Hybrid antenna array direction of arrival estimation method based on noise marginalization SBL

Abstract

The invention discloses a hybrid antenna array direction of arrival estimation method based on noise marginalization SBL. The method comprises the following steps: initializing system parameters and a sampling grid set; establishing a hybrid antenna array receiving signal model, and initializing a hybrid beam forming matrix into a block diagonal matrix meeting constant modulus constraint; constructing a hierarchical probability model under a Bayesian framework, and introducing a noise precision parameter into signal prior; integral operation is carried out on the noise precision parameter, so that the signal posterior distribution is converted into student t distribution; an objective function is constructed, an expectation maximization algorithm is adopted to iteratively update a signal energy spectrum, and the process does not involve noise parameter estimation; an alternating iteration strategy is adopted, the signal energy is fixedly updated through inner circulation, and optimization is performed through a gradient descent method after outer circulation is fixed; after convergence, constructing a target function of off-grid estimation by reconstructing a covariance matrix; and searching the off-grid direction of the maximized objective function near a spectrum peak to obtain a final DOA estimation value.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, specifically relating to a method for estimating the direction of arrival (DOA) of a hybrid antenna array based on noise edge-trimming SBL. Background Technology

[0002] Using antenna arrays for direction-of-arrival (DOA) estimation can help systems achieve beamforming, enhance transmission range, and enable multi-user communication through spatial multiplexing, thereby significantly improving spectrum utilization, signal quality, and system capacity. It has become one of the core technologies for improving the efficiency and performance of modern communication systems.

[0003] However, most existing DOA estimation algorithms are designed for traditional antenna arrays, and the traditional all-digital architecture requires an independent RF link for each antenna element. With the increasing demand for massive MIMO antenna arrays in 5G and future communication systems, this fully connected architecture will bring significant hardware complexity and power consumption issues.

[0004] One effective solution to this problem is a hybrid antenna array structure. This structure significantly reduces the number of RF links, hardware costs, and system power consumption by dividing the entire antenna array into several subarrays, each sharing a single RF link. However, this partially connected architecture also introduces new challenges. The core issue is that the hybrid beamforming process compresses the original high-dimensional array received signal into a low-dimensional signal space, causing the system to be unable to obtain complete signal information from all antenna elements, thus leading to unavoidable signal loss.

[0005] Specifically, if we consider The antenna elements are divided into Subarrays ( Then, the final output signal dimension after hybrid beamforming will be changed from... Dimensions dropped to This reduction in signal dimensionality presents two major challenges for DOA estimation in hybrid antenna array structures: (1) Decreased estimation accuracy: Traditional super-resolution DOA estimation algorithms (such as MUSIC and ESPRIT) heavily rely on the spatial information provided by the complete array covariance matrix. Therefore, the reduction in the dimensionality of the received signal under a hybrid antenna array structure directly leads to a decrease in the algorithm's resolution and a deterioration in estimation accuracy.

[0006] (2) Increased sensitivity to noise: In the hybrid antenna array structure, the high-dimensional received signal is compressed to the low-dimensional radio frequency link output through hybrid beamforming. Each observation dimension carries more synthesized information from the antenna elements, but the corresponding independent degrees of freedom are reduced, resulting in a decrease in the effective signal-to-noise ratio and a significant increase in the system's sensitivity to noise.

[0007] In the field of DOA estimation under hybrid antenna array structures, existing technologies mainly fall into two categories. The first category utilizes external supplementary information to compensate for the accuracy loss caused by signal dimensionality reduction, thereby improving the accuracy of DOA estimation. Examples include an existing flat-top beamforming algorithm using azimuth prior information (Uplink_Beam_Management_for_Millimeter_Wave_Cellular_MIMO_Systems_with_Hybrid_Beamforming) and a method for optimizing the hybrid beamforming matrix under coarse DOA prior knowledge (Hybrid BeamformingOptimization for DOA Estimation Based on the CRB Analysis_Lin_2021_). These methods are highly dependent on the accuracy of prior information and are limited in practical applications. The second category of methods is based on the inherent structure of the hybrid antenna array, directly processing the array's output signal to estimate DOA. This approach is more versatile, simplifies system design, and better adapts to environmental changes. For example, estimation can be performed using the correlation between adjacent subarrays, but its performance degrades significantly in non-line-of-sight environments or under strong noise interference; signal dimensions can be recovered through time sampling, but this is highly dependent on the system architecture and the augmentation process leads to high computational complexity.

[0008] The sparse Bayesian learning (SBL) framework offers potential for solving the aforementioned problems due to its natural ability to handle underdetermined problems and representation uncertainties. However, there are still key drawbacks when applying SBL to hybrid arrays: the performance of existing SBL methods is too sensitive to the initial values ​​of noise variance, and they generally use fixed beamforming matrices, failing to fully realize the potential of hybrid architectures in actively enhancing sensing capabilities. Summary of the Invention

[0009] The main objective of this invention is to overcome the shortcomings and deficiencies of existing DOA estimation methods for hybrid antenna array structures and provide a hybrid antenna array DOA estimation method based on noise edge-shaping SBL. This method eliminates the dependence on initial noise parameter values ​​in traditional methods through noise edge-shaping, improving the algorithm's robustness under noise interference conditions; it actively enhances the array's sensing performance through the design optimization of the hybrid beamforming matrix; and it eliminates the quantization error caused by the fixed sampling grid through off-grid search, achieving more accurate DOA estimation. This invention demonstrates superior performance in simulation data testing scenarios and is applicable to DOA estimation in 5G and future massive MIMO antenna systems.

[0010] The present invention is achieved by at least one of the following technical solutions.

[0011] A method for estimating the direction of arrival (DOA) of a hybrid antenna array based on noise-edge-trimmed scattering (SBL) includes the following steps: S1. Initialize system parameters and sampling grid set; S2. Establish a hybrid antenna array received signal model and initialize the hybrid beamforming matrix as a block diagonal matrix that satisfies constant mode constraints; represent the received signal using the hybrid beamforming matrix. S3. Sparse modeling of the received signal is performed under the sparse Bayesian learning framework to establish a Bayesian hierarchical probability model and introduce noise accuracy parameters into the signal prior. S4. Perform an integral operation on the noise accuracy parameter to transform the posterior distribution of the signal into a Student t-distribution; S5. Construct the logarithm of the joint probability density function as the objective function, and use the expectation-maximization algorithm to iteratively update the signal energy spectrum; S6. Use an alternating iterative strategy until the expectation-maximization algorithm converges; S7. After the iteration converges, the objective function for off-grid estimation is constructed by reconstructing the covariance matrix. An off-grid refinement search is performed to search for the off-grid direction that maximizes the objective function near the spectral peak, and the final DOA estimate is obtained.

[0012] Furthermore, in step S2, the received signal model of the hybrid antenna array includes multiple non-overlapping subarray structures, each subarray contains multiple antenna elements, and each subarray is driven by an independent RF link; the subarray structure can be described by a hybrid beamforming matrix, which is initialized as a block diagonal matrix.

[0013] Furthermore, in step S2, the noise accuracy parameter follows a gamma distribution, and the noise accuracy parameter is introduced into the signal prior. Each element of the signal source follows a two-layer prior distribution.

[0014] Furthermore, in step S4, the noise accuracy parameter is marginalized as a redundant variable, and the posterior distribution of the signal is transformed into a Student t-distribution with heavy-tailed characteristics. Then, signal reconstruction and parameter inference are performed based on the mean vector and covariance matrix of the Student t-distribution.

[0015] Furthermore, in step S5, by treating the signal source matrix and noise accuracy parameters as latent variables and integrating them, a marginal likelihood function that depends only on the signal energy spectrum is constructed. The logarithmic form of the marginal likelihood function is further constructed as the objective function of sparse Bayesian learning, and the expectation-maximization method is used to iteratively update the signal energy spectrum. After the iteration converges, the initial estimate of the direction of arrival is determined based on the peak position of the energy spectrum.

[0016] Furthermore, the alternating iteration strategy is an alternating inner and outer loop optimization strategy. The inner loop updates the signal energy spectrum by fixing the hybrid beamforming matrix, while the outer loop fixes the signal energy spectrum and optimizes the hybrid beamforming matrix using the gradient descent method.

[0017] Furthermore, in step S6, after each preset number of signal energy spectrum updates, a gradient descent update of the hybrid beamforming matrix is ​​performed. The optimization objective of the hybrid beamforming matrix is ​​to minimize the negative log-likelihood function of the observed data, and the gradient is derived in closed form. During the update of the hybrid beamforming matrix, its block diagonal structure is maintained by column-independent processing, and its constant mode constraint is maintained by phase projection.

[0018] Further, in step S7, an off-mesh refinement search is performed, including: For each energy spectrum peak corresponding to a discrete angle and adjacent grid points, construct the residual covariance matrix after removing the components of this angle and an adjacent angle; By introducing continuous off-grid direction variables and their corresponding energies, the expression for the array output covariance matrix is ​​reconstructed. Substitute the reconstructed covariance matrix into the likelihood function, and obtain the off-grid direction that maximizes the likelihood function through a local one-dimensional search, which is then used as the final direction of arrival estimate.

[0019] A computer device according to the present invention includes a memory and a processor, the memory being electrically connected to the processor, the memory storing a computer program, which, when executed by the processor, causes the processor to implement the method described herein.

[0020] The present invention provides a computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the processor implements the method described herein.

[0021] Compared with the prior art, the present invention has the following advantages and beneficial effects: (1) This invention introduces a noise accuracy parameter within a Bayesian framework and performs integration processing, marginalizing and eliminating it as a redundant variable from the posterior distribution of the signal, thus transforming the posterior distribution of the signal into a Student t-distribution with heavy-tailed characteristics. Under this framework, the iterative process focuses solely on recovering the signal energy spectrum, completely avoiding the estimation of the noise parameter. This fundamentally eliminates the negative impact of inaccurate initial noise values ​​being amplified by the low-dimensional observation space under a hybrid array structure, significantly improving the robustness and estimation accuracy of the algorithm under noise interference conditions.

[0022] (2) This invention proposes an optimization strategy that iteratively alternates between the hybrid beamforming matrix and signal parameters. Addressing the inherent problem of information loss due to signal dimensionality reduction in hybrid arrays, most existing methods passively adapt to a fixed beamforming matrix. This invention overcomes this limitation by treating the hybrid beamforming matrix as an optimizable variable and constructing an optimization problem aimed at minimizing the negative log-likelihood function of the observed data. By deriving its closed-form gradient, gradient descent is used to iteratively optimize it while maintaining block diagonal and constant mode constraints, forming an alternating iteration with the signal energy spectrum recovery process. This strategy enables proactive optimization of the hybrid array's direction sensing performance, compensating to some extent for information loss caused by hardware structure, thereby improving the final accuracy of DOA estimation at the system level.

[0023] (3) This invention introduces an off-grid search step. Most existing sparse Bayesian learning DOA estimation algorithms still limit the peak position obtained after the signal energy spectrum converges to a preset discrete sampling grid, while the actual signal direction often deviates from the grid point, thus introducing quantization error. This invention performs a refined search within the adjacent angle range of the peak grid and constructs a modified covariance matrix to achieve compensated estimation of the off-grid angle, thereby effectively eliminating the quantization error caused by the fixed sampling grid and obtaining an estimate that is closer to the true incident direction, showing significant advantages in both resolution and accuracy. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0025] Figure 1 This is a flowchart of the direction-of-arrival estimation method for hybrid antenna arrays based on noise edge-trimming SBL of the present invention.

[0026] Figure 2(a) is a comparison of the curves showing the change of the sparse Bayesian learning objective function value with the number of iterations before and after gradient descent optimization when the signal-to-noise ratio is 0 in the embodiment.

[0027] Figure 2(b) is a comparison of the curves showing the change of the sparse Bayesian learning objective function value with the number of iterations before and after gradient descent optimization when the signal-to-noise ratio is 10 in the embodiment.

[0028] Figure 2(c) is a comparison of algorithm performance under different hybrid beamforming matrix design methods in the embodiment.

[0029] Figure 3 This is a performance comparison chart between the present invention and existing hybrid antenna array DOA estimation schemes.

[0030] Figure 4(a) is a graph showing the change of the root mean square error of the present invention with the signal-to-noise ratio when the number of RF chains in the hardware configuration is changed, and its comparison with the Cramer-Rao boundary under the hybrid architecture.

[0031] Figure 4(b) is a comparison of the root mean square error of the present invention with the signal-to-noise ratio and the Cramer-Rao boundary of the hybrid architecture when the number of snapshots is changed in the embodiment. Detailed Implementation

[0032] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of the present application, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present application without creative effort are within the scope of protection of the present application.

[0033] Example 1 like Figure 1 As shown, the direction-of-arrival estimation method for hybrid antenna arrays based on noise-margined sparse Bayesian learning in this embodiment specifically includes the following steps: S1. Initialize parameters and set the number of information sources. , No. The center frequency of the signals from each signal source is , The propagation speed is the speed of light. , No. The center frequency of the signal from each source corresponds to the wavelength. Quick shot number Sampling grid set Array manifold vector .

[0034] S2. Establish a received signal model for the hybrid antenna array, specifically including: Each array element is divided into There are three non-overlapping subarrays, with the spacing between adjacent elements being [missing information]. Each subarray contains Each antenna element is driven by an independent RF link. The aforementioned subarray structure and related operations can be handled by a hybrid beamforming matrix. Description. Hybrid beamforming matrix. Initialized to satisfy the block diagonal structure and constant modulus constraint The matrix will receive the signal. Using hybrid beamforming matrix express.

[0035] Hybrid beamforming matrix Initialize it as a block diagonal matrix of the following form:

[0036] Each subvector Generated by an analog phase shifter, with each element satisfying constant mode constraints. Under this structure, the hybrid beamforming matrix... satisfy:

[0037] Among them, symbols Represents the hybrid beamforming matrix Each subvector is complex vectors, for 3D identity matrix.

[0038] This initialization method offers two main advantages. First, it ensures physical structure matching; the block-diagonal form clearly reflects the hardware connection method of the hybrid array, meaning each RF link drives only one independent subarray, and the subarrays do not interfere with each other. The second, and more important, advantage is that, under this property, it's possible to deduce the noise level after processing by the block-diagonal hybrid beamforming matrix. The covariance matrix is:

[0039] Among them, symbols It represents the expected value of a random variable and is used to calculate the statistical mean of the random variable. The number of antenna elements contained in each subarray. The variance of additive noise is represented. express t The noise vector at time step. It can be seen that the noise covariance matrix is ​​still a scalar matrix, meaning the noise retains its white noise characteristics. Therefore, this initialization greatly simplifies algorithm design and theoretical analysis.

[0040] Next, we assume that there exists... A far-field narrowband signal is incident on the aforementioned hybrid antenna array. The directions of arrival of the signals are respectively The received signal of the hybrid antenna array at time t is:

[0041] in and Let these represent the signal vector and noise vector at time t, respectively. The number of snapshots is... express. It is an array of manifold matrices composed of manifold vectors. It is the first k The manifold vector of each signal source is represented as:

[0042] in, Indicates the first The direction of arrival angle of each signal source; The imaginary unit; Indicates the wavelength of the signal carrier wave; Indicates the first The distance between each antenna element and the reference array element.

[0043] Discrete sampling of spatial angles yields a set of sampling grids. Array manifold matrix under sampling grid ,in This represents the number of grid cells. The number of sampling grid cells is generally much larger than the number of array elements and the number of information sources, satisfying the following condition: ; Indicates the first A discrete sampling angle Indicates the direction corresponding to the incoming wave. The array manifold vector. Then, the received signal of the hybrid antenna array in a multi-shot scenario is sparsely represented as follows:

[0044] Among them, the received signal yes In a matrix format captured at multiple speeds, the signal source... yes Matrix form under discrete sampling grid extension yes In the matrix form of multiple shots.

[0045] S3. Sparse modeling of the array received signal is performed within the sparse Bayesian learning framework to establish a Bayesian hierarchical probability model: The signal is assumed to follow a two-layer distribution prior to satisfy sparsity constraints, and a noise accuracy parameter is introduced into the signal prior. Under the assumption of complex Gaussian white noise, the probability density function of the noise after processing by the hybrid beamforming matrix is... The expression is as follows:

[0046] Among them, symbols Indicated by For mean vector, The covariance matrix is ​​a complex Gaussian distribution. Let be the noise variance, and let Indicates noise accuracy. The value of is the reciprocal of the noise variance, then the noise probability density function Represented as:

[0047] Assumption Obey the shape parameters With scale parameters The determined gamma distribution, probability density function expression as follows:

[0048] in, and It is a very small positive value.

[0049] Then the received signal can be obtained. Y The likelihood function is:

[0050] This represents the probability of observation.

[0051] Considering the prior distribution of the signal, assume The elements of follow a complex Gaussian distribution with a mean of zero:

[0052] in Represents the prior probability of the signal. Indicates signal source No. The variance of a row can be viewed as the signal energy at that grid location. express Signal energy spectrum of each line express The identity matrix. The difference between this and other classic sparse Bayesian learning-based DOA estimation methods lies in... The variance is and In mathematical analysis, this modification makes it easier for the expression after subsequent integration to be mathematically analyzable.

[0053] make It follows the following gamma distribution, with the probability density function expression as follows. for:

[0054] in, It is an extremely small positive value.

[0055] S4. Based on the Bayesian hierarchical probability model, integrating the noise accuracy parameter can reduce the signal source... The posterior probability is transformed into the Student's t-distribution, and the calculation process is as follows: According to an important property of the complex Gaussian distribution: if both the prior distribution and the likelihood function are complex Gaussian, then the posterior distribution is also complex Gaussian. Therefore, based on the prior probability... and likelihood function It can be known The posterior probability follows a complex Gaussian distribution, with the probability density function... for:

[0056] in, Indicated by For the mean, Let be the complex Gaussian distribution of the covariance matrix.

[0057] Covariance matrix of posterior probability and mean They are respectively:

[0058]

[0059] in, , diag This represents a diagonal matrix.

[0060] noise accuracy Treating it as a redundant parameter affects noise accuracy. Perform a noise integration operation to obtain the integrated noise. Posterior probability function:

[0061] Among them, symbols The standard gamma function is defined as follows: Here, is used as the normalization constant of the gamma prior distribution in the Bayesian model.

[0062]

[0063]

[0064]

[0065] in This represents the covariance matrix of the array's received data. (This is achieved by adjusting the noise accuracy.) Perform noise integration. The posterior probability density function becomes the mean. The variance is The Student t-distribution. The Student t-distribution has a sharp peak at the origin and heavy tails, which is beneficial for robust signal estimation under external noise interference.

[0066] S5. Construct the logarithm of the joint probability density function as the objective function. The expectation-maximization algorithm is used to analyze the signal energy spectrum. Iterative updates are performed, without involving noise parameter estimation during the iteration process. The execution process of the iterative update is as follows: First of all and Treating them as redundant variables, based on the Bayesian probability distribution... and Integrating yields the joint probability density function :

[0067] Construct the logarithm of the joint probability density function The objective function is as follows:

[0068] in, express The t In the column, const represents a constant that is independent of the optimization variable.

[0069] The objective function described above is maximized using the Expectation-Maximization (EM) algorithm. In the E-step, the expectation of the objective function with respect to the posterior probability is calculated. :

[0070] in, Indicates that in a given received data and signal energy spectrum Regarding latent variables The expected value is obtained from the posterior distribution. This means "proportional to", that is, the difference between the two sides of the formula is equal to the value of the optimization variable. Irrelevant constant factors; The first element represents the posterior covariance matrix of the signal. One diagonal element; The first digit represents the posterior mean of the signal. OK.

[0071] In step M, by maximizing Obtain the signal energy spectrum The update. First, calculate... Regarding the signal energy spectrum The derivative:

[0072] make Obtain the signal energy spectrum Iterative update expression as follows:

[0073] Signal energy spectrum after iterative convergence The estimated value is considered as the signal energy spectrum, the signal energy spectrum The azimuth angle corresponding to the peak position is the estimated DOA value.

[0074] S6. Employ an alternating iterative optimization strategy until the expectation-maximization algorithm converges: (a) In the inner loop, a fixed hybrid beamforming matrix is ​​used. The signal energy spectrum derived above The iterative update expression performs multiple sparse Bayesian learning update steps, preferably three iterations in this embodiment of the invention, to ensure the hyperparameters are optimized. The estimate converges and becomes stable.

[0075] (b) In the external circulation, the updated signal energy spectrum is fixed. The negative log-likelihood function of the observed data is used as the objective function. Gradient descent method is used to Perform iterative optimization, and maintain [the desired state] during the optimization process. The block diagonal structure and constant modulus constraint.

[0076] Hybrid Beamforming Matrix The optimization objective is defined as minimizing the received data. The negative log-likelihood function, whose core expression is (ignoring the constant term):

[0077] in, For the theoretical array output covariance matrix, This is the sample covariance matrix. The objective function can be calculated from this matrix. about Closed gradient Gradient descent is then used to iteratively update the data.

[0078] During the update process, the hybrid beamforming matrix is ​​maintained using a split optimization strategy. The block diagonal structure is used, and its constant modulus constraint is ensured through phase projection, thereby achieving the desired performance while ensuring hardware structure matching. Effective optimization.

[0079] S7. After convergence, the process of performing off-grid refinement search by reconstructing the covariance matrix is ​​as follows: Let the signal spatial energy spectrum be In, corresponding to the first The peak position of the estimated source is given by the sampling grid angle. ,and The adjacent left and right grid points are respectively and The corresponding energy values ​​are respectively and .definition Output covariance matrix for array Remove Components related to the array manifold vector and energy of an adjacent grid:

[0080] in,

[0081] symbol This represents the array manifold vector corresponding to a specified angle.

[0082] To characterize the off-grid effect, two variables, the off-grid signal direction and energy, are introduced to construct a new array output covariance matrix expression as follows:

[0083] in Is and Within the range, in the direction away from the grid, It corresponds to The off-grid signal energy. Substituting the reconstructed covariance matrix expression into the logarithm of the joint probability density function. The covariance matrix of the array received data The modified log-joint probability density function can be obtained. :

[0084] in,

[0085]

[0086]

[0087] By constructing a new modified covariance matrix, the signal direction and energy that deviate from the grid are recovered from the covariance matrix. The reconstructed covariance matrix is ​​then substituted into the original array covariance matrix of the objective function, extending the solution of the direction of arrival (DOA) from the grid to the off-grid. This effectively solves the problem that the signal direction is not on the preset grid, eliminates the quantization error caused by the discrete sampling grid, and thus obtains a more refined DOA estimate.

[0088] In order to obtain about The maximum value will about Differentiate and let ,get about expression ,exist Searching within the range of adjacent left and right grid cells makes the objective function estimated from the grid cell more efficient. The largest value As an estimate of DOA away from the grid.

[0089] Specifically, the process for determining the DOA estimate from the grid is as follows: make about Find the derivative and set the derivative to... You can get about expression as follows:

[0090] in,

[0091]

[0092]

[0093] In order to obtain about The maximum value will Substitution Get only variables Objective function of off-grid estimation Due to the inability to obtain middle The closed-form solution, in the two grids adjacent to the peak. and Searching within a small range will make the objective function estimated from the grid more efficient. To obtain the maximum value As an estimate of DOA away from the grid : .

[0094] Example 2 This embodiment discloses a direction-of-arrival estimation method for hybrid antenna arrays based on noise edge-shaping SBL. The test results are shown in Figure 2, which confirms the effectiveness of the block diagonal initialization plus gradient descent optimization strategy proposed in this invention for hybrid beamforming matrices.

[0095] S1. Initialize parameters. Set the number of far-field narrowband sources. K =2, the direction of the information source is set to (-5+u)° and (5+u)°, where u represents a random number between -1 and 1. Sampling grid The range is from -90° to 90°, with 1° increments. The number of snapshots is fixed. T =30.

[0096] S2. Establish a received signal model for the hybrid antenna array. Set the number of array elements. M =32, the array is divided into =8 subarrays, each subarray contains One antenna element. Carrier frequency. Corresponding wavelength The element spacing is fixed at half a wavelength. The hybrid beamforming matrix... Initialize it as a block diagonal matrix of the following form:

[0097] Each subvector It is generated by an analog phase shifter, and each element satisfies the constant modulus constraint.

[0098] Under this structure, the matrix satisfy ,go through The processed noise retains its white noise characteristics.

[0099] The received signal of the hybrid antenna array in a multi-shot scenario can be sparsely represented as follows:

[0100] in, It is an array receiving signal In the matrix format captured at various speeds It is an incident far-field narrowband signal Matrix form under discrete sampling grid extension It's noise. In the matrix form of multiple shots.

[0101] Steps S3-S7 are the same as in Example 1, and will not be repeated here.

[0102] First, we verified the improvement in algorithm convergence achieved by gradient descent optimization. In the experiments shown in Figure 2(a) and Figure 2(b), we set up... snr =0dB and snr =10dB signal-to-noise ratio (SNR) under two conditions. Under each condition, the performance of only performing the sparse Bayesian learning inner loop (before gradient descent) was compared with that of performing the full alternating iterative strategy (including the hybrid beamforming matrix). During gradient descent optimization, the objective function value learned by sparse Bayes is... How it changes with the number of iterations.

[0103] Experimental results clearly show that, under both signal-to-noise ratios, introducing an effect... After gradient descent optimization, the objective function value is significantly improved, and the convergence process is accelerated. This proves that the optimization strategy proposed in this invention can effectively guide the beamforming matrix to adapt to the observation data, thereby improving the model matching degree and enhancing the algorithm's estimation performance.

[0104] Secondly, the overall performance of the DOA estimation algorithm under different hybrid beamforming matrix processing methods is compared. In the experiment shown in Figure 2(c), in SNR from Four different hybrid beamforming matrices were compared within the range of 10dB to 15dB. Solution: 1. Random phase: Initialized as a random phase matrix, it remains fixed (marked as random). 2. FFT codebook: The column vectors of the DFT matrix are directly taken as the beam direction and then kept fixed (labeled as FFT). 3. Fixed as diagonal blocks: Once initialized as a block diagonal matrix, it remains fixed (marked as BlockDiag). 4. The strategy of this invention: After initializing to a block diagonal matrix, a gradient descent optimization strategy is adopted, and the block diagonal structure and constant modulus constraint are maintained during the update process (labeled as BlockDiag-GD). Performance comparisons were conducted using the root mean square error (RMSE) of the DOA estimation as the evaluation metric. Results show that the proposed "block diagonal initialization + gradient descent optimization" strategy achieves a lower RMSE than other fixed-matrix schemes across the entire signal-to-noise ratio range. This demonstrates that... The necessity of considering variables as optimizable variables, and the effectiveness of the optimization method of this invention, can actively improve the sensing performance of the hybrid array, compensate for the information loss caused by the hardware structure, and thus improve the estimation accuracy.

[0105] Example 3 This embodiment discloses a direction-of-arrival (DOA) estimation method for hybrid antenna arrays based on noise edge-trimming (SBL). The performance of the proposed method is compared with that of existing DOA estimation algorithms for hybrid antenna array structures. All methods were subjected to repeated simulation experiments 300 times, which demonstrates the reliability and superiority of the proposed method.

[0106] S1. Initialize parameters. Set the number of far-field narrowband sources. K =2, the direction of the information source is set to (-5+u)° and (5+u)°, where u represents a random number between -1 and 1. Sampling grid The range is from -90° to 90°, with 1° increments. The number of snapshots is fixed. T =30. The signal-to-noise ratio (SNR) test range is... 10dB to 15dB.

[0107] Steps S2-S7 are the same as in Example 1, and will not be repeated here.

[0108] The test results of this embodiment are as follows: Figure 3 As shown, the performance evaluation metric is the root mean square error (RMSE) of the direction of arrival (DOA) estimation. The experiment compared the following four DOA estimation schemes for hybrid antenna arrays: 1. H-ESPRIT: The signal dimension is recovered using the augmented beam spatial method, and then the DOA is estimated by combining it with the ESPRIT algorithm.

[0109] 2. PRE+MUSIC: A preprocessing scheme for recovering signal dimensions is proposed, and the MUSIC algorithm is applied to estimate DOA.

[0110] 3. Root-MUSIC-HDAPA: A fast root multisignal classification HDAPA method is proposed, which achieves an approximate analytical solution.

[0111] 4. The method of the present invention is denoted as HNMSBL.

[0112] Figure 3 The root mean square error (RMSE) of DOA estimation using different methods under different signal-to-noise ratios (SNRs) with a fixed number of 30 snapshots is presented. The results show that, firstly, in the low SNR region, the H-ESPRIT and PRE+MUSIC algorithms exhibit relatively good robustness. This is because these methods employ a "time-for-space" strategy, utilizing multiple time snapshots to broaden the beam space, which to some extent compensates for the signal dimensionality loss caused by the hybrid array hardware structure, thus maintaining basic estimation capability under harsh SNR conditions.

[0113] However, as the signal-to-noise ratio increases (especially in...) snr When the signal-to-noise ratio (SNR) is >0dB, the advantages of the HNMSBL algorithm proposed in this invention begin to emerge and quickly surpass other comparative schemes. This is because the signal components in the observed data are more reliable after the SNR is improved. The core advantages of the method of this invention are fully utilized: First, by integrating the noise accuracy parameter, the error introduced by the inaccurate estimation of noise parameters in traditional algorithms is avoided, making the signal recovery process purer and more accurate; Second, by alternately optimizing the hybrid beamforming matrix... This proactively enhances the array's sensing gain, making more efficient use of available signal energy. These two innovations enable the method of this invention to consistently approximate the theoretical performance lower bound (CRB) of the hybrid architecture, allowing for a fuller exploitation of the hybrid array's potential and thus achieving higher estimation accuracy.

[0114] Example 4 This embodiment discloses a method for estimating the direction of arrival (DOA) of a hybrid antenna array based on noise-margined SBL. The test results are shown in Figure 4, which demonstrate the robustness of the method proposed in this invention.

[0115] First, performance tests were conducted under hardware configuration changes to verify the algorithm's adaptability when the hardware configuration of the hybrid antenna array changes. The total number of array elements was maintained. M =32 remains unchanged, but the number of radio frequency links is changed. To adjust the hardware configuration. The experiment compared... Q =1 (corresponds to a fully digital architecture, ), Q =2( ), Q =4( Three configurations are available. Two signal sources are incident, and the number of snapshots is fixed. T =30.

[0116] The test results are shown in Figure 4(a): First, the hybrid architecture Cramer-Ray boundary, used as a performance reference, follows... Q The increase (i.e.) The decrease in [the degree of freedom] leads to an increase, reflecting the theoretical performance loss caused by the reduction in hardware degrees of freedom. The key finding is that: in different [various conditions]... Under the specified configuration, the estimation performance (RMSE curve) of the method proposed in this invention closely tracks and approximates its corresponding mixed Cramer-Rao bound. In particular, when... Q When = 1, the system degenerates into an all-digital array, and the algorithm performance approaches the theoretical limit in the all-digital case; with Q As the degree of mixing increases, the algorithm's performance still stably tracks and approximates the more demanding hybrid CRB. This fully demonstrates that the method of this invention has good adaptability and robustness to different hardware configurations, and its performance is consistent with theoretical predictions in terms of the influence of hardware degrees of freedom, without introducing additional performance loss.

[0117] Secondly, performance tests were conducted under varying observation conditions to verify the effectiveness of different observation conditions (number of snapshots). T The performance of the algorithm is as follows. The fixed array hardware configuration is... M =32, ( Q =4), with signal-to-noise ratios set to 0dB, 5dB, and 10dB respectively. (Snapshot count) It changed from 50 to 350.

[0118] The test results are shown in Figure 4(b). It can be observed that under all test signal-to-noise ratios, the estimation error of the algorithm steadily decreases with the increase of the number of snapshots. This proves that the method of the present invention can maintain stable convergence characteristics under different amounts of observation data, and its performance dependence on the number of snapshots is consistent with theoretical expectations, further verifying the reliability of the algorithm in practical applications.

[0119] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A method for estimating the direction of arrival (DOA) of a hybrid antenna array based on noise-edge-trimmed SBL (Sound-Bounded Linear Browsing), characterized in that, Includes the following steps: S1. Initialize system parameters and sampling grid set; S2. Establish a hybrid antenna array received signal model and initialize the hybrid beamforming matrix as a block diagonal matrix that satisfies constant mode constraints; represent the received signal using the hybrid beamforming matrix. S3. Sparse modeling of the received signal is performed under the sparse Bayesian learning framework to establish a Bayesian hierarchical probability model and introduce noise accuracy parameters into the signal prior. S4. Perform an integral operation on the noise accuracy parameter to transform the posterior distribution of the signal into a Student t-distribution; S5. Construct the logarithm of the joint probability density function as the objective function, and use the expectation-maximization algorithm to iteratively update the signal energy spectrum; S6. Use an alternating iterative strategy until the expectation-maximization algorithm converges; S7. After the iteration converges, the objective function for off-grid estimation is constructed by reconstructing the covariance matrix. An off-grid refinement search is performed to search for the off-grid direction that maximizes the objective function near the spectral peak, and the final DOA estimate is obtained.

2. The method for estimating the direction of arrival (DOA) of a hybrid antenna array based on noise-edge-trimmed SBL according to claim 1, characterized in that, In step S2, the received signal model of the hybrid antenna array includes multiple non-overlapping subarray structures, each subarray contains multiple antenna elements, and each subarray is driven by an independent RF link; the subarray structure can be described by a hybrid beamforming matrix, which is initialized as a block diagonal matrix.

3. The method for estimating the direction of arrival (DOA) of a hybrid antenna array based on noise-edge-trimmed SBL according to claim 1, characterized in that, In step S2, the noise accuracy parameter follows a gamma distribution and is introduced into the signal prior. Each element of the signal source follows a two-layer prior distribution.

4. The method for estimating the direction of arrival (DOA) of a hybrid antenna array based on noise-edge-trimmed SBL according to claim 1, characterized in that, In step S4, the noise accuracy parameter is marginalized as a redundant variable, and the posterior distribution of the signal is transformed into a Student t-distribution with heavy-tailed characteristics. Then, signal reconstruction and parameter inference are performed based on the mean vector and covariance matrix of the Student t-distribution.

5. The method for estimating the direction of arrival (DOA) of a hybrid antenna array based on noise-edge-trimmed SBL according to claim 1, characterized in that, In step S5, by treating the signal source matrix and noise accuracy parameters as latent variables and integrating them, a marginal likelihood function that depends only on the signal energy spectrum is constructed. The logarithmic form of the marginal likelihood function is further constructed as the objective function of sparse Bayesian learning, and the expectation-maximization method is used to iteratively update the signal energy spectrum. After the iteration converges, the initial estimate of the direction of arrival is determined based on the peak position of the energy spectrum.

6. The method for estimating the direction of arrival (DOA) of a hybrid antenna array based on noise-edge-trimmed SBL according to claim 1, characterized in that, The alternating iteration strategy is an inner and outer loop alternating optimization strategy. The inner loop updates the signal energy spectrum by fixing the hybrid beamforming matrix, while the outer loop fixes the signal energy spectrum and optimizes the hybrid beamforming matrix by gradient descent.

7. The method for estimating the direction of arrival (DOA) of a hybrid antenna array based on noise-edge-trimmed SBL according to claim 6, characterized in that, In step S6, after each preset number of signal energy spectrum updates, a gradient descent update of the hybrid beamforming matrix is ​​performed. The optimization objective of the hybrid beamforming matrix is ​​to minimize the negative log-likelihood function of the observed data, and the gradient is derived in closed form. During the update of the hybrid beamforming matrix, its block diagonal structure is maintained by column-independent processing, and its constant mode constraint is maintained by phase projection.

8. The method for estimating the direction of arrival (DOA) of a hybrid antenna array based on noise-edge-trimmed SBL according to claim 1, characterized in that, In step S7, an off-mesh refinement search is performed, including: For each energy spectrum peak corresponding to a discrete angle and adjacent grid points, construct the residual covariance matrix after removing the components of this angle and an adjacent angle; By introducing continuous off-grid direction variables and their corresponding energies, the expression for the array output covariance matrix is ​​reconstructed. Substitute the reconstructed covariance matrix into the likelihood function, and obtain the off-grid direction that maximizes the likelihood function through a local one-dimensional search, which is then used as the final direction of arrival estimate.

9. A computer device comprising a memory and a processor, the memory being electrically connected to the processor, the memory storing a computer program, characterized in that: When the computer program is executed by the processor, it causes the processor to implement the method as described in any one of claims 1 to 8.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the processor implements the method as described in any one of claims 1 to 8.

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