Array error calibration method and related equipment based on reconfigurable intelligent surface assistance

Abstract

This invention discloses an array error calibration method and related equipment based on reconfigurable smart surfaces. The method includes: receiving radar echo signals containing array amplitude and phase errors acquired by an array antenna; constructing a target model based on the radar echo signals using reconfigurable smart surfaces; introducing a cost function to transform the joint estimation problem of signal direction of arrival (DOA) and array amplitude and phase errors of the target model into a cost function minimization problem; iteratively solving the cost function minimization problem using an alternating minimum algorithm to obtain the array amplitude and phase errors and calibrate the radar echo signals; and obtaining and outputting the signal DOA estimation result based on the calibrated radar echo signals. This invention, through an array error calibration method based on reconfigurable smart surfaces, can obtain accurate array amplitude and phase error parameter estimation results even in the presence of array amplitude and phase errors.

Description

Technical Field

[0001] This invention relates to the field of array signal processing, and in particular to an array error calibration method and related equipment based on reconfigurable smart surface-assisted calibration. Background Technology

[0002] Array signal processing involves setting up multiple independent array elements at different locations in three-dimensional space according to certain rules and technical requirements to form a large-aperture antenna instead of a single antenna. This array is then used to receive radiated signal sources from different directions and to perform certain post-processing on the multiple radiated signal sources. Therefore, array signal processing technology has been practically applied in many communication fields, such as radar positioning, mobile communication, and information warfare.

[0003] In estimating the direction of arrival (DOA), many super-resolution subspace algorithms have been proposed, such as multiple signal classification algorithms and rotation-invariant signal parameter algorithms. However, to obtain an accurate estimate of the DOA, these algorithms require precise knowledge of the array steering vector, including the element positions and initial phases. In practical applications, array amplitude and phase errors exist. These errors cause deviations between the DOA angle estimated by high-resolution DOA estimation algorithms and the actual angle. In severe cases, the algorithms may even fail and be unable to obtain the DOA angle.

[0004] Therefore, existing array amplitude and phase error calibration techniques still need to be improved and developed. Summary of the Invention

[0005] The technical problem to be solved by this application is to provide an array error calibration method and related equipment based on reconfigurable intelligent surface (RIS) to address the shortcomings of the prior art. The present invention can obtain accurate array amplitude and phase error parameter estimation results in the presence of array amplitude and phase errors through the array error calibration method based on reconfigurable intelligent surface. The obtained array amplitude and phase errors are used to calibrate the radar echo signal, and the signal direction of arrival estimation result is obtained based on the calibrated radar echo signal.

[0006] To address the shortcomings of the prior art, the first aspect of this application provides an array error calibration method based on reconfigurable smart surface assistance, the method comprising:

[0007] The radar echo signal containing array amplitude and phase error is obtained by the receiving array antenna. Based on the radar echo signal, a target model is constructed with the assistance of a reconfigurable smart surface.

[0008] By introducing a cost function, the problem of jointly estimating the signal direction of arrival and the array amplitude and phase error of the target model is transformed into a problem of minimizing the cost function.

[0009] The problem of minimizing the cost function is solved iteratively using the alternating minimum algorithm to obtain the array amplitude and phase error. The obtained array amplitude and phase error is used to calibrate the radar echo signal containing the array amplitude and phase error acquired by the array antenna each time. The signal direction of arrival estimation result is obtained and output based on the calibrated radar echo signal.

[0010] The radar echo signal containing array amplitude and phase errors acquired by the receiving array antenna is used to construct a target model based on the radar echo signal through a reconfigurable smart surface, specifically including:

[0011] The reconfigurable smart surface directionally reflects the signal source at an unknown angle, obtaining the array amplitude and phase error and the signal direction of arrival estimation results, thus obtaining a calibration signal source with a determined azimuth angle.

[0012] The introduction of a cost function transforms the problem of jointly estimating the signal direction of arrival (SAR) and array amplitude and phase errors of the target model into a problem of minimizing the cost function, specifically including:

[0013] Model the array covariance matrix of the target model;

[0014] Based on the array covariance matrix obtained from modeling, eigenvalue decomposition is performed to obtain the signal subspace and noise subspace;

[0015] By leveraging the orthogonality of the obtained signal and noise subspaces and introducing a cost function, the problem of jointly estimating the signal direction of arrival and the array amplitude and phase error of the target model is transformed into a problem of minimizing the cost function.

[0016] The iterative solution of the cost function problem using the alternating minimum algorithm specifically includes:

[0017] The cost function is transformed, and the spatial spectrum function is derived based on the transformed cost function.

[0018] The Root-MUSIC algorithm is used to solve the spatial spectrum function to obtain the estimated signal angle of arrival.

[0019] Based on the obtained signal arrival angle estimate, the amplitude and phase error estimation problem is solved to obtain the array amplitude and phase error estimate.

[0020] The step of iteratively solving the minimization cost function problem using the alternating minimum algorithm to obtain the array amplitude and phase error estimate specifically includes:

[0021] Based on the obtained signal arrival angle estimate, the amplitude and phase error estimation problem is transformed into an optimization problem with constraints.

[0022] The Lagrange multiplier method is used to solve the optimization problem with constraints, and the estimated values ​​of array amplitude and phase error are obtained.

[0023] The iterative solution of the cost function problem using the alternating minimum algorithm specifically includes:

[0024] The cost function is updated based on the obtained signal angle of arrival estimate and array amplitude and phase error estimate.

[0025] The signal arrival angle estimate and array amplitude and phase error estimate are re-solved based on the updated cost function;

[0026] The process iteratively updates the cost function, the estimated angle of arrival of the signal, and the estimated amplitude and phase error of the array. When the iteration termination condition is met, the iteration process ends, and the array amplitude and phase error obtained in the last iteration is used to calibrate the radar echo signal.

[0027] The conditions for satisfying the iteration termination specifically include:

[0028] The iteration termination condition is met when the difference between the cost function obtained in the current iteration and the cost function obtained in the previous iteration is less than a predetermined threshold.

[0029] A second aspect of this application provides an array error calibration device based on a reconfigurable smart surface, the array error calibration device based on a reconfigurable smart surface includes:

[0030] The model building module receives radar echo signals containing array amplitude and phase errors obtained by the array antenna, and builds a target model based on the radar echo signals using a reconfigurable smart surface.

[0031] The problem transformation module introduces a cost function to transform the problem of jointly estimating the signal direction of arrival and the array amplitude and phase error of the target model into a problem of minimizing the cost function.

[0032] The output module iteratively solves the minimum cost function problem according to the alternating minimum algorithm to obtain the array amplitude and phase error. The obtained array amplitude and phase error is used to calibrate the radar echo signal containing the array amplitude and phase error acquired by the array antenna each time. Based on the calibrated radar echo signal, the signal direction of arrival estimation result is obtained and output.

[0033] A third aspect of this application provides a computer-readable storage medium, characterized in that the computer-readable storage medium stores one or more programs, which can be executed by one or more processors to implement the steps in the array error calibration method based on reconfigurable smart surfaces as described above.

[0034] A fourth aspect of this application provides a terminal device, characterized in that it includes: a processor, a memory, and a communication bus; the memory stores a computer-readable program that can be executed by the processor;

[0035] The communication bus enables communication between the processor and the memory;

[0036] When the processor executes the computer-readable program, it implements the steps in the array error calibration method based on reconfigurable smart surface as described above.

[0037] Beneficial effects: Compared with the prior art, this application provides an array error calibration method and related equipment based on reconfigurable smart surfaces. The method includes receiving radar echo signals containing array amplitude and phase errors acquired by an array antenna; constructing a target model based on the radar echo signals using reconfigurable smart surfaces; introducing a cost function to transform the joint estimation problem of signal direction of arrival and array amplitude and phase errors of the target model into a cost function minimization problem; iteratively solving the cost function minimization problem according to the alternating minimum algorithm to obtain the array amplitude and phase errors; calibrating the radar echo signals using the obtained array amplitude and phase errors; and obtaining and outputting the signal direction of arrival estimation result based on the calibrated radar echo signals. Through the above method, this invention enables directional reflection of signal sources at unknown angles using a reconfigurable smart surface. The signal reflected by the reconfigurable smart surface can be considered a calibration source signal with a defined azimuth angle, thus achieving active calibration of antenna errors without the addition of an additional auxiliary calibration source. Furthermore, by using a cost function, the problem of jointly estimating the signal direction of arrival (DOA) and array amplitude and phase errors of the target model is transformed into a cost function minimization problem. The alternating minimum algorithm can then output accurate array amplitude and phase errors. The output array amplitude and phase errors are used to calibrate each input radar echo signal, and the DOA estimation result is obtained based on the calibrated radar echo signal. This allows the array amplitude and phase errors to be obtained even when array amplitude and phase errors exist, thus calibrating the input radar echo signal to a signal without array amplitude and phase errors. This enables the solution of the signal echo signal, achieving accurate DOA estimation. Therefore, the method described in this invention can be used in military and civilian fields such as radar, sonar, communication, and medicine to achieve better calibration of array errors and obtain more accurate DOA estimation results from the signal. Attached Figure Description

[0038] 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.

[0039] Figure 1 A flowchart illustrating the array error calibration method based on reconfigurable smart surface assistance provided by this invention;

[0040] Figure 2 This is a signal transmission path diagram provided by an embodiment of the present invention with the assistance of a reconfigurable smart surface;

[0041] Figure 3 The MUSIC spatial spectrum provided in the embodiments of the present invention;

[0042] Figure 4 A schematic diagram illustrating the statistical performance of array amplitude error estimation under different signal-to-noise ratios provided in an embodiment of the present invention;

[0043] Figure 5 This is a schematic diagram illustrating the statistical performance of array amplitude error estimation under different snapshot numbers provided in an embodiment of the present invention;

[0044] Figure 6 This is a schematic diagram illustrating the statistical performance of array phase error estimation under different snapshot numbers provided in an embodiment of the present invention.

[0045] Figure 7 This is a schematic diagram illustrating the statistical performance of array phase error estimation under different snapshot numbers provided in an embodiment of the present invention.

[0046] Figure 8 This is a schematic diagram of the array error calibration device based on reconfigurable smart surface assistance provided in an embodiment of the present invention. Detailed Implementation

[0047] This application provides a method and related equipment for array error calibration based on reconfigurable smart surfaces. To make the objectives, technical solutions, and effects of this application clearer and more explicit, the following detailed description is provided with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only for explaining this application and are not intended to limit this application.

[0048] Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in this application means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. It should be understood that when we say an element is “connected” or “coupled” to another element, it can be directly connected or coupled to the other element, or there may be intermediate elements. Furthermore, “connected” or “coupled” as used herein can include wireless connections or wireless coupling. The term “and / or” as used herein includes all or any units and all combinations of one or more associated listed items.

[0049] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless specifically defined as herein.

[0050] Furthermore, if the embodiments of this invention involve descriptions such as "first" or "second," these descriptions are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first" or "second" may explicitly or implicitly include at least one of those features. Additionally, the technical solutions of the various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. If the combination of technical solutions is contradictory or impossible to implement, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by this invention.

[0051] Array signal processing has become a popular research area in the field of signal processing due to its numerous advantages. Array signal processing involves setting up multiple independent array elements at different locations in three-dimensional space according to certain rules and technical requirements, thereby constructing a large-aperture antenna to replace a single antenna. This array is then used to receive radiated signals from different directions, and various post-processing techniques are applied to these signals. Depending on the intended use, important signal parameters are detected and estimated, while unwanted information is suppressed. Array signal processing technology has been practically applied in many communication fields, such as radar positioning, mobile communication, and information warfare. The Direction of Arrival (DOA) estimation problem is an important research topic in array signal processing and has applications in many areas.

[0052] In calculating signal direction of arrival (DOA), numerous super-resolution subspace algorithms have been proposed, such as Multiple Signal Classification (MUSIC) and Estimation of signal parameters via rotational invariance techniques (ESPRIT). Theoretically, the performance of existing super-resolution ODA estimation algorithms has approached the Cramer-Rao lower bound. However, to obtain accurate estimates of the signal ODA, these algorithms require precise knowledge of the array steering vector, including element positions and initial phases. Therefore, classic high-resolution algorithms are highly sensitive to array model errors. If an accurate array steering vector cannot be obtained, the performance of these high-resolution algorithms will fall short of expectations. In practical applications, array amplitude and phase errors exist. These errors cause deviations between the estimated ODA angle and the actual angle obtained by high-resolution signal ODA estimation algorithms. In severe cases, this can even lead to algorithm failure, making it impossible to obtain the signal ODA angle.

[0053] To obtain accurate signal direction-of-arrival (DOA) estimation even with array amplitude and phase errors, a method for estimating and correcting the error parameters of the array antenna is urgently needed. Therefore, this invention addresses the array calibration problem under the influence of amplitude and phase errors by providing an array error calibration method based on reconfigurable smart surfaces.

[0054] Current high-resolution DOA estimation algorithms rely on ideal assumptions, namely that the array steering vector is precisely known. However, in practical engineering applications, various errors inevitably exist, such as array amplitude and phase errors, array mutual coupling errors, and array position errors. These errors can severely impact DOA estimation performance, causing it to degrade or even fail. Therefore, calibration for various errors is a necessary condition for the practical application of high-resolution DOA estimation algorithms. Current array error calibration methods are mainly divided into active calibration and passive calibration.

[0055] The main idea of ​​active calibration methods is to set up an auxiliary calibration source in the field and estimate the array error parameters. Active calibration methods have a relatively low computational load and generally achieve satisfactory results. However, this method has certain requirements on the location of the auxiliary calibration source, and the need to set up additional auxiliary array elements undoubtedly increases the cost of the direction-finding system. Passive calibration algorithms rely on optimizing the objective function to jointly estimate the direction of the spatial signal source and the array error parameters. Passive calibration algorithms have the advantages of low cost compared to active calibration, but when using iterative solutions to the error parameters, they are prone to getting trapped in local optima. If the initial parameter settings differ significantly from the actual parameters, the calibration performance will severely degrade or even fail. In the array error calibration method based on reconfigurable smart surface assistance provided in this invention, a reconfigurable smart surface is introduced as an auxiliary source. The signal after reflection can be identified as the auxiliary calibration source. Therefore, our proposed method can have the high accuracy advantage of active calibration while avoiding the algorithm getting trapped in local optima.

[0056] Instance methods

[0057] like Figure 1 The diagram shown is a flowchart of an array error calibration method based on reconfigurable smart surfaces provided in an embodiment of the present invention. This method can be applied to terminal devices. In this embodiment of the invention, combined with... Figure 1 The method is described, and the method includes the following steps:

[0058] Step S10: Receive the radar echo signal containing array amplitude and phase error obtained by the array antenna, and construct the target model based on the radar echo signal using a reconfigurable smart surface.

[0059] This invention receives radar echo signals containing array amplitude and phase errors through an array antenna, and constructs a target model using the received radar echo signals and a set reconfigurable smart surface; specifically, this invention further illustrates the construction process of the target model using a common radar echo signal model.

[0060] For a uniform linear array (ULA) with M antennas to receive L far-field narrowband signals, its angle of arrival is {θ1, θ2, ..., θ...} L In the absence of array amplitude and phase errors, the array's output vector at time t can be expressed as formula (1):

[0061]

[0062] in It is the guiding matrix of the array. is the steering vector of the direction of arrival of the l-th signal source. The signal vector is represented by , while the noise vector is represented by . We assume the noise is zero-mean Gaussian white noise and that the signal and noise are uncorrelated; therefore, they are both modeled as independent, zero-mean complex Gaussian random processes. In the case of a uniform linear array, the steering vector a(θ) is expressed as Equation (2):

[0063]

[0064] Where λ is the carrier wavelength and d represents the spacing between array elements.

[0065] According to formula (1), the covariance matrix of the array can be expressed as formula (3):

[0066] R=E{x(t)x H (t)}=ASA H +σ 2 I, (3)

[0067] Where S = E{s(t)s H Let σ(t)} represent the covariance matrix of the signal, where I represents a unit diagonal matrix. 2 Let E{·} and (·) represent the variance of the noise. H Defined as the statistical expectation and conjugate transpose operator.

[0068] When the array has received data amplitude and phase errors, and the first element of the array is calibrated while the remaining M-1 elements are uncalibrated, the amplitude error ρ and phase error of the array are related. This can be expressed as formulas (4) and (5):

[0069] ρ = [1, ρ1, ..., ρ M-1 ] T (4)

[0070]

[0071] Therefore, considering the amplitude and phase errors of the array, the steering vector of the array needs to be rewritten as formula (6):

[0072]

[0073] Its γ represents the amplitude and phase error vector of the array, which is expressed as Equation 7(7):

[0074]

[0075] where Γ(γ)=diag{γ1, γ2,…,γ M} represents an M×M diagonal matrix, and diag{·} represents the diagonalization operator. In the presence of array amplitude and phase errors, the array's output vector at time t should be expressed as formula (8):

[0076]

[0077] Therefore, the array covariance matrix is ​​expressed as formula (9).

[0078]

[0079] With the introduction of reconfigurable smart surfaces, the target model can be constructed with the assistance of reconfigurable smart surfaces.

[0080] The radar echo signal containing array amplitude and phase errors acquired by the receiving array antenna is used to construct a target model based on the radar echo signal through a reconfigurable smart surface, specifically including:

[0081] The reconfigurable smart surface directionally reflects signals from unknown angle sources to obtain a calibration signal source with a determined azimuth angle.

[0082] After introducing a reconfigurable smart surface, since the reconfigurable smart surface can precisely control the transmission direction of the reflected signal, we add the assistance of the reconfigurable smart surface to the active calibration model. In space, the reconfigurable smart surface performs directional reflection of the signal source at an unknown angle. The signal reflected by the reconfigurable smart surface can be regarded as a calibration source signal with a determined azimuth angle. In this way, the antenna error can be actively calibrated without adding an additional auxiliary calibration source. Furthermore, since the reconfigurable smart surface described in this invention performs directional reflection of the signal source at an unknown angle, the array amplitude and phase errors obtained by this invention can be applied to the calibration of each acquired radar echo signal.

[0083] The reconfigurable smart surface is made by M riｓ A uniform linear array consisting of passive reflective elements, with a spacing of d between each reflective element. ris .

[0084] Specifically, when reconfigurable smart surfaces assist in reflection, the signal transmission path diagram under the assistance of reconfigurable smart surfaces is as follows: Figure 2 As shown, the signal source, reconfigurable smart surface, and uniform linear array are all on a common plane; in one embodiment, the reconfigurable smart surface is composed of M... ris A uniform linear array composed of passive reflection units, wherein the number and spacing of the passive reflection units of the reconfigurable smart surface can be set as needed. For example, the number of passive reflection units can be set to M and the spacing to 0.5λ.

[0085] After incorporating reconfigurable smart surface assistance, the signal model of the array at time t, i.e. the target model, can be expressed as formula (10):

[0086]

[0087] Where ζ is the angle at which the reflected signal is incident on the uniform linear array. Let represent the array response vectors of the incident signal and the reflected signal at the reconfigurable smart surface, respectively, which can be expressed as formulas (11) and (12):

[0088]

[0089]

[0090] Where α r α is the angle at which the signal source is incident on the reconfigurable smart surface. l The emission angle of the reflected signal. The controllable phase matrix represents the reconfigurable smart surface. This represents the steering matrix of the array in the case of reconfigurable smart surface assistance. This represents the signal vector in the case of reconfigurable smart surface assistance. and Specifically, this can be expressed as formulas (13) and (14):

[0091]

[0092]

[0093] Step S20: Introduce a cost function to transform the problem of joint estimation of signal direction of arrival and array amplitude and phase error of the target model into a problem of minimizing the cost function;

[0094] Specifically, after constructing the target model, when solving for the signal direction of arrival of the target model, the problem of jointly estimating the signal direction of arrival and the array amplitude and phase error is transformed into a problem of minimizing the cost function by introducing a cost function.

[0095] Furthermore, the introduction of the cost function transforms the problem of jointly estimating the signal direction of arrival and the array amplitude and phase error of the target model into a problem of minimizing the cost function, specifically including:

[0096] Model the array covariance matrix of the target model;

[0097] Based on the array covariance matrix obtained from modeling, eigenvalue decomposition is performed to obtain the signal subspace and noise subspace;

[0098] By leveraging the orthogonality of the obtained signal and noise subspaces and introducing a cost function, the problem of jointly estimating the signal direction of arrival and the array amplitude and phase error of the target model is transformed into a problem of minimizing the cost function.

[0099] Specifically, considering the unknown gain and phase, based on the obtained target model, the array covariance matrix assisted by the reconfigurable smart surface can be modeled as Equation (15):

[0100]

[0101] Meanwhile, the eigenvalue decomposition of the array covariance matrix can be expressed as formula (16):

[0102]

[0103] Where E s Defined as a signal subspace consisting of L+1 principal eigenvalues, E n Let be the noise subspace composed of the remaining eigenvectors, and let represent the identity matrix of the eigenvalues.

[0104] According to the orthogonality theory of signal subspaces, E s The subspace spanned by the array manifold Γ(γ)a(θ) is the same as the subspace spanned by the array manifold Γ(γ)a(θ). At the same time, the signal subspace and the noise subspace have orthogonal properties. Therefore, we can obtain formula (17):

[0105]

[0106] Where ||·|| represents the F-norm of the matrix.

[0107] Based on formula (17), this invention proposes a cost function. Specifically, this is expressed as formula (18):

[0108]

[0109] Therefore, with the assistance of reconfigurable smart surfaces, the problem of jointly estimating the amplitude and phase error of the signal array and the direction of arrival can be transformed into a problem of minimizing the cost function, expressed as formula (19):

[0110]

[0111] Step S30: According to the alternating minimum algorithm, iteratively solve the problem of minimizing the cost function to obtain the array amplitude and phase error. Use the obtained array amplitude and phase error to calibrate the radar echo signal with array amplitude and phase error acquired by the array antenna each time. Based on the calibrated radar echo signal, obtain the signal direction of arrival estimation result and output it.

[0112] Specifically, formula (19) requires simultaneously solving for the unknown amplitude and phase error γ and the unknown directions of arrival θ of the L signal sources. l Therefore, this invention uses the Alternating Minimization (AM) algorithm to iteratively solve the problem. After transforming the joint estimation problem of the signal direction of arrival and the array amplitude and phase error of the target model into a cost function minimization problem, the cost function is minimized to obtain the array amplitude and phase error. The radar echo signal is calibrated using the obtained array amplitude and phase error, and the signal direction of arrival estimation result is obtained and output based on the calibrated radar echo signal.

[0113] Since the amplitude and phase errors are caused by physical factors, the obtained array amplitude and phase errors are used to calibrate each radar echo signal received subsequently. Then, the signal direction of arrival (DOA) estimation result is obtained through the signal DOA solution method and output accordingly. The signal DOA solution method can be ARMA spectral analysis, maximum likelihood method, entropy spectral analysis method, eigenvalue decomposition method, etc., specifically the MUSIC algorithm, ESPRIT algorithm, WSF algorithm, etc.

[0114] Furthermore, the iterative solution of the minimization cost function problem according to the alternating minimum algorithm specifically includes:

[0115] The cost function is transformed, and the spatial spectrum function is derived based on the transformed cost function.

[0116] The Root-MUSIC algorithm is used to solve the spatial spectrum function to obtain the estimated signal angle of arrival.

[0117] Based on the obtained signal arrival angle estimate, the amplitude and phase error estimation problem is solved to obtain the array amplitude and phase error estimate.

[0118] Specifically, the cost function of formula (18) can be transformed into the form expressed by the following formula (20) after equivalent mathematical operations:

[0119]

[0120] Where T(θ) l )=diag{a(θl )} is a diagonal matrix composed of array guide vectors. Since the incident angle ζ of the signal reflected from the reconfigurable smart surface is precisely known, the cost function can be subdivided into two parts: one part consists of L signal sources with unknown arrival angles, and the other part consists of reconfigurable smart surface reflection signal sources with known arrival angles. Specifically, it can be expressed as formula (21):

[0121]

[0122] P1 and P2 are specifically shown in formulas (22) and (23):

[0123]

[0124]

[0125] From formulas (22) and (23), it can be seen that P1 represents the part with unknown arrival angles, and P2 represents the part with reflected signals. Since the angle ζ is precisely known, the arrival angle information to be estimated is contained in P1. Due to the existence of amplitude and phase errors in the array, it is impossible to estimate the precise arrival angle when the array amplitude and phase errors are unknown. Therefore, the estimated values ​​of the array amplitude and phase errors and the arrival signals are obtained through iterative solutions. Since the cost function in formula (20) is similar to the spatial function of the MUSIC algorithm, in this method, the unknown arrival angle can be obtained by peak search of a similar MUSIC spatial spectrum, and the corresponding spatial spectrum function is as follows:

[0126]

[0127] When high accuracy is required, peak search of the spectrum involves a significant computational burden. Therefore, to reduce computational complexity, we use the Root-MUSIC algorithm to solve for the spatial spectral function in this method. First, we define a polynomial as shown in equation (25):

[0128]

[0129] Where p(z) = [1, z, ..., z] M-1 ] T According to the above formula (25), when z = e jω When the roots of the polynomial lie on the unit circle, p(e) jω ) is represented as the steering vector at frequency ω. According to the subspace orthogonality theory mentioned above, p(e jω This is also the signal's steering vector, so the signal's angle of arrival θ can be estimated by selecting the L roots closest to the unit circle. lFor a uniform linear array, after obtaining z, the angle that needs to be estimated can be obtained through formula (26):

[0130]

[0131] Where arg{·} is the angle operation, This represents the angle estimated using formula (26). This indicates that for p(z) = [1, z, ..., z] M-1 ] T The specific value of z in the equation.

[0132] Based on the obtained signal arrival angle estimate, the amplitude and phase error estimation problem is solved to obtain the array amplitude and phase error estimate.

[0133] Furthermore, the step of iteratively solving the minimization cost function problem using the alternating minimum algorithm to obtain the array amplitude and phase error estimate specifically includes:

[0134] Based on the obtained signal arrival angle estimate, the amplitude and phase error estimation problem is transformed into an optimization problem with constraints.

[0135] The Lagrange multiplier method is used to solve the optimization problem with constraints, and the estimated values ​​of array amplitude and phase error are obtained.

[0136] Specifically, when the angle of arrival θ l After obtaining the value through estimation, θ is then... l With ζ and ζ already fixed, the problem of estimating the array amplitude and phase error can be simplified to formula (27):

[0137]

[0138] Where Φ = P1 + P2. Since the first element in the array has already been calibrated, a constraint w is added. H γ=1, w=[1,0,…,0] T To ensure that the amplitude and phase error of the first array is 1, the amplitude and phase error estimation problem can be transformed into an optimization problem represented by constraints, as shown in formula (28):

[0139]

[0140] To solve the problem in formula (28) above, we can use the Lagrange multiplier method, and the relevant Lagrange function is shown in formula (29) below:

[0141] L(γ, μ)=γ H Φγ+μ H (w H γ-1), (29)

[0142] μ is a Lagrange multiplier. The first derivative of equation (29) is obtained by differentiating it with respect to γ, and then set to zero, as shown in equation (30):

[0143] 2Φγ+wμ=0, (30)

[0144] The estimated value of the array amplitude and phase error vector can be obtained through formula (30), as shown in formula (31):

[0145]

[0146] Substituting formula (31) back into formula (28) yields the Lagrange multipliers. Substituting the Lagrange multipliers into formula (31), the unique solution for the array amplitude and phase error is obtained as shown in formula (32):

[0147]

[0148] Furthermore, the iterative solution of the minimization cost function problem according to the alternating minimum algorithm specifically includes:

[0149] The cost function is updated based on the obtained signal angle of arrival estimate and array amplitude and phase error estimate.

[0150] The signal arrival angle estimate and array amplitude and phase error estimate are re-solved based on the updated cost function;

[0151] The process iteratively updates the cost function, the estimated angle of arrival of the signal, and the estimated amplitude and phase error of the array. When the iteration termination condition is met, the iteration process ends, and the array amplitude and phase error obtained in the last iteration is used to calibrate the radar echo signal.

[0152] Specifically, the cost function is updated based on the obtained signal arrival angle estimate and array amplitude and phase error estimate. That is, the cost function of formula (18) is updated by the signal arrival angle estimate and array amplitude and phase error estimate. The updated cost function is used to resolve the functions in formula (26) and formula (32). The process of updating the cost function and solving the signal arrival angle estimate and array amplitude and phase error estimate is repeated until the cost function meets the iteration termination condition. When the iteration process ends, the array amplitude and phase error obtained in the last iteration is used to calibrate the radar echo signal.

[0153] The conditions for satisfying the iteration termination specifically include:

[0154] The iteration termination condition is met when the difference between the cost function obtained in the current iteration and the cost function obtained in the previous iteration is less than a predetermined threshold.

[0155] Specifically, in the iterative process of using the alternating minimization algorithm, under ideal conditions, the cost function... The cost function will equal zero when the estimated value obtained during the iteration is closer to the true value. It will definitely be more cost function value than the one obtained in the previous iteration. Small, that is Therefore, in this invention, after each iteration, the obtained array amplitude and phase error vector estimate is... Angle of arrival of the signal source Substituting into formula (18) yields the cost function value for the current iteration. When the cost function value of the current iteration is compared with that of the previous iteration Once the difference between the values ​​is less than a predetermined threshold, the solution is considered to have converged. Therefore, the result obtained from the last iteration is output as the desired array amplitude and phase error, and the radar echo signal is calibrated using the array amplitude and phase error. The predetermined threshold is set according to the actual situation.

[0156] The corresponding array amplitude and phase error is obtained through the above method. The obtained array amplitude and phase error can be used to calibrate each radar echo signal containing the array amplitude and phase error received by the array antenna. Specifically, the received signal is multiplied by the inverse of the array amplitude and phase error to obtain the radar echo signal with the error eliminated. The signal direction of arrival estimation result is obtained and output based on the calibrated radar echo signal. The process of obtaining the signal direction of arrival estimation result based on the calibrated radar echo signal and outputting it can be done using methods such as ARMA spectral analysis, maximum likelihood method, entropy spectral analysis method, and eigenvalue decomposition method. Specifically, it can be the MUSIC algorithm, ESPRIT algorithm, WSF algorithm, etc.

[0157] In another embodiment of the present invention, in the process of providing external information data to vehicles using advanced array signal processing technology, the array error calibration method based on reconfigurable intelligent surface assistance described in this invention can be used to calibrate the radar echo signal in the presence of array amplitude and phase errors, thereby obtaining an accurate direction of arrival. Specifically, the radar sends radar signals, and the radar echo signal is calibrated using the method described in this invention to obtain the angle information of nearby vehicles and objects, which can effectively avoid accidents and collisions, provide technical warnings of driving risks, and implement safety measures.

[0158] In other embodiments of the present invention, the WIFI router calibrates the received signal using the array error calibration method based on reconfigurable smart surface assisted by the present invention, and then calibrates the signal of the user's mobile phone or other devices during subsequent use to obtain the accurate angle and direction of these devices. Then, the direction of the transmitted WIFI signal is adjusted by the antenna beamforming technology to concentrate the power of the transmitted signal at the user's location, thereby providing the user with a better WIFI signal.

[0159] Furthermore, this invention performs corresponding performance statistics on the array error calibration method based on reconfigurable smart surfaces. Specifically, it calculates the root mean square errors (RMSE) of the array amplitude and phase error estimates under different signal-to-noise ratios and under different snapshot numbers to determine the performance of the method.

[0160] Wherein, the root mean square error of the amplitude error, RMSE ρ Defined as formula (33):

[0161]

[0162] in This is the array amplitude error estimate for the m-th antenna in the k-th run. K is the number of Monte Carlo runs.

[0163] Wherein, the root mean square error of the amplitude error, Defined as formula (34):

[0164]

[0165] in It is the array phase error estimate of the m-th antenna during the k-th run.

[0166] Furthermore, this invention considers a 16-element ULA (Unified Alignment Array), with two equal-power narrowband signals incident from 25.5° and 46.6°, and simultaneously, a reconfigurable smart surface with 8 elements exists in space, reflecting a signal incident from -42.5°. All signals and noise are extracted from independent and identically distributed complex Gaussian processes with zero-mean, and their variances are respectively... and Signal-to-noise ratio (SNR) is defined as follows: (dB). Without loss of generality, the array amplitude and phase errors are randomly generated by a uniform distribution, wherein the array amplitude error follows a uniform distribution ρ from 0.5 to 1. m~U[0.5, 1], the array phase error follows a uniform distribution from -π to π. In the simulation provided by this invention, we fix the number of snapshots to 500. Specifically... Figure 3 The spatial spectrum of the proposed method at SNR=15 is shown, with the spectral peak positions corresponding to the signal's angle of arrival. Figure 3 It can be seen that, due to the presence of array amplitude and phase errors, the MUSIC spectrum of the original received data has almost no obvious peaks at the signal's incident angle, and the spatial spectrum exhibits small fluctuations. However, after processing by the method proposed in this invention, the received data shows obvious peaks in the MUSIC spatial spectrum, and the peak positions are close to the signal's incident angle. Therefore, the method provided by this invention can effectively calibrate the amplitude and phase errors present in the antenna array and obtain accurate estimates of the signal-of-arrival (SOA) through the spatial spectrum.

[0167] The simulation results were statistically analyzed. With K=1000, the statistical performance of the array amplitude root mean square error under different signal-to-noise ratios was tested using the method provided in this invention. Figure 4 As shown in the figure. Simulation results demonstrate that, even with unknown array amplitude and phase errors, the proposed method achieves estimation accuracy close to the lower bound of the Cramer-Rao equation under varying SNR conditions. In particular, the method exhibits excellent performance when the signal-to-noise ratio is greater than 0 dB. Figure 5 The figure shows the statistical performance of the root mean square error (RMSE) of array amplitude estimation under different snapshot numbers after simulation of an embodiment of the present invention. The array phase error estimation is performed with the number of snapshots ranging from 50 to 1000, while the signal-to-noise ratio (SNR) is fixed at 15 dB. Simulation results show that, even with array amplitude and phase errors, the RMS error of the array amplitude error estimated by the method proposed in this invention can approach the lower bound of Cramer-Rao. The statistical graph of the RMS error of array phase under different SNR conditions using the method provided in this invention is shown below. Figure 6 As shown, from Figure 6 Simulation results show that the present invention can achieve an array phase error estimation accuracy close to the lower bound of Cramer-Rao when the signal-to-noise ratio is greater than 0 dB. Figure 7 As shown in the figure, the statistical performance diagram of the root mean square error of array phase estimation under different snapshot numbers is provided after simulation of the embodiment of the invention. The simulation results show that, under different snapshot numbers, the proposed method can achieve array phase error estimation accuracy close to the lower bound of Cramer-Rao at a signal-to-noise ratio (SNR) of 15 dB. Therefore, the algorithm provided by this invention is generally not sensitive to the number of snapshots; a few hundred snapshots are sufficient for the proposed algorithm to provide satisfactory estimation accuracy.

[0168] Furthermore, in military and civilian fields such as radar, sonar, communication, and medicine, the present invention uses the method described in this invention to process the corresponding signals, thereby obtaining the array amplitude and phase error estimation results. Through the array amplitude and phase error estimation results, calibrated signals can be obtained in military and civilian fields such as radar, sonar, communication, and medicine, thus obtaining the corresponding accurate signal source direction. This facilitates the process of obtaining accurate signal direction when using radar receiving signals with array amplitude and phase errors.

[0169] like Figure 8 As shown, a second aspect of the present invention provides an array error calibration device based on a reconfigurable smart surface, the array error calibration device based on a reconfigurable smart surface includes:

[0170] The model building module S81 receives radar echo signals containing array amplitude and phase errors obtained by the array antenna, and builds a target model based on the radar echo signals with the assistance of a reconfigurable smart surface.

[0171] Problem transformation module S82 introduces a cost function to transform the problem of joint estimation of signal direction of arrival and array amplitude and phase error of the target model into a problem of minimizing the cost function.

[0172] The output module S83 solves the minimum cost function problem iteratively according to the alternating minimum algorithm to obtain the array amplitude and phase error. The obtained array amplitude and phase error is used to calibrate the radar echo signal with array amplitude and phase error acquired by the array antenna each time. Based on the calibrated radar echo signal, the signal direction of arrival estimation result is obtained and output.

[0173] A third aspect of this application provides a computer-readable storage medium, characterized in that the computer-readable storage medium stores one or more programs, which can be executed by one or more processors to implement the steps in the array error calibration method based on reconfigurable smart surfaces as described above.

[0174] A fourth aspect of this application provides a terminal device, characterized in that it includes: a processor, a memory, and a communication bus; the memory stores a computer-readable program that can be executed by the processor;

[0175] The communication bus enables communication between the processor and the memory;

[0176] When the processor executes the computer-readable program, it implements the steps in the array error calibration method based on reconfigurable smart surface as described above.

[0177] In summary, this invention provides an array error calibration method and related equipment based on reconfigurable smart surfaces. The method includes receiving radar echo signals containing array amplitude and phase errors acquired by an array antenna; constructing a target model based on the radar echo signals using reconfigurable smart surfaces; introducing a cost function to transform the joint estimation problem of signal direction of arrival and array amplitude and phase errors of the target model into a cost function minimization problem; iteratively solving the cost function minimization problem according to the alternating minimum algorithm to obtain the array amplitude and phase errors; calibrating the radar echo signals using the obtained array amplitude and phase errors; and obtaining and outputting the signal direction of arrival estimation result based on the calibrated radar echo signals. Through the above method, this invention enables directional reflection of signal sources at unknown angles using a reconfigurable smart surface. The signal reflected by the reconfigurable smart surface can be considered a calibration source signal with a defined azimuth angle, thus achieving active calibration of antenna errors without the addition of an additional auxiliary calibration source. Furthermore, by using a cost function, the problem of jointly estimating the signal direction of arrival (DOA) and array amplitude and phase errors of the target model is transformed into a cost function minimization problem. The alternating minimum algorithm can then output accurate array amplitude and phase errors. The output array amplitude and phase errors are used to calibrate each input radar echo signal, and the DOA estimation result is obtained based on the calibrated radar echo signal. This allows the array amplitude and phase errors to be obtained even when array amplitude and phase errors exist, thus calibrating the input radar echo signal to a signal without array amplitude and phase errors. This enables the solution of the signal echo signal, achieving accurate DOA estimation. Therefore, the method described in this invention can be used in military and civilian fields such as radar, sonar, communication, and medicine to achieve better calibration results for array errors and obtain more accurate DOA estimation results from the signal.

[0178] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0179] 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 by this invention 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), direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and direct memory bus dynamic RAM (RDRAM).

[0180] It should be understood that the application of the present invention is not limited to the examples above. Those skilled in the art can make improvements or modifications based on the above description, and all such improvements and modifications fall within the protection scope of the appended claims.

Claims

1. A method for array error calibration based on reconfigurable smart surfaces, characterized in that, The method comprises: The radar echo signal containing array amplitude and phase error is obtained by the receiving array antenna. Based on the radar echo signal, a target model is constructed with the assistance of a reconfigurable smart surface. By introducing a cost function, the problem of jointly estimating the signal direction of arrival and the array amplitude and phase error of the target model is transformed into a problem of minimizing the cost function. The problem of minimizing the cost function is solved iteratively using the alternating minimum algorithm to obtain the array amplitude and phase error. The obtained array amplitude and phase error is used to calibrate the radar echo signal containing the array amplitude and phase error acquired by the array antenna each time. The signal direction of arrival estimation result is obtained and output based on the calibrated radar echo signal. The radar echo signal containing array amplitude and phase errors acquired by the receiving array antenna is used to construct a target model based on the radar echo signal through a reconfigurable smart surface, specifically including: The reconfigurable smart surface directionally reflects signals from unknown angle sources to obtain a calibration signal source with a determined azimuth angle.

2. The array error calibration method based on reconfigurable smart surface assistance according to claim 1, characterized in that, The introduction of a cost function transforms the problem of jointly estimating the signal direction of arrival (SAR) and array amplitude and phase errors of the target model into a problem of minimizing the cost function, specifically including: Model the array covariance matrix of the target model; Based on the array covariance matrix obtained from modeling, eigenvalue decomposition is performed to obtain the signal subspace and noise subspace; By leveraging the orthogonality of the obtained signal and noise subspaces and introducing a cost function, the problem of jointly estimating the signal direction of arrival and the array amplitude and phase error of the target model is transformed into a problem of minimizing the cost function.

3. The array error calibration method based on reconfigurable smart surface assistance according to claim 1, characterized in that, The iterative solution of the cost function problem using the alternating minimum algorithm specifically includes: The cost function is transformed, and the spatial spectrum function is derived based on the transformed cost function. The Root-MUSIC algorithm is used to solve the spatial spectrum function to obtain the estimated signal angle of arrival. Based on the obtained signal arrival angle estimate, the amplitude and phase error estimation problem is solved to obtain the array amplitude and phase error estimate.

4. The array error calibration method based on reconfigurable smart surface assistance according to claim 3, characterized in that, The step of iteratively solving the minimization cost function problem using the alternating minimum algorithm to obtain the array amplitude and phase error estimate specifically includes: Based on the obtained signal arrival angle estimate, the amplitude and phase error estimation problem is transformed into an optimization problem with constraints. The Lagrange multiplier method is used to solve the optimization problem with constraints, and the estimated values ​​of array amplitude and phase error are obtained.

5. The array error calibration method based on reconfigurable smart surface assistance according to claim 3, characterized in that, The iterative solution of the cost function problem using the alternating minimum algorithm specifically includes: The cost function is updated based on the obtained signal angle of arrival estimate and array amplitude and phase error estimate. The signal arrival angle estimate and array amplitude and phase error estimate are re-solved based on the updated cost function; The process iteratively updates the cost function, the estimated angle of arrival of the signal, and the estimated amplitude and phase error of the array. When the iteration termination condition is met, the iteration process ends, and the array amplitude and phase error obtained in the last iteration is used to calibrate the radar echo signal.

6. The array error calibration method based on reconfigurable smart surface assistance according to claim 5, characterized in that, The conditions for satisfying the iteration termination specifically include: The iteration termination condition is met when the difference between the cost function obtained in the current iteration and the cost function value of the previous iteration is less than a predetermined threshold.

7. An array error calibration device based on reconfigurable smart surface assistance, characterized in that, The device comprises: The model building module receives radar echo signals containing array amplitude and phase errors obtained by the array antenna, and builds a target model based on the radar echo signals using a reconfigurable smart surface. The problem transformation module introduces a cost function to transform the problem of jointly estimating the signal direction of arrival and the array amplitude and phase error of the target model into a problem of minimizing the cost function. The output module iteratively solves the minimum cost function problem according to the alternating minimum algorithm to obtain the array amplitude and phase error. The obtained array amplitude and phase error is used to calibrate the radar echo signal containing the array amplitude and phase error acquired by the array antenna each time. Based on the calibrated radar echo signal, the signal direction of arrival estimation result is obtained and output. The radar echo signal containing array amplitude and phase errors acquired by the receiving array antenna is used to construct a target model based on the radar echo signal through a reconfigurable smart surface, specifically including: The reconfigurable smart surface directionally reflects signals from unknown angle sources to obtain a calibration signal source with a determined azimuth angle.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores one or more programs, which can be executed by one or more processors to implement the steps in the array error calibration method based on reconfigurable smart surfaces as described in any one of claims 1-6.

9. A terminal device, characterized in that, include: Processor, memory, and communication bus; The memory stores a computer-readable program that can be executed by the processor; The communication bus enables communication between the processor and the memory; When the processor executes the computer-readable program, it implements the steps in the array error calibration method based on reconfigurable smart surface assistance as described in any one of claims 1-6.

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