Iterative Fourier transform sparse antenna array arrangement method and system based on array element expansion-contraction

Abstract

The invention relates to an array element expansion-contraction-based iterative Fourier transform sparse antenna array distribution method and system, and the method comprises the steps: selecting a sparse array through iterative Fourier transform, solving a problem of the minimization of the sidelobe level of a directional diagram through employing a convex optimization method, enabling an array element to be expanded and contracted through employing the convex optimization method, and achieving the distribution of a sparse array. In the optimization process, in order to guarantee the minimum array element spacing, the expansion direction and the expansion distance of the array elements are limited, then in order to avoid the situation that array element excitation is too small, the linear weighting density of the array is limited in the convex optimization solving condition, and finally the low sidelobe array comprehensive problem under the given sparseness is solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of low sidelobe sparse array synthesis, and in particular relates to an array arrangement method and system of an iterative Fourier transform sparse antenna array based on array element "expansion-contraction". Background Art

[0002] Low sidelobe sparse array synthesis refers to a method of controlling the directivity of the main lobe by optimizing the current distribution of the array and the arrangement of the array elements to minimize the amplitude of the side lobes when designing the antenna array, so as to improve the radiation characteristics of the antenna. Low sidelobe sparse array synthesis is widely used in various wireless communications, radar systems and other technical fields related to electromagnetic wave radiation. In radar systems, low sidelobe sparse arrays can reduce the stray signals of radar echoes, thereby improving the accuracy and reliability of target detection. With the continuous advancement of wireless communication technology and the increasing demand for higher performance antennas, low sidelobe sparse array synthesis will play an increasingly important role.

[0003] Among the current algorithms for synthesizing low sidelobe sparse arrays, the classical analytical method can no longer meet the needs. Later, researchers proposed optimization algorithms such as convex optimization algorithms, intelligent optimization algorithms, and iterative Fourier transform. Since the iterative Fourier algorithm has a faster calculation speed and better global search capabilities, researchers have focused on the application and improvement of the iterative Fourier algorithm. The original algorithm was improved by introducing variable filling factors on the basis of the iterative Fourier algorithm, or establishing multiple parallel processes for co-evolution, or establishing a probability estimation model based on the results obtained each time. Although these improvements have been successful, they can only handle the case of equidistant arrays, which greatly limits the comprehensive performance. In the subsequent improved algorithm, sparse array synthesis is performed by optimizing the array element position and array element excitation and phase, but how to optimize the array element position and array element excitation at the same time has become a difficulty, and in order to avoid the mutual coupling effect between array elements in the actual array, it is also necessary to consider whether the minimum array element spacing meets the requirements. Therefore, it is necessary to explore an efficient algorithm to obtain the array parameters so that the array can meet the high sensitivity, high resolution and high directivity requirements of the radar system, while effectively reducing interference from other signal sources and improving detection accuracy in a complex electromagnetic interference environment. Summary of the invention

[0004] The present invention proposes an iterative Fourier transform sparse antenna array arrangement method based on array element expansion-contraction, in which a sparse array is selected by iterative Fourier transform, and then the array element position and excitation are further optimized by making the array element "expand-contract", thereby obtaining a low sidelobe sparse array with the best comprehensive performance under a given sparsity.

[0005] After selecting a sparse array through iterative Fourier transform, the present invention uses a convex optimization method to solve the problem of minimizing the sidelobe level of the directional pattern, and uses the convex optimization method to expand and shrink the array elements. In the optimization process, in order to ensure the minimum array element spacing, restrictions are imposed on the expansion direction and expansion distance of the array elements. Then, in order to avoid the situation where the array element excitation is too small, restrictions are imposed on the linear weighted density of the array in the conditions of the convex optimization solution, and finally the comprehensive problem of low sidelobe arrays under given sparsity is solved.

[0006] The technical solution of the present invention is:

[0007] The invention relates to an array arrangement method of sparse antenna array based on iterative Fourier transform of array element expansion and contraction, comprising:

[0008] Step 1: According to the number of input array elements N and sparsity f c , the sparse array is selected as the initial array by iterative Fourier transform algorithm. At this time, the excitation and position of the nth array element in the initial array are represented by c n and x n ;

[0009] Step 2: Continue to expand the array element according to the array element expansion rule. The array element position of the pth expansion element of the nth source array element after expansion is The excitation of the expansion element is Where p∈[1,2];

[0010] Step 3: Solve the row vector of the excitation of the dilation element by iteratively solving the convex problem

[0011] Step 4: Calculate the excitation of the expansion element, shrink each group of expansion elements into a shrink element, the position and excitation are equal to the weighted sum of the excitations of the expansion elements, and continue to adjust the smaller excitation;

[0012] Repeat steps 3 to 4 until the maximum number of iterations is reached, and the iterative Fourier transform sparse antenna array is completed.

[0013] Preferably, according to the present invention, a sparse array is selected as an initial array by an iterative Fourier transform algorithm; comprising:

[0014] Select a uniform linear array with N array elements as the initial array, and randomly initialize the array element excitation c n , the array element excitation is transformed by IFFT to calculate the array pattern F(u), as shown in formula (1):

[0015]

[0016] Where d is the array element spacing; λ is the operating wavelength, u = sin(θ), θ is the angle between the array axis and the radiation direction, and j is the imaginary unit;

[0017] The sidelobe area value of the array pattern is reduced to make the sidelobe area value of the array pattern lower than the set value. The adjusted array pattern is recorded as F′(u). Then, the M-point numerical result is obtained by M-point fast Fourier transform, and the M-point numerical result is used as the new array element excitation value. According to the sparsity f c Select the previous f c The values ​​of N array element excitations are set to 1, and the values ​​of the remaining array element excitations are set to 0, thus obtaining a sparse array;

[0018] Then, the array pattern is continuously adjusted until the maximum number of iterations is reached or the distribution of two array elements no longer changes, and the resulting sparse array is output.

[0019] Preferably, according to the present invention, the array element is further expanded according to the array element expansion rule; comprising:

[0020] Find the position difference of adjacent array elements, and group the array elements whose position difference of adjacent array elements is the minimum array element spacing; the array element expansion rule is as follows:

[0021] ① The array elements at both ends of the array do not expand, while the other array elements in the group expand toward the center;

[0022] ② When the number of grouped array elements is odd, the middle array element expands to both sides, and the other array elements expand in the opposite direction of the central array element; when the number of array elements is even, the array elements expand to both sides; for the array elements that only expand to one side, represents the position of the array element after expansion, and the solution process is formula (2):

[0023]

[0024] Wherein, the subscript n,p represents the pth expansion element of the nth source array element;

[0025] For array elements that expand only to both sides, It is expressed as formula (3):

[0026]

[0027] Where δ is the expansion radius (δ< <d)。

[0028] Preferably, according to the present invention, the row vector of the excitation of the expansion element is solved by iteratively solving the convex problem; comprising:

[0029] The row vector of the dilation element excitation is solved by iteratively solving the following convex problem Wherein, the superscript k represents the kth iteration process, which is expressed as formula (4):

[0030]

[0031] Among them, M UP is the upper limit of the sidelobe area level, is the steering vector corresponding to the sidelobe region, is a row vector obtained by sampling the steering vector in the main beam direction, ‖q||1 represents the e1 norm of the q vector, and its value is ∑ k |q k |,ξ k is a constant representing the tolerance, ξ k =0.9ξ k-1 , is the kth iteration according to the incentive The resulting weighted linear density, is the row vector composed of the reference linear weighted line density, where the weighted line density of the linear array with an even number of array elements is shown in formula (5):

[0032]

[0033] Where n=N / 2+1,…,N, κ is a constant coefficient, 0<κ<1, and the function of κ is to make the weighted line density at the center position 1. When the number of array elements is an odd number, the weighted line density at the center of the array is defined as 1.

[0034] According to the preferred embodiment of the present invention, the excitation row vector of the expansion element is calculated Each group of expansion elements is contracted to a position Incentive for The position and excitation of the contraction element are equal to the weighted sum of the excitations of the expansion element, as shown in equations (6) and (7):

[0035]

[0036]

[0037] in, represents the excitation of the pth dilation element of n source elements during the kth iteration;

[0038] will be less than The incentive value is adjusted to Solution and As shown in formula (8) and formula (9):

[0039]

[0040]

[0041] Where U is a lower triangular matrix with odd rows removed, x′ kis a row vector representing the position of the contraction element in the kth iteration, ” represents the Hadamard product of two vectors, is the kth iteration according to the incentive The resulting weighted linear density, is the row vector of reference linear weighted line density, is the row vector of the dilation element excitation, Row vector of contraction metaexcitations.

[0042] A computer device / equipment / system comprises a memory, a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the above-mentioned method for sparsely distributed antenna arrays based on iterative Fourier transform of array element expansion-contraction.

[0043] A computer-readable storage medium stores a computer program / instruction thereon, which, when executed by a processor, implements the steps of the above-mentioned iterative Fourier transform sparse antenna array arrangement method based on array element expansion-contraction.

[0044] A computer program product includes a computer program / instruction, which, when executed by a processor, implements the steps of the above-mentioned iterative Fourier transform sparse antenna array arrangement method based on array element expansion-contraction.

[0045] The invention relates to an iterative Fourier transform sparse antenna array system based on array element expansion and contraction, comprising:

[0046] The sparse array selection module is configured to: c , the sparse array is selected as the initial array by iterative Fourier transform algorithm. At this time, the excitation and position of the nth array element in the initial array are represented by c n and x n ;

[0047] The expansion module is configured to: continue to expand the array element according to the array element expansion rule, and the array element position of the pth expansion element of the nth source array element after expansion is The excitation of the expansion element is Where p∈[1,2];

[0048] The row vector of the excitation of the dilation element is solved by iteratively solving the convex problem

[0049] The Fourier transform sparse antenna array layout module is configured as follows: calculate the excitation of the expansion element, shrink each group of expansion elements into a contraction element, the position and excitation are equal to the weighted sum of the excitation of the expansion element, and continue to adjust the smaller excitation; repeat this step until the maximum number of iterations is reached, and the iterative Fourier transform sparse antenna array layout is completed.

[0050] The beneficial effects of the present invention are:

[0051] The present invention utilizes a convex optimization method to expand and contract the array elements, thereby further optimizing the position and excitation of the array elements to achieve a lower sidelobe level. In order to ensure the minimum inter-unit distance constraint, an expansion rule for the array elements is proposed, and the expansion direction and expansion distance of the array elements are restricted. In order to limit the array element excitation taper ratio, the linear weighted density of the array element is approximated to the reference value, the tolerance decreases with the increase in the number of iterations, and the smaller excitation is adjusted. The present invention has good adaptability to the synthesis of low sidelobe linear arrays with different array structures and different sparsities, exhibits better performance and robustness, and can also effectively synthesize low sidelobe null-sink patterns. The present invention can achieve higher directivity and gain, improve the resolution and sensitivity of the system by optimizing the array antenna arrangement, and at the same time, for drones, satellites or mobile communication scenarios, it can optimize the arrangement of antenna array elements to obtain better performance in a limited space. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 It is a principle block diagram of the sparse antenna array deployment method based on iterative Fourier transform of array element expansion-contraction of the present invention.

[0053] Figure 2 This is a schematic diagram of the grouping and expansion of array elements.

[0054] Figure 3 It is a schematic diagram of the "expansion-contraction" process of the array element.

[0055] Figure 4 It is a schematic diagram of the result of synthesizing a symmetrical linear array with a sparsity of 66% using the method provided by the present invention.

[0056] Figure 5 It is a schematic diagram of the result of synthesizing an asymmetric linear array with a sparsity of 69.5% using the method provided by the present invention.

[0057] Figure 6 It is a schematic diagram of the result of synthesizing an asymmetric null-sink linear array with a sparsity of 69.5% using the method provided by the present invention.

[0058] FIG7( a ) is a numerical diagram of array element excitation obtained through Fourier transform.

[0059] FIG7( b ) is a numerical diagram of the adjusted array element excitation. DETAILED DESCRIPTION

[0060] The present invention will be further described below in conjunction with the accompanying drawings and embodiments, but is not limited thereto.

[0061] Example 1

[0062] The invention relates to an array arrangement method of sparse antenna array based on iterative Fourier transform of array element expansion and contraction, comprising:

[0063] Step 1: According to the number of input array elements N and sparsity f c , the appropriate sparse array is selected as the initial array by iterative Fourier transform algorithm. At this time, the excitation and position of the nth array element in the initial array are represented by c n and x n ;

[0064] Step 2: Continue to expand the array element according to the array element expansion rule. The array element position of the pth expansion element of the nth source array element after expansion is The excitation of the expansion element is Where p∈[1,2];

[0065] Step 3: Solve the row vector of the excitation of the dilation element by iteratively solving the convex problem

[0066] Step 4: After calculating the excitation of the expansion element, you can enter the "contraction" process, shrinking each group of expansion elements into a contraction element, with the position and excitation equal to the weighted sum of the excitations of the expansion elements. At the same time, in order to limit the current taper ratio, the smaller excitation is further adjusted;

[0067] Repeat steps 3 to 4 until the maximum number of iterations is reached, and the iterative Fourier transform sparse antenna array is completed.

[0068] Low sidelobe array synthesis is mainly to reduce the peak sidelobe level (PSLL) while controlling the main lobe width (beam width, BW) by adjusting the position of the array elements and the phase and amplitude of the array element excitation to reduce interference and stray radiation, making the radiation of the antenna in the main direction more concentrated, which helps to improve the directivity of signal reception and transmission, and at the same time can effectively utilize spectrum resources and improve system capacity. Given an initial array with N array elements, the sparsity is f c The final comprehensive effect can be measured by the PSLL, BW and directivity in the radiation pattern of the array antenna. The solution formula for the radiation pattern F(u) is as follows:

[0069]

[0070] Among them, the excitation amplitude weighted value of each array element is c n , the array element position is x n , λ is the operating wavelength, u=sin(θ), θ is the angle between the array axis and the radiation direction, and j is the imaginary unit.

[0071] The present invention uses a convex optimization method to expand and contract the array elements, and proposes an iterative Fourier transform sparse array synthesis method based on the "expansion-contraction" of the array elements. The present invention can further optimize the array element excitation and position of the sparse array selected by IFT by iteratively solving a convex problem under a given sparsity, while ensuring the minimum spacing between array elements, and obtain lower PSLL and better directivity under the restriction of non-broadening of BW. The present invention can limit the taper ratio of the array element excitation and solve the feeding complexity problem in the actual array.

[0072] Example 2

[0073] The difference between the method for deploying a sparsely distributed antenna array based on iterative Fourier transform of array element expansion and contraction described in Example 1 is that:

[0074] Figure 1 It is a principle block diagram of the iterative Fourier transform sparse antenna array arrangement method based on array element expansion-contraction of the present invention. The present invention can be divided into two sub-steps: iterative Fourier transform and array element "expansion-contraction".

[0075] Select a suitable sparse array as the initial array by iterative Fourier transform algorithm; including:

[0076] Select a uniform linear array with N array elements as the initial array, and randomly initialize the array element excitation c n , because it is a uniform linear array, the array element excitation is transformed by IFFT to calculate the array pattern F(u), as shown in formula (1):

[0077]

[0078] Where d is the array element spacing; λ is the operating wavelength, u = sin(θ), θ is the angle between the array axis and the radiation direction, and j is the imaginary unit;

[0079] It is not difficult to see that at this time there is a Fourier transform pair relationship between the array pattern and the array element excitation. Therefore, the array pattern can be obtained by the M-point inverse Fourier transform, and the sidelobe area value of the array pattern is reduced to make the sidelobe area value of the array pattern lower than the set value. The adjusted array pattern is recorded as F′(u). After that, the M-point numerical result is obtained by the M-point fast Fourier transform, and the M-point numerical result is used as the new array element excitation value, and according to the sparsity f c Select the previous fc The values ​​of N larger array element excitations are set to 1, and the excitations of the remaining array elements are set to 0, thereby obtaining a sparse array; FIG7(a) and FIG7(b) take the sparse optimization of 200 array elements at a sparsity of 69.5% as an example to illustrate the adjustment process of the array element excitation; FIG7(a) shows the array element excitation value obtained by Fourier transform; FIG7(b) shows the adjusted array element excitation value.

[0080] Then, the array pattern is continuously adjusted until the maximum number of iterations is reached or the distribution of two array elements no longer changes, and the resulting sparse array is output.

[0081] The array element continues to expand according to the array element expansion rule; including:

[0082] In the second sub-step of the present invention, the output of the first sub-step is selected as the initial array, and the array element position and the excitation are respectively x n and c n , find the position difference of adjacent array elements, and group the array elements whose position difference of adjacent array elements is the minimum array element spacing; the array element expansion rule is as follows:

[0083] ① In order to ensure the array aperture, the array elements at both ends of the array do not expand, and the other array elements in the group expand toward the center;

[0084] ② When the number of grouped array elements is an odd number, the middle array element expands to both sides, and the other array elements expand in the opposite direction of the central array element; when the number of array elements is an even number, the array elements expand to both sides; the grouping and expansion rules are as follows Figure 2 As shown, Figure 2 In the figure, (a) represents the grouping of array elements, where numbers 1-5 represent the grouping numbers; (b) represents the restriction on whether the array element expands and how much it expands according to the rules, the direction of the arrow represents the expansion direction of the array element, and two arrows represent that the array element expands to both sides.

[0085] For an array element that expands only to one side, represents the position of the array element after expansion, and the solution process is formula (2):

[0086]

[0087] Wherein, the subscript n,p represents the pth expansion element of the nth source array element;

[0088] For array elements that expand only to both sides, It is expressed as formula (3):

[0089]

[0090] Where δ is the expansion radius (δ<<d). All variables and functions related to the expansion element are marked with “~”.

[0091] The row vector of the excitation of the dilation element is solved by iteratively solving a convex problem; including:

[0092] The row vector of the dilation element excitation is solved by iteratively solving the following convex problem Wherein, the superscript k represents the kth iteration process, which is expressed as formula (4):

[0093]

[0094] Among them, M UP is the upper limit of the sidelobe area level, is the steering vector corresponding to the sidelobe region, is a row vector obtained by sampling the steering vector in the main beam direction. ||q||1 represents the l1 norm of the q vector, and its value is ∑ k |q k |,ξ k is a constant representing the tolerance, ξ k =0.9ξ k-1 , is the kth iteration according to the incentive The resulting weighted linear density, is the row vector composed of the reference linear weighted line density, where the weighted line density of the linear array with an even number of array elements is shown in formula (5):

[0095]

[0096] Where n=N / 2+1,…,N, κ is a constant coefficient, 0<κ<1, and the function of κ is to make the weighted line density at the center position 1. When the number of array elements is an odd number, the weighted line density at the center of the array is defined as 1.

[0097] Calculate the excitation row vector of the expansion element Then we can enter the "contraction" process, shrinking each group of expansion elements to a position of Incentive for The position and excitation of the contraction element are equal to the weighted sum of the excitations of the expansion element, as shown in equations (6) and (7):

[0098]

[0099]

[0100] in, represents the excitation of the pth dilation element of n source elements during the kth iteration;

[0101] In order to limit the current amplitude ratio, the present invention will be less than The incentive value is adjusted to Solution and As shown in formula (8) and formula (9):

[0102]

[0103]

[0104] Where U is a lower triangular matrix with odd rows removed, x′ k is a row vector representing the position of the contraction element in the kth iteration, ” represents the Hadamard product of two vectors, is the kth iteration according to the incentive The resulting weighted linear density, is the row vector of reference linear weighted line density, is the row vector of the dilation element excitation, Row vector of contraction metaexcitations.

[0105] The position of the array element and the accumulated amplitude excitation jointly determine the spatial filtering characteristics of the array, and the essence of the linear weighted density is to spatially weight the accumulated excitation amplitude of the array element, so the linear weighted density represents the spatially weighted accumulated excitation amplitude, and by increasing the smaller excitation, its proportion in the overall accumulated amplitude is increased. After adjusting the excitation, the weighted density in the next iteration needs to approach the adjusted weighted density, which sets the solution boundary of the excitation to avoid the situation where the excitation is too small, and limits the current amplitude ratio. The current amplitude ratio determines the feeding complexity of the actual array antenna. A larger current amplitude ratio will make the feeding structure more complex, so it is hoped that the current amplitude ratio is as small as possible.

[0106] After reaching the maximum number of iterations, the final position x′ and excitation c′ of the contraction element can be obtained. These contraction elements can radiate the same pattern as the expansion element, and the approximate error is (βδ) 2 Order of magnitude, Figure 3 A schematic diagram of the entire process of "contraction-expansion" is given. The color depth represents the amplitude of the excitation, the dotted white circle represents the source element, and the arrow indicates the direction of element expansion. Figure 3 In the figure, (a) represents the "expansion" process of the array element, (b) represents the expansion element excitation obtained by solving the convex problem, and (c) represents the contraction element obtained by "contracting" according to the expansion element excitation.

[0107] In summary, the present invention first starts with a uniform linear array whose excitation is randomly initialized, and obtains the directional pattern by inverse Fourier transforming the excitation by utilizing the Fourier transform pair relationship between the excitation and the directional pattern in the uniform linear array. After adjusting the sidelobe area of ​​the directional pattern, the array element excitation is obtained by fast Fourier transform, and the array element excitation is truncated according to the sparsity to obtain a sparse array. Then, the sparse array is expanded according to the expansion rule, and the excitation of the expanded array element is solved by constructing a convex problem that minimizes the upper bound of the sidelobe level. The three conditions in the convex problem respectively limit the sidelobe level height of the directional pattern, the main beam pointing and the weighted linear density size, wherein the weighted linear density in each iteration will approach the reference value, and the approximation tolerance will decrease with the increase of the number of iterations. At the same time, the smaller value in the obtained excitation will be adjusted to limit the excitation solution range and the current amplitude ratio. After the excitation of the expanded array element is obtained, the expanded array element will be shrunk according to the weighted sum of the obtained excitation to obtain the final output sparse array arrangement. The invention can ensure the minimum spacing requirement of array elements and limit the current amplitude ratio under a given sparsity. Compared with the current low sidelobe sparse array synthesis method, the invention can obtain an array antenna arrangement with better performance.

[0108] Example 3

[0109] The difference between the method for deploying a sparsely distributed antenna array based on iterative Fourier transform of array element expansion and contraction described in Example 2 is that:

[0110] In order to verify the effectiveness of the algorithm in the present invention for the problem of low sidelobe sparse array synthesis under multiple constraints, this embodiment uses simulation experiments to illustrate the process and demonstrate the effect. In order to verify the comprehensive effect of the present invention on symmetric linear arrays and asymmetric linear arrays, the synthesis of low sidelobe sparse arrays with a symmetric linear array with a sparsity of 66% and a 200-element sparse array with a sparsity of 69.5% are considered respectively. First, the synthesis of a symmetric linear array with a sparsity of 66% is considered. Figure 4 This is a schematic diagram of the results of synthesizing a symmetrical linear array with a sparsity of 66% using the method provided by the present invention. The radiation performance of the obtained results is shown in Table 1:

[0111] Table 1

[0112]

[0113] It can be seen that at different scanning angles, the results obtained have excellent radiation performance, and the minimum array element spacing also meets the requirements. Then consider the asymmetric linear array sparse array synthesis with a sparsity of 69.5%.

[0114] Figure 5This is a schematic diagram of the results of synthesizing an asymmetric linear array with a sparsity of 69.5% using the method provided by the present invention. The radiation performance of the obtained results is shown in Table 2:

[0115] Table 2

[0116]

[0117] It can be seen that under different scanning angles, the present invention can have good comprehensive performance for asymmetric linear arrays while satisfying restriction conditions.

[0118] Table 3 compares the results of the latest methods TS-IFT, IFT-DE and the traditional algorithm IFT in recent years, using PSLL, BW and directivity as evaluation indicators:

[0119] Table 3

[0120]

[0121] It can be found that the present invention has good comprehensive performance under different array structures and different sparsities. In the sparse synthesis of a symmetrical linear array with a sparsity of 66%, the PSLL of the result obtained by the present invention is reduced by 1-4dB compared with other algorithms, and the main lobe width is slightly reduced, and the directivity of the radiation pattern is improved by 2-3dBi; in the sparse synthesis of an asymmetric linear array with a sparsity of 69.5%, the PSLL of the result obtained by the present invention is reduced by 1-2dB compared with other algorithms, and the main lobe width is slightly reduced, and the directivity of the radiation pattern is improved by 1-4dBi.

[0122] Example 4

[0123] The difference between the method for deploying a sparsely distributed antenna array based on iterative Fourier transform of array element expansion and contraction described in Example 2 is that:

[0124] By creating nulls for the array pattern in the direction of the interference source, the noise or interference from these directions can be significantly reduced to ensure signal quality. In order to further verify the comprehensive ability of the algorithm in the present invention to null low sidelobe patterns, a 200-element asymmetric linear array with a sparsity of 69.5% is synthesized to generate two nulls in the specified direction. The performance of the obtained results, including PSLL, null width and null depth, is summarized in Table 4 and compared with the latest method PT-IFT in recent years.

[0125] Table 4

[0126]

[0127] Figure 6This is a schematic diagram of the result of synthesizing an asymmetric null-steering linear array with a sparsity of 69.5% using the method provided by the present invention. It can be seen that two nulls are generated in the directional pattern in the directions of u=0.45 and u=0.65. The array antenna can generate nulls in these interference directions to reduce the impact of interference, thereby improving the accuracy of target detection and avoiding interference between the signal and the signal of other users in a specific direction.

[0128] From the above performance, it can be seen that the algorithm of the present invention can have better performance than other algorithms in the synthesis of low sidelobe sparse arrays under multi-task design, and can obtain a better array layout, thereby meeting the needs of high-performance radar and communication systems to suppress interference from other signal sources.

[0129] Example 5

[0130] A computer device / equipment / system, comprising a memory, a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the iterative Fourier transform sparse antenna array arrangement method based on array element expansion-contraction as described in any one of Examples 1-4.

[0131] Example 6

[0132] A computer-readable storage medium having a computer program / instruction stored thereon, which, when executed by a processor, implements the steps of the iterative Fourier transform sparse antenna array arrangement method based on array element expansion-contraction as described in any one of Examples 1-4.

[0133] Example 7

[0134] A computer program product includes a computer program / instruction, which, when executed by a processor, implements the steps of the iterative Fourier transform sparse antenna array arrangement method based on array element expansion-contraction as described in any one of Examples 1-4.

[0135] Example 8

[0136] The invention relates to an iterative Fourier transform sparse antenna array system based on array element expansion and contraction, comprising:

[0137] The sparse array selection module is configured to: c , the appropriate sparse array is selected as the initial array by iterative Fourier transform algorithm. At this time, the excitation and position of the nth array element in the initial array are represented by c n and x n ;

[0138] The expansion module is configured to: continue to expand the array element according to the array element expansion rule, and the array element position of the pth expansion element of the nth source array element after expansion is The excitation of the expansion element is Where p∈[1,2];

[0139] The row vector of the excitation of the dilation element is solved by iteratively solving the convex problem

[0140] The Fourier transform sparse antenna array layout module is configured as follows: after calculating the excitation of the expansion element, it can enter the "contraction" process, shrinking each group of expansion elements into a contraction element, and the position and excitation are equal to the weighted sum of the excitations of the expansion elements. At the same time, in order to limit the current taper ratio, the smaller excitation continues to be adjusted; repeat this step until the maximum number of iterations is reached, and the iterative Fourier transform sparse antenna array layout is completed.

Claims

1. A method for deploying sparse antenna arrays based on iterative Fourier transform of array element expansion and contraction, characterized in that: include: Step 1: According to the number of input array elements N and sparsity f c , the sparse array is selected as the initial array by iterative Fourier transform algorithm. At this time, the excitation and position of the nth array element in the initial array are represented by c n and x n ; Step 2: Continue to expand the array element according to the array element expansion rule. The array element position of the pth expansion element of the nth source array element after expansion is The excitation of the expansion element is Where p∈[1,2]; Step 3: Solve the row vector of the excitation of the dilation element by iteratively solving the convex problem Step 4: Calculate the excitation of the expansion element, shrink each group of expansion elements into a shrink element, the position and excitation are equal to the weighted sum of the excitations of the expansion elements, and continue to adjust the smaller excitation; Repeat steps 3 to 4 until the maximum number of iterations is reached, and the iterative Fourier transform sparse antenna array is completed.

2. The method for deploying a sparsely distributed antenna array based on iterative Fourier transform of array element expansion-contraction according to claim 1, characterized in that: Selecting a sparse array as an initial array by an iterative Fourier transform algorithm; including: Select a uniform linear array with N array elements as the initial array, and randomly initialize the array element excitation c n , the array element excitation is transformed by IFFT to calculate the array pattern F(u), as shown in formula (1): Where d is the array element spacing; λ is the operating wavelength, u = sin(θ), θ is the angle between the array axis and the radiation direction, and j is the imaginary unit; The sidelobe area value of the array pattern is reduced to make the sidelobe area value of the array pattern lower than the set value. The adjusted array pattern is recorded as F′(u). Then, the M-point numerical result is obtained by M-point fast Fourier transform, and the M-point numerical result is used as the new array element excitation value. According to the sparsity f c Select the previous f c The values ​​of N array element excitations are set to 1, and the values ​​of the remaining array element excitations are set to 0, thus obtaining a sparse array; Then, the array pattern is continuously adjusted until the maximum number of iterations is reached or the distribution of two array elements no longer changes, and the resulting sparse array is output.

3. The method for deploying a sparsely distributed antenna array based on iterative Fourier transform of array element expansion-contraction according to claim 1, characterized in that: The array element continues to expand according to the array element expansion rule; including: Find the position difference of adjacent array elements, and group the array elements whose position difference of adjacent array elements is the minimum array element spacing; the array element expansion rule is as follows: ① The array elements at both ends of the array do not expand, while the other array elements in the group expand toward the center; ② When the number of grouped array elements is odd, the middle array element expands to both sides, and the other array elements expand in the opposite direction of the central array element; when the number of array elements is even, the array elements expand to both sides; for the array elements that only expand to one side, represents the position of the array element after expansion, and the solution process is formula (2): Wherein, the subscript n,p represents the pth expansion element of the nth source array element; For array elements that expand only to both sides, It is expressed as formula (3): Where δ is the expansion radius.

4. The method for deploying a sparse antenna array based on iterative Fourier transform of array element expansion-contraction according to claim 1, characterized in that: The row vector of the excitation of the dilation element is solved by iteratively solving a convex problem; including: The row vector of the dilation element excitation is solved by iteratively solving the following convex problem Wherein, the superscript k represents the kth iteration process, which is expressed as formula (4): Among them, M UP is the upper limit of the sidelobe area level, is the steering vector corresponding to the sidelobe region, is a row vector obtained by sampling the steering vector in the main beam direction. ||q||1 represents the e1 norm of the q vector, and its value is ∑ k |q k |,ξ k is a constant representing the tolerance, ξ k =0.9ξ k-1 , is the kth iteration according to the incentive The resulting weighted linear density, is the row vector composed of the reference linear weighted line density, where the weighted line density of the linear array with an even number of array elements is shown in formula (5): Where n=N / 2+1,…,N, κ is a constant coefficient, 0<κ<1, and the function of κ is to make the weighted line density at the center position 1. When the number of array elements is an odd number, the weighted line density at the center of the array is defined as 1.

5. The method for deploying a sparse antenna array based on iterative Fourier transform of array element expansion-contraction according to claims 1-4, characterized in that: Calculate the excitation row vector of the expansion element Each group of expansion elements is contracted to a position Incentive for The position and excitation of the contraction element are equal to the weighted sum of the excitations of the expansion element, as shown in equations (6) and (7): in, represents the excitation of the pth dilation element of n source elements during the kth iteration; will be less than The incentive value is adjusted to Solution and As shown in formula (8) and formula (9): Where U is a lower triangular matrix with odd rows removed, x′ k is a row vector representing the position of the contraction element in the kth iteration, "ο" represents the Hadamard product of two vectors, is the kth iteration according to the incentive The resulting weighted linear density, is the row vector of reference linear weighted line density, is the row vector of the dilation element excitation, Row vector of contraction metaexcitations.

6. A computer device / equipment / system comprising a memory, a processor and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method for deploying a sparsely distributed antenna array based on iterative Fourier transform of array element expansion and contraction as described in any one of claims 1 to 5.

7. A computer-readable storage medium having a computer program / instruction stored thereon, characterized in that: When the computer program / instruction is executed by a processor, the steps of the method for deploying a sparsely distributed antenna array based on iterative Fourier transform of array element expansion-contraction as described in any one of claims 1 to 5 are implemented.

8. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instruction is executed by a processor, the steps of the method for deploying a sparsely distributed antenna array based on iterative Fourier transform of array element expansion-contraction as described in any one of claims 1 to 5 are implemented.

9. An iterative Fourier transform sparse antenna array system based on array element expansion-contraction, characterized in that: include: The sparse array selection module is configured to: c , the sparse array is selected as the initial array by iterative Fourier transform algorithm. At this time, the excitation and position of the nth array element in the initial array are represented by c n and x n ; The expansion module is configured to: continue to expand the array element according to the array element expansion rule, and the array element position of the pth expansion element of the nth source array element after expansion is The excitation of the expansion element is Where p∈[1,2]; The row vector of the excitation of the dilation element is solved by iteratively solving the convex problem The Fourier transform sparse antenna array module is configured to: calculate the excitation of the expansion element, shrink each group of expansion elements into a shrink element, the position and excitation are equal to the weighted sum of the excitations of the expansion elements, and continue to adjust the smaller excitation; Repeat this step until the maximum number of iterations is reached, and the iterative Fourier transform sparse antenna array is completed.

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