Nested array antenna mutual coupling cancellation method and device based on mixed far and near field sources

Abstract

The application belongs to the technical field of array antenna signal processing, and particularly relates to a nested array antenna mutual coupling elimination method and device based on a mixed near-field and far-field source. e The method comprises the following steps: modeling array antenna receiving signals according to an unknown mutual coupling matrix, a near-field array flow pattern, a far-field array flow pattern, a near-field source, a far-field source and noise; constructing the unknown mutual coupling matrix C e from a unit matrix I and a mutual coupling parameter matrix C whose mutual coupling parameter is not 1; when the unknown mutual coupling exists, constructing a steering vector expression, and converting the steering vector into a form of a sum of two sub-matrices; constructing the mutual coupling parameter matrix C according to the steering vector, and then solving a DOA estimation value and a mutual coupling parameter estimation value through one-dimensional search on the DOA and the mutual coupling parameter; and compensating the unknown mutual coupling matrix C e by using the mutual coupling parameter estimation value to constitute an estimation value of the unknown mutual coupling matrix. The application estimates the mutual coupling parameter of the array antenna, thereby performing mutual coupling compensation, and realizing elimination of mutual coupling interference.

Description

Technical Field

[0001] This invention belongs to the field of array antenna signal processing technology, and specifically relates to a method and apparatus for canceling mutual coupling of nested array antennas based on hybrid far-field and near-field signal sources, applicable to nested array antennas designed based on hybrid far-field and near-field signal sources. Background Technology

[0002] In fifth-generation (5G) mobile communication, massive MIMO antennas are widely used. The distance from the target source to the antenna is considered infinite, and the wavefront of the signal can be approximated as a uniform plane wave. In this case, the source model is a far-field model, and for a one-dimensional antenna array, the position of the target source is determined by the azimuth angle. However, in the pre-researched sixth-generation (6G) mobile communication system, extremely large antenna arrays (ELAAs) have become a key technology, and the target source model is a near-field model. Unlike the far-field model, the distance from the source to the antenna array is too small, and the inherent curvature of the wavefront cannot be ignored; the wavefront is represented by a spherical wave. Therefore, the position parameter of the target source is determined by both the azimuth angle and the distance, adding important distance information. This is a unique characteristic of near-field or hybrid-field antenna arrays. Thus, far-field source localization is only a special form of near-field source localization. In practical engineering, hybrid-field source localization involves both near-field and far-field sources, making the study of hybrid-field systems of great practical significance.

[0003] Nested array antennas based on hybrid near-field and far-field signal sources employ a non-equidistant arrangement of elements with a unit element spacing of one-quarter wavelength of the incident signal. However, the small element spacing in the array antenna leads to a series of problems, such as severe mutual coupling leakage between some elements, resulting in reduced spatial resolution and significantly degraded parameter estimation performance. Therefore, developing corresponding methods to address the mutual coupling elimination problem in nested array antennas based on hybrid near-field and far-field signal sources is crucial. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention proposes a method and apparatus for eliminating mutual coupling of nested array antennas based on hybrid near-field and far-field signal sources. By estimating the mutual coupling parameters of the array antennas, mutual coupling compensation is performed to eliminate mutual coupling interference.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] This invention provides a method for canceling mutual coupling of nested array antennas based on hybrid near-field and far-field signal sources, comprising the following steps:

[0007] The received signal of the array antenna is modeled based on the unknown mutual coupling matrix, near-field array manifold, far-field array manifold, near-field signal source, far-field signal source, and noise.

[0008] The unknown cross-coupling matrix C is constructed by the identity matrix I and the cross-coupling parameter matrix C, where the cross-coupling parameter is not equal to 1. e ;

[0009] When unknown mutual coupling exists, construct the guide vector expression and transform the guide vector into the form of the sum of two submatrices;

[0010] Based on the steering vector, a cross-coupling parameter matrix C is constructed. Then, based on the orthogonality principle between the signal subspace and the noise subspace, the cross-coupling parameter estimation problem is transformed into a joint optimization problem of DOA and cross-coupling parameters. Finally, the DOA estimate is obtained by performing a one-dimensional search on DOA and cross-coupling parameters. and mutual coupling parameter estimates

[0011] Using mutual coupling parameter estimation Estimates of the unknown cross-coupling matrix For unknown mutual coupling matrix C e Compensation will be provided.

[0012] According to the nested array antenna mutual coupling cancellation method based on hybrid near-field and far-field signal sources of the present invention, preferably, the received signal of the array antenna is modeled, and the modeling expression is as shown in formula (1):

[0013] x(t)=C e A FF s FF (t)+C e A NF s NF (t)+n(t) (1)

[0014] In the formula, x(t) is the signal received by the array antenna, and C e A is an unknown mutually coupled matrix. NF It is a near-field array manifold, A FF It is a far-field array manifold, s NF (t) is a near-field source, s FF (t) is the far-field source, n(t) is noise, and t is time.

[0015] According to the nested array antenna mutual coupling cancellation method based on hybrid near-field and far-field signal sources of the present invention, preferably, the unknown mutual coupling matrix C e The expression is as shown in formula (2):

[0016]

[0017] In the formula, q is the total number of uniform linear subarray sensors, T is the total number of array sensors, I is the identity matrix, and C is the unknown mutual coupling matrix. e A matrix whose mutual coupling parameter is not 1.

[0018] According to the method for eliminating mutual coupling of nested array antennas based on hybrid near-field and far-field signal sources of the present invention, preferably, when unknown mutual coupling exists, the steering vector expression is as shown in formula (3):

[0019] a(θ,r,c)=C e a(θ,r)=Q[a(θ,r)]c (3)

[0020] In the formula, θ is the direction of arrival, denoted as DOA, r is the distance parameter, c is the mutual coupling parameter, and Q represents a new matrix containing only the steering vector [a(θ,r)] after separating the mutual coupling parameter c.

[0021] According to the nested array antenna mutual coupling cancellation method based on hybrid near-field and far-field signal sources of the present invention, preferably, let L be the degree of freedom of the mutual coupling parameter matrix C, and decompose the T×L matrix Q[a(θ,r)] in formula (3) into the form of the sum of two sub-matrices:

[0022] Q[a(θ,r)]=Q[a(θ,r)]1+Q[a(θ,r)]2 (4)

[0023] The submatrices Q[a(θ,r)]1 and Q[a(θ,r)]2 satisfy the following conditions, where f and g represent the number of rows and columns of the matrix, respectively:

[0024]

[0025]

[0026] According to the nested array antenna mutual coupling cancellation method based on hybrid near-field and far-field signal sources of the present invention, preferably, based on the principle of orthogonality between the signal subspace and the noise subspace, it is known that:

[0027]

[0028] In the formula, U N It is the noise subspace, [·] H It is the conjugate transpose of the matrix;

[0029] Substituting formulas (3) and (4) into formula (7), the mutual coupling parameter matrix C is expressed as:

[0030]

[0031] According to the nested array antenna mutual coupling cancellation method based on hybrid near-field and far-field signal sources of the present invention, preferably, the mutual coupling parameter estimation problem is transformed into a joint optimization problem of DOA and mutual coupling parameters based on the orthogonality principle of signal subspace and noise subspace, and the mathematical expression is as follows:

[0032]

[0033] In the formula, Let represent the DOA estimate and the cross-coupling parameter estimate, respectively. arg min f(x) represents the value of x when f(x) reaches its minimum. The DOA estimate is obtained by performing a one-dimensional search on the DOA and cross-coupling parameters. and mutual coupling parameter estimates

[0034]

[0035]

[0036] In the formula, det represents calculating the determinant of a matrix, arg max f(x) represents the value of x when f(x) reaches its maximum value, and e min This represents the operator for finding the eigenvector corresponding to the smallest eigenvalue of a matrix.

[0037] According to the present invention, the nested array antenna mutual coupling cancellation method based on hybrid near-field and far-field signal sources preferably utilizes the mutual coupling parameter estimate. Estimates of the unknown cross-coupling matrix For unknown mutual coupling matrix C e After compensation, the received signal of the array antenna after mutual coupling compensation is expressed as follows:

[0038]

[0039] The present invention also provides a nested array antenna mutual coupling cancellation device based on hybrid near-field and far-field signal sources, comprising:

[0040] The received signal modeling module is used to model the received signal of the array antenna based on the unknown mutual coupling matrix, near-field array manifold, far-field array manifold, near-field signal source, far-field signal source, and noise.

[0041] The unknown mutual coupling matrix construction module is used to construct an unknown mutual coupling matrix C from the identity matrix I and the mutual coupling parameter matrix C, where the mutual coupling parameter is not equal to 1. e ;

[0042] The steering vector module is used to construct a steering vector expression when unknown mutual coupling exists, and to transform the steering vector into the form of the sum of two submatrices;

[0043] The DOA and mutual coupling parameter estimation module is used to construct the mutual coupling parameter matrix C based on the steering vector. Then, based on the orthogonality principle of the signal subspace and noise subspace, the mutual coupling parameter estimation problem is transformed into a joint optimization problem of DOA and mutual coupling parameters. Finally, the DOA estimate is obtained by performing a one-dimensional search on DOA and mutual coupling parameters. and mutual coupling parameter estimates

[0044] The unknown cross-coupling matrix compensation module is used to utilize the estimated values ​​of the cross-coupling parameters. Estimates of the unknown cross-coupling matrix For unknown mutual coupling matrix C e Compensation will be provided.

[0045] Compared with the prior art, the present invention has the following advantages:

[0046] This invention presents a method for eliminating mutual coupling in nested array antennas based on hybrid near-field and far-field signal sources. Firstly, it estimates the mutual coupling parameters. Then, it uses these estimated parameters to construct an estimate of the unknown mutual coupling matrix, thereby compensating for the unknown mutual coupling matrix. This achieves mutual coupling compensation for the original array antenna, eliminating mutual coupling interference and enabling more accurate estimation of the direction of arrival (DOA). It also improves distance estimation, enhancing the performance of nested array antennas based on hybrid near-field and far-field signal sources in practical engineering applications while reducing hardware costs. Attached Figure Description

[0047] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0048] Figure 1 This is a flowchart illustrating the nested array antenna mutual coupling cancellation method based on hybrid near-field and far-field signal sources according to an embodiment of the present invention.

[0049] Figure 2 This is a comparison of the normalized spatial spectrum of DOA estimation before and after mutual coupling compensation of the array antenna in this embodiment of the invention.

[0050] Figure 3 This is a comparison diagram of the normalized spatial spectrum of distance estimation before and after mutual coupling compensation of the array antenna in an embodiment of the present invention;

[0051] Figure 4 These are the DOA estimation RMSE curves of different array antennas before and after mutual coupling compensation in this embodiment of the invention.

[0052] Figure 5 These are the distance estimation RMSE curves of different array antennas before and after mutual coupling compensation in an embodiment of the present invention. Detailed Implementation

[0053] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0054] like Figure 1 As shown, the nested array antenna mutual coupling cancellation method based on hybrid near-field and far-field signal sources in this embodiment includes the following steps:

[0055] Step S1: In the field of Direction of Arrival (DOA) estimation, Unknown Mutual Coupling (UMC) can significantly interfere with the positioning performance of array antennas. Although the sparsity of the nested array antenna structure based on hybrid near-field and far-field sources can reduce unknown mutual coupling to some extent, residual unknown mutual coupling still has a significant impact on positioning performance. The received signal of the array antenna is modeled based on the unknown mutual coupling matrix, near-field array manifold, far-field array manifold, near-field source, far-field source, and noise. The modeling expression is shown in Equation (1).

[0056] x(t)=C e A FF s FF (t)+C e A NF s NF (t)+n(t) (1)

[0057] In the formula, x(t) is the signal received by the array antenna, and C e A is an unknown mutually coupled matrix. NF It is a near-field array manifold, A FF It is a far-field array manifold, s NF (t) is a near-field source, s FF n(t) is the far-field source, n(t) is the noise, which is Gaussian white noise, and t is time.

[0058] Step S2: Construct the unknown mutual coupling matrix C using the identity matrix I and the mutual coupling parameter matrix C (where the mutual coupling parameter is not equal to 1). e Unknown mutual coupling matrix C e The expression is shown in formula (2).

[0059]

[0060] Since the nested array antenna based on hybrid near-field and far-field signal sources has a symmetrical structure and contains several uniform linear subarrays, let q be the total number of sensors in the uniform linear subarray, T be the total number of array sensors, I be the identity matrix, and C be the unknown mutual coupling matrix C e A matrix whose mutual coupling parameter is not 1.

[0061] Step S3: When unknown mutual coupling exists, construct the guide vector expression and transform the guide vector into the form of the sum of two submatrices.

[0062] When unknown mutual coupling exists, the expression for the steering vector is as shown in formula (3).

[0063] a(θ,r,c)=C e a(θ,r)=Q[a(θ,r)]c (3)

[0064] In the formula, θ is the direction of arrival (DOA), r is the distance parameter, c is the mutual coupling parameter, and Q represents a new matrix containing only the steering vector [a(θ,r)] after separating the mutual coupling parameter c.

[0065] Let L be the degrees of freedom of the mutual coupling parameter matrix C. The T×L matrix Q[a(θ,r)] in formula (3) can be split into the sum of two submatrices:

[0066] Q[a(θ,r)]=Q[a(θ,r)]1+Q[a(θ,r)]2 (4)

[0067] The submatrices Q[a(θ,r)]1 and Q[a(θ,r)]2 satisfy the following conditions, where f and g represent the number of rows and columns of the matrix, respectively:

[0068]

[0069]

[0070] Step S4: Construct the cross-coupling parameter matrix C based on the steering vector. Then, based on the orthogonality principle of the signal subspace and noise subspace, transform the cross-coupling parameter estimation problem into a joint optimization problem of DOA and cross-coupling parameters. Finally, solve for the DOA estimate by performing a one-dimensional search on DOA and cross-coupling parameters. and mutual coupling parameter estimates

[0071] Specifically, based on the principle that the signal subspace and the noise subspace are orthogonal, we know that:

[0072]

[0073] In the formula, U N It is the noise subspace, [·] H It is the conjugate transpose of a matrix.

[0074] Substituting formulas (3) and (4) into formula (7), the mutual coupling parameter matrix C is expressed as:

[0075]

[0076] Based on the principle of orthogonality between the signal subspace and the noise subspace, the problem of estimating the mutual coupling parameters is transformed into a joint optimization problem of DOA and mutual coupling parameters, as expressed mathematically below:

[0077]

[0078] In the formula, Let represent the DOA estimate and the cross-coupling parameter estimate, respectively. arg min f(x) represents the value of x when f(x) reaches its minimum. Then, a one-dimensional search is performed on the DOA and cross-coupling parameters to solve for the DOA estimate. and mutual coupling parameter estimates

[0079]

[0080]

[0081] In the formula, det represents calculating the determinant of a matrix, arg max f(x) represents the value of x when f(x) reaches its maximum value, and e min This represents the operator for finding the eigenvector corresponding to the smallest eigenvalue of a matrix.

[0082] Step S5, using the estimated values ​​of the mutual coupling parameters Estimates of the unknown cross-coupling matrix For unknown mutual coupling matrix C e Compensation will be provided.

[0083] Specifically, firstly, the estimated values ​​of the mutual coupling parameters obtained in step S4 are used. The estimated values ​​of the mutual coupling parameter matrix are used to construct the estimated values ​​of the unknown mutual coupling matrix according to formula (2). Thus, the unknown mutual coupling matrix C is compensated. e This achieves the purpose of eliminating mutual coupling interference. After mutual coupling compensation, the expression for the received signal of the array antenna is as follows:

[0084]

[0085] Corresponding to the above-described method for canceling mutual coupling of nested array antennas based on hybrid near-field and far-field signal sources, this embodiment also provides a device for canceling mutual coupling of nested array antennas based on hybrid near-field and far-field signal sources, comprising:

[0086] The received signal modeling module is used to model the received signal of the array antenna based on the unknown mutual coupling matrix, near-field array manifold, far-field array manifold, near-field signal source, far-field signal source, and noise.

[0087] The unknown mutual coupling matrix construction module is used to construct an unknown mutual coupling matrix C from the identity matrix I and the mutual coupling parameter matrix C, where the mutual coupling parameter is not equal to 1. e .

[0088] The Guided Vector module is used to construct a guided vector expression when unknown mutual coupling exists, and to transform the guided vector into the form of the sum of two submatrices.

[0089] The DOA and mutual coupling parameter estimation module is used to construct the mutual coupling parameter matrix C based on the steering vector. Then, based on the orthogonality principle of the signal subspace and noise subspace, the mutual coupling parameter estimation problem is transformed into a joint optimization problem of DOA and mutual coupling parameters. Finally, the DOA estimate is obtained by performing a one-dimensional search on DOA and mutual coupling parameters. and mutual coupling parameter estimates

[0090] The unknown cross-coupling matrix compensation module is used to utilize the estimated values ​​of the cross-coupling parameters. Estimates of the unknown cross-coupling matrix For unknown mutual coupling matrix C e Compensation will be provided.

[0091] The effectiveness of the proposed method in improving DOA and distance estimation performance is verified through experiments below.

[0092] Example 2

[0093] Considering a symmetrical nested array antenna (SNA) with 9 antennas, the spatial smoothing MUSIC method is used to distinguish the angle and distance parameters of mixed-field sources. A set of mixed-field sources is set up, one of which is a near-field (NF) source (10°, 10λ) and the other is a far-field (FF) source (30°, +∞). The experimental conditions are as follows: signal-to-noise ratio SNR = 15dB, number of snapshots O = 2000, and number of Monte Carlo experiments Y = 1. Figure 2 This is a comparison of the normalized spatial spectrum for DOA estimation. In the figure, NF represents the near-field source, FF represents the far-field source, "without parameter offsetting" represents the result without mutual coupling compensation, and "with parameter offsetting" represents the result with mutual coupling compensation. The vertical dashed line represents the actual value. The SNA array antenna can successfully distinguish the same DOA between near-field and far-field sources. From... Figure 2As can be seen, the DOA estimation accuracy without mutual coupling compensation is lower than that with mutual coupling compensation. This is because the mutual coupling parameters introduce corresponding errors when solving for DOA. Figure 3 For the normalized spatial spectrum comparison map of distance estimation, based on the pairing relationship between DOA and distance, distance and angle can be automatically paired, and near-field and far-field sources can be successfully distinguished. Similarly, from Figure 3 As can be seen, the distance estimation accuracy without mutual coupling compensation is lower than that with mutual coupling compensation.

[0094] To verify the universality of the proposed method, experiments were conducted using four types of array antennas to demonstrate that the proposed method can effectively improve the DOA and range estimation performance of array antennas. The sample array antennas selected were four classic mixed-field nested array antennas: Symmetrical Nested Array (SNA), Symmetrical Double Nested Array (SDNA), Symmetrical Double Coprime Array (SDCA), and Symmetrical Enhanced Nested Array (ESNA).

[0095] This invention uses pure near-field signal sources and mixed-field signal sources to verify the change in the root mean square error (RMSE) of the estimated value of the array antenna under the condition of increasing signal-to-noise ratio (SNR).

[0096] Suppose the mathematical expression for the input signal's SNR is as follows:

[0097]

[0098] in, This represents the power of the k-th source. This represents noise power. Assuming all sources have equal power and all array elements have similar noise power, then... s k (t) and n i (t) represents the complex Gaussian white noise of the k-th source and the array, respectively.

[0099] RMSE is used as an evaluation metric for array antenna performance, and its mathematical expression is as follows:

[0100]

[0101] Where Υ represents the Monte Carlo simulation number, and D represents the number of target information sources. and α k (m) represents the parameter estimate and the actual parameter value of the k-th source in the m-th Monte Carlo experiment, respectively.

[0102] Figure 4 and Figure 5The RMSE variation trends of DOA and range estimation for four types of nested array antennas after mutual coupling compensation are presented respectively. By comparison, it can be proved that for existing classic mixed-field nested array antennas, the method proposed in this invention can improve the accuracy of DOA and range parameter estimation by performing mutual coupling compensation.

[0103] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of the present invention can be implemented using various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0104] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0105] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0106] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0107] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0108] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for canceling mutual coupling of nested array antennas based on hybrid near-field and far-field signal sources, characterized in that, Includes the following steps: Step 1: Model the received signal of the array antenna based on the unknown mutual coupling matrix, near-field array manifold, far-field array manifold, near-field signal source, far-field signal source, and noise. The modeling expression is shown in formula (1): x(t)=C e A FF s FF (t)+C e A NF s NF (t)+n(t) (1) In the formula, x(t) is the signal received by the array antenna, and C e A is an unknown mutually coupled matrix. NF It is a near-field array manifold, A FF It is a far-field array manifold, s NF (t) is a near-field source, s FF (t) is the far-field source, n(t) is noise, and t is time; Step 2: Construct the unknown cross-coupling matrix C using the identity matrix I and the cross-coupling parameter matrix C (where the cross-coupling parameter is not equal to 1). e ; Step 3: When unknown mutual coupling exists, construct the steering vector expression as shown in formula (3), and transform the steering vector into the form of the sum of two sub-matrices: a(θ,r,c)=C e a(θ,r)=Q[a(θ,r)]c(3) In the formula, θ is the direction of arrival, denoted as DOA, r is the range parameter, c is the mutual coupling parameter, and Q represents the new matrix containing only the steering vector [a(θ,r)] after separating the mutual coupling parameter c; Step 4: Construct the cross-coupling parameter matrix C based on the steering vector. Then, based on the orthogonality principle of the signal subspace and noise subspace, transform the cross-coupling parameter estimation problem into a joint optimization problem of DOA and cross-coupling parameters. Finally, solve for the DOA estimate by performing a one-dimensional search on DOA and cross-coupling parameters. and mutual coupling parameter estimates Specifically, it includes: Based on the principle that the signal subspace and the noise subspace are orthogonal, we know that: In the formula, U N It is the noise subspace, [·] H It is the conjugate transpose of the matrix; Substituting formulas (3) and (4) into formula (7), the mutual coupling parameter matrix C is expressed as: Based on the principle of orthogonality between the signal subspace and the noise subspace, the problem of estimating the mutual coupling parameters is transformed into a joint optimization problem of DOA and mutual coupling parameters, as expressed mathematically below: In the formula, Let represent the DOA estimate and the cross-coupling parameter estimate, respectively. arg min f(x) represents the value of x when f(x) reaches its minimum. The DOA estimate is obtained by performing a one-dimensional search on the DOA and cross-coupling parameters. and mutual coupling parameter estimates In the formula, det represents calculating the determinant of a matrix, arg max f(x) represents the value of x when f(x) reaches its maximum value, and e min This represents the operator for finding the eigenvector corresponding to the smallest eigenvalue of a matrix; Step 5: Use the estimated values ​​of the mutual coupling parameters Estimates of the unknown cross-coupling matrix For unknown mutual coupling matrix C e Compensation will be provided.

2. The method for canceling mutual coupling of nested array antennas based on hybrid near-field and far-field signal sources according to claim 1, characterized in that, Unknown mutual coupling matrix C e The expression is as shown in formula (2): In the formula, q is the total number of uniform linear subarray sensors, T is the total number of array sensors, I is the identity matrix, and C is the unknown mutual coupling matrix. e A matrix whose mutual coupling parameter is not 1.

3. The method for canceling mutual coupling of nested array antennas based on hybrid near-field and far-field signal sources according to claim 2, characterized in that, Let L be the degrees of freedom of the mutual coupling parameter matrix C. The T×L matrix Q[a(θ,r)] in formula (3) can be split into the sum of two submatrices: Q[a(θ,r)]=Q[a(θ,r)]1+Q[a(θ,r)]2(4) The submatrices Q[a(θ,r)]1 and Q[a(θ,r)]2 satisfy the following conditions, where f and g represent the number of rows and columns of the matrix, respectively:

4. The method for canceling mutual coupling of nested array antennas based on hybrid near-field and far-field signal sources according to claim 3, characterized in that, Using mutual coupling parameter estimation Estimates of the unknown cross-coupling matrix For unknown mutual coupling matrix C e After compensation, the received signal of the array antenna after mutual coupling compensation is expressed as follows:

5. A nested array antenna mutual coupling cancellation device based on hybrid near-field and far-field signal sources, characterized in that, For implementing the nested array antenna mutual coupling cancellation method based on hybrid near-field and far-field signal sources as described in claim 1, the apparatus comprises: The received signal modeling module is used to model the received signal of the array antenna based on the unknown mutual coupling matrix, near-field array manifold, far-field array manifold, near-field signal source, far-field signal source, and noise. The unknown mutual coupling matrix construction module is used to construct an unknown mutual coupling matrix C from the identity matrix I and the mutual coupling parameter matrix C, where the mutual coupling parameter is not equal to 1. e ; The steering vector module is used to construct a steering vector expression when unknown mutual coupling exists, and to transform the steering vector into the form of the sum of two submatrices; The DOA and mutual coupling parameter estimation module is used to construct the mutual coupling parameter matrix C based on the steering vector. Then, based on the orthogonality principle of the signal subspace and noise subspace, the mutual coupling parameter estimation problem is transformed into a joint optimization problem of DOA and mutual coupling parameters. Finally, the DOA estimate is obtained by performing a one-dimensional search on DOA and mutual coupling parameters. and mutual coupling parameter estimates The unknown cross-coupling matrix compensation module is used to utilize the estimated values ​​of the cross-coupling parameters. Estimates of the unknown cross-coupling matrix For unknown mutual coupling matrix C e Compensation will be provided.

Images