Optimization design method of rotationally symmetric four-dimensional antenna array

Abstract

The application discloses an optimization design method of a rotationally symmetric four-dimensional antenna array, which comprises the following steps: dividing the rotationally symmetric four-dimensional antenna array according to a rotationally symmetric structure and a subarray division mode, and setting a time modulation mode after the division; setting optimization variables based on the time modulation mode, simplifying constraint conditions to obtain new upper and lower bound constraint conditions; setting an optimization target and adopting the new upper and lower bound constraint conditions to construct a rotationally symmetric four-dimensional array optimization model; and based on the rotationally symmetric four-dimensional array optimization model, optimizing problems according to a harmony search-convex optimization algorithm to obtain an array layout, a time modulation time sequence and a sidelobe level of a central frequency directional diagram of an optimal rotationally symmetric four-dimensional array. The rotationally symmetric four-dimensional antenna array has higher design freedom, can simplify complex multi-constraint conditions, greatly reduce the complexity of a feed network, and can greatly improve array radiation performance, reduce a sidelobe level and suppress sideband radiation.

Description

Technical Field

[0001] This invention belongs to the field of antenna technology, and in particular relates to an optimized design method for a rotationally symmetric four-dimensional antenna array. Background Technology

[0002] Antenna arrays, characterized by high gain, low sidelobes, and scannable beams, enable wireless information transmission and are widely used in wireless communication systems, radar systems, and satellite communication systems. In recent years, antenna array system design has trended towards larger scale and digitalization. To simplify and alleviate the design difficulties of the feed network in array systems, four-dimensional antenna arrays have become a research hotspot in the field of array antenna design. Simultaneously, studying array pattern synthesis is an effective way to improve the radiation performance of antenna arrays. Currently, many scholars have conducted design and pattern synthesis research on linear four-dimensional antenna arrays, but research on planar four-dimensional antenna arrays is relatively limited, mainly due to the following shortcomings: 1) Most studies focus on optimizing the system's feed network and high-speed RF switches, with little attention paid to the array's topology; 2) The optimization problem of four-dimensional planar arrays is a complex nonlinear optimization problem involving numerous complex constraints, including the number of array elements, element spacing, array aperture, and switching timing; 3) Traditional optimization methods have slow convergence speeds, often leading to local optima and preventing the attainment of the optimal solution. Therefore, there is an urgent need to propose an optimization design method for rotationally symmetric four-dimensional antenna arrays. Summary of the Invention

[0003] To address the aforementioned technical problems, this invention proposes an optimized design method for a rotationally symmetric four-dimensional antenna array. The rotationally symmetric four-dimensional antenna array has higher design freedom, simplifies complex multi-constraint conditions, significantly reduces the complexity of the feed network, and can further improve the array radiation performance, reduce sidelobe levels, and suppress sideband radiation.

[0004] To achieve the above objectives, this invention provides an optimized design method for a rotationally symmetric four-dimensional antenna array, comprising:

[0005] The rotationally symmetric four-dimensional antenna array is divided according to the rotationally symmetric structure and subarray division method, and the time modulation method is set after the division.

[0006] Based on the time modulation method, optimization variables are set, constraints are simplified, and new upper and lower bound constraints are obtained; optimization objectives are set and new upper and lower bound constraints are adopted to construct a rotationally symmetric four-dimensional matrix optimization model.

[0007] Based on the aforementioned rotationally symmetric four-dimensional array optimization model, and using the harmony search-convex optimization algorithm to optimize the problem, the optimal array layout, time modulation sequence, and sidelobe level of the center frequency pattern of the rotationally symmetric four-dimensional array are obtained.

[0008] Optionally, the method for dividing the rotationally symmetric four-dimensional antenna array according to the rotationally symmetric structure and subarray partitioning method includes: dividing the circular array aperture with radius R into P rotationally symmetric sector regions, where the central angle of each sector region is θ.

[0009] Introduce M radii of r m The circular ring divides each sector into M sector ring regions, and the antenna elements distributed in each sector ring form a subarray m;

[0010] The total number of array elements is N, the number of elements in each sector is N / P, and the number of elements in the m-th sector subarray is N. m .

[0011] Optionally, methods for setting the time modulation method after partitioning include:

[0012] M aperiodic time modulation (T / R) components are respectively connected to N in subarray m. m One antenna element is connected;

[0013] A periodic time modulation function is generated by controlling a time modulation (T / R) component using a field-programmable gate array (FPGA).

[0014] Based on the variable aperture size time modulation method, the periodic time modulation function U m (t) is equivalent to a rectangular pulse function, in one period T s The inner waveform is determined by the pulse time τ m The only certainty:

[0015]

[0016] Optionally, the method for setting the optimization variables based on the time modulation method includes:

[0017] Set the number of elements within the fan-ring array to a vector N = (N1, N2, ..., N...). M );

[0018] Let the position of the nth antenna element in the mth sector subarray be vector a in the polar coordinate system. m,n =(r m,n ,ω m,n ), where r and ω are the polar radius vector and polar angle vector, respectively;

[0019] Set the time modulation pulse time to T = (τ1, τ2, ..., τ). M );

[0020] The optimization variable is X = (N, r, ω, T), which satisfies the following constraints:

[0021]

[0022] Where M is the number of sector ring subarrays, m is the index of the sector ring subarray, n is the index of the antenna element in the m-th sector ring subarray, and N m Let d be the number of antenna elements in the m-th sector ring subarray, N be the total number of antenna elements, P be the number of rotationally symmetric sector regions, R be the radius of the circular aperture, and d be the number of antenna elements in the m-th sector ring subarray. min This represents the minimum spacing between antenna elements. r is the central angle of the independent sector region. m,n ω m,n These are the polar radius and polar angle of the nth antenna element in the m-th sector ring subarray in polar coordinates, respectively. k,l ω k,l These are the polar radius and polar angle of the l-th antenna element in the k-th sector ring subarray in polar coordinates, respectively, τ m T represents the time modulation pulse time used by the antenna element in the m-th sector ring subarray. s The period of the time-modulated rectangular pulse function.

[0023] Optionally, methods for simplifying constraints to obtain new upper and lower bound constraints include:

[0024] Based on the optimization variables, define integer vectors and real vectors for upper and lower bound constraints, construct a mapping relationship, set new optimization variables, simplify the constraint conditions, and obtain new upper and lower bound constraints.

[0025] Optionally, the method for constructing the rotationally symmetric four-dimensional array optimization model by setting an optimization objective and adopting new upper and lower bound constraints includes: setting the sidelobe level of the center frequency pattern as the optimization objective, adopting new upper and lower bound constraints to constrain the zero-point beamwidth and the maximum level of the first sideband frequency pattern, and constructing the rotationally symmetric four-dimensional array optimization model under the condition of uniform excitation of antenna elements.

[0026] Optionally, the method for optimizing the problem based on the rotationally symmetric four-dimensional matrix optimization model and the harmony search-convex optimization algorithm includes: solving the new optimization variables using the harmony search algorithm and the convex optimization algorithm respectively; setting the control parameters in the harmony search algorithm; generating an initial harmony memory; performing convex optimization algorithm calculation on the initial harmony memory to obtain the optimal solution; calculating the fitness function value of the optimal solution; and obtaining the optimal solution in the harmony memory.

[0027] Optionally, methods for obtaining the optimal array layout, time modulation timing, and sidelobe level of the center frequency pattern of a rotationally symmetric four-dimensional array include:

[0028] Step 1: Based on the initial harmony memory, generate new solutions using random search and local perturbation, calculate the fitness function value of the new solution using a convex optimization algorithm, and compare it with the fitness function values ​​of each optimization variable in the harmony memory. Eliminate solutions with worse fitness function values ​​and update the harmony memory.

[0029] Step 2: Update the iteration number G = G+1, record the optimal variable and optimal solution in the harmony memory at this time, and determine: if G ≤ G max G max If the maximum number of iterations is reached, return to step one; if G > G max Then the optimal variables and optimal solutions of the harmony memory are output;

[0030] Step 3: Based on the optimal variables and mapping relationships of the harmony memory library, obtain the array layout and time modulation sequence of the optimal rotationally symmetric four-dimensional array; based on the optimal solution of the harmony memory library, obtain the sidelobe level of the center frequency pattern.

[0031] Technical advantages of this invention: This invention discloses an optimized design method for a rotationally symmetric four-dimensional antenna array. On the one hand, the rotationally symmetric four-dimensional antenna array proposed in this invention has a high degree of design freedom, can meet pre-set complex multi-constraint conditions during the array design process, and significantly reduces the design complexity of the feed network, thereby reducing system costs and possessing high practical value. On the other hand, compared with existing planar four-dimensional antenna arrays, the rotationally symmetric four-dimensional antenna array proposed in this invention can improve the array radiation performance to a greater extent, reduce sidelobe levels, and effectively suppress sideband radiation, achieving efficient optimization of radiation pattern synthesis. Attached Figure Description

[0032] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0033] Figure 1 This is a schematic diagram of the aperture division of the rotationally symmetric array according to an embodiment of the present invention;

[0034] Figure 2 This is a schematic diagram of the array topology and time modulation (T / R) component according to an embodiment of the present invention;

[0035] Figure 3 This is a schematic diagram of the optimal rotationally symmetric four-dimensional array topology in an embodiment of the present invention;

[0036] Figure 4 This is a schematic diagram of the time modulation timing used by the subarray units in an embodiment of the present invention;

[0037] Figure 5 This is a normalized direction pattern of the center frequency in an embodiment of the present invention;

[0038] Figure 6 This is the normalized radiation pattern of the first sideband frequency in an embodiment of the present invention;

[0039] Figure 7 This is a schematic diagram of the optimization design method for a rotationally symmetric four-dimensional antenna array according to an embodiment of the present invention. Detailed Implementation

[0040] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0041] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0042] like Figure 7 As shown, this embodiment provides an optimized design method for a rotationally symmetric four-dimensional antenna array, including the following steps:

[0043] Determine the array aperture, number of array elements, and minimum spacing between array elements;

[0044] Design rotationally symmetric structure, subarray partitioning method, and time modulation method;

[0045] The number of elements in the subarray, the position of each element, and the timing of the time modulation pulse are set as optimization variables, and the sidelobe level of the center frequency pattern is set as the optimization target.

[0046] Simplify complex constraints and establish an optimization model for a rotationally symmetric four-dimensional matrix;

[0047] The harmony search-convex optimization algorithm is used to optimize the model and obtain the optimal array layout, time modulation timing, and sidelobe level of the center frequency pattern of the rotationally symmetric four-dimensional array.

[0048] The rotationally symmetric four-dimensional antenna array of this invention includes: an N-element circular aperture antenna array, M time-modulated (T / R) components, and one field-programmable gate array (FPGA). To achieve the above objectives, the technical solution and specific implementation steps provided by this invention are as follows:

[0049] Step 1: Propose the rotationally symmetric structure and subarray partitioning method, and set the time modulation method;

[0050] Step 1 shall be carried out according to the following specific steps:

[0051] Step 1.1: Divide the circular array aperture of radius R into P rotationally symmetric sector regions, with a central angle of θ. Introduce M radii of r m The circular ring divides each sector into M sector rings, and the antenna elements distributed within each sector ring form a subarray m (m = 1, 2, ..., M), as shown in the figure. Figure 1 The total number of array elements is set to N, the number of elements in each sector is N / P, and the number of elements in the m-th sector subarray is N. m ;

[0052] Step 1.2, connect the M aperiodic time-modulated T / R components to N components within subarray m respectively. m Each antenna element is connected, and a field-programmable gate array (FPGA) is used to control the time modulation (T / R) component to generate a periodic time modulation function, referring to... Figure 2 Based on the Variable Aperture Size (VAS) time modulation method, the time modulation function U... m (t) can be equivalent to a rectangular pulse function, which has a period T. s The inner waveform is determined by the pulse time τ m The only certainty:

[0053]

[0054] Step 2: Set the number of elements in the subarray, the position of each element, and the timing of the time modulation pulse as optimization variables, and set the sidelobe level of the center frequency pattern as the optimization target. Simplify complex constraints such as the number of array elements and the spacing between array elements, and establish an optimization model of a rotationally symmetric four-dimensional array under the condition of uniform excitation of antenna elements.

[0055] Step 2 shall be carried out in accordance with the following specific steps:

[0056] Step 2.1, the number of elements in the fan-shaped subarray is denoted by the vector N = (N1, N2, ..., N...). M The position vector of the nth antenna element in the mth sector subarray in polar coordinates is denoted as a. m,n =(r m,n ,ω m,n ), where n = 1, 2, ..., N m m = 1, 2, ..., M, the polar radius vector and polar angle vector are denoted as r and ω respectively; the time modulation pulse time is denoted as T = (τ1, τ2, ..., τ M Let the optimization variables of the problem be X = (N, r, ω, T), satisfying the following constraints regarding the number of array elements, the spacing between array elements, and the switching timing:

[0057]

[0058] Where M is the number of sector ring subarrays, m is the index of the sector ring subarray, n is the index of the antenna element in the m-th sector ring subarray, and N m Let d be the number of antenna elements in the m-th sector ring subarray, N be the total number of antenna elements, P be the number of rotationally symmetric sector regions, R be the radius of the circular aperture, and d be the number of antenna elements in the m-th sector ring subarray. min This represents the minimum spacing between antenna elements. r is the central angle of the independent sector region. m,n ω m,n These are the polar radius and polar angle of the nth antenna element in the m-th sector ring subarray in polar coordinates, respectively. k,l ω k,l These are the polar radius and polar angle of the l-th antenna element in the k-th sector ring subarray in polar coordinates, respectively, τ m T represents the time modulation pulse time used by the antenna element in the m-th sector ring subarray. s The period of the time-modulated rectangular pulse function.

[0059] Step 2.2, define the integer vector NS and real vectors d, Δ, and δ that constitute the upper and lower bound constraints:

[0060]

[0061] Establish the mapping relationships: N = g1(NS), r = g2[g1(NS), d, Δ] and ω = g3[g1(NS), δ]. Set the new optimization variable as X. new = (NS,d,Δ,δ,T), where complex multi-constraint conditions are transformed into simple upper and lower bound constraints:

[0062]

[0063] Where m = 1, 2, ..., M; i = 1, 2, ..., N / P;

[0064] Step 2.3, the sidelobe level and null beamwidth of the center frequency pattern are denoted as PSLL(X) respectively. new ) and BW(X new The maximum level of the first sideband frequency pattern is denoted as SBL(X). new Set PSLL(X) new To optimize BW(X) new ) and SBL(X new To constrain the process, an optimization model is established under the condition of uniform excitation of the antenna elements:

[0065]

[0066] Where m = 1, 2, ..., M; i = 1, 2, ..., N / P; BWd and SBL d These represent the desired zero-point beamwidth and sideband suppression level, respectively.

[0067] Step 3: The harmony search-convex optimization algorithm is used to optimize the problem and calculate the optimal array layout, time modulation timing, and sidelobe level of the center frequency pattern of the rotationally symmetric four-dimensional array.

[0068] Step 3 shall be carried out in accordance with the following specific steps:

[0069] Step 3.1: The optimization model can be decomposed into a non-convex optimization subproblem with respect to variables (NS, d, Δ, δ) and a convex optimization subproblem with respect to variable T based on the definite solution E0 = (NS0, d0, Δ0, δ0). The harmony search algorithm and the convex optimization algorithm are used to solve for variables (NS, d, Δ, δ) and variable T, respectively.

[0070]

[0071] Step 3.2: Set the control parameters in the harmony search algorithm: harmony memory size HMS, harmony memory retention probability HMCR, pitch adjustment probability PAR, pitch adjustment step size bw, and maximum number of iterations G. max ;

[0072] Step 3.3: Based on the initial settings in Step 3.2, generate the initial harmony memory library E. i,G =(NS) i,G ,d i,G ,Δ i,G ,δ i,G ), i=1,2,···,HMS, G=1,2,···,G max For each individual E i,G The convex optimization subproblem is solved using a convex optimization algorithm, and the optimal solution is denoted as T. i,G Calculate all variables X. i,G =(E i,G ,T i,G The fitness function value of ), i.e., PSLL(NS) i,G ,d i,G ,Δ i,G ,δ i,G ,T i,G Record the optimal solution X in the harmony memory. best,G ;

[0073] Step 3.4: Generate a new solution through random search and local perturbation, calculate its fitness function value, and update the harmony memory. G = G + 1. Record the optimal variable X in the updated harmony memory. best,G With the optimal solution PSLL(X) best,G );

[0074] Step 3.5, if G≤G max If G > G, then repeat step 3.4; max If the algorithm terminates, the output will be X. best With PSLL(X) best According to X) best =(NS) best ,d best ,Δ best ,δ best ,T best The mapping relationships N = g1(NS), r = g2[g1(NS), d, Δ] and ω = g3[g1(NS), δ] are used to obtain N. best r best ω best T best That is, the array layout and timing modulation sequence of the optimal rotationally symmetric four-dimensional array.

[0075] The simulation environment for this invention is: MATLAB R2018b, i7-9700K CPU 3.60GHz, WINDOWS10.

[0076] Set the optimization algorithm control parameters as follows: Harmony Memory Size HMS = 50, Harmony Memory Retention Probability HMCR = 0.9, Pitch Adjustment Probability PAR = 0.3, Pitch Adjustment Step Size bw = 0.1, Maximum Number of Iterations G max =500. The CVX toolkit for convex optimization, based on MATLAB, was used.

[0077] 1. Initial parameter settings for a four-dimensional matrix:

[0078] The total number of antenna array elements is N = 200, the radius of the circular aperture is R = 5λ, the circular aperture is divided into P = 5 sector regions, each sector region is divided into M = 8 sector ring subarrays, and the minimum element spacing d is constrained. min =0.5λ. Desired null beamwidth BW d =15°, sideband suppression level SBL d = -30.

[0079] 2. Simulation content and results:

[0080] Following step 2 and the initial parameters of the four-dimensional matrix, set the optimization variables for the optimization problem: X = (N, r, ω, T) and X... new =(NS,d,Δ,δ,T), where NS=(NS1,NS2,…,NS8), d=(d1,d2,…,d8), Δ=(Δ1,Δ2,…,Δ 40 ), δ=(δ1,δ2,…,δ 40), T=(τ1,τ2,…,τ8); Objective function: PSLL(X new Constraint: 0 ≤ NS m ≤2πm / 5, 0.5λ≤d m ≤λ, 0≤Δ i ≤0.5λ, 0≤δ i ≤2π / 5, 0≤τ m ≤T s , m=1,2,…,8,i=1,2,…,40。Establish an optimization model for a uniformly excited rotationally symmetric four-dimensional matrix as shown in the formula.

[0081] Following step 3 and the set optimization algorithm parameters, the embodiment was optimized using the harmony search-convex optimization algorithm and run independently 10 times. The optimal time modulation sequence and array layout of the rotationally symmetric four-dimensional array were calculated, and the elements within the 8 sector ring subarrays were optimized within one period T. s The switching pulse timing τ / T used internally s As shown in Table 1, the optimal rotationally symmetric four-dimensional matrix layout parameters are shown in Table 2.

[0082] Table 1

[0083]

[0084] Table 2

[0085]

[0086] Table 3

[0087]

[0088] The optimal rotationally symmetric four-dimensional matrix topology obtained after optimization using the harmony search-convex optimization algorithm is as follows: Figure 3 ; Figure 4 Table 3 lists the switching pulse times used by the elements within the 8-sector ring subarray during the period; it also lists the performance parameters of the optimal rotationally symmetric four-dimensional array; the normalized radiation pattern of this array at the center frequency is shown in Table 3. Figure 5 It has a peak sidelobe level of -23.74 dB and a null beamwidth of 14°; the normalized pattern of this array at the first sideband frequency is as follows. Figure 6 The sideband level is less than -31.77dB.

[0089] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. An optimization design method for a rotationally symmetric four-dimensional antenna array, characterized in that, include: The rotationally symmetric four-dimensional antenna array is divided according to the rotationally symmetric structure and subarray division method, and the time modulation method is set after the division. Based on the time modulation method, optimization variables are set, constraints are simplified, and new upper and lower bound constraints are obtained; optimization objectives are set and new upper and lower bound constraints are adopted to construct a rotationally symmetric four-dimensional matrix optimization model. Based on the aforementioned rotationally symmetric four-dimensional array optimization model, and according to the harmony search-convex optimization algorithm optimization problem, the optimal array layout, time modulation timing, and sidelobe level of the center frequency pattern of the rotationally symmetric four-dimensional array are obtained. The method for dividing a rotationally symmetric four-dimensional antenna array based on its rotationally symmetric structure and subarray partitioning includes: dividing the array into subarrays with a radius of... R The circular array aperture is divided into P A rotationally symmetric sector, with a central angle of ∆. φ =2 π / P ; Introduction M A radius is r m The annulus divides each sector into... M Each sector ring region contains antenna elements that form a subarray. m ; Set the total number of array cells to N The number of units in each sector region is N / P , No. m The number of elements within each fan-shaped ring array is N m ; Methods for setting the time modulation mode after division include: Will M Each aperiodic time-modulated T / R component is connected to the subarray. m within N m One antenna element is connected; A periodic time modulation function is generated by controlling a time modulation (T / R) component using a field-programmable gate array (FPGA). Based on the variable aperture size time modulation method, the periodic time modulation function U m ( t This is equivalent to a rectangular pulse function, which occurs within one period. T s The inner waveform is determined by the pulse moment. τ m The only certainty: ； Methods for simplifying constraints to obtain new upper and lower bound constraints include: Based on the optimization variables, define integer vectors and real vectors for upper and lower bound constraints, construct a mapping relationship, set new optimization variables, simplify the constraint conditions, and obtain new upper and lower bound constraints.

2. The optimization design method for a rotationally symmetric four-dimensional antenna array as described in claim 1, characterized in that, The method for setting the optimization variables based on the time modulation method includes: Set the number of elements within the fan-ring array as a vector. N =( N 1, N 2,···, N M ); Set the first m The first fan-shaped array n The position of each antenna element in the polar coordinate system is a vector. a m,n =( r m,n , ω m,n ),in r , ω These are the polar radius vector and the polar angle vector, respectively. Set the time modulation pulse time to T =( τ 1, τ 2,…, τ M ); The optimization variables are: X =( N , r , ω , T The following constraints are met: ， in, M The number of fan-shaped subarrays. m The sequence number of the fan-shaped subarray. n For the first m Antenna element number in a sector ring subarray For the first m The number of antenna elements in a sector ring subarray N This represents the total number of antenna elements. P The number of rotationally symmetric sector regions. R Where is the radius of the circular opening. This represents the minimum spacing between antenna elements. The central angle of the independent sector region, , The first m The first in the fan ring formation n Polar radius and polar angle of each antenna element in polar coordinates , The first k The first in the fan ring formation l Polar radius and polar angle of each antenna element in polar coordinates For the first m The timing of the time-modulated pulses used by the antenna elements in each sector ring subarray The period of the time-modulated rectangular pulse function.

3. The optimization design method for a rotationally symmetric four-dimensional antenna array as described in claim 1, characterized in that, The method for constructing the rotationally symmetric four-dimensional array optimization model by setting an optimization objective and adopting new upper and lower bound constraints includes: setting the sidelobe level of the center frequency pattern as the optimization objective, adopting new upper and lower bound constraints to constrain the zero-point beamwidth and the maximum level of the first sideband frequency pattern, and constructing the rotationally symmetric four-dimensional array optimization model under the condition of uniform excitation of antenna elements.

4. The optimization design method for a rotationally symmetric four-dimensional antenna array as described in claim 3, characterized in that, Based on the rotationally symmetric four-dimensional matrix optimization model, the method for optimizing the problem using the harmony search-convex optimization algorithm includes: solving the new optimization variables using the harmony search algorithm and the convex optimization algorithm respectively; setting the control parameters in the harmony search algorithm; generating an initial harmony memory; using the initial harmony memory to calculate the optimal solution using the convex optimization algorithm; calculating the fitness function value of the optimal solution; and obtaining the optimal solution in the harmony memory.

5. The optimization design method for a rotationally symmetric four-dimensional antenna array as described in claim 4, characterized in that, Methods for obtaining the optimal array layout, time modulation sequence, and sidelobe level of the center frequency pattern of a rotationally symmetric four-dimensional array include: Step 1: Based on the initial harmony memory, generate new solutions using random search and local perturbation, calculate the fitness function value of the new solution using a convex optimization algorithm, and compare it with the fitness function values ​​of each optimization variable in the harmony memory. Eliminate solutions with worse fitness function values ​​and update the harmony memory. Step 2: Update the iterative algebra G = G +1, record the optimal variable and optimal solution in the harmony memory at this time, and determine: if... G ≤ G max , G max If the maximum number of iterations is reached, then return to step one; if... G > G max Then the optimal variables and optimal solutions of the harmony memory are output; Step 3: Based on the optimal variables and mapping relationships of the harmony memory library, obtain the array layout and time modulation sequence of the optimal rotationally symmetric four-dimensional array; based on the optimal solution of the harmony memory library, obtain the sidelobe level of the center frequency pattern.

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