Millimeter wave phased array antenna beamforming calibration method

Abstract

The application discloses a millimeter wave phased array antenna beamforming calibration method and belongs to the technical field of antenna beamforming calibration. The method comprises the following steps: obtaining initial amplitude and phase excitation data of antenna array elements; constructing a multi-target phase disturbance injection function based on the difference between mismatch and ideal beam pattern; generating an initial calibration weight matrix through iterative optimization; pre-compensating the phase distribution and collecting measured pattern data; performing envelope decomposition on the measured data to extract independent error components of the main lobe and the sidelobe; constructing a multi-frequency error representation function; correcting the initial calibration weight matrix by using a gradient descent update strategy to generate a frequency-variable calibration weight sequence; and mapping the frequency-variable calibration weight sequence to each channel phase shifter to complete calibration. The method solves the problems of beam distortion and error coupling under multi-frequency points and realizes high-precision closed-loop calibration of wideband beamforming.

Description

Technical Field

[0001] This invention relates to the field of antenna beamforming calibration technology, specifically a method for beamforming calibration of millimeter-wave phased array antennas. Background Technology

[0002] In actual operation, millimeter-wave phased array antennas are affected by factors such as amplitude and phase consistency deviations between channels, mutual coupling effects, and device discreteness, resulting in a mismatch between the actual beam pattern and the ideal design beam. Existing technologies often rely on single-frequency or narrow-band assumptions for conventional beamforming calibration, correcting channel weights by collecting radiation field data from a small number of sampling points and comparing it with an ideal template. This method is insufficient to effectively address the frequency dispersion effects caused by the increased operating bandwidth in the millimeter-wave band. Each array element channel exhibits differentiated amplitude attenuation and phase shift characteristics at different frequencies, making it impossible for single-frequency calibration results to simultaneously constrain the main lobe pointing accuracy and side lobe level distribution across the entire operating frequency band. The shortcomings of existing solutions lie in the fact that they generally treat the overall distortion of the beam pattern as a general optimization objective, lacking independent identification and decoupling mechanisms for main lobe and side lobe error components. When multiple frequency errors simultaneously affect the beam pattern, conventional least mean square or single-objective optimization strategies easily fall into local trade-offs, manifesting as a decrease in main lobe gain at high frequencies when low-frequency sidelobe suppression meets targets, or inconsistent calibration effects across multiple scanning angles. Furthermore, existing methods typically rely on fixed step sizes or empirical update rules during iterative calibration, lacking fine-grained convergence control based on the error gradient structure. This results in an inefficient and prone-to-divergent search process on the multidimensional, multi-frequency joint error surface.

[0003] To address the aforementioned issues, it is necessary to solve how to introduce envelope decomposition methods into the beam calibration process in millimeter-wave broadband operating scenarios. This would allow for the separation and extraction of main lobe phase errors and side lobe amplitude errors, and the construction of a frequency-varying joint error characterization, thereby enhancing the independent control capability of multi-frequency errors. Simultaneously, it is necessary to solve how to combine pre-optimization with multi-target phase perturbation injection and closed-loop correction with gradient descent to construct a two-level progressive calibration framework. This framework aims to achieve a balance between global search and local fine convergence, enabling accurate adjustment of array weights with frequency. Summary of the Invention

[0004] The purpose of this invention is to provide a beamforming calibration method for millimeter-wave phased array antennas. By using envelope decomposition, the error components of the main lobe and side lobe regions in the measured radiation pattern are decoupled into independent phase error terms and amplitude error terms. These are then weighted and fused at multiple discrete frequency points to form a multi-frequency error characterization function, achieving a refined frequency-varying description of broadband beam distortion. Simultaneously, by establishing a multi-target phase perturbation injection function and performing global iterative optimization to generate an initial calibration weight matrix, and then combining it with frequency-varying error closed-loop correction based on gradient descent, a two-level calibration mechanism from pre-compensation to fine modulation is formed, thereby uniformly controlling the main lobe pointing and side lobe level at different frequencies.

[0005] To achieve the above objectives, this invention provides the following technical solution: This invention provides a beamforming calibration method for millimeter-wave phased array antennas. This method effectively solves the beam distortion problem caused by channel inconsistency and broadband effects by multi-level approximation and frequency-varying compensation of the amplitude and phase errors of array elements. It can achieve high-precision beamforming calibration without relying on precise device models. After obtaining the initial amplitude and phase excitation data of the antenna array elements, this method establishes a multi-objective phase perturbation injection function based on the difference between the mismatched beam pattern and the ideal beam pattern. This function uses phase perturbation as the optimization variable and takes into account both the main lobe fitting accuracy and the side lobe suppression capability. The function is used for iterative optimization to generate an initial calibration weight matrix, realizing element-by-element pre-compensation of the phase of each array element. This allows the antenna array to have an initial state that approximates the ideal pattern envelope before precise measurement and closed-loop calibration, providing excellent initial conditions for subsequent fine calibration and significantly reducing the complexity of subsequent iterations.

[0006] Based on this, a pre-compensated antenna array is used to collect spatial radiation field data, obtain measured radiation pattern data, and then envelop the measured radiation pattern data. As a preferred embodiment of this invention, a complex analytical envelope is obtained by performing a Hilbert transform on the measured radiation pattern data. This complex analytical envelope is then divided into main lobe and side lobe regions in the angular domain, and the corresponding phase error and amplitude error terms are extracted respectively. This independently separates the errors of the main lobe and side lobe, obtaining independent error components that accurately reflect the distortion characteristics of different beam regions. Considering the broadband operating characteristics of millimeter waves, based on the aforementioned independent error components, the main lobe phase error and side lobe amplitude error are weighted and fused at multiple frequency points to construct a multi-frequency error characterization function that comprehensively characterizes the degree of beam mismatch within the frequency band.

[0007] Guided by the gradient of the multi-frequency error representation function, a gradient descent update strategy is used to correct the initial calibration weight matrix. Partial derivatives are repeatedly calculated and the weight matrix is ​​updated along the negative gradient direction until the norm of the multi-frequency error representation function converges, thus generating a frequency-varying calibration weight sequence. In this process, the initial calibration weight matrix provides a starting point close to the global optimum, and the gradient descent correction performs a fine search only within a local range, avoiding the shortcomings of traditional amplitude and phase calibration methods that easily get trapped in local extrema or have slow convergence in multi-frequency joint optimization. This allows the calibration weights to smoothly transition with frequency changes. Preferably, the converged weight matrix is ​​split row-wise into sub-weight vectors corresponding to each discrete frequency point, and arranged in ascending order of frequency to form a frequency-varying calibration weight sequence. Then, the phase components in this frequency-varying calibration weight sequence are converted into phase shifter control code values, which are stored in a lookup table according to the array element channel number and the corresponding discrete frequency point. During beam scanning, the corresponding control code value is called according to the actual operating frequency and written to each phase shifter, directly driving the phase shifter to complete beamforming calibration in a hardware-executable manner. By combining the above-mentioned pre-compensation, multi-frequency error decoupling characterization and gradient correction, the entire calibration process achieves progressive optimization from initial blind calibration to precise closed-loop compensation. The synchronous control capability of main lobe pointing accuracy and side lobe level is significantly enhanced, and it has good compensation robustness for consistency deviation of each channel of the array in the broadband range.

[0008] The technical effects and advantages provided by the present invention in the above technical solution are as follows: Measured radiation pattern data was obtained by acquiring the pre-compensated array spatial radiation field. A Hilbert transform was then performed to obtain the complex analytic envelope. The main lobe and side lobe intervals in the angular domain were divided, and discrete Fourier transforms were performed separately to separate the phase error term of the main lobe and the amplitude error term of the side lobe. This decoupling process allows different types of errors originally coupled in the main lobe pointing deviation and side lobe rise processes to be extracted independently, avoiding the compromise between main lobe accuracy and side lobe suppression under conventional overall fitting methods. Based on this, multiple discrete frequency points within the millimeter-wave operating band were selected, and the main lobe phase error term and side lobe amplitude error term at each frequency point were weighted, fused, and combined into a multi-dimensional error vector to construct a multi-frequency error characterization function. The resulting error function provides a detailed description of radiation pattern distortion in the frequency dimension and has a distinguishing characterization effect on differential distortion caused by broadband frequency dispersion, enabling subsequent calibration to independently adjust the beamforming effect at each frequency point. In the construction of the multi-objective phase perturbation injection function, the ideal beam pattern at a specified scanning angle is used as a reference template. The gain deviation of the current mismatch pattern on multiple azimuth sections is calculated, and the minimization of gain deviation and the suppression of sidelobe peaks are simultaneously incorporated into the optimization objectives. The phase offset is used as a variable to perform a global iterative solution, generating an initial calibration weight matrix superimposed with the initial amplitude and phase excitation data. This method takes into account multiple objectives of the main lobe profile and sidelobe envelope in the early stage of iteration, making the pre-compensated array radiation field close to the target state, providing an initial point conducive to gradient convergence for subsequent closed-loop correction. The gradient matrix is ​​constructed based on the partial derivatives of the multi-frequency error characterization function with respect to each element of the initial calibration weight matrix. The weight matrix is ​​repeatedly updated along the negative gradient direction with a preset step size until the error norm converges, finally forming a frequency-varying calibration weight sequence arranged in frequency order. Its phase components are converted into phase shifter control code values ​​and stored in a lookup table according to channel and frequency. The step update driven by partial derivatives progresses along the optimal descent direction on the joint error surface of multiple frequencies, avoiding low-frequency oscillations or high-frequency stagnation caused by fixed rule updates. The compensation amount of the frequency-varying weight sequence for each discrete frequency point is independent yet converges uniformly. From the large-scale pattern shape correction in the pre-compensation stage to the fine error clearing of multiple frequencies in the closed-loop stage, a hierarchical progression is formed. Finally, the accurate maintenance of the main lobe pointing and the stable suppression of the side lobe level are achieved synchronously in the millimeter-wave broadband. Attached Figure Description

[0009] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0010] Figure 1 This is a flowchart of the beamforming calibration method for millimeter-wave phased array antennas; Figure 2 This is a flowchart of the construction process for the multi-target phase perturbation injection function of the antenna array; Figure 3 This is a flowchart of the differential evolution algorithm for solving the multi-objective phase perturbation injection function and generating the initial calibration weight matrix; Figure 4 This is a flowchart of measured radiation pattern envelope decomposition and multi-frequency point error characterization; Figure 5 This is a flowchart of the generation process for frequency-varying calibration weight sequences based on gradient descent; Figure 6 This is a flowchart of frequency-varying calibration weight mapping and beamforming calibration. Detailed Implementation

[0011] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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, 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.

[0012] See Figure 1This invention provides a beamforming calibration method for millimeter-wave phased array antennas. First, the amplitude and phase responses of the antenna elements before calibration are collected and normalized to form a reference amplitude and phase vector as initial amplitude and phase excitation data. Based on this, using an ideal beam pattern as a reference template, and considering the gain deviation of the mismatched beam pattern across multiple azimuth sections, the phase offset is used as an optimization variable to construct a multi-objective phase perturbation injection function aimed at minimizing gain deviation and suppressing sidelobe peaks. Within a preset phase perturbation search space, a differential evolution algorithm is used for global iteration. The phase perturbation vector corresponding to the optimal fit is superimposed with the initial amplitude and phase excitation data to generate an initial calibration weight matrix. After performing element-by-element pre-compensation on the phase distribution of the antenna elements based on this matrix, the probe antenna is aligned with the phase center of the antenna array under test in a microwave anechoic chamber. Measured beam pattern data is obtained through transmitting test sequences, probe reception, time-domain sampling, and Fourier transform. Hilbert transform is performed on the measured radiation pattern data to obtain the complex analytical envelope, and the main lobe interval and side lobe interval are divided. Discrete Fourier transform is used to extract the phase error term and amplitude error term for each interval. Then, multiple discrete frequency points within the millimeter-wave operating frequency band are selected, and the phase error term of the main lobe interval and the amplitude error term of the side lobe interval are weighted and fused to form a multi-frequency error characterization function. The partial derivatives of this function with respect to each element of the initial calibration weight matrix are calculated, and a gradient matrix is ​​constructed. The weight matrix is ​​iteratively updated along the negative gradient direction until the norm of the multi-frequency error characterization function converges. The converged weight matrix is ​​then split row-wise into sub-weight vectors corresponding to each discrete frequency point, and arranged in frequency order to form a frequency-varying calibration weight sequence. The phase components in this sequence are converted into phase shifter control code values, which are stored in a lookup table according to the array element channel number and the discrete frequency point. During beam scanning, the corresponding control code value is called according to the operating frequency and written to each phase shifter to complete the beamforming calibration.

[0013] Example 1: In specific implementation, please refer to Figure 2 The process of acquiring the initial amplitude and phase excitation data of the antenna array elements includes: using a vector network analyzer to measure the complex transmission coefficient of each element channel of the antenna array in an uncalibrated state, obtaining the amplitude response value and phase response value of each element channel. The amplitude and phase response values ​​of all element channels are arranged in order of element number to form an initial amplitude and phase vector. The element channel with the largest amplitude response value in the initial amplitude and phase vector is used as a reference, and its amplitude response value and phase response value are used as the amplitude reference and phase reference, respectively. For each element channel, the amplitude response value of the element channel is divided by the amplitude reference to obtain the normalized amplitude value of the element channel; the phase response value of the element channel is subtracted from the phase reference to obtain the normalized phase value of the element channel. The normalized amplitude and normalized phase values ​​of all element channels are combined in order of element number to generate a reference amplitude and phase vector.

[0014] In practical implementation, the process of constructing a multi-target phase perturbation injection function based on the difference between the mismatched beam pattern and the ideal beam pattern includes: selecting a beam scanning angle as the specified scanning angle; calculating the pattern function of the array antenna under the condition of no amplitude and phase error based on array antenna theory, using the element position distribution, operating frequency, and specified scanning angle; and using this pattern function as a reference template for the ideal beam pattern. The reference template is represented as a gain curve that varies with the elevation angle on the azimuth section at the specified scanning angle. Based on the initial amplitude and initial phase data in the reference amplitude and phase vector, combined with the element position distribution and operating frequency, the actual pattern gain values ​​of the current antenna array on multiple azimuth sections when uncalibrated are calculated to obtain the mismatched beam pattern. For each selected azimuth section, the difference between the gain value of the mismatched beam pattern and the gain value of the reference template is calculated at the elevation angle sampling point to obtain a gain deviation sequence. The gain deviation sequences of all azimuth sections are combined into a gain deviation set.

[0015] With the objectives of minimizing gain deviation and suppressing sidelobe peaks, a multi-objective phase perturbation injection function is constructed by using the phase offset to be injected into each array element channel as an optimization variable. The optimization variables form a phase perturbation vector equal to the number of array elements, where each element represents the phase offset value of the corresponding array element channel. The specific form of the multi-objective phase perturbation injection function is as follows: in, This is the phase perturbation vector. , The total number of array elements, Indicates the first The phase offset of each element channel, in radians; This represents the total number of selected azimuth sections. For the first Number of pitch angle sampling points on each azimuth section; Indicates the first In the first directional section One pitch angle sampling point; For reference templates, in the first Pitch angle on each azimuth plane The gain value at that point is scaled linearly. To inject phase perturbation vector The mismatched beam pattern obtained after calculation is in the first... Pitch angle on each azimuth plane The gain value at that point is scaled linearly. This is the first weighting coefficient, and its value range is... to ; This is the second weighting coefficient. ; This is the set of angle sampling points for the sidelobe regions of all orientation sections; These are angle sampling points within the sidelobe region; To inject phase perturbation vector The mismatched beam pattern obtained after calculation has the following sidelobe angle. The gain value at that location.

[0016] First weighting coefficient Second weighting coefficient The setting method is as follows: when the element position error and channel amplitude and phase error of the antenna array to be calibrated are large, causing a significant drop in main lobe gain, then... Set as When elevated sidelobe levels are the primary factor contributing to performance degradation, Set as In cases other than the two typical categories mentioned above, Set as Phase perturbation vector Each element The search space constraint is .

[0017] Example 2: In specific implementation, please refer to Figure 3 The process of iteratively optimizing the multi-objective phase perturbation injection function and generating the initial calibration weight matrix is ​​implemented using the differential evolution algorithm. The input to the differential evolution algorithm is the multi-objective phase perturbation injection function, and the output is the optimal phase perturbation vector. The control parameters of the differential evolution algorithm include population size, scaling factor, crossover probability, and maximum number of iterations.

[0018] In practical implementation, when setting the phase disturbance search space, the search space is defined based on the minimum phase shift step achievable by the phase shifter and the periodicity of the phase. A hypercube in 3D real space, where This is equal to the total number of elements in the antenna array. Each dimension of the search space corresponds to the phase offset of one element channel, and the lower bound of each dimension is... radians, upper bound is radian.

[0019] In practical implementation, the method for initializing a set of random phase perturbation vectors is as follows: In each dimension of the search space, a real number is randomly generated according to a uniform distribution, forming a... A dimensional vector, as an individual. Repeatedly generated. Individuals constitute the initial population, among which Population size. Set as This is to ensure that the search space is fully sampled.

[0020] In practice, the process of global iteration within the phase perturbation search space using the differential evolution algorithm includes population initialization, mutation, crossover, selection, and termination condition determination. Each iteration is called a generation, and each generation generates a new population.

[0021] Before the first iteration begins, an initial population has been generated. Each individual in the initial population is a candidate phase perturbation vector. For each individual in the initial population, the pattern fit is evaluated. The pattern fit is obtained by calculating the value of the multi-target phase perturbation injection function; a smaller value indicates a higher fit. The multi-target phase perturbation injection function value of each individual in the initial population is recorded as its fitness value, and the individual with the smallest fitness value is selected as the current best individual.

[0022] Upon entering the next iteration, a mutation operation is performed on the current population. The mutation operation applies to every individual in the current population. Generate a mutation vector The formula for generating the mutation vector is: in, Indicates the current iteration algebra number; Indicates the first The first generation of the population Individual; Indicates the first The corresponding generation in the population The variation vector of each individual; , , Indicates from the first Three distinct individuals randomly selected from the population, each different from the others. Individuals; This is the scaling factor, and its value is... Scaling factor Values The basis is: when Values ​​in to When considering intervals, the differential evolution algorithm strikes a balance between global search capability and convergence speed, selecting... This allows the mutation vector to effectively point to a better region while maintaining diversity.

[0023] After the mutation operation is completed, for each pair of individuals and mutation vector Perform crossover operations to generate test vectors. The crossover operation uses a binomial crossover method. For the test vector... The Dimensional components Generate a space between and A uniformly distributed random number between the two; if the random number is less than or equal to the crossover probability. Or a randomly selected dimension index equal to Then the mutation vector The Dimensional components Assign to Otherwise, the individual The Dimensional components Assign to Crossover probability Set as Crossover probability Set as The rationale is as follows: when the number of function evaluations is finite, a higher crossover probability can accelerate convergence; for the phase calibration problem, the computational cost of pattern fit evaluation is large, therefore... This can reduce the number of iterations required.

[0024] After the crossover operation is completed, for each trial vector Perform boundary constraint processing. If any component of the test vector exceeds the lower bound of the search space... or upper boundary If so, then the component is reset to the boundary value.

[0025] In practice, the method for evaluating the pattern fit after each iteration is as follows: For each individual in the current population and each newly generated experimental vector, the phase offset represented by the individual or experimental vector is injected into the reference amplitude-phase vector, the corresponding mismatched beam pattern is calculated, and the function value is calculated based on the multi-target phase perturbation injection function. The function value is used as a measure of pattern fit. The smaller the function value, the higher the pattern fit.

[0026] The selection operation is performed on each pair of individuals. and test vector Perform: Calculate the test vector Multi-target phase perturbation injection function values, and individual The multi-target phase perturbation injection function values ​​are compared; if the function value of the experimental vector is less than or equal to the function value of the individual, the individual is replaced by the experimental vector and enters the next generation population; otherwise, the original individual is retained. After the selection operation is completed, the first generation is formed. Generational population.

[0027] In practice, mutation, crossover, boundary constraint handling, pattern fit evaluation, and selection operations are repeated until the maximum number of iterations is reached. The maximum number of iterations is set to... The maximum number of iterations is set to... The basis is: when dimension At higher population densities, the population requires more iterations to fully explore the search space. Doubling the dimension ensures that the algorithm converges under various array element sizes.

[0028] After the iteration process terminates, the individual with the smallest multi-target phase perturbation injection function value is selected from the final population as the optimal phase perturbation vector. The phase offset of each element channel contained in the optimal phase perturbation vector is added to the corresponding phase value of the element channel in the initial amplitude-phase excitation data, while keeping the amplitude value in the initial amplitude-phase excitation data unchanged, forming the complex excitation coefficients of each element channel. The complex excitation coefficients of all element channels are then used to form the initial calibration weight matrix. The initial calibration weight matrix is ​​a single... A multidimensional complex vector, where each element corresponds to a pre-compensated weight for a single array element channel.

[0029] Example 3: In specific implementation, please refer to Figure 4 The process of enveloping the measured radiation pattern data and extracting the independent error components of the main lobe and side lobes includes three steps: signal transformation, interval division, and frequency domain analysis.

[0030] In practice, the method for obtaining the complex analytic envelope by performing a Hilbert transform on the measured radiation pattern data is as follows: the measured radiation pattern data is represented as a sequence of real numbers, where each element of the sequence corresponds to the radiation pattern amplitude value at an angle sampling point. The angle sampling points of the real number sequence cover the pitch angle range from -90 degrees to +90 degrees, with an angle sampling interval of 0.1 degrees. The measured radiation pattern data sequence is defined as follows: ,in For the angle sampling point index, , This represents the total number of angle sampling points. The calculation method for performing the Hilbert transform is as follows: first, perform... Perform a discrete Fourier transform to obtain the frequency domain sequence; multiply the amplitude of the positive frequency component in the frequency domain sequence by two, and set the amplitudes of the zero frequency component and the negative frequency component to zero; then perform an inverse discrete Fourier transform on the processed frequency domain sequence to obtain a complex sequence. The real part of the complex sequence is the original measured radiation pattern data sequence. The imaginary part is the result of the Hilbert transform. Combining the real and imaginary parts yields the complex analytic envelope. ,in It is the imaginary unit.

[0031] In practical implementation, the method of dividing the complex analytical envelope into main lobe and side lobe regions according to the angular domain is as follows: Based on the zero-power width of the main lobe at the corresponding frequency point of the ideal beam pattern, the angular range of the main lobe region is determined. The half-power beamwidth of the ideal beam pattern is calculated, and multiplied by a coefficient of 2.5 to obtain the angular width of the main lobe region. The center of the main lobe region is the beam pointing angle. The angular sampling range outside the main lobe region is divided into side lobe regions. For each angular sampling point index... Determine whether the corresponding pitch angle value falls within the main lobe interval; if it does, then calculate the complex analytic envelope value corresponding to the angle sampling point. If the sampled value does not fall within the main lobe region, it is included in the main lobe envelope sequence; if it does not fall within the main lobe region, the complex analytical envelope value corresponding to the sampling point at that angle is used. It is incorporated into the sidelobe envelope sequence. The coefficient 2.5 is chosen because 2.5 times the half-power beamwidth can completely encompass the entire angular range of the main lobe from the peak to the first null, ensuring the energy integrity of the main lobe region.

[0032] In practice, the discrete Fourier transform (DFT) is performed on the main lobe and side lobe intervals respectively to extract the corresponding phase and amplitude error terms. The DFT is applied to the main lobe envelope sequence to obtain the main lobe spectrum sequence; the DFT is applied to the side lobe envelope sequence to obtain the side lobe spectrum sequence. The argument of each spectral component in the main lobe spectrum sequence is used as an element of the main lobe phase error term, and the magnitude of each spectral component is used as an element of the main lobe amplitude error term. Similarly, the argument of each spectral component in the side lobe spectrum sequence is used as an element of the side lobe phase error term, and the magnitude of each spectral component is used as an element of the side lobe amplitude error term. The main lobe phase and amplitude error terms constitute independent main lobe error components, and the side lobe phase and amplitude error terms constitute independent side lobe error components.

[0033] In practical implementation, the process of constructing a multi-frequency error characterization function based on independent error components includes two steps: frequency selection and error fusion. When selecting multiple discrete frequency points within the millimeter-wave operating frequency band, they are selected at equal intervals within the start and end frequency range of the millimeter-wave operating frequency band. A discrete frequency point, The value is five. Each discrete frequency point corresponds to a center frequency value, and the frequency interval between adjacent discrete frequency points is the operating frequency band bandwidth divided by four. The basis for choosing a value of five is that, based on the coverage of the low, middle and high ends of the working frequency band, five discrete frequency points can add an interpolation point between the low and middle ends and between the middle and high ends, so that the error of the five frequency points can represent the error change trend of the approximate whole frequency band.

[0034] In practical implementation, for each discrete frequency point, the weighted fusion method for the phase error term of the main lobe interval and the amplitude error term of the side lobe interval is as follows: For the th A discrete frequency point, The measured radiation pattern data obtained at the corresponding frequency point is used to obtain the main lobe phase error term vector by following the envelope decomposition and error extraction steps described above. and sidelobe amplitude error term vector Define the fusion vector. fusion vector The Each component The calculation formula is: in, Indicates the first The main lobe phase error term vector corresponding to each discrete frequency point The first in One element, in radians; Indicates the first The sidelobe amplitude error term vector corresponding to each discrete frequency point The first in Each element is scaled linearly. The main lobe error weighting coefficient, with a value range of [value missing]. to ; The sidelobe error weighting coefficient has a range of values. to , and The value satisfies ; These are the element indices of the error term vector. The range of values ​​is from The total number of elements in the corresponding error term vector.

[0035] Main lobe error weighting coefficient The setting method is as follows: when the difference between the main lobe gain of the measured beam pattern and the main lobe gain of the ideal beam pattern is greater than one decibel, then... Set as When the difference between the sidelobe level of the measured beam pattern and the sidelobe level of the ideal beam pattern is greater than two dB, Set as In other cases, Set as Sidelobe error weighting coefficient Depend on Calculated.

[0036] In practical implementation, the weighted fusion results of all discrete frequency points are combined into a multi-dimensional error vector. The way to construct the multi-frequency error representation function is as follows: the fusion vector corresponding to each discrete frequency point is... According to frequency point index The elements are concatenated sequentially to form a total multidimensional error vector. ,Right now The multi-frequency error characterization function is defined as the multi-dimensional error vector. The Euclidean norm, the value of the multi-frequency error characterization function, is used to measure the overall error level of the current frequency-varying calibration weight sequence across all discrete frequency points.

[0037] Example 4: In specific implementation, please refer to Figure 5 Based on the multi-frequency error representation function, the process of correcting the initial calibration weight matrix and generating the frequency-varying calibration weight sequence by adopting the gradient descent update strategy includes four steps: gradient calculation, matrix update, convergence determination and sequence generation.

[0038] In practical implementation, the partial derivative of the multi-frequency error characterization function with respect to each element in the initial calibration weight matrix is ​​calculated as follows: the initial calibration weight matrix is ​​represented as a two-dimensional matrix. Two-dimensional matrix The number of rows is the total number of array elements. The number of columns is the total number of discrete frequency points. Two-dimensional matrix The Middle Line number Column elements Indicates the first Each array element channel in the first The initial calibration weights at discrete frequency points are complex numbers containing amplitude and phase components. The multi-frequency error characterization function is represented as a two-dimensional matrix. Real-valued function of the independent variable Its function value is determined by the aforementioned multidimensional error vector. The Euclidean norm is given.

[0039] The partial derivatives are calculated using the finite difference method. For a two-dimensional matrix... The Middle Line number Column elements Calculate the real and imaginary partial derivatives separately. When calculating the real partial derivatives, keep all other elements of the two-dimensional matrix unchanged, and only modify the imaginary elements. Add a small perturbation to the real part , Values Calculate the multi-frequency error characterization function value after perturbation. Then, keeping the other elements unchanged, change the element... The real part reduces the amount of small disturbances. Calculate the multi-frequency error characterization function value after perturbation. The real partial derivative is The imaginary partial derivative is calculated in the same way as the real partial derivative, except that a perturbation is applied to the element. The imaginary part is obtained by finding the partial derivative of the imaginary part. Small perturbation amount Values The basis for this is: for an operational environment that uses double-precision floating-point numbers to represent complex number weights, It is much larger than the rounding error, but much smaller than the typical change in weights, thus balancing the numerical stability and accuracy of partial derivative calculations. The real and imaginary partial derivatives are combined into a single complex number, which is used as the element. The complex partial derivatives of .

[0040] In practical implementation, the method of constructing the gradient matrix using partial derivatives is as follows: The complex partial derivatives of all elements are arranged according to the two-dimensional matrix... Arranging rows and columns in the same positions forms the gradient matrix. Gradient matrix The Middle Line number Column elements That is, element The complex partial derivatives of .

[0041] In practice, the method of updating the initial calibration weight matrix along the negative gradient direction with a preset step size is as follows: The current two-dimensional matrix... Subtract the gradient matrix from each element Corresponding elements and preset step size The product of these two elements yields the updated two-dimensional matrix. The updated formula is: in, For updating the iteration round index, The initial value is This corresponds to the initial calibration weight matrix; Indicates the first Two-dimensional matrix after round of iteration The Middle Line number Column elements; Indicates the first gradient matrix during round iteration The Middle Line number The complex partial derivatives of the column; The preset step size is set to a value of [value]. Preset step size Values The rationale is as follows: under the scale of the multi-frequency error characterization function, an excessively large step size will cause the iteration process to oscillate around the minimum value and fail to converge, while an excessively small step size will result in a slow convergence speed. After normalization calibration, the step size is adjusted by about five percent of the change in the main lobe phase error, which can ensure convergence while taking into account iterative efficiency.

[0042] In practice, the partial derivative calculation and gradient matrix update operations are repeatedly performed until the norm of the multi-frequency error representation function converges. This is achieved by calculating the updated two-dimensional matrix after each iteration. Corresponding multi-frequency error characterization function value And compared with the multi-frequency error characterization function value of the previous iteration Compare them. Define the convergence criterion as follows: The convergence threshold Values Convergence threshold Values The basis is: when the change in the value of the multi-frequency error characterization function is less than At this point, the corresponding change in the pattern gain is already less than the noise floor of the measurement system, and continuing the iteration has no practical significance for improving the calibration accuracy. When the convergence criterion is met, the iteration stops, and the current two-dimensional matrix is... As the converged weight matrix.

[0043] In practical implementation, when using the converged weight matrix as the frequency-varying calibration weight sequence, the method of splitting the converged weight matrix into sub-weight vectors corresponding to each discrete frequency point by row is as follows: The converged weight matrix is... OK A two-dimensional matrix with columns, where each column is treated as a sub-weight vector. All elements of the column constitute the first The sub-weight vectors corresponding to each discrete frequency point have a length of . The first sub-weight vector The element represents the first element. Each array element channel in the first The final calibration weights at each discrete frequency point.

[0044] In practical implementation, the method of arranging the sub-weight vectors into a frequency-varying calibration weight sequence according to frequency from low to high is as follows: Discrete frequency points are arranged in ascending order of their center frequency values, and correspondingly, the sub-weight vectors corresponding to the discrete frequency points are arranged in the same order. These are, in order, the first sub-weight vector, the second sub-weight vector, and so on, up to the [previous sequence]. The sub-weight vectors, arranged as described above, constitute the frequency-varying calibration weight sequence.

[0045] In practice, the process of acquiring measured radiation pattern data by using a pre-compensated antenna array to collect spatial radiation fields is as follows: A probe antenna is erected in a microwave anechoic chamber, aligning its phase center with the phase center of the antenna array under test. The antenna array is controlled to transmit a test sequence, which is a continuous wave signal with equal amplitude and phase, at a frequency that is one of the discrete frequency points to be measured. At each discrete frequency point, a turntable is controlled to rotate the antenna array at a constant angular velocity within the elevation angle range, and the probe antenna receives the radiated signal at each elevation angle position. The received radiated signal is sampled in the time domain, with the sampling rate set to ten times the signal frequency, and the sampling duration being the time it takes for the turntable to sweep across the entire elevation angle range, resulting in a time-domain sampling sequence. A Fourier transform is performed on the time-domain sampling sequence to extract the spectral components corresponding to the signal frequencies. The amplitude and phase of the spectral components are recorded as the complex radiation pattern values ​​at that elevation angle position. After traversing all elevation angle sampling points, the measured radiation pattern data for that discrete frequency point is obtained. Change the discrete frequency points and repeat the above process until all measured radiation pattern data for all discrete frequency points have been collected.

[0046] Example 5: In specific implementation, please refer to Figure 6 The process of mapping the frequency-varying calibration weight sequence to the phase shifters of each channel to complete beamforming calibration includes three steps: phase component extraction and conversion, lookup table storage, and beam scanning retrieval.

[0047] In practical implementation, the method for converting the phase component in each sub-weight vector into phase shifter control code values ​​is as follows: the frequency-varying calibration weight sequence is derived from... The system consists of several sub-weight vectors arranged in sequence, each sub-weight vector corresponding to a discrete frequency point, and each sub-weight vector contains... Each of the elements is a final calibration weight in complex form. For the element... The first discrete frequency point corresponding to the Sub-weight vector, extract the first The argument of each complex element in the sub-weight vector, where the unit of argument is radians, and the numerical range of argument is... The formula for converting the argument value to the phase shifter control code value is: in, For discrete frequency points, The value is ; This refers to the number of the array element channel. The value is ; Indicates the first Each array element channel in the first The phase components of the final calibration weights at discrete frequency points, in radians; The quantization bits of the phase shifter, The value is determined by the actual phase shifter hardware used; Representing binary The power of the power represents the total number of states that the phase shifter can output. Indicates the first Each array element channel in the first The phase shifter control code values ​​corresponding to each discrete frequency point It is an integer. The range of values ​​is to ; This represents the rounding function.

[0048] Phase shifter quantization bits The setting method is as follows: when the phase shifter uses a five-digit digital phase shifter, Values At this point, the phase shifter can output thirty-two phase states, with a phase interval of 11.25 degrees between adjacent states; when a six-bit digital phase shifter is used, Values At this time, the phase shifter can output sixty-four phase states, with a phase interval of 5.625 degrees between adjacent states.

[0049] In practical implementation, the phase shifter control code values ​​are stored in a lookup table according to the array element channel number and discrete frequency point correspondence as follows: a two-dimensional lookup table is established, which has... lines and Column. The first column of the two-dimensional lookup table. The row corresponds to the first Each array element channel, the first Column corresponds to the first The discrete frequency points. The second discrete frequency point in the two-dimensional lookup table. Line number The phase shifter control code value is written into the column's storage cell. The two-dimensional lookup table is stored in the non-volatile memory of the beam controller, which communicates with all beam controllers via the control bus. The phase shifters of each array element channel are connected together.

[0050] In practice, during beam scanning, the corresponding control code value from the lookup table is retrieved based on the operating frequency and written to each phase shifter as follows: The beam controller receives the beam pointing command and the operating frequency command, the operating frequency command containing the current operating frequency value. The beam controller compares the current operating frequency value with... For each discrete frequency point, the discrete frequency point with the smallest absolute value of its frequency difference from the current operating frequency value is selected as the matching discrete frequency point, and the column index corresponding to the matching discrete frequency point is determined. The beam controller reads the first beam from the two-dimensional lookup table. All of the columns The phase shifter control code values ​​are as follows: The beam controller transmits the beam through the control bus to the first... Phase shifter control code value Write to the The phase shifter of the first array element channel will... Phase shifter control code value Write to the The phase shifters for each array element channel are repeated, and so on, until all are... Each phase shifter control code value is written to the corresponding... The phase shifter of each array element channel. The phase shifter adjusts the phase of the RF signal according to the written control code value to complete the beamforming calibration at the current operating frequency.

[0051] For cases where the operating frequency is among the discrete frequency points covered by the frequency-varying calibration weight sequence, the beam controller adopts the nearest neighbor matching method, always selecting the sub-weight vector corresponding to the discrete frequency point with the smallest absolute value of the frequency difference. When there are two discrete frequency points with the same absolute value of the frequency difference as the current operating frequency value, the beam controller selects the discrete frequency point with the lower center frequency value as the matching discrete frequency point.

[0052] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A beamforming calibration method for millimeter-wave phased array antennas, characterized in that, Includes the following steps: Obtain the initial amplitude and phase excitation data of the antenna array elements; Based on the difference between the mismatched beam pattern and the ideal beam pattern, a multi-target phase perturbation injection function is constructed; The multi-objective phase perturbation injection function is solved through iterative optimization to generate an initial calibration weight matrix; Based on the initial calibration weight matrix, the phase distribution of the antenna array elements is pre-compensated element by element. The space radiation field is collected using a pre-compensated antenna array to obtain measured radiation pattern data; The measured radiation pattern data is subjected to envelope decomposition to extract the independent error components of the main lobe and side lobes. The specific steps include: Perform a Hilbert transform on the measured radiation pattern data to obtain the complex analytic envelope; The complex analytical envelope is divided into main lobe interval and side lobe interval according to the angular domain; Perform Discrete Fourier Transform on the main lobe interval and the side lobe interval respectively, and extract the corresponding phase error term and amplitude error term; The specific steps for constructing a multi-frequency error representation function based on the independent error components include: Select multiple discrete frequency points within the millimeter-wave operating frequency band; For each discrete frequency point, the phase error term of the main lobe interval and the amplitude error term of the side lobe interval are weighted and fused. The weighted fusion results of all discrete frequency points are combined into a multi-dimensional error vector, which constitutes the multi-frequency error representation function. Based on the multi-frequency error characterization function, the initial calibration weight matrix is ​​corrected by a gradient descent update strategy to generate a frequency-varying calibration weight sequence. The frequency-varying calibration weight sequence is mapped to the phase shifter of each channel to complete the beamforming calibration.

2. The millimeter-wave phased array antenna beamforming calibration method according to claim 1, characterized in that, The steps for obtaining the initial amplitude and phase excitation data of the antenna array elements specifically include: Acquire amplitude and phase response data for each element channel of the antenna array in an uncalibrated state; The amplitude and phase response data are normalized according to the array element number to generate a reference amplitude and phase vector.

3. The millimeter-wave phased array antenna beamforming calibration method according to claim 1, characterized in that, The step of constructing a multi-target phase perturbation injection function based on the difference between the mismatched beam pattern and the ideal beam pattern specifically includes: Select an ideal beam pattern at a specified scanning angle as a reference template; Calculate the gain deviation between the current mismatched beam pattern and the reference template in multiple azimuth sections; With the goal of minimizing the gain deviation and suppressing the sidelobe peak, the phase offset of the amplitude-phase excitation is used as the optimization variable to construct the multi-objective phase perturbation injection function.

4. The millimeter-wave phased array antenna beamforming calibration method according to claim 1, characterized in that, The step of iteratively optimizing the multi-objective phase perturbation injection function to generate the initial calibration weight matrix specifically includes: Set up a phase perturbation search space and initialize a set of random phase perturbation vectors; The differential evolution algorithm is used to perform global iterations in the phase perturbation search space to evaluate the pattern fit after each iteration. The phase perturbation vector corresponding to the optimal fit is superimposed with the initial amplitude and phase excitation data to form the initial calibration weight matrix.

5. The millimeter-wave phased array antenna beamforming calibration method according to claim 1, characterized in that, The step of modifying the initial calibration weight matrix and generating a frequency-varying calibration weight sequence based on the multi-frequency error characterization function using a gradient descent update strategy specifically includes: Calculate the partial derivative of the multi-frequency error characterization function with respect to each element in the initial calibration weight matrix; The gradient matrix is ​​constructed using the partial derivatives, and the initial calibration weight matrix is ​​updated along the negative gradient direction with a preset step size. Repeat the partial derivative calculation and gradient matrix update operations until the norm of the multi-frequency error characterization function converges; The converged weight matrix is ​​used as the frequency-varying calibration weight sequence.

6. The millimeter-wave phased array antenna beamforming calibration method according to claim 5, characterized in that, The step of using the converged weight matrix as the frequency-varying calibration weight sequence specifically includes: The converged weight matrix is ​​split into sub-weight vectors corresponding to each discrete frequency point by rows; The sub-weight vectors are arranged into the frequency-varying calibration weight sequence in order of increasing frequency.

7. The millimeter-wave phased array antenna beamforming calibration method according to claim 6, characterized in that, The step of mapping the frequency-varying calibration weight sequence to the phase shifters of each channel to complete the beamforming calibration specifically includes: The phase component in each of the sub-weight vectors is converted into a phase shifter control code value; The phase shifter control code values ​​are stored in a lookup table according to the array element channel number and the discrete frequency point; During beam scanning, the corresponding control code value in the lookup table is called according to the operating frequency and written to each phase shifter.

8. The millimeter-wave phased array antenna beamforming calibration method according to claim 7, characterized in that, The step of acquiring measured radiation pattern data by using a pre-compensated antenna array to collect spatial radiation field specifically includes: Set up the probe antenna in the microwave anechoic chamber and align it with the phase center of the antenna array under test; The control antenna array transmits test sequences, and the probe antenna is used to receive radiation signals at each scanning angle; The received radiation signal is sampled in the time domain and subjected to Fourier transform to obtain the measured radiation pattern data.

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