 iterations, respectively, when the signal-to-noise ratio is -10dB and the incident angle is -30° and 10° in an experiment. Figure 9 This is a schematic diagram illustrating the convergence speed of the proposed method and the ISTA method during iteration in an experiment. Figure 10 This is a schematic diagram illustrating the errors of Monte Carlo simulations performed by our method and the ISTA method under different signal-to-noise ratios in an experiment. Figure 11 This is a structural block diagram of an asynchronous spatiotemporal coded metasurface orientation finding device in one embodiment; Figure 12 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0021] To address the shortcomings of existing technologies, traditional metasurface direction finding methods often employ synchronous modulation, which can lead to ambiguity in the direction finding angle and difficulty in distinguishing small angular intervals and multiple incident signals with the same frequency. Conventional solutions rely on multi-channel receiving arrays, resulting in complex hardware architecture, high equipment costs, and difficult deployment. Furthermore, they only directly construct a sparse dictionary based on spatial domain features without achieving harmonic domain feature alignment, leading to weak anti-interference capability and large sparse reconstruction errors under low signal-to-noise ratio conditions. In addition, traditional solution algorithms suffer from insufficient accuracy in direction-of-arrival estimation and poor convergence stability under limited snapshot conditions. This application provides an asynchronous spatiotemporal coded metasurface direction finding method, which specifically includes the following steps: Step S100: The incident signal is received by a metasurface consisting of a linear array structure composed of multiple units. The temporal characteristics of the incident signal are characterized by an asynchronous spatiotemporally coded metasurface array model.

[0022] Step S110: By configuring an independent binary phase coding sequence and a unique modulation frequency for each unit of the metasurface, the corresponding incident signal is asynchronously periodically time-controlled to obtain the modulated signal. Step S120: Receive the superimposed signal of multiple modulated signals through a single receiving antenna, sample the superimposed signal and perform discrete Fourier transform to extract the multi-order positive and negative harmonic components centered on the carrier frequency to form an observation vector.

[0023] Step S130: The angle space to be estimated is uniformly discretized to generate angle grid points. Based on the encoded harmonic transformation matrix that characterizes the asynchronous modulation characteristics of the metasurface, an overcomplete dictionary matrix is ​​constructed in combination with the path response vector of the metasurface unit array. A linear mapping relationship between the observation vector and the array space response is established, and the direction finding problem is transformed into a sparse signal recovery problem, thus obtaining a sparse representation model for metasurface direction finding estimation.

[0024] Step S140: Based on the structurally sparse Bayesian learning framework, a probabilistic model of complex Gaussian distribution is established for the sparse representation model. The hyperparameters and noise power are iteratively updated through the expectation-maximization algorithm until the convergence condition is met and the iteration is terminated.

[0025] Step S150: Perform spectral peak search on the posterior mean of the sparse vector after iterative convergence, and determine the direction of arrival of the incident signal based on the angle grid points corresponding to the peaks.

[0026] In this application, the direction-of-arrival (DOA) estimation problem is transformed into a problem of recovering the support set from a known overcomplete dictionary. Simultaneously, an improved statistical model is constructed to accurately characterize the intra-block correlation of the received signal. For the sparse recovery problem, a structurally sparse Bayesian learning algorithm is proposed. This algorithm utilizes the intra-signal correlation and is applicable to scenarios with limited data support and low signal-to-noise ratio. Furthermore, compared with traditional Bayesian algorithms, the proposed algorithm has lower computational cost. Simulation results demonstrate that this algorithm achieves more accurate ODA performance than traditional multiple signal classification algorithms and other compressed sensing recovery algorithms.

[0027] In step S100, the metasurface is composed of a linear array of N units (encoding units), with the spacing between each unit being... It is usually set to half wavelength, that is ,in The wavelength of the incident signal is denoted as λ. Simultaneously, the incident signals received by each unit are characterized according to a pre-defined asynchronous spatiotemporal coded metasurface array model. This asynchronous spatiotemporal coded metasurface array model is constructed based on the structural parameters of the metasurface linear array and a mathematical model for the time-domain reception of multiple incident signals. The time-domain reception mathematical model characterizes the time-domain carrier characteristics, spatial phase difference, and additive white Gaussian noise distribution of the incident signals received by each unit of the metasurface.

[0028] In this embodiment, based on such Figure 2 The asynchronous spatiotemporal coded metasurface single-antenna direction-finding system structure shown can be represented by the asynchronous spatiotemporal coded metasurface array model as follows: (1) In formula (1), n =1, 2, ..., N , t =1,2,…,T , T For the number of snapshots, m =1,2,…, M , M The number of signals, and The first The complex amplitude and initial phase of the signal, For carrier frequency, For wave number, It is additive white Gaussian noise.

[0029] In step S110, the binary phase coding sequence of each unit of the metasurface is configured in a one-to-one correspondence with the modulation frequency. The modulation frequencies of each unit are different from each other, and each unit periodically generates a time-limited modulation function based on its own modulation frequency to generate the binary phase coding sequence.

[0030] In this embodiment, each coding unit on the asynchronous spatiotemporal coding metasurface is independently assigned a binary phase coding sequence of length L. ,in , respectively corresponding and The reflection phase. All encoded sequences constitute the encoding matrix, represented as... At the same time, each unit uses its unique modulation frequency. By periodically repeating its encoded sequence, a continuous temporal control function is generated. Each unit has its own unique modulation frequency. It can be set manually. Within one modulation cycle. Inside, yes The time-domain expansion. After modulation, the first... The signal reflected by each unit is: (2) like Figure 3 The diagram shows the asynchronous spatiotemporal coded modulation sequence of a metasurface. It displays the spatiotemporal modulation matrix of each 10×10 metasurface unit. Each row represents the modulation sequence of one unit, with a total of 8 coded sequences. Yellow indicates a modulation coefficient of 1, meaning the metasurface modulation phase is 0°, and blue indicates a modulation coefficient of -1, meaning the metasurface modulation phase is 180°. Each column represents the modulation code of each unit, with a total of 10 units undergoing modulation.

[0031] In step S120, a single receiving antenna is placed in the near-field region of the metasurface array. This antenna receives all... The superposition of the modulated signals of each unit, taking into account the different path delays from each unit to the receiving antenna. Receive signal It can be represented as: (3) In formula (3), For the first Path attenuation factor of each unit, This refers to the synthesized noise at the receiver. In practical signal models, path delay... The main feature is the introduction of a fixed phase shift. .make If the path response vector is used, the received signal can be simplified to: (4) in,

[0032]

[0033] In formula (4), It represents the Hadamardi (or Hadama) stack.

[0034] In this embodiment, due to the formula (4) It is a periodic function and can be expanded into a Fourier series. (Received signal) The spectrum will include carrier frequency Components and their modulation frequencies with each unit Harmonics of each order The mixed components of the received signal. Sample the data and perform a discrete Fourier transform to obtain its spectrum. Based on Extract to Centered The positive and negative harmonic components constitute the observation vector. , represented as: (5) In formula (5), This indicates the fundamental frequency resolution.

[0035] In step S130, the observation vector Spatial response of metasurface arrays The existence of a linear mapping relationship can be expressed as: (6) In formula (6), The coded harmonic transform matrix has elements derived from the coded sequence. Determined by the modulation frequency, To observe noise.

[0036] In this embodiment, after uniformly discretizing the angle space to be estimated to generate angle grid points, a spatial array response is constructed based on the ideal space response and path response vector corresponding to each grid point in the angle grid, and an overcomplete dictionary matrix is ​​obtained.

[0037] Specifically, the angle space to be measured Uniform discretization grid points For each grid point Its corresponding ideal space response is This ideal spatial response fully characterizes the spatial phase difference of each element in the metasurface array under different incident angles, and is the core physical basis for DOA estimation. However, traditional methods directly construct a spatial dictionary based solely on this ideal response, without considering actual propagation characteristics and asynchronous modulation features, resulting in serious deficiencies in dictionary accuracy, robustness, and multi-target adaptability. In this application, a path response that incorporates the actual response is introduced. The Hadamard product is then performed between the Hadamard product and the ideal spatial response corresponding to each angle, incorporating real characteristics such as actual propagation attenuation and phase shift. Finally, the harmonic transformation matrix is ​​encoded. The fused spatial response is mapped as a whole to the harmonic domain to construct a vector with the observation vector. Overcomplete dictionary matrix of the same feature domain , represented as: (7) By using cross-domain mapping of the encoded harmonic transform matrix, complete alignment of the observation vector with the feature domain of the dictionary is achieved. Simultaneously, the coding and frequency characteristics of asynchronous modulation are deeply integrated into the dictionary structure, fundamentally eliminating the direction-finding ambiguity problem of traditional synchronous modulation schemes and significantly improving the resolution of multiple superimposed incident signals at the same frequency. Furthermore, the actual path response is fused. The design makes the dictionary more closely resemble the real-world propagation environment, significantly improving the accuracy and robustness of sparse reconstruction in low signal-to-noise ratio and complex propagation scenarios.

[0038] In one embodiment, an angular grid is generated by uniform discretization in the angular interval [-60°, 60°] with a grid interval of 1°, resulting in a total of 121 angular grid points.

[0039] Furthermore, the DOA estimation problem is transformed into a sparse signal recovery problem, based on the aforementioned overcomplete dictionary matrix. The DOA estimation problem is precisely transformed into a sparse signal recovery problem, expressed as: (8) In formula (8), It is a sparse vector, where the positions of non-zero values ​​correspond to the actual directions of incoming waves. The amplitude of non-zero values ​​contains the energy information of the corresponding signal. Compared with traditional sparse representation models, this transformation is based on an original dictionary that integrates asynchronous modulation features, actual path characteristics and harmonic domain mapping. The accuracy, noise resistance and multi-target resolution of sparse recovery are all significantly improved, providing a scientific model foundation for subsequent high-precision DOA estimation.

[0040] In step S130, in the probabilistic model of complex Gaussian distribution for sparse representation model based on structural sparse Bayesian learning framework, the prior distribution of sparse vector is set as complex Gaussian distribution with independent Gaussian components, the hyperparameter vector controls the accuracy of each component of sparse vector, and the hyperparameter and noise power are jointly iteratively updated through expectation maximization algorithm.

[0041] In this embodiment, addressing the technical shortcomings of traditional sparse signal recovery algorithms (such as L1 norm regularization and traditional Bayesian methods) in conditions of limited snapshots and low signal-to-noise ratio, including large sparse reconstruction errors, poor convergence stability, and difficulty in accurately distinguishing multiple signals with the same frequency at small angle intervals, this application, based on the Structural Sparse Bayesian Learning (SBL) framework, uses the Expectation-Maximization (EM) algorithm to achieve joint iterative optimization of hyperparameters and noise power, providing core algorithmic support for accurate solution of sparse vectors and high-precision DOA estimation.

[0042] Furthermore, assuming noise It follows a complex circular symmetric Gaussian distribution, i.e. ,in For noise power, assume a sparse vector. If the prior distribution is a complex Gaussian distribution with independent Gaussian components, then the probability model can be expressed as: (9) In formula (9), It is a hyperparameter vector that controls each component. The accuracy, .

[0043] Furthermore, based on the aforementioned sparse representation model formula (8), the posterior distribution of sparse vectors is derived within the framework of structurally sparse Bayesian learning, given the observation vector. sparse vectors The posterior distribution of follows a complex Gaussian distribution, which can be expressed as: (10) In formula (10), Indicates a complex Gaussian distribution. Represents the posterior mean vector. Let represent the covariance matrix. The posterior mean vector and covariance matrix are expressed as follows: (11) (12) In formulas (11) and (12), For hyperparameters The diagonal matrix formed For an overcomplete dictionary matrix The conjugate transpose of . Let be the noise power. This posterior distribution fully characterizes the statistical properties of sparse vectors: the covariance matrix. The estimation uncertainty of each component of the sparse vector is quantified, and the posterior mean is... This provides the optimal estimate of the minimum mean square error for sparse vectors, laying the core statistical foundation for subsequent iterative updates of hyperparameters.

[0044] Furthermore, in order to achieve hyperparameters With noise power For accurate estimation, this application employs the Expectation Maximization (EM) algorithm for joint iterative optimization. Compared to traditional methods that update hyperparameters and noise power separately or fix the noise power, this joint optimization method can adaptively match the actual noise environment, significantly improving the convergence speed and sparse recovery accuracy.

[0045] Specifically, in the first In this iteration, the posterior statistic is calculated first. ,in yes The One diagonal element. Then update the hyperparameters. The following formula is used: (13) The noise power is then updated using the following formula: (14) In this embodiment, after multiple iterations, until the hyperparameters are obtained... The change is less than the preset threshold Or it may reach the maximum number of iterations. After the iterations converge, the sparse vector... The final estimate is the posterior mean. .right Perform a spectral peak search to find the most significant peaks. The angle grid corresponding to each peak is then used. That is, the estimated direction of arrival. ,in The estimated number of signal sources is determined by the number of peak values ​​exceeding a preset threshold.

[0046] Furthermore, in the simulation experiments, the signal-to-noise ratio (SNR) was set to range from -10dB to 20dB to verify the robustness of the algorithm under different noise environments. To obtain stable and reliable DOA estimation results, it is necessary to reasonably set the maximum number of iterations and the convergence threshold of the SBL algorithm. On the one hand, too few iterations may cause the algorithm to terminate prematurely before reaching the optimal solution, resulting in a decrease in estimation accuracy; on the other hand, too many iterations will significantly increase the computation time and may lead to overfitting when the SNR is high.

[0047] In this embodiment, an early stopping mechanism with a convergence threshold of 1e-6 is introduced. When the relative change of the hyperparameter vector between two adjacent iterations is less than this threshold, the algorithm automatically terminates the iteration, effectively balancing estimation accuracy and computational efficiency. Figure 4 The curves showing the relationship between the relative rate of change of hyperparameters and the number of iterations are presented. When the maximum number of iterations is set to 600, the algorithm can converge within 100 iterations under most signal-to-noise ratio conditions, and maintains sub-degree estimation accuracy over a wide signal-to-noise ratio range of -10dB to 20dB. At 0dB, the root mean square error of the estimation of both -20° and 10° signals is less than 0.5°. Therefore, considering both estimation accuracy and computational efficiency, this embodiment sets the maximum number of iterations of the SBL algorithm to 600 and the convergence threshold to 1e-6.

[0048] To verify the effectiveness of the proposed method, namely the DOA estimation method based on Sparse Bayesian Learning (SBL), tests were conducted under the set parameters. Figure 5 It is a signal-to-noise ratio of 0 dB, with the two incident signals having directions of... and The diagram shows the spatial spectrum of the direction of arrival obtained after iterative solution using the SBL algorithm. The diagram clearly shows sharp and accurate spectral peaks at two actual angular locations. Figure 6 Using the same SBL algorithm, for angles with closer intervals, respectively and The diagram shows the spatial spectrum of the direction of arrival (DOA) obtained by estimating the two signals. The algorithm can still successfully distinguish and obtain two sharp spectral peaks. It can be seen that the SBL method used in this paper can effectively estimate the DOA of multiple signals with the same frequency with high accuracy. The SBL framework automatically learns the sparsity and noise statistics of the signal through Bayesian inference, without relying on the assumption of signal incoherence, thus effectively overcoming the problem of severe performance degradation or even failure of traditional subspace decomposition-based methods when processing coherent signals. Furthermore, the performance of this method mainly depends on the coverage of the true direction by the constructed overcomplete angle dictionary, therefore it also has strong estimation and generalization capabilities for angles outside the training set.

[0049] To verify the advantages of this method over the traditional ISTA method, the spatial spectrum estimation results of the two methods were compared under the same experimental scenario. Figure 7 It has a signal-to-noise ratio of 0dB and an incident angle of 0dB. and When the DOA spatial spectra calculated by the SBL algorithm with 600 iterations and the ISTA method are compared, it can be seen that the DOA estimation obtained by the SBL algorithm is more accurate. Figure 8 It has a signal-to-noise ratio of -10dB and an incident angle. and The spatial spectra of the direction of arrival (DOA) calculated by the SBL algorithm with 600 iterations and the ISTA method respectively show that the SBL algorithm can still measure the angle with high accuracy even when the ISTA algorithm fails. Figure 9 The convergence speeds of the two methods during iteration are compared, and the proposed method exhibits a faster convergence speed. Therefore, compared to the ISTA method, the proposed method can improve accuracy and convergence speed with fewer iterations and a lower signal-to-noise ratio, resulting in better performance.

[0050] To further verify the robustness and accuracy of this method under different signal-to-noise ratios Figure 10 This is a Monte Carlo comparison of the proposed method and the ISTA algorithm under the same simulation conditions. In the simulation, 140 Monte Carlo simulations were performed independently for each signal-to-noise ratio (SNR) point. Within a wide SNR range of -5dB to 25dB, the proposed method consistently exhibited lower estimation errors, especially when the SNR was above 0dB, where the error approached zero, demonstrating excellent estimation accuracy. Compared to the ISTA algorithm, this method achieved superior performance at all tested SNR points, further validating its robustness under low SNR conditions and its high accuracy under high SNR conditions.

[0051] In the aforementioned asynchronous spatiotemporal coded metasurface direction finding method, differentiated asynchronous periodic temporal control is achieved by configuring an independent binary phase coding sequence and a unique modulation frequency for each metasurface unit. This fundamentally overcomes the inherent defects of traditional synchronous modulation, which easily leads to ambiguity in direction finding angles and makes it difficult to distinguish multiple incident signals with the same frequency superimposed. At the same time, a single antenna is used to receive the superimposed components of multiple modulation signals and extract the multi-order positive and negative harmonic components around the carrier frequency through discrete Fourier transform to construct the observation vector. This breaks away from the hardware constraints of conventional direction finding schemes that rely on multi-channel receiving arrays, effectively simplifying the system architecture and reducing equipment costs and deployment difficulty. Based on this, the coded harmonic transform matrix, which characterizes the core attributes of asynchronous modulation, is used to complete the cross-domain mapping from the array's spatial response to the harmonic domain. Combined with the path response vector of the metasurface unit array, an overcomplete dictionary matrix aligned with the feature domain of the observation vector is constructed to establish an accurate and reliable linear mapping relationship. This overcomes the shortcomings of traditional dictionary construction based solely on the spatial domain, which results in feature domain misalignment and large sparse reconstruction errors under low signal-to-noise ratio conditions. Furthermore, a complex Gaussian distribution probability model is built based on structural sparse Bayesian learning, and the expectation-maximization algorithm is used to achieve joint iterative optimization of hyperparameters and noise power. This significantly enhances the signal identification capability and noise robustness under limited snapshots and complex electromagnetic interference scenarios. Finally, spectral peak search is performed on the posterior mean of the sparse vectors after iterative convergence, and the corresponding angle grid points are matched to lock the direction of arrival. This significantly improves the resolution accuracy and direction-finding stability of small-angle interval targets, thereby systematically solving the core technical problems in the background technology of complex hardware architecture, weak anti-interference of modulation methods, difficulty in separating multiple co-frequency signals, and insufficient DOA estimation accuracy under low signal-to-noise ratio conditions in traditional metasurface direction-finding.

[0052] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0053] In one embodiment, such as Figure 11 As shown, an asynchronous spatiotemporally coded metasurface direction-finding device is provided, comprising: an incident signal receiving module 200, an incident signal modulation module 210, an observation vector construction module 220, a sparse representation model construction module 230, a probability model iterative solution module 240, and a direction-of-arrival (DOA) obtaining module 250, wherein: The incident signal receiving module 200 is used to receive incident signals through a metasurface composed of a linear array structure of multiple units, wherein the time-domain characteristics of the incident signals are characterized by an asynchronous spatiotemporally coded metasurface array model. The incident signal modulation module 210 is used to asynchronously periodically modulate the corresponding incident signal by configuring an independent binary phase coding sequence and a unique modulation frequency for each unit of the metasurface, so as to obtain the modulated signal. The observation vector construction module 220 is used to receive the superimposed signal of multiple modulated signals through a single receiving antenna, sample the superimposed signal and perform discrete Fourier transform to extract the multi-order positive and negative harmonic components centered on the carrier frequency to form the observation vector. The sparse representation model construction module 230 is used to uniformly discretize the angle space to be estimated to generate angle grid points, construct an overcomplete dictionary matrix based on the encoded harmonic transformation matrix that characterizes the asynchronous modulation characteristics of the metasurface and the path response vector of the metasurface unit array, establish a linear mapping relationship between the observation vector and the array space response, transform the direction finding problem into a sparse signal recovery problem, and obtain a sparse representation model for metasurface direction finding estimation. The probability model iterative solution module 240 is used to establish a complex Gaussian distribution probability model for the sparse representation model based on the structural sparse Bayesian learning framework, and iteratively updates the hyperparameters and noise power through the expectation-maximization algorithm until the convergence condition is met and the iteration is terminated. The direction of arrival module 250 is used to perform spectral peak search on the posterior mean of the sparse vector after iterative convergence, and determine the direction of arrival of the incident signal based on the angle grid points corresponding to the peaks.

[0054] Specific limitations regarding the asynchronous spatiotemporal coded metasurface direction-finding device can be found in the limitations of the asynchronous spatiotemporal coded metasurface direction-finding method described above, and will not be repeated here. Each module in the aforementioned asynchronous spatiotemporal coded metasurface direction-finding device can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in hardware or independently of the processor in a computer device, or stored in software in the memory of a computer device, so that the processor can call and execute the operations corresponding to each module.

[0055] In one embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as follows: Figure 12As shown, the computer device includes a processor, memory, network interface, display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The network interface is used to communicate with external terminals via a network connection. When executed by the processor, the computer program implements an asynchronous spatiotemporally coded metasurface orientation method. The display screen can be a liquid crystal display (LCD) or an e-ink display. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad mounted on the computer device's casing, or an external keyboard, touchpad, or mouse.

[0056] Those skilled in the art will understand that Figure 12 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0057] In one embodiment, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to perform the following steps: An incident signal is received by a metasurface consisting of a linear array of multiple units, and the temporal characteristics of the incident signal are characterized by an asynchronous spatiotemporally coded metasurface array model. By configuring each unit of the metasurface with an independent binary phase coding sequence and a unique modulation frequency, the corresponding incident signal is asynchronously and periodically timed to obtain the modulated signal; The superimposed signal of multiple modulated signals is received by a single receiving antenna, and the superimposed signal is sampled and subjected to discrete Fourier transform to extract the multi-order positive and negative harmonic components centered on the carrier frequency to form an observation vector. The angle space to be estimated is uniformly discretized to generate angle grid points. Based on the encoded harmonic transformation matrix that characterizes the asynchronous modulation characteristics of the metasurface, an overcomplete dictionary matrix is ​​constructed in combination with the path response vector of the metasurface unit array. A linear mapping relationship between the observation vector and the array space response is established, and the direction finding problem is transformed into a sparse signal recovery problem, resulting in a sparse representation model for metasurface direction finding estimation. Based on the structurally sparse Bayesian learning framework, a probabilistic model with a complex Gaussian distribution is established for the sparse representation model. The hyperparameters and noise power are iteratively updated through the expectation-maximization algorithm until the convergence condition is met and the iteration is terminated. A spectral peak search is performed on the posterior mean of the sparse vector after iterative convergence, and the direction of arrival of the incident signal is determined based on the angle grid points corresponding to the peak values.

[0058] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, the computer program performing the following steps when executed by a processor: An incident signal is received by a metasurface consisting of a linear array of multiple units, and the temporal characteristics of the incident signal are characterized by an asynchronous spatiotemporally coded metasurface array model. By configuring each unit of the metasurface with an independent binary phase coding sequence and a unique modulation frequency, the corresponding incident signal is asynchronously and periodically timed to obtain the modulated signal; The superimposed signal of multiple modulated signals is received by a single receiving antenna, and the superimposed signal is sampled and subjected to discrete Fourier transform to extract the multi-order positive and negative harmonic components centered on the carrier frequency to form an observation vector. The angle space to be estimated is uniformly discretized to generate angle grid points. Based on the encoded harmonic transformation matrix that characterizes the asynchronous modulation characteristics of the metasurface, an overcomplete dictionary matrix is ​​constructed in combination with the path response vector of the metasurface unit array. A linear mapping relationship between the observation vector and the array space response is established, and the direction finding problem is transformed into a sparse signal recovery problem, resulting in a sparse representation model for metasurface direction finding estimation. Based on the structurally sparse Bayesian learning framework, a probabilistic model with a complex Gaussian distribution is established for the sparse representation model. The hyperparameters and noise power are iteratively updated through the expectation-maximization algorithm until the convergence condition is met and the iteration is terminated. A spectral peak search is performed on the posterior mean of the sparse vector after iterative convergence, and the direction of arrival of the incident signal is determined based on the angle grid points corresponding to the peak values.

[0059] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0060] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0061] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. An asynchronous spatiotemporally coded metasurface orientation finding method, characterized in that, The method includes: An incident signal is received by a metasurface consisting of a linear array of multiple units, and the temporal characteristics of the incident signal are characterized by an asynchronous spatiotemporally coded metasurface array model. By configuring each unit of the metasurface with an independent binary phase coding sequence and a unique modulation frequency, the corresponding incident signal is asynchronously and periodically timed to obtain the modulated signal; The superimposed signal of multiple modulated signals is received by a single receiving antenna, and the superimposed signal is sampled and subjected to discrete Fourier transform to extract the multi-order positive and negative harmonic components centered on the carrier frequency to form an observation vector. The angle space to be estimated is uniformly discretized to generate angle grid points. Based on the encoded harmonic transformation matrix that characterizes the asynchronous modulation characteristics of the metasurface, an overcomplete dictionary matrix is ​​constructed in combination with the path response vector of the metasurface unit array. A linear mapping relationship between the observation vector and the array space response is established, and the direction finding problem is transformed into a sparse signal recovery problem, resulting in a sparse representation model for metasurface direction finding estimation. Based on the structurally sparse Bayesian learning framework, a probabilistic model with a complex Gaussian distribution is established for the sparse representation model. The hyperparameters and noise power are iteratively updated through the expectation-maximization algorithm until the convergence condition is met and the iteration is terminated. A spectral peak search is performed on the posterior mean of the sparse vector after iterative convergence, and the direction of arrival of the incident signal is determined based on the angle grid points corresponding to the peak values.

2. The asynchronous spatiotemporal coded metasurface direction finding method according to claim 1, characterized in that, The asynchronous spatiotemporal coded metasurface array model is constructed based on the structural parameters of the metasurface linear array and the mathematical model for time-domain reception of multiple incident signals. The time-domain receiving mathematical model characterizes the time-domain carrier characteristics, spatial phase difference, and additive white Gaussian noise distribution of the incident signal received by each unit of the metasurface.

3. The asynchronous spatiotemporal coded metasurface direction finding method according to claim 1, characterized in that, The binary phase coding sequence and modulation frequency of each unit of the metasurface are configured in a one-to-one correspondence. The modulation frequencies of each unit are different from each other, and each unit periodically generates a time-limited modulation function based on its own modulation frequency to generate the binary phase coding sequence.

4. The asynchronous spatiotemporal coded metasurface direction finding method according to claim 1, characterized in that, The coded harmonic transform matrix, based on the asynchronous modulation characteristics of the metasurface, is combined with the path response vector of the metasurface unit array to construct an overcomplete dictionary matrix, including: The spatial array response is constructed based on the ideal spatial response corresponding to each grid point in the angle grid and the path response vector, thereby constructing the overcomplete dictionary matrix.

5. The asynchronous spatiotemporal coded metasurface direction finding method according to claim 1, characterized in that, In the structural sparse Bayesian learning framework, a probabilistic model based on a complex Gaussian distribution is established for the sparse representation model. The prior distribution of the sparse vector is set as a complex Gaussian distribution with independent Gaussian components. The hyperparameter vector controls the precision of each component of the sparse vector, and the hyperparameter and noise power are jointly iteratively updated through the expectation-maximization algorithm.

6. The asynchronous spatiotemporal coded metasurface direction finding method according to claim 1, characterized in that, The peak search involves performing a peak search on the posterior mean of the sparse vector after iterative convergence, and determining the direction of arrival of the incident signal based on the angle grid points corresponding to the peaks.

7. An asynchronous spatiotemporally coded metasurface orientation finding device, characterized in that, The device includes: An incident signal receiving module is used to receive incident signals through a metasurface consisting of a linear array structure of multiple units, wherein the time-domain characteristics of the incident signals are characterized by an asynchronous spatiotemporally coded metasurface array model. An incident signal modulation module is used to asynchronously and periodically modulate the corresponding incident signal by configuring an independent binary phase coding sequence and a unique modulation frequency for each unit of the metasurface, so as to obtain a modulated signal. The observation vector construction module is used to receive the superimposed signal of multiple modulated signals through a single receiving antenna, sample the superimposed signal and perform discrete Fourier transform to extract the multi-order positive and negative harmonic components centered on the carrier frequency to form the observation vector. The sparse representation model construction module is used to uniformly discretize the angle space to be estimated to generate angle grid points. Based on the encoded harmonic transformation matrix that characterizes the asynchronous modulation characteristics of the metasurface, an overcomplete dictionary matrix is ​​constructed in combination with the path response vector of the metasurface unit array. The linear mapping relationship between the observation vector and the array space response is established, and the direction finding problem is transformed into a sparse signal recovery problem, thus obtaining a sparse representation model for metasurface direction finding estimation. The probability model iterative solution module is used to establish a complex Gaussian distribution probability model for the sparse representation model based on the structural sparse Bayesian learning framework. It iteratively updates the hyperparameters and noise power through the expectation-maximization algorithm until the convergence condition is met and the iteration is terminated. The direction-of-arrival (DOA) module is used to perform spectral peak search on the posterior mean of the sparse vector after iterative convergence, and determine the DOA of the incident signal based on the angle grid points corresponding to the peak values.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 6.

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