CN113779795A - Array design method and device - Google Patents

Array design method and device Download PDF

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CN113779795A
CN113779795A CN202111068436.0A CN202111068436A CN113779795A CN 113779795 A CN113779795 A CN 113779795A CN 202111068436 A CN202111068436 A CN 202111068436A CN 113779795 A CN113779795 A CN 113779795A
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郝程鹏
黎子皓
闫晟
朱东升
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Abstract

The embodiment of the application discloses an array design method and a device, wherein the method comprises the following steps: sampling a first beam transmitted by the uniform linear array to obtain first beam data; l of the second beam data0Converting the atomic norm into the rank of the Toeplitz matrix, wherein the second beam data is the beam data of a second beam to be transmitted by the designed array on each sampling point; determining a Toeplitz matrix with the minimum rank according to the rank of the Toeplitz matrix, wherein the Toeplitz matrix with the minimum rank is represented by using an atom so as to further determine the number of array elements of the designed array; determining the frequency and the weight of atoms according to the Toeplitz matrix with the minimum rank; and determining the array element position and excitation of the designed array according to the frequency and/or weight of the atoms and a preset mapping relation. The technical scheme overcomes the problem of grid mismatching of the traditional compressed sensing algorithm and the problem that the traditional compressed sensing algorithm seriously depends on grid intervals corresponding to the discrete dictionary, improves the designed array,i.e. sparsity of the target array.

Description

Array design method and device
Technical Field
The invention relates to the technical field of communication. And more particularly to an array design method and apparatus.
Background
In recent years, antennas and transducers have become common electronic components in the fields of communications, detection, and the like. In order to enhance the information transmission effect, a plurality of same elements can be arranged according to a certain rule to form an array and work according to a specified feeding mode. Such arrays have been widely used in radar, sonar and satellite communication systems.
The uniform linear arrays with the array element spacing of half wavelength are researched by many scholars due to simple arrangement modes, for example, the radiation pattern with different shapes is designed by calculating the array element excitation of the uniform linear arrays. In practical engineering, in order to improve the angular resolution of the uniform linear array and reduce the width of the main lobe, the aperture of the array needs to be enlarged. However, for large aperture arrays, more array elements are required to be filled and arranged, thereby increasing the cost and maintenance difficulty of the system. In order to reduce the cost of array systems and the complexity of the devices, the optimal design of the array has attracted much attention, i.e., relatively few antenna elements are used to achieve the same array performance while keeping the array size almost unchanged. For this reason, arrays were designed using dynamic programming algorithms, but due to early computer performance limitations, the designed arrays did not perform well.
Disclosure of Invention
The application provides an array design method and device, which can solve the problems that the traditional compressed sensing algorithm seriously depends on grid intervals corresponding to a discrete dictionary and the algorithm has grid mismatch.
In a first aspect, the present application provides an array design method, including:
sampling a first beam transmitted by the uniform linear array to obtain first beam data;
l of the second beam data0Converting the atomic norm into a rank of a Toeplitz matrix, wherein the rank of the Toeplitz matrix is used for representing the number of array elements of the designed array, the second beam data is beam data of a second beam to be transmitted by the designed array on each sampling point, and an error between the second beam data and the first beam data is smaller than an error threshold;
determining a Toeplitz matrix with the minimum rank by a weighted atomic norm minimization method according to the rank of the Toeplitz matrix, wherein the Toeplitz matrix with the minimum rank is represented by using atoms, and the atoms are represented by using basis vectors of the designed array;
determining the array element number of the designed array according to the Toeplitz matrix with the minimum rank;
determining the frequency and the weight of the atom by using a rotation invariant propagation operator method according to the Toeplitz matrix with the minimum rank;
and determining the array element position and excitation of the designed array according to the frequency and/or weight of the atoms and a preset mapping relation.
In one possible implementation, the rank of the toeplitz matrix is represented using a logarithmic penalty function;
the determining the Toeplitz matrix with the minimum rank by a weighted atomic norm minimization method according to the rank of the Toeplitz matrix comprises the following steps of:
converting the rank of the Topritz matrix into a first function, wherein the first function is an iterative optimization form of a weighted mesh-free compressed sensing algorithm;
and determining that the last iteration result of the first function is the Toeplitz matrix with the minimum rank by a weighted atomic norm minimization method.
In one possible implementation, the determining the number of array elements of the designed array according to the topeliz matrix with the minimum rank includes:
performing characteristic decomposition on the Topritz matrix with the minimum rank to obtain a first diagonal matrix;
and determining the number of array elements of the designed array according to the energy ratio of the diagonal elements of the first diagonal matrix.
In one possible implementation, the determining the frequencies and weights of the atoms using a rotation invariant propagation operator method according to the topliez matrix with the smallest rank comprises:
determining the frequency of the atoms according to the Topritz matrix with the minimum rank;
determining a first matrix according to the frequency of the atom and the atom, wherein the first matrix and the second beam data have a linear relation;
determining a weight of the atom from the first matrix and the second beam data.
In one possible implementation, the preset mapping relationship includes: the first mapping relation and/or the second mapping relation;
determining array element positions and excitations of the designed array according to the frequencies and/or weights of the atoms and a preset mapping relation, wherein the method comprises the following steps:
determining the array element position of the designed array according to the frequency of the atom and the first mapping relation, wherein the first mapping relation is the corresponding relation between the array element position of the designed array and the frequency of the atom;
and determining the excitation of the designed array according to the frequency, the weight and the second mapping relation of the atoms, wherein the second mapping relation is the corresponding relation between the array element position of the designed array and the frequency and the weight of the atoms.
In a second aspect, the present application provides an array design apparatus, comprising:
the acquisition unit is used for sampling a first beam transmitted by the uniform linear array to acquire first beam data;
a conversion unit for converting the second beam data0Converting the atomic norm into a rank of a Toeplitz matrix, wherein the rank of the Toeplitz matrix is used for representing the number of array elements of the designed array, the second beam data is beam data of a second beam to be transmitted by the designed array on each sampling point, and an error between the second beam data and the first beam data is smaller than an error threshold;
a determining unit, configured to determine, according to the rank of the toeplitz matrix, a toeplitz matrix with a minimum rank by a weighted atomic norm minimization method, where the toeplitz matrix with the minimum rank is represented by using atoms, and the atoms are represented by using basis vectors of the designed array;
the determining unit is configured to determine the number of array elements of the designed array according to the topelitz matrix with the minimum rank;
the determining unit is used for determining the frequency and the weight of the atom by using a rotation invariant propagation operator method according to the Toeplitz matrix with the minimum rank;
and the determining unit is used for determining the array element position and excitation of the designed array according to the frequency and/or weight of the atoms and a preset mapping relation.
In a third aspect, the present application also proposes an array design apparatus comprising at least one processor configured to execute a program stored in a memory, which when executed, causes the apparatus to perform the steps as in the first aspect and the various possible implementations.
In a fourth aspect, the present application also proposes a non-transitory computer-readable storage medium having stored thereon a computer program which, when executed by a processor, implements the steps as in the first aspect and the various possible implementations.
According to the technical scheme, the weighted grid compressive Sensing (RGCS) algorithm is introduced, the grid mismatch problem of the traditional compressive Sensing algorithm and the problem that the traditional compressive Sensing algorithm depends on the grid interval corresponding to the discrete dictionary seriously are solved, and the sparsity of the designed array, namely the target array, is improved.
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In order to more clearly illustrate the technical solutions in the embodiments or one possible implementation of the present application, the drawings needed to be used in the embodiments or one possible implementation will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present application, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
Fig. 1 is a schematic flowchart of an array design method according to an embodiment of the present disclosure;
fig. 2 is a schematic diagram illustrating a comparison between an RGCS, a Bayes Compressed Sensing (BCS), and a cosecant beam synthesized based on Compressed Sensing (CS) and a cosecant beam transmitted by a uniform linear array provided in an embodiment of the present application;
fig. 3 is a schematic diagram illustrating a comparison between a flat-top beam synthesized by RGCS, BCS, and CS and a flat-top beam transmitted by a uniform linear array according to an embodiment of the present application;
fig. 4 is a schematic structural diagram of an array design apparatus according to an embodiment of the present disclosure.
Detailed Description
The technical solutions in the embodiments of the present application will be described below with reference to the drawings in the embodiments of the present application. The following examples are only for illustrating the technical solutions of the present application more clearly, and the protection scope of the present application is not limited thereby.
It should be noted that the term "and/or" in this application is only one kind of association relationship describing the associated object, and means that three relationships may exist, for example, a and/or B may mean: a exists alone, A and B exist simultaneously, and B exists alone. The terms "first" and "second," and the like, in the description and in the claims of the embodiments of the present application are used for distinguishing between different objects and not for describing a particular order of the objects. For example, the first mapping relation, the second mapping relation, and the like are used for distinguishing different mapping relations, and are not used for describing a specific order of the target objects. In the embodiments of the present application, words such as "exemplary," "for example," or "such as" are used to mean serving as examples, illustrations, or illustrations. Any embodiment or design described herein as "exemplary," "for example," or "such as" is not necessarily to be construed as advantageous over other embodiments or designs. Rather, use of the word "exemplary" or "such as" is intended to present concepts related in a concrete fashion. In the description of the embodiments of the present application, the meaning of "a plurality" means two or more unless otherwise specified.
In one possible implementation, the design algorithm for the array may solve for array element positions and excitations from an optimized perspective representation, i.e. under the constraint that the matching error of the radiation beams emitted by the array is sufficiently low. Based on the angle, an array design method based on Compressed Sensing (CS) and Bayesian Compressed Sensing (BCS) is provided, and the effectiveness of the algorithm is verified.
Although CS and BCS can be used to design arrays, such algorithms suffer from lattice mismatch, i.e., a discrete dictionary is required to be constructed and the array element position and excitation of the array are solved through the discrete dictionary. However, the mesh spacing of the discrete dictionary directly affects the algorithm effect. If the grid interval of the discrete dictionary is larger, the array element position has larger error; if the grid spacing is small, the correlation between column vectors of the discrete dictionary is increased, so that the finite equidistant nature of the algorithm is disabled and the sparsest solution cannot be obtained. Therefore, the arrays designed by the algorithms such as CS and BCS are not the arrays with the highest sparse rate.
In view of the foregoing problems, an embodiment of the present application provides an array design method. Fig. 1 shows a schematic flowchart of an array design method proposed in an embodiment of the present application. The flow diagram comprises S101-S106, the problem that the traditional compressed sensing algorithm seriously depends on the grid distance corresponding to the discrete dictionary and the problem that the algorithm has grid mismatch are solved, and the sparsity of the designed array is improved.
A detailed description of an array design method as shown in fig. 1 provided in the embodiments of the present application is provided below.
In one possible implementation, the array design method provided by the embodiment of the present application is implemented by the following steps:
s101, sampling a first beam transmitted by the uniform linear array to obtain first beam data.
In the embodiment of the application, in a possible implementation, for a uniform linear array with an array aperture of L and an array element number of M, and whose excitation of the array elements is determined, the beams generated by the uniform linear array are sampled, and first beam data on each sampling point is obtained. The first beam data is represented using atoms under a mesh-free compressive sensing framework, where the atoms are represented using basis vectors of the designed array, thereby defining a first mapping between array element positions of the designed array and frequencies of the atoms and a second mapping between excitations of the designed array and frequencies and weights of the atoms.
In one specific example, first, assume that the array element position vector of the uniform linear array is [ d ]1，d2，...，dM]The ith array element position is di(i-1) × λ/2, λ being the wavelength. For the uniform linear array, the excitation vector of the array element is [ w1，w2，...，wM]2J-1 first beam data are sampled for the first beam generated by the uniform linear array, i.e.
Figure BDA0003259253350000041
Wherein the sampling interval Δ needs to satisfy Δ ∈ (0, 1/(J-1)), then the first beam data at the corresponding sampling point is
Figure BDA0003259253350000042
Where k is 2 pi/λ, the wave number is expressed. For subsequent use
Figure BDA0003259253350000043
Refers to 2J-1 first beam data
Figure BDA0003259253350000044
Second, a first mapping between array element positions of the designed array and the frequencies of the atoms and a second mapping between excitations of the designed array and the frequencies and weights of the atoms are established.
Specifically, an atom with a frequency f and a phase phi is defined as
a(f,φ)＝ei2πφ[1,ei2πf,...,ei2π(n-1)f]T (3)
Then for a frequency range f e 0, 1]The phase range is phi ∈ [0, 2 pi ]]All atoms of (a) may constitute the original subset a ═ { a (f, Φ): f is belonged to 0, 1]，φ∈[0，2π]}. For the 2J-1 first waves in the formula (2)Bundle data, assuming the designed array uses K array elements (K)<M) the same first beam data can be transmitted
Figure BDA0003259253350000045
Namely, it is
Figure BDA0003259253350000046
The array element position of the designed array can be obtained from the formula (4)
Figure BDA0003259253350000047
Frequency with atoms
Figure BDA0003259253350000048
First mapping relation and excitation between
Figure BDA0003259253350000049
Frequency with atoms
Figure BDA00032592533500000410
And weight
Figure BDA00032592533500000411
The second mapping relationship between the following:
Figure BDA00032592533500000412
the relation between the array element positions and the atoms of the designed array established by the formula (4) is based on the directional diagram data of the beams generated by the whole uniform linear array, so that the framework can design symmetrical pencil beams and asymmetrical shaped beams. And the traditional matrix beam algorithm cannot design a designed array for transmitting an asymmetric shaped beam, so that the non-grid compressed sensing algorithm has a wider application range.
The above is a detailed description of establishing the preset mapping relationship (i.e. formula (5)), where the preset mapping relationship includes the first mapping relationship and/or the second mapping relationship. The first mapping relation is the corresponding relation between the array element position of the designed array and the frequency of the atoms; the second mapping relation is the corresponding relation between the array element positions of the designed array and the frequencies and weights of the atoms.
Next, in this embodiment of the present application, since the second beam transmitted by the designed array is not necessarily completely equal to the first beam transmitted by the uniform linear array, the second beam data at each sampling point can be obtained by sampling the second beam transmitted by the designed array. Representing the second beam data as a variable
Figure BDA0003259253350000051
And also conforms to the linear relationship with atoms as expressed by equation (4). Then transmitting a second beam as equal as possible to the first beam using as few array elements as possible may be denoted as
Figure BDA0003259253350000052
Wherein η represents an error threshold between the second beam data and the first beam data, an error between the second beam data and the first beam data is smaller than the error threshold, min represents a minimum of the objective function, s.t. represents a constraint condition,
Figure BDA0003259253350000053
represents l0Atomic norm, i.e. objective function, expressed as
Figure BDA0003259253350000055
S102, converting the second beam data to l0The atomic norm is converted to the rank of the Toeplitz matrix.
It should be noted that, in the embodiment of the present application, the rank of the toeplitz matrix is used to characterize the number of array elements of the designed array. This step converts the second beam data to0Atomic norm conversion toThe rank of the Topritz matrix, i.e., equation (6) is equivalent to
Figure BDA0003259253350000058
Where tr denotes the trace of the matrix. However, the objective function of equation (6)
Figure BDA0003259253350000059
That is, rank (t (u)) in equation (8) is non-convex and NP (non-deterministic polymeric) is difficult to solve, so that the conventional optimization algorithm cannot directly solve equation (6). Wherein rank (T (u)) is the rank of the Toeplitz matrix.
S103, determining the Toeplitz matrix with the minimum rank by a weighted atomic norm minimization method according to the rank of the Toeplitz matrix.
In the embodiment of the present application, the atomic norm after convex relaxation is considered
Figure BDA00032592533500000510
The method can also play a role in reducing the number of array elements, but the sparsity of the array elements is limited so that the optimization cannot achieve the optimal effect and the sparsity cannot achieve the effect, so that the optimization problem of the formula (6) is converted into the optimization problem of a weighted non-grid compressive sensing algorithm for solving, and the limitation of the sparsity of the atomic norm can be broken through.
Introducing a logarithmic penalty function to approximate the effect of equation (8), i.e.
Figure BDA00032592533500000511
However, the objective function of equation (9) is a concave function, which cannot be solved directly by convex optimization, so equation (9) can be converted into an iteratively optimized form of a weighted mesh-free compressive sensing algorithm, i.e., the first function, by a maximum Minimization (maximization) algorithm. And determining that the last iteration result of the first function is the Toeplitz matrix with the minimum rank by a weighted atomic norm minimization method. Specifically, the weighted non-grid compressed sensing algorithm is an iterative optimization method, an optimal solution is obtained after iteration is terminated, each iteration is in a semi-definite programming form, and the solution can be carried out by means of a convex optimization algorithm. It can be converted into a form of iterative optimization, e.g. the optimization problem for the jth iteration is expressed as
Figure BDA0003259253350000061
Wherein W is (T (u)j-1)+∈I)-1Representing the weight coefficient, I representing the identity matrix, e being taken to approximate l0The function of the atomic norm, when ∈ → 0, the objective function of equation (9) is equivalent to l0And (3) setting an atomic norm, so that a smaller epsilon is set to improve the performance of a result solved by the formula (8), namely the sparsity of the designed array is improved. The CVX programming package is typically used to solve for the variables u, t,
Figure BDA0003259253350000064
in addition, the iteration end condition is set to
Figure BDA0003259253350000065
Wherein the content of the first and second substances,
Figure BDA0003259253350000066
and representing the j-th second beam data, wherein the sigma serves as an iteration termination parameter. After the iteration is terminated, the last result is the optimal Topritz matrix
Figure BDA0003259253350000067
The representation, i.e. the Toeplitz matrix with the smallest rank.
And S104, determining the array element number of the designed array according to the Toeplitz matrix with the minimum rank.
In the embodiment of the present application, the number of atoms, that is, the number K of array elements of the designed array, is first estimated, and the rank is first minimizedToplitz matrices
Figure BDA0003259253350000068
Can be obtained by characteristic decomposition
Figure BDA0003259253350000069
Where Λ is a diagonal matrix, referred to herein as a first diagonal matrix, the number of elements K can be estimated by the energy ratio of the diagonal elements of the first diagonal matrix, i.e., satisfying the following equation
Figure BDA00032592533500000610
The value of K can be regarded as
Figure BDA00032592533500000611
I.e. the number of frequencies, wherein J has the same meaning as J in equation (1). In the embodiment of the present application, setting δ to 0.99 may accurately estimate the value of the number K of array elements.
And S105, determining the frequency and the weight of the atom by using a rotation invariant propagation operator method according to the Toeplitz matrix with the minimum rank.
In the embodiment of the present application,
Figure BDA00032592533500000612
can be viewed as a covariance matrix and the frequency of K atoms can be solved by Van der Mongolian decomposition
Figure BDA00032592533500000613
The technical scheme uses a rotation invariant propagation operator method to solve the frequency vector by constructing a rotation invariant structure
Figure BDA00032592533500000614
Followed by estimation
Figure BDA00032592533500000615
The process of (1).
Firstly, the following components are mixed
Figure BDA00032592533500000616
Divided into two sub-matrices
Figure BDA00032592533500000617
Wherein the content of the first and second substances,
Figure BDA00032592533500000618
and is
Figure BDA00032592533500000619
Further having a structure P of
Figure BDA00032592533500000620
Wherein I denotes a K-dimensional unit matrix,
Figure BDA00032592533500000621
represents the pseudo-inverse operator, (-)HRepresenting a conjugate transpose operation. There is a rotation invariant property between the sub-matrices of P, so that the frequency of an atom can be quickly estimated, which can be expressed as
Figure BDA0003259253350000071
Wherein the content of the first and second substances,
Figure BDA0003259253350000072
and
Figure BDA0003259253350000073
p is the matrix with the first and last rows deleted, respectively, and P isaAnd PbThere is a rotation invariant property in between. A. the1Is a non-singular square matrix, thus passing through the pairs
Figure BDA0003259253350000074
The diagonal matrix phi can be obtained by matrix decomposition, where phi is related to the frequency of the atoms
Figure BDA0003259253350000075
There is a linear relationship between:
Figure BDA0003259253350000076
in the embodiment of the application, the frequency vector is estimated through
Figure BDA0003259253350000077
And the atom construction matrix A in equation (3), referred to herein as the first matrix, i.e.
Figure BDA0003259253350000078
The frequency can be further used
Figure BDA0003259253350000079
Matrix A formed by corresponding atoms and second beam data
Figure BDA00032592533500000710
Estimating weights of atoms
Figure BDA00032592533500000711
The following were used:
Figure BDA00032592533500000712
wherein the content of the first and second substances,
Figure BDA00032592533500000713
a vector of the weights is represented, which is formed,
Figure BDA00032592533500000714
and S106, determining the array element position and excitation of the designed array according to the frequency and/or weight of the atoms and a preset mapping relation.
At the frequency of the obtained atoms
Figure BDA00032592533500000715
And weight
Figure BDA00032592533500000716
Then, the position vector of the array element corresponding to the designed array can be converted according to the formula (5)
Figure BDA00032592533500000717
And excitation
Figure BDA00032592533500000718
This completes the design of the array.
It should be noted that, in order to verify the advantages of the weighted mesh-free compressed sensing algorithm, the cosecant beam and the flat-top beam are taken as the second beam, and the matching error and the sparsity rate are used as the evaluation criteria of the algorithm. The matching error is used for measuring the precision of a radiation directional diagram of the second array, the sparse rate is used for measuring the magnitude of the reduced array element number of the designed array compared with the uniform linear array, the two indexes are respectively represented by xi and alpha, and the formula is as follows
Figure BDA00032592533500000719
In the expression of the sparsity rate alpha, M represents the number of array elements of the uniform linear array, and K represents the number of array elements required by the designed array. In the expression for the match error ξ,
Figure BDA00032592533500000720
which represents the first beam of the beam or beams,
Figure BDA00032592533500000721
representing the second beam.
For different design algorithms, the larger alpha corresponding to the designed array is better, which represents that the array is reduced by more array elements compared with a uniform linear array, and the smaller xi is, the better is, the second wave beam representing the designed array is close to the first wave beam, and the larger performance is not lost on a directional diagram. However, these two parameters tend to exhibit an inverse relationship. In order to compare the performance of the algorithms reasonably, the sparsity of the designed arrays is compared on the premise of controlling the matching error of each algorithm to be in the same order of magnitude in two possible implementations.
In a first possible implementation, a Cosecant beam (Cosecant beam) generated by a uniform line array of 16 elements is selected as the first beam. For the algorithm of RGCS, initialize ∈ ═ 1e-2And 25 second beam data are used as the input of the RGCS algorithm, and the simulation experiment result shows that the cosecant beam can be synthesized only by using 12 array elements, the matching error is 3.25 multiplied by 10-4. For comparison, CS, BCS were used to design a designed array of identical cosecant beams. BCS needs 22 array elements to synthesize error in 10 order of magnitude-4The BCS cannot function to reduce the array elements. CS requires 15 array elements to design the matching error in the order of 10-4The designed array of (1). Therefore, the RGCS algorithm has obvious advantages in designing the designed array of the cosecant beam, and the designed array with high matching precision can be obtained by using the minimum array element number. The cosecant beams corresponding to the arrays of each algorithm design are shown in fig. 2. It is obvious from fig. 2 that the matching accuracy of the RGCS algorithm is higher in the main lobe or side lobe region than that of the other algorithms. The abscissa x, i.e. cos θ, is [0.001,0.844 ]]And in the time, the corresponding graph is a main lobe, and the graphs corresponding to the horizontal coordinates in the rest ranges are side lobes. The parameters of the array for each algorithm design are shown in table 1. It can be seen that the RGCS algorithm has obvious advantages in both matching precision and sparsity.
TABLE 1
Figure BDA0003259253350000081
In a second possible implementation, a Flat-topped beam (Flat-topped beam) generated by a uniform line of 16 elements is also used as the first beam. For RGAlgorithm of CS, we initialize ∈ ═ 1e-1And 21 wave beam data are used as the input of the algorithm, experiments show that the flat-top wave beam with higher precision can be synthesized only by using 13 array elements, and the matching error is 2.81 multiplied by 10-5. For comparison, CS, BCS are used to design sparse arrays of identical beams. The BCS needs 38 array elements to synthesize the error with the order of magnitude of 10-5Flat-top beam. The CS needs 16 array elements to synthesize the error with the order of magnitude of 10-5The flat-top beam of (2) does not play a role in reducing the number of array elements as does the BCS. The flat-top beam corresponding to the sparse array designed by each algorithm is shown in fig. 3. It is obvious from fig. 3 that the matching accuracy of the RGCS algorithm is higher in the main lobe or side lobe region than that of the remaining algorithms. The abscissa x, i.e. cos θ, is [ -0.594, 0.563)]And in the time, the corresponding graph is a main lobe, and the graphs corresponding to the abscissas in the rest ranges are side lobes. The sparse array parameters for each algorithm design are shown in table 1. It can be seen that the RGCS algorithm has obvious advantages in both matching precision and sparsity.
Based on the same concept as the method embodiment described above, the present application provides an array design apparatus 400. Fig. 4 is a schematic structural diagram of an array design apparatus 400 according to an embodiment of the present application, which is used for implementing the method described in the foregoing method embodiment. In a possible implementation, the array design apparatus may include a module or a unit corresponding to one or more of the methods/operations/steps/actions performed in the foregoing method embodiments, and the unit may be a hardware circuit, a software circuit, or a combination of a hardware circuit and a software circuit. In one possible implementation, the apparatus includes:
an obtaining unit 401, configured to sample a first beam transmitted by the uniform linear array, so as to obtain first beam data;
a conversion unit 402 for converting l of the second beam data0The atomic norm is converted into the rank of the Toeplitz matrix, the rank of the Toeplitz matrix is used for representing the array element number of the designed array, the second beam data is the beam data of a second beam to be transmitted by the designed array on each sampling point, and the error between the second beam data and the first beam data is smallAt an error threshold;
a determining unit 403, configured to determine, according to the rank of the toeplitz matrix, a toeplitz matrix with a smallest rank by a weighted atomic norm minimization method, where the toeplitz matrix with the smallest rank is represented by an atom and the atom is represented by a basis vector of the designed array;
the determining unit 403 is configured to determine the number of array elements of the designed array according to the topelitz matrix with the minimum rank;
the determining unit 403 is configured to determine, according to the topeliz matrix with the minimum rank, the frequency and the weight of the atom by using a rotation invariant propagation operator method;
the determining unit 403 is configured to determine the array element position and excitation of the designed array according to the frequency and/or weight of the atom and a preset mapping relationship.
An embodiment of the present application provides an array design apparatus, including at least one processor configured to execute a program stored in a memory, and when the program is executed, cause the apparatus to perform:
sampling a first beam transmitted by the uniform linear array to obtain first beam data;
l of the second beam data0Converting the atomic norm into a rank of a Toeplitz matrix, wherein the rank of the Toeplitz matrix is used for representing the number of array elements of the designed array, the second beam data is beam data of a second beam to be transmitted by the designed array on each sampling point, and an error between the second beam data and the first beam data is smaller than an error threshold;
determining a Toeplitz matrix with the minimum rank by a weighted atomic norm minimization method according to the rank of the Toeplitz matrix, wherein the Toeplitz matrix with the minimum rank is represented by using atoms, and the atoms are represented by using basis vectors of the designed array;
determining the array element number of the designed array according to the Toeplitz matrix with the minimum rank;
determining the frequency and the weight of the atom by using a rotation invariant propagation operator method according to the Toeplitz matrix with the minimum rank;
and determining the array element position and excitation of the designed array according to the frequency and/or weight of the atoms and a preset mapping relation.
An embodiment of the application provides a non-transitory computer readable storage medium, on which a computer program is stored, the computer program, when executed by a processor, implementing the steps of:
sampling a first beam transmitted by the uniform linear array to obtain first beam data;
l of the second beam data0Converting the atomic norm into a rank of a Toeplitz matrix, wherein the rank of the Toeplitz matrix is used for representing the number of array elements of the designed array, the second beam data is beam data of a second beam to be transmitted by the designed array on each sampling point, and an error between the second beam data and the first beam data is smaller than an error threshold;
determining a Toeplitz matrix with the minimum rank by a weighted atomic norm minimization method according to the rank of the Toeplitz matrix, wherein the Toeplitz matrix with the minimum rank is represented by using atoms, and the atoms are represented by using basis vectors of the designed array;
determining the array element number of the designed array according to the Toeplitz matrix with the minimum rank;
determining the frequency and the weight of the atom by using a rotation invariant propagation operator method according to the Toeplitz matrix with the minimum rank;
and determining the array element position and excitation of the designed array according to the frequency and/or weight of the atoms and a preset mapping relation.
The above-described embodiments of the apparatus are merely illustrative, and the units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of the present embodiment. One of ordinary skill in the art can understand and implement it without inventive effort.
Through the above description of the embodiments, those skilled in the art will clearly understand that each embodiment can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware. With this understanding in mind, the above-described technical solutions may be embodied in the form of a software product, which can be stored in a computer-readable storage medium such as ROM/RAM, magnetic disk, optical disk, etc., and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the methods described in the embodiments or some parts of the embodiments.
It should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, and not to limit the same; although the present application has been described in detail with reference to the foregoing embodiments, it should be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions in the embodiments of the present application.

Claims (8)

1. An array design method, comprising:
sampling a first beam transmitted by the uniform linear array to obtain first beam data;
l of the second beam data0Converting the atomic norm into a rank of a Toeplitz matrix, wherein the rank of the Toeplitz matrix is used for representing the number of array elements of the designed array, the second beam data is beam data of a second beam to be transmitted by the designed array on each sampling point, and an error between the second beam data and the first beam data is smaller than an error threshold;
determining a Toeplitz matrix with the minimum rank by a weighted atomic norm minimization method according to the rank of the Toeplitz matrix, wherein the Toeplitz matrix with the minimum rank is represented by using atoms, and the atoms are represented by using basis vectors of the designed array;
determining the array element number of the designed array according to the Toeplitz matrix with the minimum rank;
determining the frequency and the weight of the atom by using a rotation invariant propagation operator method according to the Toeplitz matrix with the minimum rank;
and determining the array element position and excitation of the designed array according to the frequency and/or weight of the atoms and a preset mapping relation.
2. The method according to claim 1, characterized in that the rank of the Topritz matrix is expressed using a logarithmic penalty function;
the determining the Toeplitz matrix with the minimum rank by a weighted atomic norm minimization method according to the rank of the Toeplitz matrix comprises the following steps of:
converting the rank of the Topritz matrix into a first function, wherein the first function is an iterative optimization form of a weighted mesh-free compressed sensing algorithm;
and determining that the last iteration result of the first function is the Toeplitz matrix with the minimum rank by a weighted atomic norm minimization method.
3. The method of claim 1, wherein determining the number of elements of the designed array according to the Toeplitz matrix with the minimum rank comprises:
performing characteristic decomposition on the Topritz matrix with the minimum rank to obtain a first diagonal matrix;
and determining the number of array elements of the designed array according to the energy ratio of the diagonal elements of the first diagonal matrix.
4. The method of claim 1, wherein determining the frequencies and weights of the atoms using a rotation invariant propagation operator method according to the Toplitz matrix with the minimum rank comprises:
determining the frequency of the atoms according to the Topritz matrix with the minimum rank;
determining a first matrix according to the frequency of the atom and the atom, wherein the first matrix and the second beam data have a linear relation;
determining a weight of the atom from the first matrix and the second beam data.
5. The method of claim 4,
the preset mapping relationship comprises: the first mapping relation and/or the second mapping relation;
determining array element positions and excitations of the designed array according to the frequencies and/or weights of the atoms and a preset mapping relation, wherein the method comprises the following steps:
determining the array element position of the designed array according to the frequency of the atom and the first mapping relation, wherein the first mapping relation is the corresponding relation between the array element position of the designed array and the frequency of the atom;
and determining the excitation of the designed array according to the frequency, the weight and the second mapping relation of the atoms, wherein the second mapping relation is the corresponding relation between the array element position of the designed array and the frequency and the weight of the atoms.
6. An array design apparatus, comprising:
the acquisition unit is used for sampling a first beam transmitted by the uniform linear array to acquire first beam data;
a conversion unit for converting the second beam data0Converting the atomic norm into a rank of a Toeplitz matrix, wherein the rank of the Toeplitz matrix is used for representing the number of array elements of the designed array, the second beam data is beam data of a second beam to be transmitted by the designed array on each sampling point, and an error between the second beam data and the first beam data is smaller than an error threshold;
a determining unit, configured to determine, according to the rank of the toeplitz matrix, a toeplitz matrix with a minimum rank by a weighted atomic norm minimization method, where the toeplitz matrix with the minimum rank is represented by using atoms, and the atoms are represented by using basis vectors of the designed array;
the determining unit is configured to determine the number of array elements of the designed array according to the topelitz matrix with the minimum rank;
the determining unit is used for determining the frequency and the weight of the atom by using a rotation invariant propagation operator method according to the Toeplitz matrix with the minimum rank;
and the determining unit is used for determining the array element position and excitation of the designed array according to the frequency and/or weight of the atoms and a preset mapping relation.
7. An array design apparatus comprising at least one processor configured to execute a program stored in a memory, the program when executed causing the apparatus to perform:
the method of any one of claims 1-5.
8. A non-transitory computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out the method according to any one of claims 1-5.
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Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2016204451A1 (en) * 2015-06-16 2016-12-22 포항공과대학교 산학협력단 Method and apparatus for beamforming
CN107402380A (en) * 2017-05-12 2017-11-28 电子科技大学 A kind of quick self-adapted alternative manner for realizing Doppler beam sharpened imaging
CN110045323A (en) * 2019-03-14 2019-07-23 电子科技大学 A kind of relatively prime battle array robust adaptive beamforming algorithm based on matrix fill-in
CN111562545A (en) * 2020-04-30 2020-08-21 南京理工大学 Sparse array DOA estimation method based on PD-ALM algorithm
WO2020212569A1 (en) * 2019-04-17 2020-10-22 Université Du Luxembourg Method and device for beamforming in a mimo radar system
CN113219461A (en) * 2021-04-23 2021-08-06 浙江理工大学 Millimeter wave radar sparse array design method based on maximized signal-to-noise ratio

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2016204451A1 (en) * 2015-06-16 2016-12-22 포항공과대학교 산학협력단 Method and apparatus for beamforming
CN107402380A (en) * 2017-05-12 2017-11-28 电子科技大学 A kind of quick self-adapted alternative manner for realizing Doppler beam sharpened imaging
CN110045323A (en) * 2019-03-14 2019-07-23 电子科技大学 A kind of relatively prime battle array robust adaptive beamforming algorithm based on matrix fill-in
WO2020212569A1 (en) * 2019-04-17 2020-10-22 Université Du Luxembourg Method and device for beamforming in a mimo radar system
CN111562545A (en) * 2020-04-30 2020-08-21 南京理工大学 Sparse array DOA estimation method based on PD-ALM algorithm
CN113219461A (en) * 2021-04-23 2021-08-06 浙江理工大学 Millimeter wave radar sparse array design method based on maximized signal-to-noise ratio

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