Amplitude-phase weighted beamforming method for array antennas based on sine-cosine optimization algorithm

Abstract

The present invention discloses an array antenna amplitude-phase weighted beamforming method based on a sine-cosine optimization algorithm, and belongs to the technical field of array antenna beamforming. The present invention obtains the desired shaped beam pattern by adjusting the amplitude and phase of the array element to meet the detection needs in different situations. The fitness function of the constructed different shaped beams is used as the fitness function, and the sine-cosine optimization algorithm is used to iteratively optimize each individual in the population under the constructed fitness function until the optimal amplitude-phase weight vector is output as the target amplitude-phase weight vector after the conditions are met, thereby obtaining the beamforming result, and the volatility and periodicity of the sine-cosine function are used as the design goals of the realization operator to search and iterate the optimal solution. The sine-cosine oscillation variation characteristics bring about a good solution space search capability, with the characteristics of few parameters, simple structure, easy implementation and fast convergence speed, and can quickly search and obtain the ideal beam pattern to meet the detection needs in different situations.

Description

Technical Field

[0001] The invention belongs to the technical field of array antenna beamforming, and in particular relates to an array antenna amplitude-phase weighted beamforming method based on a sine-cosine optimization algorithm. Background Art

[0002] Radar is a device that obtains target-related information by emitting electromagnetic waves to the target and receiving electromagnetic waves reflected from the target. When transmitting, the radar needs to concentrate its energy to the direction of the target; when receiving, the echo power received in the direction of the target needs to be strong enough to measure the azimuth and elevation angle of the target. Therefore, the detection performance of the radar is closely related to the response of the radar pattern.

[0003] Array antenna beamforming technology forms a special beam by changing the amplitude and phase of the excitation of each element in the antenna array, so as to obtain a more effective radiation intensity within a specific range. Therefore, the methods of antenna beamforming can be divided into two categories: the first category is to adjust the excitation amplitude and phase of the unit at the same time, that is, the amplitude and phase are weighted at the same time; the second category is to only adjust the excitation phase of the unit, that is, phase weighting. The current mainstream methods of array antenna beamforming technology are mainly divided into two categories: analytical methods and intelligent optimization algorithms. The analytical method mainly converts the desired antenna pattern into a function expression, and approximates the desired pattern result through different types of polynomial fitting or equation solving. The analytical method usually has a complex solution process and a large amount of calculation, and it is difficult to solve non-convex optimization problems that are only phase-weighted.

[0004] Intelligent optimization algorithms mainly include: genetic algorithm, particle swarm algorithm, simulated annealing algorithm, etc. Due to their strong global optimization performance, strong versatility, and suitability for parallel processing, they have attracted widespread attention from system designers and have been applied in many technical requirements for beamforming with array antenna patterns. Existing intelligent optimization algorithms for beamforming generally have complex structures, long convergence time, and are prone to falling into local optimal solutions. Existing optimization algorithms only optimize through amplitude weighting or phase weighting, making it difficult for beamforming technology to achieve the desired pattern shape due to its low degree of freedom, and the accuracy of the obtained shaped beam is poor. In addition, existing beamforming algorithms that only use phase weighting mainly use intelligent optimization algorithms such as genetic algorithms and particle swarm algorithms. These algorithms are sensitive to population initialization, and have complex structures, long convergence time, are prone to falling into local optimal solutions, and are difficult to find global optimal solutions. Summary of the invention

[0005] In order to solve the above problems existing in the prior art, the present invention provides a beamforming method of array antenna amplitude and phase weighting based on sine and cosine optimization algorithm. The technical problem to be solved by the present invention is achieved by the following technical solutions:

[0006] The present invention provides a beamforming method for array antenna amplitude and phase weighting based on a sine-cosine optimization algorithm, the method comprising:

[0007] Based on the radar array information and scanning range, the coordinates and steering vectors of each array element in the radar array are obtained as array element parameters of each array element;

[0008] Based on the radar application scenario, array information and array element parameters, the expected radiation pattern and fitness function of the shaped beam are constructed;

[0009] According to the array information, array element parameters and the expected directional pattern of the shaped beam, the maximum number of iterations, the population size and the iteration parameters of the preset iterative equation of the sine-cosine optimization algorithm are selected;

[0010] Based on the fitness function, the fitness of each individual in the population is obtained, and the optimal fitness and the optimal amplitude and phase weight vector corresponding to the optimal fitness are recorded; based on a preset iterative equation, each individual in the population is updated; and the iterative parameters in the preset iterative equation are updated to complete an iterative process;

[0011] Based on the updated preset iterative equation, the updated individuals in the population are iterated for several times until the number of current iterative processing reaches the maximum number of iterations or the optimal fitness in the current iterative processing is less than the preset standard, and the optimal amplitude-phase weight vector in the current iterative processing is output as the target amplitude-phase weight vector;

[0012] A beamforming result is obtained based on the target amplitude and phase weight vector.

[0013] Beneficial effects of the present invention:

[0014] In the solution provided by the present invention, the expected radiation pattern of the shaped beam is obtained by the amplitude and phase of the corresponding array element to meet the detection needs in different situations. The fitness function corresponding to the different shaped beams is constructed, and the sine-cosine optimization algorithm is used to iteratively optimize each individual in the population under the constructed fitness function until the optimal amplitude-phase weight vector is output as the target amplitude-phase weight vector after the conditions are met, thereby obtaining the beamforming result, and the volatility and periodicity of the sine and cosine functions are used as the design goals of the implementation operator to search and iterate the optimal solution. The sine-cosine oscillation variation characteristics bring good solution space search capabilities, with the characteristics of few parameters, simple structure, easy implementation and fast convergence speed, and can quickly search and obtain a beam radiation pattern with a more ideal expected shape to meet the detection needs in different situations. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 A schematic diagram of the steps of a beamforming method for array antenna amplitude and phase weighting based on a sine-cosine optimization algorithm provided in an embodiment of the present invention;

[0016] Figure 2 A schematic diagram of the principle of a sine-cosine optimization algorithm in an array antenna amplitude-phase weighted beamforming method based on a sine-cosine optimization algorithm provided in an embodiment of the present invention;

[0017] Figure 3 An angle definition diagram of a linear array provided by an embodiment of the present invention;

[0018] Figure 4 An angle definition diagram of a planar array provided by an embodiment of the present invention;

[0019] Figure 5 Iteration parameters in the preset iterative equation provided in the embodiment of the present invention Amplitude variation diagram of ;

[0020] Figure 6 In the preset iterative equation provided in the embodiment of the present invention and Amplitude variation diagram of ;

[0021] Figure 7 A fitness evolution curve diagram of the cosecant square beam provided in an embodiment of the present invention;

[0022] Figure 8 A shaped directivity pattern of a cosecant square beam provided by an embodiment of the present invention;

[0023] Fig. 9 A timing diagram of a shaping procedure for a cosecant square beam provided in an embodiment of the present invention;

[0024] Fig.10 A fitness evolution curve diagram of a flat-top beam provided in an embodiment of the present invention;

[0025] Fig.11 A shaped pattern of a flat-top beam provided by an embodiment of the present invention;

[0026] Fig.12 A timing diagram of a shaping procedure for a flat-top beam provided in an embodiment of the present invention;

[0027] Fig.13 A fitness evolution curve diagram of a pencil beam provided in an embodiment of the present invention;

[0028] Fig.14 A shaped pattern of a pencil beam provided by an embodiment of the present invention;

[0029] Fig.15 A timing diagram of a pencil beam shaping procedure provided in an embodiment of the present invention;

[0030] Fig.16A diagram of the layout of a planar array provided by an embodiment of the present invention;

[0031] Fig.17 The original directional pattern of the planar array provided by the embodiment of the present invention;

[0032] Fig.18 The original 3D direction diagram of the planar array provided by the embodiment of the present invention;

[0033] Fig.19 A flat-top beam fitness evolution curve diagram of a planar array provided in an embodiment of the present invention;

[0034] Fig. 20 A flat-top beamforming pattern of a planar array provided by an embodiment of the present invention;

[0035] Fig.21 This is a flat-top beamforming 3D pattern of a planar array provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0036] The present invention is further described in detail below with reference to specific embodiments, but the embodiments of the present invention are not limited thereto.

[0037] The embodiment of the present invention provides a beamforming method for an array antenna based on a sine-cosine optimization algorithm and an amplitude-phase weighted beamforming method. Figure 1 As shown, it may include:

[0038] S1, based on the radar array information and scanning range, obtain the coordinates and steering vectors of each array element in the radar array as array element parameters of each array element;

[0039] S2, based on the radar application scenario, array information and array element parameters, construct the expected radiation pattern and fitness function of the shaped beam;

[0040] S3, selecting the maximum number of iterations, the population size and the iteration parameters of the preset iteration equation of the sine-cosine optimization algorithm according to the array information, the array element parameters and the expected directivity pattern of the shaped beam;

[0041] S4, based on the fitness function, obtain the fitness of each individual in the population, record the optimal fitness and the optimal amplitude and phase weight vector corresponding to the optimal fitness; based on the preset iterative equation, update each individual in the population; update the iterative parameters in the preset iterative equation to complete one iteration process;

[0042] S5, based on the updated preset iterative equation, perform several iterative processes on the updated individuals in the population until the number of current iterative processes reaches the maximum number of iterative processes or the optimal fitness in the current iterative process is less than the preset standard, and output the optimal amplitude-phase weight vector in the current iterative process as the target amplitude-phase weight vector;

[0043] S6, obtaining a beamforming result based on the target amplitude and phase weight vector.

[0044] The embodiments of the present invention solve the problem that it is difficult to obtain an ideal radiation pattern only by phase weighting or amplitude weighting and that the existing intelligent optimization algorithm is prone to fall into the optimal solution. The embodiments of the present invention construct the fitness function of different shaped beams of linear arrays and planar arrays as the fitness function, use the sine-cosine optimization algorithm to iteratively optimize each individual in the population under the constructed fitness function, and output the optimal amplitude-phase weight vector as the target amplitude-phase weight vector after the conditions are met, thereby obtaining the beamforming result, using the volatility and periodicity of the sine and cosine functions as the design goal of the operator to search and iterate the optimal solution, adjust the amplitude and phase simultaneously, have greater freedom, can obtain more accurate beamforming results, and have good engineering application value.

[0045] For ease of understanding, each step of the beamforming method for array antenna amplitude and phase weighting based on the sine-cosine optimization algorithm proposed in an embodiment of the present invention is described below.

[0046] First, the sine-cosine optimization algorithm is introduced. The sine-cosine optimization algorithm uses the periodic volatility of sine and cosine functions to construct a preset iterative equation that realizes the two thread functions of global search and local development, and applies disturbances and updates the solution set by updating the preset iterative equation.

[0047] For a schematic diagram of the principle of the sine-cosine optimization algorithm, see Figure 2 , the main contents of the sine-cosine optimization algorithm can include randomly generating an initial population containing a certain number of individuals, using the evolutionary formula to update individuals during the iteration process, searching the solution space, finding the probability of the optimal solution and stopping the search after the condition is met, and outputting the optimal amplitude-phase weight vector as the target amplitude-phase weight vector, thereby obtaining the beamforming result. It can be understood that the population individual refers to each candidate solution in the algorithm, which is randomly generated in the search space and their quality is evaluated by calculating the fitness. Each individual has its specific position and fitness value, and the fitness value is used to measure the pros and cons of the individual for solving the optimization problem. During the execution of the algorithm, the position of the individual will be continuously updated to find a better solution; the individuals in the population represent a set of amplitude-phase weight vectors, and the amplitude-phase weight vector represents the amplitude-phase excitation required to achieve beamforming for each array element in the array.

[0048] For S1, based on the radar array information and scanning range, the coordinates and steering vectors of each array element in the radar array are obtained as array element parameters of each array element.

[0049] Specifically, the array information may include:

[0050] Array type, number of elements, element spacing, main beam pointing and antenna operating wavelength.

[0051] Among them, array types can include linear arrays and planar arrays.

[0052] For a linear array, the coordinates of each element in the array are expressed as follows:

[0053] ;

[0054] in, Indicates The coordinates of the array elements, represents the array element spacing, Can be a natural number greater than 0, , represents the number of elements in the array, Can be a natural number greater than 0;

[0055] The expressions of the steering vectors of all elements in the array are as follows:

[0056] ;

[0057] in, , express The steering vector of each array element in is , represents the scanning angle, The value range of , Indicates the antenna operating wavelength.

[0058] Understandably, for A linear array of elements, the individual dimensions of which are , Represents the spacing between elements in the array.

[0059] For a planar array, the coordinates of each element in the array are expressed as follows:

[0060] ;

[0061] in, Indicates the number of rows of elements in the array, , Indicates the total number of rows in the array, Can be a natural number greater than 0, represents the spacing between the elements in each row of the array, Can be a natural number greater than 0, Indicates the number of columns of array elements in the array, , Indicates the total number of columns in the array, Can be a natural number greater than 0, represents the spacing between array elements in each column. Can be a natural number greater than 0;

[0062] The expressions of the steering vectors of all elements in the array are as follows:

[0063] ;

[0064] in, , express The steering vector of each array element in is represents the beam pointing direction, represents the transpose operation, represents the imaginary unit, represents the scanning angle in pitch dimension, represents the scanning angle in the azimuth dimension, represents the antenna operating wavelength, The value range of , The value range of .

[0065] It is understandable that for the number of array elements The individual dimensions of the planar array are .

[0066] For S2, based on the radar's application scenario, array information and array element parameters, the expected radiation pattern and fitness function of the shaped beam are constructed.

[0067] According to the radar's application scenario, array information and array element parameters, the radar's beam pointing, main lobe width, side lobe level and other parameters are determined, and the expected radiation pattern and fitness function of the shaped beam are constructed.

[0068] Specifically, the expected radiation pattern of the shaped beam corresponds to the application scenario of the radar.

[0069] For the expectation Cosecant square beamforming is achieved within the range, and the expected sidelobe level in other detection directions is lower than In the application scenario, the expected directivity pattern of the shaped beam is constructed as follows:

[0070] ;

[0071] in, Indicates the main lobe beam pointing.

[0072] For the expectation The main lobe flat-top beamforming is achieved within the range, and the side lobe level is expected to be lower than Based on the application requirements, the expected directional pattern of the shaped beam is constructed as follows:

[0073] .

[0074] For a pencil beam that is expected to have as low side lobes as possible, the desired directional pattern of the shaped beam is constructed as follows:

[0075] .

[0076] It can be understood that the corresponding desired shaped beam pattern can be constructed according to the specific application scenario.

[0077] for Element linear array, angle definition diagram of linear array, see Figure 3 ,from Figure 3 It can be seen that in The far-field array pattern in the direction can be expressed as: ;

[0078] in, is the amplitude and phase weight vector of all individuals ,in, express Middle The amplitude phase excitation of each individual.

[0079] For the number of array elements For the planar array and the angle definition diagram of the planar array, see Figure 4 ,from Figure 4 It can be seen that in The far-field array pattern of the direction can be expressed as:

[0080] ;

[0081] in, is the amplitude and phase weight vector of all individuals , express Middle The amplitude phase excitation of each individual.

[0082] The expression of the fitness function is as follows:

[0083] ;

[0084] ;

[0085] in, Indicates minimization processing, represents the optimization objective function, represents the scanning angle in pitch dimension, represents the weighted coefficient of the fitness function constraining the main lobe area, represents the weighted coefficient of the fitness function constraining the sidelobe area, represents the initial directional pattern, represents the desired directivity pattern of the shaped beam, represents the main lobe area scanning angle, represents the sidelobe area scanning angle, represents the constraints, represents the amplitude and phase weight vector of all individuals, , express Middle The amplitude phase excitation of each individual, Indicates the total number of rows in the array, Indicates the total number of columns in the array, , Indicates The amplitude phase excitation of each individual, Indicates the population The amplitude value of the amplitude-phase excitation of each individual, represents the imaginary unit, Indicates the population The phase of the amplitude excitation of each individual, represents the conjugate transpose operation, Indicates that the array is at an angle The steering vector at express The real part of the magnitude-phase weight vector, express The imaginary part of the dimensional phase weight vector.

[0086] It can be understood that there is a one-to-one correspondence between array elements and individuals.

[0087] For S3, the maximum number of iterations, the population size, and the iteration parameters of the preset iterative equation of the sine-cosine optimization algorithm are selected according to the array information, array element parameters, and the expected radiation pattern of the shaped beam.

[0088] Specifically, the solution process of the sine-cosine optimization algorithm can be:

[0089] Assume that the population size can be , the search space can be dimension.

[0090] exist Dimensional solution space is randomly generated The location of an individual .

[0091] Understandably, The individual position representation produces Set of different amplitude and phase weight vectors.

[0092] For S4, this may include:

[0093] S41, based on the fitness function, obtain the fitness of each individual in the population, and record the optimal fitness and the optimal amplitude-phase weight vector corresponding to the optimal fitness.

[0094] The fitness function is used as the fitness function, and the fitness of each individual in the population is obtained based on the fitness function , , It can be a natural number greater than 0; select and retain the fitness value of the current optimal fitness from the fitness of all individuals obtained The optimal amplitude and phase weight vector corresponding to the optimal fitness .

[0095] Specifically, The fitness value of an individual can be expressed as ;in,

[0096] ;

[0097] Record the best position in the population : .

[0098] It can be understood that the time complexity of step S41 can be .

[0099] S42, based on the preset iterative equation, each individual in the population is updated.

[0100] The expression of the preset iteration equation is as follows:

[0101] ;

[0102] in, Indicates In the iteration process The value corresponding to each individual, Indicates that the candidate solution set is In the iteration process The weight of the dimension, , , and Represents the iteration parameter in the preset iteration equation.

[0103] It can be understood that the time complexity of step S42 can be .

[0104] S43, updating the iteration parameters in the preset iteration equation to complete one iteration process.

[0105] The expression for the iteration parameter is as follows:

[0106] ;

[0107] ;

[0108] ;

[0109] ;

[0110] in, Indicates the preset parameters. Indicates the current iteration number, represents the maximum number of iterations, express exist evenly distributed within the range.

[0111] Specifically, , , Can be a random number, The area or moving direction of the next position is determined by the specific update function; Determines the distance to move toward or away from the target, ; is the random weight of the target, randomly emphasizing or weaken The effect of the distance of the target, ; select sine and cosine functions for equal probability to iterate, .

[0112] The update function is as follows:

[0113] ;

[0114] in, Indicates the preset parameters. Can be a natural number greater than 0, Indicates the current iteration number, represents the maximum number of iterations, It can be a natural number greater than 0. It can be understood that the preset parameter can be set according to specific requirements. In the embodiment of the present invention, the preset parameter can be set to 2.

[0115] Iteration parameters in preset iteration equations For the amplitude variation diagram of Figure 5 .from Figure 5 It can be seen that the iteration parameter The amplitude is correlated with the number of iterations and the preset parameters.

[0116] The positions of each individual in the initial population can be ;in, , express The real part of express The imaginary part of .

[0117] It can be understood that for linear arrays, the individual dimensions are , for a planar array the individual dimensions are Since the amplitude and phase weight vector of the array is in the complex domain, in order to facilitate the individual coding search for the optimal result, the real and imaginary parts of the individuals in the initial population are calculated separately to expand the individual dimension. Therefore, the positions of each individual in the initial population are expressed as Denote the real part by Represents the imaginary part.

[0118] It can be understood that the time complexity of step S43 can be .

[0119] In the preset iterative equation provided in the embodiment of the present invention, and For the amplitude variation diagram of Figure 6 .from Figure 6 As can be seen from the figure, the sine-cosine optimization algorithm divides the iterative strategy into two threads, which can be global search and local development. In the global search thread, individuals in the population will be subject to greater random disturbances during evolution, thereby expanding the individual search range in order to explore the entire search space as comprehensively as possible; in the local development stage, the random disturbances to individual evolution will be weakened, and the individual search space will be centered in the individual neighborhood, fully searching the solution space around the individual.

[0120] It can be understood that step S4 is a complete iterative processing process.

[0121] For S5, based on the updated preset iterative equation, the updated individuals in the population are iterated several times until the number of current iterative processing reaches the maximum number of iterations or the optimal fitness in the current iterative processing is less than the preset standard, and the optimal amplitude-phase weight vector in the current iterative processing is output as the target amplitude-phase weight vector.

[0122] It is understandable that the preset standard can be set according to the complexity of the array information, array element parameters and the expected directional pattern of the shaped beam. In the embodiment of the present invention, the preset standard Set to . The iteration termination condition can be set as the number of current iterations reaching the maximum number of iterations or the optimal fitness in the current iteration process is less than the preset standard. For each iteration process, the number of iterations and the optimal fitness corresponding to the iteration process are judged. If the number of iterations corresponding to the iteration process reaches the maximum number of iterations, or the optimal fitness corresponding to the iteration process is less than any one of the preset standards, the optimal amplitude-phase weight vector corresponding to the iteration process is output as the target amplitude-phase weight vector. It can be understood that if the number of iterations corresponding to the iteration process does not reach the maximum number of iterations, and the optimal fitness corresponding to the iteration process is greater than or equal to the preset standard, the individual updated in the iteration process is used as the individual for the next iteration process, and the updated preset iteration equation is used as the preset iteration equation for the next iteration process, so as to perform corresponding processing to realize the iterative processing process. The time complexity of the outermost loop of step S5 can be In each iteration, the time complexity of step S41 can be , the time complexity of step S42 can be , the time complexity of step S43 can be , the time complexity of the outermost loop of step S5 can be , and Both The total time complexity of the sine-cosine optimization algorithm can be .

[0123] For S6, the beamforming result is obtained based on the target amplitude and phase weight vectors.

[0124] The corresponding beamforming result is obtained using the following formula.

[0125] .

[0126] in, It can represent the target amplitude-phase weight vector. It can be understood that the sine-cosine optimization algorithm is used to iteratively optimize each individual in the population under the constructed fitness function until the optimal amplitude-phase weight vector is output as the target amplitude-phase weight vector after the conditions are met; thus, the beamforming result is obtained according to the target amplitude-phase weight vector.

[0127] For ease of understanding, a simulation experiment is performed on the beamforming method of the array antenna amplitude and phase weighting based on the sine-cosine optimization algorithm proposed in the embodiment of the present invention.

[0128] A 16-element linear array can be selected for simulation experiments.

[0129] Specifically, various parameter settings of the 16-element linear array pattern are shown in Table 1, a linear parameter setting table.

[0130] Table 1 Linear parameter setting table

[0131]

[0132] 1) Cosecant Square Shaped Beam

[0133] For a cosecant square shaped beam, the expected normalized pattern can be defined as

[0134] .

[0135] MATLAB2023a can be used to simulate the sine-cosine optimization algorithm (SCA), genetic algorithm (SGA), and particle swarm algorithm (PSO) under the same fitness function, the same population size, and the same number of iterations. The corresponding fitness evolution curve of the cosecant square beam is as follows: Figure 7 As shown, the shaped pattern of the cosecant square beam is as follows Figure 8 As shown in the figure, the time taken by the shaping procedure of the cosecant square beam is as follows Fig. 9 As shown. Figure 7 , Figure 8 and Fig. 9 It can be seen from the figure that, in terms of optimization results, the sine-cosine optimization algorithm avoids the local optimal problem, and the fitness function obtained is significantly smaller than the other two traditional algorithms. The shaped beam shape is also closer to the expected beam. At the same time, under the same conditions, the simulation program will take less time when using the sine-cosine optimization algorithm than other traditional algorithms.

[0136] 2) Flat-top shaped beam

[0137] For a flat-top shaped beam, the desired pattern can be defined as

[0138] .

[0139] MATLAB2023a can be used to simulate the sine-cosine optimization algorithm (SCA), genetic algorithm (SGA), and particle swarm algorithm (PSO) under the same fitness function, the same population size, and the same number of iterations. The corresponding fitness evolution curve of the flat-top beam is shown in the figure below: Fig.10 As shown, the shaped radiation pattern of the flat-top beam is as follows Fig.11 As shown in the figure, the time taken for the shaping procedure of the flat-top beam is as follows Fig.12 As shown. Fig.10 , Fig.11 and Fig.12It can be seen that in terms of optimization results, the fitness function obtained by the sine-cosine optimization algorithm is significantly smaller than that of the genetic algorithm, and the obtained shaped beam shape is also closer to the expected beam. At the same time, under the same conditions, the simulation program uses the sine-cosine optimization algorithm. The time is close to the particle swarm algorithm, but significantly less than the genetic algorithm.

[0140] 3) Pencil-shaped beam

[0141] For a pencil-shaped beam, the desired pattern can be defined as

[0142] .

[0143] MATLAB2023a can be used to simulate the sine-cosine optimization algorithm (SCA), genetic algorithm (SGA), and particle swarm algorithm (PSO) under the same fitness function, the same population size, and the same number of iterations. The corresponding fitness evolution curve of the pencil beam is shown in the figure below: Fig.13 As shown, the shaped directivity pattern of the pencil beam is as follows Fig.14 The time taken for the pencil beam shaping procedure is shown in Fig.15 As shown. Fig.13 , Fig.14 and Fig.15 It can be seen that in terms of optimization results, the fitness function obtained by the sine-cosine optimization algorithm is significantly smaller than that of the genetic algorithm, and the maximum sidelobe level of the pencil-shaped beam obtained is also more than 2dB lower than that of the genetic algorithm. At the same time, under the same conditions, the simulation program will take less time when using the sine-cosine optimization algorithm than other traditional algorithms.

[0144] It can be understood that the embodiment of the present invention uses the sine-cosine optimization algorithm, the genetic algorithm and the particle swarm algorithm for comparison. Among the three beamforming algorithms, the sine-cosine optimization algorithm is superior to the other two traditional algorithms in terms of computing time. Although the particle swarm algorithm can obtain better optimization results in flat-top beam and pencil beamforming, it converges to the local optimum earlier in the cosecant square beamforming process, while the sine-cosine optimization algorithm can converge to a better result value more stably, which reflects the good adaptability and stability of the sine-cosine optimization algorithm.

[0145] A 25-element planar array is selected for simulation experiments.

[0146] Specifically, various parameter settings of the 25-element planar array pattern are shown in Table 2 Planar Parameter Setting Table.

[0147] Table 2 Plane parameter setting table

[0148]

[0149] The array element spacing of the 25-element planar array can be uniformly arranged with a half-wavelength. Fig.16 As shown, Fig.16 In Indicates the position of each array element, from Fig.16 It can be seen that the spacing between each element of the planar array is equal. The original directional pattern obtained by digital beamforming is as follows: Fig.17 As shown, the original 3D direction map is Fig.18 The sine-cosine optimization algorithm is used to perform flat-top beamforming on a 25-element planar array, and the obtained fitness evolution curve is shown in Fig.19 As shown in , as the number of iterations increases, the fitness results of the population are gradually optimized and convergence is close to 800 generations. The results of planar array flat-top beamforming are shown in Fig. 20 As shown, the 3D direction map is Fig.21 As shown. Fig. 20 and Fig.17 , Fig.21 and Fig.18 It can be seen that the beamforming is achieved by adjusting the amplitude and phase weights of the planar array using the sine-cosine optimization algorithm. The beamforming result has a wider main lobe than the original pattern and is closer to the expected pattern shape.

[0150] It is understandable that the randomness of global search and local development in the sine-cosine optimization algorithm has stronger adaptability and stability than the two-stage search and development. From the above three beamforming, it can be seen that the sine-cosine optimization algorithm is superior to the other two algorithms in terms of computing time when compared with the genetic algorithm and the particle swarm algorithm. At the same time, it has better adaptability and stability and can stably converge to a better result value.

[0151] The embodiment of the present invention obtains the desired radiation pattern of the shaped beam by adjusting the amplitude and phase of the array element to meet the detection requirements in different situations. The fitness function of the different shaped beams is constructed as the fitness function, and the sine-cosine optimization algorithm is used to iteratively optimize each individual in the population under the constructed fitness function until the optimal amplitude-phase weight vector is output as the target amplitude-phase weight vector after the conditions are met, thereby obtaining the beamforming result, and using the volatility and periodicity of the sine and cosine functions as the design goals of the implementation operator to search and iterate the optimal solution. The sine-cosine oscillation variation characteristics bring good solution space search capabilities, with the characteristics of few parameters, simple structure, easy implementation and fast convergence speed, and can achieve rapid search to obtain a beam radiation pattern of a more ideal desired shape to meet the detection requirements in different situations.

[0152] It should be noted that in the description of the present invention, it should be understood that the terms "first" and "second" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, the meaning of "plurality" is two or more, unless otherwise clearly and specifically defined.

[0153] The above description is only a preferred embodiment of the present invention and is not intended to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention are included in the protection scope of the present invention.

Claims

1. A beamforming method for array antenna amplitude and phase weighting based on sine-cosine optimization algorithm, characterized in that: include: Based on the radar array information and scanning range, the coordinates and steering vectors of each array element in the radar array are obtained as array element parameters of each array element; Based on the application scenario, array information and array element parameters of the radar, the expected radiation pattern of the shaped beam and the fitness function are constructed; the expression of the fitness function is as follows: Wherein, min represents minimization processing, f represents optimization objective function, θ represents the scanning angle in pitch dimension, α represents the weight coefficient of fitness function constraining main lobe area, β represents the weight coefficient of fitness function constraining side lobe area, p1(θ) represents initial radiation pattern, Pd(θ) represents expected radiation pattern of shaped beam, θmainlobe represents the scanning angle in main lobe area, θsidelobe represents the scanning angle in side lobe area, st represents constraint condition, w represents amplitude and phase weight vector of all individuals, w=[w1,…,wi,…,wM*N]T, wi represents amplitude and phase excitation of the i-th individual in w, M represents the total number of rows of array, N represents the total number of columns of array, wn=|An|exp(jψn), wn represents amplitude and phase excitation of i-th individual, An represents the amplitude value of amplitude and phase excitation of i-th individual in population, j represents imaginary unit, ψn represents the phase of amplitude and phase excitation of i-th individual in population, H represents conjugate transpose operation, a(θ) represents steering vector of array at angle θ, represents the real part of the M*N-dimensional amplitude and phase weight vector, Represents the imaginary part of the M*N-dimensional amplitude and phase weight vector; According to the array information, array element parameters and the expected directional pattern of the shaped beam, the maximum number of iterations of the sine-cosine optimization algorithm, the number of populations and the iteration parameters of the preset iteration equation are selected; the positions of each individual in the initial population can be in, express The real part of express The imaginary part of Based on the fitness function, the fitness of each individual in the population is obtained, and the optimal fitness and the optimal amplitude and phase weight vector corresponding to the optimal fitness are recorded; based on a preset iterative equation, each individual in the population is updated; and the iterative parameters in the preset iterative equation are updated to complete an iterative process; Based on the updated preset iterative equation, the updated individuals in the population are iterated for several times until the number of current iterative processing reaches the maximum number of iterations or the optimal fitness in the current iterative processing is less than the preset standard, and the optimal amplitude-phase weight vector in the current iterative processing is output as the target amplitude-phase weight vector; A beamforming result is obtained based on the target amplitude and phase weight vector.

2. The beamforming method of array antenna amplitude and phase weighting based on sine-cosine optimization algorithm according to claim 1, characterized in that: The array information includes: Array type, number of elements, element spacing, main beam pointing and antenna operating wavelength.

3. The beamforming method of array antenna amplitude and phase weighting based on sine-cosine optimization algorithm according to claim 2, characterized in that: For a linear array, the coordinates of each element in the array are expressed as follows: in, represents the coordinates of the n1th array element, d represents the array element spacing, n1=1,2,…,N1, N1 represents the number of array elements in the array; The expressions of the steering vectors of all elements in the array are as follows: in, represents the steering vector of each array element in a(θ), n1=1,2,…,N1, θ represents the scanning angle in the elevation dimension, and λ represents the operating wavelength of the antenna.

4. The beamforming method of array antenna amplitude and phase weighting based on sine-cosine optimization algorithm according to claim 2, characterized in that: For a planar array, the coordinates of each element in the array are expressed as follows: (xm,yn)=((m-1)dx,(n-1)dy); Wherein, m represents the number of rows of array elements in the array, m=1,2,…,M, M represents the total number of rows of the array, dx represents the spacing between array elements in each row of the array, n represents the number of columns of array elements in the array, n=1,2,…,N, N represents the total number of columns of the array, and dy represents the spacing between array elements in each column of the array; The expressions of the steering vectors of all elements in the array are as follows: in, express The steering vector of each array element in is represents the beam pointing, T represents the transposition operation, j represents the imaginary unit, θ represents the elevation scanning angle, represents the scanning angle in azimuth dimension, and λ represents the operating wavelength of the antenna.

5. The beamforming method of array antenna amplitude and phase weighting based on sine-cosine optimization algorithm according to claim 1, characterized in that: The expected radiation pattern of the shaped beam corresponds to the application scenario of the radar.

6. The beamforming method of array antenna amplitude and phase weighting based on sine-cosine optimization algorithm according to claim 1, characterized in that: The expression of the preset iterative equation is as follows: in, represents the value corresponding to the i-th individual in the t-th iteration process, represents the component of the i-th dimension of the candidate solution set in the t-th iteration process, and r1, r2, r3 and r4 represent the iteration parameters in the preset iteration equation.

7. The beamforming method of array antenna amplitude and phase weighting based on sine-cosine optimization algorithm according to claim 1, characterized in that: The expression of the iteration parameter is as follows: r2～U(0,2π)； r3∈(0,∞)； r4∈(0,1)； Among them, b represents the preset parameter, t represents the current number of iterations, Tmax represents the maximum number of iterations, and r2~U(0,2π) represents that r2 is uniformly distributed in the range of (0,2π).

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