Antenna feed amplitude and phase quantization method and system based on improved non-dominated genetic algorithm

Abstract

This invention discloses an antenna feed amplitude and phase quantization method and system based on an improved non-dominated genetic algorithm, belonging to the field of phased array antenna technology. The method first establishes a far-field radiation pattern calculation model of the phased array, and then uses an improved non-dominated genetic algorithm to optimize the continuous phase and continuous amplitude of the feed in two stages: the first stage aims to minimize beam pointing error to obtain the optimal phase quantization operation; the second stage, based on the phase optimization result, aims to minimize the maximum sidelobe level of the beam to obtain the optimal amplitude quantization operation; finally, control signals are generated to directly drive the digital phase shifter and attenuator. This invention systematically controls the amplitude and phase quantization error by introducing a random quantization interval threshold and error covariance matching technology. Combined with elite preservation and adaptive genetic operations, it effectively coordinates beam pointing accuracy and sidelobe suppression performance, significantly improving the overall electrical performance of the antenna under the influence of quantization error.

Description

Technical Field

[0001] This invention relates to the field of phased array antenna technology, and in particular to an antenna feed amplitude and phase quantization method and system based on an improved non-dominated genetic algorithm. Background Technology

[0002] In a phased array system, phase shifters and attenuators control the phase and amplitude of each signal unit, respectively, thereby achieving precise beam direction control. Digital phase shifters and attenuators are widely used due to their simple structure and high reliability. However, the discrete nature of digital devices leads to errors in amplitude and phase adjustment, causing problems such as beam pointing deviation, reduced signal gain, and enhanced sidelobe interference. Currently, compensation methods for digital amplitude and phase quantization errors mainly include: deterministic rounding methods, such as rounding to the nearest integer, which are simple but introduce systematic errors; and traditional random amplitude and phase quantization methods, which randomly determine "carry" or "truncate" during quantization through a preset probability distribution. This can break the periodicity of errors statistically, but since each quantization decision is probabilistic, it cannot guarantee that the optimal quantization result can be obtained for a specific beam pointing requirement.

[0003] For a combination of a q-bit digital attenuator and a p-bit digital phase shifter, the minimum amplitude attenuation of its output is... ( (This represents the maximum attenuation of the attenuator) and the minimum phase shift. This means that when given an ideal antenna excitation with continuous amplitude and phase, the amplitude and phase of the excitation need to be quantized and rounded, and then attenuated by the minimum amplitude. and minimum phase shift The amplitude attenuation and phase shift of the output excitation are expressed in integer multiples. When quantizing and rounding the continuous ideal amplitude and phase excitation, the traditional rounding method introduces significant quantization errors, resulting in higher beam pointing errors and increased sidelobe levels.

[0004] To reduce the impact of feed amplitude and phase quantization errors on antenna electrical performance, more rational decisions need to be made regarding the quantization operation of feed amplitude and phase. For example, in the paper "SLL Degradation due to Quantized Phase Control in Moderate Phased Arrays," Kochar and Vinoy proposed an algorithm based on an ordered binary decision graph to compensate for the degradation of the highest sidelobe level caused by phase quantization in analog phased arrays. In the paper "Sidelobe-reduction techniques for phased arrays using digital phase shifters," Goto proposed a systematic phase adjustment method based on the minimum mean square pattern error criterion, which achieves peak sidelobe suppression of over 9dB under specific beam pointing in a non-reciprocal phased array using 4 phase shifters by optimizing the phase of specific array elements in a single step. In the paper "Two-Dimensional Quantization Method for Phased-Array Scanning," Chris proposed a fixed quantization operation table method based on the two-dimensional array phase quantization error distribution, which shows superior performance in terms of sidelobe suppression and pointing accuracy.

[0005] As can be seen from the above schemes, a series of quantization methods for antenna feed amplitude and phase have been proposed to reduce the negative impact of quantization errors on antenna electrical performance. However, considering the current state of research, there are still significant shortcomings: Most methods focus only on single quantization errors, such as amplitude or phase, failing to comprehensively consider the combined impact of the coupling effect of amplitude and phase quantization errors on antenna performance. Furthermore, existing methods often optimize single performance indicators such as beam pointing or sidelobe level, lacking a coordinated optimization strategy for the overall electrical performance of the array antenna. Particularly in Pareto-dominated multi-objective optimization methods, decision-makers still need to select the final solution, and the algorithm complexity is high, hindering real-time engineering applications. Meanwhile, previous stochastic quantization or single-objective optimization methods often cannot effectively control both antenna pointing accuracy and sidelobe level simultaneously.

[0006] The amplitude-phase quantization method used in this application introduces an improved non-dominated sorting genetic algorithm at the algorithmic level, which can find high-performance amplitude-phase quantization combinations in a complex solution space, ensuring from the algorithmic basis that the found solution approximates Pareto optimality. At the strategy level, a phased collaborative optimization framework is adopted, decomposing the high-dimensional coupled problem into two relatively independent low-dimensional problems, significantly reducing optimization complexity and computation time. In the phase stage, the genetic algorithm ensures that the solution with the minimum pointing error is found; in the amplitude stage, the solution with the minimum sidelobes is found based on this "optimal phase". This ensures that the final output is the globally optimal solution under this optimization framework, rather than a random result. At the mechanism level, a random quantization interval threshold is introduced to narrow the search space. Summary of the Invention

[0007] To address the technical problems existing in the background art, this invention proposes an antenna feed amplitude and phase quantization method and system based on an improved non-dominated genetic algorithm.

[0008] The antenna feed amplitude and phase quantization method based on an improved non-dominated genetic algorithm proposed in this invention includes the following steps: S1. Obtain the array element structure parameters of the phased array antenna and the ideal amplitude and phase excitation of all array elements; S2. Using electromagnetic field theory models to process the array element structure parameters, a far-field radiation pattern calculation model for the phased array is obtained. S3. Obtain the preset parameters of the improved non-dominated genetic algorithm and the threshold of the random quantization interval; S4. An improved non-dominated genetic algorithm is used to process the continuous phase, far-field pattern calculation model, and random quantization interval threshold in ideal amplitude-phase excitation. The optimal phase quantization operation that minimizes beam pointing error is obtained through the first stage of optimization. S5. An improved non-dominated genetic algorithm is used to process the continuous amplitude, optimal phase quantization operation, far-field pattern calculation model and random quantization interval threshold in ideal amplitude and phase excitation. The optimal amplitude quantization operation that minimizes the maximum sidelobe level of the beam is obtained through the second stage optimization. S6. Based on the optimal phase quantization operation and the optimal amplitude quantization operation, generate a drive control signal for directly configuring the digital phase shifter and the digital attenuator, and output the drive control signal to the phased array antenna feeding system.

[0009] Preferably, the array element structural parameters include the array element coordinate vector, the operating frequency of the phased array, and the array element radiation pattern function; the far-field radiation pattern calculation model is specifically as follows: ; in, Indicates the far-field azimuth angle; Indicates the far-field pitch angle; Indicates the number of phased array elements; express Amplitude excitation of the array elements; express Phase excitation of the array elements; express Unit vector in the direction; For free space wavenumber; The imaginary unit; Far-field observation point Radiated electric field in the direction; The antenna array element position vector; for Array element orientation pattern in the direction.

[0010] Preferably, step S4 specifically includes: S41. Generate an initial population consisting of multiple phase quantization operation individuals based on the ideal continuous phase and the phase random quantization interval threshold. S42. Substitute each phase quantization operation individual in the initial population into the far-field pattern calculation model, calculate the corresponding beam pointing error, and use the beam pointing error as the first body fitness value. S43. Based on the fitness value of the first individual, the first parent individual is selected from the current phase population using a sorting-based roulette wheel selection mechanism. S44. Perform single-point crossover and random site mutation operations on the first parent individual to generate the first offspring individual; S45. Adopt the elite retention strategy and directly retain the first offspring with the best fitness in the current phase population to the next phase population. S46. Iteratively execute steps S42 to S45 until the preset first maximum evolutionary generation or the first body fitness value satisfies the preset fitness first threshold. S47. Select the first individual with the best body fitness value from the final phase population, and take the phase quantization operation represented by the best individual as the optimal phase quantization operation.

[0011] Preferably, step S5 specifically includes: S51. Generate an initial amplitude population based on the ideal continuous amplitude and the amplitude random quantization interval threshold, wherein the initial amplitude population contains multiple amplitude quantization operation individuals; S52. Combine the current amplitude quantization operation individual with the optimal phase quantization operation to form an amplitude-phase quantization scheme, and substitute it into the far-field radiation pattern calculation model to calculate the corresponding maximum sidelobe level value of the beam. S53. Record the current amplitude quantization operation individual and its corresponding maximum sidelobe level value to the amplitude optimization result set; S54. Using a sorting-based roulette wheel selection mechanism, the second parent individual is selected from the current amplitude population based on the maximum sidelobe level value of the beam. S55. Perform single-point crossover and random site mutation operations on the second parent individual to generate the second offspring individual; S56. The population is updated using an elite preservation strategy, and steps S52 to S55 are repeated until the preset second maximum number of generations is reached. S57. In the set of all recorded amplitude optimization results, determine whether there is an amplitude quantization operation where the maximum sidelobe level of the beam is less than or equal to the preset ideal sidelobe level threshold; if so, record it as the optimal amplitude quantization operation; if not, select the amplitude quantization operation corresponding to the minimum maximum sidelobe level of the beam as the optimal amplitude quantization operation.

[0012] Preferably, the elite retention strategy includes: Identify the elite individuals with the best fitness values ​​from the current population; The elite individuals will be directly preserved to the next generation of the population; New individuals generated through genetic manipulation are used to fill the remaining positions in the next generation population.

[0013] Preferably, the random quantization interval threshold is determined by error covariance matching technology to ensure that the mathematical expectation of the quantization error is zero.

[0014] Preferably, the generation of drive control signals for directly configuring the digital phase shifter and the digital attenuator specifically includes: The optimal phase quantization operation is converted into a corresponding phase control word, wherein the phase control word is an integer multiple of the minimum phase shift of the digital phase shifter; The optimal amplitude quantization operation is converted into a corresponding amplitude control word, wherein the amplitude control word is an integer multiple of the minimum attenuation of the digital attenuator; The phase control word and amplitude control word are combined to form a drive control signal, and the drive control signal is output to the phased array antenna feeding system to configure the digital phase shifter and digital attenuator of each array element.

[0015] The antenna feed amplitude and phase quantization system based on an improved non-dominated genetic algorithm proposed in this invention includes: The data acquisition module is used to acquire the array element structure parameters of the phased array antenna and the ideal amplitude and phase excitation of all array elements; The model building module is used to process the array element structure parameters using electromagnetic field theory models to obtain the far-field radiation pattern calculation model of the phased array. The data acquisition module is also used to acquire preset parameters of the improved non-dominated genetic algorithm and the threshold of the random quantization interval; The first optimization module is used to process the continuous phase, far-field pattern calculation model and random quantization interval threshold in ideal amplitude-phase excitation using an improved non-dominated genetic algorithm. The optimal phase quantization operation that minimizes beam pointing error is obtained through the first stage of optimization. The second optimization module is used to process the continuous amplitude, optimal phase quantization operation, far-field pattern calculation model and random quantization interval threshold in ideal amplitude and phase excitation using an improved non-dominated genetic algorithm. The second-stage optimization obtains the optimal amplitude quantization operation that minimizes the maximum sidelobe level of the beam. The signal generation module is used to generate drive control signals for directly configuring the digital phase shifter and the digital attenuator based on the optimal phase quantization operation and the optimal amplitude quantization operation, and output the drive control signals to the phased array antenna feeding system.

[0016] The proposed antenna feed amplitude and phase quantization method and system based on an improved non-dominated genetic algorithm achieves a synergistic improvement in beam pointing accuracy and sidelobe suppression capability by constructing a phased collaborative optimization framework and introducing a random quantization interval threshold mechanism. This effectively overcomes the performance degradation problem caused by amplitude and phase error coupling in traditional quantization methods. The improved genetic algorithm significantly enhances the convergence speed and stability in large-scale array optimization through elite retention and adaptive selection strategies. At the same time, the systematic design with zero expected error suppresses the propagation of quantization error at its source. The final generated amplitude and phase control signal is compatible with various hardware configurations, forming a complete technical chain from algorithm optimization to hardware driving, ensuring high-precision beam control while also possessing excellent engineering applicability. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating the process of the antenna feed amplitude and phase quantization method based on an improved non-dominated genetic algorithm proposed in this invention. Figure 2 This is a schematic diagram of the angle and vector relationship of an implementation method for antenna feed amplitude and phase quantization based on an improved non-dominated genetic algorithm proposed in this invention. Figure 3 This is a schematic diagram illustrating the workflow of one implementation of the antenna feed amplitude and phase quantization method based on an improved non-dominated genetic algorithm proposed in this invention. Figure 4 The phase shifter and attenuator combination 1 of the antenna feed amplitude and phase quantization method based on the improved non-dominated genetic algorithm proposed in this invention is configured as follows: Comparison of angle phase scan results; Figure 5 The phase shifter and attenuator combination 2 configuration is based on the antenna feed amplitude and phase quantization method based on the improved non-dominated genetic algorithm proposed in this invention. Comparison of angle phase scan results; Figure 6 The phase shifter and attenuator combination 3 configuration is based on the antenna feed amplitude and phase quantization method based on the improved non-dominated genetic algorithm proposed in this invention. Comparison of angle phase scan results; Figure 7 The phase shifter and attenuator combination configuration 4 is based on the antenna feed amplitude and phase quantization method proposed in this invention using an improved non-dominated genetic algorithm. Comparison of angle phase scan results; Figure 8 The phase shifter and attenuator combination 1 of the antenna feed amplitude and phase quantization method based on the improved non-dominated genetic algorithm proposed in this invention is configured as follows: Comparison of results from a single scan; Figure 9 The phase shifter and attenuator combination 2 configuration is based on the antenna feed amplitude and phase quantization method based on the improved non-dominated genetic algorithm proposed in this invention. Comparison of results from a single scan; Figure 10 The antenna feed amplitude and phase quantization method based on the improved non-dominated genetic algorithm and the combination of phase shifter and attenuator in configuration 3 proposed in this invention. Comparison of results from a single scan; Figure 11 The phase shifter and attenuator combination configuration 4 is based on the antenna feed amplitude and phase quantization method proposed in this invention using an improved non-dominated genetic algorithm. Comparison of results from a single scan; Figure 12 This is a schematic diagram of the system architecture of the antenna feeding amplitude and phase quantization system based on the improved non-dominated genetic algorithm proposed in this invention. Detailed Implementation

[0018] Reference Figure 1-11 The antenna feed amplitude and phase quantization method based on an improved non-dominated genetic algorithm proposed in this invention includes the following steps: S1. Obtain the array element structure parameters of the phased array antenna and the ideal amplitude and phase excitation of all array elements.

[0019] S2. The array element structure parameters are processed using electromagnetic field theory models to obtain the far-field radiation pattern calculation model of the phased array.

[0020] In this embodiment, the array element structure parameters include the array element coordinate vector, the operating frequency of the phased array, and the array element radiation pattern function; the far-field radiation pattern calculation model is as follows: ; in, Indicates the far-field azimuth angle; Indicates the far-field pitch angle; Indicates the number of phased array elements; express Amplitude excitation of the array elements; express Phase excitation of the array elements; express Unit vector in the direction; For free space wavenumber; The imaginary unit; Far-field observation point Radiated electric field in the direction; The antenna array element position vector; for Array element orientation pattern in the direction.

[0021] Specifically, the operating frequency of the phased array is determined by the array element arrangement of the phased array antenna. Determine the array element orientation pattern .

[0022] In this embodiment, while establishing the far-field radiation pattern calculation model of the phased array, an optimized model of the far-field radiation pattern calculation model of the phased array is also established. The optimization evaluation process of the optimized model includes: modeling the amplitude-phase quantization problem as a multi-objective optimization problem; the improved algorithm uses a heuristic random search method to decide the quantization operation by setting a threshold and random probability; its evaluation process depends on the radiation pattern function, which is used as an "evaluator" to "score" each randomly generated quantization scheme, and finally selects the scheme with the highest score. Specifically, before the optimization begins, the ideal continuous amplitude-phase excitation is substituted into the initial far-field radiation pattern function to obtain the ideal electrical performance benchmark without the influence of quantization error. After entering the model optimization stage, the algorithm randomly generates multiple candidate amplitude-phase discretization schemes based on the quantization error and the preset threshold. These candidate schemes are input into the basic calculation model one by one to calculate the radiation pattern corresponding to each scheme. Subsequently, the evaluation system compares the radiation pattern performance of all schemes, mainly the beam pointing accuracy and sidelobe level, and selects the set of amplitude-phase quantization schemes with the best overall performance, which is the optimal amplitude-phase quantization scheme.

[0023] S3. Obtain the preset parameters of the improved non-dominated genetic algorithm and the threshold of the random quantization interval.

[0024] In this embodiment, the random quantization interval threshold is determined by error covariance matching technology to ensure that the mathematical expectation of the quantization error is zero.

[0025] In this embodiment, the improved non-dominated genetic algorithm optimizes the traditional non-dominated genetic algorithm solution process by implementing a phased collaborative optimization strategy. This strategy decouples the amplitude and phase values, which are initially coupled. In the phase-priority optimization phase, minimizing the beam pointing error is the sole objective. Under a fixed ideal amplitude excitation, the improved non-dominated genetic algorithm searches through a large number of random phase quantization schemes to quickly identify the optimal phase quantization operation combination that makes the beam pointing closest to the ideal direction. In the amplitude collaborative optimization phase, based on the determined optimal phase scheme, the goal is to minimize the maximum sidelobe level. The algorithm continues to search for the optimal amplitude quantization scheme based on the optimal phase, ultimately selecting the optimal amplitude quantization operation combination that minimizes the sidelobe level. The phased strategy aims to avoid the local Pareto front that is easily trapped when optimizing multiple objectives simultaneously, making the algorithm's search path clearer and its convergence better.

[0026] In this embodiment, a random quantization interval threshold is introduced. The threshold is set based on a statistical error control method where the expected value of the quantization error is 0, rather than based on experience. Theoretically, when the threshold is set to 0.5, the random quantization process degenerates into rounding to the nearest integer; when the threshold is set to 0, it becomes completely random, leading to excessive error variance and poor convergence. To balance this, the threshold range is set between 0 and 0.5. This threshold constraint avoids the difficulty of traditional completely random methods in ensuring optimal compensation results in a single run.

[0027] S4. The improved non-dominated genetic algorithm (NSGA-Ⅲ) is used to process the continuous phase, far-field pattern calculation model and random quantization interval threshold in the ideal amplitude and phase excitation. The optimal phase quantization operation that minimizes the beam pointing error is obtained through the first stage optimization.

[0028] In this embodiment, step S4 specifically includes: S41. Generate an initial population consisting of multiple phase quantization operations individuals based on the ideal continuous phase and the threshold of the phase random quantization interval. S42. Substitute each phase quantization operation individual in the initial population into the far-field pattern calculation model, calculate the corresponding beam pointing error, and use the beam pointing error as the first body fitness value. S43. Based on the fitness value of the first individual, the first parent individual is selected from the current phase population using a sorting-based roulette wheel selection mechanism. S44. Perform single-point crossover and random site mutation operations on the first parent individual to generate the first offspring individual; S45. Adopt the elite retention strategy and directly retain the first offspring with the best fitness in the current phase population to the next phase population. S46. Iteratively execute steps S42 to S45 until the preset first maximum evolutionary generation or the first body fitness value satisfies the preset fitness first threshold. S47. Select the first individual with the best body fitness value from the final phase population, and take the phase quantization operation represented by the best individual as the optimal phase quantization operation.

[0029] S5. An improved non-dominated genetic algorithm is used to process the continuous amplitude, optimal phase quantization operation, far-field pattern calculation model, and random quantization interval threshold in ideal amplitude and phase excitation. The optimal amplitude quantization operation that minimizes the maximum sidelobe level of the beam is obtained through the second stage optimization.

[0030] In this embodiment, step S5 specifically includes: S51. Generate an initial amplitude population based on the ideal continuous amplitude and the threshold of the amplitude random quantization interval. The initial amplitude population contains multiple amplitude quantization operation individuals. S52. Combine the current amplitude quantization operation with the optimal phase quantization operation to form an amplitude-phase quantization scheme, and substitute it into the far-field pattern calculation model to calculate the corresponding maximum sidelobe level value of the beam. S53. Record the current amplitude quantization operation individual and its corresponding maximum sidelobe level value to the amplitude optimization result set; S54. A sorting-based roulette wheel selection mechanism is adopted to select the second parent individual from the current amplitude population based on the maximum sidelobe level of the beam. S55. Perform single-point crossover and random site mutation operations on the second parent individual to generate the second offspring individual; S56. The population is updated using an elite preservation strategy, and steps S52 to S55 are repeated until the preset second maximum number of generations is reached. S57. In the set of all recorded amplitude optimization results, determine whether there is an amplitude quantization operation where the maximum sidelobe level of the beam is less than or equal to the preset ideal sidelobe level threshold. If it exists, record it as the optimal amplitude quantization operation. If it does not exist, select the amplitude quantization operation corresponding to the minimum maximum sidelobe level of the beam as the optimal amplitude quantization operation.

[0031] In this embodiment, the elite retention strategy includes: Identify the elite individuals with the best fitness values ​​from the current population; The elite individuals are directly preserved to the next generation of the population; New individuals generated through genetic manipulation are used to fill the remaining positions in the next generation population.

[0032] S6. Based on the optimal phase quantization operation and the optimal amplitude quantization operation, generate drive control signals for directly configuring the digital phase shifter and the digital attenuator, and output the drive control signals to the phased array antenna feeding system.

[0033] In this embodiment, the generation of drive control signals for directly configuring the digital phase shifter and the digital attenuator specifically includes: The optimal phase quantization operation is converted into the corresponding phase control word, which is an integer multiple of the minimum phase shift of the digital phase shifter. The optimal amplitude quantization operation is converted into the corresponding amplitude control word, which is an integer multiple of the minimum attenuation of the digital attenuator. The phase control word and amplitude control word are combined to form a drive control signal, which is then output to the phased array antenna feeding system to configure the digital phase shifter and digital attenuator of each array element. Example 1

[0034] With one The object is a linear array of equal spacing, with the element spacing being... The antenna is a half-wavelength array, with ideal omnidirectional elements operating at 30 GHz. The excitation amplitude is determined by a Taylor weighted form of the ideal maximum sidelobe level -30 dB and the number of equal sidelobes being 5. Ignoring element mutual coupling, the radiation pattern function in the plane for this linear array is as follows: ; in, It is a radiated electric field; Indicates the far-field pitch angle; This indicates the number of phased array elements, ranging from 0 to 23, for a total of 24 elements; express Amplitude excitation of the array elements; express Phase excitation of the array elements; The imaginary unit; For free space wavenumber; Indicates the distance between two array elements; This represents the m-th array element.

[0035] In this embodiment, a multi-objective optimization model is established using the quantization operations of the feed amplitude and phase of all array elements as optimization variables. The objective function is to minimize the following three functions: in, These are the actual azimuth and elevation angles of the beam under the current quantization operation. These are the azimuth and elevation angles of the ideal beam pointing, respectively, and FSLL is the maximum sidelobe level under the current quantization operation; This represents the ideal sidelobe level. (H) represents the difference between the actual and ideal azimuth values. (H) represents the difference between the actual and ideal pitch angle. (H) and (H) Controls beam pointing accuracy. (H) Controls sidelobe level suppression.

[0036] In the phase optimization stage, the main optimization is... and In other words, the beam pointing error is calculated by generating different quantization schemes and substituting them into the radiation pattern model to calculate the actual beam pointing. The optimal quantization scheme is then optimized based on the determined optimal scheme. That is, the sidelobe level, in The scheme with the smallest sidelobe amplitude is selected based on fitness value.

[0037] In this embodiment, the process of constructing and evaluating the fitness function specifically includes: obtaining an optimized population matrix composed of candidate solutions, where each row of the matrix represents a candidate solution and each column corresponds to an amplitude-phase quantization parameter to be optimized. In the evaluation of the beam pattern, the number of sampling points for the far-field angle is set to 18001 to cover the scanning range from -90° to +90° and ensure calculation accuracy. The constructed fitness function is used to optimize the beamforming parameters of the array antenna; this function calculates a comprehensive fitness value by comprehensively evaluating two key performance indicators of the beam pattern: beam pointing error and maximum sidelobe level, which guides the algorithm to efficiently find the global optimum.

[0038] In this embodiment, the core parameters of the improved non-dominated genetic algorithm are configured as follows: the population size is set to 80, and the maximum number of generations is 100. In each generation, individuals are first sorted according to their fitness values, and a roulette wheel selection mechanism based on this sorting is used to retain the top 40 superior individuals as parents. Subsequently, a single-point crossover operation is performed on the parent individuals, with the crossover point randomly selected, and the randomly selected gene loci are flipped at a mutation rate of 0.05. To ensure the convergence of the algorithm and prevent the loss of superior genes, an elite retention strategy is adopted, directly retaining the individual with the best fitness in the current generation into the next generation without undergoing genetic operations.

[0039] In this embodiment, optimization is carried out in stages: first the phase is optimized, then the amplitude is optimized, and by setting a random interval threshold, the expected value of the quantization error is controlled to be zero.

[0040] Specifically, define a single array element. Amplitude and phase quantization operations ,when At that time, the amplitude is quantized by rounding off the tails. When quantizing, the amplitude is carried over, and the phase quantization rule is similar; for continuous phase signals... Perform random quantization to obtain the feed phase value and calculate Normalized phase quantization error ,make For the set phase random quantization interval threshold, when When, the current phase is rounded down; when At that time, based on probability , Randomly generate phase quantization trade-off; when At this time, the current phase is rounded up. This phase rounding ensures that, under the current phase random quantization rule, the expected value of the generated random phase quantization error is 0. Random quantization feed value The calculation formula is as follows: in, Indicates the random quantization feed value. This indicates the current continuous feed phase value. For the minimum phase shift, To normalize the phase quantization error, To set the interval quantization threshold, For random selection probability, , .

[0041] In this embodiment, as Figure 3 As shown, the first stage of phase optimization specifically includes: defining the length of the individual genes in the genetic algorithm based on the number of phase quantization operations to be optimized. For these operation bits, 0 (representing rounding down) or 1 (representing rounding up) are randomly generated according to their normalized quantization error values ​​to fill them, thereby generating the initial population. The optimization process then begins: based on the individual's fitness value (i.e., beam pointing error), a sorting-based roulette wheel selection mechanism is used to select parent individuals; subsequently, single-point crossover and random site mutation operations are performed to generate offspring; simultaneously, an elite retention strategy is used to directly retain the best individuals of the current generation to the next generation. This process iterates until the beam pointing error meets a preset threshold or reaches the maximum number of generations, ultimately outputting the optimal phase quantization operation.

[0042] In this embodiment, as Figure 3As shown, the second stage of amplitude optimization specifically includes: initializing the amplitude optimization loop and defining the individual gene length based on the number of amplitude quantization operations. Similarly, based on the probability distribution of amplitude quantization error, a sequence of 0s and 1s is randomly generated to initialize the population. In each generation, the current amplitude quantization operation individual is combined with the optimal phase quantization operation obtained in the first stage to form a complete amplitude-phase quantization scheme, which is then substituted into the pattern function calculation model. The maximum sidelobe level of the beam is calculated under the premise of minimizing beam pointing error, and recorded in the result set. The selection, crossover, mutation, and elite retention strategies of the genetic algorithm are similar to those in the phase optimization stage. This stage is repeated until the maximum number of generations is reached. Finally, from all recorded schemes, the amplitude quantization operation that minimizes the maximum sidelobe level of the beam is selected as the optimal amplitude quantization scheme, and the optimal amplitude quantization scheme is output. The aforementioned optimal phase quantization operation is combined with the optimal amplitude quantization operation to generate the final amplitude-phase quantization control signal that can directly drive the digital phase shifter and digital attenuator, and output to the phased array antenna feeding system.

[0043] Specifically, as shown in Table 1 below, different combinations of digital phase shifters and digital attenuators with varying bit depths are presented, including Combinations 1 to 4. To verify the optimization effect of the NSGA-Ⅲ amplitude-phase quantization method under different amplitude-phase quantization threshold settings, the quantization thresholds were set separately. Four sets of quantitative simulations were conducted under the given conditions. For phase quantization threshold, This indicates the amplitude quantization threshold. The random loop count for amplitude and phase quantization is set to 100 times each. The maximum number of iterations is adjusted based on different hardware combinations. The population size is 80, the crossover probability is 0.5, the probability of participating in mutation is 0.5, the mutation rate is 0.05, and the number of sampling points is 18001 based on the angle range [-90:90] with an angular resolution of 0.01. Table 2 below shows a comparison of pointing performance data for combinations 1-4 in Table 1 under different random amplitude and phase quantization methods. Table 3 below shows a comparison of sidelobe suppression performance data for combinations 1-4 in Table 1 under different random amplitude and phase quantization methods. Table 4 below shows a comparison of single-shot pointing performance data for combinations 1-4 in Table 1 under different random amplitude and phase quantization methods. Table 4 below shows a comparison of single-shot sidelobe suppression performance data for combinations 1-4 in Table 1 under different random amplitude and phase quantization methods.

[0044] Table 1. Combination of digital phase shifter and digital attenuator

[0045] Table 2 Comparison of pointing performance of improved random amplitude and phase quantization methods

[0046] Table 3 Comparison of Sidelobe Suppression Performance of Improved Random Amplitude and Phase Quantization Method

[0047] Table 4 Comparison of single-shot pointing performance of the improved random amplitude-phase quantization method

[0048] Table 5 Comparison of single-shot sidelobe suppression performance of the improved random amplitude-phase quantization method

[0049] In this embodiment, as Figures 8-11 As shown, the waveform curves corresponding to Tables 2-5 are reflected, from which it can be concluded that in Single-shot simulation experiments were conducted at different scanning angles to verify the single-shot optimization of the improved amplitude-phase quantization method. Compared with the nearest-round quantization method, the random amplitude-phase quantization method achieved a pointing accuracy improvement of 20.16%–63.01%, while suppressing sidelobe rise by 0.05dB–1.92dB. The improved random amplitude-phase quantization method achieved a pointing accuracy improvement of 27.58%–71.23%, while suppressing sidelobe rise by 0.43dB–2.52dB.

[0050] Reference Figure 1-12 The antenna feed amplitude and phase quantization system based on an improved non-dominated genetic algorithm proposed in this invention includes: The data acquisition module is used to acquire the array element structure parameters of the phased array antenna and the ideal amplitude and phase excitation of all array elements; The model building module is used to process the array element structure parameters using electromagnetic field theory models to obtain the far-field radiation pattern calculation model of the phased array. The data acquisition module is also used to acquire preset parameters of the improved non-dominated genetic algorithm and the threshold of the random quantization interval; The first optimization module is used to process the continuous phase, far-field pattern calculation model and random quantization interval threshold in ideal amplitude-phase excitation using an improved non-dominated genetic algorithm. The optimal phase quantization operation that minimizes beam pointing error is obtained through the first stage of optimization. The second optimization module is used to process the continuous amplitude, optimal phase quantization operation, far-field pattern calculation model and random quantization interval threshold in ideal amplitude and phase excitation using an improved non-dominated genetic algorithm. The second-stage optimization obtains the optimal amplitude quantization operation that minimizes the maximum sidelobe level of the beam. The signal generation module is used to generate drive control signals for directly configuring digital phase shifters and digital attenuators based on optimal phase quantization and optimal amplitude quantization operations, and outputs the drive control signals to the phased array antenna feeding system.

[0051] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. An antenna feed amplitude and phase quantization method based on an improved non-dominated genetic algorithm, characterized in that, Includes the following steps: S1. Obtain the array element structure parameters of the phased array antenna and the ideal amplitude and phase excitation of all array elements; S2. Using electromagnetic field theory models to process the array element structure parameters, a far-field radiation pattern calculation model for the phased array is obtained. S3. Obtain the preset parameters of the improved non-dominated genetic algorithm and the threshold of the random quantization interval; S4. An improved non-dominated genetic algorithm is used to process the continuous phase, far-field pattern calculation model, and random quantization interval threshold in ideal amplitude-phase excitation. The optimal phase quantization operation that minimizes beam pointing error is obtained through the first stage of optimization. S5. An improved non-dominated genetic algorithm is used to process the continuous amplitude, optimal phase quantization operation, far-field pattern calculation model and random quantization interval threshold in ideal amplitude and phase excitation. The optimal amplitude quantization operation that minimizes the maximum sidelobe level of the beam is obtained through the second stage optimization. S6. Based on the optimal phase quantization operation and the optimal amplitude quantization operation, generate a drive control signal for directly configuring the digital phase shifter and the digital attenuator, and output the drive control signal to the phased array antenna feeding system.

2. The antenna feed amplitude and phase quantization method based on the improved non-dominated genetic algorithm according to claim 1, characterized in that, The array element structural parameters include the array element coordinate vector, the operating frequency of the phased array, and the array element radiation pattern function; the far-field radiation pattern calculation model is specifically as follows: ； in, Indicates the far-field azimuth angle; Indicates the far-field pitch angle; Indicates the number of phased array elements; express Amplitude excitation of the array elements; express Phase excitation of the array elements; express Unit vector in the direction; For free space wavenumber; The imaginary unit; Far-field observation point Radiated electric field in the direction; The antenna array element position vector; for Array element orientation pattern in the direction.

3. The antenna feed amplitude and phase quantization method based on the improved non-dominated genetic algorithm according to claim 1, characterized in that, Step S4 specifically includes: S41. Based on the continuous phase in the ideal amplitude-phase excitation and the random quantization interval threshold in step S4, generate an initial population composed of multiple phase quantization operation individuals. S42. Substitute each phase quantization operation individual in the initial population into the far-field pattern calculation model, calculate the corresponding beam pointing error, and use the beam pointing error as the first body fitness value. S43. Based on the fitness value of the first individual, the first parent individual is selected from the current phase population using a sorting-based roulette wheel selection mechanism. S44. Perform single-point crossover and random site mutation operations on the first parent individual to generate the first offspring individual; S45. Adopt the elite retention strategy and directly retain the first offspring with the best fitness in the current phase population to the next phase population. S46. Iteratively execute steps S42 to S45 until the preset first maximum evolutionary generation or the first body fitness value satisfies the preset fitness first threshold. S47. Select the first individual with the best body fitness value from the final phase population, and take the phase quantization operation represented by the best individual as the optimal phase quantization operation.

4. The antenna feed amplitude and phase quantization method based on the improved non-dominated genetic algorithm according to claim 1, characterized in that, Step S5 specifically includes: S51. Based on the continuous amplitude in the ideal amplitude-phase excitation and the random quantization interval threshold of step S5, an initial amplitude population is generated, which contains multiple amplitude quantization operation individuals. S52. Combine the current amplitude quantization operation individual with the optimal phase quantization operation to form an amplitude-phase quantization scheme, and substitute it into the far-field radiation pattern calculation model to calculate the corresponding maximum sidelobe level value of the beam. S53. Record the current amplitude quantization operation individual and its corresponding maximum sidelobe level value to the amplitude optimization result set; S54. Using a sorting-based roulette wheel selection mechanism, the second parent individual is selected from the current amplitude population based on the maximum sidelobe level value of the beam. S55. Perform single-point crossover and random site mutation operations on the second parent individual to generate the second offspring individual; S56. The population is updated using an elite preservation strategy, and steps S52 to S55 are repeated until the preset second maximum number of generations is reached. S57. In the set of all recorded amplitude optimization results, determine whether there is an amplitude quantization operation where the maximum sidelobe level of the beam is less than or equal to the preset ideal sidelobe level threshold; if so, record it as the optimal amplitude quantization operation; if not, select the amplitude quantization operation corresponding to the minimum maximum sidelobe level of the beam as the optimal amplitude quantization operation.

5. The antenna feed amplitude and phase quantization method based on an improved non-dominated genetic algorithm according to claim 3 or 4, characterized in that, The elite retention strategy includes: Identify the elite individuals with the best fitness values ​​from the current population; The elite individuals will be directly preserved to the next generation of the population; New individuals generated through genetic manipulation are used to fill the remaining positions in the next generation population.

6. The antenna feed amplitude and phase quantization method based on the improved non-dominated genetic algorithm according to claim 1, characterized in that, The threshold for the random quantization interval is determined using error covariance matching technology to ensure that the mathematical expectation of the quantization error is zero.

7. The antenna feed amplitude and phase quantization method based on the improved non-dominated genetic algorithm according to claim 1, characterized in that, The generation of drive control signals for directly configuring the digital phase shifter and digital attenuator specifically includes: The optimal phase quantization operation is converted into a corresponding phase control word, wherein the phase control word is an integer multiple of the minimum phase shift of the digital phase shifter; The optimal amplitude quantization operation is converted into a corresponding amplitude control word, wherein the amplitude control word is an integer multiple of the minimum attenuation of the digital attenuator; The phase control word and amplitude control word are combined to form a drive control signal, and the drive control signal is output to the phased array antenna feeding system to configure the digital phase shifter and digital attenuator of each array element.

8. An antenna feed amplitude and phase quantization system based on an improved non-dominated genetic algorithm, characterized in that, include: The data acquisition module is used to acquire the array element structure parameters of the phased array antenna and the ideal amplitude and phase excitation of all array elements; The model building module is used to process the array element structure parameters using electromagnetic field theory models to obtain the far-field radiation pattern calculation model of the phased array. The data acquisition module is also used to acquire preset parameters of the improved non-dominated genetic algorithm and the threshold of the random quantization interval; The first optimization module is used to process the continuous phase, far-field pattern calculation model and random quantization interval threshold in ideal amplitude-phase excitation using an improved non-dominated genetic algorithm. The optimal phase quantization operation that minimizes beam pointing error is obtained through the first stage of optimization. The second optimization module is used to process the continuous amplitude, optimal phase quantization operation, far-field pattern calculation model and random quantization interval threshold in ideal amplitude and phase excitation using an improved non-dominated genetic algorithm. The second-stage optimization obtains the optimal amplitude quantization operation that minimizes the maximum sidelobe level of the beam. The signal generation module is used to generate drive control signals for directly configuring the digital phase shifter and the digital attenuator based on the optimal phase quantization operation and the optimal amplitude quantization operation, and output the drive control signals to the phased array antenna feeding system.

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