CN111143983A - Low sidelobe comprehensive optimization method of sparse antenna array based on improved water circulation algorithm - Google Patents

Low sidelobe comprehensive optimization method of sparse antenna array based on improved water circulation algorithm Download PDF

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CN111143983A
CN111143983A CN201911321011.9A CN201911321011A CN111143983A CN 111143983 A CN111143983 A CN 111143983A CN 201911321011 A CN201911321011 A CN 201911321011A CN 111143983 A CN111143983 A CN 111143983A
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芮义斌
王欢
谢仁宏
李鹏
郭山红
孙泽渝
吕宁
王丽妍
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Nanjing University of Science and Technology
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Abstract

The invention discloses a comprehensive optimization method for a low side lobe of a thin-cloth antenna array based on an improved water circulation algorithm. The method comprises the following steps: firstly, an antenna array directional diagram is mathematically modeled, a functional relation between the array directional diagram and the antenna array element position is constructed, and the search space of an array element position solution is reduced by performing constant separation on the array element position; then, classifying, converging, evaporating and rainfall the array element position set in the array according to a water circulation algorithm; and finally, obtaining the final individual corresponding to the sea through multiple rounds of iteration, and taking the position of each array element in the sea as the optimal arrangement mode of the array elements in the array. The method has the advantages of low side lobe level, simple algorithm, high convergence speed, good robustness and good convergence result.

Description

Low sidelobe comprehensive optimization method of sparse antenna array based on improved water circulation algorithm
Technical Field
The invention relates to the technical field of an optimization arrangement method of an antenna array, in particular to a sparse-arrangement antenna array optimization method based on an improved water circulation algorithm.
Background
Generally, a single antenna can well complete tasks of transmitting and receiving electromagnetic waves, but the single antenna has the defects of low directivity, low gain, wide main lobe and the like, so that the single antenna is often difficult to meet the requirements of specific working environments, working tasks or working performance. Therefore, in some practical application scenarios, a plurality of antenna elements are required to be arranged in a certain manner to form an array antenna.
Evenly spaced array antennas have gained extensive research and application due to the ease of mathematical manipulation and ease of assembly of the array structure. However, there are two serious drawbacks to an evenly spaced antenna array: first, to ensure that no grating lobes occur inside the visible region, the spacing between adjacent array elements of a uniform antenna array cannot be greater than half a wavelength. Furthermore, when the antenna array is required to have high gain and high resolution, the aperture length of the array must be large, and the uniform spacing requires a large number of antenna elements, which makes the antenna system expensive. Second, the main lobe width of the array antenna pattern is inversely proportional to the aperture size, so when a narrower main lobe width is to be achieved, the designed antenna aperture tends to be larger, which also results in increased cost of the array design.
These drawbacks can be effectively avoided if a non-uniformly spaced sparse array is used, while a non-uniformly spaced sparse antenna array can also provide substantial cost savings. The array design is realized by adopting the method of sparsely distributing the antenna array elements on a certain aperture, and higher gain and higher resolution can be obtained by fewer antenna array elements, so that the structure is simplified, the manufacturing cost is reduced, and the sparsely distributed antenna array has important research significance.
The problem of array element position optimization in the sparse antenna array comprehensive problem is a nonlinear optimization problem, and various intelligent optimization algorithms such as a genetic algorithm, a simulated annealing algorithm, a particle swarm algorithm, a cuckoo algorithm and the like are successfully applied to the existing problem. Among the algorithms, the genetic algorithm gets attention of many scholars due to good performance and large optimization space, and simultaneously obtains good effect in the problem of sparse antenna array synthesis, however, the genetic algorithm has many parameters and complex algorithm flow, so that the use difficulty is high and the convergence effect is unstable.
Compared with a genetic algorithm, the water circulation algorithm is proposed by Hadi Eskandar et al in 2012, and as a novel intelligent optimization algorithm, research aiming at the algorithm is relatively less, and related application in a sparse array low side lobe comprehensive problem is lacked.
Disclosure of Invention
The invention aims to provide a sparse antenna array optimization method based on an improved water circulation algorithm, which is low in side lobe level, simple in algorithm, high in convergence speed, good in robustness and good in convergence result.
The technical solution for realizing the invention is as follows: a low sidelobe comprehensive optimization method of a sparse antenna array based on an improved water circulation algorithm is characterized by comprising the following steps:
step 1, establishing a low side lobe comprehensive optimization model of a sparse array, separating array element positions to be optimized, and converting the sparse array comprehensive model into a water circulation optimization problem;
step 2, setting initial parameters required by algorithm simulation, wherein the initial parameters comprise an initial population size, rainfall condition parameters and the maximum iteration times of the algorithm;
step 3, calculating the fitness of all individuals in the initial population, and sorting all individuals in the population according to the fitness to obtain oceans, rivers and streams in the initial state;
step 4, calculating the number of streams connected with the sea by each river;
step 5, realizing the process that part of streams flow into the ocean, updating the positions of the streams according to a stream updating formula, if the solutions of individuals corresponding to the updated positions of the streams are better than those of ocean individuals, exchanging the positions of the streams and the ocean, and if not, not exchanging the positions of the streams and the ocean;
step 6, realizing the process that the stream flows into the river, updating the position of the stream according to a stream updating formula, if the updated stream is superior to the river, exchanging the positions of the stream and the river and jumping to the step 8, otherwise, executing the step 7;
step 7, realizing stream invasion behaviors and generating new stream individuals;
step 8, realizing the process that the river flows into the ocean, updating the position of the river according to a river updating formula, if the corresponding individual of the updated river position is better than the solution of the individual of the ocean, exchanging the position of the river and the position of the ocean, otherwise, not exchanging;
step 9, judging whether the evaporation condition is met, and if the evaporation condition is met, executing a rainfall process;
step 10, updating parameters and judging whether the preset maximum iteration times are reached, if so, ending the algorithm and returning to the currently solved optimal solution; and if not, skipping to the step 4, and continuing to execute the algorithm optimizing process.
Compared with the prior art, the invention has the following remarkable advantages: (1) the stream invasion behavior is proposed, and the comprehensive optimization capability of the thin cloth array is enhanced; (2) the algorithm is simpler to realize, and the parameters required to be manually set in the simulation are fewer; (3) the sparse array side lobe level obtained by algorithm synthesis is lower, and the comprehensive effect is better; (4) through multiple simulation tests on the algorithm, the algorithm is verified to have better robustness in solving the multivariate problems of sparse array synthesis, and the problem of poor robustness caused by early maturity of other algorithms is avoided.
Drawings
Fig. 1 is a schematic flow chart of the sparse antenna array low sidelobe comprehensive optimization method based on the improved water circulation algorithm.
FIG. 2 is a graph of the convergence of multiple simulations of a genetic algorithm in an embodiment of the present invention.
FIG. 3 is a graph illustrating the convergence of the modified water circulation algorithm in an embodiment of the present invention.
FIG. 4 is a schematic diagram of a scrim array in an embodiment of the present invention.
FIG. 5 is a diagram illustrating a position distribution of the thin cloth array elements in an embodiment of the present invention.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings.
With reference to fig. 1, the invention relates to a sparse antenna array low sidelobe comprehensive optimization method based on an improved water circulation algorithm, which comprises the following steps:
step 1, establishing a sparse array antenna low side lobe comprehensive optimization model, separating array element positions to be optimized, and converting the sparse array comprehensive model into a water circulation optimization problem, wherein the method specifically comprises the following steps:
setting the aperture size of the antenna array to be L, wherein the array actually comprises N antenna array elements, and the distance between adjacent array elements is unequal, so that the directional diagram of the uneven array is as follows:
Figure BDA0002327146490000031
where λ is the operating wavelength, dmIs the distance of the m-th array element from the first array element, theta0The main bit beam points to the direction;
in order to guarantee that the aperture size of the array is unchanged, array elements must be placed at the two ends of the array, and then the requirements are met:
Figure BDA0002327146490000032
in order to avoid grating lobes, the distance between adjacent array elements in the array needs to satisfy:
min{di-dj}≥dc,1≤j＜i≤N (3)
wherein, min is [.]For minimum calculation, dcThe minimum distance interval between two adjacent array elements is represented, and the minimum distance interval is generally half the wavelength;
further, in order to reduce the search space of the array element position solution, the distance d between the ith array element and the first array element is usediThe resolution is carried out to obtain:
Figure BDA0002327146490000033
wherein x is1≤x2≤…≤xN；
The binding formula (3) can be obtained:
x1≤x2≤…≤xN∈[0,L-(N-1)dc](5)
spacing array elements in the array by d through the operationiIndirect conversion to xiSearch space from [0, L simultaneously]Reduced to [0, L- (N-1) dc]；
Because the aim of the sparse antenna array low side lobe comprehensive optimization problem is to reduce the peak side lobe level, the algorithm fitness function is defined as follows:
Figure BDA0002327146490000041
wherein x { (x)1,x2,…,xN)|x1≤x2≤…≤xN∈[0,L-(N-1)dc]Is a set of feasible solutions of equation (6), FmaxTo represent the main lobe peak level, max.]For maximum operation, PSLL is the peak side lobe level. Therefore, the sparse array low sidelobe problem is converted into the problem that the array element position is optimized by optimizing x, and the peak sidelobe level is reduced.
Step 2, setting initial parameters required by algorithm simulation, including initial population size, rainfall condition parameters and algorithm maximum iteration times, as follows:
setting the problem to be solved as an N-dimensional variable problem, and the number of the solved population as NpopIf the maximum number of simulation iterations is Max, then an N may be formed according to the upper and lower bounds of the problempopX N initial matrix X:
X＝X1+rand×(X2-X1) (7)
wherein, X1And X2Representing the upper and lower bounds of the variable sought, respectively, and rand being uniformly distributed between 0 and 1Random numbers, where each row in the matrix represents an individual. According to the analysis in step 1, the lower bound X of the variable is obtained1Is a zero matrix, X2All the element values in the formula are L- (N-1) dcAnd (4) matrix.
Step 3, calculating the fitness of all individuals in the initial population, and sequencing and classifying all the individuals in the population according to the fitness to obtain oceans, rivers and streams in the initial state, wherein the method specifically comprises the following steps:
calculating a fitness function value corresponding to each individual, wherein the calculation formula is as follows:
Figure BDA0002327146490000042
wherein f is a fitness function,
Figure BDA0002327146490000043
is the jth variable component in the ith individual;
selecting the sea with the best fitness function value, the better individuals as rivers and the rest as streams, and dividing the results as follows:
Figure BDA0002327146490000051
step 4, calculating the number of streams connected with the sea by each river, which is specifically as follows:
each stream flows to a river or a sea, and the amount of the stream flowing into each river and the sea is different due to different flow rates of the river and the sea, and the calculation formula is as follows:
Figure BDA0002327146490000052
Figure BDA0002327146490000053
wherein NSnThe number of streams flowing into a river or ocean, round [.]For rounding-down。
Step 5, realizing the process that part of streams flow into the ocean, updating the stream positions according to a stream updating formula, exchanging the stream and the ocean positions if the updated stream positions correspond to individuals with better solutions than ocean individuals, or not exchanging, and specifically comprising the following steps:
the method realizes the updating process of the stream position to the sea position, and finds a more optimal solution close to the sea, and the specific updating expression is as follows:
Figure BDA0002327146490000054
where C is a constant greater than 1, typically set to 2, and rand is a function satisfying a uniform distribution for generating random numbers between 0 and 1; and if the updated stream solution is superior to the sea solution, exchanging the positions of the stream and the sea, and taking the updated stream as a new sea.
Step 6, realizing the process that the stream flows into the river, updating the position of the stream according to a stream updating formula, exchanging the positions of the stream and the river and jumping to step 8 if the updated stream is superior to the river, otherwise, executing step 7, specifically as follows:
the method realizes the process of updating the stream position to the river position, and finds a more optimal solution close to the river, and the specific updating expression is as follows:
Figure BDA0002327146490000055
where C is a constant greater than 1, typically set to 2, and rand is a function satisfying a uniform distribution for generating random numbers between 0 and 1; and if the updated stream solution is superior to the river solution, exchanging the positions between the stream and the river, taking the updated stream as a new river and jumping to the step 8, otherwise, executing the step 7.
Step 7, realizing stream invasion behaviors and generating new stream individuals, wherein the stream invasion behaviors are as follows:
realizes the stream invasion process and generates [0,1 ]]Coe, and randomly selecting any one stream from the stream set
Figure BDA0002327146490000061
The stream is compared with the current stream individuals
Figure BDA0002327146490000062
Updating according to equation (14) to generate a new stream:
Figure BDA0002327146490000063
step 8, realizing the process that the river flows into the ocean, updating the position of the river according to a river updating formula, if the corresponding individual of the updated river position is better than the solution of the individual of the ocean, exchanging the position of the river and the position of the ocean, otherwise, not exchanging, specifically as follows:
the method realizes the process of updating the river position to the sea position, and finds a more optimal solution close to the sea, and the specific updating expression is as follows:
Figure BDA0002327146490000064
where C is a constant greater than 1, typically set to 2, and rand is a function satisfying a uniform distribution for generating random numbers between 0 and 1. And if the updated stream solution is better than the river solution, exchanging the positions between the stream and the river, and taking the updated stream as a new river.
Step 9, judging whether the evaporation condition is met, and if so, executing the rainfall process, specifically as follows:
rainfall is generally divided into two types according to the position of the rainfall: a rainfall is located in a stream or river area for creating a new solution to the problem; the other is located in the sea field and is mainly used for local optimization in a small range. Generally, we judge whether the conditions for generating rainfall are met by the following conditions:
Figure BDA0002327146490000065
Figure BDA0002327146490000066
wherein NS1For the number of streams flowing into the sea, rand is a function satisfying a uniform distribution for generating random numbers between 0 and 1, dmax(t) a threshold value for controlling the size of the sea position search area in the tth iteration is usually a small positive number;
if the formula (16) is satisfied, performing a rainfall process near the stream, wherein the rainfall operation is as follows:
Figure BDA0002327146490000067
if the formula (17) is satisfied, performing a rainfall process near the sea, wherein the rainfall operation is as follows:
Figure BDA0002327146490000068
where μ is a fixed value, typically set to 0.1.
Step 10, updating parameters and judging whether the preset maximum iteration times are reached, if so, ending the algorithm and returning to the currently solved optimal solution; if not, skipping to the step 4, and continuing to execute the algorithm optimizing process, specifically as follows:
for parameter d in rainfall conditionmaxUpdating is carried out, and the updating expression is as follows:
Figure BDA0002327146490000071
wherein d ismax(t +1) is a threshold value for controlling the size of the search area in the t +1 th iteration.
Example 1
1. Setting simulation parameters: setting the aperture size of the linear array as 50 lambda and the array beam direction as theta0＝0oThe number of array elements in the sparse array is 25, and the population number is N pop50, 500 maximum iterations Max, 4 river and ocean total, and d variablemaxIs an initial value of 10-5。
2. Simulation content: according to the setting, the sparse array is integrated with the goal of reducing peak sidelobe level by utilizing an improved water circulation algorithm. For comparison, parameters required by genetic algorithm simulation are set, the maximum iteration number is G500, and the cross probability is Pc0.8, the mutation probability is PmThe number of initial population P is 0.05 and 50. And respectively carrying out ten times of simulation on the two algorithms to respectively obtain the worst result, the optimal result and the average result. It can be seen from fig. 2 that the genetic algorithm is early trapped in local optimization, while the improved water circulation algorithm in fig. 3 approaches to the optimal solution all the time under the optimal condition, and the convergence result is better than the genetic algorithm, and the worst result and average obtained by the improved water circulation algorithm are better than the genetic algorithm, so that a lower peak side lobe level can be obtained. Fig. 4 shows the array element distribution obtained under the optimal condition of the improved water circulation algorithm, and fig. 5 shows the corresponding array directional diagram obtained at the lowest peak side lobe level obtained by the improved water circulation algorithm.

Claims (10)

1. A low sidelobe comprehensive optimization method of a sparse antenna array based on an improved water circulation algorithm is characterized by comprising the following steps:
step 1, establishing a low side lobe comprehensive optimization model of a sparse array, separating array element positions to be optimized, and converting the sparse array comprehensive model into a water circulation optimization problem;
step 2, setting initial parameters required by algorithm simulation, wherein the initial parameters comprise an initial population size, rainfall condition parameters and the maximum iteration times of the algorithm;
step 3, calculating the fitness of all individuals in the initial population, and sorting all individuals in the population according to the fitness to obtain oceans, rivers and streams in the initial state;
step 4, calculating the number of streams connected with the sea by each river;
step 5, realizing the process that part of streams flow into the ocean, updating the positions of the streams according to a stream updating formula, if the solutions of individuals corresponding to the updated positions of the streams are better than those of ocean individuals, exchanging the positions of the streams and the ocean, and if not, not exchanging the positions of the streams and the ocean;
step 6, realizing the process that the stream flows into the river, updating the position of the stream according to a stream updating formula, if the updated stream is superior to the river, exchanging the positions of the stream and the river and jumping to the step 8, otherwise, executing the step 7;
step 7, realizing stream invasion behaviors and generating new stream individuals;
step 8, realizing the process that the river flows into the ocean, updating the position of the river according to a river updating formula, if the corresponding individual of the updated river position is better than the solution of the individual of the ocean, exchanging the position of the river and the position of the ocean, otherwise, not exchanging;
step 9, judging whether the evaporation condition is met, and if the evaporation condition is met, executing a rainfall process;
step 10, updating parameters and judging whether the preset maximum iteration times are reached, if so, ending the algorithm and returning to the currently solved optimal solution; and if not, skipping to the step 4, and continuing to execute the algorithm optimizing process.
2. The method for comprehensively optimizing the low sidelobe of the sparse antenna array based on the improved water circulation algorithm according to claim 1, wherein the step 1 is to establish a comprehensive optimization model of the low sidelobe of the sparse antenna array, separate the positions of array elements to be optimized, and convert the comprehensive model of the sparse antenna array into a water circulation optimization problem, and specifically comprises the following steps:
setting the aperture size of the antenna array to be L, wherein the array actually comprises N antenna array elements, and the distance between adjacent array elements is unequal, so that the directional diagram of the uneven array is as follows:
Figure FDA0002327146480000011
where λ is the operating wavelength, dmIs the distance of the m-th array element from the first array element, theta0The main bit beam points to the direction;
in order to guarantee that the aperture size of the array is unchanged, array elements must be placed at the two ends of the array, and then the requirements are met:
Figure FDA0002327146480000012
in order to avoid grating lobes, the distance between adjacent array elements in the array needs to satisfy:
min{di-dj}≥dc,1≤j＜i≤N (3)
wherein, min is [.]For minimum calculation, dcRepresenting the minimum distance interval between two adjacent array elements, and taking the minimum distance interval as half wavelength;
in order to reduce the search space of the position solution of the array element, the distance d between the ith array element and the first array element is usediSplitting to obtain:
Figure FDA0002327146480000021
wherein x is1≤x2≤…≤xN；
The combination formula (3) is as follows:
x1≤x2≤…≤xN∈[0,L-(N-1)dc](5)
spacing array elements in the array by d through the operationiIndirect conversion to xiSearch space from [0, L simultaneously]Reduced to [0, L- (N-1) dc]；
Because the aim of the sparse antenna array low side lobe comprehensive optimization problem is to reduce the peak side lobe level, the algorithm fitness function is defined as follows:
Figure FDA0002327146480000022
wherein x { (x)1,x2,…,xN)|x1≤x2≤…≤xN∈[0,L-(N-1)dc]Is a set of feasible solutions of equation (6), FmaxTo represent the main lobe peak level, max.]For maximum value calculation, PSLL is peak side lobe level;
therefore, the problem of sparse array low sidelobe is converted into the problem of optimizing array element positions by optimizing x, and further the peak sidelobe level is reduced;
step 2, setting initial parameters required by algorithm simulation, including initial population size, rainfall condition parameters and algorithm maximum iteration times, specifically as follows:
setting the problem to be solved as an N-dimensional variable problem, and the number of the solved population as NpopIf the simulation maximum iteration number is Max, then an N is formed according to the upper and lower bounds of the problempopX N initial matrix X:
X＝X1+rand×(X2-X1) (7)
wherein, X1And X2Respectively representing the upper bound and the lower bound of the solved variable, rand is a random number uniformly distributed between 0 and 1, and each row in the matrix represents an individual;
according to the analysis in the step 1, the lower bound X of the variable is obtained1Is a zero matrix, X2All the element values in the formula are L- (N-1) dcAnd (4) matrix.
3. The method for comprehensively optimizing the low sidelobe of the sparse antenna array based on the improved water circulation algorithm according to claim 2, wherein the fitness of all individuals in the initial population is calculated in step 3, and all individuals in the population are sorted according to the fitness to obtain oceans, rivers and streams in the initial state, and the method is specifically as follows:
calculating a fitness function value corresponding to each individual, wherein the calculation formula is as follows:
Figure FDA0002327146480000031
wherein f is a fitness function,
Figure FDA0002327146480000032
is the jth variable component in the ith individual;
selecting the sea with the best fitness function value, selecting the better individual as River and selecting the rest as Stream River, wherein the division results are as follows:
Figure FDA0002327146480000033
4. the method for comprehensively optimizing the low sidelobe of the sparse antenna array based on the improved water circulation algorithm of claim 2, wherein the number of streams connecting each river and the sea is calculated in step 4, and specifically as follows:
each stream flows to a river or a sea, and the amount of the stream flowing into each river and the sea is different due to different flow rates of the river and the sea, and the calculation formula is as follows:
Figure FDA0002327146480000034
Figure FDA0002327146480000035
wherein NSnThe number of streams flowing into a river or ocean, round [.]Is a rounding down operation.
5. The method for comprehensively optimizing the low sidelobe of the sparse antenna array based on the improved water circulation algorithm of claim 2, wherein in the step 5, the process that part of streams flow into the ocean is realized, the stream positions are updated according to a stream updating formula, if the updated stream positions correspond to individuals and are better than the solutions of ocean individuals, the stream and the ocean positions are exchanged, otherwise, the exchange is not performed, and the method is specifically as follows:
the method realizes the updating process of the stream position to the sea position, and finds a more optimal solution close to the sea, and the specific updating expression is as follows:
Figure FDA0002327146480000041
wherein C is a constant greater than 1; rand is a function satisfying uniform distribution for generating random numbers between 0 and 1;
and if the updated stream solution is superior to the sea solution, exchanging the positions of the stream and the sea, and taking the updated stream as a new sea.
6. The method for comprehensively optimizing the low sidelobe of the sparse antenna array based on the improved water circulation algorithm of claim 2, wherein the step 6 is to realize the stream flowing into the river, update the stream position according to the stream updating formula, exchange the stream and the river position and jump to the step 8 if the updated stream is better than the river, otherwise execute the step 7 specifically as follows:
Figure FDA0002327146480000042
wherein C is a constant greater than 1; rand is a function satisfying uniform distribution for generating random numbers between 0 and 1;
and if the updated stream solution is superior to the river solution, exchanging the positions between the stream and the river, taking the updated stream as a new river and jumping to the step 8, otherwise, executing the step 7.
7. The sparse antenna array low sidelobe comprehensive optimization method based on the improved water circulation algorithm of claim 2, wherein the step 7 of realizing the stream invasion behavior and generating new stream individuals is as follows:
realizes the stream invasion process and generates [0,1 ]]Coe, and randomly selecting any one stream from the stream set
Figure FDA0002327146480000043
The stream is compared with the current stream individuals
Figure FDA0002327146480000044
Updating according to equation (14) to generate a new stream:
Figure FDA0002327146480000045
8. the comprehensive optimization method for the low sidelobe of the sparse antenna array based on the improved water circulation algorithm of claim 2, wherein the step 8 is to realize the river inflow ocean process, update the river position according to a river updating formula, if the updated river position corresponding individual is better than the solution of the ocean individual, exchange the river position and the ocean position, otherwise, do not exchange, specifically as follows:
the method realizes the process of updating the river position to the sea position, and finds a more optimal solution close to the sea, and the specific updating expression is as follows:
Figure FDA0002327146480000051
wherein C is a constant greater than 1; rand is a function satisfying uniform distribution for generating random numbers between 0 and 1;
and if the updated stream solution is better than the river solution, exchanging the positions between the stream and the river, and taking the updated stream as a new river.
9. The comprehensive optimization method for the low sidelobe of the sparse antenna array based on the improved water circulation algorithm as claimed in claim 2, wherein the step 9 of judging whether the evaporation condition is met or not, if so, executing the rainfall process, specifically as follows:
the rainfall is divided into two types according to the different rainfall positions: a rainfall is located in a stream or river area for creating a new solution to the problem; the other is positioned in the sea field and used for local optimization;
judging whether the conditions of rainfall generation are met or not by adopting the following conditions:
Figure FDA0002327146480000052
Figure FDA0002327146480000053
wherein NS1Number of streams flowing into the sea; rand is a function satisfying uniform distribution for generating random numbers between 0 and 1; dmax(t) controlling the size threshold of the sea position search area in the t-th iteration, wherein the value is positive;
if the formula (16) is satisfied, performing a rainfall process in the stream field, wherein the rainfall operation is as follows:
Figure FDA0002327146480000054
if the formula (17) is satisfied, performing a rainfall process in the sea area, wherein the rainfall operation is as follows:
Figure FDA0002327146480000055
where μ is a fixed value and is set to 0.1.
10. The comprehensive optimization method for the low sidelobe of the sparse antenna array based on the improved water circulation algorithm as claimed in claim 2, wherein the parameters are updated and whether the preset maximum iteration times are reached is judged in step 10, and if the preset maximum iteration times are reached, the algorithm is ended and the currently solved optimal solution is returned; if not, skipping to the step 4, and continuing to execute the algorithm optimizing process, specifically as follows:
for parameter d in rainfall conditionmaxUpdating is carried out, and the updating expression is as follows:
Figure FDA0002327146480000061
wherein d ismax(t +1) is the size of the control search area in the t +1 th iterationAnd (4) a threshold value.
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CN112307588A (en) * 2020-11-10 2021-02-02 西安工程大学 Non-uniform parabolic array antenna design method
CN113937513A (en) * 2021-11-25 2022-01-14 清华大学 Two-dimensional sparse antenna array design method, device, equipment and medium

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CN112016209A (en) * 2020-08-28 2020-12-01 哈尔滨工业大学 Distributed nested circular array comprehensive array arrangement method based on ant colony algorithm
CN112016209B (en) * 2020-08-28 2021-09-03 哈尔滨工业大学 Distributed nested circular array comprehensive array arrangement method based on ant colony algorithm
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