Comprehensive method for thin cloth rectangular plane broadband array antenna

Abstract

The invention relates to a thin cloth rectangular plane broadband array antenna synthesis method, and belongs to the technical field of array antenna optimization. The method comprises the following steps: firstly, establishing a mathematical model of a rectangular plane broadband array antenna, initializing parameters of the broadband array antenna, and performing sparse processing on a full array by using a Kaiser weighting function; secondly, initializing a sparse array position population by adopting Tent chaotic mapping, calculating an array element to generate a population fitness function value, and recording an optimal individual; thirdly, adopting an improved grey wolf optimization algorithm to carry out sparse optimization on the sparse array, calculating an updated array element fitness value, extracting an optimal fitness value, recording a corresponding array element position, and outputting an optimal array element position arraying scheme; and finally, obtaining a frequency invariance directional diagram with a smaller side lobe based on the SRV constraint of infinite norm. According to the invention, the number of antenna array elements can be effectively reduced, the frequency-invariant wave beam of the minimum side lobe is realized, and the cost of an antenna system is reduced while the performance of the broadband array antenna is ensured.

Description

Technical Field

[0001] The invention belongs to the field of array antenna synthesis and relates to a method for joint optimization of broadband array antenna position and excitation, which is used for realizing broadband array antenna synthesis of minimum sidelobe frequency invariant beam. Background Art

[0002] Broadband beamforming can narrowband broadband signals by dividing them into sub-bands. Different sub-arrays process each sub-band, so that the directional pattern of each sub-array is approximately constant, and then the sub-arrays are nested to achieve frequency invariance of the broadband directional pattern. Broadband beamforming can be divided into time domain method and frequency domain method. The time domain broadband beamforming method is mainly based on the design method based on the finite impulse response (FIR) filter developed based on the structure proposed by Frost. Its core idea is: when the desired signal is incident vertically into the array, the array pointing error is zero, and the signals of other non-vertically incident arrays can be appropriately delayed so that the delayed signals are transformed into vertically incident signals, and then beamforming is performed. Later, based on this structure, methods based on convex optimization methods, inverse fast Fourier transform methods, and least squares methods appeared to solve the FIR filter coefficients of the frequency invariant beamformer. However, most of these methods study uniform arrays or cannot accurately control the sidelobes, and require a large number of array elements and a high filter order, which will greatly increase the complexity of the system.

[0003] Compared with uniform arrays, non-uniformly spaced arrays (NUSAs) have greater freedom of element position and avoid grating lobes, resulting in better radiation performance. In addition, a smaller number of array elements can achieve advantages such as small system size, low manufacturing cost, and low system power consumption, and are widely used in direction finding, radar, wireless communication and other fields. Therefore, by simultaneously optimizing the filter coefficients and the position distribution of NUSA, the synthesis of broadband frequency-invariant (FI) patterns under multiple constraints can be met to adapt to more application scenarios. In the past few decades, a series of advanced techniques have been proposed to synthesize NUSA arrays with FI, such as harmonic nesting, direct method, l1-based description of spatial response variation (SRV) method, etc. All of the above methods design broadband FI diagrams by optimizing NUSA geometry and FIR filter coefficients. This is very useful for reducing the number of elements required for a given FI pattern requirement. However, in practice, it may be necessary to optimize the excitation weights or element positions to achieve optimization under multiple constraints, such as improving SRV characteristics, reducing beamwidth, suppressing sidelobe levels, specifying array aperture, and sparse array element array design. This is an important issue, but there is little discussion on such NUSA cases. In addition, most frequency-invariant beam arrays are designed from uniform linear arrays or circular arrays, and some have also been developed, such as logarithmically spaced arrays and arbitrary geometric arrays. Different geometric structures produce different performances, but there is little research on rectangular planar arrays.

[0004] With the advancement of numerical computing, intelligent optimization algorithms such as genetic algorithms, particle swarm algorithms, differential evolution algorithms, and sparrow search algorithms have been applied to the analysis and synthesis of antenna arrays, improving computational efficiency and accuracy. However, with the development and application of broadband array antennas and the increasing complexity of antenna structures, traditional optimization algorithms have low solution efficiency and are prone to falling into local optimal solutions when dealing with complex nonlinear problems, and can no longer meet the optimization needs of array antennas. Therefore, it is necessary to find an algorithm with stronger search capabilities and faster convergence performance to achieve array synthesis, reduce computational time, and improve the accuracy of problem solving. Summary of the invention

[0005] The present invention aims to address the deficiencies of the above-mentioned existing methods and provide a synthesis method for a sparse rectangular planar broadband frequency-invariant array antenna based on a hybrid optimization algorithm. First, a sparse rectangular planar broadband array optimization model based on an FIR filter is established, and the initial array position is recorded. The array is weighted using the Kaiser weight function, and the resulting position distribution matrix is ​​used to sparse the array to obtain more possible array distributions. Then, the improved gray wolf optimization algorithm is used to sparsely optimize the array element positions of the sparse array. Then, the SRV l ∞ The norm relaxation convex optimization technology optimizes the array element excitation to achieve frequency-invariant shaping of the main lobe area of ​​the broadband signal. Finally, the final array position distribution and array element excitation optimization scheme are obtained. This method can significantly reduce the number of array elements under multiple constraints, and can further reduce the side lobes of the array antenna pattern while achieving frequency-invariant beams.

[0006] To achieve the above object, the antenna array optimization method of the present invention comprises the following steps:

[0007] Under the constraints of array aperture, number of array elements and minimum array element spacing, the position distribution matrix generated by the Kaiser weight function is used to optimize the number of array elements. Based on the improved grey wolf optimization algorithm, the population is initialized through the Tent chaotic sequence to enhance the diversity of the population and make the algorithm more efficient. ∞ The norm relaxation convex optimization technique is used to optimize the array excitation to achieve frequency-invariant shaping of the main lobe region of the broadband signal, so that it can obtain a lower peak sidelobe level.

[0008] Firstly, based on the hybrid optimization algorithm for broadband frequency-invariant sparse rectangular planar array antenna synthesis, a rectangular broadband array antenna model is defined. According to the geometric requirements, the symmetrical rectangular array aperture is set to 2L×2H, the number of array elements is N, and the array element spacing is the minimum spacing d. c The initial array; set the bandwidth [f L ,fU ], filter order P, reference frequency f r , sampling frequency f s , we can get the directivity function of the sparse rectangular planar broadband array antenna based on FIR filter. At frequency f, angle The directional pattern of the array at is:

[0009]

[0010] in,

[0011]

[0012] w n =[w n,0 ,w n,1 ,...,w n,P-1 ] T

[0013]

[0014] It is characterized by optimizing the array position distribution through the improved gray wolf optimization algorithm, and then using SRV's l ∞ The norm relaxation convex optimization technique performs frequency-invariant beamforming on broadband signals, minimizes the sidelobe level, and maximizes the enhancement in the desired direction. The signal's anti-interference ability includes the following steps:

[0015] 1) The Kaiser weight function is used to obtain the array element position distribution matrix, and the position distribution matrix is ​​used to sparse the uniform array within the aperture. The constraints for array position optimization are obtained based on the sparse array, and the Tent chaotic sequence is used to initialize the population to obtain the initial position distribution of the array antenna, and the corresponding fitness function value is calculated;

[0016] 2) According to the position model part and position optimization constraints of the established sparse rectangular broadband planar array model, the optimized PSLL is taken as the optimization target, and the optimization strategy of the improved gray wolf optimization algorithm is used to fine-tune the above-mentioned initialization population, and the PSLL is substituted into the objective function to calculate the PSLL, and the optimal PSLL and the corresponding array position distribution are obtained;

[0017] 3) Based on the array position distribution obtained by the improved Grey Wolf optimization algorithm, according to the established sparse rectangular broadband planar array model, the optimization of the minimum PSLL is taken as the objective function, and the l of SRV is used. ∞ The norm relaxation convex optimization technique optimizes the array excitation to achieve frequency-invariant shaping of the main lobe area of ​​the broadband signal;

[0018] 4) The optimized array element position distribution is combined with the array element excitation to obtain the final optimization solution, which can reduce the number of array elements while achieving a broadband frequency-invariant beam with strong anti-interference performance.

[0019] Furthermore, the initial array coordinates of the broadband uniform rectangular planar array antenna are:

[0020]

[0021] Among them, P and Q are the maximum number of array elements in the rows and columns of the array.

[0022] Furthermore, the directional pattern function of the sparse rectangular array antenna is:

[0023]

[0024] Where N is the number of array elements; θ is the elevation angle, is the azimuth; (x i ,y i ) represents the coordinate position of the ith array element; T is the position distribution matrix, a matrix composed of 0s and 1s, and the number of 1s is N.

[0025] Use the Kaiser weight function to generate the weight coefficients W of rows and columns respectively m and W n , multiplied by each other, we can get the weighting coefficient of each array element:

[0026]

[0027] Among them, I0 is the first Bessel function; α is the control variable.

[0028] Using the size of the weighted coefficient, the array element position distribution matrix T is generated:

[0029] sum(T) = N.

[0030] Furthermore, the initialization population of the Tent chaotic sequence includes:

[0031] Z i+1 =(2Z i )mod1+rand(0,1) / N p t max

[0032] Among them, Z i+1 is the chaotic sequence obtained after this iteration; mod is the remainder operation; N p is the population, i.e. the number of array antennas; t max is the maximum number of iterations of the algorithm.

[0033] According to the constraints, the generated Tent chaotic sequence is constrained to the set solution range:

[0034]

[0035] Among them, Z d is the generated Tent chaotic sequence; [l xi ,U xi ]=[0,L-(P i -0.5)d c ] is the distributable space of variable dx;

[0036] [l yj ,U yj ]=[0,H-(Q j -0.5)d c ] is the distributable space of variable dy.

[0037] The initial position distribution of the array antenna is obtained according to the array constraints and the initial population generated by the Tent chaotic sequence:

[0038]

[0039]

[0040] Where Δx i,j and Δy i,j Satisfy Δx i,j ∈[l xi ,U xi ], Δy i,j ∈[l yj ,U yj ].

[0041] Furthermore, the optimization function includes:

[0042]

[0043] Where min is the minimum value; f(X,Y) is the fitness function of the array position matrices X and Y; d c is the minimum spacing between units, taken as c / 2f U ; P and Q are the maximum number of array elements placed along the Y-axis and X-axis in the first quadrant;

[0044] P and Q can be determined by the following calculation formula:

[0045]

[0046] Selection of fitness function: Select minimum frequency and maximum frequency The sum of the maximum sidelobe levels of the two planes θ0=0° and θ0=0° is used as the fitness function, then

[0047]

[0048] Among them, max represents the maximum value function; FF max is the maximum value of the main lobe; AF(f U ,θ,0) is the maximum frequency Time direction diagram; is the directivity diagram when the maximum frequency θ0 = 0; AF(f L ,θ,0) is the minimum frequency Time direction diagram;

[0049] This is the radiation pattern when the minimum frequency θ0=0°.

[0050] Furthermore, the optimization strategy of the improved grey wolf optimization algorithm is used to update the position of the array antenna, including:

[0051] 1) After sorting according to the calculated initial fitness function value, select the top three gray wolf individuals with the highest fitness, record them as α wolf, β wolf and δ wolf, and the other individuals as ω wolf. The position of α wolf is defined as the historical optimal solution, the position of β wolf is defined as the second optimal solution, the position of δ wolf is defined as the third optimal solution, and the positions of the other individual ω wolf are defined as candidate solutions.

[0052] 2) The location update process of the gray wolf population is described as follows:

[0053]

[0054] Among them, D α , D β and D δ Respectively represent the distances between other individuals and α, β and δ wolves; X α (t), X β (t) and X δ (t) represents the current position of α, β and δ gray wolves respectively; C1, C2 and C3 are random vectors; X(t) is the current position of the gray wolf; t is the current iteration number. The generation formula of vectors A and C is:

[0055] A=2a·rand(0,1)-a; C=2·rand(0,1)

[0056] Among them, rand(0,1) is a random number in [0,1]; the nonlinear convergence factor a is:

[0057]

[0058] The position update formula of the gray wolf individual is:

[0059]

[0060] Among them, η1, η2, η3 are the weights of gray wolves; η max and η min are the maximum weight factor and the minimum weight factor, which are 4 / 9 and 2 / 9 respectively; X(t+1) is the position of the gray wolf in the next generation.

[0061] 3) After each position update, determine whether the position of each individual, i.e., the unit position of the array, meets the constraint conditions. If not, perform an out-of-bounds correction on its position.

[0062] 4) Combine the optimized array with the position distribution matrix T and calculate the corresponding fitness function value.

[0063] 5) After completing one iteration, the best fitness function value is compared with the recorded initial fitness value. If its fitness value is better, the fitness value and array element position calculated this time are retained and recorded, otherwise they remain unchanged.

[0064] 6) Determine whether the maximum number of iterations has been reached. If so, end the iteration process to obtain the optimal PSLL and the corresponding array position distribution; if not, return to the beginning of the algorithm and recalculate.

[0065] Furthermore, using SRV ∞ The norm-relaxed convex optimization technique updates the matrix excitations including:

[0066] 1) Definition of the maximum peak sidelobe level between different frequencies:

[0067]

[0068] Where i = 1, ..., I, I is the number of sampling points of the elevation visible area set Φ within the passband range; j = 1, ..., J, J is the number of sampling points of the azimuth visible area set Θ within the passband angle range; k = 1, ..., K, K is the number of sampling points within the frequency range; θ s , is the set of sidelobe regions in the elevation and azimuth angles within the passband angle range. The sum of the maximum sidelobe levels of the two planes θ=0° and θ=0° is used as the fitness function, then

[0069]

[0070] Among them, P max (f k ,θ i ,θ j ) is the maximum value of the main lobe; is the maximum value of the directivity pattern when θ0 = 0°; P max (fi ,θ s ,0) is The maximum value of the directional pattern at .

[0071] 2) SRV is defined as a measure of the fluctuation of the array spatial response over the desired frequency band, expressed in discrete form as:

[0072]

[0073] Where, Ω is the frequency band; θ FI is the main lobe area at the pitch angle; is the main lobe area in azimuth. ∞ Describe SRV, its l ∞ The form is as follows:

[0074]

[0075] Among them, ||·|| ∞ Indicates l ∞ norm. In general, in θ FI , After maintaining the FI characteristic, the actual first null point of the main beam will continue to sink deeper and expand outward. Therefore, the actual main beam range is about 2° or 3° larger than this. ∞ represents the maximum value of a vector, which allows constraining each element of the vector. In addition, to synthesize the FI beam diagram, must be small enough to limit the fluctuations in the array spatial response to the desired frequency band, so and θ0=0°, the two planes have:

[0076]

[0077]

[0078] 3) For a two-dimensional rectangular planar array, at both the elevation angle θ and the azimuth angle Constraints on:

[0079] min PSLL1

[0080]

[0081] In order to avoid trivial solutions, the expected direction is introduced response constraints.

[0082] Compared with the prior art, the present invention has the following advantages: the present invention realizes multi-objective optimization (sidelobe level and SRV performance, etc.) under multiple constraints (array aperture and minimum array element spacing, etc.) by simultaneously optimizing array position distribution and array excitation, wherein the improved gray wolf optimization algorithm is used to optimize the array element position of the rectangular planar sparse array antenna, and the SRV l is used to optimize the array element position of the rectangular planar sparse array antenna. ∞ The norm relaxation convex optimization technique is used to optimize the element excitation of the rectangular planar sparse array antenna; the improved gray wolf optimization algorithm is used to optimize the element position of the rectangular planar sparse array antenna, which speeds up the optimization speed compared with other swarm intelligence random search algorithms; the l of SRV is used ∞ The norm relaxation convex optimization technology optimizes the array element excitation, has greater flexibility, and has a smaller variance than the original SRV constraint. Therefore, it realizes the frequency-invariant shaping of the main lobe area of ​​the broadband signal while further reducing the side lobes of the broadband two-dimensional rectangular plane sparse array antenna pattern. Compared with the uniform array antenna with the same caliber, the sparse array antenna of the present invention can significantly reduce the side lobe level while reducing a certain number of array elements and reducing the cost of the system, thereby providing a solution for the optimization of low side lobe array antennas.

[0083] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] In order to make the objectives, technical solutions and advantages of the present invention more clear, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0085] Figure 1 It is a general flow chart for realizing the present invention;

[0086] Figure 2 is a flow chart of the hybrid algorithm of the present invention;

[0087] Figure 3 is the different frequencies obtained by the gray wolf optimization algorithm and the normalized radiation pattern of the θ0 = 0° section;

[0088] Figure 4 This is a schematic diagram of the position distribution of the sparse rectangular array broadband array obtained by the Grey Wolf optimization algorithm;

[0089] Figure 5 The hybrid algorithm is optimized for different frequencies. θ0=0° normalized radiation pattern; DETAILED DESCRIPTION

[0090] The embodiments of the present invention are described by the following specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner, and the following embodiments and the features in the embodiments can be combined with each other without conflict.

[0091] Figure 1 For the overall flow chart of the present invention, refer to Figure 1 , the implementation steps of the present invention are as follows:

[0092] Step 1: Based on the hybrid optimization algorithm, a broadband frequency-invariant sparse rectangular planar array antenna is synthesized. A rectangular broadband array antenna model is defined. According to the geometric requirements, the symmetrical rectangular array aperture is set to 2L×2H, the number of array elements is N, and the array element spacing is the minimum spacing d. c The initial array; set the bandwidth [f L ,f U ], filter order P, reference frequency f r , sampling frequency f s , we can get the directivity function of the sparse rectangular planar broadband array antenna based on FIR filter. At frequency f, angle The directional pattern of the array at is:

[0093]

[0094] in,

[0095]

[0096] w n =[w n,0 ,w n,1 ,...,w n,P-1 ] T

[0097]

[0098] Step 2: The initial array coordinates of the uniform rectangular planar array antenna are:

[0099]

[0100] Among them, P and Q are the maximum number of array elements in the rows and columns of the array.

[0101] Step 3, the directional pattern function of the sparse rectangular broadband array antenna is:

[0102] According to the actual antenna aperture range of the sparse rectangular broadband array antenna, the antenna aperture is determined to be 2L×2H, where the unit is one wavelength; the number of array elements is N; and the minimum spacing between array elements is d c , we get the directional pattern function of the sparse rectangular array antenna:

[0103]

[0104] Where N is the number of array elements; θ is the elevation angle, is the azimuth; (x i ,y i ) represents the coordinate position of the ith array element; T is the position distribution matrix, a matrix composed of 0s and 1s, and the number of 1s is N.

[0105] Step 4: Use the Kaiser weight function to generate the weight coefficients W for rows and columns respectively m and W n , multiplied by each other, we can get the weighting coefficient of each array element:

[0106]

[0107] Among them, I0 is the first Bessel function; α is the control variable.

[0108] Using the size of the weighted coefficient, the array element position distribution matrix T is generated:

[0109]

[0110] Step 5: Use the Tent chaotic sequence to initialize the population, obtain the initial position distribution of the array antenna and calculate its corresponding fitness function value.

[0111] The Tent chaotic sequence is used to initialize the population, and the following formula is used for self-mapping of Tent chaos:

[0112] Z i+1 =(2Z i )mod1+rand(0,1) / N p t max (6)

[0113] Among them, Z i+1 is the chaotic sequence obtained after this iteration; mod is the remainder operation; N P is the population, i.e. the number of array antennas; t max is the maximum number of iterations of the algorithm.

[0114] According to the constraints, the generated Tent chaotic sequence is constrained to the set solution range:

[0115]

[0116] Among them, Z d is the generated Tent chaotic sequence; [l xi ,U xi ]=[0,L-(P i -0.5)d c ] is the distributable space of variable dx;

[0117] [l yj ,U yj ]=[0,H-(Q j -0.5)d c ] is the distributable space of variable dy.

[0118] In order to narrow the search range of the position matrix, the X-axis and Y-axis coordinate matrices of the array element position are expressed as:

[0119]

[0120] Where Δx i,j and Δy i,j Satisfy Δx i,j ∈[l xi ,U xi ], Δy i,j ∈[l yj ,U yj ].

[0121] Step 6: Based on the array antenna aperture L×H, number of array elements N, and minimum array element spacing d determined in step 3 c Optimization objectives and constraints for constructing rectangular planar sparse array antennas:

[0122]

[0123] Where min is the minimum value; f(X,Y) is the fitness function of the array position matrices X and Y; d c is the minimum spacing between units, taken as c / 2f U ; P and Q are the maximum number of array elements placed along the Y-axis and X-axis in the first quadrant;

[0124] P and Q are the maximum number of array elements that can be placed along the Y-axis and X-axis in the first quadrant, which are determined by the following calculation formula:

[0125]

[0126] When N=P×Q, the array is full; when N<P×Q, the array is a sparse matrix. According to the constraints of the array aperture, P×QN array elements with smaller weights are sparsely removed, and the outermost array elements, that is, the array elements in the Pth row and the Qth column, are always retained.

[0127] Select minimum and maximum frequencies The sum of the maximum sidelobe levels of the two planes θ0=0° and θ0=0° is used as the fitness function, then

[0128]

[0129] Among them, max represents the maximum value function; FF max is the maximum value of the main lobe; AF(f U ,θ,0) is the maximum frequency Time direction diagram; is the directivity diagram when the maximum frequency θ0 = 0; AF(f L ,θ,0) is the minimum frequency Time direction diagram;

[0130] This is the radiation pattern when the minimum frequency θ0=0°.

[0131] Step 7, after sorting according to the calculated initial fitness function value, select the top three gray wolf individuals with the highest fitness, record them as α wolf, β wolf and δ wolf, and the other individuals as ω wolf. The position of α wolf is defined as the historical optimal solution, the position of β wolf is defined as the suboptimal solution, the position of δ wolf is defined as the third optimal solution, and the positions of the other individual ω wolf are defined as candidate solutions.

[0132] The position update process of the gray wolf population is described as follows:

[0133]

[0134] Among them, D α , D β and D δ Respectively represent the distances between other individuals and α, β and δ wolves, X α (t), X β (t) and X δ (t) represents the current position of the gray wolf α, β and δ respectively, C1, C2 and C3 are random vectors, X(t) is the current position of the gray wolf, and t is the current iteration number. The generation formula of vectors A and C is:

[0135] A=2a·rand(0,1)-a; C=2·rand(0,1) (14)

[0136] Where rand(0,1) is a random number in the range [0,1]. The nonlinear convergence factor a is:

[0137]

[0138] The position update formula of the gray wolf individual is:

[0139]

[0140] Among them, η1, η2, η3 are the weights of gray wolves; η max and η min are the maximum weight factor and the minimum weight factor, which are 4 / 9 and 2 / 9 respectively; X(t+1) is the position of the gray wolf in the next generation.

[0141] After each position update, the present invention extracts the X coordinate and Y coordinate of the position of each array element in each array, and determines whether it is within [l xi ,U xi ]=[0,L-(P i -0.5)d c ] and [l yj ,U yj ]=[0,H-(Q j -0.5)d c ], if it exceeds the boundary range, it is corrected for the out-of-bounds situation, and after obtaining the optimized values ​​of variables dx and dy, it is substituted into equations (8) and (9) to obtain the coordinates (x, y) of the initial array unit position distribution.

[0142] Step 8, combine the optimized array and the array element position distribution matrix T and substitute them into the fitness function to iteratively calculate the fitness function value, and compare the objective function value of this optimization result with the recorded highest sidelobe level. If the fitness function value of this optimization result is less than the highest sidelobe level, save this optimization result and make the highest sidelobe level equal to the fitness function value of this optimization result. Otherwise, ignore this optimization result.

[0143] Return to step 7 until the loop ends, and the optimal PSLL and array element position distribution are obtained.

[0144] Step 9, use SRV l ∞ The norm-relaxed convex optimization technique updates the matrix excitations including:

[0145] 1) Definition of the maximum peak sidelobe level between different frequencies:

[0146]

[0147] Where i = 1, ..., I, I is the number of sampling points of the elevation visible area set Φ within the passband range; j = 1, ..., J, J is the number of sampling points of the azimuth visible area set Θ within the passband angle range; k = 1, ..., K, K is the number of sampling points within the frequency range; θ s , is the set of sidelobe regions in the elevation and azimuth angles within the passband angle range. The sum of the maximum sidelobe levels of the two planes θ=0° and θ=0° is used as the fitness function, then

[0148]

[0149] Among them, P max (f k ,θ i ,θ j ) is the maximum value of the main lobe; is the maximum value of the directivity pattern when θ0 = 0°; P max (f i ,θ s ,0) is The maximum value of the directional pattern at .

[0150] 2) SRV is defined as a measure of the fluctuation of the array spatial response over the desired frequency band, expressed in discrete form as:

[0151]

[0152] Where, Ω is the frequency band; θ FI is the main lobe area at the pitch angle; is the main lobe area in azimuth. ∞ Describe SRV, its l ∞ The form is as follows:

[0153]

[0154] Among them, ||·|| ∞ Indicates l ∞ norm. In general, in θ FI , After maintaining the FI characteristic, the actual first null point of the main beam will continue to sink deeper and expand outward. Therefore, the actual main beam range is about 2° or 3° larger than this. ∞ represents the maximum value of a vector, which allows constraining each element of the vector. In addition, to synthesize the FI beam diagram, must be small enough to limit the fluctuations in the array spatial response to the desired frequency band, so and θ0=0°, the two planes have:

[0155]

[0156] For a two-dimensional rectangular planar array, at both the elevation angle θ and the azimuth angle Constraints on:

[0157]

[0158] In order to avoid trivial solutions, the expected direction is introduced response constraints.

[0159] The effect of the present invention is further illustrated by the following simulation experiment:

[0160] The present invention uses an improved grey wolf optimization algorithm to optimize the element positions of rectangular planar sparse array antennas, using SRV's l ∞ The norm relaxation convex optimization technology optimizes the array element excitation, which has the characteristics of better optimization speed and flexibility. Compared with the sparse rectangular planar broadband array that only optimizes the array element position, it can significantly reduce the sidelobe electric while achieving the FI characteristic.

[0161] 1) Simulation parameter setting: The aperture of the rectangular sparse array antenna is 2L×2H=9.5λ U ×4.5λ U , the number of array elements N = 108, the minimum array element spacing constraint d c =0.5λ U , bandwidth is [300, 400] MHz, filter order P = 10, sampling frequency is f s =2f U , the reference frequency is f r =(f L +f U ) / 2, at θ0 = 0°, the main beam width is set to 10°, Section, the main beam width is set to 5°, and the array element positions of the rectangular sparse array antenna are symmetrical about the center of the array antenna. The simulation experiment is carried out on MATLAB software.

[0162] 2) Simulation content

[0163] According to the parameter settings, the objective function and constraints of the rectangular sparse array antenna are constructed according to step 6. In this simulation experiment, the fitness function f(X, Y) is set to and θ0=0° is the sum of the maximum sidelobe levels in the two planes.

[0164] according to Figure 2 Write a program according to the process in , with the number of loops I = 300 in the program, and run the program to obtain the optimal PSLL and its corresponding array element position distribution matrix.

[0165] Figure 3 To optimize the array position only, the different frequencies are obtained. The normalized radiation pattern of the section with θ0 = 0° is obtained by optimizing this method. The peak sidelobe level under the cut plane is -16.29dB; the peak sidelobe level under the cut plane of θ0=0° is -14.15dB.

[0166] Figure 5 The array position and excitation optimization are optimized simultaneously. The normalized radiation pattern of the section with θ0 = 0 is obtained by optimizing this method. The peak sidelobe level under the cut plane is -19.32dB, and the main beam width is [-7°, 7°]; the peak sidelobe level under the cut plane of θ0=0° is -21.74dB, and the main beam width is [-12°, 12°].

[0167] From the comparison of the sidelobe level optimization results, it can be seen that under the premise of fixing the array aperture and the number of array elements, the method of simultaneous optimization of array position and excitation optimization can achieve the frequency invariance of the main beam and better suppress the sidelobe level of the array antenna compared to only optimizing the unit position of the array.

[0168] It should be noted that the above embodiments are only illustrative of the principles and effects of the present invention, and are not intended to limit the present invention. Anyone familiar with the technology may modify or change the above embodiments without violating the spirit and scope of the present invention. Therefore, all equivalent modifications or changes made by those with ordinary knowledge in the technical field without departing from the spirit and technical ideas disclosed by the present invention should still be covered by the claims of the present invention.

Claims

1. Synthesis of broadband frequency-invariant sparse rectangular planar array antenna based on hybrid optimization algorithm. Define the rectangular broadband array antenna model. According to the geometric requirements, set the symmetrical rectangular array aperture 2L×2H, the number of array elements N, and the array element spacing to the minimum spacing d. c The initial array; set the bandwidth [f L ,f U ], filter order P, reference frequency f r , sampling frequency f s , the directional pattern function of the sparse rectangular planar broadband array antenna based on the finite impulse response (FIR) filter is obtained. At frequency f, angle The directional pattern of the array at is: in, In n =[in n,0 ,In n,1 ,...,In n,P-1 ] T It is characterized by optimizing the array position distribution through the improved gray wolf optimization algorithm, and then using the spatial response variation (SRV) algorithm on this basis. ∞ The norm relaxation convex optimization technique performs frequency-invariant beamforming on broadband signals, minimizes the sidelobe level, and maximizes the enhancement in the desired direction. The anti-interference ability of the signal. Specifically includes the following steps: 1) The Kaiser weight function is used to obtain the array element position distribution matrix, and the position distribution matrix is ​​used to sparse the uniform array within the aperture. The constraints for array position optimization are obtained based on the sparse array, and the Tent chaotic sequence is used to initialize the population to obtain the initial position distribution of the array antenna, and the corresponding fitness function value is calculated; 2) According to the position model part and position optimization constraints of the established sparse rectangular broadband planar array model, the optimized peak sidelobe level (PSLL) is taken as the optimization target, and the optimization strategy of the improved grey wolf optimization algorithm is used to perform fine-tuning on the above-mentioned initialization population; 3) Calculate the fitness, select the array position distribution with the lowest PSLL and symmetrically obtain the array position distribution scheme; 4) Based on the array position distribution obtained by the improved Grey Wolf optimization algorithm, according to the established sparse rectangular broadband planar array model, the optimization of the minimum PSLL is taken as the objective function, and the l of SRV is used. ∞ The norm relaxation convex optimization technology optimizes the array element excitation to achieve frequency-invariant shaping of the main lobe area of ​​the broadband signal; 5) The optimized array element position distribution is combined with the array element excitation to obtain the final optimization solution, which can reduce the number of array elements while achieving a broadband frequency-invariant beam with strong anti-interference performance.

2. The method according to claim 1, characterized in that 1) The initial array coordinates of the broadband uniform rectangular planar array antenna are: Among them, P and Q are the maximum number of array elements in the rows and columns of the array. 2) The directional pattern function of the sparse rectangular array antenna is: Where N is the number of array elements; θ is the elevation angle, is the azimuth; (x i ,y i ) represents the coordinate position of the ith array element; T is the position distribution matrix, a matrix composed of 0s and 1s, and the number of 1s is N. Use the Kaiser weight function to generate the weight coefficients W of rows and columns respectively m and W n , multiplied by each other, we can get the weighting coefficient of each array element: Among them, I0 is the first Bessel function; α is the control variable. Using the size of the weighted coefficient, the array element position distribution matrix T is generated:

3. The method according to claim 1, characterized in that The initialization population of Tent chaotic sequence includes: Z i+1 =(2Z i )mod1+rand(0,1) / N p t max Among them, Z i+1 is the chaotic sequence obtained after this iteration; mod is the remainder operation; N p is the population, i.e. the number of array antennas; t max is the maximum number of iterations of the algorithm. According to the constraints, the generated Tent chaotic sequence is constrained to the set solution range: Among them, Z d is the generated Tent chaotic sequence; [l xi ,U xi ]=[0,L-(P i -0.5)d c ] is the distributable space of variable dx; [l yj ,U yj ]=[0,H-(Q j -0.5)d c ] is the distributable space of variable dy. The initial position distribution of the array antenna is obtained according to the array constraints and the initial population generated by the Tent chaotic sequence: Among them, Δx i,j Sum Δy i,j full foot Δx i,j ∈[l xi ,U xi ], Δy i,j ∈[l yj ,U yj ].

4. The method according to claim 1, characterized in that: The optimization function includes: Where min is the minimum value; f(X,Y) is the fitness function of the array position matrices X and Y; d c is the minimum spacing between units, taken as c / 2f U ; P and Q are the maximum number of array elements placed along the Y-axis and X-axis in the first quadrant; P and Q can be determined by the following calculation formula: Selection of fitness function: Select minimum frequency and maximum frequency The sum of the maximum sidelobe levels of the two planes θ0=0° and θ0=0° is used as the fitness function, then Among them, max represents the maximum value function; FF max is the maximum value of the main lobe; AF(f U ,θ,0) is the maximum frequency Time direction diagram; is the directivity diagram when the maximum frequency θ0 = 0°; AF(f L ,θ,0) is the minimum frequency Time direction diagram; This is the radiation pattern when the minimum frequency θ0=0°.

5. The method according to claim 1, characterized in that The optimization strategy of the improved grey wolf optimization algorithm for updating the array antenna position includes: 1) After sorting according to the calculated initial fitness function value, select the top three gray wolf individuals with the highest fitness, record them as α wolf, β wolf and δ wolf, and the other individuals as ω wolf. The position of α wolf is defined as the historical optimal solution, the position of β wolf is defined as the second optimal solution, the position of δ wolf is defined as the third optimal solution, and the positions of the other individual ω wolf are defined as candidate solutions. 2) The location update process of the gray wolf population is described as follows: Among them, D α , D β and D δ Respectively represent the distances between other individuals and α, β and δ wolves; X α (t), X β (t) and X δ (t) represents the current position of α, β and δ gray wolves respectively; C1, C2 and C3 are random vectors; X(t) is the current position of the gray wolf; t is the current iteration number. The generation formula of vectors A and C is: A=2a·rand(0,1)-a; C=2·rand(0,1) Among them, rand(0,1) is a random number in [0,1]; the nonlinear convergence factor a is: The position update formula of the gray wolf individual is: Among them, η1, η2, η3 are the weights of gray wolves; η max and η min are the maximum weight factor and the minimum weight factor, which are 4 / 9 and 2 / 9 respectively; X(t+1) is the position of the gray wolf in the next generation. 3) After each position update, determine whether the position of each individual, i.e., the unit position of the array, meets the constraint conditions. If not, perform an out-of-bounds correction on its position. 4) The optimized array is combined with the position distribution matrix T obtained in claim 2 to calculate the corresponding fitness function value. 5) After completing one iteration, the best fitness function value is compared with the recorded initial fitness value. If its fitness value is better, the fitness value and array element position calculated this time are retained and recorded, otherwise they remain unchanged. 6) Determine whether the maximum number of iterations has been reached. If so, end the iteration process to obtain the optimal PSLL and the corresponding array position distribution; if not, return to the beginning of the algorithm and recalculate.

6. The method according to claim 1, characterized in that Using SRV ∞ The norm-relaxed convex optimization technique updates the matrix excitations including: 1) Definition of the maximum peak sidelobe level between different frequencies: Where i = 1, ..., I, I is the number of sampling points of the elevation visible area set Φ within the passband range; j = 1, ..., J, J is the number of sampling points of the azimuth visible area set Θ within the passband angle range; k = 1, ..., K, K is the number of sampling points within the frequency range; θ s , is the set of sidelobe regions in the elevation and azimuth angles within the passband angle range. The sum of the maximum sidelobe levels of the two planes θ=0° and θ=0° is used as the fitness function, then Among them, P max (f k ,θ i ,θ j ) is the maximum value of the main lobe; is the maximum value of the directivity pattern when θ0 = 0°; P max (f i ,θ s ,0) is The maximum value of the directional pattern at . 2) SRV is defined as a measure of the fluctuation of the array spatial response over the desired frequency band, expressed in discrete form as: Where, Ω is the frequency band; θ FI is the main lobe area at the pitch angle; is the main lobe area in azimuth. ∞ Describe SRV, its l ∞ The form is as follows: Among them, ||·|| ∞ Indicates l ∞ norm. In general, in θ FI , After maintaining the FI characteristic, the actual first null point of the main beam will continue to sink deeper and expand outward. Therefore, the actual main beam range is about 2° or 3° larger than this. ∞ represents the maximum value of a vector, which allows constraining each element of the vector. In addition, to synthesize the FI beam diagram, must be small enough to limit the fluctuations in the array spatial response to the desired frequency band, so and θ0=0°, the two planes have: 3) For a two-dimensional rectangular planar array, at both the elevation angle θ and the azimuth angle Constraints on: In order to avoid trivial solutions, the expected direction is introduced response constraints.

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