A 3D beamforming method based on antenna array

Abstract

The present application relates to the field of electric communication technology, specifically to a 3D beamforming method based on antenna array. The present application obtains the spatial position of each frequency band of the array element in the multi-frequency common-aperture array, the feed network channel and the current phase shift state, determines the local influence neighborhood according to the geometric distance between the different frequency array elements; obtains the cross-frequency disturbance codebook based on the local influence neighborhood, determines the cross-frequency compensation data of each frequency band for the target electric regulating state according to the amplitude disturbance mapping and phase manifold mapping therein; corrects the basic weighting value by using the cross-frequency compensation data, and obtains the three-dimensional preset beam; obtains the terminal pilot feedback in the ground target area and the low-altitude target area, constructs the joint coverage function in combination with the terminal pilot feedback and the three-dimensional preset beam; performs joint gradient optimization on the joint coverage function based on the array manifold constraint, updates the initial correction weight value by using the converged optimization result, and outputs the cooperative weighting value of each frequency band.

Description

Technical Field

[0001] This invention relates to the field of telecommunications technology, specifically to a 3D beamforming method based on an antenna array. Background Technology

[0002] As mobile communication networks evolve towards multi-frequency coordination, three-dimensional coverage, and intelligent control, multi-frequency co-aperture antennas are increasingly being applied to base station communication systems. These antennas arrange multiple array elements operating at different frequency bands within a limited physical aperture, and change the beam direction and coverage range of each frequency band through a feed network and phase-shift control. For base stations that simultaneously undertake communication tasks in both ground and low-altitude areas, it is also necessary to dynamically adjust the three-dimensional beam according to the spatial location of different target areas to meet the requirements of wide-area ground coverage and directional coverage of low-altitude targets.

[0003] Existing beamforming methods typically calculate the amplitude and phase control data of each array element based on array structure parameters, target orientation, and preset beamforming rules. Some methods also utilize pre-established beam parameter tables or array response models for control. However, in multi-frequency co-aperture arrays, there are spatial relationships, feed paths, and phase shift states between array elements in different frequency bands. When the electrically tunable state or the three-dimensional orientation of the target changes, the amplitude and phase disturbances between different frequency bands will also change accordingly. Using fixed compensation parameters is difficult to continuously adapt to these dynamic changes, while overall modeling and real-time solving of all frequency bands and all array elements would result in a large data scale and computational load. Furthermore, the beam state obtained based on the theoretical array model may be affected by the propagation environment and equipment status, making it difficult for the beamforming weights obtained by simply relying on the preset model to accurately reflect the actual coverage.

[0004] Therefore, the core technical problem that urgently needs to be solved is to effectively filter and structure the data with practical relevance to the cross-frequency amplitude and phase disturbances generated by multi-frequency co-aperture arrays during dynamic electrical adjustment and three-dimensional joint coverage, so as to obtain cooperative shaping weights that are adapted to the current electrical adjustment state and the three-dimensional direction of the target.

[0005] To address this, a 3D beamforming method based on an antenna array is proposed. Summary of the Invention

[0006] The purpose of this invention is to provide a 3D beamforming method based on an antenna array, which performs joint gradient optimization on the joint coverage function based on array manifold constraints, updates the initial correction weights using the converged optimization results, and outputs the cooperative beamforming weights for each frequency band.

[0007] To achieve the above objectives, the present invention provides the following technical solution: A 3D beamforming method based on an antenna array includes: The spatial location of array elements, feed network channels, and current phase shift state of each frequency band in the multi-frequency common aperture array are obtained, and the local influence neighborhood is determined based on the geometric distance between the different frequency array elements. The cross-frequency perturbation codebook is obtained based on the local influence neighborhood. The cross-frequency perturbation codebook includes the amplitude perturbation mapping and phase manifold mapping established by the frequency band reference direction response under the reference electrically regulated state. Receive joint coverage instructions and acquire the three-dimensional orientation and electrical control status of targets in ground target areas and low-altitude target areas; combine amplitude perturbation mapping and phase manifold mapping to determine the cross-frequency compensation data for each frequency band in response to the electrical control status of the targets; The basic beamforming weights of each frequency band are corrected using cross-frequency compensation data to obtain initial corrected weights, and three-dimensional preset beams of the corresponding frequency bands are generated based on the initial corrected weights. The terminal pilot feedback in the ground target area and the low-altitude target area is obtained. The terminal pilot feedback is combined with the three-dimensional preset beam to construct a joint coverage function including a cross-frequency overlap penalty term. Joint gradient optimization is performed on the joint coverage function based on array manifold constraints. The initial correction weights are updated using the converged optimization results, and the cooperative shaping weights of each frequency band are output.

[0008] The steps for determining the local influence neighborhood based on the geometric distance between different frequency array elements include: converting the spatial position of the array elements into three-dimensional coordinate parameters in the base station coordinate system, and calculating the three-dimensional spatial distance between the array element to be compensated and the other different frequency array elements; initially screening the different frequency array elements whose three-dimensional spatial distance is less than a preset distance benchmark as initial candidate array elements; analyzing the feed network channel and the current phase shift state, and extracting the feed correlation degree and continuous phase difference between the array element to be compensated and the initial candidate array elements; synchronously performing nonlinear mapping on the three-dimensional spatial distance, feed correlation degree and continuous phase difference to convert them into continuous cross-frequency weights; selecting the initial candidate array elements whose continuous cross-frequency weights are higher than a preset weight threshold, and performing spatial clustering association with the array element to be compensated to generate the local influence neighborhood of the corresponding array element to be compensated.

[0009] The steps for obtaining the cross-frequency perturbation codebook include: injecting reference test signals into a multi-frequency common-aperture array under multiple reference electrically tunable states to obtain measured radiation sequences of each frequency band in a predetermined discrete direction; comparing the measured radiation sequences with the reference radiation sequences under uncoupled states to separate the fundamental amplitude offset and fundamental phase offset corresponding to each frequency band; extracting periodic transition nodes in the fundamental phase offset and mapping the transition phases to smooth phase data in a continuous smooth space using phase dewinding processing; constructing an amplitude perturbation mapping based on the fundamental amplitude offset and the corresponding reference electrically tunable states, and simultaneously constructing a phase manifold mapping based on the smooth phase data and the corresponding reference electrically tunable states; and combining the amplitude perturbation mapping and the phase manifold mapping in a structured data manner according to the topological relationship of the local influence neighborhood to generate the cross-frequency perturbation codebook.

[0010] The steps for determining the cross-frequency compensation data for each frequency band in relation to the target electrically regulated state include: extracting nearby calibration nodes distributed around the target electrically regulated state and the target three-dimensional direction in the cross-frequency disturbance codebook, using the local influence neighborhood as the index boundary; obtaining the amplitude disturbance value and unwinding phase value corresponding to the nearby calibration nodes; performing local polynomial fitting on the amplitude disturbance value to obtain the amplitude compensation data in the current corresponding state; performing manifold interpolation on the unwinding phase value to obtain transition phase data, and performing reverse phase winding processing on the transition phase data to generate phase compensation data that matches the electromagnetic period; and combining the phase compensation data with the amplitude compensation data to obtain the cross-frequency compensation data.

[0011] The steps for generating a corresponding frequency band three-dimensional preset beam based on the initial corrected weights include: The array topology features of each frequency band are obtained, including the physical arrangement parameters and radio frequency boundary parameters of the multi-frequency co-aperture array. The initial correction weights are combined with the array topology features to construct the input feature data of the radiation prediction network. The input feature data is input into the pre-trained radiation prediction network, and the implicit correlation features between the shaping weights and the spatial radiation gain are extracted using the multi-layer neuron nodes in the radiation prediction network. The radiation prediction network outputs the predicted radiation intensity of each frequency band in each direction of the target coverage space, and the corresponding three-dimensional preset beam is generated by spatially stitching the predicted radiation intensity.

[0012] The steps for constructing a joint coverage function including a cross-frequency overlap penalty term include: receiving pilot reception strengths reported by a first type of terminal in the ground target area and a second type of terminal in the low-altitude target area; establishing quality assessment terms regarding ground signal distribution and low-altitude signal distribution based on the pilot reception strengths; extracting the main lobe pointing vector and side lobe suppression coefficient of the three-dimensional preset beam in each frequency band, and calculating the spatial pointing deviation between the pointing vectors of different frequency bands; introducing the spatial pointing deviation into a preset nonlinear penalty model to generate a cross-frequency overlap penalty term for constraining the coverage overlap rate of different frequency bands; and weighting and summing the quality assessment term and the cross-frequency overlap penalty term to generate the joint coverage function.

[0013] The steps for establishing quality assessment items for ground signal distribution and low-altitude signal distribution include: analyzing the horizontal distribution nodes fed back by the terminal within the ground target area, and constructing a first evaluation network with the horizontal wide-area coverage compliance rate as the convergence target, in conjunction with the preset ground beamwidth constraint; analyzing the three-dimensional height nodes fed back by the terminal within the low-altitude target area, and constructing a second evaluation network with the low-altitude target energy concentration as the convergence target, in conjunction with the preset low-altitude beam narrow and sharp constraint; inputting the received pilot reception strengths into the first evaluation network and the second evaluation network respectively, and outputting the ground coverage score scalar and the low-altitude tracking score scalar respectively through network node feature extraction; and performing dimensionless splicing and combination of the ground coverage score scalar and the low-altitude tracking score scalar using normalization processing to generate the quality assessment items.

[0014] The steps for joint gradient optimization of the joint cover function based on array manifold constraints include: The initial correction weights of each frequency band are combined into a global state matrix, and the physical aperture topology of the multi-frequency co-aperture array is extracted as the optimization boundary constraint. The partial derivative parameter of the joint coverage function with respect to the global state matrix is ​​calculated to determine the multivariate descent gradient under the current numerical state. The global state matrix is ​​synchronously updated along the multivariate descent gradient according to the dynamic iteration step size, and after each update, it is checked whether it has crossed the optimization boundary constraint. When the numerical rate of change of the joint coverage function is lower than the preset convergence threshold, the iterative optimization calculation is stopped, and the converged global state matrix is ​​output as the cooperative shaping weight.

[0015] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This application obtains the spatial location, feed network channel, and current phase shift state of each frequency band array element in a multi-frequency common-aperture array. It then determines the local influence neighborhood based on the spatial distance, feed correlation, and phase relationship between different frequency array elements, eliminating the need for indiscriminate calculations on all different frequency array elements in subsequent data processing. Furthermore, it structures the amplitude perturbation data and continuous phase perturbation data obtained under different reference electrical adjustment states and spatial directions according to the local influence neighborhood, establishing a cross-frequency perturbation codebook. This improves the correspondence between amplitude compensation and phase compensation and the actual array state during dynamic electrical adjustment and reduces data redundancy caused by the participation of a large amount of weakly correlated array data in real-time calculations.

[0016] 2. After obtaining the initial corrected weights by correcting the basic shaping weights using cross-frequency compensation data, this application further combines the array topology characteristics to obtain the three-dimensional preset beams corresponding to each frequency band through a radiation prediction network; the actual coverage status is evaluated by using the pilot reception strength fed back by the terminal in the ground target area and the low-altitude target area respectively, and the array-side prediction data and the actual feedback data from the terminal side can be used for joint evaluation, so that the ground wide-area coverage requirements and the low-altitude directional coverage requirements can be evaluated separately in the same data processing process and jointly participate in the subsequent optimization, thereby improving the coordination and adaptability of the multi-frequency three-dimensional beams in operation.

[0017] 3. This application unifies the initial correction weights of each frequency band into global state data, and performs joint optimization of the joint coverage function within the executable range defined by the array physical aperture, feed relationship, and RF control range. By unifying the beamforming weights of different frequency bands and checking the amplitude control range, phase control range, and shared channel relationship during each update, the possibility of numerical optimization results exceeding the actual antenna control capability can be reduced. At the same time, the iteration step size is adjusted according to the changes in the joint coverage function. When the current update increases the joint coverage function, the corresponding update is canceled and the step size is reduced, so that the beamforming control quantities of different frequency bands can be coordinated around the unified coverage target, improving the consistency between the coordinated beamforming weight calculation process and the actual antenna execution conditions. Attached Figure Description

[0018] Figure 1 This is a flowchart illustrating a 3D beamforming method based on an antenna array according to the present invention. Figure 2 This is a logical schematic diagram of a 3D beamforming method based on an antenna array according to the present invention; Figure 3 This is a schematic diagram illustrating the process of obtaining the local influence neighborhood in this invention. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] Example 1: This invention proposes a 3D beamforming method based on an antenna array, the process of which is as follows: Figure 1 As shown, the data logic of the method is as follows: Figure 2 As shown, it specifically includes: The spatial location of array elements, feed network channels, and current phase shift state of each frequency band in the multi-frequency common aperture array are obtained, and the local influence neighborhood is determined based on the geometric distance between the different frequency array elements. The cross-frequency perturbation codebook is obtained based on the local influence neighborhood. The cross-frequency perturbation codebook includes the amplitude perturbation mapping and phase manifold mapping established by the frequency band reference direction response under the reference electrically regulated state. Receive joint coverage instructions and acquire the three-dimensional orientation and electrical control status of targets in ground target areas and low-altitude target areas; combine amplitude perturbation mapping and phase manifold mapping to determine the cross-frequency compensation data for each frequency band in response to the electrical control status of the targets; The basic beamforming weights of each frequency band are corrected using cross-frequency compensation data to obtain initial corrected weights, and three-dimensional preset beams of the corresponding frequency bands are generated based on the initial corrected weights. The terminal pilot feedback in the ground target area and the low-altitude target area is obtained. The terminal pilot feedback is combined with the three-dimensional preset beam to construct a joint coverage function including a cross-frequency overlap penalty term. Joint gradient optimization is performed on the joint coverage function based on array manifold constraints. The initial correction weights are updated using the converged optimization results, and the cooperative shaping weights of each frequency band are output.

[0021] The process of determining the local influence neighborhood based on the geometric distance between different frequency array elements is as follows: Figure 3As shown, the process includes: converting the spatial position of the array element into three-dimensional coordinate parameters in the base station coordinate system; calculating the three-dimensional spatial distance between the array element to be compensated and other inter-frequency array elements; initially screening inter-frequency array elements whose three-dimensional spatial distance is less than a preset distance benchmark as initial candidate array elements; analyzing the feed network channel and the current phase shift state, and extracting the feed correlation degree and continuous phase difference between the array element to be compensated and the initial candidate array elements; synchronously performing nonlinear mapping on the three-dimensional spatial distance, feed correlation degree, and continuous phase difference to convert them into continuous cross-frequency weights; selecting the initial candidate array elements whose continuous cross-frequency weights are higher than a preset weight threshold, and performing spatial clustering association with the array element to be compensated to generate a local influence neighborhood corresponding to the array element to be compensated.

[0022] In this embodiment, the geometric center of the antenna panel is used as the origin of the base station coordinate system. The horizontal direction along the antenna panel is defined as the first coordinate direction, the vertical direction along the antenna panel is defined as the second coordinate direction, and the direction perpendicular to the antenna panel and pointing towards the radiation space is defined as the third coordinate direction. Based on the antenna structure design documents or assembly measurement data, the position values ​​of each array element in the above three directions are obtained sequentially. For data from different design coordinate systems, coordinate alignment is first performed using no fewer than three fixed reference points on the antenna panel to unify the positions of all array elements to the same base station coordinate system.

[0023] For a given array element to be compensated, the coordinates of array elements belonging to other operating frequency bands are read sequentially, the straight-line spatial distance between them and the array element to be compensated is calculated, and a distance data list is generated.

[0024] The preset distance reference can be obtained during the antenna product finalization and calibration phase. Specifically, in an anechoic chamber or other calibration environment that can maintain stable measurement conditions, combinations of different frequency array elements with varying spatial distances are selected sequentially. The input signal of the element to be compensated is fixed, and the excitation state of the candidate frequency array elements is changed accordingly. Specifically, when determining the preset distance reference, a reference test signal is injected into the operating frequency band corresponding to the element to be compensated, while keeping the feed state and test environment of the element to be compensated unchanged. For a candidate frequency array element, no additional independent carrier signals for comparison are injected into its corresponding other operating frequency bands. Instead, the feed channel corresponding to the candidate frequency array element is set to the actual operating connection state and the calibration matching state, respectively. The target direction amplitude and phase response corresponding to the two states are measured in the frequency band to be compensated. The response change between the two states is used to evaluate the impact of the candidate frequency array element's structure, port load, and feed connection state on the frequency band to be compensated.

[0025] Record the amplitude and phase changes in the target direction of the frequency band to be compensated. When the amplitude change caused by a different frequency array element outside a certain spatial distance during multiple state switching is consistently lower than the product's pre-specified measurement resolution, and the phase change is consistently lower than the allowable error, the upper limit value near that spatial distance is determined as the preset distance reference. Therefore, the distance reference is determined by the calibration data of the actual array.

[0026] Different frequency array elements with a distance less than the distance reference are used as initial candidate array elements, and then the feed network connection table is read.

[0027] The feed network connection table should at least record the feed port corresponding to each array element, its associated final-stage power distribution branch, the previous-stage power distribution node, and the RF input port. For the array element to be compensated and an initial candidate array element, the feed correlation is determined based on their nearest common connection level in the feed network. In one specific implementation, if two array elements are directly fed by the same final-stage power distribution node, the feed correlation is set to 1. If they belong to different final-stage branches but share the same previous-stage power distribution node, the correlation is set to 0.75. If they only share a higher-stage input branch, the correlation is set to 0.5. If they only have a common connection at the RF input and subsequent feed paths are independent, the correlation is set to 0.25. If they correspond to completely independent feed inputs and distribution paths, the correlation is set to 0. The above values ​​are only one calibration method that can be directly implemented; when the product already has feed isolation test data, the actual isolation level can also be normalized to a range from 0 to 1 and used as the feed correlation.

[0028] Then, the current phase control values ​​of the phase shifters corresponding to the element to be compensated and the candidate element are read. Since the phase control values ​​have periodic variation characteristics, the phase states of the previous control cycle and the current control cycle are read in continuous time sequence. When there is a jump of more than 180 degrees between two adjacent phase data, the current and subsequent data are increased or decreased by 360 degrees according to the direction of change to keep the phase sequence in the control process continuous. Then, the absolute continuous phase difference between the element to be compensated and the candidate element is calculated to obtain the continuous phase difference value. Among them, for the element to be compensated and the initial candidate element belonging to different operating frequency bands, the reference electronically regulated state corresponding to their respective frequency bands is first used as the phase reference. The current phase shift control value is unwound and normalized according to the adjustable phase range of their respective frequency bands to obtain continuous state data characterizing the phase shift control process of each element. Then, the difference between the two continuous state data is calculated as the continuous phase difference value. The continuous phase difference value is used to reflect the relative closeness between the current control states of the two different frequency elements and is used as one of the data features for local influence neighborhood screening, rather than representing the absolute phase difference between two different carrier frequency electromagnetic waves.

[0029] To form continuous cross-frequency weights, the three types of data are first processed using a unified scale. For spatial distance, 0 represents the state of reaching the distance reference, and 1 represents the state of the two array elements being closest in spatial position, with the values ​​decreasing continuously from near to far. For feed correlation, the aforementioned values ​​of 0 to 1 are directly used. For continuous phase difference, normalization is performed according to the principle that the smaller the phase difference, the larger the corresponding value, where a phase difference of 0 degrees corresponds to 1, and a phase difference of 180 degrees or more corresponds to 0. In one specific implementation, the contribution ratio of feed correlation features is set to 0.3, the contribution ratio of phase features is set to 0.2, and the contribution ratio of distance features is set to 0.5. The three types of normalized data are multiplied by their respective contribution ratios, summed, and then the sum is squared. The result between 0 and 1 is used as the continuous cross-frequency weight. The weighted summation result is squared to keep the continuous cross-frequency weights within the range of zero to one and to change the numerical distribution of the weights corresponding to different candidate array elements. The actual differentiation effect of the squared process on candidate array elements with different degrees of correlation is verified based on positive and negative samples obtained during the product calibration stage. This is a specific implementation of nonlinear mapping.

[0030] The weight threshold is determined during the product calibration phase. Array element pairs known to generate measurable cross-frequency disturbances are considered positive samples, while array element pairs whose actual disturbances are consistently below the allowable error are considered negative samples. Continuous cross-frequency weights are calculated separately. Candidate thresholds are tested at 0.05 intervals within the range of 0.2 to 0.8. For each candidate threshold, the proportion of retained positive samples to the total number of positive samples and the proportion of excluded negative samples to the total number of negative samples are statistically analyzed. The sum of these two proportions is calculated, and the candidate threshold with the largest sum is selected as the preset weight threshold. When the sum of proportions corresponding to two or more candidate thresholds is the same, the candidate threshold with the higher positive sample retention proportion is preferred. For example, if 0.45 is determined to meet the above conditions after calibration, 0.45 is used for screening during operation. Candidate inter-frequency array elements with weights higher than 0.45 are retained, and an array element association set is established based on spatial adjacency. For the same array element to be compensated, all inter-frequency array elements that meet the threshold conditions and their corresponding continuous cross-frequency weights are recorded in the same data table.

[0031] Furthermore, the element to be compensated is used as the center element of the current spatial cluster. Initial candidate elements with consecutive cross-frequency weights higher than a preset weight threshold are sorted in ascending order of their three-dimensional spatial distance from the element to be compensated. Candidate elements are read sequentially. When the distance between a candidate element and the element to be compensated is less than the preset distance benchmark, it is added to the current cluster set. For candidate elements already added to the set, their spatial distances to other retained candidate elements are checked. If the distance between any of the remaining candidate elements and any already added element is still less than the preset distance benchmark, and their consecutive cross-frequency weights are higher than the preset weight threshold, they are added to the current set. This process is repeated until no new elements can be added. The final set is then determined as the local influence neighborhood of the element to be compensated. This local influence neighborhood is used as the boundary of the element range when establishing the cross-frequency disturbance codebook and querying compensation data. Compared to establishing a fixed neighborhood based solely on physical distance, this invention enables the neighborhood range to simultaneously reflect the array geometry, power supply network relationships, and the current ESC operating status. Since subsequent cross-frequency disturbance calibration and compensation queries use the filtered local influence neighborhood as the data organization and query boundary, it can reduce data redundancy caused by weakly correlated inter-frequency array elements participating in cross-frequency disturbance codebook establishment and online compensation queries, and enable subsequent disturbance codebooks to centrally record cross-frequency response data that are strongly correlated with the array elements to be compensated.

[0032] The steps for obtaining the cross-frequency perturbation codebook include: injecting reference test signals into a multi-frequency common-aperture array under multiple reference electrically tunable states to obtain measured radiation sequences of each frequency band in a predetermined discrete direction; comparing the measured radiation sequences with the reference radiation sequences under uncoupled states to separate the fundamental amplitude offset and fundamental phase offset corresponding to each frequency band; extracting periodic transition nodes in the fundamental phase offset and mapping the transition phases to smooth phase data in a continuous smooth space using phase dewinding processing; constructing an amplitude perturbation mapping based on the fundamental amplitude offset and the corresponding reference electrically tunable states, and simultaneously constructing a phase manifold mapping based on the smooth phase data and the corresponding reference electrically tunable states; and combining the amplitude perturbation mapping and the phase manifold mapping in a structured data manner according to the topological relationship of the local influence neighborhood to generate the cross-frequency perturbation codebook.

[0033] Before the antenna is put into field operation, a cross-frequency disturbance codebook is established in a microwave anechoic chamber or other test environment that meets the antenna pattern calibration conditions. First, multiple reference electrically adjustable states are set according to the allowable operating range of the electrically adjustable antenna; for example, when the allowable electrical downtilt range of the antenna is 0 to 12 degrees, seven reference electrically adjustable states can be set at 2-degree intervals: 0 degrees, 2 degrees, 4 degrees, 6 degrees, 8 degrees, 10 degrees, and 12 degrees. If the actual variation of the product is more drastic in certain ranges, the calibration interval for the corresponding range can be reduced. In each reference electrically adjustable state, the phase shifter position is fixed through the antenna controller, and the mechanical position feedback and the electrically adjustable control state are kept stable for several consecutive sampling cycles. After confirming that the state is stable, a reference test signal with known amplitude and frequency is injected into the frequency band to be tested.

[0034] Radiation response is collected according to a preset three-dimensional directional grid, which includes at least azimuth and elevation directions. In one embodiment, the azimuth direction is sampled at 2-degree intervals within the target coverage area, and the elevation direction is sampled at 1-degree intervals. For each direction, the received amplitude and received phase are recorded simultaneously, and sorted according to the reference electronic tuning state, frequency band number, azimuth direction, and elevation direction to form a measured radiation sequence.

[0035] The reference radiation sequence is used to represent the baseline response after minimizing the interaction between different frequency array elements. In this embodiment, the reference radiation sequence is obtained through a product calibration model. Specifically, the array elements of the frequency band under test are set according to the normal excitation state, while the different frequency channels that do not participate in the reference measurement of this frequency band are set to the matched terminal state. The reference array model that has been calibrated by a single frequency is used to calibrate the frequency band under test. For cases where mutual coupling cannot be completely eliminated in the physical structure, the reference radiation sequence does not require absolute zero mutual coupling in physical terms. Instead, a reference state with different frequency effects lower than the product's allowable error after independent array element calibration or electromagnetic simulation correction is used as the mutual-coupling-free reference state.

[0036] Align the measured radiation sequence point by point with the reference radiation sequence under the same electrically controlled state and the same spatial orientation.

[0037] For amplitude data, the change in measured amplitude relative to reference amplitude is calculated as the basic amplitude offset for that state and direction; for phase data, the difference between measured phase and reference phase is calculated to form a basic phase offset sequence.

[0038] Since phase is typically recorded within a range of -180 degrees to 180 degrees, when the actual phase changes continuously and crosses boundaries, the original data may exhibit numerical jumps approaching 360 degrees. Therefore, the basic phase offset is checked sequentially along adjacent spatial sampling directions. If the difference between the previous and subsequent sampling points is greater than 180 degrees, the subsequent sampling point and all subsequent data are reduced by 360 degrees; if the result is less than -180 degrees, the subsequent sampling point and all subsequent data are increased by 360 degrees. This process is repeated until there are no large non-physical jumps caused by phase period boundaries between adjacent sampling points; the resulting data is continuous and smooth phase data. Furthermore, for each reference ESC state, the center direction of the target coverage area is first selected as the unwinding reference node. In each fixed pitch direction, starting from the center azimuth node, phase unwinding is performed sequentially in both the azimuth-increasing and azimuth-decreasing directions. After completing all azimuth rows, the data corresponding to the center azimuth direction is used as a reference, and adjacent data are compared row by row along the pitch direction. Continuity between adjacent pitch rows is maintained by adding or subtracting a complete phase cycle. Smoothed phase data is obtained after these two stages of processing.

[0039] For the basic amplitude offset, a three-dimensional index is established according to the reference ESC state, azimuth direction and pitch direction; each index node stores the corresponding amplitude offset value, thus forming an amplitude disturbance mapping.

[0040] For continuous smooth phase data, indexes are established according to the reference EAC state, azimuth direction, and pitch direction, preserving the data adjacency relationships between adjacent states and adjacent spatial directions, thus forming a phase manifold mapping. The core of this manifold is to preserve the phase continuity after unwinding, so that subsequent interpolation between adjacent calibration nodes is processed along the continuous phase change direction, without directly crossing the phase period boundary. Specifically, for each reference EAC state, state direction adjacency relationships are established with data nodes in the same azimuth and pitch directions; for the same reference EAC state, a first spatial adjacency relationship is established with data nodes adjacent in the azimuth direction and in the same pitch direction, and a second spatial adjacency relationship is established with data nodes adjacent in the pitch direction and in the same azimuth direction. This establishes adjacency relationships between each non-boundary calibration node and its preceding and following EAC state nodes, left and right azimuth nodes, and up and down pitch nodes. When performing subsequent phase interpolation, interpolation data is selected only along the aforementioned interconnected continuous nodes, without directly performing phase averaging across nodes without establishing adjacency relationships.

[0041] Subsequently, the determined local influence neighborhood is read. For each array element to be compensated, the local influence neighborhood corresponding to that element is used as the organization boundary for the cross-frequency disturbance data. Based on the measured radiation sequence obtained when the array element to be compensated is in the actual working connection state of the local influence neighborhood, and the reference radiation sequence obtained under the same reference electrically tunable state and the same spatial direction, the corresponding amplitude offset and continuous phase offset are determined. The amplitude offset and continuous phase offset represent the radiation response change of the current array element to be compensated relative to the reference state under the overall effect of the corresponding local influence neighborhood. The amplitude offset or phase offset that has not been independently measured and separated is not further attributed to any single different frequency array element in the local influence neighborhood. When storing in a structured manner, the data set includes the array element number to be compensated, the set of different frequency array elements contained in the local influence neighborhood, the frequency band number, the reference electrical adjustment state, the spatial direction, the amplitude offset, and the continuous phase offset. The array element to be compensated and the corresponding local influence neighborhood are used as the first-level index, the frequency band as the second-level index, the reference electrical adjustment state as the third-level index, and the azimuth and elevation directions as the fourth-level index. The resulting data set is the cross-frequency disturbance codebook.

[0042] When compensation is performed later, the complete anechoic chamber test is not re-executed. Instead, queries and interpolations are performed in the codebook according to the current array element neighborhood, the target's electrical adjustment state, and the target's three-dimensional orientation.

[0043] This invention transforms the cross-frequency amplitude and phase perturbations, which originally required online solution, into structured calibration data that can be pre-measured, organized, and queried. By establishing amplitude perturbation mappings and continuous phase perturbation mappings in multiple reference electrically controlled states and three-dimensional spatial directions, the codebook can reflect the variation of cross-frequency perturbations with electrical control states and spatial directions. For phase data, dewinding is performed before mapping is established, which avoids erroneous large changes in phase caused by direct interpolation near the period boundary and provides a traceable measured data basis for feedforward compensation under subsequent target states.

[0044] During the calibration process of establishing the cross-frequency perturbation codebook, a correspondence between the shaping control quantity and the change in the radiation response in the target direction was also established for each array element to be compensated. Specifically, while keeping the shaping weights of the other array elements unchanged in a reference electrically adjusted state, preset increments and decrements were applied to the amplitude control quantity of the current array element to be compensated, and the radiation amplitude change in the three-dimensional direction of the target was measured. Then, keeping the other states unchanged, preset forward and reverse changes were applied to the phase control quantity of the current array element to be compensated, and the radiation phase change in the three-dimensional direction of the target was measured. Based on the data of multiple control quantity changes and corresponding radiation response changes, the amplitude control relationship and phase control relationship of the current array element to be compensated in different reference electrically adjusted states were determined, and stored accordingly according to the array element number, frequency band, and reference electrically adjusted state.

[0045] The steps for determining the cross-frequency compensation data for each frequency band for the target ESC state include: When the antenna control system receives the joint coverage command, it first obtains the target's electrical adjustment status, and at the same time obtains the target's azimuth and elevation directions corresponding to the ground target area and the low-altitude target area.

[0046] For a given array element to be compensated, its corresponding local influence neighborhood is first read, and the array element to be compensated and its corresponding local influence neighborhood are used as the codebook query boundary. Only calibration nodes that are close to the current target electrical control state and the target's three-dimensional orientation are searched in the corresponding neighborhood records. In one embodiment, the three most effective calibration positions closest to the target state are preferentially selected in the electrical control state dimension, azimuth dimension, and pitch dimension, respectively, and a set of local nodes distributed around the target's electrical control state and the target's three-dimensional orientation is formed according to the combination relationship of the calibration positions in the three dimensions. Before performing subsequent polynomial fitting, the number of effective calibration nodes in the set of local nodes is checked. When using second-order polynomial fitting, the number of effective calibration nodes should be no less than ten, and different effective calibration nodes should have different calibration values ​​in at least one of the electrical control state, azimuth direction, or pitch direction. When the number of calibration nodes is sufficient, effective calibration nodes obtained by combining three electrical control states, three azimuth directions, and three pitch directions are preferentially used for fitting. When the target state is close to the codebook boundary and the number of effective calibration nodes is less than ten, the calibration nodes corresponding to the adjacent reference ESC states, adjacent azimuth directions, or adjacent pitch directions are selected from the closest to the target state in order of distance from the target state until the number of effective calibration nodes meets the requirements of second-order polynomial fitting. When it is still impossible to obtain no less than ten effective calibration nodes under the codebook boundary conditions, the fitting order of the current amplitude disturbance data is reduced to first order, and the effective calibration node closest to the target state is used for fitting.

[0047] Furthermore, before employing second-order polynomial fitting, a set of fitting equations is established based on the ESC state, azimuth direction, and pitch direction corresponding to each effective calibration node. The rank of the coefficient matrix corresponding to the fitting equations is then checked to ensure it is equal to the number of coefficients to be determined in the second-order polynomial. If the rank is ten, second-order polynomial fitting is performed; if the rank is less than ten, adjacent calibration nodes are added in order of increasing distance from the target state, and the check is repeated. If the above conditions are still not met after adding available calibration nodes, the fitting order is reduced to first order. When using first-order polynomial fitting, it is checked whether the corresponding fitting equations can uniquely determine the constant term and the three linear terms. If they cannot be uniquely determined, extrapolation is not performed, and the effective calibration data closest to the target state is selected as the current amplitude disturbance reference value.

[0048] Read the amplitude offset and the continuous phase offset that has been unwound from each adjacent calibration node.

[0049] For amplitude perturbations, when the number of effective calibration nodes in the local node set meets the requirements for second-order polynomial fitting, local second-order polynomial fitting is used, with the electronic control state, azimuth direction, and pitch direction as the three independent variables, and the corresponding amplitude offset as the fitting target. When the number of effective calibration nodes is insufficient to support second-order polynomial fitting, local first-order polynomial fitting is used, still with the electronic control state, azimuth direction, and pitch direction as the three independent variables, and the corresponding amplitude offset as the fitting target. When using local second-order polynomial fitting, the fitting term includes a constant term, a first-order variation term of the three independent variables, a second-order variation term of the three independent variables, and pairwise cross-variation terms between different independent variables. When using local first-order polynomial fitting, the fitting term includes a constant term and a first-order variation term of the three independent variables. The corresponding fitting coefficients are determined using the least squares error principle, and then the current target electronic control state, target azimuth direction, and target pitch direction are substituted into the fitting results to obtain the amplitude perturbation estimate of the current state.

[0050] To convert the disturbance estimate into compensation data, the compensation direction is set to be opposite to the measured disturbance. For example, if calibration results indicate that the actual amplitude is 0.8 dB lower than the reference amplitude under the current target state, then within the allowable range of the basic beamforming amplitude, the amplitude disturbance estimate is converted into an amplitude control correction that can produce a reverse radiation change to compensate for this loss, based on the amplitude control relationship under the corresponding reference electrically tunable state. If the actual amplitude is higher than the reference value, the beamforming amplitude is reduced accordingly. For compensation amounts exceeding the hardware-allowed adjustment range, the maximum amplitude range allowed by the RF channel is limited.

[0051] For phase data, since unwinding has been completed, continuous phase adjacency relationships are first established between neighboring nodes. Normalization is performed using the electrical control state difference, azimuth difference, and pitch difference, and the comprehensive distance between each neighboring node and the target state is calculated. Nodes with smaller distances are assigned higher interpolation weights. The continuous phase offsets of each node are then weighted and averaged to obtain the transition phase data under the target state.

[0052] When the local phase change has a significant bending trend, the number of neighboring nodes can be increased, and the interpolation weight can be calculated along the continuous change path between the calibration nodes to avoid directly crossing areas with significantly different changes. After obtaining the transition phase, reverse phase winding is performed; when the transition phase is greater than 180 degrees, it is reduced by 360 degrees each time until it enters the range of -180 degrees to 180 degrees; when the transition phase is less than -180 degrees, it is increased by 360 degrees each time until it enters the same range; then, according to the phase control relationship under the corresponding reference electronic control state, the phase disturbance amount corresponding to the transition phase data is converted into a phase control correction amount that can generate a reverse radiation phase change, and the phase control correction amount is used as phase compensation data. The amplitude compensation data and phase compensation data corresponding to the same array element to be compensated are bound according to frequency band, feed channel and array element number to form cross-frequency compensation data. Then, the cross-frequency compensation data is sent to the basic shaping weight correction step to perform gain compensation on the amplitude control quantity and phase offset compensation on the phase control quantity to form the initial correction weights; This invention obtains continuous amplitude compensation values ​​while maintaining a small computational scale by performing low-order polynomial fitting on amplitude data within a local node range. For phase data with periodic boundaries, interpolation is first performed in the unwound continuous space before restoring to the actual phase period range, avoiding phase direction errors caused by ordinary numerical interpolation near -180 degrees and 180 degrees. This enables the offline discrete codebook to be transformed into online, continuously usable amplitude and phase compensation data, improving the continuity and stability of feedforward compensation under different target ESC states.

[0053] The steps for generating a corresponding frequency band three-dimensional preset beam based on the initial corrected weights include: During the training phase of the radiation prediction network, an array dataset consistent with the actual antenna hardware is first established. For each frequency band, the first, second, and third coordinates of the array elements are recorded in fixed element number order, along with the minimum, maximum, minimum, and maximum allowable amplitude control values ​​for each feed channel. For array element groups that cannot be controlled individually, their shared feed channel numbers are also recorded. This data forms the array topology characteristics. During anechoic chamber calibration, multiple sets of different shaping weights are set; each set of shaping weights must be within the hardware's allowable range; for each set of weights, the actual radiation intensity is measured according to the aforementioned three-dimensional directional grid.

[0054] A set of shaping weights and array topology features are used as inputs to a training sample, and the measured radiation intensity in all three dimensions under this set of weights is used as the output of the training sample. To ensure that different numerical ranges can be trained together, the array element coordinates are normalized according to the maximum antenna size, the amplitude control is normalized according to the maximum allowable amplitude of the corresponding RF channel, and the phase control is normalized by 180 degrees. In one specific implementation, the samples are divided into training data, validation data, and test data in a ratio of 70:15:15.

[0055] The radiation prediction network employs a multi-layer feedforward neural network. Input nodes sequentially input array element coordinate data, radio frequency boundary data, initial correction amplitude weights, and initial correction phase weights in a fixed order. Four intermediate feature processing layers are configured, with node numbers of 512, 256, 128, and 64 respectively. These intermediate layers utilize conventional nonlinear activation methods that preserve positive effective responses. Specifically, the intermediate feature processing layers employ modified linear unit activation. Mini-batch gradient updates are used during training, with 64 training samples selected per batch. The initial training step size is set to 0.1%, and the maximum training cycle is set to 500 cycles. Training is stopped early when the validation data shows no improvement after 10 consecutive training cycles. The number of output layer nodes equals the number of sampling directions in a predetermined 3D orientation grid, with each output node corresponding to a predicted radiation intensity in a fixed azimuth and elevation direction.

[0056] During training, the predicted radiation intensity output by the network is compared with the measured radiation intensity in the same direction, and the average squared value of the prediction error in all directions is used as the training error. The training error is reduced by updating the network's internal parameters in reverse. Training is stopped when the validation data no longer shows improvement after 10 consecutive training epochs, and the network parameters corresponding to the lowest validation error are saved.

[0057] During the operation phase, the output cross-frequency compensation data first corrects the basic beamforming weights to obtain the initial corrected weights.

[0058] Subsequently, following the same data sorting and normalization methods used in the training phase, the initial modified weights are combined with the current array topology features to form the network input data, which is then input into the already trained radiation prediction network. The network outputs the predicted radiation intensity for each discrete direction in the target space grid; the controller rearranges each output node into a two-dimensional angular grid according to the azimuth and elevation directions, and then uses the corresponding gain values ​​as the third-dimensional data for spatial organization. For locations where there are no direct output nodes between adjacent sampling directions, conventional linear interpolation is used to obtain continuous radiation intensity. This yields the complete three-dimensional predicted radiation distribution corresponding to the current initial modified weights, and this result is defined as the three-dimensional preset beam.

[0059] For each three-dimensional node in the fixed low-altitude space grid, the corresponding azimuth and elevation directions are determined according to the spatial position of the node relative to the reference position of the base station array, and the corresponding predicted radiation intensity is read from the three-dimensional preset beam according to the azimuth and elevation directions; when the azimuth or elevation direction is between adjacent predicted directions, the corresponding predicted radiation intensity is obtained by using the same interpolation method as in the three-dimensional preset beam generation stage.

[0060] The spatial location of array elements, radio frequency boundary parameters, and shared channel information are used to ensure that the input data of the radiation prediction network corresponds to the current antenna hardware configuration and that the trained network parameters are suitable for the corresponding array structure. The radiation prediction network is used to predict the three-dimensional spatial radiation state corresponding to the candidate shaping weights. Its output results are not used as the basis for determining whether the shaping weights meet the hardware control conditions. The candidate shaping weights are still subject to executability checks according to the amplitude control range, phase control range, and shared channel relationship specified in the subsequent joint optimization steps.

[0061] The steps for constructing a joint coverage function including a cross-frequency overlap penalty term include: receiving pilot reception strengths reported by a first type of terminal in the ground target area and a second type of terminal in the low-altitude target area; establishing quality assessment terms regarding ground signal distribution and low-altitude signal distribution based on the pilot reception strengths; extracting the main lobe pointing vector and side lobe suppression coefficient of the three-dimensional preset beam in each frequency band, and calculating the spatial pointing deviation between the pointing vectors of different frequency bands; introducing the spatial pointing deviation into a preset nonlinear penalty model to generate a cross-frequency overlap penalty term for constraining the coverage overlap rate of different frequency bands; and weighting and summing the quality assessment term and the cross-frequency overlap penalty term to generate the joint coverage function.

[0062] The base station controller collects pilot reception strength reports from terminals within the ground target area and the low-altitude target area according to a fixed feedback period. First, based on terminal identity, serving cell information, and spatial location, terminals are classified as ground terminals and low-altitude terminals. Pilot data from ground terminals is sent to the first evaluation network, and pilot data from low-altitude terminals is sent to the second evaluation network, where ground coverage scores and low-altitude tracking scores are obtained respectively.

[0063] Simultaneously, the generated three-dimensional preset beams for each frequency band are read. For a frequency band, the direction with the highest predicted radiation intensity is searched within the target coverage space, and this direction is determined as the main lobe center direction. Three-dimensional unit direction data is obtained by converting the azimuth and elevation angles of this direction; this three-dimensional direction data serves as the main lobe pointing vector. After determining the main lobe center, the effective width range of the main lobe is excluded from all spatial directions, and the maximum radiation intensity in the remaining directions is searched. The intensity difference between the main lobe peak and the maximum sidelobe is calculated and normalized according to a pre-set sidelobe control range to obtain the sidelobe suppression coefficient. The larger the intensity difference, the higher the degree of sidelobe suppression.

[0064] Subsequently, pairwise comparisons are performed on different frequency bands that need to maintain cooperative coverage. The spatial angle between the main lobe pointing vectors of the two frequency bands is calculated, and this angle is used as the main spatial pointing deviation. In joint coverage tasks, if different frequency bands should point to the same ground area or the same low-altitude target according to network planning, the target spatial deviation is set to 0 degrees. If two frequency bands undertake different but fixed relative coverage tasks, the planned target direction difference is used as a benchmark, and the deviation of the actual direction difference from this benchmark is calculated. In this embodiment, normal cross-frequency beam overlap is not penalized; instead, the degree of deviation from the predetermined cross-frequency overlap relationship is penalized.

[0065] A nonlinear penalty rule is established for spatial pointing deviation. For example, if the allowed directional deviation is preset to 2 degrees, the spatial pointing deviation is first divided by the allowed directional deviation to obtain a dimensionless deviation ratio. When the deviation ratio is not greater than one, the square of the deviation ratio is used as the base penalty; when the deviation ratio is greater than one, one is used as the base penalty value for exceeding the allowed deviation position, and then the portion exceeding one is amplified to the fourth power and added to the base penalty value, so that the penalty result remains continuous at the allowable deviation boundary. When the effective widths of the main lobes of the two frequency bands are different, the spatial pointing deviation is compared with the smaller effective width of the main lobe; for the same directional deviation, the narrower the main lobe, the higher the corresponding cross-frequency overlap penalty.

[0066] Meanwhile, the sidelobe suppression coefficient is used as the basis for correction. When the main lobe directions of two frequency bands are close but the sidelobes spread significantly to another target region, the corresponding penalty result is increased, thus obtaining the cross-frequency overlap penalty term.

[0067] The dimensionless splicing combination includes first combining the ground coverage score scalar and the low-altitude tracking score scalar in a fixed order, then performing a weighted merging of the two scores according to preset ground evaluation weights and low-altitude evaluation weights, and finally obtaining a single quality assessment scalar, which serves as the quality assessment term in the joint coverage function.

[0068] To maintain consistency with the subsequent gradient descent process, the joint coverage function is defined as the cost function to be reduced in this implementation. Both the ground coverage score and the low-altitude tracking score are first normalized to 0 to 1, where 1 represents high coverage quality. When combining the scores, a negative weight is applied to the coverage score, and a positive weight is applied to the cross-frequency overlap penalty. For example, the weight for the ground coverage portion is -0.4, the weight for the low-altitude coverage portion is -0.4, and the weight for the cross-frequency overlap penalty portion is 0.2. Therefore, when the ground and low-altitude coverage scores increase, the value of the joint coverage function decreases. When the cross-frequency spatial deviation increases, the value of the joint coverage function increases. Gradient optimization aims to reduce this function value, thus maintaining consistency in the actual optimization direction. The weights of the three components can be adjusted according to the operational network requirements in different scenarios, but the weights remain fixed or change according to a clearly defined preset rule during the same optimization process.

[0069] Furthermore, when calculating the cross-frequency overlap penalty term, in addition to the spatial pointing deviation, the effective main lobe width and side lobe suppression coefficient of each three-dimensional preset beam are simultaneously read. For the same spatial pointing deviation, when the effective main lobe widths of the two frequency bands are small, the penalty weight corresponding to the spatial pointing deviation is increased; when the sidelobe of the three-dimensional preset beam enters the coverage area of ​​another target and its predicted radiation intensity exceeds the allowable intensity of the corresponding sidelobe, the corresponding penalty is further increased. This allows the spatial pointing deviation to reflect the spatial coverage relationship of different frequency bands in combination with the actual beamwidth and sidelobe status.

[0070] This invention incorporates the cross-frequency spatial relationship between actual terminal feedback and predicted beams into a single optimization objective. The actual pilot signal reception strength reflects coverage differences caused by terrain obstruction, multipath propagation, and changes in actual terminal location, while the three-dimensional preset beams reflect the main lobe and side lobe states generated by different frequency bands on the array side. By converting cross-frequency directional deviation into a nonlinear penalty, small allowable errors prevent over-adjustment, while rapidly increasing the penalty when different frequency band beams deviate beyond the allowable range, thereby guiding joint optimization towards a predetermined cooperative coverage relationship. This avoids significant drift in spatial coverage of other frequency bands caused by simply increasing the signal strength of one frequency band.

[0071] The steps for establishing quality assessment items for ground signal distribution and low-altitude signal distribution include: analyzing the horizontal distribution nodes fed back by the terminal within the ground target area, and constructing a first evaluation network with the horizontal wide-area coverage compliance rate as the convergence target, in conjunction with the preset ground beamwidth constraint; analyzing the three-dimensional height nodes fed back by the terminal within the low-altitude target area, and constructing a second evaluation network with the low-altitude target energy concentration as the convergence target, in conjunction with the preset low-altitude beam narrow and sharp constraint; inputting the received pilot reception strengths into the first evaluation network and the second evaluation network respectively, and outputting the ground coverage score scalar and the low-altitude tracking score scalar respectively through network node feature extraction; and performing dimensionless splicing and combination of the ground coverage score scalar and the low-altitude tracking score scalar using normalization processing to generate the quality assessment items.

[0072] For the ground target area, the ground coverage boundary is first obtained according to the network planning. The ground coverage area is then divided into fixed horizontal grids; for example, the target area is divided into 10 equally spaced segments along the first and second horizontal directions, forming 100 horizontal grids. The base station assigns each ground terminal to a corresponding grid based on the terminal's positioning information. If multiple terminals exist in the same grid within a feedback cycle, the average pilot received signal strength of all valid terminals in that grid is calculated as the signal strength of that node. For grids with no terminal feedback temporarily, valid data from the most recent feedback cycles can be used to maintain the signal strength. When there is no valid feedback for several consecutive cycles, the grid is marked as temporarily excluded from the current evaluation.

[0073] Each grid center location with valid data and its corresponding pilot signal reception strength constitutes a horizontally distributed node.

[0074] Ground beamwidth constraints are set during the network planning phase; specifically, they include the target horizontal coverage angle range and the maximum allowable signal fluctuation within the area. For example, the target horizontal angle range is required to be 60 degrees, and the pilot reception strength of most nodes within the effective area is required to reach a preset communication threshold, while there should be no sustained strength drop exceeding the set range between different effective nodes.

[0075] The first evaluation network uses a fixed set of one hundred horizontal grids as input positions. Each horizontal grid is assigned a corresponding pilot reception strength input position; when multiple valid terminals exist in a grid, the average pilot reception strength of that grid is input; when there are no valid terminals in the current feedback period but valid data existed previously, the most recent valid data is input; when no valid data exists for more than a preset hold period, the corresponding pilot reception strength input is set to the normalized minimum value, and the node is simultaneously marked as having no valid feedback, ensuring that the number of input positions and data sorting remain the same throughout the network training and operation phases. The inputs of the first evaluation network, in a fixed order, include the normalized position of each horizontally distributed node, the corresponding pilot reception strength, the valid feedback state of the node, the target coverage angle range, and the allowable signal fluctuations; the valid feedback state is used to distinguish between the case where there is no valid terminal feedback at the current node and the case where there is a terminal but the pilot reception strength is low. Training samples consist of historical network test data or joint test data from an anechoic chamber and off-site. The sample labels are the proportion of the number of valid nodes that actually reach the reception strength threshold to the total number of valid nodes, and are corrected according to the signal uniformity within the area.

[0076] The correction process specifically includes: first, calculating the proportion of effective ground nodes reaching a preset communication threshold to the total number of effective ground nodes to obtain a basic coverage score; then, calculating the difference between the maximum and minimum values ​​of the pilot received strength of all effective nodes, and comparing this difference with the allowable signal fluctuations specified in the network planning. When the difference does not exceed the allowable signal fluctuations, the basic coverage score is not reduced; when it exceeds the allowable signal fluctuations, the basic coverage score is reduced according to the excess proportion; the corrected result is used as the training label for the first evaluation network.

[0077] The first evaluation network outputs a ground coverage score between 0 and 1; the closer the value is to 1, the higher the proportion of nodes that meet the coverage requirements in the ground target area and the more continuous the signal distribution.

[0078] For low-altitude target areas, horizontal position and altitude information are obtained based on positioning information reported by UAVs or other low-altitude terminals. The target low-altitude area is divided according to horizontal angle, pitch angle, and altitude range; each position with valid terminal feedback, along with its corresponding altitude and pilot signal reception strength, constitutes a three-dimensional altitude node.

[0079] The evaluation targets for low-altitude beams differ from those for wide-area ground coverage. Low-altitude targets typically require maintaining high energy near the target aircraft while minimizing ineffective radiation from non-target spatial directions. Therefore, in this embodiment, the low-altitude beam constraint is set to ensure that the main lobe width does not exceed a preset angle, and that the received intensity of nodes near the target aircraft is significantly higher than that of nodes outside the target area. Furthermore, the low-altitude target area is pre-divided into a fixed number of three-dimensional nodes according to fixed azimuth, pitch, and altitude intervals, and the same node order is maintained during training and operation. When a node currently lacks effective low-altitude terminal feedback, the same data retention and no-feedback-marking method as the ground evaluation network is used. The spatial range near the target aircraft is a spatial region centered on the three-dimensional node where the target aircraft is located, extending outwards by one grid interval along the azimuth, pitch, and altitude directions to adjacent nodes.

[0080] The second evaluation network input includes the horizontal position, altitude, azimuth, pitch, pilot signal reception strength, preset low-altitude main lobe width, and effective feedback status of the corresponding stereo nodes of the low-altitude terminal. During training, the predicted radiation intensity of each node in the fixed low-altitude spatial grid is obtained based on the preset 3D beam corresponding to the current training sample. The predicted radiation intensity of the stereo node where the target aircraft is located and within a grid interval adjacent to it along the azimuth, pitch, and altitude directions are accumulated to obtain the effective energy corresponding to the target area. Then, the predicted radiation intensity of all effective nodes within the fixed low-altitude spatial grid is accumulated to obtain the overall effective energy of the corresponding beam. The proportion of the effective energy in the target area to the overall effective energy is used as the energy concentration label. The terminal pilot signal reception strength is used as input data for the second evaluation network and is not directly used to calculate the overall spatial radiation energy at locations where no terminal is set. The more concentrated the energy is in the target area, the closer the label is to 1; the second evaluation network outputs a low-altitude tracking score between 0 and 1.

[0081] When the predicted radiation intensity in the three-dimensional preset beam is expressed in logarithmic gain or logarithmic power form, the predicted radiation intensity corresponding to each node is converted into linear power data before energy accumulation; when the predicted radiation intensity is expressed in linear normalized power form, the corresponding values ​​are directly used for accumulation.

[0082] Both the first and second evaluation networks can use a 3-layer feedforward neural network; the number of input layers is determined by the number of fixed nodes, the middle two layers are used to extract the correlation between location distribution and signal strength, and the last layer outputs a single score value.

[0083] During online operation, the ground coverage score and low-altitude tracking score are limited to the range of 0 to 1, and then combined according to the set ground weight and low-altitude weight to form a quality assessment item. For cases where the number of effective terminals varies greatly in different feedback periods, the effective node ratio and average node strength are uniformly normalized before being sent to the evaluation network to avoid abnormal changes in scores due to the increase in the number of terminals alone. Ground networks focus more on continuous coverage and signal uniformity over a larger horizontal area, while low-altitude aircraft communication focuses more on energy concentration in the target direction and spatial tracking capability that changes with the target's position. This implementation uses two independent evaluation branches to process the two types of terminal feedback separately, avoiding the use of a single average signal strength to evaluate different space tasks. By encoding ground horizontal nodes and low-altitude 3D nodes separately and finally outputting score data with unified dimensions, the two types of coverage targets can be jointly incorporated into the subsequent joint coverage function while maintaining independent evaluation of the two types of coverage targets. This allows the multi-frequency 3D beamforming process to take into account both the needs of wide-area ground coverage and low-altitude directional coverage. The steps for joint gradient optimization of the joint cover function based on array manifold constraints include: All frequency bands are arranged from low to high according to their frequency band numbers. Within each frequency band, the shaping weights are arranged from small to large according to their array element numbers. Each array element weight includes amplitude control and phase control. In this embodiment, all amplitude control values ​​are arranged continuously to form the first half of the global state matrix, and the corresponding phase control values ​​are arranged in the same array element order to form the second half. This ensures that there is a fixed correspondence between each matrix position and the specific frequency band, array element, and control type. The allowable amplitude and phase ranges for each feed channel are read based on the hardware capabilities of the antenna RF controller. For example, the normalized amplitude control range is limited to 0 to 1, and the phase control range is limited to -180 degrees to 180 degrees. At the same time, variables that cannot be controlled independently are restricted based on the array physical aperture and feed relationship. For example, when two array elements share the same phase shift channel, it is not allowed to generate contradictory phase control values ​​between them during the optimization process. The above amplitude range, phase range, and channel linkage relationship together form the optimization boundary constraints. In the first iteration, the global state matrix corresponding to the initial modified weights is used as the starting state.

[0084] Within the same joint gradient optimization cycle, the propagation environment of the ground target area and the low-altitude target area is considered to remain relatively stable within the current feedback cycle. First, the actual pilot reception intensity of each terminal under the current actual beamforming weight is recorded, and the predicted radiation intensity of each terminal in the corresponding spatial direction is obtained using the radiation prediction network. When a perturbation is applied to an amplitude control or phase control quantity in the global state matrix, the perturbed beamforming weight is input into the radiation prediction network to obtain the updated predicted radiation intensity in the same terminal spatial direction. The change in the updated predicted radiation intensity relative to the current predicted radiation intensity is calculated, and this change is used to correct the current actual pilot reception intensity. The corrected pilot reception intensity is then input into the first evaluation network and the second evaluation network according to the corresponding ground terminal and low-altitude terminal, respectively, to re-obtain the ground coverage score and low-altitude tracking score under the current perturbation state. The joint coverage function is then regenerated by combining this with the three-dimensional preset beam under the current perturbation state. The predicted radiation intensity change is converted to the same logarithmic power dimension as the actual pilot received intensity before being used to correct it. When the radiation prediction network directly outputs logarithmic gain data, the difference between the updated predicted radiation intensity and the current predicted radiation intensity is used as the correction amount. The corrected pilot received intensity is used as the estimated data for the evaluation candidate beamforming weights in the current feedback cycle and does not replace the actual pilot feedback remeasured by the terminal. After entering the next feedback cycle, the current evaluation benchmark is updated with the actual pilot received intensity re-reported by the terminal.

[0085] In this embodiment, the partial derivative parameter of the joint covering function with respect to the global state matrix is ​​obtained by applying positive and negative small perturbations to the current shaping variable and comparing the numerical changes of the joint covering function under the two perturbation states. This approximate rate of change is used to determine the descent direction near the current state. For cases where the joint covering function has discontinuous derivatives in the local state or where the analytical partial derivatives cannot be directly obtained, it is not required to calculate the strict partial derivatives of the analytical form. Instead, the above-mentioned bidirectional perturbation results are used to determine the approximate descent direction under the current numerical state.

[0086] For an amplitude variable that needs to be calculated, first add a small perturbation to the current value and recalculate the joint covering function, then reduce the same perturbation to the current value and recalculate the joint covering function; estimate the partial derivatives of the amplitude variable based on the direction and degree of change of the two joint covering functions; use the same method for phase variables.

[0087] In one implementation, the initial perturbation of the normalized amplitude is set to 0.01, and the initial perturbation of the phase is set to 1 degree; after all active variables have completed the partial derivative calculation, the multivariate descent gradient of the current state is obtained; then the global state matrix is ​​updated synchronously according to the descent direction of the joint covering function indicated by the gradient.

[0088] The initial amplitude update step size is set to 0.02, and the phase update step size is set to 1 degree. If the joint coverage function continues to decrease after three consecutive iterations, the next update step size will be increased by 10%, but not exceeding twice the initial step size. If an update causes the joint coverage function to increase, the update will be canceled, and the corresponding step size will be reduced by half before recalculation. Boundary checks are performed after each state matrix update. When the amplitude control value exceeds the corresponding hardware maximum value, it is limited to the maximum allowable value. When it is lower than the minimum value, it is limited to the minimum allowable value. The phase data is limited or periodically mapped according to the allowable range of the actual phase shifter. For array elements sharing the control channel, synchronous correction is performed according to the actual hardware linkage rules.

[0089] After completing the amplitude control range, phase control range, and shared channel relationship checks, the currently updated candidate shaping weights are input into the radiation prediction network to obtain the three-dimensional preset beam corresponding to the candidate shaping weights. Based on the target azimuth and elevation directions in the current joint coverage command, it is checked whether the main lobe center direction of the three-dimensional preset beam is within the allowable deviation range of the corresponding target direction. When the candidate shaping weights simultaneously satisfy both the radio frequency control range and the target direction allowable deviation, the current candidate shaping weights are retained and the next iteration begins. When the main lobe center direction corresponding to the candidate shaping weights after boundary correction exceeds the target direction allowable deviation, the current candidate update is cancelled, the global state matrix before the update is restored, and the current iteration step size is reduced before a new update is performed.

[0090] After each iteration, a new joint coverage function value is recorded. In one implementation, when the relative rate of change of the joint coverage function in two consecutive iterations is less than 0.001, the optimization is considered to have converged. When the above condition is not met after 200 iterations, the current round of online optimization is stopped, and the state matrix with the lowest joint coverage function in each iteration is selected as the current output. The final state matrix is ​​re-split according to the original frequency band and array element number to obtain the amplitude shaping control quantity and phase shaping control quantity corresponding to each frequency band, i.e., the cooperative shaping weight. In this embodiment, the array manifold constraint includes the spatial direction response constraint determined by the three-dimensional spatial position of each frequency band array element, the current working frequency band, and the target azimuth direction and target pitch direction, as well as the control range constraint determined by the amplitude control range of the feed channel, the phase control range, and the relationship of the shared phase shift channel. After each global state matrix update, only the shaping states that can satisfy the current array spatial direction response relationship and are within the actual radio frequency control range are retained to participate in the subsequent joint coverage function calculation. This invention organizes the beamforming weights of each frequency band into a single optimized state constrained by hardware conditions, so that the adjustments of different frequency bands are no longer performed independently, but can be updated synchronously according to a unified joint coverage function. The dynamic step size mechanism can appropriately increase the adjustment speed when the objective function is continuously improved, and reduce the step size when an incorrect update direction occurs, thereby balancing convergence speed and iterative stability. At the same time, each update is constrained by the actual RF amplitude and phase range, shared channel relationship, and array physical structure, which can avoid numerical optimization from obtaining control states that the actual antenna cannot execute, so that the final output cooperative beamforming weights can directly correspond to the controllable range of the actual feed network and phase shifter.

[0091] Example 2: This invention proposes a 3D beamforming method based on an antenna array, comprising: The spatial location of array elements, feed network channels, and current phase shift state of each frequency band in the multi-frequency common aperture array are obtained, and the local influence neighborhood is determined based on the geometric distance between the different frequency array elements. The cross-frequency perturbation codebook is obtained based on the local influence neighborhood. The cross-frequency perturbation codebook includes the amplitude perturbation mapping and phase manifold mapping established by the frequency band reference direction response under the reference electrically regulated state. Receive joint coverage instructions and acquire the three-dimensional orientation and electrical control status of targets in ground target areas and low-altitude target areas; combine amplitude perturbation mapping and phase manifold mapping to determine the cross-frequency compensation data for each frequency band in response to the electrical control status of the targets; The basic beamforming weights of each frequency band are corrected using cross-frequency compensation data to obtain initial corrected weights, and three-dimensional preset beams of the corresponding frequency bands are generated based on the initial corrected weights. The terminal pilot feedback in the ground target area and the low-altitude target area is obtained. The terminal pilot feedback is combined with the three-dimensional preset beam to construct a joint coverage function including a cross-frequency overlap penalty term. Joint gradient optimization is performed on the joint coverage function based on array manifold constraints. The initial correction weights are updated using the converged optimization results, and the cooperative shaping weights of each frequency band are output.

[0092] Based on Example 1, the following steps are further included: The step of obtaining the target electrical control status for ground target areas and low-altitude target areas includes: The mechanical position feedback quantity is read by the underlying feedback sensing device and used as the first criterion for determining the current physical state. The direction of motion change of the current ESC control action is obtained to determine whether the tilt adjustment is in an increasing or decreasing execution state. The direction of motion change is used as an additional state for calling compensation, and according to the reference ESC state corresponding to the current mechanical position, the hysteresis compensation parameter corresponding to the current motion direction is matched in the hysteresis compensation parameter table that uses the same reference ESC state index as the cross-frequency disturbance codebook. The hysteresis compensation parameter is used to correct the idle error of the mechanical position feedback quantity to obtain the target ESC state after eliminating the influence of mechanical transmission backlash.

[0093] During the antenna product calibration phase, mechanical hysteresis data corresponding to different directions of motion are first obtained. The electrically adjustable mechanism is then driven sequentially from the minimum allowable downtilt state to multiple fixed calibration positions along the downtilt increasing direction. At each position, the mechanism is waited to stop, and the feedback value is read using a mechanical position sensor. Simultaneously, the actual antenna electrically adjustable position is measured using an external high-precision angle measuring device. After completing the calibration in the increasing direction, the mechanism is moved to the maximum position, and then reversed along the downtilt decreasing direction according to the same calibration position. The position sensor feedback value and the actual measured position are recorded again.

[0094] For the same calibration position, compare the feedback state when the direction is increased and when the direction is decreased; the directional difference between the two caused by gear backlash, lead screw backlash or other transmission mechanisms is recorded as hysteresis error; save the increased directional compensation amount and decreased directional compensation amount according to the calibration position to form a directional hysteresis compensation parameter table.

[0095] This parameter table establishes a corresponding index with the reference electronic adjustment state in the cross-frequency disturbance codebook, so that each reference electronic adjustment position can obtain the mechanical correction parameters corresponding to the increasing and decreasing directions.

[0096] During on-site operation, the current mechanical position feedback is read through the underlying feedback sensing device, which can be an encoder, displacement sensor, or the original electronically controlled position sensor of the antenna. Then, the current electronically controlled control command is compared with the control command of the previous cycle. When the required downward tilt is greater than the previous state, the direction of motion change is determined to be an increase execution state; when the required downward tilt is less than the previous state, the direction of motion change is determined to be a decrease execution state; when the two commands are the same, the previous effective motion direction is kept as the reference for the current hysteresis state until a new motion direction change occurs.

[0097] Based on the current position and direction of movement, the data corresponding to the two most recent calibration positions are searched in the hysteresis compensation parameter table. When the current position is exactly at a calibration position, the compensation parameters for that position and direction are directly read; when the current position is between two calibration positions, linear interpolation is performed based on the distance between the current position and the two calibration positions to obtain the hysteresis compensation amount corresponding to the current state. Subsequently, the mechanical position feedback is corrected. If the calibration indicates that the position sensor feedback value is smaller than the actual position when directional movement is increased, the corresponding compensation amount is increased during the increased execution state. If the calibration indicates that the feedback value is larger than the actual position when directional movement is decreased, the corresponding compensation amount is decreased accordingly.

[0098] The corrected state data serves as the basis for determining the current actual ESC position. When the network has given the target ESC command, the controller compares the corrected mechanical position with the target command position. Only when the difference between the two is lower than the allowable position error is the state confirmed as the achieved target ESC state, and the target ESC state is used to enter the cross-frequency disturbance codebook lookup process. If the difference between the two is still greater than the allowable error, the ESC mechanism continues to be driven to make small adjustments until the position conditions are met. Thus, the ESC state used for cross-frequency disturbance compensation is not simply derived from the software command value, but is based on the actual mechanical position feedback and the state after motion direction correction.

[0099] During forward and reverse adjustment, mechanically electrically adjustable antennas may experience discrepancies in actual mechanical positions corresponding to the same software commands due to gaps in gears, lead screws, or other transmission mechanisms. If the software-set angle is directly used as the query condition for the cross-frequency disturbance codebook, amplitude and phase compensation data that does not fully correspond to the actual array state may be selected. This implementation addresses this by separately calibrating the hysteresis errors in the increasing and decreasing directions and using actual mechanical position feedback for directional correlation correction. This makes the electrically adjustable state entering the cross-frequency disturbance compensation process closer to the true physical position, thereby reducing the possibility of underlying mechanical errors continuing to propagate into the cross-frequency compensation, beam prediction, and joint beamforming processes.

[0100] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A 3D beamforming method based on an antenna array, characterized in that, include: The spatial location of array elements, feed network channels, and current phase shift state of each frequency band in the multi-frequency common aperture array are obtained, and the local influence neighborhood is determined based on the geometric distance between the different frequency array elements. The cross-frequency perturbation codebook is obtained based on the local influence neighborhood. The cross-frequency perturbation codebook includes the amplitude perturbation mapping and phase manifold mapping established by the frequency band reference direction response under the reference electrically regulated state. Receive joint coverage instructions and acquire the three-dimensional orientation and electrical control status of targets in ground target areas and low-altitude target areas; combine amplitude perturbation mapping and phase manifold mapping to determine the cross-frequency compensation data for each frequency band in response to the electrical control status of the targets; The basic beamforming weights of each frequency band are corrected using cross-frequency compensation data to obtain initial corrected weights, and three-dimensional preset beams of the corresponding frequency bands are generated based on the initial corrected weights. The terminal pilot feedback in the ground target area and the low-altitude target area is obtained. The terminal pilot feedback is combined with the three-dimensional preset beam to construct a joint coverage function including a cross-frequency overlap penalty term. Joint gradient optimization is performed on the joint coverage function based on array manifold constraints. The initial correction weights are updated using the converged optimization results, and the cooperative shaping weights of each frequency band are output.

2. The 3D beamforming method based on an antenna array according to claim 1, characterized in that: The steps for determining the local influence neighborhood based on the geometric distance between different frequency array elements include: converting the spatial position of the array elements into three-dimensional coordinate parameters in the base station coordinate system, and calculating the three-dimensional spatial distance between the array element to be compensated and the other different frequency array elements; initially screening the different frequency array elements whose three-dimensional spatial distance is less than a preset distance benchmark as initial candidate array elements; analyzing the feed network channel and the current phase shift state, and extracting the feed correlation degree and continuous phase difference between the array element to be compensated and the initial candidate array elements; synchronously performing nonlinear mapping on the three-dimensional spatial distance, feed correlation degree and continuous phase difference to convert them into continuous cross-frequency weights; selecting the initial candidate array elements whose continuous cross-frequency weights are higher than a preset weight threshold, and performing spatial clustering association with the array element to be compensated to generate the local influence neighborhood of the corresponding array element to be compensated.

3. The 3D beamforming method based on an antenna array according to claim 2, characterized in that: The steps for obtaining the cross-frequency perturbation codebook include: injecting reference test signals into a multi-frequency common-aperture array under multiple reference electrically tunable states to obtain measured radiation sequences of each frequency band in a predetermined discrete direction; comparing the measured radiation sequences with the reference radiation sequences under uncoupled states to separate the fundamental amplitude offset and fundamental phase offset corresponding to each frequency band; extracting periodic transition nodes in the fundamental phase offset and mapping the transition phases to smooth phase data in a continuous smooth space using phase dewinding processing; constructing an amplitude perturbation mapping based on the fundamental amplitude offset and the corresponding reference electrically tunable states, and simultaneously constructing a phase manifold mapping based on the smooth phase data and the corresponding reference electrically tunable states; and combining the amplitude perturbation mapping and the phase manifold mapping in a structured data manner according to the topological relationship of the local influence neighborhood to generate the cross-frequency perturbation codebook.

4. The 3D beamforming method based on an antenna array according to claim 3, characterized in that: The steps for determining the cross-frequency compensation data for each frequency band in relation to the target electrically regulated state include: extracting nearby calibration nodes distributed around the target electrically regulated state and the target three-dimensional direction in the cross-frequency disturbance codebook, using the local influence neighborhood as the index boundary; obtaining the amplitude disturbance value and unwinding phase value corresponding to the nearby calibration nodes; performing local polynomial fitting on the amplitude disturbance value to obtain the amplitude compensation data in the current corresponding state; performing manifold interpolation on the unwinding phase value to obtain transition phase data, and performing reverse phase winding processing on the transition phase data to generate phase compensation data that matches the electromagnetic period; and combining the phase compensation data with the amplitude compensation data to obtain the cross-frequency compensation data.

5. The 3D beamforming method based on an antenna array according to claim 1, characterized in that: The steps for generating a corresponding frequency band three-dimensional preset beam based on the initial corrected weights include: The array topology features of each frequency band are obtained, including the physical arrangement parameters and radio frequency boundary parameters of the multi-frequency co-aperture array. The initial correction weights are combined with the array topology features to construct the input feature data of the radiation prediction network. The input feature data is input into the pre-trained radiation prediction network, and the implicit correlation features between the shaping weights and the spatial radiation gain are extracted using the multi-layer neuron nodes in the radiation prediction network. The radiation prediction network outputs the predicted radiation intensity of each frequency band in each direction of the target coverage space, and the corresponding three-dimensional preset beam is generated by spatially stitching the predicted radiation intensity.

6. The 3D beamforming method based on an antenna array according to claim 5, characterized in that: The steps for constructing a joint coverage function including a cross-frequency overlap penalty term include: receiving pilot reception strengths reported by a first type of terminal in the ground target area and a second type of terminal in the low-altitude target area; establishing quality assessment terms regarding ground signal distribution and low-altitude signal distribution based on the pilot reception strengths; extracting the main lobe pointing vector and side lobe suppression coefficient of the three-dimensional preset beam in each frequency band, and calculating the spatial pointing deviation between the pointing vectors of different frequency bands; introducing the spatial pointing deviation into a preset nonlinear penalty model to generate a cross-frequency overlap penalty term for constraining the coverage overlap rate of different frequency bands; and weighting and summing the quality assessment term and the cross-frequency overlap penalty term to generate the joint coverage function.

7. A 3D beamforming method based on an antenna array according to claim 6, characterized in that: The steps for establishing quality assessment items for ground signal distribution and low-altitude signal distribution include: analyzing the horizontal distribution nodes fed back by the terminal within the ground target area, and constructing a first evaluation network with the horizontal wide-area coverage compliance rate as the convergence target, in conjunction with the preset ground beamwidth constraint; analyzing the three-dimensional height nodes fed back by the terminal within the low-altitude target area, and constructing a second evaluation network with the low-altitude target energy concentration as the convergence target, in conjunction with the preset low-altitude beam narrow and sharp constraint; inputting the received pilot reception strengths into the first evaluation network and the second evaluation network respectively, and outputting the ground coverage score scalar and the low-altitude tracking score scalar respectively through network node feature extraction; and performing dimensionless splicing and combination of the ground coverage score scalar and the low-altitude tracking score scalar using normalization processing to generate the quality assessment items.

8. A 3D beamforming method based on an antenna array according to claim 7, characterized in that: The steps for joint gradient optimization of the joint cover function based on array manifold constraints include: The initial correction weights of each frequency band are combined into a global state matrix, and the physical aperture topology of the multi-frequency co-aperture array is extracted as the optimization boundary constraint. The partial derivative parameter of the joint coverage function with respect to the global state matrix is ​​calculated to determine the multivariate descent gradient under the current numerical state. The global state matrix is ​​synchronously updated along the multivariate descent gradient according to the dynamic iteration step size, and after each update, it is checked whether it has crossed the optimization boundary constraint. When the numerical rate of change of the joint coverage function is lower than the preset convergence threshold, the iterative optimization calculation is stopped, and the converged global state matrix is ​​output as the cooperative shaping weight.

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