Pure phase array pattern synthesis method and system based on improved bat algorithm

Abstract

The application discloses a pure phase array pattern synthesis method and system based on an improved bat algorithm, which comprises the following steps: setting an array model constructed by a plurality of antenna units; constructing an optimization objective function of the array model; minimizing the objective function according to a bat algorithm to complete optimization training of the array model; and performing pure phase array pattern synthesis according to the optimized array model. The embodiment of the application is aimed at pure phase symmetric pattern synthesis, an initial phase distribution is created by using a parabolic function, the distribution has the characteristic of an approximately flat-top mode, thereby accelerating the optimization process, in addition, the excitation distribution is expressed in a polynomial form, the optimization problem is converted into optimization of polynomial coefficients, thereby realizing antenna pattern synthesis, and the application can be widely applied to the technical field of computers.

Description

Technical Field

[0001] This invention relates to the field of computer technology, and in particular to a pure phase array pattern synthesis method and system based on an improved bat algorithm. Background Technology

[0002] Phased array radars alter the antenna pattern shape by controlling the excitation amplitude and phase of antenna elements, enabling more flexible spatial filtering and space-time processing capabilities—a process known as antenna pattern synthesis. While excellent antenna pattern synthesis can be achieved by simultaneously weighting and adjusting amplitude and phase, amplitude weighting typically requires adding amplitude attenuators to the array, increasing both antenna design complexity and cost. In contrast, phase weighting achieves a similar effect using only the phase shifter of the phased array antenna, offering benefits such as maximized sensitivity and power efficiency. Therefore, phase weighting methods have significant practical value in engineering applications.

[0003] The goal of pure phase antenna pattern synthesis is to form the desired antenna pattern by optimizing the excitation phase while maintaining the consistency of the excitation amplitude of the antenna elements. However, this process is inherently a nonlinear and nonconvex optimization problem because the feasible region corresponds to the intersection of circles, and its global optimal solution remains unknown.

[0004] To achieve pure phase pattern synthesis of antennas, early researchers relaxed the amplitude constraint to a convex constraint and applied an alternating optimization algorithm to solve the pure phase antenna pattern synthesis problem. However, due to the convex relaxation, amplitude consistency is difficult to guarantee, making it unsuitable for practical systems. Evolutionary algorithms, based on Darwin's theory of evolution, simulate natural selection, survival of the fittest, and evolve the optimal solution to the problem through multiple generations of inheritance, mutation, crossover, and replication. In recent years, evolutionary algorithms have received widespread attention due to their efficiency in handling complex non-convex problems, including Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Bat Algorithm (BA). Therefore, applying evolutionary algorithms to solve the pure phase pattern synthesis problem has significant advantages.

[0005] In the field of phase-only array pattern synthesis, the following problems mainly exist:

[0006] 1. Most existing optimization algorithms directly optimize the phase of antenna elements. As the array size and the number of antenna elements increase, the concentration of local optima becomes denser and more complex. This complexity makes optimization algorithms more prone to getting trapped in local optima. To obtain a satisfactory solution, more experiments are needed, further increasing the computational load.

[0007] 2. Some improvements to the optimization algorithm focus on relaxing the optimization problem, resulting in optimization results that are not strictly constant and are difficult to apply directly to real-world systems. Summary of the Invention

[0008] The main objective of this invention is to propose a pure phase array pattern synthesis method and system based on an improved bat algorithm, which can realize antenna pattern synthesis and accelerate the optimization process.

[0009] To achieve the above objectives, one aspect of this invention proposes a pure phase array pattern synthesis method based on an improved bat algorithm, comprising the following steps:

[0010] Set up an array model constructed from multiple antenna elements;

[0011] Construct the optimization objective function for the array model;

[0012] The array model is optimized and trained by minimizing the objective function using the bat algorithm.

[0013] Based on the optimized array model, pure phase array pattern synthesis is performed.

[0014] In some embodiments, setting up an array model constructed from multiple antenna elements includes the following steps:

[0015] Determine the number of antenna elements in a uniform linear array; determine the spacing between each antenna element in the uniform linear array; determine the excitation amplitude and excitation phase of each antenna element;

[0016] The expression for constructing the far-field radiation pattern of the array is:

[0017]

[0018] Where θ is the scanning angle, k is the wave number; n represents the nth antenna element; N represents the total number of antenna elements; Φ n d represents the excitation phase of the nth antenna element; j represents the imaginary unit; d represents the spacing between antenna elements.

[0019] In some embodiments, constructing the optimization objective function of the array model includes the following steps:

[0020] The selection of orthogonal basis functions is determined based on the shape of the basis functions. The phase distribution of the array is expanded using M-order orthogonal basis functions to obtain the expression for the target phase distribution of the array.

[0021] An initial phase distribution is generated using a quadratic polynomial, which initially exhibits flat-top pattern characteristics.

[0022] Based on the initial phase distribution, the expression for the target phase distribution is adjusted and optimized;

[0023] A loss function for the array model is constructed to optimize the objective function of the array model.

[0024] In some embodiments, the expression for the target phase distribution is: Where, Φ n The target phase distribution is represented by ΔΦ; the range of values ​​for the polynomial is represented by ΔΦ; M represents the order of the orthogonal basis functions; m represents the m-th order basis function; k m f represents the corresponding real coefficient of the weight; m d represents an m-th order polynomial; n represents the distance from the nth array element to the center of the array element; D represents the total length of the array.

[0025] The initial phase distribution A n The expression is: Where ΔA is the range constant of the initial phase;

[0026] The expression for the loss function is:

[0027] Where c represents the loss function; H represents the number of sampling points in the main lobe region; F(θ) h ) represents the radiation pattern; S represents the number of sampling points for the maxima in the sidelobe region; θ h The sampling angle representing the main lobe region; P d () represents the desired orientation pattern; w1 and w2 represent weighting coefficients; θ s The sampling angle represents the maximum value of the sidelobe region.

[0028] In some embodiments, minimizing the objective function according to the bat algorithm to complete the optimized training of the array model includes the following steps:

[0029] Introducing non-linearly decreasing inertia weights To adjust the velocity term coefficient, the inertia weight is defined as follows: in, Represents inertia weight; w min and w max The constant is t; t represents time t; T represents the maximum number of iterations of the algorithm.

[0030] Instead of updating the firing rate in the standard bat algorithm, a chaotic mapping is used. A sine mapping is employed, transforming the firing rate in the standard bat algorithm into a chaotic number between 0 and 1. The update formula for the sine mapping is defined as: r t+1 =a(r t )2 sin(πr t ), where a represents the mapping magnitude constant; r t Represents the emission rate at time t;

[0031] The array model was optimized and trained using the improved bat algorithm.

[0032] In some embodiments, the step of optimizing the training of the array model based on the improved bat algorithm includes the following steps:

[0033] Configure the population size and maximum number of iterations;

[0034] Randomly initialize the initial positions of each bat in the population;

[0035] Initialize the loudness, firing rate, and frequency of pulses emitted by each bat when searching for prey;

[0036] If the maximum number of iterations is not reached, according to formula f i =f min +(f max -f min )β updates and adjusts the frequency of pulses emitted by bats at various locations, and according to the formula and The positions and speeds of each bat are updated and adjusted; among them, f i f represents the frequency of the emitted pulse of the i-th bat; min f represents the minimum frequency. max β represents the maximum frequency; β represents a random vector that follows a uniform distribution. This represents the position of bat i at time t; This represents the velocity of bat i at time t; Represents inertia weight; x * Represents the global optimal solution in the current iteration;

[0037] When the random number is less than the current transmission rate, then according to the formula x new =x old +εA t New local solutions are generated from the optimal solution, and new solutions are generated through random flight until the random number is not less than the current launch rate; where x new Represents a new local solution; x old Represents the old optimal solution; ε represents a random number; A t This represents the average loudness of all bats in the current iteration;

[0038] Based on the new local solution, the loudness and transmission rate of the transmitted pulse are updated, and the frequency of the current transmitted pulse is calculated to obtain the optimal solution for the frequency of the current transmitted pulse, until the maximum number of iterations is reached.

[0039] In some embodiments, the expression for updating the loudness of the transmitted pulse is:

[0040] The expression for updating the transmission rate of the transmitted pulse is:

[0041] in, α represents the loudness of the emission pulse of the i-th bat at time t; α and γ represent constants. Represents the initial launch rate; This represents the firing rate of the i-th bat at time t+1.

[0042] Another aspect of this invention provides a pure phase array pattern synthesis system based on an improved bat algorithm, comprising:

[0043] The first module is used to set up an array model constructed from multiple antenna elements;

[0044] The second module is used to construct the optimization objective function of the array model;

[0045] The third module is used to minimize the objective function according to the bat algorithm to complete the optimized training of the array model;

[0046] The fourth module is used to perform pure phase array pattern synthesis based on the optimized array model.

[0047] To achieve the above objectives, another aspect of the present invention provides an electronic device, which includes a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the method described above.

[0048] To achieve the above objectives, another aspect of the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the methods described above.

[0049] This invention also discloses a computer program product or computer program, which includes computer instructions stored in a computer-readable storage medium. A processor of a computer device can read the computer instructions from the computer-readable storage medium and execute the computer instructions, causing the computer device to perform the aforementioned method.

[0050] The embodiments of this invention include at least the following beneficial effects: This invention provides a pure phase array pattern synthesis method and system based on an improved bat algorithm. This scheme involves setting up an array model constructed from multiple antenna elements; constructing an optimization objective function for the array model; minimizing the objective function using the bat algorithm to complete the optimization training of the array model; and performing pure phase array pattern synthesis based on the optimized array model. For pure phase symmetric pattern synthesis, this invention utilizes a parabolic function to create an initial phase distribution, which has the characteristic of an approximately flat-top mode, thereby accelerating the optimization process. Furthermore, this invention expresses the excitation distribution in polynomial form, transforming the optimization problem into optimizing the polynomial coefficients, thus achieving antenna pattern synthesis. Attached Figure Description

[0051] Figure 1 This is a schematic diagram of an implementation environment provided by an embodiment of the present invention;

[0052] Figure 2 This is a flowchart of the overall steps provided in the embodiments of the present invention;

[0053] Figure 3 This is a flowchart illustrating the specific implementation steps provided in the embodiments of the present invention;

[0054] Figure 4 This is a schematic diagram of the equivalent phase distribution of the six Chebyshev polynomials provided in an embodiment of the present invention;

[0055] Figure 5 This invention provides a phase distribution map and a corresponding array pattern obtained from a quadratic polynomial, as provided in an embodiment of the invention.

[0056] Figure 6 This is a flowchart of the iterative steps of the improved bat algorithm provided in this embodiment of the invention;

[0057] Figure 7 This is a schematic diagram of the convergence curve of the loss function provided in an embodiment of the present invention; wherein, Figure 7 (a) represents the convergence curve of the loss function of the standard BA, N=12; Figure 7 (b) represents the convergence curve of the loss function of the improved BA, N=12; Figure 7 (c) represents the convergence curve of the loss function of the standard BA, N = 32; Figure 7 (d) represents the convergence curve of the loss function of the improved BA, N = 32;

[0058] Figure 8 These are the radiation pattern synthesis results and corresponding phase diagrams provided in the embodiments of the present invention;

[0059] Figure 9This is a schematic diagram of the hardware structure of the electronic device provided in an embodiment of the present invention. Detailed Implementation

[0060] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In the following description, when referring to the accompanying drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the embodiments of this invention; they are merely examples of apparatuses and methods consistent with some aspects of the embodiments of this invention as detailed in the appended claims.

[0061] It is understood that the terms “first,” “second,” etc., used in this invention may be used herein to describe various concepts, but unless specifically stated otherwise, these concepts are not limited by these terms. These terms are used only to distinguish one concept from another. For example, first information may also be referred to as second information without departing from the scope of embodiments of the invention, and similarly, second information may also be referred to as first information. Depending on the context, the words “if,” “when,” or “in response to determination” as used herein may be interpreted as “when…” or “when…” or “in response to determination.”

[0062] The terms “at least one,” “multiple,” “each,” “any,” etc., used in this invention, “at least one” includes one, two, or more than two; “multiple” includes two or more than two; “each” refers to each of the corresponding multiple; and “any” refers to any one of the multiple.

[0063] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein is for the purpose of describing embodiments of the invention only and is not intended to limit the invention.

[0064] Before providing a detailed description of the embodiments of the present invention, some related technologies involved in the embodiments of the present invention will be described first, as follows:

[0065] Phased array radar: A phase-controlled electronically scanned array radar, consisting of a large number of identical radiating elements. Each radiating element is independently controlled in phase and amplitude by waveguides and phase shifters, enabling precise and predictable radiation patterns and beam pointing. During radar operation, the transmitter distributes power to each antenna element through a feed network. The energy is radiated through numerous independent antenna elements and combined in space to form the desired beam pointing.

[0066] Pure phase pattern synthesis: This method changes the shape of the antenna pattern solely by controlling the excitation phase of the antenna elements. It combines low-level features to form more abstract high-level representations of attribute categories or features, thereby discovering distributed feature representations of the data.

[0067] Bat Algorithm: An optimization algorithm. Bats use echolocation to locate prey. While roaming, bats emit short pulses; once they detect approaching prey, their pulse emission rate increases, and the pulse frequency rises. The Bat Algorithm idealizes the echolocation behavior of bats to solve specific optimization problems.

[0068] The pure phase array pattern synthesis method and system based on the improved Bat algorithm provided in this invention relates to the field of computer technology. The pure phase array pattern synthesis method based on the improved Bat algorithm provided in this invention can be applied to terminals, servers, or software running on terminals or servers. In some embodiments, the terminal can be a smartphone, tablet, laptop, desktop computer, smart speaker, smartwatch, or vehicle terminal, but is not limited to these. The server can be configured as an independent physical server, a server cluster composed of multiple physical servers, or a distributed system. It can also be configured as a cloud server providing basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, CDN, and big data and artificial intelligence platforms. The server can also be a node server in a blockchain network. The software can be an application implementing the pure phase array pattern synthesis method based on the improved Bat algorithm, but is not limited to the above forms.

[0069] This invention can be used in a wide variety of general-purpose or special-purpose computer system environments or configurations. Examples include: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, and distributed computing environments including any of the above systems or devices. This invention can be described in the general context of computer-executable instructions, such as program modules, that are executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform specific tasks or implement specific abstract data types. This invention can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.

[0070] like Figure 1 The diagram shown is a schematic representation of an implementation environment provided by an embodiment of the present invention. (Refer to...) Figure 1 The implementation environment includes at least one terminal 102 and a server 101. The terminal 102 and the server 101 can be connected via a network, either wirelessly or via a wired connection, to complete data transmission and exchange.

[0071] Server 101 can be a standalone physical server, a server cluster or distributed system composed of multiple physical servers, or a cloud server that provides basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, CDN (Content Delivery Network), and big data and artificial intelligence platforms.

[0072] Additionally, server 101 can also be a node server in a blockchain network. Blockchain is a novel application model of computer technologies such as distributed data storage, peer-to-peer transmission, consensus mechanisms, and encryption algorithms.

[0073] Terminal 102 can be a smartphone, tablet, laptop, desktop computer, smart speaker, smartwatch, etc. It can also be a vehicle-mounted terminal of the various device types described above, but is not limited to these. Terminal 102 and server 101 can be directly or indirectly connected via wired or wireless communication, and this embodiment of the invention does not impose any limitations.

[0074] Exemplary based on Figure 1 The implementation environment shown in this embodiment of the invention provides a pure phase array pattern synthesis method based on the improved bat algorithm. The following description uses the application of this pure phase array pattern synthesis method based on the improved bat algorithm in server 101 as an example. It can be understood that this method can also be applied to terminal 102.

[0075] Reference Figure 2 , Figure 2 This is a flowchart illustrating a pure phase array pattern synthesis method based on an improved bat algorithm applied to a server, provided in an embodiment of the present invention. The execution subject of this method can be any of the aforementioned computer devices (including servers or terminals). (Refer to...) Figure 2 The method may include the following steps:

[0076] Set up an array model constructed from multiple antenna elements;

[0077] Construct the optimization objective function for the array model;

[0078] The array model is optimized and trained by minimizing the objective function using the bat algorithm.

[0079] Based on the optimized array model, pure phase array pattern synthesis is performed.

[0080] In some embodiments, setting up an array model constructed from multiple antenna elements includes the following steps:

[0081] Determine the number of antenna elements in a uniform linear array; determine the spacing between each antenna element in the uniform linear array; determine the excitation amplitude and excitation phase of each antenna element;

[0082] The expression for constructing the far-field radiation pattern of the array is:

[0083]

[0084] Where θ is the scanning angle, k is the wave number; n represents the nth antenna element; N represents the total number of antenna elements; Φ n d represents the excitation phase of the nth antenna element; j represents the imaginary unit; d represents the spacing between antenna elements.

[0085] In some embodiments, constructing the optimization objective function of the array model includes the following steps:

[0086] The selection of orthogonal basis functions is determined based on the shape of the basis functions. The phase distribution of the array is expanded using M-order orthogonal basis functions to obtain the expression for the target phase distribution of the array.

[0087] An initial phase distribution is generated using a quadratic polynomial, which initially exhibits flat-top pattern characteristics.

[0088] Based on the initial phase distribution, the expression for the target phase distribution is adjusted and optimized;

[0089] A loss function for the array model is constructed to optimize the objective function of the array model.

[0090] In some embodiments, the expression for the target phase distribution is: Where, Φ n The target phase distribution is represented by ΔΦ; the range of values ​​for the polynomial is represented by ΔΦ; M represents the order of the orthogonal basis functions; m represents the m-th order basis function; k m f represents the corresponding real coefficient of the weight; m d represents an m-th order polynomial; n represents the distance from the nth array element to the center of the array element; D represents the total length of the array.

[0091] The initial phase distribution A n The expression is: Where ΔA is the range constant of the initial phase;

[0092] The expression for the loss function is:

[0093] Where c represents the loss function; H represents the number of sampling points in the main lobe region; F(θ) h ) represents the radiation pattern; S represents the number of sampling points for the maxima in the sidelobe region; θ h The sampling angle representing the main lobe region; P d () represents the desired orientation pattern; w1 and w2 represent weighting coefficients; θ s The sampling angle represents the maximum value of the sidelobe region.

[0094] In some embodiments, minimizing the objective function according to the bat algorithm to complete the optimized training of the array model includes the following steps:

[0095] Introducing non-linearly decreasing inertia weights To adjust the velocity term coefficient, the inertia weight is defined as follows: in, Represents inertia weight; w min and w max The constant is t; t represents time t; T represents the maximum number of iterations of the algorithm.

[0096] Instead of updating the firing rate in the standard Bat Algorithm (BA), a chaotic mapping is used. A sine mapping is employed, transforming the firing rate in the standard BA into a chaotic number between 0 and 1. The update formula for the sine mapping is defined as: r t+1 =a(r t ) 2 sin(πr t ), where a represents the mapping magnitude constant; r t Represents the emission rate at time t;

[0097] The array model was optimized and trained using the improved bat algorithm.

[0098] In some embodiments, the step of optimizing the training of the array model based on the improved bat algorithm includes the following steps:

[0099] Configure the population size and maximum number of iterations;

[0100] Randomly initialize the initial positions of each bat in the population;

[0101] Initialize the loudness, firing rate, and frequency of pulses emitted by each bat when searching for prey;

[0102] If the maximum number of iterations is not reached, according to formula f i =f min +(f max -f min )β updates and adjusts the frequency of pulses emitted by bats at various locations, and according to the formula and The positions and speeds of each bat are updated and adjusted; among them, f i f represents the frequency of the emitted pulse of the i-th bat; min f represents the minimum frequency. max β represents the maximum frequency; β represents a random vector that follows a uniform distribution. This represents the position of bat i at time t; This represents the velocity of bat i at time t; Represents inertia weight; x * Represents the global optimal solution in the current iteration;

[0103] When the random number rand is less than the current transmission rate, then according to the formula x new =x old +εA t New local solutions are generated from the optimal solution, and new solutions are generated through random flight until the random number rand is not less than the current launch rate; where x new Represents a new local solution; x old Represents the old optimal solution; ε represents a random number; A t This represents the average loudness of all bats in the current iteration;

[0104] Based on the new local solution, the loudness and transmission rate of the transmitted pulse are updated, and the frequency of the current transmitted pulse is calculated to obtain the optimal solution for the frequency of the current transmitted pulse, until the maximum number of iterations is reached.

[0105] In some embodiments, the expression for updating the loudness of the transmitted pulse is:

[0106] The expression for updating the transmission rate of the transmitted pulse is:

[0107] in, α represents the loudness of the emission pulse of the i-th bat at time t; α and γ represent constants. Represents the initial launch rate; This represents the firing rate of the i-th bat at time t+1.

[0108] The specific implementation process of this invention will be described in detail below using a specific application scenario as an example:

[0109] refer to Figure 3The specific implementation steps of the present invention include:

[0110] [1] Set up the array model;

[0111] Consider a uniform linear array consisting of N elements, where the spacing between each antenna element is d, and the excitation amplitude of the nth element is I. n The excitation phase is Φ n Assuming the antenna elements are isotropic, the far-field radiation pattern of the array can be represented as:

[0112]

[0113] Where θ is the scanning angle, k = 2π / λ is the wave number, and λ is the wavelength.

[0114] [2] Construct the optimization objective function;

[0115] Based on the condition that the transmitting component needs to saturate output in engineering applications, i.e., I n =1, n=1,...,N, requiring only adjustment of the excitation phase Φ n This is to achieve pattern synthesis. In previous array pattern synthesis processes, Φ was usually directly processed. n Optimization is performed to obtain the desired array pattern. However, the computational complexity increases dramatically with the number of array elements. Since any function can be represented by a linear combination of orthogonal basis functions, the phase distribution can also be described by a weighted sum of appropriate basis functions. Using this method, even an array consisting of hundreds of elements can have its phase distribution described by a few basis functions. Subsequent optimization can be performed on the weights of the basis functions, thus significantly reducing the number of unknowns and speeding up the optimization process. The choice of orthogonal basis functions depends on their shape. For example, for a symmetric pattern, a symmetric phase distribution is required, so only even-order basis functions are considered. Expanding the phase distribution of the array using M-order orthogonal basis functions can be expressed as follows:

[0116]

[0117] Among them, f m (2d n / D) represents an m-order polynomial, ΔΦ is the range of values ​​for the polynomial, and k m ∈[-1,1] represents the corresponding real coefficients of the weights, d n Let ΔΦ be the distance from the nth element to the center of the array, and D be the total length of the array. Taking the Chebyshev polynomial as an example, taking the first M = 6th order polynomial, letting ΔΦ = 30 and extending it to [-30°, 30°], we obtain the phase distribution as follows: Figure 4 As shown.

[0118] In the optimization of symmetric desired radiation patterns, the initial phase can be sampled from a symmetric distribution. Therefore, a quadratic polynomial is used to generate an initial phase distribution, which initially exhibits flat-top radiation pattern characteristics. Optimization based on this distribution helps to accelerate the entire optimization process. The initial phase is defined as...

[0119]

[0120] Where ΔA is the range constant of the initial phase. Taking a uniform linear array of N = 32 and d = 0.5λ as an example, the initial phase distribution and the resulting radiation pattern of the array when ΔA = 400° are as follows: Figure 5 As shown, Figure 5 In the diagram, the horizontal axis represents the antenna element number; the vertical axis represents the excitation phase (°).

[0121] 2. Horizontal axis: Scanning angle θ (°); Vertical axis: Antenna pattern (dB). Clearly, the phase distribution obtained from the quadratic polynomial is suitable as the initial phase for pure phase-symmetric pattern synthesis. By adjusting the value of ΔA, the width of the main lobe can be easily adjusted to meet the requirements.

[0122] In summary, the phase Φ n Can be rewritten as

[0123]

[0124] For N-element pure phase pattern synthesis, it is only necessary to search within the M-dimensional Chebyshev phase space to solve for Φ. n The process of converting n = 1, ..., N into solving for the polynomial coefficients k is transformed into solving for the polynomial coefficients k. m k = 1,...,M. By solving for the polynomial coefficients k... m This allows us to obtain the desired symmetrical pattern.

[0125] Construct the following loss function:

[0126]

[0127] Where w1 and w2 are weighting coefficients, used to measure the differences between the synthesized results of the main lobe fluctuation and the side lobe level and the expected results, respectively; θ h h = 1, ..., H is the sampling angle of the main lobe region, θ s ,s=1,...,S is the sampling angle of the maxima in the sidelobe region, P d (θ) represents the desired radiation pattern. Minimizing equation (5) yields the desired radiation pattern.

[0128] [3] The bat algorithm minimizes the loss function;

[0129] Bats use echolocation to locate prey. While roaming, they emit short pulses; once they detect approaching prey, their pulse emission rate increases, and the pulse frequency rises. The bat algorithm idealizes this echolocation behavior to solve specific optimization problems.

[0130] In standard BA, assume there are G bats in an L-dimensional search space, where bats i, i = 1, ..., G are at position x. i With velocity v i Random flight, at frequency f i Loudness A i It uses pulses to search for prey and can automatically adjust the frequency f of the emitted pulses based on the target's proximity. i Loudness A i and emission rate r i At time t, the position of bat i and speed Updated to:

[0131] f i =f min +(f max -f min )β (6)

[0132]

[0133] Among them, [f min ,f max [x] represents the frequency range of pulses emitted by each bat, β∈[0,1] is a random vector following a uniform distribution, and x * It is the global optimal solution for the current iteration.

[0134] BA has the ability to perform both global and local searches simultaneously, and can automatically transition from global to local search by adjusting relevant parameters. During the local search phase, the algorithm performs random walks around the current optimal solution, generating a new solution locally for each bat.

[0135] x new =x old +εA t (9)

[0136] Where ε∈[-1,1] is a random number, A t It is the average loudness of all bats in the current iteration.

[0137] Furthermore, as the iteration proceeds, the loudness A of the transmitted pulse... i and emission rate r i It must also be updated accordingly. Assuming that loudness typically decreases after prey is detected, and firing rate increases after prey is detected, it can be set as follows:

[0138]

[0139]

[0140] Where α and γ are constants, and the initial loudness is... Typically, it can be [1,2], with an initial emission rate r. i 0 It can usually be [0,1].

[0141] This method makes some improvements to the standard BA. First, it introduces a non-linearly decreasing inertia weight w. t To adjust the velocity term coefficient, the inertia weight of this method Defined as

[0142]

[0143] Among them, w min and w max Let T be a constant, and T be the maximum number of iterations of the algorithm. After adding the inertia weight, the velocity update formula (7) becomes...

[0144]

[0145] Secondly, this method replaces the update of the emission rate *r* in the standard BA with a chaotic mapping to improve the performance of the BA. In the standard BA, the emission rate changes monotonically within [0,1]. This method uses a sinusoidal mapping, transforming it into a chaotic number between 0 and 1. The sinusoidal mapping update formula is defined as follows:

[0146] r t+1 =a(r t ) 2 sin(πr t (14)

[0147] In this embodiment of the invention, the training iteration process diagram after the improvement of the bat algorithm is as follows: Figure 6 As shown.

[0148] [4] Results of the present invention:

[0149] (1) Convergence performance:

[0150] For comparison, the algorithm of this invention and standard BA were used for array pattern synthesis. The desired pattern was set to have a flat-topped main lobe in θ∈[-16°, 16°] and side lobes not exceeding -14dB in θ∈[-90°, -20°]∪[20°, 90°]. For N=12 and N=32, the three algorithms were tested 100 times each, and the convergence results of the loss function are as follows. Figure 7 As shown, Figure 7 middle, Figure 7The x-axis of (a) represents the number of iterations, and the y-axis represents the loss function c. Figure 7 The x-axis of (b) represents the number of iterations, and the y-axis represents the loss function c. Figure 7 The x-axis of (c) represents the number of iterations, and the y-axis represents the loss function c. Figure 7 The x-axis of (d) represents the number of iterations, and the y-axis represents the loss function c. It can be seen that the standard BA gets trapped in different local optima in each trial, and the convergence curves of multiple trials are relatively dispersed. In contrast, the convergence curves of the improved BA are more densely distributed, and the convergence values ​​of the loss function are closer. On the other hand, as the number of array elements increases, the dispersion of the standard BA convergence curve intensifies, while the improved BA can converge relatively well with the increase of the number of array elements.

[0151] (2) Overall results of the directional pattern:

[0152] For the desired radiation pattern in (1) with N=32, 100 tests were conducted using the improved BA of this invention, the standard BA, and the standard PSO. The optimal radiation pattern synthesis results and their corresponding phases are as follows: Figure 8 As shown, Figure 8 In the left figure, the horizontal axis represents the scanning angle θ (°); the vertical axis represents the antenna pattern (dB). Figure 8 In the right-hand figure, the horizontal axis represents the antenna element number, and the vertical axis represents the excitation phase (°). It can be seen that the improved BA algorithm of this invention outperforms the other two algorithms in terms of both the maximum main lobe fluctuation and the maximum sidelobe level.

[0153] In summary, the present invention has the following characteristics:

[0154] This invention improves upon the Bat algorithm and proposes an optimization method for pattern synthesis of symmetrical antennas by incorporating series expansion. This method demonstrates excellent performance in main lobe ripple control, sidelobe suppression, convergence curve concentration, and computational time. The optimization model is based on series expansion and initial phase distribution: to improve optimization efficiency, series expansion is applied to reduce the number of optimization variables; and initial values ​​with flat-top pattern characteristics are assigned to the phase to further improve efficiency. This invention also makes two improvements to the standard Bat algorithm: introducing inertial weights and chaotic mapping to mitigate the problem of the algorithm getting trapped in local optima.

[0155] Compared with the prior art, the present invention has the following advantages:

[0156] 1. This invention utilizes series expansion to reduce the number of optimization variables and lower the complexity of the optimization problem.

[0157] 2. The initial value setting can be adjusted according to the desired direction pattern, which can improve optimization efficiency while avoiding premature convergence.

[0158] 3. Compared with the standard BA, this invention introduces an inertial weight in the velocity update and then uses chaotic mapping to update the transmission rate, thereby improving the overall performance of the array pattern.

[0159] Another aspect of this invention provides a pure phase array pattern synthesis system based on an improved bat algorithm, comprising:

[0160] The first module is used to set up an array model constructed from multiple antenna elements;

[0161] The second module is used to construct the optimization objective function of the array model;

[0162] The third module is used to minimize the objective function according to the bat algorithm to complete the optimized training of the array model;

[0163] The fourth module is used to perform pure phase array pattern synthesis based on the optimized array model.

[0164] It is understood that the content of the above method embodiments is applicable to this system embodiment. The specific functions implemented in this system embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.

[0165] This invention also provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the above-described pure phase array pattern synthesis method based on the improved bat algorithm. This electronic device can be any smart terminal, including tablet computers, in-vehicle computers, etc.

[0166] It is understood that the content of the above method embodiments is applicable to this device embodiment. The specific functions implemented by this device embodiment are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0167] Please see Figure 9 , Figure 9 The hardware structure of an electronic device according to another embodiment is illustrated. The electronic device includes:

[0168] The processor 901 can be implemented using a general-purpose CPU (Central Processing Unit), microprocessor, application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided in the embodiments of the present invention.

[0169] The memory 902 can be implemented as a read-only memory (ROM), static storage device, dynamic storage device, or random access memory (RAM). The memory 902 can store the operating system and other application programs. When the technical solutions provided in the embodiments of this specification are implemented through software or firmware, the relevant program code is stored in the memory 902 and is called and executed by the processor 901 to execute the pure phase array pattern synthesis method based on the improved bat algorithm of the embodiments of this invention.

[0170] The input / output interface 903 is used to implement information input and output;

[0171] The communication interface 904 is used to enable communication and interaction between this device and other devices. Communication can be achieved through wired means (such as USB, Ethernet cable, etc.) or wireless means (such as mobile network, WIFI, Bluetooth, etc.).

[0172] Bus 905 transmits information between various components of the device (e.g., processor 901, memory 902, input / output interface 903, and communication interface 904);

[0173] The processor 901, memory 902, input / output interface 903, and communication interface 904 are connected to each other within the device via bus 905.

[0174] This invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described pure phase array pattern synthesis method based on the improved bat algorithm.

[0175] It is understood that the content of the above method embodiments is applicable to this storage medium embodiment. The specific functions implemented in this storage medium embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.

[0176] Memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs and non-transitory computer-executable programs. Furthermore, memory may include high-speed random access memory, and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, memory may optionally include memory remotely located relative to the processor, and these remote memories can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0177] It should be noted that in various specific embodiments of the present invention, when processing data related to user identity or characteristics, such as user information, user behavior data, user historical data, and user location information, user permission or consent is obtained first. Furthermore, the collection, use, and processing of this data comply with relevant laws, regulations, and standards. In addition, when embodiments of the present invention require access to sensitive personal information of users, separate permission or consent from the user is obtained through pop-ups or redirection to a confirmation page. Only after obtaining the user's separate permission or consent is the necessary user-related data for the normal operation of the embodiments of the present invention acquired.

[0178] The embodiments described in this invention are for the purpose of more clearly illustrating the technical solutions of the embodiments of this invention, and do not constitute a limitation on the technical solutions provided by the embodiments of this invention. As those skilled in the art will know, with the evolution of technology and the emergence of new application scenarios, the technical solutions provided by the embodiments of this invention are also applicable to similar technical problems.

[0179] Those skilled in the art will understand that the technical solutions shown in the figures do not constitute a limitation on the embodiments of the present invention, and may include more or fewer steps than shown, or combine certain steps, or different steps.

[0180] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0181] Those skilled in the art will understand that all or some of the steps in the methods disclosed above, as well as the functional modules / units in the systems and devices, can be implemented as software, firmware, hardware, or suitable combinations thereof.

[0182] The terms "first," "second," "third," "fourth," etc. (if present) in the specification and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0183] It should be understood that in this invention, "at least one (item)" refers to one or more, and "more than one" refers to two or more. "And / or" describes the relationship between related objects, indicating that three relationships can exist. For example, "A and / or B" can represent three cases: only A exists, only B exists, and both A and B exist simultaneously, where A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one (item) of the following" or similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one (item) of a, b, or c can represent: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, and c can be single or multiple.

[0184] In the several embodiments provided by this invention, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of the units described above is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0185] The units described above as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0186] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0187] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes multiple instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing programs, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0188] The preferred embodiments of the present invention have been described above with reference to the accompanying drawings, but this does not limit the scope of the claims of the present invention. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and spirit of the present invention should be within the scope of the claims of the present invention.

Claims

1. A pure phase array pattern synthesis method based on improved bat algorithm, characterized in that, The method comprises the following steps: setting an array model constructed by a plurality of antenna units; constructing an optimization objective function of the array model; optimizing and training the array model according to a bat algorithm by minimizing the objective function; performing pure phase array pattern synthesis according to the optimized array model; the step of optimizing and training the array model according to the bat algorithm by minimizing the objective function comprises the following steps: Introducing a nonlinearly decreasing inertial weight to adjust the velocity term coefficient, the inertial weight is defined as: ; where, represents the inertial weight; and are constants; represents the current time; represents the maximum number of iterations of the algorithm; The updating of the emission rate in the standard bat algorithm is replaced by a chaotic mapping, and the emission rate in the standard bat algorithm is changed into a chaotic number between 0 and 1 by using a sine mapping; wherein the updating formula of the sine mapping is defined as: Wherein, represents a mapping amplitude constant; represents the emission rate at the moment t. optimizing and training the array model according to the improved bat algorithm; the step of optimizing and training the array model according to the improved bat algorithm comprises the following steps: configuring a population size and a maximum number of iterations; randomly initializing initial positions of each bat in the population; initializing the loudness, emission rate and frequency of emitting pulses of each bat when searching for prey; If the maximum number of iterations is not reached, according to the formula The frequency of pulses emitted by bats at various locations is updated and adjusted, and based on the formula... and The positions and speeds of each bat were updated and adjusted; among them, Representing the The frequency of the pulses emitted by a single bat; This represents the minimum frequency. Represents the maximum frequency; It represents a random vector that follows a uniform distribution; Represents bats exist The position at that moment; Represents bats The velocity at time t; Represents inertia weight; Represents the global optimal solution in the current iteration; When the random number is less than the current emission rate, then according to the formula A new local solution is generated from the optimal solution, and a new solution is generated by random flight until the random number is not less than the current emission rate; wherein, represents a new local solution; represents an old optimal solution; represents a random number; represents the average value of the loudness of all bats at the current iteration; updating the loudness and emission rate of emitting pulses according to a new local solution, calculating the current frequency of emitting pulses, obtaining an optimal solution of the current frequency of emitting pulses, and stopping until the maximum number of iterations is reached.

2. The pure phase array pattern synthesis method based on improved bat algorithm according to claim 1, wherein, The step of setting an array model constructed by a plurality of antenna units comprises the following steps: determining the number of antenna units included in a uniform linear array, determining the spacing between the antenna units of the uniform linear array, and determining the excitation amplitude and excitation phase of each antenna unit; constructing an expression of the far-field pattern of the array as: ， wherein is the scan angle, is the wave number; represents the first antenna element; represents the total number of antenna elements; represents the first antenna element excitation phase; represents the imaginary unit; represents the antenna element spacing.

3. The method of claim 1, wherein, The step of constructing an optimization objective function of the array model comprises the following steps: determining the selection of orthogonal basis functions according to the shape of the basis functions, expanding the phase distribution of the array with M-order orthogonal basis functions to obtain an expression of the target phase distribution of the array; generating an initial phase distribution using a quadratic polynomial, which preliminarily presents flat-top pattern characteristics; adjusting and optimizing the expression of the target phase distribution according to the initial phase distribution; constructing a loss function of the array model to optimize the objective function of the array model.

4. The pure phase array pattern synthesis method based on the improved bat algorithm according to claim 3, wherein an expression of the loss function is: The expression of the target phase distribution is: wherein, represents the target phase distribution; represents a polynomial value range; represents an orthogonal basis function order; represents an mth order basis function; represents a corresponding weight real coefficient; represents an mth order polynomial; represents an mth order polynomial; represents a distance from an mth array element to an array center; represents a total length of an array; The initial phase distribution The expression is: wherein, is a range constant for the initial phase.

5. The pure phase array pattern synthesis method based on the improved bat algorithm according to claim 1, wherein the method comprises: ， wherein, represents a loss function; represents the number of sampling points in the main lobe region; represents a directional pattern; represents the number of sampling points of the side lobe region maximum; represents the sampling angle of the main lobe region; represents a desired directional pattern; and represents a weight coefficient; represents the sampling angle of the side lobe region maximum. a first module for setting an array model constructed by a plurality of antenna units; The updated expression for the loudness of the emitted pulse is: The updated expression for the emission rate of the emission pulses is: wherein, represents the emission rate of the i-th bat at the time instant t; the loudness of the emission pulse of the i-th bat; and represents a constant; represents the initial emission rate; represents the emission rate of the i-th bat at the time instant t; the emission rate of the i-th bat at the time instant t.

6. A system for implementing the improved bat algorithm based pure phase array pattern synthesis method according to any one of claims 1-5, characterized in that, a second module for constructing an optimization objective function of the array model; a third module for optimizing and training the array model according to a bat algorithm by minimizing the objective function; a fourth module for performing pure phase array pattern synthesis according to the optimized array model. a processor and a memory; the memory is used to store a program; 7. An electronic device, comprising: the processor executes the program to implement the method according to any one of claims 1 to 5. The storage medium stores a program, and the program is executed by a processor to implement the method according to any one of claims 1 to 5. ​ 8. A computer-readable storage medium, characterized in that, ​

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