Method for improving genetic algorithm based on liquid crystal optical phased array rarefaction

Abstract

The invention discloses a method for improving a genetic algorithm based on liquid crystal optical phased array rarefaction, which comprises the following steps of: firstly, constructing a liquid crystal optical phased array physical model, then setting optimization parameters and fitness functions of the genetic algorithm according to array characteristics, obtaining a far-field directional diagram by utilizing space fast Fourier transform, and screening the fitness functions to obtain a far-field directional diagram; and performing coding, crossing, variation, inheritance, decoding and array population updating operation on the array population after the fitness function screening, and finally obtaining a final optimization result according to iteration stopping conditions. According to the method, through the improved genetic algorithm applied to the liquid crystal optical phased array, the number of control units of the phased array with the same aperture is reduced, under the condition that the total number of the control units is limited, the size, the weight and the complexity of a system are not changed, the larger aperture of the liquid crystal optical phased array can be achieved, and the method has a good application prospect for grating lobe suppression of the liquid crystal optical phased array. The number of control units is reduced, the aperture is increased, and an algorithm which is high in efficiency and easy to implement is provided.

Description

Technical Field

[0001] The invention belongs to the technical field of optical phased arrays, and in particular relates to a method for improving a genetic algorithm based on liquid crystal optical phased array sparseness. Background Art

[0002] In many application scenarios such as space laser communication, laser radar, target tracking, etc., optical phased arrays represented by liquid crystal optical phased arrays can effectively overcome many shortcomings of existing mechanical pointing: non-agile response, mechanical pointing inertia, large system size, low effective communication aperture, high cost, etc. Optical phased arrays (OPA) have the advantages of fast response, accurate pointing, small control system size, low cost, etc., and have broad application value and prospects. Among them, liquid crystal optical phased arrays (LC-OPA) are transmissive passive optical phased arrays with the characteristics of large light aperture and high light power. For laser communication links, the improvement of the optical antenna aperture plays a decisive role in improving the optical antenna gain and communication link margin in the communication link. Therefore, the method of improving the aperture of liquid crystal optical phased arrays is an important research content.

[0003] Sparse array antenna technology is a technique that achieves the same number and distribution of phase centers as a full array antenna with a smaller number of transceiver units by sparsely arranging sub-arrays in space, while avoiding the generation of grating lobes and higher side lobes. In the context of space laser communication applications, to increase the gain of the communication link, it is necessary to increase the aperture of the optical antenna, which requires more control units, resulting in problems such as increased volume and weight of the optical phased array system and a limited number of control units. At the same time, the physical characteristics of the liquid crystal optical phased array are transmissive passive optical phased arrays, which are 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] In order to solve the above technical problems, the present invention proposes a method of improving genetic algorithm based on liquid crystal optical phased array sparseness. By applying the improved genetic algorithm to the liquid crystal optical phased array, the number of control units of the same caliber phased array is reduced. Therefore, under the condition of limiting the total number of control units, the system volume, weight and complexity remain unchanged, and a larger liquid crystal optical phased array caliber can be achieved.

[0005] The technical solution adopted by the present invention is: a method for improving genetic algorithm based on liquid crystal optical phased array sparseness, and the specific steps are as follows:

[0006] S1. Construct a physical model of 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 radiation field strengths of all array elements at that point. Based on the near-field phase distribution, a uniformly distributed liquid crystal optical phased array physical model is constructed, and a uniformly distributed array far-field model is set. E(θ) is the far-field intensity, and its expression is as follows:

[0008]

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

[0010] The spacing between array elements allows grating lobes to appear in the far field:

[0011] Among them, m, θ m They represent the array element position number and the antenna array pointing direction of m array elements, m = 0 corresponds to the main lobe, and when m ≠ 0, the s =θ m Grating lobes appear.

[0012] Based on the physical model of uniformly distributed liquid crystal optical phased array and the characteristics of controllable element shape coefficients of liquid crystal optical phased array, a near-field phase distribution model is constructed, and the model of far-field intensity distribution of randomly sparse liquid crystal optical phased array is obtained. The expression is as follows:

[0013]

[0014] Among them, N1 represents the number of array elements in the first generation population array, a i represents the width of the i-th array element, d m Represents the mth array element spacing.

[0015] Set all array elements of the array as an individual of the first generation population, and merge the random number of array elements at random positions of this individual array into the same array element, so the total number of array elements is reduced, that is, the spacing d of the array is randomly generated. m and the width a of this array element i .

[0016] S2, based on step S1, setting the optimization parameters and fitness function of the genetic algorithm according to the array characteristics, and using spatial fast Fourier transform to obtain the far-field pattern, and performing fitness function screening;

[0017] First, the population size, inheritance probability, crossover probability, mutation probability, iteration stop condition and fitness function are set, and all individuals of the first generation population are generated according to the population size.

[0018] Among them, the iteration stop condition is to meet the set maximum number of iterations; the fitness function fitness 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 represents the grating lobe strength of the uniform array, E slmax,non-uniform represents the grating lobe strength of the sparse array, η uniform represents the deflection efficiency of the uniform array, η non-uniform Represents the deflection efficiency of the sparse array.

[0021] Then the genetic algorithm is iterated, and the near-field phase distribution is generated according to the pointing angle and 2π positioning is performed. Then, the far-field pattern is obtained through spatial fast Fourier transform FFT, and the fitness function of the array population is calculated. The fitness of all individuals is accumulated and sorted to generate the cumulative probability as the screening step in the genetic algorithm, and the individual with the first cumulative probability greater than the random number is inherited;

[0022] S3, based on step S2, performing encoding, crossover, mutation, inheritance, decoding and array population update operations on the array population after being screened by the cumulative probability of the fitness function;

[0023] First, the array population after the fitness function screening is encoded, crossed, and mutated, as follows:

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

[0025] The array element with an increased phase step is coded as '1', and the array element with the same phase as the previous array element is coded as '0'.

[0026] Crossover: Randomly generate crossover positions for two individuals in the population and exchange the binary codes of the crossover positions with the crossover probability.

[0027] Mutation: Random individuals select random positions to reverse the binary code.

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

[0029] Decoding: The binary code of the population is reconverted to generate a stepped phase array. The array elements coded as "1" are the array elements whose near-field phase increases after decoding, and the array elements coded as "0" are the array elements whose near-field phase remains unchanged after decoding.

[0030] Update array population: matrix concatenate the population regenerated after decoding with the population screened 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 conditions are met and stop the iteration. The final population is screened out to find the array individual with the highest fitness as the final output of the algorithm, which is the sparse array, i.e., the final optimization result.

[0032] Beneficial effects of the present invention: The method of the present invention first constructs a liquid crystal optical phased array physical model, then sets the optimization parameters and fitness function of the genetic algorithm according to the array characteristics, obtains the far-field directional diagram using spatial fast Fourier transform, performs fitness function screening, and then performs encoding, crossover, mutation, inheritance, decoding and updating operations on the array population after the fitness function screening, and finally obtains the final optimization result according to the stop iteration condition. The method of the present invention reduces the number of control units of the same caliber phased array by applying an improved genetic algorithm to the liquid crystal optical phased array. Under the condition that the total number of control units is limited, the system volume, weight and complexity remain unchanged, and a larger liquid crystal optical phased array caliber can be achieved, which provides an efficient and easy-to-implement algorithm for grating lobe suppression of the liquid crystal optical phased array, reducing the number of control units and increasing the caliber. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 The present invention is a flow chart of a method for improving a genetic algorithm based on liquid crystal optical phased array sparseness.

[0034] Figure 2 This is a near-field phase distribution diagram of a 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 Graph showing the fitness function of different iteration parameters changing with the number of iterations in an embodiment of the present invention.

[0037] Figure 5 4 is a distribution diagram of the relationship between the number of iterations and the sparsity rate in an embodiment of the present invention. DETAILED DESCRIPTION

[0038] The method of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0039] like Figure 1 As shown, a flow chart of a method for improving genetic algorithm based on liquid crystal optical phased array sparseness of the present invention is shown, and the specific steps are as follows:

[0040] S1. Construct a physical model of 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 radiation field strengths of all array elements at that point. Based on the near-field phase distribution, a uniformly distributed liquid crystal optical phased array physical model is constructed, and a uniformly distributed array far-field model is set. E(θ) is the far-field intensity, and its expression is as follows:

[0042]

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

[0044] Single element shape factor The algorithm can be optimized to destroy the conditions for the appearance of grating lobes, reduce the number of control units, and thus increase the array aperture. This depends on the physical structural characteristics of the liquid crystal optical phased array. Due to the limitation of process size, the spacing between array elements makes it possible for grating lobes to appear in the far field:

[0045] Among them, λ, m, θ m They represent the wavelength, array element position number, and antenna array pointing direction of m array elements, respectively. m = 0 corresponds to the main lobe. When m ≠ 0, the s =θ m Grating lobes appear.

[0046] Based on the physical model of uniformly distributed liquid crystal optical phased array and the characteristics of controllable element shape coefficients of liquid crystal optical phased array, a near-field phase distribution model is constructed, and the model of far-field intensity distribution of randomly sparse liquid crystal optical phased array is obtained. The expression is as follows:

[0047]

[0048] Among them, N1 represents the number of array elements in the first generation population array, a i represents the width of the i-th array element, d m Represents the mth array element spacing.

[0049] Set all array elements of the array as an individual of the first generation population, and merge the random number of array elements at random positions of this individual array into the same array element, so the total number of array elements is reduced, that is, the spacing d of the array is randomly generated. m and the width a of this array element i .

[0050] S2, based on step S1, setting the optimization parameters and fitness function of the genetic algorithm according to the array characteristics, and using spatial fast Fourier transform to obtain the far-field pattern, and performing fitness function screening;

[0051] In this embodiment, firstly, 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 stop condition and the fitness function are set, and all individuals of the first generation population are generated according to the population size.

[0052] The iteration stop condition is to meet the set maximum number of iterations. In this embodiment, the maximum number of iterations InterationTimes=4000; the fitness function fitness 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 represents the grating lobe strength of the uniform array, E slmax,non-uniform represents the grating lobe strength of the sparse array, η uniform represents the deflection efficiency of the uniform array, η non-uniform Represents the deflection efficiency of the sparse array.

[0055] Then enter the genetic algorithm iteration, such as Figure 2 As shown, the near-field phase distribution is generated according to the pointing angle and is positioned by 2π, and then the far-field pattern is obtained through spatial fast Fourier transform FFT, the fitness function of the array population is calculated, the fitness of all individuals is accumulated and sorted, and the cumulative probability as the screening step in the genetic algorithm is generated, and the individual at the position with the first cumulative probability larger than the random number is inherited, and then the individual with high fitness is accepted with a greater probability.

[0056] S3, based on step S2, performing encoding, crossover, mutation, inheritance, decoding and array population update operations on the array population after being screened by the cumulative probability of the fitness function;

[0057] First, the array population after the fitness function screening is encoded, crossed, and mutated, as follows:

[0058] Encoding: Figure 3 As shown, the near-field phase distribution is generated into a step-pattern phase distribution and is binary-coded.

[0059] The array element with an increased phase step is coded as '1', and the array element with the same phase as the previous array element is coded as '0'.

[0060] Crossover: Randomly generate crossover positions for two individuals in the population and exchange the binary codes of the crossover positions with the crossover probability.

[0061] Mutation: Random individuals select random positions to reverse the binary code.

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

[0063] Decoding: The binary code of the population is reconverted to generate a stepped phase array. The array elements coded as "1" are the array elements whose near-field phase increases after decoding, and the array elements coded as "0" are the array elements whose near-field phase remains unchanged after decoding.

[0064] Update array population: matrix-join the population regenerated after decoding with the population screened by the cumulative probability of the fitness function in step S2 to generate the next generation of population, thereby maintaining a stable 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 conditions are met and stop the iteration. The final population is screened out to find the array individual with the highest fitness as the final output of the algorithm, which is the sparse array, i.e., the final optimization result.

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

[0067] Among them, the array phase calculation division step is 2.8*10 -2 μm, when the beam scanning angle is 0.5°~0.8°, the relationship between the number of iterations and the fitness function is distributed as follows Figure 4 As shown in the figure, the relationship between the number of iterations and the sparsity rate is distributed as follows Figure 5As shown, MATLAB simulation is used to generate a distribution diagram of the relationship between the number of iterations and the fitness function, and a distribution diagram of 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 setting of population size, genetic probability, crossover probability and mutation probability parameters affects the number of iterations of the genetic algorithm. By changing its parameters and comparing them, it can be seen that the algorithm can eventually obtain the required fitness function under several different conditions. Figure 4 The fitness function shown in Figure 5 The array sparseness rate shown can obtain the required sparseness rate and corresponding fitness of the liquid crystal optical phased array.

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

[0070] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A method for improving genetic algorithm based on liquid crystal optical phased array sparseness, the specific steps are as follows: S1. Construct a physical model of 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 radiation field strengths of all array elements of the array antenna at that point; based on the near-field phase distribution, a uniformly distributed liquid crystal optical phased array physical model is constructed, and a uniformly distributed array far-field model is set. E(θ) is the far-field intensity, and its expression is as follows: in, N represents the number of array elements. represents the far-field pattern of a single antenna unit, α represents the single antenna element factor, and a represents the width of the array element, λ represents the wavelength; A i , k, d, θ and θ s They represent the light amplitude, wave number, array element spacing, observation direction, and beam scanning angle emitted by the i-th unit respectively; The spacing between array elements allows grating lobes to appear in the far field: Among them, m, θ m They represent the array element position number and the antenna array pointing direction of m array elements, respectively. m = 0 corresponds to the main lobe. When m ≠ 0, the s =θ m Grating lobes appear; Based on the physical model of uniformly distributed liquid crystal optical phased array and the characteristics of controllable element shape coefficients of liquid crystal optical phased array, a near-field phase distribution model is constructed, and the model of far-field intensity distribution of randomly sparse liquid crystal optical phased array is obtained. The expression is as follows: Among them, N1 represents the number of array elements in the first generation population array, a i represents the width of the i-th array element, d m represents the mth array element spacing; Set all array elements of the array as an individual of the first generation population, and merge the random number of array elements at random positions of this individual array into the same array element, so the total number of array elements is reduced, that is, the spacing d of the array is randomly generated. m and the width a of this array element i ; S2, based on step S1, setting the optimization parameters and fitness function of the genetic algorithm according to the array characteristics, and using spatial fast Fourier transform to obtain the far-field pattern, and performing fitness function screening; First, set the population size, inheritance probability, crossover probability, mutation probability, iteration stop condition and fitness function, and generate all individuals of the first generation population according to the population size; Among them, the iteration stop condition is to meet the set maximum number of iterations; the fitness function fitness expression is as follows: Where n represents the total number of optimized deflection angles, i represents the deflection angle number, and E slmax,uniform represents the grating lobe strength of the uniform array, E slmax,non-uniform represents the grating lobe strength of the sparse array, η uniform represents the deflection efficiency of the uniform array, η non-uniform represents the deflection efficiency of the sparse array; Then the genetic algorithm is iterated, and the near-field phase distribution is generated according to the pointing angle and 2π positioning is performed. Then, the far-field pattern is obtained through spatial fast Fourier transform FFT, and the fitness function of the array population is calculated. The fitness of all individuals is accumulated and sorted to generate the cumulative probability as the screening step in the genetic algorithm, and the individual with the first cumulative probability greater than the random number is inherited; S3, based on step S2, performing encoding, crossover, mutation, inheritance, decoding and array population update operations on the array population after being screened by the cumulative probability of the fitness function; First, the array population after the fitness function screening is encoded, crossed, and mutated, as follows: Encoding: Generate a step-pattern phase distribution from the near-field phase distribution and encode it in binary format; The array element with an increased phase step is coded as '1', and the array element with the same phase as the previous array element is coded as '0'; Crossover: Randomly generate crossover positions for two individuals in the population, and exchange the binary codes of the crossover positions with the crossover probability; Mutation: Random individuals select random positions to reverse the binary code; Then, the array population after encoding, crossover and mutation operations is decoded and the array population is updated, as follows: Decoding: Reconvert the binary code of the population to generate a stepped phase array. The array elements coded as "1" are the array elements whose near-field phase increases after decoding, and the array elements coded as "0" are the array elements whose near-field phase remains unchanged after decoding. Update array population: perform matrix splicing on the population regenerated after decoding and the population screened 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 conditions are met and stop the iteration. The final population is screened out to find the array individual with the highest fitness as the final output of the algorithm, which is the sparse array, i.e., the final optimization result.

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