Satellite-borne digital-analog hybrid multi-beam pattern synthesis method and system based on particle swarm algorithm
Patent Information
- Application Number
- CN202610844995.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-06-11
- Publication Date
- 2026-09-15
Smart Images
Figure CN122764255A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the fields of satellite communication and array signal processing technology, specifically to a method and system for satellite-borne hybrid digital-analog multi-beam pattern synthesis based on particle swarm optimization algorithm. Background Technology
[0002] In the fields of satellite communication and array signal processing, multi-beam pattern synthesis technology for phased array antennas faces the dual challenges of accuracy and efficiency. While traditional all-digital beamforming architectures can achieve high degrees of freedom in beam control, their high baseband processing complexity, high power consumption, and expensive RF links make them difficult to meet the stringent resource and power constraints of spaceborne platforms. Therefore, hybrid analog-digital array architectures have become a compromise, but their pattern synthesis problem is more complex: on the one hand, analytical methods (such as Chebyshev weighted and Taylor weighted methods), although computationally fast, have limited joint control over the main lobe profile, side lobe level, and directivity coefficients, and are difficult to adapt to subarray constraints in hybrid analog-digital architectures; on the other hand, among numerical optimization methods, convex optimization and alternating projection methods heavily rely on the gradient information of the objective function, resulting in insufficient global optimization capabilities when dealing with non-convex and discontinuous constraints. While stochastic heuristic algorithms (such as particle swarm optimization and genetic algorithms) do not rely on gradients, existing implementations typically employ random initialization strategies, leading to severe blindness in the search within the high-dimensional solution space.
[0003] The aforementioned limitations lead to the following problems in existing schemes for multi-beam pattern synthesis: The stochastic initialization particle swarm optimization algorithm lacks prior knowledge guidance in the early stages of iteration, resulting in slow convergence, huge computational overhead, and a tendency to get trapped in local optima. It also struggles to simultaneously achieve accurate main lobe contour fitting, precise directional coefficient approximation, and effective sidelobe level suppression. Furthermore, due to the coupling constraint of shared analog domain weights and independent digital domain weights in the hybrid analog-digital architecture, existing methods often simplify the fitness function construction, failing to accurately characterize the trade-offs between multiple objectives. This ultimately results in significant deviations in key performance indicators for the synthesized multi-beam patterns, leading to generally low synthesis accuracy and efficiency. Summary of the Invention
[0004] Based on this, this application provides a method and system for satellite-borne hybrid digital-analog multi-beam pattern synthesis based on particle swarm optimization, which can improve the synthesis accuracy and efficiency of multi-beam patterns.
[0005] Firstly, this application provides a spaceborne hybrid digital-analog multi-beam pattern synthesis method based on particle swarm optimization, including:
[0006] The satellite antenna array parameters, multi-beam mission parameters, and particle swarm optimization (PSO) algorithm parameters are obtained. The PSO algorithm parameters include the number of particles, the maximum number of iterations, the inertial weight, and the acceleration factor. The desired radiation pattern for each beam is constructed based on the multi-beam mission parameters; Based on the satellite antenna array parameters, solve for the initial values of the digital domain weights and the initial values of the analog domain weights; Based on the number of particles in the particle swarm algorithm parameters, the initial values of the digital domain weights and the initial values of the analog domain weights are used as search centers to complete the initialization of multiple particles. Based on the inertia weight and the acceleration factor, the individual extreme value and global extreme value of each particle are updated through iterative optimization until the number of iterations reaches the maximum number of iterations. The global extremum obtained after the maximum number of iterations is decoded, and the optimal digital domain weight vector and the optimal analog domain weight vector are output. The optimal digital domain weight vector and the optimal analog domain weight vector are used to synthesize the desired pattern.
[0007] Optionally, constructing the desired radiation pattern for each beam based on the multi-beam mission parameters includes: Based on the satellite's operating altitude and the radius of the coverage cell, calculate the target beamwidth and target directivity coefficient for each beam; A target power pattern model is established, which includes beamwidth control parameters, sidelobe oscillation control parameters, and sidelobe envelope parameters. Using the target directional coefficient as a constraint, the optimal value of the sidelobe envelope parameter is solved; Based on the optimal values of the sidelobe envelope parameters, the desired power pattern of each beam relative to its beam direction is generated.
[0008] Optionally, the step of solving for the optimal value of the sidelobe envelope parameter with the target directivity coefficient as a constraint includes: Minimize the absolute difference between the constructed pattern directivity coefficient and the target directivity coefficient, wherein the constructed pattern directivity coefficient is determined by the ratio of the value of the target power pattern at the beam center to the hemispherical spatial integral value, and the target power pattern is represented as the larger value of the Gaussian main lobe function and the sinusoidal square side lobe function.
[0009] Optionally, the optimal value of the sidelobe envelope parameter is determined by the following optimization model:
[0010]
[0011] in, To construct the directivity coefficients of the radiation pattern, For the target directionality coefficient, The target power pattern of the k-th beam is shown. For the angle of deviation from the beam direction, For the side lobe envelope parameters, For beamwidth control parameters, These are the sidelobe oscillation control parameters. and Let the elevation and azimuth angles be those of the k-th beam. and For spatial integration variables, Let be the target beamwidth of the k-th beam.
[0012] Optionally, the step of solving for the initial values of the digital domain weights and the initial values of the analog domain weights based on the satellite antenna array parameters includes: Based on the target beamwidth of each beam, determine the Chebyshev weighted main-side lobe ratio parameter; Based on the main lobe-side lobe ratio parameter, the one-dimensional weighted vector in the row direction and the one-dimensional weighted vector in the column direction are calculated using Chebyshev polynomials respectively. Multiply the row-direction one-dimensional weighted vector with the column-direction one-dimensional weighted vector to obtain a two-dimensional weight matrix; The two-dimensional weight matrix is vectorized to obtain the initial value of the digital domain amplitude distribution vector.
[0013] Optionally, the initial value of the digital domain amplitude distribution vector is calculated using the following formula:
[0014] in, It is a two-dimensional weight matrix. Let be a one-dimensional Chebyshev weighted vector in the row direction. Let be a one-dimensional Chebyshev weighted vector along the column direction, and the one-dimensional Chebyshev weighted vector is expressed as:
[0015] in, The number of array elements in the row or column direction. The normalized frequency domain excitation coefficients are uniquely determined by the Chebyshev weighted beam unwinding factor.
[0016] Optionally, based on the number of particles in the particle swarm optimization algorithm parameters, the initial values of the digital domain weights and the initial values of the analog domain weights are used as search centers to initialize multiple particles, including: The initial values of the digital domain weights and the initial values of the analog domain weights are encoded as a center point in the solution space; Using the center point as the mean, a random perturbation is generated in the solution space, and the random perturbation is superimposed on the center point to generate the initial position of each particle. Assign a random velocity vector with zero mean to the initial position of each particle as the initial velocity of each particle.
[0017] Optionally, the step of iteratively updating the individual extremum and global extremum of each particle based on the inertia weight and the acceleration factor until the maximum number of iterations is reached includes: Calculate the joint fitness function for each particle in the current generation. The joint fitness function is the weighted sum of squares of the fitness functions of all beams. The fitness function of each beam includes a fitting error term in the 3dB contour region of the main lobe, a fitting error term in the remaining regions of the main lobe, a penalty term for exceeding the threshold in the side lobe region, and a directional coefficient approximation error term. If the joint fitness function of the current particle is better than the individual extreme value of the particle, then the individual extreme value is updated to the position of the current particle; If the joint fitness function of the current particle is better than the global extremum, then the global extremum is updated to the position of the current particle; Based on the inertia weight, the acceleration factor, and the random number, the current velocity of each particle is weighted and combined with the individual extreme value, the global extreme value, and the current position of the particle to update the velocity of each particle; The position of each particle is updated based on the sum of the updated velocity and the current position of the particle.
[0018] Optionally, the joint fitness function for:
[0019] in, For the first Initial values of the fitness function for each beam; For the current generation Fitness function for each beam:
[0020] in, These are the target weight coefficients for different regions. This refers to the area within and around the 3dB outline of the main lobe of the radiation pattern. The rest of the main lobe, This is the side lobe region. For the first The current generation weight of each beam at the spatial grid point The corresponding amplitude direction pattern, For the first A beam at a spatial grid point The desired amplitude radiation pattern is derived from the target power radiation pattern. The square root is obtained after coordinate mapping. The preset sidelobe threshold To construct the directivity coefficients of the radiation pattern, This is the target directionality coefficient.
[0021] Secondly, this application provides a spaceborne hybrid digital-analog multi-beam pattern synthesis system based on particle swarm optimization, comprising: The parameter configuration module is used to obtain satellite antenna array parameters, multi-beam mission parameters, and particle swarm optimization (PSO) algorithm parameters, including particle number, maximum number of iterations, inertial weight, and acceleration factor. The desired pattern construction module is used to construct the desired pattern of each beam based on the multi-beam mission parameters. The initial value solving module is used to solve for the initial values of the digital domain weights and the initial values of the analog domain weights based on the satellite antenna array parameters; The particle swarm initialization module is used to initialize multiple particles by using the initial values of the digital domain weights and the initial values of the analog domain weights as search centers, based on the number of particles in the particle swarm algorithm parameters. The iterative optimization module is used to update the individual extreme value and global extreme value of each particle through iterative optimization based on the inertia weight and the acceleration factor, until the number of iterations reaches the maximum number of iterations. The weight output module is used to decode the global extremum obtained after the number of iterations reaches the maximum number of iterations, and output the optimal digital domain weight vector and the optimal analog domain weight vector. The optimal digital domain weight vector and the optimal analog domain weight vector are used to synthesize the desired orientation pattern.
[0022] Compared with existing technologies, the advantages of this application are as follows: By using the initial weights as the search center for the particle swarm optimization (PSO) algorithm, the blindness of searching in a large-scale solution space by traditional random initialization PSO algorithms is effectively overcome. Prior guidance information with clear physical meaning is obtained before iterative optimization, enabling the PSO to perform a fine search near a high-quality starting point, thereby significantly accelerating the convergence speed and reducing computational overhead. Simultaneously, since the initial values themselves possess good pattern performance, the final optimization result is less likely to get trapped in local optima, and can simultaneously consider multiple objectives such as main lobe contour fitting, directional coefficient approximation, and sidelobe suppression. The optimal digital domain weights and analog domain weights obtained by decoding the global extrema can improve the overall accuracy and efficiency of the multi-beam pattern. Attached Figure Description
[0023] Figure 1 A schematic diagram illustrating the steps of the spaceborne digital-analog hybrid multibeam pattern synthesis method based on particle swarm optimization algorithm provided in this application embodiment.
[0024] Figure 2This is a schematic diagram of a spaceborne hybrid digital-analog antenna array architecture provided in an embodiment of this application.
[0025] Figure 3 This is a schematic diagram of the simulation results of the first beam pattern synthesized from the embodiments of this application.
[0026] Figure 4 This is a schematic diagram of the simulation results of the radiation pattern of the second beam synthesized from the embodiments of this application.
[0027] Figure 5 This is a schematic diagram of the simulation results of the radiation pattern of the third beam synthesized from the embodiments of this application.
[0028] Figure 6 This is a schematic diagram of the simulation results of the radiation pattern of the fourth beam synthesized from the embodiments of this application. Detailed Implementation
[0029] The present application will now be described in further detail with reference to experimental examples and specific embodiments. However, this should not be construed as limiting the scope of the subject matter of the present application to the following embodiments. All technologies implemented based on the content of the present application fall within the scope of protection of the present application.
[0030] In the description of the embodiments in this application, "a plurality of" means two or more, unless otherwise expressly specified. The reference to "embodiment" herein means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places in the specification does not necessarily refer to the same embodiment, nor is it a mutually exclusive, independent, or alternative embodiment. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.
[0031] Please refer to Figure 1 , Figure 1 A schematic diagram illustrating the steps of a spaceborne hybrid digital-analog multi-beam pattern synthesis method based on particle swarm optimization (PSO) algorithm provided in this application embodiment. The method may include: S1. Obtain satellite antenna array parameters, multi-beam mission parameters, and particle swarm algorithm parameters.
[0032] The particle swarm optimization (PSO) algorithm parameters include the number of particles, maximum number of iterations, inertia weight, and acceleration factor. Satellite antenna array parameters specifically include the total size of the antenna array (e.g., ...). Individual array elements), simulated subarray size (e.g., Satellite antenna array parameters, such as satellite operating frequency and altitude, characterize the array's physical configuration and the basic characteristics of the satellite-to-ground link. Multi-beam mission parameters include the center pointing angles (elevation angles) of the multiple ground beams that need to be served simultaneously. With azimuth ,in And the cell radius that each beam needs to cover. Multi-beam mission parameters characterize the service requirements of satellite communication systems. Particle swarm optimization (PSO) control parameters include the particle swarm size. Maximum number of iterations Inertia weight and acceleration factor and The particle swarm optimization (PSO) control parameters are used to guide the subsequent intelligent optimization process.
[0033] S2. Construct the desired radiation pattern for each beam based on the multi-beam mission parameters.
[0034] The desired radiation pattern is an ideal target power radiation pattern. It depends on the angle of deviation from the beam center. And an adjustable sidelobe envelope parameter By setting the target beamwidth With target directionality coefficient And solve a problem using This is a constrained optimization problem for variables, aiming to construct a radiation pattern that satisfies the beamwidth required for cell coverage, makes the actual directivity coefficients as close as possible to the target values, and controls the shape of the sidelobes. The construction of the desired radiation pattern provides an accurate fitting benchmark for subsequent synthesis.
[0035] S3. Based on the satellite antenna array parameters, solve for the initial values of the digital domain weights and the initial values of the analog domain weights.
[0036] In this embodiment, the initial values of the weights in the digital and analog domains can be solved analytically. Specifically, the initial value of the amplitude distribution vector in the digital domain can be calculated using the Chebyshev weighted algorithm based on the target beamwidth of each beam. For the phase distribution in the digital and analog domains, the initial phase values are calculated separately using conventional beamforming methods (i.e., phase conjugate pointing towards the desired beam center). and .
[0037] S4. Based on the number of particles in the particle swarm algorithm parameters, use the initial values of the digital domain weights and the initial values of the analog domain weights as the search centers to complete the initialization of multiple particles.
[0038] The initial values of amplitude and phase in the digital domain and the initial value of phase in the analog domain are jointly encoded into a center point in the solution space. Then, using this center point as the mean, random perturbations are superimposed in the solution space to generate... The initial position of each particle Each particle is given a random initial velocity with zero mean. Based on these initial positions and velocities, the individual extrema of each particle are further initialized. (i.e., the best position in the particle's history) and the global extremum of the entire population. (That is, the position with the highest fitness among all particles).
[0039] S5. Based on the inertia weight and acceleration factor, update the individual extreme value and global extreme value of each particle through iterative optimization until the maximum number of iterations is reached.
[0040] The iterative optimization process follows the standard evolutionary rules of the particle swarm optimization algorithm. In each generation, the joint fitness function of each particle is first calculated. This function comprehensively evaluates the pattern performance of all beams under the digital and analog domain weights corresponding to the current particle, including the main lobe profile fitting error, whether the side lobe level exceeds a preset threshold, and the deviation of the directivity coefficient from the target value. Then, the individual extreme values of each particle are updated based on the fitness values: if the fitness of the current particle is better than its historical best, its individual extreme value is replaced; simultaneously, if there is a particle better than the global extreme value, the global extreme value is updated. Afterwards, inertial weights are used... Accelerator , And random numbers, updated according to the speed formula Adjust the velocity of each particle and update the formula according to its position. Move each particle to its new position. Repeat this process until the current iteration count reaches the preset maximum iteration count. .
[0041] S6. Decode the global extremum obtained after the maximum number of iterations, and output the optimal digital domain weight vector and the optimal analog domain weight vector.
[0042] The optimal digital domain weight vector and the optimal analog domain weight vector are used to synthesize the desired radiation pattern. When the iteration terminates, the global extremum is... This corresponds to the optimal solution found throughout the entire search process. The global extremum is decoded to extract the optimal numerical domain weight vector. (Each beam is independent) and the optimal simulation domain weight vector (Shared by all beams). These two sets of weight vectors are the final synthesis result. Applying them to a spaceborne hybrid digital-analog antenna array can achieve the best compromise between multiple targets in the multi-beam pattern generated by the array, accurately fitting the desired pattern of each beam.
[0043] For example, please see Figure 2 , Figure 2This is a schematic diagram of the spaceborne hybrid digital-analog antenna array architecture provided in an embodiment of this application. The spaceborne hybrid digital-analog antenna array architecture employs a sub-array cascade mode: the antenna array is divided into several smaller subarrays. Within each subarray, low-power analog amplitude and phase control is achieved using variable amplitude and phase units and combiners. At the output of each subarray, an independent RF link and ADC are connected, and finally, the data is sent to a DSP for baseband digital domain processing. In this architecture, analog beamforming is achieved within each subarray using analog amplitude and phase units and combiners, while digital beamforming is achieved between subarrays through independent RF links, ADCs, and DSPs, thus balancing system power consumption and beam control performance.
[0044] Under this architecture, let the total size of the antenna array be... Simulated subarray size The number of digital channels is For the first Each beam direction, array radiation pattern in full space This can be represented as the synthesis of each analog subarray factor and the digital weighting vector, as shown in equation (1):
[0045] in, Indicates the first Each beam corresponds to a digital domain weight vector. For the equivalent digital domain guided vector, where the first... The element represents the first The radiation pattern response of each subarray after simulated beamforming is as follows:
[0046] in, The simulation domain weight vector is shared by all subarrays; For the first Subarray guiding vector.
[0047] Set the operating frequency of the satellite antenna array Operating height Number of multibeams Set service ground beam angle information Coverage radius Set the number of particles in the particle swarm optimization algorithm. Maximum number of iterations Inertia weight Accelerator , Initialize the current iteration count. .
[0048] In some embodiments, constructing the desired radiation pattern for each beam based on the multi-beam mission parameters may include: Based on the satellite's operating altitude and the radius of the coverage cell, the target beamwidth and target directivity coefficient of each beam are calculated; a target power pattern model is established, which includes beamwidth control parameters, sidelobe oscillation control parameters, and sidelobe envelope parameters; the optimal value of the sidelobe envelope parameters is solved using the target directivity coefficient as a constraint; and the desired power pattern of each beam relative to its beam direction is generated based on the optimal value of the sidelobe envelope parameters.
[0049] The antenna directivity coefficient is the ratio of the array's maximum transmit density to its average transmit density.
[0050] Then, based on the satellite's operating altitude With coverage cell radius Calculate the first one respectively Target beamwidth of each beam With target directionality coefficient .
[0051] Using the target directivity coefficient as a constraint, the optimal value of the sidelobe envelope parameter is solved, specifically including: Minimize the absolute difference between the constructed pattern directivity coefficient and the target directivity coefficient, wherein the constructed pattern directivity coefficient is determined by the ratio of the value of the target power pattern at the beam center to the hemispherical spatial integral value, and the target power pattern is represented as the larger value of the Gaussian main lobe function and the sinusoidal square side lobe function.
[0052] The optimal values of the sidelobe envelope parameters are determined using the following optimization model:
[0053]
[0054] in, To construct the directivity coefficients of the radiation pattern, For the target directionality coefficient, The target power pattern of the k-th beam is shown. For the angle of deviation from the beam direction, For the side lobe envelope parameters, For beamwidth control parameters, These are the sidelobe oscillation control parameters. and Let the elevation and azimuth angles be those of the k-th beam. and For spatial integration variables, Let be the target beamwidth of the k-th beam.
[0055] Optionally, the step of solving for the initial values of the digital domain weights and the initial values of the analog domain weights based on the satellite antenna array parameters includes: Based on the target beamwidth of each beam, the Chebyshev-weighted main-sidelobe ratio parameter is determined; based on the main-sidelobe ratio parameter, the row-direction one-dimensional weighted vector and the column-direction one-dimensional weighted vector are calculated using Chebyshev polynomials respectively; the row-direction one-dimensional weighted vector and the column-direction one-dimensional weighted vector are multiplied to obtain a two-dimensional weight matrix; the two-dimensional weight matrix is vectorized to obtain the initial value of the digital domain amplitude distribution vector.
[0056] To improve the convergence efficiency of the algorithm, the initial values of the weights in each domain are solved analytically in this embodiment. Regarding the amplitude distribution, the Chebyshev weighted algorithm is used to solve for the amplitude vector distribution in the digital domain. Regarding the phase distribution, the initial digital domain phase values are calculated using conventional beamforming methods (i.e., phase conjugate pointing towards the desired beam center). Initial phase value of the analog domain The calculation of the initial phase value is relatively straightforward, while solving for the initial amplitude value requires mapping the Chebyshev polynomial to the array pattern. The specific process is as follows: To map Chebyshev polynomials to an array of orientation patterns, it is necessary to... Each digital domain unit performs frequency sampling in cosine space:
[0057] in, Determine the parameters of the Chebyshev polynomial in the main lobe region. Main lobe ratio with beam spreader The only certainty:
[0058] The Chebyshev polynomial is expressed as:
[0059] variable The range of values for determines the characteristics of the radiation pattern. There are within the sidelobe region. At this point, the polynomial is expressed as a cosine function: The main lobe region contains ,because At this point, the polynomial is a hyperbolic cosine function: Finally, the frequency domain excitation coefficients are obtained through normalization. :
[0060] Based on the principle of Inverse Discrete Cosine Transform (IDCT), the amplitude weighting values of the array elements are extracted:
[0061] in For the array center index, The number of array elements in the row or column direction. The normalized frequency domain excitation coefficients are uniquely determined by the Chebyshev weighted beam unwinding factor.
[0062] The above one-dimensional weighted vector This corresponds to the amplitude distribution along the row (or column) direction. Since the amplitude distribution of a two-dimensional planar array can be decomposed into the product of the weights of two independent one-dimensional linear arrays, the two-dimensional amplitude distribution coefficients... It can be decomposed into the product of the weights of two independent one-dimensional linear matrices:
[0063] in, , These are the one-dimensional Chebyshev weighted vectors in the row and column directions, respectively. Vectorizing the two-dimensional amplitude distribution yields the initial values of the digital domain amplitude distribution vector. :
[0064] Optionally, based on the number of particles in the particle swarm optimization algorithm parameters, the initial values of the digital domain weights and the initial values of the analog domain weights are used as search centers to initialize multiple particles, including: The initial values of the digital domain weights and the initial values of the analog domain weights are encoded as a center point in the solution space; a random perturbation is generated in the solution space with the center point as the mean, and the random perturbation is superimposed on the center point to generate the initial position of each particle; a random velocity vector with zero mean is assigned to the initial position of each particle as the initial velocity of each particle.
[0065] In the particle swarm initialization phase, the initial values of the digital domain weights obtained from the analytical solution and the initial values of the analog domain weights are first encoded together as a center point in the solution space. This center point represents the highest priority information obtained based on Chebyshev weighting and conventional beamforming, and serves as the starting point and benchmark for the entire particle swarm search. Specifically, the initial values of the digital domain weights include the initial values of the amplitude distribution vectors of each beam. Initial value of phase distribution vector The initial values of the simulation domain weights are the initial values of the simulation domain phase distribution vector. These values are concatenated or encoded into a high-dimensional vector, which serves as the center point in the solution space.
[0066] Using the center point as the mean, a random perturbation conforming to a certain probability distribution (e.g., uniform or normal distribution) is generated in the solution space. For each particle, the random perturbation is superimposed on the center point to generate the initial position of the particle. ( Each particle is assigned a random velocity vector with zero mean at its initial position. The initial velocity is denoted as . The magnitude of the initial velocity is usually controlled within a certain range to ensure that the particle can effectively search near the center in the early stages of iteration.
[0067] After setting the initial position and initial velocity, the individual extreme values of each particle are further initialized. and the global extreme value of the entire population. Specifically, the individual extremum of each particle is initialized to its own initial position. That is, the initial position is assumed to be the optimal solution found by the particle; the global extremum is initialized to the position of the particle with the best fitness function value (minimum or maximum, depending on the optimization objective) among all particles.
[0068] Optionally, the step of iteratively updating the individual extremum and global extremum of each particle based on the inertia weight and the acceleration factor until the maximum number of iterations is reached includes: Calculate the joint fitness function for each particle in the current generation. The joint fitness function is the weighted sum of squares of the fitness functions of all beams. The fitness function of each beam includes a fitting error term within the 3dB contour region of the main lobe, a fitting error term within the remaining regions of the main lobe, a penalty term for exceeding the threshold in the side lobe region, and a directional coefficient approximation error term. If the joint fitness function of the current particle is better than the individual extreme value of the particle, then the individual extreme value is updated as the position of the current particle. If the joint fitness function of the current particle is better than the global extreme value, then the global extreme value is updated as the position of the current particle. Based on the inertia weight, the acceleration factor, and a random number, the current velocity of each particle is weighted and combined with the individual extreme value, the global extreme value, and the current position of the particle to update the velocity of each particle. The position of each particle is updated based on the sum of the updated velocity and the current position of the particle.
[0069] Calculate the joint fitness function for each particle in the current generation. Its construction method is as follows:
[0070] in, For the first Initial values of the fitness function for each beam; For the current generation The fitness function of each beam. The error is integrated into four aspects: fitting error in the 3dB contour region of the main lobe, fitting error in the remaining regions of the main lobe, penalty error for side lobe regions exceeding the preset threshold, and directional coefficient approximation error. The specific expression is:
[0071]
[0072] in, These are the target weight coefficients for different regions. This refers to the area within and around the 3dB outline of the main lobe of the radiation pattern. The rest of the main lobe, This is the side lobe region. For the first The current generation weight of each beam at the spatial grid point The corresponding amplitude direction pattern, For the first A beam at a spatial grid point The desired amplitude radiation pattern is derived from the target power radiation pattern. The square root is obtained after coordinate mapping. The preset sidelobe threshold To construct the directivity coefficients of the radiation pattern, This is the target directionality coefficient.
[0073] After obtaining the joint fitness function for each particle, the individual extreme values and the global extreme value are updated accordingly. Specifically, if the joint fitness function of the current particle is better than the individual extreme value recorded in the particle's history, then... Then the individual extreme value is updated to the current particle position. If the joint fitness function of the current particle is better than the global optimum of the entire population. If the global extremum is not found, the position of the current particle is updated. Then, the velocity and position of each particle are updated according to the evolution rules of the particle swarm optimization algorithm. The velocity update formula is:
[0074] in, For inertial weights, , As an acceleration factor, it reflects the weights of individual cognitive and social learning terms in particles. , In order to be in A random number that is uniformly distributed within the range; and For individual extrema and global extrema, This represents the particle's current position.
[0075] Position updates are achieved by superimposing the current speed and the current position, that is:
[0076] The above process is repeated until the current iteration number reaches the preset maximum iteration number. In each iteration, all particles dynamically adjust their search direction based on their fitness, gradually approaching the global optimum.
[0077] Based on this, after each generation of iterative optimization is completed, the current generation is determined. Is it less than the preset maximum number of iterations? If the condition is met, increment the current algebra by one (let...). ), and return to the iterative optimization process, continuing to execute the joint fitness function calculation, extreme value update, and particle position and velocity evolution; if the condition is not met (i.e., the current generation has reached), If the iteration search terminates, the global extremum is found. This is the optimal solution found during the entire search process.
[0078] After the iteration terminates, the global extremum is... Decoding is performed to extract the optimal result of the corresponding digital domain weight vector and analog domain weight vector. Specifically, the optimal result of the digital domain weight vector is denoted as... (Each beam is independent), the optimal result of the simulated domain weight vector is denoted as... (Shared by all beams). By applying these two sets of optimal weights to the spaceborne hybrid digital-analog antenna array, the desired radiation patterns of each beam can be accurately synthesized, so that the actual generated multi-beam radiation pattern achieves an optimal trade-off in multiple indicators such as main lobe profile, directivity coefficient, and sidelobe suppression, thus realizing the synthesis of the desired radiation patterns of multiple beams.
[0079] In the above implementation process, by using the initial weights as the search center for the particle swarm optimization (PSO) algorithm, the blindness of searching in a large-scale solution space by traditional stochastic initialization PSO algorithms is effectively overcome. Prior guidance information with clear physical meaning is obtained before iterative optimization, enabling the PSO to perform a fine search near a high-quality starting point, thus significantly accelerating the convergence speed and reducing computational overhead. Simultaneously, since the initial values themselves possess good pattern performance, the final optimization result is less likely to get trapped in local optima, and can simultaneously consider multiple objectives such as main lobe contour fitting, directional coefficient approximation, and sidelobe suppression. The optimal digital domain weights and analog domain weights obtained by decoding the global extrema can improve the overall accuracy and efficiency of the multi-beam pattern.
[0080] To further verify the performance of the method of the present invention, a simulation experiment was conducted. The relevant parameter configurations for this simulation experiment are shown in Table 1. Table 1
[0081] Please refer to Figures 3 to 6 , Figures 3 to 6 The radiation pattern performance of four typical beams synthesized in this application is shown. A comprehensive observation of each pattern reveals that the joint optimization method proposed in this invention exhibits excellent synergistic improvement effects on several key indicators: Regarding the main lobe contour fitting, as can be seen from the 3dB contour comparison in the upper left corner of each image, the optimized... The contour line can fit the desired radiation pattern contour line well; regarding the directional coefficient, with Figure 6 For example, the target directionality coefficient The actual directionality coefficient optimized by the method of this invention reaches The error is only The remaining beams ( Figures 3 to 5 The directional coefficient error is strictly controlled. Meanwhile, as can be seen from the directional cosine domain radiation pattern section below each figure and the three-dimensional radiation pattern in the upper right corner, all sidelobes are suppressed within the preset threshold. In summary, the method of this invention achieves joint optimization of the main lobe shape, radiation directivity coefficient, and sidelobe levels of a multi-beam hybrid architecture, thus ensuring good overall radiation pattern performance.
[0082] Based on the same concept, embodiments of this application also provide a spaceborne hybrid digital-analog multi-beam pattern synthesis system based on particle swarm optimization, including: The parameter configuration module is used to obtain satellite antenna array parameters, multi-beam mission parameters, and particle swarm optimization (PSO) algorithm parameters, including particle number, maximum number of iterations, inertial weight, and acceleration factor. The desired pattern construction module is used to construct the desired pattern of each beam based on the multi-beam mission parameters. The initial value solving module is used to solve for the initial values of the digital domain weights and the initial values of the analog domain weights based on the satellite antenna array parameters; The particle swarm initialization module is used to initialize multiple particles by using the initial values of the digital domain weights and the initial values of the analog domain weights as search centers, based on the number of particles in the particle swarm algorithm parameters. The iterative optimization module is used to update the individual extreme value and global extreme value of each particle through iterative optimization based on the inertia weight and the acceleration factor, until the number of iterations reaches the maximum number of iterations. The weight output module is used to decode the global extremum obtained after the number of iterations reaches the maximum number of iterations, and output the optimal digital domain weight vector and the optimal analog domain weight vector. The optimal digital domain weight vector and the optimal analog domain weight vector are used to synthesize the desired orientation pattern.
[0083] It should be understood that when the various modules of the system provided in the above embodiments are working, the division of each functional module in the above description is only used as an example. In actual applications, the above functions can be assigned to different functional modules as needed. That is, the internal structure of the device can be divided into different functional modules to complete all or part of the functions described above.
[0084] The functional modules in the above embodiments 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. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of the embodiments of this application.
[0085] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.
Claims
1. A spaceborne hybrid digital-analog multi-beam pattern synthesis method based on particle swarm optimization, characterized in that, include: The satellite antenna array parameters, multi-beam mission parameters, and particle swarm optimization (PSO) algorithm parameters are obtained. The PSO algorithm parameters include the number of particles, the maximum number of iterations, the inertial weight, and the acceleration factor. The desired radiation pattern for each beam is constructed based on the multi-beam mission parameters; Based on the satellite antenna array parameters, solve for the initial values of the digital domain weights and the initial values of the analog domain weights; Based on the number of particles in the particle swarm algorithm parameters, the initial values of the digital domain weights and the initial values of the analog domain weights are used as search centers to complete the initialization of multiple particles. Based on the inertia weight and the acceleration factor, the individual extreme value and global extreme value of each particle are updated through iterative optimization until the number of iterations reaches the maximum number of iterations. The global extremum obtained after the maximum number of iterations is decoded, and the optimal digital domain weight vector and the optimal analog domain weight vector are output. The optimal digital domain weight vector and the optimal analog domain weight vector are used to synthesize the desired pattern.
2. The spaceborne hybrid digital-analog multi-beam pattern synthesis method based on particle swarm optimization algorithm according to claim 1, characterized in that, The step of constructing the desired radiation pattern for each beam based on the multi-beam mission parameters includes: Based on the satellite's operating altitude and the radius of the coverage cell, calculate the target beamwidth and target directivity coefficient for each beam; A target power pattern model is established, which includes beamwidth control parameters, sidelobe oscillation control parameters, and sidelobe envelope parameters. Using the target directional coefficient as a constraint, the optimal value of the sidelobe envelope parameter is solved; Based on the optimal values of the sidelobe envelope parameters, the desired power pattern of each beam relative to its beam direction is generated.
3. The spaceborne hybrid digital-analog multi-beam pattern synthesis method based on particle swarm optimization algorithm according to claim 2, characterized in that, The step of solving for the optimal value of the sidelobe envelope parameter, constrained by the target directional coefficient, includes: Minimize the absolute difference between the constructed pattern directivity coefficient and the target directivity coefficient, wherein the constructed pattern directivity coefficient is determined by the ratio of the value of the target power pattern at the beam center to the hemispherical spatial integral value, and the target power pattern is represented as the larger value of the Gaussian main lobe function and the sinusoidal square side lobe function.
4. The spaceborne hybrid digital-analog multi-beam pattern synthesis method based on particle swarm optimization algorithm according to claim 3, characterized in that, The optimal values of the sidelobe envelope parameters are determined by the following optimization model: in, To construct the directivity coefficients of the radiation pattern, For the target directionality coefficient, The target power pattern of the k-th beam is shown. For the angle of deviation from the beam direction, For the side lobe envelope parameters, For beamwidth control parameters, These are the sidelobe oscillation control parameters. and Let the elevation and azimuth angles be those of the k-th beam. and For spatial integration variables, Let be the target beamwidth of the k-th beam.
5. The spaceborne hybrid digital-analog multi-beam pattern synthesis method based on particle swarm optimization algorithm according to claim 1, characterized in that, The step of solving for the initial values of the digital domain weights and the initial values of the analog domain weights based on the satellite antenna array parameters includes: Determine the Chebyshev weighted main-sidelobe ratio parameter based on the target beamwidth of each beam; Based on the main lobe-side lobe ratio parameter, the one-dimensional weighted vector in the row direction and the one-dimensional weighted vector in the column direction are calculated using Chebyshev polynomials respectively. Multiply the row-direction one-dimensional weighted vector with the column-direction one-dimensional weighted vector to obtain a two-dimensional weight matrix; The two-dimensional weight matrix is vectorized to obtain the initial value of the digital domain amplitude distribution vector.
6. The spaceborne hybrid digital-analog multi-beam pattern synthesis method based on particle swarm optimization algorithm according to claim 5, characterized in that, The initial value of the digital domain amplitude distribution vector is calculated using the following formula: in, It is a two-dimensional weight matrix. Let be a one-dimensional Chebyshev weighted vector in the row direction. Let be a one-dimensional Chebyshev weighted vector along the column direction, and the one-dimensional Chebyshev weighted vector is expressed as: in, The number of array elements in the row or column direction. The normalized frequency domain excitation coefficients are uniquely determined by the Chebyshev weighted beam unwinding factor.
7. The spaceborne hybrid digital-analog multi-beam pattern synthesis method based on particle swarm optimization algorithm according to claim 1, characterized in that, Based on the number of particles in the particle swarm optimization algorithm parameters, the initial values of the digital domain weights and the initial values of the analog domain weights are used as search centers to initialize multiple particles, including: The initial values of the digital domain weights and the initial values of the analog domain weights are encoded as a center point in the solution space; Using the center point as the mean, a random perturbation is generated in the solution space, and the random perturbation is superimposed on the center point to generate the initial position of each particle. Assign a random velocity vector with zero mean to the initial position of each particle as the initial velocity of each particle.
8. The spaceborne hybrid digital-analog multi-beam pattern synthesis method based on particle swarm optimization algorithm according to claim 1, characterized in that, The step of iteratively updating the individual extremum and global extremum of each particle based on the inertia weight and the acceleration factor until the maximum number of iterations is reached includes: Calculate the joint fitness function for each particle in the current generation. The joint fitness function is the weighted sum of squares of the fitness functions of all beams. The fitness function of each beam includes a fitting error term in the 3dB contour region of the main lobe, a fitting error term in the remaining regions of the main lobe, a penalty term for exceeding the threshold in the side lobe region, and a directional coefficient approximation error term. If the joint fitness function of the current particle is better than the individual extreme value of the particle, then the individual extreme value is updated to the position of the current particle; If the joint fitness function of the current particle is better than the global extremum, then the global extremum is updated to the position of the current particle; Based on the inertia weight, the acceleration factor, and the random number, the current velocity of each particle is weighted and combined with the individual extreme value, the global extreme value, and the current position of the particle to update the velocity of each particle; The position of each particle is updated based on the sum of the updated velocity and the current position of the particle.
9. The spaceborne hybrid digital-analog multi-beam pattern synthesis method based on particle swarm optimization algorithm according to claim 8, characterized in that, Joint fitness function for: in, For the first Initial values of the fitness function for each beam; For the current generation Fitness function for each beam: in, These are the target weight coefficients for different regions. This refers to the area within and around the 3dB outline of the main lobe of the radiation pattern. The rest of the main lobe, This is the side lobe region. For the first The current generation weight of each beam at the spatial grid point The corresponding amplitude direction pattern, For the first A beam at a spatial grid point The desired amplitude radiation pattern is derived from the target power radiation pattern. The square root is obtained after coordinate mapping. The preset sidelobe threshold To construct the directivity coefficients of the radiation pattern, This is the target directionality coefficient.
10. A spaceborne hybrid digital-analog multi-beam pattern synthesis system based on particle swarm optimization algorithm, characterized in that, include: The parameter configuration module is used to obtain satellite antenna array parameters, multi-beam mission parameters, and particle swarm optimization (PSO) algorithm parameters, including particle number, maximum number of iterations, inertial weight, and acceleration factor. The desired pattern construction module is used to construct the desired pattern of each beam based on the multi-beam mission parameters. The initial value solving module is used to solve for the initial values of the digital domain weights and the initial values of the analog domain weights based on the satellite antenna array parameters; The particle swarm initialization module is used to initialize multiple particles by using the initial values of the digital domain weights and the initial values of the analog domain weights as search centers, based on the number of particles in the particle swarm algorithm parameters. The iterative optimization module is used to update the individual extreme value and global extreme value of each particle through iterative optimization based on the inertia weight and the acceleration factor, until the number of iterations reaches the maximum number of iterations. The weight output module is used to decode the global extremum obtained after the number of iterations reaches the maximum number of iterations, and output the optimal digital domain weight vector and the optimal analog domain weight vector. The optimal digital domain weight vector and the optimal analog domain weight vector are used to synthesize the desired orientation pattern.