A design method of a new symmetric sparse array based on hybrid far and near field

Abstract

The application relates to a novel symmetric sparse array design method based on mixed far and near fields, which comprises the following steps: establishing a DOA estimation model under mixed far and near field sources; constructing a specific fourth-order cumulant matrix by using a received signal to eliminate a distance parameter, and designing an extended sparse array model with a symmetric structure; vectorizing and straightening a fourth-order cumulant matrix and removing a redundant term to obtain a column vector; performing angle estimation of multiple targets by using a sparse reconstruction algorithm; combining estimated angle information to construct a fourth-order cumulant matrix containing a distance parameter, respectively solving distances of the targets, and distinguishing far and near field signals. The application can realize the distinction of mixed field signals, high-resolution estimation of the direction angle and distance of multiple targets, greatly improves the array degree of freedom and virtual aperture, and improves the estimation performance and stability.

Description

Technical Field

[0001] This invention belongs to the field of signal processing and relates to a symmetric sparse array design method, specifically a symmetric sparse array design method for multi-target estimation under mixed near-field and far-field conditions. Background Technology

[0002] Array signal processing is an important branch of signal processing, with applications spanning numerous military and economic sectors, including communications, sonar, seismology, radar, exploration, radio astronomy, and biomedical engineering. Compared to traditional single antennas, array signal processing offers advantages such as high signal gain, high spatial resolution, and strong anti-interference capabilities. The degrees of freedom of traditional uniform linear arrays are limited by the number of array elements; traditional DOA methods can only estimate the direction of arrival (DOA) of one fewer element than the number of array elements.

[0003] Currently, most research focuses on DOA estimation for far-field signal sources. Because of the large distance between the far-field source and the array, it can be considered a plane wave when incident on the receiving antenna array. However, when the source is located in the Fresnel region of the near field, the received wavefront is no longer a plane wave, requiring the simultaneous use of the incident angle and distance to estimate the source. In practical applications, near-field and far-field sources may coexist; however, research on parameter estimation for mixed-field signals is limited, and many problems remain to be solved.

[0004] Compared to traditional uniform linear arrays, sparse arrays offer higher degrees of freedom and array aperture, improving estimation accuracy and the number of estimable targets. In recent years, coprime arrays and nested arrays have been two typical types of sparse arrays, leading to the development of many improved sparse arrays. However, these array types are not suitable for mixed-field models. Therefore, some scholars have proposed symmetric arrays and directly extended nested arrays to stacked sparse arrays, but this is not the optimal array design. Thus, designing a symmetric sparse array with a maximum fourth-order difference virtual matrix has become a worthy research problem. Summary of the Invention

[0005] Technical problems to be solved

[0006] To address the problems of DOA and range estimation for targets with multiple degrees of freedom (DOA) under mixed near-field and far-field conditions, and to improve estimation accuracy and resolution by expanding the array's DOA and virtual array aperture, this invention proposes a method for estimating signal source parameters using an extended sparse array with symmetric characteristics under mixed-field signal conditions. In cases where multiple mixed signals coexist, this method significantly improves the number of signal sources that can be estimated, the near-field and far-field discrimination capabilities, and the estimation resolution.

[0007] Technical solution

[0008] A novel design method for symmetric sparse arrays based on hybrid near and far fields, characterized by the following steps:

[0009] Step 1: Establish a DOA estimation model for mixed far-field and near-field sources;

[0010] Step 2: Construct a specific fourth-order cumulant matrix using the received signal to eliminate the distance parameter and design an extended sparse array model with a symmetric structure;

[0011] Step 3: Vectorize and straighten the fourth-order cumulant matrix and remove redundant terms to obtain the column vector;

[0012] Step 4: Use the sparse reconstruction algorithm to estimate the angles of multiple targets;

[0013] Step 5: Combine the estimated angle information to construct a fourth-order cumulant matrix containing the distance parameter, calculate the distance to each target, and distinguish between near and far field signals.

[0014] A further technical solution of the present invention: The process of establishing the DOA estimation model under the hybrid far-field and near-field information sources described in step 1 is as follows:

[0015] For a symmetric sparse linear array with 2N+1 elements, assume there are K narrowband and uncorrelated desired signals in space: k M A near-field source and Kk M For a far-field source, the received signal model of a symmetric sparse linear array can be expressed as:

[0016] x(t)=A N s N (t)+A F s F (t)+n(t)

[0017] in and Let represent the array manifolds for near-field and far-field signals, respectively, and have and s N (t) and s F (t) represents the received signal envelope, and n(t) represents the existing Gaussian white noise.

[0018] A further technical solution of the present invention: In step 2, a specific fourth-order cumulant matrix is ​​constructed using the received signal as follows:

[0019]

[0020] in To eliminate the influence of the distance term, we define m = -n; ρ = -q, therefore, we can obtain [(p m -p n)-(p ρ -p q )]ω k ≠0; The above fourth-order cumulant matrix can be expressed as:

[0021]

[0022] in c FOC,k This represents the kurtosis of the k-th source; therefore, a set of virtual arrays is constructed using the difference set.

[0023] Based on the special characteristics of mixed fields, a symmetric extended sparse array, called an extended symmetric nested array, is designed to achieve greater freedom. The element spacing in the array is an integer multiple of 1 / 4 wavelength, and the number of elements is assumed to be Q = 2(M + N + p) - 1, where M, N, and p are all positive integers. This array consists of three subarrays, and the specific arrangement of the subarrays is as follows:

[0024]

[0025]

[0026]

[0027] Where i1∈[0,M], i2∈[1,N-1] and i3∈[0,p-1]; after calculation, this array can obtain a maximum of 4p(M+N+1)+4N(M+1)-7 virtual array elements.

[0028] A further technical solution of the present invention: In step 3, the fourth-order cumulant matrix is ​​vectorized, straightened, and redundant terms are removed to obtain the column vector, according to the above expression. We can obtain:

[0029]

[0030] in Therefore, after straightening matrix C, we can obtain the column vector:

[0031] r z =vec(C)=(B * ⊙B)p

[0032] Where p = [c FOC,1 ,c FOC,2 ,...,c FOC,K ] T By removing duplicate elements from the column vector and rearranging them, we can obtain a column vector containing the full virtual array, which can be used for subsequent DOA estimation.

[0033] A further technical solution of the present invention: In step 4, a sparse reconstruction algorithm is used to estimate the angles of multiple targets, which is implemented using the LASSO algorithm.

[0034]

[0035] Where ε is the small error term, the objective cost function in the above equation can also be expressed as:

[0036]

[0037] Where h is the regularization parameter, used to balance the l1 and l2 norms. It is a complete dictionary.

[0038] A further technical solution of the present invention: In step 5, combining the estimated angle information, a fourth-order cumulant matrix containing distance parameters is constructed, and the distances to each target are calculated to distinguish between near and far field signals.

[0039]

[0040] C′ differs from C in that it does not have specific restrictions, thus including both the DOA and the distance parameter. Following step 4, the calculated DOA is substituted into the equation, and then only the unknown distance parameter is estimated, which can be specifically expressed as:

[0041]

[0042] U noise It is the noise subspace after the eigendecomposition of matrix C′. If the calculated incident signal distance is located in the Fresnel zone, then the signal is a near-field source signal.

[0043] A computer system is characterized by comprising: one or more processors, and a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method described above.

[0044] A computer-readable storage medium is characterized by storing computer-executable instructions, which, when executed, are used to implement the above-described method.

[0045] Beneficial effects

[0046] This invention provides a novel symmetric sparse array design method based on mixed near-field and far-field signals. Considering the presence of mixed near-field and far-field signals, it utilizes a designed high-degree-of-freedom symmetric extended sparse array to achieve a method for estimating underdetermined targets with super-degrees-of-freedom capabilities. This invention can distinguish mixed-field signals and provide high-resolution estimation of the arrival direction angle and range of multiple targets, significantly improving the array's degrees of freedom and virtual aperture, thereby enhancing estimation performance and stability. Attached Figure Description

[0047] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0048] Figure 1 This is a schematic diagram illustrating the principle of the method of the present invention;

[0049] Figure 2 A schematic diagram of the symmetrical sparse array structure designed for this invention;

[0050] Figure 3 A schematic diagram of the virtual array elements generated by the symmetric sparse array designed in this invention;

[0051] Figure 4 This is the DOA estimation result of the present invention;

[0052] Figure 5 This is the distance estimation result of the present invention;

[0053] Figure 6 This is a schematic diagram illustrating the relationship between the root mean square error (RMSE) and signal-to-noise ratio (SNR) of the DOA estimation in this invention.

[0054] Figure 7 This is a schematic diagram illustrating the relationship between the root mean square error of distance estimation and the signal-to-noise ratio in this invention. Detailed Implementation

[0055] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0056] To address the problem that super-resolution algorithms cannot effectively distinguish or estimate parameters when the number of signal sources to be estimated is much greater than the number of array elements under mixed near-field and far-field signal conditions, this embodiment provides a technique for signal source estimation and source differentiation using a newly designed symmetric extended sparse array under mixed far-field and near-field conditions. Figure 1 As shown, the specific processes include the following:

[0057] Step 1: First, construct a DOA estimation model for mixed far-field and near-field sources. Assume there are K narrowband uncorrelated sources in space, including k... N One is the near-field signal and Kk N If there are 1 far-field signal, then the signal received by the i-th array element can be represented as:

[0058]

[0059] According to the second-order Taylor expansion, the time delay can be expressed as: And ω k = -2πdsin(θ) k ) / λ and φ k =πd 2 cos 2 (θ k ) / (λr k When the signal is in the far-field condition, r k →∞. Therefore, the received signal model can be further expressed as:

[0060]

[0061] The receiving model of the entire array can then be represented as:

[0062] x(t)=A N s N (t)+A F s F (t)+n(t)

[0063] Step 2: Fourth-order cumulants can provide more degrees of freedom for arrays and are widely used in sparse array design. The expression for fourth-order cumulants is given first:

[0064]

[0065] in To eliminate the influence of the distance term, we define m = -n; ρ = -q, therefore, we can obtain [(p m -p n )-(p ρ -p q )]ω k ≠0; A specific fourth-order cumulant matrix can be represented as:

[0066]

[0067] in c FOC,k This represents the kurtosis of the k-th source. Therefore, a set of virtual arrays is constructed using the difference set.

[0068] Subsequently, considering the unique characteristics of mixed fields, an ESNA array structure with greater flexibility was designed. The element spacing in the array is an integer multiple of 1 / 4 wavelength, and the number of elements is assumed to be Q = 2(M + N + p) - 1, where M, N, and p are all positive integers. This array consists of three subarrays, the specific structure of which is as follows... Figure 2 As shown, the specific positions of the array elements can be represented as follows:

[0069]

[0070] The elements of each subarray can be represented as follows:

[0071]

[0072]

[0073]

[0074] Where i1∈[0,M], i2∈[1,N-1] and i3∈[0,p-1].

[0075] Figure 3 The diagram shows the structure of a virtual array formed by the non-negative half-axis when the number of array elements is 13. Due to symmetry, only a portion needs to be depicted. In the diagram, we compare it with several other typical sparse arrays; our designed array offers more degrees of freedom. The specific derivation is as follows.

[0076] The virtual array elements of this formation can be represented as:

[0077]

[0078] We then reorganized the formation into two parts: the positive half-axis and the negative half-axis. and therefore and The sets of differences are the same:

[0079]

[0080] In addition, due to Any array element in can be regarded as Therefore, the difference set of two submatrices can be represented as:

[0081]

[0082] Using the two equations above, the fully virtual array element of this formation can be represented as:

[0083]

[0084] Calculations show that this formation can obtain a maximum of 4p(M+N+1)+4N(M+1)-7 virtual array elements, which is also an absolute degree of freedom.

[0085] Step 3: Next, the fourth-order cumulant matrix is ​​vectorized, straightened, and redundant terms are removed to obtain the column vector.

[0086] According to the above expression We can obtain:

[0087]

[0088] in Therefore, after straightening matrix C, we can obtain the column vector:

[0089] r z =vec(C)=(B * ⊙B)p

[0090] Where p = [c FOC,1 ,c FOC ,2,...,c FOC,K ] T By removing duplicate elements from the column vector and rearranging them, we can obtain a column vector containing the full virtual array, which can be used for subsequent DOA estimation.

[0091] Step 4: Perform DOA estimation for mixed sources using a sparse reconstruction algorithm. We will use the LASSO algorithm to implement this.

[0092]

[0093] Where ε is the small error term, the objective cost function in the above equation can also be expressed as:

[0094]

[0095] Where h is the regularization parameter, used to balance the l1 and l2 norms. It uses a complete dictionary. h = 0.6 is selected using the L-curve.

[0096] Figure 4 A simulation example of DOA estimation is given, using a 13-element array. It is assumed that there are two far-field signals and two near-field signals in space: {θ1=-30°, r1=40λ}, {θ1=-10°, r1=+∞}, {θ1=10°, r1=60λ}, and {θ1=30°, r1=+∞}. As can be seen from the figure, the DOA of four signals can be effectively estimated with high accuracy.

[0097] Step 5: Construct another fourth-order cumulant matrix, substitute it into the obtained DOA, solve for the distance term information, and distinguish between far-field and near-field signals.

[0098]

[0099] Unlike C, it does not have specific restrictions, therefore it includes both DOA and distance parameters. According to step 4, the calculated DOA is substituted into it, and then only the unknown distance is estimated.

[0100]

[0101] Figure 5 A simulation example for distance estimation is given, still using a 13-element array. It is assumed that there are two far-field and two near-field signals in space, with parameters identical to those in step 4. Figure 5 As can be seen, the distance between the four signals can be effectively estimated with high accuracy.

[0102] Figure 6 and Figure 7 The RMSE curves of DOA and distance as a function of signal-to-noise ratio are presented, showing that the designed array can achieve better performance.

[0103] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the scope of the technology disclosed in the present invention, and such modifications or substitutions should all be covered within the scope of protection of the present invention.

Claims

1. A novel design method for symmetric sparse arrays based on hybrid near and far fields, characterized in that... The steps are as follows: Step 1: Establish a DOA estimation model for mixed far-field and near-field sources; including: For 2 A symmetric sparse linear array with +1 elements, assuming there are K narrowband and uncorrelated desired signals in space: A near-field source and For a far-field source, the received signal model of a symmetric sparse linear array can be expressed as: in and Let represent the array manifolds for near-field and far-field signals, respectively, and have and , and This represents the received signal envelope. This indicates the presence of Gaussian white noise; Step 2: Construct a specific fourth-order cumulant matrix using the received signal to eliminate the distance parameter, and design an extended sparse array model with a symmetric structure; including: in To eliminate the influence of the distance term, define Therefore, we can obtain The aforementioned fourth-order cumulant matrix can be expressed as: in , , This represents the kurtosis of the k-th source; therefore, a set of virtual arrays is constructed using the difference set. ; Based on the special properties of mixed fields, a symmetric extended sparse array, called an extended symmetric nested array, is designed to achieve greater freedom. The element spacing in the array is an integer multiple of 1 / 4 wavelength, and the number of elements is assumed to be... Q =2( M+N+ p )-1, where M, N, p All values ​​are positive integers; this formation consists of three sub-formations, and the specific arrangement of the sub-formations is as follows: in Calculations show that this formation can achieve the most... One virtual array element; Step 3: Vectorize and straighten the fourth-order cumulant matrix and remove redundant terms to obtain the column vector; according to the above expression We can obtain: in Therefore, straighten the matrix Then, the column vector can be obtained: in By removing duplicate elements from the column vector and rearranging them, we can obtain a column vector containing the entire virtual array, which can be used for subsequent DOA estimation. Step 4: Perform angle estimation for multiple targets using a sparse reconstruction algorithm; implement this using the LASSO algorithm: in Since it is a small error term, the objective cost function in the above equation can also be expressed as: in h It is a regularization parameter used for balancing and Norm, It is a complete dictionary; Step 5: Combining the estimated angle information, construct a fourth-order cumulant matrix containing the distance parameter, and calculate the distance to each target to distinguish between near and far field signals; specifically: and Unlike other parameters, it does not have specific limitations, therefore it includes both DOA and distance parameters; according to step 4, the calculated DOA is substituted in, and then only the unknown distance parameters are estimated, which can be specifically expressed as: in It is a matrix The noise subspace after eigenvalue decomposition If the calculated incident signal distance is located in the Fresnel zone, then the signal is a near-field source signal.

2. A computer system, characterized in that... include: One or more processors, a computer-readable storage medium for storing one or more programs, wherein, when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method of claim 1.

3. A computer-readable storage medium, characterized in that... The device stores computer-executable instructions, which, when executed, are used to implement the method of claim 1.

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