A method and device for optimizing the gain of an array antenna shaped beam with constrained weights

Abstract

The present invention discloses a method and device for optimizing the shaped beam gain of an array antenna with constrained weights. The method sets an array structure and target shaped beam parameters according to a set target; constructs a shaped beam maximization directivity coefficient weight optimization model based on a relationship between weights and directivity coefficients; obtains initial array weights based on the target beam main lobe width; solves and optimizes variables in the optimization model using an alternating direction multiplier method to obtain optimization results, and calculates the raw errors of the variables based on the results, and obtains the maximum raw error through calculation; compares the raw errors with a set error threshold, and if the raw errors are less than the set error threshold, stops iteration and outputs the final array element weights; if the raw errors are not less than the set error threshold, iteratively calculates the raw errors until a set number of iterations is reached, and outputs the final array element weights. The present invention can improve the main lobe gain and reduce the amplitude dynamic range ratio while satisfying the beam shape.

Description

Technical Field

[0001] The present invention relates to the technical field of array antenna optimization design, and in particular to a method and device for optimizing the gain of an array antenna shaped beam with constrained weights. Background Art

[0002] Phased array technology has been widely used in fields such as communications, sonar, navigation, and unmanned driving. In different application fields, the requirements for array beam shapes vary. For example, if a longer effective range is required, a pencil beam is usually used; if the effective range is relatively short, but the effective airspace range is large, a wide beam is usually used. In order to achieve different beam shapes, the signals of individual antennas (i.e., array elements) in the array can be amplitude- and phase-weighted, thereby changing the synthetic ratio of electromagnetic waves in space. Appropriate amplitude- and phase-weighting can often improve the beam performance of the antenna array and provide support for subsequent signal processing such as target detection and recognition. Therefore, the development of a beamforming method with fast optimization speed and good beam performance is of great significance for the application of antenna arrays.

[0003] Currently, many parameters must be considered when implementing beamforming, primarily including mainlobe gain, sidelobe levels, and the dynamic range ratio of the weight amplitude. Determining the weights for a given desired beam is a typical inverse problem, typically solved using optimization algorithms. Widely applicable methods include the SDR method using a semidefinite relaxation strategy. While these methods yield weights that can form the desired beam shape, they overlook two crucial parameters: the dynamic range ratio and mainlobe gain. In practical phased array systems, the mainlobe gain influences range capability, while the dynamic range ratio impacts hardware implementation.

[0004] Therefore, in beamforming, how to improve the mainlobe gain and reduce the amplitude dynamic range ratio while satisfying the beam shape is of great practical significance. Summary of the Invention

[0005] To this end, the present invention provides a method and device for optimizing the shaped beam gain of an array antenna with constrained weights. The method adopts the idea of ​​the alternating direction multiplier method to split the expression of the directivity coefficient. By replacing variables, the mainlobe gain fluctuation, sidelobe level and weight dynamic range are constrained, ultimately achieving the effect of improving the shaped beam gain under multiple constraints.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a method for optimizing the gain of an array antenna shaped beam with constrained weights, comprising:

[0007] According to the set target, set the array structure and target shaped beam parameters;

[0008] According to the relationship between weight and directivity coefficient, a shaped beam maximization directivity coefficient weight optimization model is constructed;

[0009] Obtaining initial array weights according to a target beam main lobe width in the target shaped beam parameters;

[0010] Solving and optimizing the variables in the shaped beam maximization directivity coefficient weight optimization model by an alternating direction multiplier method to obtain an optimization result;

[0011] According to the optimization result, the original error of the variable is calculated; according to the original error, the maximum value of the original error is obtained by calculation;

[0012] The original error is compared with a set error threshold. If the original error is less than the set error threshold, the iterative calculation is stopped and the final array element weight is output. If the original error is not less than the set error threshold, the original error is iteratively calculated until a set number of iterations is reached, and the final array element weight is output.

[0013] As a preferred solution for a method for optimizing the shaped beam gain of an array antenna with constrained weights, the array structure and the target shaped beam parameters include: the number of array elements of the input array, the array element spacing, the main lobe spatial domain range, the side lobe spatial domain range, the upper limit of the target main lobe gain fluctuation, the upper limit of the target side lobe level and the dynamic range of the target weight amplitude.

[0014] As a preferred solution for a method for optimizing the gain of a shaped beam of an array antenna with constrained weights, in the process of constructing the shaped beam maximizing directivity coefficient weight optimization model, an original single-variable model is constructed based on the relationship between the weight and the directivity coefficient; the original single-variable model is rewritten into a multivariable model through an auxiliary variable method and an augmented Lagrange multiplier method; the multivariable model is the shaped beam maximizing directivity coefficient weight optimization model;

[0015] The expression of the shaped beam maximization directivity coefficient weight optimization model is:

[0016]

[0017] st1≤|q m | 2 ≤a mll

[0018] |p s |≤a sll

[0019] ||x|| 2 =1

[0020] L ω ≤|vn |≤U ω

[0021] m=1,2,…,M

[0022] s=1,2,…,S

[0023] n=1,2,…,N

[0024]

[0025] A q =[a(θ1),…,a(θ m ),…,a(θ M )]

[0026] A p =[a(θ1),…,a(θ s ),…,a(θ S )]

[0027] p=[p1,…,p s ,…,p S ] T

[0028] q=[q1,…,q m ,…,q M ] T

[0029] Where, superscript T represents transposition operation; superscript H represents conjugate transposition operation; ρ is the penalty factor; χ q , χ p , χ x , χ v are the Lagrange multipliers of the corresponding variables; M, S, and N are the number of spatial samples within the main lobe range, the number of spatial samples within the side lobe range, and the number of array elements, respectively; μ is the weight scaling factor; x is the total beam power scaling factor; q is the electric field strength of the main lobe of the beam; p is the electric field strength of the side lobe of the beam; x is the total beam electric field strength; v is the weight auxiliary variable; ω is the array weight to be optimized; α mll is the upper bound of the target main lobe gain fluctuation; α sll Target sidelobe level upper limit; a(θ m ), a(θ s ) represent the steering vectors of the mth sampling point in the main lobe and the sth sampling point in the side lobe, respectively; A matrix consisting of array steering vectors for the main lobe region; is the matrix composed of the array steering vectors in the sidelobe area; C is the unit matrix; q m is the electric field intensity at the mth sampling point in the main lobe space; p s is the electric field intensity at the sth sampling point in the main lobe space; Lω is the lower limit of the dynamic range of the target weight amplitude; U ω The upper limit of the dynamic range of the target weight amplitude.

[0030] As an optimal solution for the array antenna shaped beam gain optimization method with constrained weights, in the process of solving and optimizing the variables in the shaped beam maximization directivity coefficient weight optimization model through the alternating direction multiplier method, the variables are divided into two variable blocks; by setting a solution strategy, the variable blocks are solved to complete the solution optimization of the variables.

[0031] As a preferred solution of a weight-constrained array antenna shaped beam gain optimization method, the expression of the original error is:

[0032]

[0033] Where k is the number of iterations.

[0034] The present invention also provides a device for optimizing the gain of an array antenna shaped beam with a constrained weight. The method for optimizing the gain of an array antenna shaped beam with a constrained weight is based on the above method, comprising:

[0035] Array parameter setting module, used to set array structure and target shaped beam parameters according to the set target;

[0036] A module for constructing a shaped beam maximization directivity coefficient weight optimization model is used to construct a shaped beam maximization directivity coefficient weight optimization model based on a relationship between the weight and the directivity coefficient;

[0037] An initial array weight acquisition module is used to acquire initial array weights according to the target beam main lobe width in the target shaped beam parameters;

[0038] A variable solving and optimization module is used to solve and optimize the variables in the shaped beam maximization directivity coefficient weight optimization model by using an alternating direction multiplier method to obtain an optimization result;

[0039] an original error maximum value calculation module, configured to calculate the original error of the variable according to the optimization result; and obtain the original error maximum value by calculation according to the original error;

[0040] The final element weight acquisition module is configured to compare the original error with a set error threshold. If the original error is less than the set error threshold, the iterative calculation is stopped and the final element weight is output. If the original error is not less than the set error threshold, the original error is iteratively calculated until a set number of iterations is reached, and the final element weight is output.

[0041] As a preferred solution for an array antenna shaped beam gain optimization device with constrained weights, in the array parameter setting module, the array structure and the target shaped beam parameters include: the number of array elements of the input array, the array element spacing, the main lobe spatial domain range, the side lobe spatial domain range, the target main lobe gain fluctuation upper limit, the target side lobe level upper limit and the dynamic range of the target weight amplitude.

[0042] As a preferred solution for a device for optimizing the gain of an array antenna shaped beam with constrained weights, in the shaped beam maximizing directivity coefficient weight optimization model construction module, in the process of constructing the shaped beam maximizing directivity coefficient weight optimization model, an original single variable model is constructed according to the relationship between the weight and the directivity coefficient; the original single variable model is rewritten into a multivariable model through the auxiliary variable method and the augmented Lagrange multiplier method; the multivariable model is the shaped beam maximizing directivity coefficient weight optimization model;

[0043] The expression of the shaped beam maximization directivity coefficient weight optimization model is:

[0044]

[0045] st1≤|q m | 2 ≤a mll

[0046] |p s |≤a sll

[0047] ||x|| 2 =1

[0048] L ω ≤|v n |≤U ω

[0049] m=1,2,…,M

[0050] s=1,2,…,S

[0051] n=1,2,…,N

[0052]

[0053] A q =[a(θ1),…,a(θ m ),…,a(θ M )]

[0054] A p =[a(θ1),…,a(θ s ),…,a(θ S )]

[0055] p=[p1,…,p s ,…,p S ] T

[0056] q=[q1,…,q m ,…,q M ] T

[0057] Where, superscript T represents transposition operation; superscript H represents conjugate transposition operation; ρ is the penalty factor; χ q , χ p , χ x , χ v are the Lagrange multipliers of the corresponding variables; M, S, and N are the number of spatial samples within the main lobe range, the number of spatial samples within the side lobe range, and the number of array elements, respectively; μ is the weight scaling factor; x is the total beam power scaling factor; q is the electric field strength of the main lobe of the beam; p is the electric field strength of the side lobe of the beam; x is the total beam electric field strength; v is the weight auxiliary variable; ω is the array weight to be optimized; α mll is the upper bound of the target main lobe gain fluctuation; α sll Target sidelobe level upper limit; a(θ m ), a(θ s ) represent the steering vectors of the mth sampling point in the main lobe and the sth sampling point in the side lobe, respectively; A matrix consisting of array steering vectors for the main lobe region; is the matrix composed of the array steering vectors in the sidelobe area; C is the unit matrix; q m is the electric field intensity at the mth sampling point in the main lobe space; p s is the electric field intensity at the sth sampling point in the main lobe space; L ω is the lower limit of the dynamic range of the target weight amplitude; U ω The upper limit of the dynamic range of the target weight amplitude.

[0058] As an optimal solution for an array antenna shaped beam gain optimization device with constrained weights, in the variable solution optimization module, in the process of solving and optimizing the variables in the shaped beam maximization directivity coefficient weight optimization model by the alternating direction multiplier method, the variables are divided into two variable blocks; by setting a solution strategy, the variable blocks are solved to complete the solution optimization of the variables.

[0059] As a preferred solution of a device for optimizing array antenna shaped beam gain with weight constraints, in the original error maximum value calculation module, the original error is expressed as follows:

[0060]

[0061] Where k is the number of iterations.

[0062] The present invention has the following advantages: according to the set target, the array structure and the target shaped beam parameters are set; according to the relationship between the weight and the directivity coefficient, a shaped beam maximization directivity coefficient weight optimization model is constructed; according to the target beam main lobe width in the target shaped beam parameters, the initial array weight is obtained; the variables in the shaped beam maximization directivity coefficient weight optimization model are solved and optimized by the alternating direction multiplier method to obtain the optimization result; according to the optimization result, the original error of the variable is calculated; according to the original error, the maximum value of the original error is obtained by calculation; the original error is compared with the set error threshold, if the original error is less than the set error threshold, the iterative calculation is stopped and the final array element weight is output; if the original error is not less than the set error threshold, the original error is iteratively calculated until the set number of iterations is reached, and the final array element weight is output. This invention employs the principle of the alternating direction multiplier method, first decomposing the expression for the directivity coefficient. Then, through variable substitution, constraints are imposed on the mainlobe gain fluctuation, sidelobe level, and weight dynamic range. Ultimately, this method improves the shaped beam gain under multiple constraints. This method improves the shaped beam gain while simultaneously controlling the maximum mainlobe gain fluctuation, the highest sidelobe level, and the weight dynamic range to be below preset thresholds. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for the embodiments or the description of the prior art. Obviously, the drawings described below are merely exemplary, and those skilled in the art can, without inventive effort, derive other implementation drawings based on the provided drawings.

[0064] The structures, proportions, sizes, etc. illustrated in this specification are intended solely to complement the contents disclosed herein and to facilitate understanding and reading by persons skilled in the art. They are not intended to limit the conditions under which the present invention may be implemented and therefore have no substantive technical significance. Any structural modifications, changes in proportions, or adjustments in sizes, without affecting the efficacy and objectives of the present invention, shall remain within the scope of the technical contents disclosed herein.

[0065] Figure 1 This is a schematic flow chart of a method for optimizing array antenna shaped beam gain with constrained weights provided in Example 1 of the present invention;

[0066] Figure 2Schematic diagram of initial array weights and normalized directions in a possible embodiment provided in Example 1 of the present invention; wherein (a) is a schematic diagram of the amplitude distribution of initial array weights; (b) is a schematic diagram of the phase distribution of initial array weights; and (c) is a schematic diagram of the initial normalized direction pattern of the array.

[0067] Figure 3 A schematic diagram of a curve showing a change in the original error versus the number of iterations in a possible embodiment provided in Example 1 of the present invention;

[0068] Figure 4 An array pattern obtained by optimizing the iterative convex optimization method, the semi-positive relaxation method, and the method of the present invention in a possible embodiment provided in embodiment 1 of the present invention;

[0069] Figure 5 Schematic diagram of the weight amplitude and weight phase distribution obtained after optimization using the iterative convex optimization method, the semi-positive relaxation method, and the method of the present invention in a possible embodiment provided in Example 1 of the present invention; wherein (a) is a schematic diagram of the weight amplitude distribution; (b) is a schematic diagram of the weight phase distribution;

[0070] Figure 6 This is a schematic diagram of the architecture of an array antenna shaped beam gain optimization device with constrained weights provided in Example 2 of the present invention. DETAILED DESCRIPTION

[0071] The following describes the implementation of the present invention using specific embodiments. Those skilled in the art will readily understand the other advantages and benefits of the present invention from the disclosure herein. Obviously, the embodiments described are only a portion of the present invention, not all of it. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort are intended to fall within the scope of protection of the present invention.

[0072] Example 1

[0073] See also Figure 1 Embodiment 1 of the present invention provides a method for optimizing the gain of an array antenna shaped beam with constrained weights, comprising the following steps:

[0074] S1. Set the array structure and target shaped beam parameters according to the set target;

[0075] S2. Based on the relationship between weight and directivity, a shaped beam maximization directivity coefficient weight optimization model is constructed;

[0076] S3. Obtaining initial array weights according to the target beam main lobe width in the target shaped beam parameters;

[0077] S4. Solving and optimizing the variables in the shaped beam maximization directivity coefficient weight optimization model by an alternating direction multiplier method to obtain an optimization result;

[0078] S5. Calculate the original error of the variable according to the optimization result; and calculate the maximum value of the original error according to the original error;

[0079] S6. Compare the original error with a set error threshold. If the original error is less than the set error threshold, stop the iterative calculation and output the final array element weight. If the original error is not less than the set error threshold, iteratively calculate the original error until a set number of iterations is reached, and output the final array element weight.

[0080] In this embodiment, in step S1, the array structure and target shaped beam parameters are set according to the set target;

[0081] Specifically, according to the set target, set the array structure and target shaped beam parameters. Input the number of array elements N, the element spacing d, the main lobe spatial range [κ1, κ2], the side lobe spatial range [κ3, κ4], the target main lobe gain fluctuation upper bound α mll , target sidelobe level upper bound α sll And the dynamic range of the target weight amplitude [L ω ,U ω ].

[0082] The spatial range of the shaped beam is expressed by angles, where -90<κ1<κ2<90, -90<κ3<κ4<90, and κ3<κ1<κ2<κ4.

[0083] The dynamic range ratio of the weight amplitude refers to the ratio of the maximum amplitude to the minimum amplitude of the weight, that is:

[0084]

[0085] The dynamic range of the preset weight amplitude [L ω ,U ω ] is usually determined according to the following formula:

[0086]

[0087] U ω =γ·L ω

[0088] Where, L ω is the lower limit of the dynamic range of the target weight amplitude; U ω The upper limit of the dynamic range of the target weight amplitude.

[0089] In this embodiment, in step S2, a shaped beam maximizing directivity coefficient weight optimization model is constructed according to the relationship between the weight and the directivity coefficient;

[0090] Specifically, a weight optimization model for shaped beam maximization directivity coefficients is established. First, the original single-variable model is established based on the relationship between weights and directivity coefficients. Then, the auxiliary variable method and augmented Lagrange multiplier method are used to rewrite the original model into a multivariable model.

[0091] A weight optimization model for shaped beam maximization directivity coefficient is established; the optimization model of the original single variable is as follows:

[0092]

[0093] stη≤|a H (θ m )ω|≤a mll η

[0094] |a H (θ s )ω|≤a sll η

[0095] ω H Gω=1

[0096] L ω ≤|ω n |≤U ω

[0097] m=1,2,…,M

[0098] s=1,2,…,S

[0099] n=1,2,…,N

[0100] Where η represents the minimum gain within the main lobe range; M, S, and N represent the number of spatial samples within the main lobe range, the number of spatial samples within the side lobe range, and the number of array elements, respectively. Let the wavelength be λ, and we have:

[0101] a(θ)=[a1(θ),a2(θ),…,a n (θ)…,a N (θ)] T

[0102]

[0103] δ i,j =|ij|d

[0104] 1≤i≤N,1≤j≤N

[0105] Rewrite the original single-variable optimization model into a multi-variable optimization model;

[0106]

[0107] st1≤|q m| 2 ≤a mll

[0108] |p s |≤a sll

[0109] ||x|| 2 =1

[0110] L ω ≤|v n |≤U ω

[0111] m=1,2,…,M

[0112] s=1,2,…,S

[0113] n=1,2,…,N

[0114]

[0115] A q =[a(θ1),…,a(θ m ),…,a(θ M )]

[0116] A p =[a(θ1),…,a(θ s ),…,a(θ S )]

[0117] p=[p1,…,p s ,…,p S ] T

[0118] q=[q1,…,q m ,…,q M ] T

[0119] Where, superscript T represents transposition operation; superscript H represents conjugate transposition operation; ρ is the penalty factor; χ q , χ p , χ x , χ vare the Lagrange multipliers of the corresponding variables; M, S, and N are the number of spatial samples within the main lobe range, the number of spatial samples within the side lobe range, and the number of array elements, respectively; μ is the weight scaling factor; x is the total beam power scaling factor; q is the electric field strength of the main lobe of the beam; p is the electric field strength of the side lobe of the beam; x is the total beam electric field strength; v is the weight auxiliary variable; ω is the array weight to be optimized; α mll is the upper bound of the target main lobe gain fluctuation; α sll Target sidelobe level upper limit; a(θ m ), a(θ s ) represent the steering vectors of the mth sampling point in the main lobe and the sth sampling point in the side lobe, respectively; A matrix consisting of array steering vectors for the main lobe region; is the matrix composed of the array steering vectors in the sidelobe area; C is the unit matrix; q m is the electric field intensity at the mth sampling point in the main lobe space; p s is the electric field intensity at the sth sampling point in the main lobe space; L ω is the lower limit of the dynamic range of the target weight amplitude; U ω The upper limit of the dynamic range of the target weight amplitude.

[0120] In this embodiment, in step S3, initial array weights are obtained according to the target beam main lobe width in the target shaped beam parameters;

[0121] Specifically, the initial array weight ω0 is determined according to the target beam main lobe width:

[0122]

[0123] Where c0 is a parameter that varies with the desired beam shape, and its value range is c0∈[0,1].

[0124] In this embodiment, in step S4, the variables in the shaped beam maximization directivity coefficient weight optimization model are solved and optimized by an alternating direction multiplier method to obtain an optimization result;

[0125] Specifically, each variable is optimized sequentially based on the alternating direction multiplier method. First, the variables in the shaped beam maximization directivity coefficient weight optimization model in step S2 are divided into two variable blocks, thereby converting the original optimization problem into two sub-problems; then, the two sub-problems are solved sequentially.

[0126] The two variable blocks are {q, p, x, v} and {m, x, ω}, and all variables have closed-form expressions.

[0127] 1. Solve the variable block {q,p,x,v}. At the kth (k≥1) iteration,

[0128]

[0129]

[0130] 2. Solve the variable block {m,x,ω}. At the kth (k≥1) iteration,

[0131] ω (k) =(K·K H ) -1 ·K·y

[0132]

[0133] ω (k) =(K·K H ) -1 ·K·y

[0134]

[0135] f m =v (k) -ρ (k-1) χ v (k-1)

[0136]

[0137] Update the penalty factor and dual variable:

[0138] ρ (k) =c1·ρ (k-1)

[0139]

[0140] In this embodiment, in step S5, the original error of the variable is calculated based on the optimization result; and the maximum value of the original error is obtained by calculation based on the original error;

[0141] Specifically, the expression of the original error is:

[0142]

[0143] Where k is the number of iterations.

[0144] In this embodiment, in step S6, the original error is compared with a set error threshold. If the original error is less than the set error threshold, the iterative calculation is stopped and the final array element weight is output. If the original error is not less than the set error threshold, the original error is iteratively calculated until a set number of iterations is reached, and the final array element weight is output.

[0145] Specifically, the original error is compared with a preset error threshold. If the error is less than the threshold, the iteration is stopped and the final element weight is output; otherwise, steps S4 and S5 are repeated until the preset maximum number of iterations is reached.

[0146] In a possible embodiment, a specific example of array antenna shaped beam gain optimization is provided as follows:

[0147] T1, given array structure and multi-beam range;

[0148] Specifically, set the number of array elements N = 32 and the array element spacing Main lobe spatial range [-10°, 10°], side lobe spatial range [-15°, 15°], expected main lobe gain fluctuation upper bound α mll =10 0.2 / 10 , the upper bound of the expected sidelobe level α sll =10 -30 / 10 And the dynamic range ratio of the expected weight amplitude is 5.63, so L ω =0.8769, U ω =4.9370. In addition, a null region is set within the angle [35°, 40°], and the null depth is -60dB.

[0149] T2, shaped beam maximization directivity coefficient weight optimization model;

[0150] Specifically,

[0151]

[0152] st1≤|q m | 2 ≤a mll

[0153] |p s |≤a sll

[0154] ||x|| 2 =1

[0155] L ω ≤|v n |≤U ω

[0156] m=1,2,…,M

[0157] s=1,2,…,S

[0158] n=1,2,…,N

[0159]

[0160] Aq =[a(θ1),…,a(θ m ),…,a(θ M )]

[0161] A p =[a(θ1),…,a(θ s ),…,a(θ S )]

[0162] Take the initial value ρ (0) =1,

[0163] T3, determine the initial array weight ω0 according to the target beam main lobe width;

[0164] Specifically,

[0165]

[0166] Among them, c0 takes The amplitude and phase distribution of the weights and the corresponding directions are as follows: Figure 2 shown.

[0167] T4. In the kth iteration, solve the two variable blocks {q, p, x, v} and {m, x, ω}. Get μ (k) ,x (k) ,q (k) ,p (k) ,x (k) ,v (k) ,ω (k) .

[0168] The value of c1 is:

[0169]

[0170] T5, calculating the original error after the kth iteration based on the result of step T4;

[0171] Specifically,

[0172]

[0173] T6. If Or if k>10000, the iteration is stopped and the final weight ω is output. (k) Otherwise, return to step T4 and perform the k+1th iteration. The logarithm of the original error of all iterations is as follows: Figure 3 As shown in the figure, it can be seen that the method of the present invention has good convergence. After no more than 10,000 iterations, the error is reduced to 10 -8 the following.

[0174] like Figure 4As shown, it can be seen that the semi-definite relaxation method and the method of the present invention can both achieve the same main lobe gain of 6.82 dBi, with a main lobe gain fluctuation of 0.2 dB, while the gain of the iterative convex optimization method is only 6.08 dBi, and the gain fluctuation is much larger than that of the method of the present invention, which is 1.4 dBi.

[0175] like Figure 5 As shown in FIG, after calculation, the amplitude dynamic range ratios of the three methods are 5.63, 437.74 and 5.63 respectively. By comparison, it can be seen that the amplitude dynamic range of the weights optimized by the present invention reaches the minimum value.

[0176] Minimum main lobe gain Sidelobe level Zero sink depth Weighted Dynamic Range Ratio Solution time Iterative Convex Optimization Method 6.08dBi -17.53dB -22.27dB 5.63 12.41 seconds Semidefinite relaxation method 6.82dBi -30dB -60dB 437.74 55.03 seconds Method of the present invention 6.82dBi -30dB -60dB 5.63 3.53 seconds

[0177] Table 1 Performance of different methods

[0178] As shown in Table 1, the performance comparison of the three methods under the same computing environment shows that, under the premise of achieving the same gain, the solution speed of the present invention is increased by 3.5 times and 15 times respectively compared with the existing methods.

[0179] In summary, the present invention sets the array structure and target shaped beam parameters according to the set target; constructs a shaped beam maximization directivity coefficient weight optimization model according to the relationship between the weight and the directivity coefficient; obtains the initial array weight according to the target beam main lobe width in the target shaped beam parameters; solves and optimizes the variables in the shaped beam maximization directivity coefficient weight optimization model by the alternating direction multiplier method to obtain an optimization result; calculates and obtains the original error of the variable according to the optimization result; obtains the maximum value of the original error by calculation according to the original error; compares the original error with the set error threshold, if the original error is less than the set error threshold, stops the iterative calculation and outputs the final array element weight; if the original error is not less than the set error threshold, iteratively calculates the original error until the set number of iterations is reached, and outputs the final array element weight. This invention employs the principle of the alternating direction multiplier method, first decomposing the expression for the directivity coefficient. Then, through variable substitution, constraints are imposed on the mainlobe gain fluctuation, sidelobe level, and weight dynamic range. Ultimately, this method improves the shaped beam gain under multiple constraints. This method improves the shaped beam gain while simultaneously controlling the maximum mainlobe gain fluctuation, the highest sidelobe level, and the weight dynamic range to be below preset thresholds.

[0180] It should be noted that the method of the embodiments of the present disclosure can be performed by a single device, such as a computer or server. The method of the embodiments of the present disclosure can also be applied in a distributed scenario, where multiple devices cooperate to perform the method. In such a distributed scenario, one of the multiple devices may only perform one or more steps of the method of the embodiments of the present disclosure, and the multiple devices will interact with each other to complete the method.

[0181] It should be noted that the above description is limited to some embodiments of the present disclosure. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims may be performed in an order different from that described in the above embodiments and still achieve the desired results. Furthermore, the processes depicted in the accompanying drawings do not necessarily require the specific order or sequential order shown to achieve the desired results. In certain embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0182] Example 2

[0183] See also Figure 6 Embodiment 2 of the present invention further provides an array antenna shaped beam gain optimization device with constrained weights, comprising:

[0184] Array parameter setting module 001 is used to set array structure and target shaped beam parameters according to the set target;

[0185] The shaped beam maximization directivity coefficient weight optimization model construction module 002 is used to construct the shaped beam maximization directivity coefficient weight optimization model according to the relationship between the weight and the directivity coefficient;

[0186] An initial array weight acquisition module 003 is configured to acquire initial array weights according to the target beam main lobe width in the target shaped beam parameters;

[0187] The variable solving and optimizing module 004 is used to solve and optimize the variables in the shaped beam maximization directivity coefficient weight optimization model by using an alternating direction multiplier method to obtain an optimization result;

[0188] The original error maximum value calculation module 005 is used to calculate the original error of the variable according to the optimization result; and obtain the original error maximum value by calculation based on the original error;

[0189] The final element weight acquisition module 006 is configured to compare the raw error with a set error threshold. If the raw error is less than the set error threshold, the iterative calculation is stopped and the final element weight is output. If the raw error is not less than the set error threshold, the raw error is iteratively calculated until a set number of iterations is reached, and the final element weight is output.

[0190] In this embodiment, in the array parameter setting module 001, the array structure and the target shaped beam parameters include: the number of array elements of the input array, the array element spacing, the main lobe spatial domain range, the side lobe spatial domain range, the target main lobe gain fluctuation upper limit, the target side lobe level upper limit and the dynamic range of the target weight amplitude.

[0191] In this embodiment, in the shaped beam maximization directivity coefficient weight optimization model construction module 002, in the process of constructing the shaped beam maximization directivity coefficient weight optimization model, an original single variable model is constructed according to the relationship between the weight and the directivity coefficient; the original single variable model is rewritten into a multivariable model through the auxiliary variable method and the augmented Lagrange multiplier method; the multivariable model is the shaped beam maximization directivity coefficient weight optimization model;

[0192] The expression of the shaped beam maximization directivity coefficient weight optimization model is:

[0193]

[0194] st1≤|q m | 2 ≤a mll

[0195] |p s |≤a sll

[0196] ||x|| 2 =1

[0197] L ω ≤|v n |≤U ω

[0198] m=1,2,…,M

[0199] s=1,2,…,S

[0200] n=1,2,…,N

[0201]

[0202] A q =[a(θ1),…,a(θ m ),…,a(θM )]

[0203] A p =[a(θ1),…,a(θ s ),…,a(θ S )]

[0204] p=[p1,…,p s ,…,p S ] T

[0205] q=[q1,…,q m ,…,q M ] T

[0206] Where, superscript T represents transposition operation; superscript H represents conjugate transposition operation; ρ is the penalty factor; χ q , χ p , χ x , χ v are the Lagrange multipliers of the corresponding variables; M, S, and N are the number of spatial samples within the main lobe range, the number of spatial samples within the side lobe range, and the number of array elements, respectively; μ is the weight scaling factor; x is the total beam power scaling factor; q is the electric field strength of the main lobe of the beam; p is the electric field strength of the side lobe of the beam; x is the total beam electric field strength; v is the weight auxiliary variable; ω is the array weight to be optimized; α mll is the upper bound of the target main lobe gain fluctuation; α sll Target sidelobe level upper limit; a(θ m ), a(θ s ) represent the steering vectors of the mth sampling point in the main lobe and the sth sampling point in the side lobe, respectively; A matrix consisting of array steering vectors for the main lobe region; is the matrix composed of the array steering vectors in the sidelobe area; C is the unit matrix; q m is the electric field intensity at the mth sampling point in the main lobe space; p s is the electric field intensity at the sth sampling point in the main lobe space; L ω is the lower limit of the dynamic range of the target weight amplitude; U ω The upper limit of the dynamic range of the target weight amplitude.

[0207] In this embodiment, in the variable solution optimization module 004, in the process of solving and optimizing the variables in the shaped beam maximization directivity coefficient weight optimization model by the alternating direction multiplier method, the variables are divided into two variable blocks; by setting a solution strategy, the variable blocks are solved to complete the solution optimization of the variables.

[0208] In this embodiment, in the original error maximum value calculation module 005, the original error is expressed as:

[0209]

[0210] Where k is the number of iterations.

[0211] It should be noted that the information interaction, execution process, etc. between the modules of the above-mentioned system are based on the same concept as the method embodiment in Example 1 of the present application, and the technical effects they bring are the same as those of the method embodiment of the present application. For specific contents, please refer to the description in the method embodiment shown above in the present application, and no further details will be given here.

[0212] Example 3

[0213] Embodiment 3 of the present invention provides a non-transitory computer-readable storage medium, in which a program code for an array antenna shaped beam gain optimization method with a constrained weight is stored. The program code includes instructions for executing an array antenna shaped beam gain optimization method with a constrained weight of embodiment 1 or any possible implementation thereof.

[0214] Computer-readable storage media can be any available medium that can be accessed by a computer or a data storage device such as a server or data center that includes one or more available media. The available media can be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., DVDs), or semiconductor media (e.g., solid-state drives (SSDs)).

[0215] Example 4

[0216] Embodiment 4 of the present invention provides an electronic device, including: a memory and a processor;

[0217] The processor and the memory communicate with each other through a bus; the memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute a constrained weight array antenna shaped beam gain optimization method of embodiment 1 or any possible implementation method thereof.

[0218] Specifically, the processor can be implemented by hardware or by software. When implemented by hardware, the processor can be a logic circuit, an integrated circuit, etc.; when implemented by software, the processor can be a general-purpose processor, which is implemented by reading software code stored in a memory. The memory can be integrated into the processor or located outside the processor and exist independently.

[0219] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the process or function described in the embodiment of the present invention is generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable systems. The computer instructions can be stored in a computer-readable storage medium, or transmitted from one computer-readable storage medium to another computer-readable storage medium. For example, the computer instructions can be transmitted from a website, computer, server or data center to another website, computer, server or data center via a wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) mode.

[0220] Obviously, those skilled in the art will appreciate that the various modules or steps of the present invention described above can be implemented using a general-purpose computing system. They can be centralized on a single computing system or distributed across a network of multiple computing systems. Alternatively, they can be implemented using program code executable by a computing system, and thus, they can be stored in a storage system and executed by the computing system. In some cases, the steps shown or described herein can be performed in a different order than that shown, or they can be fabricated into separate integrated circuit modules, or multiple modules or steps can be fabricated into a single integrated circuit module. Thus, the present invention is not limited to any particular combination of hardware and software.

[0221] Although the present invention has been described in detail above using general descriptions and specific embodiments, it will be apparent to those skilled in the art that modifications and improvements may be made thereto. Therefore, such modifications and improvements, without departing from the spirit of the present invention, are intended to be within the scope of protection claimed herein.

Claims

1. A method for optimizing the gain of an array antenna shaped beam with constrained weights, characterized in that: include: According to the set target, set the array structure and target shaped beam parameters; According to the relationship between weight and directivity coefficient, a shaped beam maximization directivity coefficient weight optimization model is constructed; Obtaining initial array weights according to a target beam main lobe width in the target shaped beam parameters; Solving and optimizing the variables in the shaped beam maximization directivity coefficient weight optimization model by an alternating direction multiplier method to obtain an optimization result; According to the optimization result, the original error of the variable is calculated; according to the original error, the maximum value of the original error is obtained by calculation; Comparing the original error with a set error threshold, if the original error is less than the set error threshold, stopping the iterative calculation and outputting the final array element weight; If the original error is not less than the set error threshold, iteratively calculating the original error until a set number of iterations is reached, and outputting the final array element weight; The array structure and the target shaped beam parameters include: the number of array elements, the array element spacing, the main lobe spatial range, the side lobe spatial range, the target main lobe gain fluctuation upper limit, the target side lobe level upper limit and the dynamic range of the target weight amplitude; In the process of constructing the shaped beam maximizing directivity coefficient weight optimization model, an original single variable model is constructed according to the relationship between the weight and the directivity coefficient; the original single variable model is rewritten into a multivariable model through the auxiliary variable method and the augmented Lagrange multiplier method; the multivariable model is the shaped beam maximizing directivity coefficient weight optimization model; The expression of the shaped beam maximization directivity coefficient weight optimization model is: s.t.1≤|q m | 2 ≤α mll |p s |≤α sll ||x|| 2 ＝1 L ω ≤|v n |≤U ω m=1,2,…,M s=1,2,…,S n=1,2,…,N A q =[a(θ1),…,a(θ m ),…,a(θ M )] A p =[a(θ1),…,a(θ s ),…,a(θ S )] p=[p1,…,p s ,…,p S ] T q=[q1,…,q m ,…,q M ] T Where, superscript T represents transposition operation; superscript H represents conjugate transposition operation; ρ is the penalty factor; χ q , χ p , χ x , χ v are the Lagrange multipliers of the corresponding variables; M, S, and N are the number of spatial samples within the main lobe range, the number of spatial samples within the side lobe range, and the number of array elements, respectively; μ is the weight scaling factor; ξ is the total beam power scaling factor; q is the main lobe electric field strength of the beam; p is the side lobe electric field strength of the beam; x is the total beam electric field strength; v is the weight auxiliary variable; ω is the array weight to be optimized; α mll is the upper bound of the target mainlobe gain fluctuation; α sll Target sidelobe level upper limit; a(θ m ), a(θ s ) represent the steering vectors of the mth sampling point in the main lobe and the sth sampling point in the side lobe, respectively; A matrix consisting of array steering vectors for the main lobe region; is the matrix composed of the array steering vectors in the sidelobe area; C is the unit matrix; q m is the electric field intensity at the mth sampling point in the main lobe space; p s is the electric field intensity at the sth sampling point in the main lobe space; L ω is the lower limit of the dynamic range of the target weight amplitude; U ω is the upper limit of the dynamic range of the target weight amplitude.

2. The method for optimizing the shaped beam gain of an array antenna with constrained weights according to claim 1, wherein: In the process of solving and optimizing the variables in the shaped beam maximization directivity coefficient weight optimization model by the alternating direction multiplier method, the variables are divided into two variable blocks; by setting a solution strategy, the variable blocks are solved to complete the solution optimization of the variables.

3. The method for optimizing the shaped beam gain of an array antenna with constrained weights according to claim 2, wherein: The expression of the original error is: Where k is the number of iterations.

4. A device for optimizing the shaped beam gain of an array antenna with a constrained weight, adopting the method for optimizing the shaped beam gain of an array antenna with a constrained weight according to any one of claims 1 to 3, characterized in that: include: Array parameter setting module, used to set array structure and target shaped beam parameters according to the set target; A module for constructing a shaped beam maximization directivity coefficient weight optimization model is used to construct a shaped beam maximization directivity coefficient weight optimization model based on a relationship between the weight and the directivity coefficient; An initial array weight acquisition module is used to acquire initial array weights according to the target beam main lobe width in the target shaped beam parameters; A variable solving and optimization module is used to solve and optimize the variables in the shaped beam maximization directivity coefficient weight optimization model by using an alternating direction multiplier method to obtain an optimization result; an original error maximum value calculation module, configured to calculate the original error of the variable according to the optimization result; and obtain the original error maximum value by calculation according to the original error; a final element weight acquisition module, configured to compare the original error with a set error threshold, and if the original error is less than the set error threshold, stop the iterative calculation and output the final element weight; If the original error is not less than the set error threshold, the original error is iteratively calculated until a set number of iterations is reached, and the final array element weight is output.

5. The apparatus for optimizing array antenna shaped beam gain with constrained weights according to claim 4, wherein: In the variable solution optimization module, in the process of solving and optimizing the variables in the shaped beam maximization directivity coefficient weight optimization model by the alternating direction multiplier method, the variables are divided into two variable blocks; by setting a solution strategy, the variable blocks are solved to complete the solution optimization of the variables.

6. The device for optimizing array antenna shaped beam gain with constrained weights according to claim 5, characterized in that: In the original error maximum value calculation module, the original error expression is: Where k is the number of iterations.

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