A fast optimization method for grating sidelobe suppression of irregular phased array antennas

Abstract

The present invention discloses a fast optimization method for suppressing grating side lobes of irregular phased array antennas. The present invention starts from the physical mechanism of the generation of grating lobes caused by the phase center distribution of periodic subarrays of irregular phased array antennas, and considers that the subarray arrangement mode rather than the subarray-level amplitude and phase excitation plays a decisive role in the grating lobes. First, the grating lobes of the irregular phased array antenna corresponding to the regular array grating lobe position within the expected maximum beam scanning range are minimized to obtain the best array topology. This problem can be summarized as a low-dimensional integer programming problem, which can be quickly solved using an integer optimization solver; then a convex optimization problem is established with the peak side lobe level of the irregular phased array antenna as a constraint, the directivity coefficient as an objective function, and the subarray-level amplitude and phase excitation as an optimization variable. The convex optimization algorithm is used to quickly solve the best subarray-level amplitude and phase excitation, thereby avoiding directly solving the high-dimensional mixed integer optimization problem.

Description

Technical Field

[0001] The present invention belongs to the field of antenna technology and relates to a rapid optimization method for suppressing grating side lobes of irregular phased array antennas. Specifically, it refers to a method for rapidly obtaining an irregular phased array antenna with low grating side lobe levels by comprehensively optimizing the arrangement of irregular phased array antenna subarrays and the amplitude and phase excitation of subarrays. Background Art

[0002] Active electronically scanned antenna arrays (phased array antennas) are widely used in modern communications, radar and other wireless electronic systems. Moreover, with the increasing system requirements and increasingly stringent technical indicators, active electronically scanned antenna arrays are also playing an increasingly important role in the system. Traditional full-coverage phased array antennas are equipped with a transceiver component at the rear end of each array element to independently control the amplitude and phase of the signal. Since it has the most design freedom, it is the best antenna solution for the system in terms of performance. However, for the next generation of communications and radar systems, due to the higher frequency band of electromagnetic waves carrying information, greater air attenuation, and lower device efficiency, full-coverage phased array antennas have problems such as high cost, high power consumption, and difficult heat dissipation, making it difficult to adapt to the development of next generation communications and radar systems. Since more than half of the cost of the phased array system is used to manufacture active channel transceiver components, the most direct way to reduce cost and power consumption of full-coverage phased array antennas is to reduce the number of active channel transceiver components. Therefore, the irregular phased array antenna in which multiple continuous array elements share an active transceiver channel (using the same power amplifier, phase shifter, and low noise amplifier) ​​is a new array architecture that achieves a balanced design of cost, power consumption, heat dissipation, and electrical performance, and has very important engineering research significance and research value.

[0003] The biggest problem with irregular phased array antennas is the grating sidelobe problem that is difficult to suppress using amplitude and phase excitation during beam scanning due to the periodic arrangement of the subarray phase centers. It is usually necessary to jointly consider the irregular subarray division method and the corresponding amplitude and phase excitation to achieve effective grating sidelobe suppression. Mathematically, for a given aperture, based on all possible subarray filling methods and exact complete filling constraints, the grating sidelobe suppression problem of irregular phased array antennas can be summarized as a non-convex mixed integer second-order cone optimization problem. It is difficult to obtain the global optimal solution of the problem within polynomial time (finite time), and the problem of low solution efficiency is more prominent for large-scale irregular phased array antennas. However, for actual engineering design, the design cycle is sometimes as important as the design cost. Therefore, designing irregular phased array antennas with low grating sidelobe characteristics remains a very challenging open problem.

[0004] In order to solve the problem of fast optimization of grating sidelobe suppression of irregular phased array antennas, researchers at home and abroad have proposed a variety of efficient comprehensive optimization methods. In his 2015 paper "Irregular polyomino tiling via integer programming with application in phased array antenna design", Professor RJ Mailloux of the United States first revealed that the grating lobes or high sidelobes of irregular phased array antennas are caused by a certain periodicity in the arrangement of subarray phase centers, and that the grating lobe level can be effectively suppressed by breaking this periodic arrangement. Based on this idea, by introducing information entropy to quantitatively describe the non-periodicity of the subarray phase center arrangement, an integer optimization problem with maximizing the information entropy of the subarray arrangement as the objective function is established and linearized, which indirectly achieves fast and efficient suppression of grating lobes. Although this method avoids the problem of numerical calculation of the radiation pattern, it lacks the knowledge and understanding of the optimization results from a physical level, and it is difficult to establish a direct relationship between the optimization problem and the beam scanning angle. More importantly, when the subarray structure (shape and size), array aperture, and array grid change, the expression of information entropy needs to be re-derived. This process is very cumbersome and complicated, which will take up a lot of time and reduce the optimization efficiency. In 2022, Francesco Alessio Dicandia et al. from the University of Pisa, Italy, proposed a subarray division method for irregular array phased array antennas based on Penrose tiling in their 2015 paper "Wide-Scan and Energy-Saving Phased Arrays by Exploiting Penrose Tiling Subarrays". This method uses two isosceles triangles with different side lengths to cover the given triangular array grid aperture, and finds the common vertices of multiple triangles. Then the array elements located in the area surrounded by these triangles belong to the same subarray. This method also does not require a directional pattern, but only needs to control the arrangement of the subarray phase center according to the side length of the triangle, and the design efficiency is also high. However, this method lacks a quantitative explanation and description of the quality of the optimized subarray division method from a physical level, and it is difficult to establish a direct relationship with the beam scanning angle. More importantly, the size and shape of the subarray obtained by this method are difficult to control, and the subarray structure is not self-similar, which is not convenient for modular array formation and maintenance. In China, the patent number CN 107230843A discloses a random generation method for irregular subarray arrangement based on a dime-shaped subarray structure, which is very efficient in calculation. However, the array radiation pattern is not considered in the arrangement process, and the obtained pattern performance is poor. Moreover, due to the randomness of the generation method, the results generated each time may be different, and the engineering application value is limited.Patent number CN13067168 A discloses a non-adjacent irregularly connected subarray architecture based on alternating iterative solutions of main problem subproblems. The main problem subproblems are split based on the Bender decomposition algorithm, and the original mixed integer optimization problem is converted into a continuous variable optimization problem and an integer linear optimization problem, which reduces the complexity of the optimization problem and greatly improves the solution efficiency. However, for large-scale optimization problems, the optimization speed of this method is still slow, and it belongs to a method of reducing the complexity of the optimization problem from the optimization theory level. In general, the current irregular phased array antenna grating sidelobe suppression still lacks a fast optimization method that is directly based on the physical level of the cause of grating lobe formation and is applicable to arbitrary subarray structures, array apertures, and array grids. Summary of the invention

[0005] In view of the above technical background, the present invention proposes a fast optimization method for grating sidelobe suppression of irregular phased array antennas. The purpose is to start from the physical mechanism of the generation of grating lobes caused by the phase center distribution of periodic sub-arrays of irregular phased array antennas, and consider that the sub-array arrangement mode rather than the sub-array level amplitude and phase excitation plays a decisive role in the grating lobes. First, the grating lobes of the irregular phased array antenna corresponding to the regular array grating lobe position within the expected maximum beam scanning range are minimized to obtain the optimal array topology (sub-array arrangement). This problem can be summarized as a low-dimensional integer programming problem, which can be quickly solved using an integer optimization solver. When the sub-array arrangement structure is determined, a convex optimization problem with the peak sidelobe level of the irregular phased array antenna as a constraint, the directivity coefficient as an objective function, and the sub-array level amplitude and phase excitation as an optimization variable can be established, and a convex optimization algorithm can be used to quickly solve the optimal sub-array level amplitude and phase excitation, thereby avoiding directly solving a high-dimensional mixed integer optimization problem.

[0006] Consider a fully spaced regular phased array antenna consisting of M×N elements. The antenna elements are located on a rectangular grid (which remains unchanged for other types of grid analysis methods). The element spacing along the x and y directions is d x and d y Considering the convenience of grating lobe suppression and engineering application, such as Figure 1 As shown in the figure, it is assumed that the three hybrid subarray structures of monodomino, didomino (including horizontal subarray and vertical subarray) and quaternary domino are used to divide the above-mentioned fully regular phased array antenna into irregular subarrays (the analysis method for other subarray structures remains unchanged), and all units of the same subarray use the same amplitude and phase excitation. If the total number of subarrays is T, the number of each subarray is N t , then the corresponding far-field radiation pattern of the irregular phased array antenna can be expressed as:

[0007]

[0008] Where β represents the wave number corresponding to the operating frequency f. Represents the viewing angle in the spherical coordinate system. t represents the amplitude excitation of the t-th sub-array, represents the stepped phase excitation of the t-th subarray. Indicates the desired scanning angle in uv space. (x t ,y t ) represents the phase center coordinates corresponding to the t-th sub-array, (Δx tw ,Δy tw ) represents the coordinate of the wth unit in the tth subarray relative to the phase center (x t ,y t ) position. It is not difficult to find from formula (1) that the far-field radiation pattern of the irregular phased array antenna can be decomposed into the product of the subarray-level array factor and the subarray radiation pattern. The grating lobe is mainly due to the subarray phase center (x t ,y t ) is caused by the periodic distribution of the phase center of the irregular phased array antenna. Therefore, if the radiation grating lobes of the irregular phased array antenna are to be suppressed, the periodicity of the phase center distribution of the subarray needs to be broken. Considering that the subarray phase center distribution of the regular phased array antenna composed of a single monodomino, horizontal didomino, vertical didomino, and quadruple domino has the strongest periodicity, the most effective and simple way to suppress the radiation grating lobes of the irregular phased array antenna is to suppress the irregular array radiation grating lobes corresponding to the position of the regular array grating lobe with the strongest periodicity.

[0009] According to the array antenna theory, the far-field radiation pattern of a regular phased array antenna under uniform amplitude stepped phase excitation composed of a chain of dominoes can be expressed as:

[0010]

[0011] Where (u0, v0) represents the maximum beam scanning range θ m The determined scanning angle, let u'=u-u0 v'=v-v0, (2) can be expressed as:

[0012]

[0013] The value range of u' and v' can be determined according to the maximum scanning range θ m By using this method, the grating lobe analysis problem under scanning conditions is transformed into the grating lobe analysis problem under side-firing conditions, which is very helpful for simplifying the optimization problem. Therefore, the position of the grating lobe in the (u', v') space is determined by the following formula:

[0014]

[0015] Where Z represents an integer set. The above formula can be simplified to:

[0016]

[0017] The specific value of k is determined according to the value range of u' and v'.

[0018] Similarly, the far-field radiation pattern of a regular phased array antenna with uniform amplitude stepped phase excitation composed of horizontal diominoes can be expressed as:

[0019]

[0020] The position of the grating lobe in (u',v') space is determined by the following formula:

[0021]

[0022] The far-field radiation pattern of a regular phased array antenna with uniform amplitude stepped phase excitation composed of vertical diominoes can be expressed as:

[0023]

[0024] The position of the grating lobe in (u',v') space is determined by the following formula:

[0025]

[0026] The far-field radiation pattern of the regular phased array antenna with uniform amplitude stepped phase excitation composed of quadruple dominoes can be expressed as:

[0027]

[0028] The position of the grating lobe in (u',v') space is determined by the following formula:

[0029]

[0030] The grating lobe position vector L is constructed based on all possible grating lobe positions mentioned above. g .

[0031] The present invention starts from suppressing the grating lobe level caused by the regular array phase center distribution with the strongest periodicity, and performs a rapid comprehensive optimization design for the grating sidelobe suppression of irregular phased array antennas. The specific implementation steps are as follows:

[0032] 1) First, according to the expected maximum beam scanning range θ m , and construct the grating lobe position vector L of the regular array with the strongest periodicity according to formulas (5), (7), (9), and (11) g , and then establish a method to minimize the position vector L of the irregular phased array antenna in the grating lobe gThe grating lobe level at is the objective function, and the integer optimization problem is to satisfy the constraints that the antenna array surface is accurately divided (no gaps, no overlap, and no excess of the matrix grid boundary) and the number of subarrays is equal to the expected value. Mathematically, the problem can be expressed as:

[0033]

[0034]

[0035] Among them, the vector z b The 0-1 optimization variable indicating whether a certain subarray is used in the irregular phased array antenna directly determines the array topology of the irregular phased array antenna. Γ represents a set consisting of elements 0 and 1. T represents a binary matrix containing only 0-1 variables consisting of all possible situations when the array surface is filled with each subarray. U represents a column vector whose elements are all 1. B(L g ) represents the array structure and the grating lobe position vector L g The determined matrix. The optimization problem (12)-(13) is recorded as optimization problem 1. Obviously, optimization problem 1 is an integer optimization problem, and an integer optimization solver can be used to solve it quickly and efficiently to obtain the vector z b , thereby determining the matrix T1 that characterizes the array topology structure of the irregular phased array antenna.

[0036] 2) According to the optimization results of step 1), the topological structure of the irregular phased array antenna array composed of T subarrays can be determined, and its far-field radiation pattern is calculated according to formula (1), and the remaining unknown variables are the subarray-level amplitude and phase excitation. Then, a convex optimization problem with minimizing the radiated power of the irregular phased array antenna as the objective function, the field strength value in the desired scanning direction (u0, v0) equal to 1, the peak sidelobe level in the sidelobe area less than δ as the constraint conditions, and the subarray-level amplitude and phase excitation as the optimization variable can be established. Mathematically, it can be expressed as:

[0037]

[0038] Where w=[w1,w2,…,w T ] T Indicates that the sub-array level amplitude phase excitation I t and The complex excitation vector. T represents the transpose operator. D(u0,v0) represents the steering row vector determined by the beam scanning angle (u0,v0). g(u,v) represents the direction of the side lobe area Θ sidelobe The steering vector determined by all angles in . C represents a set of complex numbers. B represents the Hermite matrix determined by the corresponding full array topology structure, and its (i, j)th element can be calculated according to the following formula:

[0039]

[0040] The convex optimization algorithm can be used to quickly find the global optimal solution of optimization problems (14)-(15), obtain the best subarray-level amplitude and phase excitation, and complete the rapid comprehensive optimization of irregular phased array antennas with low grating sidelobe levels. Optimization problems (14)-(15) are recorded as optimization problem 2.

[0041] Compared with the existing irregular phased array antenna low grating sidelobe pattern synthesis technology, the present invention has the following two advantages:

[0042] 1. Based on the physical reasons for the generation of grating lobes in the radiation of irregular phased array antennas, the grating lobe position of the irregular phased array antenna is determined by the grating lobe position of the regular phased array antenna composed of a single subarray structure, thereby minimizing the grating lobe of the irregular phased array antenna, greatly reducing the dimension of the grating lobe suppression problem of the irregular phased array antenna and reducing the complexity;

[0043] 2. Based on the effective distinction between the influencing factors of grating lobes and side lobes, the originally complex and high-dimensional optimization problem is decoupled into two interrelated simple low-dimensional problems. The first optimization problem is an integer optimization problem, which can achieve rapid suppression of grating lobes only by optimizing the subarray structure. On this basis, the second optimization problem is a convex optimization problem, which can achieve rapid suppression of peak sidelobe levels only by optimizing the subarray-level amplitude and phase excitation, thereby realizing the rapid synthesis of irregular phased array antennas with low grating sidelobe levels. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is a monodomino, horizontal didomino, vertical didomino and tetradomino array structure.

[0045] Figure 2 It is an irregular phased array antenna architecture based on a hybrid subarray structure.

[0046] Figure 3 The optimized irregular phased array antenna array topology.

[0047] Figure 4 Beam scan to Normalized direction diagram when .

[0048] Figure 5 Beam scan to Normalized direction diagram when .

[0049] Figure 6 Beam scan to Normalized direction diagram when . DETAILED DESCRIPTION

[0050] Consider the problem of fast synthesis of low grating sidelobe patterns for an irregular phased array antenna with M×N=16×16 array elements. Assume that the element spacing along the x and y directions is half a wavelength (d x =d y =λ / 2), the subarrays include monodominoes, diptychs (including horizontal subarrays and vertical subarrays), and tetrominoes. In this implementation case, the expected number of subarrays is 128, and the expected maximum beam scanning range is θ m =30°, the desired beam scanning angle is The expected peak sidelobe level is δ = -20 dB. All examples in the implementation cases of the present invention are run on a desktop computer with an Intel(R) Core(TM) i9-13900K CPU and 128G memory, and the simulation platform is MATLAB 2023a.

[0051] The fast optimization method proposed in the present invention is used to optimize the design of the irregular phased array antenna. First, integer optimization is used to solve the optimization problem 1. An irregular phased array antenna consisting of 128 subarrays is obtained within 0.31 seconds. Compared with a full phased array, half of the number of TR components is saved. The corresponding array topology is as follows: Figure 3 As shown in the figure, the entire array is precisely and completely divided and presents an irregular distribution state, where the number of one-joint bone brand sub-arrays is 40, the number of horizontal two-joint bone brand sub-arrays is 38, the number of vertical two-joint bone brand sub-arrays is 30, and the number of four-joint bone brand sub-arrays is 20. According to the optimized array topology, the convex optimization algorithm is used to solve the optimization problem 2. For the desired beam scanning angle, the optimal sub-array level amplitude and phase excitation that meets the peak sidelobe level constraint and maximizes the directivity coefficient can be obtained. The corresponding normalized radiation patterns are as follows: Figure 4 , Figure 5 and Figure 6 As shown in the figure, the optimization time is 8.4 seconds, 8.7 seconds, and 10.3 seconds respectively, and the optimization speed is extremely fast. As can be seen from the figure, the peak sidelobe level of the optimized normalized directional pattern is less than -20dB on average, which meets the pre-set constraint conditions.

[0052] The above is a description of the present invention and its implementation scheme provided to engineers and technicians familiar with the field of the present invention. These descriptions should be regarded as illustrative rather than restrictive. Engineers and technicians can implement specific operations based on the ideas in the claims of the invention in combination with specific problems, and naturally can make a series of changes to the implementation scheme based on the above. All of the above should be regarded as the scope of the present invention.

Claims

1. A fast optimization method for grating sidelobe suppression of irregular phased array antenna, characterized in that Considering that the subarray arrangement mode rather than the subarray-level amplitude and phase excitation plays a decisive role in its grating lobe, firstly, an integer optimization problem of minimizing the grating lobe of the irregular phased array antenna corresponding to the regular array grating lobe position within the expected maximum beam scanning range is established to quickly obtain the best irregular phased array antenna subarray arrangement. Then, a convex optimization problem is established with the peak sidelobe level of the irregular phased array antenna as the constraint condition, the directivity coefficient as the objective function, and the subarray-level amplitude and phase excitation as the optimization variable. The convex optimization algorithm is used to quickly solve the best subarray-level amplitude and phase excitation. The steps of the whole fast optimization method are as follows: 1) According to the expected maximum beam scanning range θ m , calculate the most periodic regular grating lobe position vector L g , and establish to minimize the irregular phased array antenna in the grating lobe position vector L g The grating lobe level at is the objective function, which satisfies the integer optimization problem with the constraints that the antenna array is accurately divided and the number of subarrays is equal to the expected setting value: Among them, the vector z b Indicates the 0-1 optimization variable whether a certain subarray is used in the irregular phased array antenna, Γ represents a set consisting of elements 0 and 1, T represents a binary matrix containing only 0-1 variables consisting of all possible situations when the array surface is filled with each subarray, U represents a column vector with all elements 1, B(L g ) represents the array structure and the grating lobe position vector L g The determined matrix, optimization problems (1)-(2) belong to integer optimization problems, and integer optimization solvers can be used to quickly and efficiently solve the vector z b , thereby determining the matrix T1 that represents the array topology of the irregular phased array antenna; 2) According to the array topology optimized in step 1), a convex optimization problem can be established with the minimization of the radiated power of the irregular phased array antenna as the objective function, the field strength value in the desired scanning direction (u0, v0) equal to 1, the peak sidelobe level in the sidelobe area less than δ as the constraint conditions, and the subarray level amplitude and phase excitation as the optimization variables: Where w=[w1,w2,…,w T ] T represents the complex excitation vector composed of subarray-level amplitude and phase excitation, (·) T represents the transpose operator, D(u0,v0) represents the steering row vector determined by the beam scanning angle (u0,v0), and g(u,v) represents the sidelobe area Θ sidelobe The steering vectors determined by all angles in , C represents a complex number set, and B represents a Hermitian matrix determined by the corresponding fully-filled array topology. The convex optimization algorithm can be used to quickly find the global optimal solution to the optimization problems (3)-(4), obtain the best sub-array level amplitude and phase excitation, and complete the rapid comprehensive optimization of irregular phased array antennas with low grating sidelobe levels.

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