Improved sparrow search algorithm and convex optimization-based sparse array antenna synthesis method

Abstract

The invention discloses a thin cloth array antenna synthesis method based on an improved sparrow search algorithm and convex optimization, which combines the improved sparrow search algorithm and the convex optimization method to realize low side lobe array synthesis by performing joint optimization on array antenna unit positions and excitation amplitudes. Under the constraint conditions of array aperture, array element number, minimum array element spacing and the like, a sparse rectangular planar array model is established, and the number of array units of a position distribution matrix generated by a Taylor window function is sparse. And then, based on an improved sparrow search algorithm, through a Tent chaotic sequence, initializing a population, enhancing diversity of the population, and meanwhile, introducing an adaptive t distribution variation method, disturbing individual positions, and improving the ability of the algorithm to jump out of local optimum and solving efficiency. And finally, on the basis of array element position optimization, the array element excitation amplitude is optimized by using a convex optimization method, and an optimal peak side lobe level value is calculated in combination with an optimization result. Through joint optimization of the positions and excitation amplitudes of the array antenna units, the design flexibility can be effectively improved, and meanwhile, the side lobe level of an array antenna directional diagram is further reduced.

Description

Technical Field

[0001] The invention relates to the technical field of array antennas, and in particular to a method for jointly optimizing array antenna unit positions and excitation amplitudes, which is used for suppressing the sidelobe level of the array antenna radiation pattern. Background Art

[0002] Antennas, as terminals for transmitting and receiving signals, play an irreplaceable role in wireless communication systems. In practical applications, a single antenna is often difficult to meet specific working requirements, and array antennas composed of several antenna units arranged in a certain way have come into being. Compared with a single antenna, array antennas have the advantages of high gain and low sidelobe, and are easier to achieve multi-beam and beamforming requirements. They have been widely used in satellites, communications, radar, sonar, medical imaging, and electronic countermeasures. With the advancement of science and technology, in these fields, the performance requirements for array antennas are gradually increasing, such as fast tracking speed, high reliability, strong anti-interference ability, and at the same time low cost and easy implementation. Therefore, studying the synthesis method of array antennas has important academic value and engineering significance.

[0003] Modern communication technology has higher and higher requirements for the radiation characteristics of array antennas. Smaller arrays composed of several or even dozens of antenna units can no longer meet the needs of practical applications. The scale of array antennas has become larger and larger, resulting in a sharp increase in optimization parameters and system costs. Compared with uniform arrays, sparse arrays can reduce the number of array elements, thereby reducing system costs, suppressing sidelobe levels, and obtaining good directivity. In the past few decades, with the advancement of numerical optimization technology, global optimization algorithms such as genetic algorithms and particle swarm algorithms have been used to sparsely distribute unit positions in array antennas. However, the optimization method for array unit positions is limited by constraints such as array aperture, number of array elements, and array element spacing, and its ability to suppress sidelobe levels is relatively limited. In recent years, convex optimization methods have also been introduced into array antenna synthesis to achieve sidelobe suppression, beamforming, and broadband synthesis. Some scholars combine intelligent optimization algorithms with convex optimization methods to reduce sidelobes by jointly optimizing array unit positions and excitation amplitudes. However, with the development and application of large-scale array antennas, antenna structures are becoming increasingly complex. Traditional optimization algorithms are inefficient in solving complex nonlinear problems and are prone to falling into local optimal solutions, which can no longer meet the optimization needs of array antennas. Therefore, it is still worthwhile to find more efficient synthesis methods for the problem of array antenna synthesis. Summary of the invention

[0004] The purpose of the present invention is to address the shortcomings of the above-mentioned methods and propose a method for synthesizing sparse array antennas based on an improved sparrow search algorithm and convex optimization. First, a sparse rectangular planar array optimization model is established, and the array is weighted by a Taylor window function, and the resulting position distribution matrix is ​​used to sparse the array. Then, an improved sparrow search algorithm is used to optimize the array element position to achieve array antenna layout. Finally, on the basis of fixed position, a convex optimization method is used to optimize the excitation amplitude of the array element, thereby achieving better suppression of the sidelobe level of the sparse array. By combining the improved sparrow search algorithm and the convex optimization method and applying them to the synthesis of sparse arrays, the joint optimization of the position and excitation amplitude of the array antenna unit can effectively improve the design flexibility, while further reducing the sidelobe level of the array antenna pattern.

[0005] To achieve the above object, the antenna array optimization method of the present invention comprises the following steps:

[0006] Under the constraints of array aperture, number of array elements and minimum array element spacing, the number of sparse array elements is generated by the position distribution matrix generated by the Taylor window function. Based on the improved sparrow search algorithm, the population is initialized through the Tent chaotic sequence to enhance the diversity of the population. At the same time, the adaptive t distribution mutation method is introduced to perturb the individual position to improve the algorithm's ability to jump out of the local optimum and the solution efficiency. On the basis of the optimization of the array element position, the convex optimization method is used to optimize the array element excitation amplitude so that the array antenna pattern can obtain a lower peak sidelobe level. The detailed steps are as follows:

[0007] 1. Establish a sparse rectangular planar array model located in the xoy plane. The model contains N array elements and is symmetrically distributed about the x-axis and y-axis. The array aperture is 2L×2H, and the minimum spacing between array elements is d. min , get the directional pattern function of the sparse rectangular planar array;

[0008] 2. According to the established sparse rectangular planar array model, the minimization of the peak sidelobe level (PSLL) is taken as the optimization goal, and constraints are set to establish the optimization model;

[0009] 3. Use the Taylor window function to obtain the position distribution matrix, and use the matrix to sparse the array antenna;

[0010] 4. Use the Tent chaotic sequence to initialize the population and obtain the initial position distribution of the array antenna. Then use the sparrow search algorithm that introduces the adaptive t distribution mutation method to optimize the array unit position.

[0011] 5. After the array element position is optimized, the excitation amplitude of the array element is optimized using the convex optimization method. The array unit position and excitation amplitude are substituted into the objective function to calculate the PSLL and obtain the optimal PSLL.

[0012] Furthermore, the directional pattern function of the sparse rectangular array antenna is:

[0013]

[0014] Where N is the number of array elements; (x i ,y i ) and w i They represent the coordinate position and excitation amplitude of the ith array element respectively; k = 2π / λ is the wave number, λ is the wavelength; θ is the pitch angle, is the azimuth.

[0015] Furthermore, the optimization model includes:

[0016]

[0017] Among them, min is the minimum value; st represents the constraint condition; d min is the minimum spacing between units, which is taken as λ / 2; P and Q are the maximum number of array elements that can be placed along the y-axis and x-axis in the first quadrant; f(X,Y,w) is the fitness function with respect to the array position matrix X, Y and the excitation amplitude w.

[0018] Furthermore, P and Q can be determined by the following calculation formula:

[0019]

[0020] Furthermore, the fitness function is:

[0021] Select and The sum of the maximum sidelobe levels of the two planes is used as the fitness function, then

[0022]

[0023] Among them, max represents the maximum value function; F max is the maximum value of the main lobe; F (θ,0) for Sidelobe area on the plane; F (θ,π / 2) for Sidelobe area on the plane.

[0024] Furthermore, the Taylor window function is used to generate the weight coefficients a of the rows and columns respectively. m and b n, multiplied by each other, we can get the weighting coefficient of each array element:

[0025] c mn =a m ×b n

[0026] Using the size of the weighted coefficient, the array element position distribution matrix T is generated:

[0027]

[0028] Furthermore, the initialization population of the Tent chaotic sequence includes:

[0029] z i+1 =(2z i )mod1+rand(0,1) / N p I ter

[0030] Among them, z i+1 is the chaotic sequence obtained after this iteration; mod is the remainder operation; N p is the population, i.e. the number of array antennas; I ter is the maximum number of iterations of the algorithm.

[0031] According to the constraints, the generated Tent chaotic sequence is constrained to the set solution range:

[0032]

[0033] Among them, Z d is the generated Tent chaotic sequence; [l bx ,U bx ]=[0,L-(P-0.5)d min ] is the distributable space of variable dx; [l by ,U by ]=[0,H-(Q-0.5)d min ] is the distributable space of variable dy.

[0034] Furthermore, the initial position distribution of the array antenna is obtained according to the array constraints and the initial population generated by the Tent chaotic sequence:

[0035]

[0036] Where Δx i,j and Δy i,j Satisfy Δx i,j ∈[l bx ,U bx ], Δy i,j ∈[l by ,U by ].

[0037] Further, the array antenna position update using the sparrow search algorithm optimization strategy that introduces the adaptive t-distribution mutation method includes the following steps:

[0038] 1) After sorting according to the calculated initial fitness function value, select the top 10% to 20% of sparrow individuals with good fitness as explorers, and use the following formula to update the position:

[0039]

[0040] Among them, η is a uniform random number between (0,1], Q r is a random number that obeys the standard normal distribution, L1 represents a matrix whose elements are all 1, R1∈(0,1) and ST represent the warning value and safety value respectively;

[0041] 2) Individuals other than explorers act as followers, and their position update formula is:

[0042]

[0043] Among them, d p is the optimal position currently occupied by the explorer, d worst It represents the position of the current global worst individual in the group, A + It represents a matrix whose elements are randomly composed of 1 and -1, and n is the population size;

[0044] 3) Randomly select 10% to 20% of the sparrows in the population for reconnaissance and early warning, and the corresponding position update formula is:

[0045]

[0046] Among them, d best is the current global optimal position, β is a normally distributed random number, K r ∈[-1,1] is a random number, f i is the fitness value of the current sparrow individual, f g and f w are the fitness values ​​of the current global optimal and worst individuals, respectively, and ε0 is a very small constant;

[0047] 4) After judging by the dynamic selection probability, the position is disturbed using the adaptive t-distribution mutation method;

[0048] 5) After each position update, determine whether the position of each individual, i.e., the unit position of the array, satisfies (l bx ,U bx ) and (l by ,U by) constraint range, if it is not satisfied, the position is corrected for crossing the boundary, and after obtaining the optimized array layout, the array element position is converted into the real distance interval;

[0049] 6) The updated real distance position of the array element is combined with the array excitation amplitude optimized by the convex optimization method to calculate the corresponding fitness function;

[0050] 7) After completing one iteration, the best fitness function value is compared with the recorded initial fitness value. If the fitness value is lower, the fitness value and array element position calculated this time are retained and recorded, otherwise they remain unchanged.

[0051] 8) Determine whether the maximum number of iterations has been reached. If so, end the iteration process to obtain the optimal PSLL; if not, return to step 1).

[0052] Furthermore, the position disturbance using the adaptive t-distribution variation method includes:

[0053] 1) Dynamic selection probability p is used to adjust the use of adaptive t-distribution mutation operator, and its calculation formula is as follows:

[0054] p=w1-w2×(I ter -it) / I ter

[0055] Among them, w1 and w2 determine the upper limit and change range of the dynamic selection probability respectively. Generally, w1 = 0.5, w2 = 0.1, I ter is the maximum number of iterations, and it is the current number of iterations.

[0056] 2) After dynamic selection probability judgment, the t-distribution mutation operator is used to perturb the array position. The calculation formula is as follows:

[0057]

[0058] in, is the position of the sparrow after disturbance, is the position of sparrow i at the it-th iteration.

[0059] Furthermore, when the position is fixed, the subproblem of minimizing the peak sidelobe level is transformed into a convex problem under the beamwidth constraint, and the excitation amplitude of the array is updated using a convex optimization method:

[0060]

[0061] In the formula, ε represents the approximation error, which is usually set to 0.01, A(u k ,v k )w represents the main beam shape of the established array antenna pattern, F d(u k ,v k ) represents the desired main beam shape of the array antenna pattern. Substitute the updated array excitation amplitude into the fitness function to iteratively calculate the fitness function value and obtain the optimal PSLL.

[0062] Compared with the prior art, the present invention has the following advantages and effective effects:

[0063] 1. The present invention uses an improved sparrow search algorithm to optimize the element positions of a rectangular planar sparse array antenna. Compared with other swarm intelligence random search algorithms, it speeds up the optimization speed and improves the optimization performance;

[0064] 2. The present invention uses the Tent chaotic sequence to initialize the population, which enhances the diversity of the population and makes the algorithm more efficient;

[0065] 3. The present invention adopts an adaptive t-distribution variation method to perturb the position of the sparrows, so that the algorithm has better global development ability in the early stage of iteration, good local exploration ability in the later stage of iteration, and accelerates the convergence speed of the algorithm;

[0066] 4. The present invention simultaneously considers the problem of joint optimization of the array element position and the excitation amplitude of the two-dimensional rectangular planar sparse array antenna, thereby further reducing the side lobes of the two-dimensional rectangular planar sparse array antenna pattern;

[0067] 5. Compared with uniform array antennas with the same aperture, the sparse array antenna of the present invention can significantly reduce the sidelobe level while reducing the number of array elements to a certain extent, thereby reducing the cost of the system, and provides a solution for the optimization of low sidelobe array antennas.

[0068] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] In order to make the objectives, technical solutions and advantages of the present invention more clear, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0070] Figure 1 It is a general flow chart for realizing the present invention;

[0071] Figure 2 It is a flow chart of the improved sparrow search algorithm of the present invention;

[0072] Figure 3 is the result obtained when only the array element position is optimized and The normalized radiation pattern of

[0073] Figure 4 The value obtained when optimizing both the array unit position and the excitation amplitude is and Normalized radiation pattern;

[0074] Figure 5 A comparison chart of the array position distribution results of optimizing only the array position and optimizing the array position distribution results of combining the excitation amplitude with the excitation amplitude;

[0075] Figure 6 Schematic diagram of array position and excitation amplitude distribution obtained by simultaneously optimizing array unit position and excitation amplitude. DETAILED DESCRIPTION

[0076] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0077] Figure 1 For the overall flow chart of the present invention, refer to Figure 1 , the experimental steps of the present invention are as follows:

[0078] Step 1: According to the actual antenna aperture range of the rectangular planar sparse array antenna, determine the antenna aperture 2L×2H, where the unit is one wavelength; the number of array elements is N; the minimum array element spacing d min , we get the directional pattern function of the sparse rectangular array antenna:

[0079]

[0080] Where N is the number of array elements; (x i ,y i ) and w i They represent the coordinate position and excitation amplitude of the ith array element respectively; k = 2π / λ is the wave number, λ is the wavelength; θ is the pitch angle, is the azimuth.

[0081] Step 2: Based on the array antenna aperture 2L×2H, number of array elements N, and minimum array element spacing d determined in step 1 minOptimization objectives and constraints for constructing rectangular planar sparse array antennas:

[0082]

[0083] Among them, min is the minimum value; st represents the constraint condition; d min is the minimum spacing between units, which is taken as λ / 2; P and Q are the maximum number of array elements that can be placed along the y-axis and x-axis in the first quadrant; f(X,Y,w) is the fitness function with respect to the array position matrix X, Y and the excitation amplitude w.

[0084] Select and The sum of the maximum sidelobe levels of the two planes is used as the fitness function, then

[0085]

[0086] Among them, max represents the maximum value function; F max is the maximum value of the main lobe; F (θ,0) for Sidelobe area on the plane; F (θ,π / 2) for Sidelobe area on the plane.

[0087] In order to narrow the search range of the position matrix, the x-axis and y-axis coordinate matrices of the array element position are expressed as:

[0088]

[0089]

[0090] Where Δx i,j and Δy i,j Satisfy Δx i,j ∈[l bx ,U bx ], Δy i,j ∈[l by ,U by ].

[0091] P and Q are the maximum number of array elements that can be placed along the y-axis and x-axis in the first quadrant, which are determined by the following calculation formula:

[0092]

[0093] When N=P×Q, the array is full; when N<P×Q, the array is a sparse matrix. According to the constraints of the array aperture, P×QN array elements with smaller weights are sparsely removed, and the outermost array elements, that is, the array elements in the Pth row and the Qth column, are always retained.

[0094] Step 3: Use the Taylor window function to generate the weight coefficients a for rows and columns respectively m and b n , multiplied by each other, we can get the weighting coefficient of each array element:

[0095] c mn =a m ×b n (7)

[0096] Using the size of the weighted coefficient, the array element position distribution matrix T is generated:

[0097]

[0098] Step 4: Use the Tent chaotic sequence to initialize the population, obtain the initial position distribution of the array antenna and calculate its corresponding fitness function value.

[0099] 1) Use the Tent chaotic sequence to initialize the population, and use the following formula to perform the self-mapping of Tent chaos:

[0100] z i+1 =(2z i )mod1+rand(0,1) / N p I ter (9)

[0101] Among them, z i+1 is the chaotic sequence obtained after this iteration; mod is the remainder operation; N p is the population, i.e. the number of array antennas; I ter is the maximum number of iterations of the algorithm.

[0102] According to the constraints, the generated Tent chaotic sequence is constrained to the set solution range:

[0103]

[0104] Among them, Z d is the generated Tent chaotic sequence; [l bx ,U bx ]=[0,L-(P-0.5)d min ] is the distributable space of variable dx; [l by ,U by ]=[0,H-(Q-0.5)d min ] is the distributable space of variable dy.

[0105] 2) Substituting the values ​​of variables dx and dy into equations (4) and (5) to obtain the coordinates (x, y) of the initial array unit position distribution, the array position layout can be expressed as d i,g =x i,g +j·yi,g ,(i=1,2,3,…,N P ; g = 1, 2, 3, ..., dim), the position of each row of array elements in each array is used as an individual in the gray wolf population to create an initial population, N p is the number of arrays, and dim is the number of elements contained in an array.

[0106] The fitness value of a sparrow individual is:

[0107]

[0108] Substitute the element position corresponding to each array into the fitness function described in step 2, calculate its corresponding initial fitness value, and record the optimal value and its corresponding position by sorting.

[0109] Step 5, use the optimization strategy of the improved sparrow search algorithm to optimize the position of the array units. After sorting according to the calculated initial fitness function value, select the top 10% to 20% of the sparrow individuals with good fitness as explorers, and the individuals other than the explorers as followers. At the same time, randomly select 10% to 20% of the sparrow individuals in the population for reconnaissance and early warning.

[0110] The update formula of the explorer position is:

[0111]

[0112] Among them, η is a uniform random number between (0,1], Q r is a random number that obeys the standard normal distribution, L1 represents a matrix whose elements are all 1, R1∈(0,1) and ST represent the warning value and safety value respectively.

[0113] The follower position update formula is:

[0114]

[0115] Among them, d p is the optimal position currently occupied by the explorer, d worst It represents the position of the current global worst individual in the group, A + It represents a matrix whose elements are randomly composed of 1 and -1, and n is the population size.

[0116] The formula for updating the individual position of the sparrow for reconnaissance and early warning is:

[0117]

[0118] Among them, d best is the current global optimal position, β is a normally distributed random number, K r∈[-1,1] is a random number, f i is the fitness value of the current sparrow individual, f g and f w are the fitness values ​​of the current global optimal and worst individuals respectively, and ε0 is a very small constant.

[0119] After the position is updated, it is perturbed using the adaptive t-distribution mutation method, determined by the dynamic selection probability.

[0120] The dynamic selection probability p is calculated as follows:

[0121] p=w1-w2×(I ter -it) / I ter (15)

[0122] Among them, w1 and w2 determine the upper limit and change range of the dynamic selection probability respectively. Generally, w1 = 0.5, w2 = 0.1, I ter is the maximum number of iterations, and it is the current number of iterations.

[0123] After dynamic selection probability judgment, the t-distribution mutation operator is used to perturb the array position. The calculation formula is as follows:

[0124]

[0125] in, is the position of the sparrow after disturbance, is the position of sparrow i at the it-th iteration.

[0126] After each position update, the present invention extracts the real part and imaginary part of the position of each array element, and determines whether each individual, i.e., the unit position of the array satisfies (l bx ,U bx ) and (l by ,U by ) constraint range, if it is not satisfied, the position is corrected for out-of-bounds, and after obtaining the optimized values ​​of variables dx and dy, they are substituted into equations (4) and (5) to obtain the coordinates (x, y) of the array unit position distribution.

[0127] Step 6, when the position is fixed, the subproblem of minimizing the peak sidelobe level is transformed into a convex problem under the beamwidth constraint, and the excitation amplitude of the array is updated using a convex optimization method:

[0128]

[0129] In the formula, ε represents the approximation error, which is usually set to 0.01, A(u k ,v k )w represents the main beam shape of the established array antenna pattern, F d(u k ,v k ) represents the desired main beam shape of the array antenna pattern. Substitute the updated array excitation amplitude into the fitness function to iteratively calculate the fitness function value and obtain the optimal PSLL.

[0130] Step 7, substitute the array element position distribution matrix T combined with the optimized array element position and excitation amplitude into the fitness function to iteratively calculate the fitness function value, and compare the objective function value of this optimization result with the recorded optimal peak sidelobe level. If the fitness function value of this optimization result is less than the optimal peak sidelobe level, save this optimization result and make the optimal peak sidelobe level equal to the fitness function value of this optimization result. Otherwise, ignore this optimization result.

[0131] Return to step 5 until the loop ends, and the optimal PSLL, array element position distribution and excitation amplitude are obtained.

[0132] The effect of the present invention is further illustrated by the following simulation experiment:

[0133] The present invention adopts the Tent chaotic sequence to initialize the population, so that the diversity of the population is enhanced and the algorithm solving efficiency is higher; the present invention adopts the adaptive t distribution mutation method to disturb the sparrow position, so that the algorithm has a good global development ability in the early stage of iteration, and has a good local exploration ability in the late stage of iteration, and accelerates the convergence speed of the algorithm; the present invention simultaneously considers the problem of joint optimization of the array element position and the excitation amplitude of the two-dimensional rectangular plane sparse array antenna, thereby further reducing the side lobe of the two-dimensional rectangular plane sparse array antenna radiation pattern; compared with the uniform array antenna under the same caliber, the sparse array antenna of the present invention can reduce a certain number of array elements while greatly reducing the side lobe level, thereby reducing the cost of the system.

[0134] 1) Simulation parameter settings: The aperture of the rectangular sparse array antenna is 2L×2H=9.5λ×4.5λ, the number of array elements is N=108, and the minimum array element spacing constraint is d min =0.5λ, the array element positions of the rectangular sparse array antenna are symmetrical about the center of the array antenna. The simulation experiment is carried out on MATLAB software.

[0135] 2) Simulation content

[0136] According to the parameter settings, the objective function and constraints of the rectangular sparse array antenna are constructed according to step 2. In this simulation experiment, the fitness function f(x,y) is set to and The sum of the maximum sidelobe levels of the two planes, that is:

[0137]

[0138] according to Figure 2 Write a program according to the process in , with the number of loops I = 300 in the program, and run the program to obtain the optimal PSLL and its corresponding array element position distribution matrix.

[0139] Figure 3 To optimize only the array position, and The normalized radiation pattern of the sidelobe is -60.81dB (at flat, the peak sidelobe level is -26.21dB; flat, with a peak sidelobe level of -34.60dB).

[0140] Figure 4 The joint optimization of the array element position and the excitation amplitude is obtained in and The normalized radiation pattern of the sidelobe is -71.37 dB (at plane, the peak sidelobe level is -29.73dB; flat, with a peak sidelobe level of -41.64dB).

[0141] From the comparison of the sidelobe level optimization results, it can be seen that under the premise of fixed array aperture and number of array elements, the sidelobe level of the array antenna is better suppressed by jointly optimizing the array element position and excitation amplitude than by only optimizing the array unit position.

[0142] Figure 5 A comparison chart of the array position distribution results obtained by only optimizing the array position and the method of the present invention is given.

[0143] Figure 6 A schematic diagram of array position and excitation amplitude distribution obtained by simultaneously optimizing array unit position and excitation amplitude is given.

[0144] The above results show that the present invention can achieve better sidelobe level suppression effect by further optimizing the array element excitation amplitude on the basis of optimizing the sparse distribution of array unit positions while significantly reducing the number of array elements.

[0145] It should be noted that the above embodiments are only illustrative of the principles and effects of the present invention, and are not intended to limit the present invention. Anyone familiar with the technology may modify or change the above embodiments without violating the spirit and scope of the present invention. Therefore, all equivalent modifications or changes made by those with ordinary knowledge in the technical field without departing from the spirit and technical ideas disclosed by the present invention should still be covered by the claims of the present invention.

Claims

1. A sparse array antenna synthesis method based on an improved sparrow search algorithm and convex optimization, characterized in that: The method comprises the following steps: Step 1: Establish a sparse rectangular planar array model located in the xoy plane. The model contains N array elements and is symmetrically distributed about the x-axis and y-axis. The array aperture is 2L×2H, and the minimum spacing between array elements is d. min , get the directional pattern function of the sparse rectangular planar array; Step 2, according to the established sparse rectangular planar array model, minimizing the peak sidelobe level (PSLL) is taken as the optimization goal, and constraints are set to establish an optimization model; Step 3, using the Taylor window function to obtain the position distribution matrix, and using the matrix to perform sparse processing on the array antenna; Step 4, using the Tent chaotic sequence to initialize the population, obtain the initial position distribution of the array antenna, and then use the sparrow search algorithm that introduces the adaptive t distribution mutation method to optimize the array unit position; Step 5: After the array element position is optimized, the excitation amplitude of the array element is optimized using a convex optimization method. The array element position and the excitation amplitude are substituted into the objective function to calculate the PSLL and obtain the optimal PSLL.

2. The method according to claim 1, characterized in that The directional pattern function of the sparse rectangular array antenna in step 1 is: Where N is the number of array elements; (x i ,y i ) and w i They represent the coordinate position and excitation amplitude of the ith array element respectively; k = 2π / λ is the wave number, λ is the wavelength; θ is the pitch angle, is the azimuth.

3. The method according to claim 1, characterized in that The optimization model described in step 2 includes: Among them, min is the minimum value; st represents the constraint condition; d min is the minimum spacing between units, which is taken as λ / 2; P and Q are the maximum number of array elements that can be placed along the y-axis and x-axis in the first quadrant; f(X,Y,w) is the fitness function with respect to the array position matrix X, Y and the excitation amplitude w. P and Q can be determined by the following calculation formula: Selection of fitness function: Select and The sum of the maximum sidelobe levels of the two planes is used as the fitness function, then Among them, max represents the maximum value function; F max is the maximum value of the main lobe; F (θ,0) for Sidelobe area on the plane; F| (θ,π / 2) for Sidelobe area on the plane.

4. The method according to claim 1, characterized in that: In step 3, the Taylor window function is used to generate the array element position distribution matrix, which specifically includes the following steps: 1) Use Taylor window function to generate row and column weight coefficients a respectively m and b n , multiplied by each other, we can get the weighting coefficient of each array element: c mn =a m ×b n 2) Using the size of the weighted coefficient, generate the array element position distribution matrix T:

5. The method according to claim 1, characterized in that: In step 4, the tent chaotic sequence initialization population includes: z i+1 =(2z i )mod1+rand(0,1) / N p I ter Among them, z i+1 is the chaotic sequence obtained after this iteration; mod is the remainder operation; N p is the population, i.e. the number of array antennas; I ter is the maximum number of iterations of the algorithm. According to the constraints, the generated Tent chaotic sequence is constrained to the set solution range: Among them, Z d is the generated Tent chaotic sequence; [l bx ,U bx ]=[0,L-(P-0.5)d min ] is the distributable space of variable dx; [l by ,U by ]=[0,H-(Q-0.5)d min ] is the distributable space of variable dy.

6. The method according to claim 1, characterized in that The array constraints and the initial population generated by the Tent chaotic sequence obtain the initial position distribution of the array antenna: Among them, Δx i,j Sum Δy i,j full foot Δx i,j ∈[l bx ,U bx ], Δy i,j ∈[l by ,U by ].

7. The method according to claim 1, characterized in that In step 4, the array antenna position update using the sparrow search algorithm optimization strategy with the introduction of the adaptive t-distribution mutation method includes the following steps: 1) After sorting according to the calculated initial fitness function value, select the top 10% to 20% of sparrow individuals with good fitness as explorers, and use the following formula to update the position: Among them, η is a uniform random number between (0,1], Q r is a random number that obeys the standard normal distribution, L1 represents a matrix whose elements are all 1, R1∈(0,1) and ST represent the warning value and safety value respectively; 2) Individuals other than explorers act as followers, and their position update formula is: Among them, d p is the optimal position currently occupied by the explorer, d worst It represents the position of the current global worst individual in the group, A + It represents a matrix whose elements are randomly composed of 1 and -1, and n is the population size; 3) Randomly select 10% to 20% of the sparrows in the population for reconnaissance and early warning, and the corresponding position update formula is: Among them, d best is the current global optimal position, β is a normally distributed random number, K r ∈[-1,1] is a random number, f i is the fitness value of the current sparrow individual, f g and f w are the fitness values ​​of the current global optimal and worst individuals, respectively, and ε0 is a very small constant; 4) After judging by the dynamic selection probability, the position is disturbed using the adaptive t-distribution mutation method; 5) After each position update, determine whether the position of each individual, i.e., the unit position of the array, satisfies (l bx ,U bx ) and (l by ,U by ) constraint range, if it is not satisfied, the position is corrected for crossing the boundary, and after obtaining the optimized array layout, the array element position is converted into the real distance interval; 6) The updated real distance position of the array element is combined with the array excitation amplitude optimized by the convex optimization method to calculate the corresponding fitness function; 7) After completing one iteration, the best fitness function value is compared with the recorded initial fitness value. If the fitness value is lower, the fitness value and array element position calculated this time are retained and recorded, otherwise they remain unchanged. 8) Determine whether the maximum number of iterations has been reached. If so, end the iteration process to obtain the optimal PSLL; if not, return to step 1).

8. The method according to claim 1, characterized in that The position disturbance using the adaptive t-distribution mutation method includes: 1) Dynamic selection probability p is used to adjust the use of adaptive t-distribution mutation operator, and its calculation formula is as follows: p=w1-w2×(I ter -it) / I ter Among them, w1 and w2 determine the upper limit and change range of the dynamic selection probability respectively. Generally, w1=0.5, w2=0.1, I ter is the maximum number of iterations, and it is the current number of iterations. 2) After dynamic selection probability judgment, the t-distribution mutation operator is used to perturb the array position. The calculation formula is as follows: in, is the position of the sparrow after disturbance, is the position of sparrow i at the it-th iteration.

9. The method according to claim 1, characterized in that: When the position is fixed, the subproblem of minimizing the peak sidelobe level is transformed into a convex problem under the beamwidth constraint, and the excitation amplitude of the array is updated using a convex optimization method: Among them, ε represents the approximation error, which is usually set to 0.01, A(u k ,v k )w represents the main beam shape of the established array antenna pattern, F d (u k ,v k ) represents the desired main beam shape of the array antenna pattern. Substitute the updated array excitation amplitude into the fitness function to iteratively calculate the fitness function value and obtain the optimal PSLL.

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