A method for improving genetic algorithm based on liquid crystal optical phased array thinning

Abstract

The application discloses a method for improving genetic algorithm based on liquid crystal optical phased array thinning, first constructs a physical model of the liquid crystal optical phased array, then sets optimization parameters and fitness functions of the genetic algorithm according to array characteristics, obtains a far-field directional diagram by using a spatial fast Fourier transform, carries out fitness function screening, encodes, crosses, mutates, genetically, decodes and updates the array population after the screening, and finally obtains final optimization results according to a stop iteration condition. The method is applied to the improved genetic algorithm of the liquid crystal optical phased array, realizes reduction of the number of control units of the phased array with the same aperture, under the condition of limitation of the total number of control units, the system volume, weight and complexity remain unchanged, and larger aperture of the liquid crystal optical phased array can be realized, which provides an efficient and easy-to-implement algorithm for grating lobe suppression of the liquid crystal optical phased array, reduction of the number of control units and increase of the aperture.

Description

Technical Field

[0001] This invention belongs to the field of optical phased array technology, specifically relating to a method for improving genetic algorithms based on the sparsity of liquid crystal optical phased arrays. Background Technology

[0002] In numerous applications such as space laser communication, lidar, and target tracking, optical phased arrays, represented by liquid crystal optical phased arrays (LC-OPA), effectively overcome many drawbacks of existing mechanical pointing systems: non-agile response, mechanical pointing inertia, large system size, low effective communication aperture, and high cost. LC-OPA offers advantages such as fast response, accurate pointing, small control system size, and low cost, making it widely applicable and promising. Among them, the liquid crystal optical phased array (LC-OPA) is a transmissive passive optical phased array, characterized by a large optical aperture and high optical power. For laser communication links, increasing the aperture of the optical antenna plays a decisive role in improving the antenna gain and communication margin. Therefore, methods for increasing the aperture of liquid crystal optical phased arrays are an important research topic.

[0003] Sparse array antenna technology is a technique that uses aperture synthesis by sparsely arranging subarrays in space to achieve the same number and distribution of phase centers as a full-array antenna with fewer transceiver elements, while avoiding grating lobes and high sidelobes. In the context of space laser communication applications, increasing the gain of the communication link requires increasing the aperture of the optical antenna, thus necessitating a greater number of control units. This leads to problems such as increased size and weight of the optical phased array system, and limitations on the number of control units. Furthermore, the physical characteristics of liquid crystal optical phased arrays are those of a transmissive passive optical phased array, fundamentally different from active T / R array antennas and silicon-based optical phased arrays, posing a challenge to increasing the aperture of the optical antenna. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention proposes a method based on an improved genetic algorithm for sparsification of liquid crystal optical phased arrays. By applying the improved genetic algorithm to liquid crystal optical phased arrays, the number of control units for phased arrays of the same aperture can be reduced. Therefore, under the condition of limiting the total number of control units, the system volume, weight, and complexity remain unchanged, and a larger aperture of liquid crystal optical phased arrays can be achieved.

[0005] The technical solution adopted in this invention is: a method for improving a genetic algorithm based on the sparsity of a liquid crystal optical phased array, the specific steps of which are as follows:

[0006] S1. Construct a physical model of a liquid crystal optical phased array;

[0007] According to the superposition theorem, the total field strength at any point in the far field is the sum of the radiated field strengths of all array elements at that point. Based on the near-field phase distribution, a physical model of a uniformly distributed liquid crystal optical phased array is constructed. A far-field model of the uniformly distributed array is then established, where E(θ) represents the far-field intensity, expressed as follows:

[0008]

[0009] Where N represents the number of array elements, The far-field radiation pattern of a single antenna element is represented, where α represents the single antenna element factor, and a represents the element width, λ represents the wavelength; A i ,k,d,θ and θ s These represent the light amplitude, wavenumber, element spacing, observation direction, and beam scanning angle emitted by the i-th element, respectively.

[0010] The spacing between array elements allows for the conditional appearance of grating lobes in the far field:

[0011] Where m, θ m These represent the element position index and the antenna array pointing direction of m elements, respectively. m = 0 corresponds to the main lobe, and m ≠ 0 corresponds to the direction of the main lobe at θ. s =θ m A grid lobe appears.

[0012] Based on the physical model of a uniformly distributed liquid crystal optical phased array and the controllable shape coefficients of the array elements, a near-field phase distribution model is constructed, resulting in a model for the far-field intensity distribution of a randomly sparse liquid crystal optical phased array, expressed as follows:

[0013]

[0014] Where N1 represents the number of array elements in the first-generation population array. a i d represents the width of the i-th element. m This represents the spacing between the m-th array elements.

[0015] If all array elements are set as a single individual from the first generation population, and a random number of elements at random positions in this individual's array are merged into a single element, then the total number of array elements is reduced, i.e., the array spacing d is randomly generated. m and the width a of this array element i .

[0016] S2. Based on step S1, set the optimization parameters and fitness function of the genetic algorithm according to the array characteristics, and use spatial fast Fourier transform to obtain the far-field radiation pattern and perform fitness function screening.

[0017] First, set the population size, genetic probability, crossover probability, mutation probability, iteration stopping condition, and fitness function, and then generate all individuals of the first generation population based on the population size.

[0018] The iteration stopping condition is the maximum number of iterations set; the fitness function expression is as follows:

[0019]

[0020] Where n represents the total number of optimized deflection angles, i represents the deflection angle number, and E slmax,uniform E represents the intensity of the grating lobe in a uniform array. slmax,non-uniform η represents the grating lobe intensity of the sparse array. uniform η represents the deflection efficiency of a uniform array. non-uniform This represents the deflection efficiency of a sparse array.

[0021] Then, the genetic algorithm iterates, generates the near-field phase distribution based on the pointing angle and sets it to 2π, then obtains the far-field pattern through spatial fast Fourier transform (FFT), calculates the fitness function of the array population, sorts the fitness of all individuals cumulatively, generates the cumulative probability as the screening step in the genetic algorithm, and passes on the individual with the first cumulative probability greater than the random number.

[0022] S3. Based on step S2, perform encoding, crossover, mutation, genetics, decoding and updating operations on the array population after the cumulative probability screening by the fitness function.

[0023] First, the array population selected by the fitness function is subjected to encoding, crossover, and mutation operations, as follows:

[0024] Encoding: Generate a step-pattern phase distribution from the near-field phase distribution and encode it in binary.

[0025] Among them, the array element with a phase step increase is coded as '1', and the array element with the same phase as the previous array element is coded as '0'.

[0026] Crossover: Two individuals in a population are randomly selected, and their crossover positions are randomly generated. The binary codes of the crossover positions are exchanged with a crossover probability.

[0027] Mutation: A random individual selects a random position to reverse the binary code.

[0028] Then, the array population, after encoding, crossover, and mutation operations, is decoded and updated, as follows:

[0029] Decoding: The binary code of the population is re-converted to generate a ladder phase array. The array element encoded as "1" is the array element whose near-field phase increases after decoding, and the array element encoded as "0" is the array element whose near-field phase remains unchanged after decoding.

[0030] Update the array population: Combine the population regenerated after decoding with the population filtered by the cumulative probability of the fitness function in step S2 to generate the next generation population.

[0031] S4. Based on step S3, determine whether the number of iterations meets the maximum number of iterations. If not, repeat steps S2 to S3 until the condition is met and the iteration stops. Select the individuals with the highest fitness from the final population as the final output of the algorithm. The sparsed array is the final optimization result.

[0032] The beneficial effects of this invention are as follows: The method of this invention first constructs a physical model of a liquid crystal optical phased array, then sets the optimization parameters and fitness function of a genetic algorithm based on the array characteristics, and obtains the far-field radiation pattern using spatial fast Fourier transform. Fitness function screening is then performed, followed by encoding, crossover, mutation, genetics, decoding, and updating of the array population after fitness function screening. Finally, the final optimization result is obtained based on the stopping iteration condition. This invention, through an improved genetic algorithm applied to liquid crystal optical phased arrays, reduces the number of control units for phased arrays of the same aperture. Under the condition of a limited total number of control units, the system volume, weight, and complexity remain unchanged, enabling larger aperture liquid crystal optical phased arrays. This provides a highly efficient and easily implemented algorithm for grating lobe suppression, reducing the number of control units, and increasing the aperture of liquid crystal optical phased arrays. Attached Figure Description

[0033] Figure 1 This is a flowchart of a method for improving a genetic algorithm based on the sparsity of a liquid crystal optical phased array according to the present invention.

[0034] Figure 2 This is a near-field phase distribution diagram of the liquid crystal optical phased array in an embodiment of the present invention.

[0035] Figure 3 This is a sparse array phase encoding diagram in an embodiment of the present invention.

[0036] Figure 4 This is a graph showing the change of fitness function with the number of iterations for different iteration parameters in an embodiment of the present invention.

[0037] Figure 5 This is a distribution diagram showing the relationship between the number of iterations and the sparsity rate in an embodiment of the present invention. Detailed Implementation

[0038] The method of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0039] like Figure 1 The flowchart of a method for improving a genetic algorithm based on the sparsity of a liquid crystal optical phased array, as shown in the figure, includes the following specific steps:

[0040] S1. Construct a physical model of a liquid crystal optical phased array;

[0041] According to the superposition theorem, the total field strength at any point in the far field is the sum of the radiated field strengths of all array elements at that point. Based on the near-field phase distribution, a physical model of a uniformly distributed liquid crystal optical phased array is constructed. A far-field model of the uniformly distributed array is then established, where E(θ) represents the far-field intensity, expressed as follows:

[0042]

[0043] Where N = 720 represents the number of array elements. The far-field radiation pattern (shape factor) of a single antenna element is represented by α, where α represents the single antenna element factor. a = 12 μm represents the element width, and λ = 1550 nm represents the wavelength. i ,k,d,θ and θ s These represent the light amplitude, wavenumber, element spacing, observation direction, and beam scanning angle emitted by the i-th element, respectively. In this embodiment, the light amplitude A i =1, wavenumber k = 2π / λ, element spacing d = 2μm, beam scanning angle θ s =0.7°.

[0044] Single element shape coefficient Algorithm optimization can disrupt the conditions for grating lobe formation, reduce the number of control units, and thus increase the array aperture. This depends on the physical structure characteristics of the liquid crystal optical phased array. Due to process size limitations, the spacing between array elements allows for the formation of grating lobes in the far field.

[0045] Where λ, m, θ m These represent the wavelength, element position number, and antenna array pointing direction of m elements, respectively. m = 0 corresponds to the main lobe, and m ≠ 0 corresponds to the direction of the main lobe at θ. s =θ m A grid lobe appears.

[0046] Based on the physical model of a uniformly distributed liquid crystal optical phased array and the controllable shape coefficients of the array elements, a near-field phase distribution model is constructed, resulting in a model for the far-field intensity distribution of a randomly sparse liquid crystal optical phased array, expressed as follows:

[0047]

[0048] Where N1 represents the number of array elements in the first-generation population array. a i d represents the width of the i-th element. m This represents the spacing between the m-th array elements.

[0049] If all array elements are set as a single individual from the first generation population, and a random number of elements at random positions in this individual's array are merged into a single element, then the total number of array elements is reduced, i.e., the array spacing d is randomly generated. m and the width a of this array element i .

[0050] S2. Based on step S1, set the optimization parameters and fitness function of the genetic algorithm according to the array characteristics, and use spatial fast Fourier transform to obtain the far-field radiation pattern and perform fitness function screening.

[0051] In this embodiment, the population size pop = 200, the genetic probability SelectRate = 0.5, the crossover probability CrossoverRate = 0.5, the mutation probability VariationRate = 1 / 720, the iteration stopping condition, and the fitness function are first set, and all individuals of the first generation population are generated according to the population size.

[0052] The iteration stopping condition is the fulfillment of the set maximum number of iterations, which in this embodiment is InterationTimes = 4000; the fitness function expression is as follows:

[0053]

[0054] Where n represents the total number of optimized deflection angles, i represents the deflection angle number, and E slmax,uniform E represents the intensity of the grating lobe in a uniform array. slmax,non-uniform η represents the grating lobe intensity of the sparse array. uniform η represents the deflection efficiency of a uniform array. non-uniform This represents the deflection efficiency of a sparse array.

[0055] Then the genetic algorithm iterates, such as Figure 2 As shown, a near-field phase distribution is generated based on the pointing angle and then set to 2π. The far-field pattern is obtained by spatial fast Fourier transform (FFT). The fitness function of the array population is calculated, and the fitness of all individuals is cumulatively sorted to generate a cumulative probability as a screening step in the genetic algorithm. The individual with the first cumulative probability greater than the random number is inherited, and then individuals with high fitness are accepted with a higher probability.

[0056] S3. Based on step S2, perform encoding, crossover, mutation, genetics, decoding and updating operations on the array population after the cumulative probability screening by the fitness function.

[0057] First, the array population selected by the fitness function is subjected to encoding, crossover, and mutation operations, as follows:

[0058] Encoding: such as Figure 3 As shown, a step-pattern phase distribution is generated from the near-field phase distribution and then encoded in binary.

[0059] Among them, the array element with a phase step increase is coded as '1', and the array element with the same phase as the previous array element is coded as '0'.

[0060] Crossover: Two individuals in a population are randomly selected, and their crossover positions are randomly generated. The binary codes of the crossover positions are exchanged with a crossover probability.

[0061] Mutation: A random individual selects a random position to reverse the binary code.

[0062] Then, the array population, after encoding, crossover, and mutation operations, is decoded and updated, as follows:

[0063] Decoding: The binary code of the population is re-converted to generate a ladder phase array. The array element encoded as "1" is the array element whose near-field phase increases after decoding, and the array element encoded as "0" is the array element whose near-field phase remains unchanged after decoding.

[0064] Update the array population: Combine the population regenerated after decoding with the population filtered by the cumulative probability of the fitness function in step S2 to generate the next generation population, thereby maintaining the stability of the population size.

[0065] S4. Based on step S3, determine whether the number of iterations meets the maximum number of iterations. If not, repeat steps S2 to S3 until the condition is met and the iteration stops. Select the individuals with the highest fitness from the final population as the final output of the algorithm. The sparsed array is the final optimization result.

[0066] In this embodiment, the method of the present invention is simulated using MATLAB to obtain the distribution of the relationship between the number of iterations and the fitness function, and the distribution of the relationship between the number of iterations and the sparsity rate.

[0067] The array phase calculation step is 2.8*10. -2 For μm, when the beam scanning angle is 0.5° to 0.8°, the distribution of the relationship between the number of iterations and the fitness function is as follows: Figure 4 As shown, the distribution of the relationship between the number of iterations and the sparsity rate is as follows: Figure 5As shown, MATLAB simulations were used to generate distribution graphs showing the relationship between the number of iterations and the fitness function, and the relationship between the number of iterations and the sparsity rate, to verify the feasibility of the method of the present invention.

[0068] In this embodiment, the settings of parameters such as population size, genetic probability, crossover probability, and mutation probability affect the number of iterations in the genetic algorithm. By changing these parameters and comparing the results, it can be seen that the algorithm can ultimately obtain the desired fitness function under several different conditions. According to... Figure 4 The fitness function shown and as Figure 5 The array sparsity shown can be used to obtain the required sparsity and corresponding fitness of a liquid crystal optical phased array.

[0069] In summary, the method of this invention reduces the number of control units for phased arrays of the same aperture by applying an improved genetic algorithm to liquid crystal optical phased arrays. Under the condition of limiting the total number of control units, the system volume, weight, and complexity remain unchanged, and a larger aperture of liquid crystal optical phased arrays can be achieved. This provides a highly efficient and easy-to-implement algorithm for grating lobe suppression, reducing the number of control units, and increasing the aperture of liquid crystal optical phased arrays.

[0070] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A method for improving a genetic algorithm based on the sparsity of a liquid crystal optical phased array, the specific steps of which are as follows: S1. Construct a physical model of a liquid crystal optical phased array; According to the superposition theorem, the total field strength at any point in the far field is the sum of the radiated field strengths of all array elements at that point. Based on the near-field phase distribution, a physical model of a uniformly distributed liquid crystal optical phased array is constructed. A far-field model of the uniformly distributed array is then established, where E(θ) represents the far-field intensity, expressed as follows: in, N represents the number of array elements. The far-field radiation pattern of a single antenna element is represented, where α represents the single-antenna element factor, and a represents the element width, λ represents the wavelength; A i ,k,d,θ and θ s These represent the light amplitude, wavenumber, element spacing, observation direction, and beam scanning angle emitted by the i-th element, respectively. The spacing between array elements allows for the conditional appearance of grating lobes in the far field: Where m, θ m These represent the element position index and the antenna array pointing direction of m elements, respectively. m = 0 corresponds to the main lobe, and m ≠ 0 corresponds to the direction of the main lobe at θ. s =θ m A grid lobe appears; Based on the physical model of a uniformly distributed liquid crystal optical phased array and the controllable shape coefficients of the array elements, a near-field phase distribution model is constructed, resulting in a model for the far-field intensity distribution of a randomly sparse liquid crystal optical phased array, expressed as follows: Where N1 represents the number of array elements in the first-generation population array. a i d represents the width of the i-th element. m This represents the spacing between the m-th array elements; If all array elements are set as a single individual from the first generation population, and a random number of elements at random positions in this individual's array are merged into a single element, then the total number of array elements is reduced, i.e., the spacing d of the array is randomly generated. m and the width a of this array element i ; S2. Based on step S1, set the optimization parameters and fitness function of the genetic algorithm according to the array characteristics, and use spatial fast Fourier transform to obtain the far-field radiation pattern and perform fitness function screening. First, set the population size, genetic probability, crossover probability, mutation probability, iteration stopping condition, and fitness function, and then generate all individuals of the first generation population based on the population size; The iteration stopping condition is the maximum number of iterations set; the fitness function expression is as follows: Where n represents the total number of optimized deflection angles, i represents the deflection angle number, and E slmax,uniform E represents the intensity of the grating lobe in a uniform array. slmax,non-uniform η represents the grating lobe intensity of the sparse array. uniform η represents the deflection efficiency of a uniform array. non-uniform This indicates the deflection efficiency of a sparse array; Then, the genetic algorithm iterates, generates the near-field phase distribution based on the pointing angle and sets it to 2π, then obtains the far-field pattern through spatial fast Fourier transform (FFT), calculates the fitness function of the array population, sorts the fitness of all individuals cumulatively, generates the cumulative probability as the screening step in the genetic algorithm, and passes on the individual with the first cumulative probability greater than the random number. S3. Based on step S2, perform encoding, crossover, mutation, genetics, decoding and updating operations on the array population after the cumulative probability screening by the fitness function. First, the array population selected by the fitness function is subjected to encoding, crossover, and mutation operations, as follows: Encoding: Generate a step-pattern phase distribution from the near-field phase distribution and encode it in binary; Among them, the array element with a phase step increase is coded as '1', and the array element with the same phase as the previous array element is coded as '0'; Crossover: Two individuals within a population are randomly selected, and their crossover positions are randomly generated. The binary codes of the crossover positions are then exchanged with a crossover probability. Mutation: A random individual selects a random position to reverse the binary code; Then, the array population, after encoding, crossover, and mutation operations, is decoded and updated, as follows: Decoding: The binary code of the population is re-converted to generate a ladder phase array. The array element encoded as "1" is the array element whose near-field phase increases after decoding, and the array element encoded as "0" is the array element whose near-field phase remains unchanged after decoding. Update the array population: Combine the decoded and regenerated population with the population filtered by the cumulative probability of the fitness function in step S2 to generate the next generation population; S4. Based on step S3, determine whether the number of iterations meets the maximum number of iterations. If not, repeat steps S2 to S3 until the condition is met and the iteration stops. Select the individuals with the highest fitness from the final population as the final output of the algorithm. The sparsed array is the final optimization result.

Images