阅读说明：本技术 基于自适应二进制粒子群遗传算法的混沌序列抗干扰波形设计方法 (Chaos sequence anti-interference waveform design method based on self-adaptive binary particle swarm genetic algorithm ) 是由 包敏 王咫毅 郭亮 李亚超 邢孟道 史林 于 2020-12-24 设计创作，主要内容包括：本发明公开了一种基于自适应二进制粒子群遗传算法的混沌序列抗干扰波形设计方法,包括：随机产生一组二进制编码组成初始种群,将所述二进制编码转化为十进制并归一化后作为混沌序列的初始值,并产生一组随机数作为所述初始种群中个体的速度；利用具有自适应惯性权重的二进制粒子群算法对种群中的父代个体进行成熟操作；利用自适应二进制遗传算法对种群中的染色体进行交叉和变异操作；进行精英保留操作；继续进化,当进化代数达到设定的最大进化代数时,则以当前代种群的染色体作为产生混沌序列的初始值。该方法具有局部搜索和全局搜索能力,能够在维持种群多样性的条件下提高搜索效率,产生抗干扰性能较好的混沌序列。(The invention discloses a chaotic sequence anti-interference waveform design method based on a self-adaptive binary particle swarm genetic algorithm, which comprises the following steps of: randomly generating a group of binary codes to form an initial population, converting the binary codes into decimal numbers and normalizing the decimal numbers to be used as initial values of a chaotic sequence, and generating a group of random numbers to be used as the speeds of individuals in the initial population; performing maturation operation on parent individuals in the population by using a binary particle swarm algorithm with self-adaptive inertial weight; carrying out cross and variation operation on chromosomes in the population by using a self-adaptive binary genetic algorithm; performing elite reservation operation; and continuing to evolve, and when the evolution algebra reaches the set maximum evolution algebra, taking the chromosomes of the current generation population as the initial values for generating the chaotic sequences. The method has the capability of local search and global search, can improve the search efficiency under the condition of maintaining the population diversity, and generates the chaotic sequence with better anti-interference performance.)

1. A chaotic sequence anti-interference waveform design method based on a self-adaptive binary particle swarm genetic algorithm is characterized by comprising the following steps of:

s1: randomly generating a group of binary codes to form an initial population, converting the binary codes into decimal numbers and normalizing the decimal numbers to be used as initial values of a chaotic sequence, and generating a group of random numbers to be used as the speeds of individuals in the initial population;

s2: calculating the fitness of individuals in the initial population according to a fitness function;

s3: performing maturation operation on parent individuals in the population by using a binary particle swarm algorithm with self-adaptive inertial weight;

s4: performing cross operation and mutation operation on chromosomes in the population by using a self-adaptive binary genetic algorithm;

s5: calculating the fitness value of each individual after variation and the maximum value of the fitness in the population, and performing elite reservation operation to obtain a next generation population;

s6: and repeating the steps S2-S5, continuing to evolve by utilizing the next generation population, stopping the evolution when the evolution generation reaches the set maximum evolution generation, and taking the chromosome of the current generation population as an initial value for generating the chaotic sequence.

2. The method for designing the chaotic sequence anti-interference waveform based on the adaptive binary particle swarm genetic algorithm according to claim 1, wherein the S1 comprises:

s11: initializing parameters: setting an initial value G of an algebra counter to be 1, a maximum evolution algebra G, an evolution early-stage algebra G', a population size Popsize and a cross probability coefficient k₁、k₂Coefficient of variation probability k₃、k₄Learning factor c₁、c₂Number of populations N_gAdaptive maximum value w of inertial weight_maxAnd a minimum value w_minAnd a particle velocity limit v_max、v_min；

S12: randomly generating a group of binary codes with the size of Popsize to form an initial population P (0), converting the binary codes into decimal, normalizing the decimal codes to be used as an initial value of a chaotic sequence, and performing normalization on an interval [ v ] to obtain a binary code with the size of Popsize_min,v_max]Generating a set of random numbers of size Popsize as the velocity of individuals in the initial population;

s13: use ofAs chromosomes, wherein i is more than or equal to 1 and less than or equal to Popsize,as binary code corresponding to the initial value, f_iIs the fitness of the chromosome;

s14: generating chaos sequences with the length of 2N, wherein the first N are used as the coding sequences of a first period phase coding signal, the last N are used as the coding sequences of a second period phase coding signal, and generating echo signals:

wherein, s (t, X)_i) Being phase-encoded signals of chaotic sequence, X_iIs a chaotic sequence, s_rn(t,X′_i) Phase-encoded echo signal, X ', of an nth periodic chaotic sequence'_iFor chaotic sequences with distance occlusion, f₀Is a carrier frequency, f_dIs the doppler frequency.

3. The method for designing the chaotic sequence anti-interference waveform based on the adaptive binary particle swarm genetic algorithm according to claim 2, wherein the S2 comprises:

use ofCalculating the fitness of the initial value in the initial population as a fitness function and recording the maximum value f of the fitness in the population_maxAnd the corresponding chromosome Ch_maxWherein s is_r1(t,X′_i) And s_r2(t,X′_i) Respectively representing a first pulse-period echo signal and a second pulse-period echo signal, R(s)_r2(t,X′_i),s_r1(t,X′_i) Is a value of a cross-correlation function of the first pulse-period echo signal and the second pulse-period echo signal, R(s)_r2(t,X′_i),s_r2(t,X′_i) ) is the autocorrelation function value of the echo signal of the second pulse period.

4. The method for designing the chaotic sequence anti-interference waveform based on the adaptive binary particle swarm genetic algorithm according to claim 1, wherein the S3 comprises:

judging the size relationship between a current algebra counter G and an initially set evolutionary early algebra G ', and if G is less than G', updating the speed and the position of an individual by using a binary particle swarm algorithm with self-adaptive inertial weight; if G ═ G', making the individual extreme value of the individual as the individual of the present generation population; and if G is larger than G', generating the initial value of the next generation population according to the proportion of the fitness value of each individual in the total fitness value sum of the whole population.

5. The method for designing the chaotic sequence anti-interference waveform based on the adaptive binary particle swarm genetic algorithm according to claim 4, wherein in the process of updating the speed and the position of an individual by using the binary particle swarm algorithm with adaptive inertial weight, the evolution formula of the binary particle swarm algorithm with adaptive inertial weight is as follows:

wherein v is_id、x_idD-dimensional components, c, of the i-th individual's velocity and position, respectively₁And c₂Two non-negative learning factors, pos_idAnd pos_gdAn individual extremum and a global extremum, respectively, and rand () is [0, 1%]W is the adaptive inertial weight, w_minAnd w_maxRespectively representing the minimum and maximum values of w, f_maxIs the maximum fitness value, f, of all individuals in the population_avgIs the average fitness value of all individuals in the population, f is the fitness value of the current individual,

6. the method for designing the chaotic sequence anti-interference waveform based on the adaptive binary particle swarm genetic algorithm according to claim 4, wherein the S4 comprises:

traversing chromosomes in the population, finding out different positions of two chromosome genes, setting a set of the different positions of the genes as Z, and setting the number of elements in the set as N_Z；

Judging whether the set Z is an empty set, if so, not performing cross operation, if not, calculating the self-adaptive cross probability of the two chromosomes, judging whether to perform cross operation according to the self-adaptive cross probability, and if so, generating a cross operation smaller than or equal to N_ZThe random number is used as a cross digit to carry out cross operation;

traversing chromosomes in the population, calculating self-adaptive mutation probability, judging whether mutation operation is performed according to the self-adaptive mutation probability, and if the mutation operation is performed, randomly selecting one bit from the current chromosome binary code for mutation.

7. The method for designing the chaotic sequence anti-interference waveform based on the adaptive binary particle swarm genetic algorithm according to claim 4, wherein the crossover operator and the mutation operator of the adaptive binary genetic algorithm are as follows:

wherein k is₁And k₂Is a cross probability coefficient, k₃And k₄Is the coefficient of variation probability, f_maxIs the maximum value of fitness in the population, f_avgIs the average value of fitness in the population, f' is the larger fitness value of the two crossed individuals, and f is the fitness value of the variant individual.

8. The method for designing the chaotic sequence anti-interference waveform based on the adaptive binary particle swarm genetic algorithm according to any one of claims 1 to 7, wherein the S5 comprises:

calculating the fitness value of each individual after the variation operation and the maximum value f 'of the fitness in the population'_maxIf f'_max＜f_maxReplacing the individual with the largest fitness value before the maturation operation with the individual with the smallest fitness value in the population after the mutation operation, wherein f_maxRepresenting the maximum fitness value among all individuals in the initial population.

Technical Field

The invention belongs to the technical field of signal processing, and particularly relates to a chaotic sequence anti-interference waveform design method based on a self-adaptive binary particle swarm genetic algorithm.

Background

The radar is an electronic system, and can acquire the position of a target and other information by transmitting and receiving electromagnetic waves to realize all-weather detection, identification and tracking of the target all day long. With the increasing complexity of electromagnetic environments in battlefields and the development of radar interception technologies, the performance and the viability of radar detection targets face severe tests, and therefore higher and higher requirements are provided for the interception resistance, the interference resistance, the resolution, the working distance and the measurement accuracy of radars. Therefore, the designed waveform has anti-interception performance and plays an important role in low interception performance of the radar. Under the condition of large time-bandwidth product, the phase coding signal has larger main-side lobe ratio, good pulse pressure performance and the fuzzy graph is of a tack type and receives more and more extensive attention, and because the signal waveform has randomness and is easy to generate agility, the anti-interception, anti-interference and anti-stealth capabilities of the radar system can be effectively improved.

For a phase-coded pulse compression radar system, the code sequence of a phase-coded signal has a great influence on the radar performance, so that more and more attention is paid to the use of a series of algorithms for waveform design to obtain a phase-coded signal with superior performance. In the case of short codes, a code pattern meeting the requirement can be obtained by adopting a traversal search mode. However, when the code is long, the efficiency of the mode of traversing the search can be greatly reduced. Therefore, the method for generating the code sequence of the phase code signal by the optimization search method so as to improve the anti-interference performance of the radar signal becomes a research hotspot.

In 2007, Li Ming provides an orthogonal phase coding waveform design based on a hybrid genetic algorithm, the algorithm adopts a method of combining a simulated genetic algorithm and a genetic algorithm, the specific process is to randomly generate a group of coding sequences as an initial population, and after searching, crossing, mutating and the like are carried out on the population, a group of coding sequences with better orthogonality is generated. However, the method has the main disadvantages of low algorithm efficiency, long optimization time consumption, longer iteration time for solving the coding sequence and poor orthogonality when the number of transmitted waveforms is large, and is not suitable for designing waveforms with large number of waveforms or large number of coding bits. In 2012, the chaos sequence with good randomness, autocorrelation and cross-correlation properties is used as a coding sequence by the cattle rising sun and the like, and random optimization is not needed in the method, so that the method has obvious advantage in the aspect of algorithm efficiency, and any number of orthogonal waveforms can be designed. However, the method is sensitive to initial values, and the difference of the cross-correlation normalization peak values of the generated phase coding signals can reach more than 5dB due to the different initial values.

Disclosure of Invention

In order to solve the problems in the prior art, the invention provides a chaotic sequence anti-interference waveform design method based on a self-adaptive binary particle swarm genetic algorithm. The technical problem to be solved by the invention is realized by the following technical scheme:

the invention provides a chaotic sequence anti-interference waveform design method based on a self-adaptive binary particle swarm genetic algorithm, which comprises the following steps of:

s1: randomly generating a group of binary codes to form an initial population, converting the binary codes into decimal numbers and normalizing the decimal numbers to be used as initial values of a chaotic sequence, and generating a group of random numbers to be used as the speeds of individuals in the initial population;

s2: calculating the fitness of individuals in the initial population according to a fitness function;

s3: performing maturation operation on parent individuals in the population by using a binary particle swarm algorithm with self-adaptive inertial weight;

s4: performing cross operation and mutation operation on chromosomes in the population by using a self-adaptive binary genetic algorithm;

s5: calculating the fitness value of each individual after variation and the maximum value of the fitness in the population, and performing elite reservation operation to obtain a next generation population;

s6: and repeating the steps S2-S5, continuing to evolve by utilizing the next generation population, stopping the evolution when the evolution generation reaches the set maximum evolution generation, and taking the chromosome of the current generation population as an initial value for generating the chaotic sequence.

In an embodiment of the present invention, the S1 includes:

s11: initializing parameters: setting an initial value G of an algebra counter to be 1, a maximum evolution algebra G, an evolution early-stage algebra G', a population size Popsize and a cross probability coefficient k₁、k₂Coefficient of variation probability k₃、k₄Learning factor c₁、c₂Number of populations N_gMaximum and minimum values w of adaptive inertial weight_min、w_maxAnd a particle velocity limit v_max、v_min；

S12: randomly generating a group of binary codes with the size of Popsize to form an initial population P (0), converting the binary codes into decimal, normalizing the decimal codes to be used as an initial value of a chaotic sequence, and performing normalization on an interval [ v ] to obtain a binary code with the size of Popsize_min,v_max]Generating a set of random numbers of size Popsize as the velocity of individuals in the initial population;

s13: use ofAs chromosomes, wherein i is more than or equal to 1 and less than or equal to Popsize,as binary code corresponding to the initial value, f_iIs the fitness of the chromosome;

s14: generating chaos sequences with the length of 2N, wherein the first N are used as the coding sequences of a first period phase coding signal, the last N are used as the coding sequences of a second period phase coding signal, and generating echo signals:

wherein, s (t, X)_i) Being phase-encoded signals of chaotic sequence, X_iIs a chaotic sequence, s_rn(t,X’_i) Phase-encoded echo signal, X ', of an nth periodic chaotic sequence'_iFor chaotic sequences with distance occlusion, f₀Is a carrier frequency, f_dIs the doppler frequency.

In an embodiment of the present invention, the S2 includes:

use ofCalculating the fitness of the initial value in the initial population as a fitness function and recording the maximum value f of the fitness in the population_maxAnd the corresponding chromosome Ch_maxWherein s is_r1(t,X’_i) And s_r2(t,X’_i) Respectively representing a first pulse-period echo signal and a second pulse-period echo signal, R(s)_r2(t,X’_i),s_r1(t,X’_i) Is a value of a cross-correlation function of the first pulse-period echo signal and the second pulse-period echo signal, R(s)_r2(t,X’_i),s_r2(t,X’_i) ) is the autocorrelation function value of the echo signal for the second pulse period.

In an embodiment of the present invention, the S3 includes:

judging the size relationship between a current algebra counter G and an initially set evolutionary early algebra G ', and if G is less than G', updating the speed and the position of an individual by using a binary particle swarm algorithm with self-adaptive inertial weight; if G ═ G', making the individual extreme value of the individual as the individual of the present generation population; and if G is larger than G', generating the initial value of the next generation population according to the proportion of the fitness value of each individual in the total fitness value sum of the whole population.

In one embodiment of the present invention, in the updating of the speed and the position of the individual by using the binary particle swarm algorithm with adaptive inertial weight, the evolutionary formula of the binary particle swarm algorithm with adaptive inertial weight is as follows:

wherein v is_id、x_idD-dimensional components, c, of the i-th individual's velocity and position, respectively₁And c₂Two non-negative learning factors, pos_idAnd pos_gdAn individual extremum and a global extremum, respectively, and rand () is [0, 1%]W is the adaptive inertial weight, w_minAnd w_maxRespectively representing the minimum and maximum values of w, f_maxIs the maximum fitness value, f, of all individuals in the population_avgIs the average fitness value of all individuals in the population, f is the fitness value of the current individual,

in an embodiment of the present invention, the S4 includes:

traversing chromosomes in the population, finding out different positions of two chromosome genes, setting a set of the different positions of the genes as Z, and setting the number of elements in the set as N_Z；

Judging whether the set Z is an empty set, if so, not performing cross operation, if not, calculating the self-adaptive cross probability of the two chromosomes, judging whether to perform cross operation according to the self-adaptive cross probability, and if so, generating a cross operation smaller than or equal to the sum of the two chromosomesN_ZThe random number is used as a cross digit to carry out cross operation;

traversing chromosomes in the population, calculating self-adaptive mutation probability, judging whether mutation operation is performed according to the self-adaptive mutation probability, and if the mutation operation is performed, randomly selecting one bit from the current chromosome binary code for mutation.

In one embodiment of the present invention, the crossover operator and mutation operator of the adaptive binary genetic algorithm are:

wherein k is₁And k₂To cross probability, k₃And k₄Is the mutation probability, f_maxIs the maximum value of fitness in the population, f_avgIs the average value of fitness in the population, f' is the larger fitness value of the two crossed individuals, and f is the fitness value of the variant individual.

In an embodiment of the present invention, the S5 includes:

calculating the fitness value of each individual after the variation operation and the maximum value f 'of the fitness in the population'_maxIf f is_m'_ax＜f_maxReplacing the individual with the largest fitness value before the maturation operation with the individual with the smallest fitness value in the population after the mutation operation, wherein f_maxRepresenting the maximum fitness value among all individuals in the initial population.

Compared with the prior art, the invention has the beneficial effects that:

the chaotic sequence anti-interference waveform design method based on the self-adaptive binary particle swarm genetic algorithm takes the self-adaptive genetic algorithm as a basic frame on the basis of adopting an elite reservation strategy, introduces the binary particle swarm algorithm using the self-adaptive inertial weight to replace early genetic selection operation, has local search capability and global search capability, is suitable for solving the problem of combination optimization of chaotic sequence anti-interference waveform design, and improves the search efficiency under the condition of maintaining the diversity of the population. Simulation results show that the method can still converge on a high-quality solution with higher probability when the code length of the chaotic sequence is longer, and the anti-interference performance of the waveform obtained by the anti-interference waveform design method of the chaotic sequence when the code length is longer is effectively improved.

The present invention will be described in further detail with reference to the accompanying drawings and examples.

Drawings

FIG. 1 is a flow chart of a chaotic sequence anti-interference waveform design method based on an adaptive binary particle swarm genetic algorithm according to an embodiment of the present invention;

FIG. 2 is a detailed flowchart of a chaotic sequence anti-interference waveform design method based on an adaptive binary particle swarm genetic algorithm according to an embodiment of the present invention;

FIG. 3 is a schematic diagram of an invalid crossover;

FIG. 4 is a graph of the anti-interference performance results using Logistic chaotic sequences as phase encoding sequences;

FIG. 5a is a graph of the optimal fitness value and the average fitness value of each generation of individuals along with the evolution algebra during the iteration of the adaptive binary particle swarm genetic algorithm;

FIG. 5b is a result diagram of two periodic phase-encoded echo signals generated by using the obtained optimal initial value of the Logistic chaotic sequence after cross-correlation and normalization;

FIG. 6 is a graph of the comparison of the search performance against the interference rejection of a 100-bit Logistic sequence phase-encoded signal using the method and genetic algorithm of an embodiment of the present invention;

FIG. 7 is a graph of the comparison of search performance for interference rejection of 100-bit Logistic sequence phase encoded signals using the method and genetic algorithm of an embodiment of the present invention.

Detailed Description

In order to further explain the technical means and effects of the present invention adopted to achieve the predetermined invention purpose, the following detailed description is made on the chaos sequence anti-interference waveform design method based on the adaptive binary particle swarm genetic algorithm according to the present invention with reference to the accompanying drawings and the detailed implementation manner.

The foregoing and other technical matters, features and effects of the present invention will be apparent from the following detailed description of the embodiments, which is to be read in connection with the accompanying drawings. The technical means and effects of the present invention adopted to achieve the predetermined purpose can be more deeply and specifically understood through the description of the specific embodiments, however, the attached drawings are provided for reference and description only and are not used for limiting the technical scheme of the present invention.

It is noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that an article or device that comprises a list of elements does not include only those elements but may include other elements not expressly listed. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of additional like elements in the article or device comprising the element.

Referring to fig. 1 and fig. 2, fig. 1 is a flow chart of a method for designing an anti-interference waveform of a chaotic sequence based on an adaptive binary particle swarm genetic algorithm according to an embodiment of the present invention; fig. 2 is a detailed flowchart of the chaotic sequence anti-interference waveform design method based on the adaptive binary particle swarm genetic algorithm provided by the embodiment of the invention. The anti-interference waveform design method of the chaotic sequence comprises the following steps:

s1: randomly generating a group of binary codes to form an initial population, converting the binary codes into decimal numbers and normalizing the decimal numbers to be used as initial values of a chaotic sequence, and generating a group of random numbers to be used as the speeds of individuals in the initial population;

the chaotic sequence is a pseudo-random sequence generated by irregular motion in a determined system, and has both determinacy and randomness. The determinacy means that the iterative relationship of the chaotic sequences is determined, the randomness means that different chaotic random sequences can be generated for different initial values, and different chaotic sequences can also be generated by different mapping relationships. By utilizing the initial value sensitivity of chaotic mapping, a plurality of mutually orthogonal sequences can be easily obtained, and each group of sequences corresponds to an initial value and a mapping relation, so that the chaotic sequences have good agility and orthogonality.

Further, the S1 specifically includes:

s11: initializing parameters: setting an initial value G of an algebra counter to be 1, a maximum evolution algebra G and an evolution early-stage algebra G', namely the evolution algebra of genetic selection operation, population size Popsize and a cross probability coefficient k₁、k₂Coefficient of variation probability k₃、k₄Learning factor c₁、c₂Number of populations N_gAnd the maximum and minimum values w of the adaptive inertial weight_min、w_maxThe particle (i.e., the individual in the population) velocity is limited to v_max＝5,v_min＝-5。

S12: population initialization: randomly generating a group of Popsize binary codes to form an initial population P (0), converting the binary codes into decimal numbers, normalizing the decimal numbers to obtain initial values of chaotic sequences, and dividing the initial values into a region [ v ]_min,v_max]Generating a set of random numbers of size Popsize as the velocity of individuals (individual particles) in the initial population;

s13: and (3) encoding: use ofAs chromosome, binary coding the initial value of the chaotic sequence, i.e. converting the binary number into decimal number and normalizing, as the initial value of the chaotic sequence, wherein i is more than or equal to 1 and less than or equal to Popsize,as binary code corresponding to the initial value, f_iIs the fitness of the chromosome.

In this embodiment, the initial value is binary coded, i.e. chromosome Ch_i：

Wherein the content of the first and second substances,is the value of the initial chromosome, f_iIs the fitness of the chromosome. The chromosome is converted into decimal and normalized to be an initial value of a chaotic sequence, and the initial value is generated into X through the Logistic chaotic sequence_i. n-bit binary chromosome structure Ch_i(g) (1. ltoreq. i.ltoreq.Popsize) is P (g), wherein Popsize is the number of individuals in the population.

P(g)＝{Ch_i(g)},i＝1,2,3···,Popsize

S14: generating chaos sequences with the length of 2N, wherein the first N are used as the coding sequences of a first period phase coding signal, the last N are used as the coding sequences of a second period phase coding signal, and generating echo signals:

wherein, s (t, X)_i) Being phase-encoded signals of chaotic sequence, X_iIs a chaotic sequence, s_m(t,X’_i) Phase-encoded echo signal, X ', of an nth periodic chaotic sequence'_iFor chaotic sequence phase-coded echo signals with range occlusion, f₀Is a carrier frequency, f_dIs the doppler frequency.

S2: individual evaluation: and calculating the fitness of the individual initial register value in the initial population according to a fitness function.

In particular, use is made ofCalculating the fitness of the initial value in the initial population as a fitness function and recording the maximum value f of the fitness in the population_maxAnd the corresponding chromosome Ch_maxWherein s is_r1(t,X’_i) And s_r2(t,X’_i) Respectively representing a first pulse-period echo signal and a second pulse-period echo signal, R(s)_r2(t,X’_i),s_r1(t,X’_i) Is a value of a cross-correlation function of the first pulse-period echo signal and the second pulse-period echo signal, R(s)_r2(t,X’_i),s_r2(t,X’_i) ) is the autocorrelation function value of the echo signal for the second pulse period. The obtained fitness f_iThe magnitude is indicative of the interference rejection capability of the phase encoded signal.

And calculating the fitness value of each individual in the population P (g) according to the fitness function formula, and adjusting the fitness value according to the actual condition in order to avoid unreasonable distribution of the fitness value or difficulty in embodying individuality, wherein the adjustment method mainly comprises linear change, power exponent transformation, exponential change, Goldberg linear stretching change and the like. And recording the maximum value f of fitness in the population_maxAnd the corresponding chromosome Ch_max。

S3: and (4) utilizing a binary particle swarm algorithm with self-adaptive inertial weight to mature parent individuals in the population.

Judging the relationship between a current algebra counter G and an originally set algebra G 'at the early stage of evolution, if G is less than G', calculating an individual extreme value and a global extreme value of the particles (namely, individuals in a population), and then updating the speed and the position of the particles (individuals) by adopting a formula with self-adaptive inertia weight; if G ═ G', let the individual extremum of the particles (individuals) as the individuals of the present generation population; if G > G', generating filial generations by adopting selection operation in the traditional adaptive genetic algorithm, specifically, generating the next generation population with a larger proportion of individuals with larger initial value fitness values according to the proportion of the fitness value of each individual in the sum of the whole population fitness values, and therefore selecting the next generation population more easily so as to be directly copied into the next generation individual. In the embodiment, in the early stage of evolution, a binary particle swarm algorithm with adaptive inertial weight is used for maturing parent individuals; in the later period of evolution, individuals who survive the next generation were selected by "roulette".

Specifically, in particle swarm optimization, each particle (i.e., an individual in the population) has a position, which represents the encoding of the particle, and a velocity, which determines the distance and direction of the particle search. All particles are searched based on the particle with the largest current fitness value. And each time the optimal particle is searched, the optimal particle is changed, other particles follow the new optimal particle to search, and the steps are repeated and iterated. At the start of an iteration, each particle initializes its position and velocity in space in a random manner, and in the iterative process, the particle changes its position and velocity in solution space by tracking two extrema, one of which is the optimal position of the individual particle itself in the iterative process, called the individual extrema of the particle, and the other of which is the optimal position of all the particles in the population in the iterative process, called the global extremum.

The evolutionary formula of the particle swarm algorithm is as follows:

wherein v is_id、x_idD-dimensional components of the ith particle velocity and position, respectively, w is the inertial weight, c₁And c₂Two non-negative learning factors that determine the effect of the empirical information of the particle itself and other particles on the particle search trajectory, pos_idAnd pos_gdRand () for individual and global extrema is 0,1]The random number of (2).

Aiming at the problem of discrete space constraint, a binary particle swarm algorithm is proposed, and the difference between the binary particle swarm algorithm and the particle swarm algorithm is as follows: particles are inThe state space can only take 0/1 two values, and each bit of the speed represents the possibility that the corresponding bit of the particle position takes 0/1 value, therefore, in the binary particle swarm optimization, the updating formula of the particle speed is kept unchanged, the position of the particle speed is updated in a probability mapping mode, and the speed is mapped to [0,1 ] by using a sigmoid function]Interval as probability s (v)_id) This probability is the probability that the next position of the particle becomes 1:

the update formula of the particle position is:

among the adjustable parameters of the binary particle swarm algorithm, the inertia weight w is an important parameter because the inertia weight w is used for controlling the global search capability and the local search capability of the algorithm, wherein a larger w enhances the global search capability of the algorithm but weakens the local search capability of the algorithm, and a smaller w is beneficial to enhancing the local search capability of the algorithm but weakens the global search capability of the algorithm. The traditional binary particle swarm algorithm adopts a fixed weight method, namely a fixed inertia weight is used. In the present embodiment, in order to balance the global search capability and the local search capability of the binary particle swarm algorithm, the velocity v_idAdopting self-adaptive inertia weight, and the expression is as follows:

wherein, w_min、w_maxRespectively representing the minimum and maximum values of w, f_maxIs the maximum fitness value of all particles in the population, f_avgIs the average fitness value of all the particles in the particle swarm, and f is the fitness value of the current particle.

According to the expression of the self-adaptive inertia weight, when the fitness value of the particle is larger than the average fitness value, the particle has smaller inertia weight, so that the particle has smaller speed, and the particle is protected from being damaged; conversely, when the fitness value of a particle is less than the average fitness value, then there is a greater inertial weight, so that the particle has a greater velocity, which may tend to better search for a region. Therefore, the adaptive inertia weight can dynamically calculate the inertia weight of each particle according to the state of the whole current particle, so that the searching capability of the algorithm is globally improved.

The selection operation is to generate the population of the next generation according to the proportion of the fitness value of each individual in the total fitness value sum of the whole population. This operation has imitated the law that the fittest survived in nature, and the big individual of fitness value can be directly become next generation individual through duplicating, and the individual that the fitness value is big then can be the most probable by the repeated selection, in the later stage of evolution, this kind of operation is favorable to the quick convergence of algorithm, and in the earlier stage of evolution, this kind of operation can lead to the population diversity to reduce, is unfavorable for the evolution of population, because the father generation individual directly becomes the offspring individual, this individual itself does not change, can reduce the search efficiency of algorithm.

Aiming at the defects, the improved binary particle swarm algorithm with the self-adaptive inertial weight is used for maturing the parent individuals in the early stage of evolution, so that the offspring individuals are generated, the reduction of population diversity caused by directly copying the parent individuals is avoided, the individuals with small fitness values move towards the individuals with large fitness values, and the searching efficiency of the algorithm is effectively improved. However, the randomness of the binary particle swarm algorithm becomes stronger and stronger in the later stage, so that the algorithm is not easy to converge to the global optimal solution, and the selection operation of the self-adaptive genetic algorithm is still adopted to generate filial generation individuals in the later stage of evolution, thereby being beneficial to the rapid convergence of the algorithm. The operation replaces the original selection operation, thereby ensuring that the population can be quickly drawn to the global optimal solution in the early stage of evolution and ensuring that the individuals in the population can be quickly converged in the later stage of evolution.

S4: and performing cross operation and mutation operation on chromosomes in the population by using an adaptive binary genetic algorithm.

Traversing chromosomes in the population by taking 2 as a step length to find out different positions of two chromosome genes, setting a set of the different positions of the genes as Z, and setting the number of elements in the set as N_ZIf the set Z is an empty set, the cross operation is not carried out, otherwise, the self-adaptive cross probability of the two chromosomes is calculated, whether the cross operation is carried out or not is judged according to the cross probability, and if the cross operation is carried out, a result that the number of the chromosomes is less than or equal to N is generated_ZThe random numbers of (2) are interleaved as the number of interleaving bits.

Traversing chromosomes in the population by taking 2 as a step length, calculating self-adaptive mutation probability, judging whether mutation operation is performed or not according to the mutation probability, and randomly selecting one bit in the current chromosome binary code for mutation if the mutation operation is performed.

Specifically, the traditional genetic algorithm adopts a mode of fixing a cross operator and a mutation operator, and the cross probability and the mutation probability of the traditional genetic algorithm cannot reflect the state of evolution, so that random roaming or premature phenomena can be caused. The algorithm for solving the optimization problem should have two capabilities: the method has the advantages that global search capability is realized, namely, a new solution space can be opened up in the process of searching a global optimal solution; the second is local search capability, i.e., the ability to converge on the optimal solution in the region containing the optimal solution. In genetic algorithms, the balance of these two capabilities is represented by the crossover probability P_cAnd the mutation probability P_mDetermined, wherein, the cross probability P_cDetermining the frequency, P, at which individuals cross_cThe larger the more frequently a new individual is generated, when P_cWhen the size is too large, the possibility of individual damage is increased, and the individual with high fitness is quickly damaged, but when P is too large_cIf the time is too small, the searching speed is slow and even stopped; probability of variation P_mDetermining the frequency of individual variation when P_mIf it is too large, the genetic algorithm will become a completely random search algorithm, but when P is too large_mIf it is too small, new individuals are not easy to produce. For a complex optimization problem, it is difficult to find the optimal crossover probability and mutation probability suitable for each individual, so the present embodiment adopts the crossover operator and mutation operator of the adaptive genetic algorithm:

wherein k is₁And k₂Is a cross probability coefficient, k₃And k₄Is the coefficient of variation probability, k₁、k₂、k₃And k₄Is [0,1 ]]A value of f_maxIs the maximum value of fitness in the population, f_avgIs the average value of fitness in the population, f' is the larger fitness value in the crossed individuals, and f is the fitness value of the variant individuals. Specifically, the crossover operation is to randomly select two chromosomes, determine whether to crossover according to the crossover probability, and f' is the one with the higher fitness of the two chromosomes.

As can be seen from the crossover operator and mutation operator in the above formula, in the adaptive genetic algorithm, P is_cAnd P_mAnd the self-adaptation is changed according to the fitness value of each individual. When the population is more divergent, P is properly increased_cAnd P_m(ii) a When the population is more concentrated, P is properly reduced_cAnd P_m. Meanwhile, for individuals with fitness value higher than population average fitness value, lower P is adopted_cAnd P_mSo that the method has higher probability of entering the next generation; and for individuals with fitness value lower than the population average fitness value, higher P is adopted_cAnd P_mTherefore, the method has higher probability to be advanced into a better solution. Therefore, the self-adaptive genetic algorithm not only ensures the convergence capability of the algorithm, but also keeps the diversity of population individuals and improves the optimization capability of the genetic algorithm.

The cross operation is to randomly select two chromosomes, judge whether to cross according to the cross probability, and randomly select a position to realize the cross operation if the cross is performed, and the common cross modes are single-point cross and multi-point cross. In the early stages of evolution, the chromosomes have low similarity, and most of the chromosomes have low similarityThe crossover operations are all effective, but at the later stages of evolution, the similarity of chromosomes becomes higher and higher, and many ineffective crossover operations are carried out, as shown in FIG. 3, the chromosome Ch_iAnd Ch_kThe 1-3 sites and the 7-10 sites of the gene are the same, if the positions are selected for cross operation, new chromosomes cannot be generated, the method belongs to invalid cross, and only the positions 4-6 sites, namely the positions with different genes, are selected for cross operation, the new chromosomes can be generated.

Aiming at the problem of invalid crossing, the increase of validity judgment before the crossing operation of two chromosomes is considered, firstly, different positions of genes of the two chromosomes to be crossed are found, a set of the different positions of the genes is set as Z, and the number of elements in the set is N_ZThen, it is determined whether the set Z is an empty set, i.e., N_ZIf it is 0, if N_ZIf 0, no crossover operation is performed, and if N_ZIf not 0, a value less than or equal to N is generated_ZAs the number of interleaving bits. The operations are added before the crossover operation, so that the generation of invalid crossover can be effectively avoided, and the searching efficiency of the algorithm is improved.

S5: elite preservation

Calculating the fitness value of each individual after variation and the maximum value f 'of the fitness in the population'_maxIf f'_max＜f_maxLet the individual Ch with the greatest fitness value before maturation_maxSubstituting individual Ch 'with minimum fitness value in population after mutation operation'_minWherein f is_maxRepresenting the maximum fitness value among all individuals in the initial population. By adopting the operation, the optimal individual can be ensured to directly enter the next generation, and the loss of the elite individual caused by the randomness of the algorithm is avoided. After maturation operation, cross operation, mutation operation and elite reservation, a new generation of population P (g +1) is generated.

S6: and repeating the steps S2-S5, and stopping evolution when the evolution algebra reaches the set maximum evolution algebra.

Specifically, let g be g +1, repeat steps S2-S6, and perform iterative evolution; judging whether the current evolution algebra G reaches the set maximum evolution algebra G or not, if G is less than GGo to S2 until G ═ G, or the optimal fitness value f_maxAnd stopping calculation if the continuous generations have no large change, and obtaining the chromosomes of the population of the current generation as the optimal initial value for generating the chaotic sequence.

Next, performance simulation and comparative analysis are performed on the adaptive binary particle swarm genetic algorithm proposed in this embodiment. The Logistic sequence is one of chaotic sequences, and the anti-interference performance of an echo signal of the Logistic sequence is tested by taking the Logistic sequence as a coding sequence. Specifically, the mapping relationship of the Logistic sequence is as follows:

x(k+1)＝λx(k)(1-x(k))

wherein, x (k) is the iteration result value of the chaotic sequence, k is the iteration number, when k is 0, x (0) is the initial value of the chaotic sequence, and the value range is 0 < x (0) < 1. Lambda is a system parameter, and the value range of lambda is more than 3.5699456 … and less than or equal to 4.

The chaotic phase coding is to take a binary sequence obtained by quantization processing of the chaotic sequence as a phase coding sequence. Mean value of chaotic sequence E_nComprises the following steps:

the chaos sequence obtained by chaos mapping is subjected to binary quantization processing to obtain:

the phase sequence of the chaotic two-phase coded signal is as follows:

it is found through experiments that when λ is 4 without changing the initial value, the obtained sequence has the best chaos. Therefore, selecting a proper initial value x (0) is the core of generating high agility and orthogonality Logistic sequence.

In this embodiment, an initial value of the Logistic sequence is selected, and a phase-encoded signal with a code length P of 100 and a symbol pulse width T of 0.1 μ s is generated, and the simulation result is shown in fig. 4. As can be seen from the figure, the anti-interference performance of the echo signal of the Logistic sequence with the randomly selected code length P being 100 is 9.3704 dB.

Under the same condition, the performance of the anti-interference waveform of the chaotic sequence designed by the simulation self-adaptive binary particle swarm genetic algorithm is improved. The parameter settings of the adaptive binary particle swarm genetic algorithm are shown in table 1.

TABLE 1 adaptive binary particle swarm genetic algorithm parameter table

The adaptive binary particle swarm genetic algorithm of the embodiment of the invention simulates a Logistic sequence with a code length P of 100 by using the parameters shown in table 1, and when a target speed v is 0m/s and an echo signal is not shielded, the simulation result refers to fig. 5a and 5b, wherein fig. 5a is a graph showing the variation of the optimal fitness value and the average fitness value of each generation of individuals along with the evolution algebra during iteration of the adaptive binary particle swarm genetic algorithm, and fig. 5b is a graph showing the cross correlation and normalization result of two periodic Logistic sequence echo signals generated by using the obtained optimal initial value.

As shown in fig. 5a, after the optimized search method provided by the embodiment of the present invention is used, the maximum fitness value is 15.9176dB, and the anti-interference performance result obtained by using the result after the search to perform Logistic sequence anti-interference waveform design is shown in fig. 5b, where the maximum peak value is 16.4782dB, which is higher than that before the phase encoding search, and is 7.3788 dB higher than that before the phase encoding search. As can be seen from the optimal fitness value curve of each generation in fig. 5a, the method has good global search capability in the early stage and can quickly converge to a better solution, and the average fitness value curve of each generation can show that the algorithm has good local search capability in the later stage, can continuously jump out of the local optimal solution and gradually converge to the searched optimal solution, so that the algorithm has both global search capability and local search capability.

The adaptive binary particle swarm genetic algorithm is suitable for solving the problem of combinatorial optimization, the algorithm is used for searching and generating an optimal initial value of a Logistic sequence, the target function of the algorithm is the ratio of the cross-correlation peak value of the echo signal of the Logistic sequence between the current pulse period and the coat pulse period and the self-correlation peak value of the current pulse period, then the fitness value is the ratio of the cross-correlation peak value of the current pulse period and the coat pulse period and the self-correlation peak value of the current pulse period, normalization is carried out, the individual with the largest fitness value is the optimal initial value, and the Logistic sequence corresponding to the individual is the optimal Logistic sequence. In real life, in a radar using a transmitting and receiving common antenna, since a signal cannot be received during a signal transmission period, echoes of some targets cannot be completely received, and this problem is called range blocking, which is also called echo truncation or echo blocking. Under the condition of distance shielding, pulse compression is partially correlated, so that the side lobe performance of the pulse compression is deteriorated, a certain influence is caused on a detection target, and the energy of a signal is also lost to a certain extent. And the echo signal is often accompanied by the doppler effect, so that the modulation phase mismatch of the echo signal and the transmitting signal can cause the loss of pulse compression, and even the target can not be compressed, therefore, the doppler shift and the range occlusion should be taken into consideration.

In the prior art, the performance of the Genetic Algorithm (GA) in the prior art and the performance of the binary particle swarm genetic algorithm (agapso) in the invention are simulated and compared under the conditions of no doppler shift, no range occlusion, doppler shift and range occlusion. Because both algorithms need to generate initial values in a random mode, the operation results of each time are not completely the same, the result of a certain time is not representative and cannot explain the practical problem, the simulation result presented in the part is the result obtained by operating each algorithm for fifty times under different conditions, and the result can effectively reflect the performance of each algorithm and has certain practical significance. And (3) respectively simulating the Logistic sequences with the code length P ═ 100,500,1000,5000 by using five algorithms, wherein the simulation result of the Logistic sequence with the code length of 100 is presented in a form of a graph, and the simulation results of the Logistic sequences with the rest code lengths are presented in a form of a table.

(1) The echo signal has no Doppler frequency shift and no range shielding

The results of the simulation of a 100-bit Logistic sequence using both algorithms are shown in fig. 6. As shown in fig. 6, under the condition that an echo signal has no doppler shift and no distance shielding, 100-bit Logistic sequence is simulated by using two algorithms respectively, the anti-interference performance obtained by using a binary particle swarm genetic algorithm is about 16.5dB, and the anti-interference performance obtained by using the genetic algorithm is about 15.5dB, so that the optimal fitness value obtained by using the binary particle swarm algorithm is higher, the anti-interference performance is better, and the optimal solution is easier to converge into a global optimal solution through a series of improvements. While the genetic algorithm converges faster than the example algorithm, but is not a globally optimal solution.

Table 2 shows the optimal fitness value obtained by simulating the Logistic sequence with the code length P ═ 100,500,1000,5000 using the two algorithms and the optimal initial register obtained by the adaptive binary particle swarm genetic algorithm.

TABLE 2 simulation result table of two algorithms without Doppler shift and range shielding

Code length	GA(dB)	AGABPSO(dB)	Improved anti-interference performance (dB)
				100	15.3910	16.4782	1.0872
500	19.6453	20.3546	0.7093
				1000	22.0475	22.8534	0.8059
5000	27.8010	28.1434	0.3424

As shown in table 2, the Logistic sequence having a code length P ═ 100,500,1000,5000 was simulated by using two algorithms without doppler shift and range occlusion of the echo signal. And when the code length of the Logistic sequence is P ═ 100,500,1000,5000, the anti-interference performance of the Logistic sequence obtained by the binary particle swarm genetic algorithm is superior to that of the genetic algorithm. Compared with a genetic algorithm, the algorithm is more likely to jump out of local optimum through a series of improvements to obtain a global optimum solution.

(2) The echo signal has Doppler frequency shift and range shielding

The results of the simulation of a 100-bit Logistic sequence using both algorithms are shown in fig. 7. As can be seen from fig. 7, when the target speed v is 50m/s and the echo distance occlusion is 30%, the 100-bit Logistic sequence is simulated by using two algorithms, and the anti-interference result is influenced to some extent. Due to the speed-sensitive characteristic of the phase-coded signal, the autocorrelation peak value is reduced, so that the anti-interference performance is reduced by about 1dB compared with the former case. However, from the comparison in the figure, the algorithm proposed by the example converges to a better solution relative to the genetic algorithm, and the anti-interference performance is about 0.7dB better than that of the genetic algorithm.

The optimal fitness values obtained by simulating a Logistic sequence with a code length P ═ 100,500,1000,5000 using two algorithms are shown in table 3.

TABLE 3 simulation result table of two algorithms with Doppler shift and range shielding

Code length	GA(dB)	AGABPSO(dB)	Improved anti-interference performance (dB)
				100	13.9794	15.3183	1.3389
500	18.6738	19.0601	0.3863
				1000	20.8792	21.1954	0.3162
5000	25.9893	26.7990	0.8097

As shown in table 3, when the doppler velocity of the echo signal is 50m/s and the distance occlusion is 30% of the previous occlusion, the Logistic sequence with P ═ 100,500,1000,5000 is simulated by using two algorithms, and compared with the genetic algorithm, the algorithm is easier to jump out the local optimal solution to the global optimal solution in terms of the anti-interference performance, so as to solve the initial value of the Logistic sequence corresponding to the optimal fitness value. As can be seen from the above table, the phase-encoded signal after the occlusion and the addition speed are degraded in the anti-interference performance, which is determined by the characteristics of the phase-encoding itself. But the algorithm can still obtain a global optimal solution under the condition that the speed and the occlusion influence are reduced to the minimum.

In summary, the embodiment of the invention provides a chaotic sequence anti-interference waveform design method based on an adaptive binary particle swarm genetic algorithm, and experiments take Logistic chaotic sequences as an example to verify that the adaptive binary particle swarm genetic algorithm has local search capability and global search capability at the same time, so that the method is suitable for solving the problem of combination optimization of chaotic sequence anti-interference waveform design and improving the search efficiency under the condition of maintaining the diversity of the population. Simulation results show that: the method can still converge on a high-quality solution with a high probability when the code length of the chaotic sequence is long, and effectively improves the performance of the anti-interference waveform design method of the chaotic sequence for obtaining the waveform when the code length is long.

The self-adaptive binary particle swarm genetic algorithm provided by the embodiment of the invention overcomes the defect that the genetic algorithm is easy to fall into local convergence and cannot obtain a global optimum value by improving the method for maturation of filial generations and changing the probability of intersection and variation in a self-adaptive manner. In addition, due to the orthogonal characteristic of the chaotic sequence, the algorithm can easily search the initial value with the optimal anti-interference performance on the basis, the time consumption for optimization is greatly reduced, and the anti-interference performance can be maintained in a higher range when the number of coded bits is more. In conclusion, the anti-interference performance of the anti-interference waveform designed by the method is superior to that of the existing method.

The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.