CN112763988B - Anti-interference waveform design method based on self-adaptive binary particle swarm genetic algorithm - Google Patents

Abstract

The invention discloses an anti-interference waveform design method based on an adaptive binary particle swarm genetic algorithm, which includes: randomly generating a set of binary codes to form an initial population, converting the binary codes into decimal and normalizing them as a chaotic sequence initial value, and generate a set of random numbers as the speed of individuals in the initial population; use the binary particle swarm algorithm with adaptive inertia weights to perform mature operations on the parent individuals in the population; use the adaptive binary genetic algorithm to Perform crossover and mutation operations on the chromosomes; perform elite retention operations; continue to evolve. When the evolutionary generations reach the set maximum evolutionary generations, the chromosomes of the current generation population will be used as the initial value to generate the chaotic sequence. This method has local search and global search capabilities, can improve search efficiency while maintaining population diversity, and generate chaotic sequences with better anti-interference performance.

Description

Anti-interference waveform design method based on adaptive binary particle swarm genetic algorithm

Technical field

The invention belongs to the field of signal processing technology, and specifically relates to an anti-interference waveform design method based on an adaptive binary particle swarm genetic algorithm.

Background technique

Radar is an electronic system that can obtain target location and other information by transmitting and receiving electromagnetic waves, and can detect, identify and track targets all day and all day. With the increasingly complex electromagnetic environment on the battlefield and the development of radar interception technology, the performance and survivability of radar detection targets are facing severe tests. Therefore, the anti-interception ability, anti-interference ability, resolution, range and measurement accuracy of radar are Make higher and higher demands. Therefore, the designed waveform itself has anti-interception performance and plays an important role in the low interception performance of the radar. The phase-encoded signal has a large main-side lobe ratio, good pulse pressure performance, and a pushpin-shaped fuzzy image under the condition of large time-width bandwidth product, and has attracted more and more widespread attention. Because this signal waveform has "random" "Agility" and easy to produce "agility", so it can effectively improve the anti-interception, anti-interference and anti-stealth capabilities of the radar system.

For phase-encoded pulse compression radar systems, the encoding sequence of the phase-encoded signal has a great impact on radar performance. Therefore, the use of a series of algorithms for waveform design to obtain phase-encoded signals with superior performance has attracted more and more attention. When the code is short, traversal search can usually be used to obtain a code pattern that meets the requirements. However, when the encoding is long, the traversal search method will greatly reduce the efficiency. Therefore, it has become a research hotspot to use an optimized search method to generate a coding sequence of phase coding signals to improve the anti-interference performance of radar signals.

In 2007, Li Ming proposed an orthogonal phase coding waveform design based on a hybrid genetic algorithm. The algorithm uses a combination of simulated genetic algorithms and genetic algorithms. The specific process is to randomly generate a set of coding sequences as the initial population, and After this population undergoes operations such as search, crossover, and mutation, a set of coding sequences with good orthogonality is generated. However, the main shortcomings of this method are low algorithm efficiency and long optimization time. When the number of transmitted waveforms is large, it takes a long time to solve the coding sequence and the orthogonality becomes worse. It is not suitable for designing a large number of waveforms or a large number of coding bits. Many waveforms. In 2012, Niu Chaoyang and others used chaotic sequences with good randomness, autocorrelation and cross-correlation properties as coding sequences. This method does not require random optimization, so it has obvious advantages in algorithm efficiency, and any number of positive sequences can be designed. Cross waveform. However, because this method is sensitive to the initial value and the initial value is different, the difference in the normalized peak value of the cross-correlation of the generated phase-encoded signals can reach more than 5dB.

Contents of the invention

In order to solve the above problems existing in the prior art, the present invention provides an anti-interference waveform design method based on an adaptive binary particle swarm genetic algorithm. The technical problems to be solved by the present invention are achieved through the following technical solutions:

The invention provides an anti-interference waveform design method based on adaptive binary particle swarm genetic algorithm, including:

S1: Randomly generate a set of binary codes to form the initial population, convert the binary codes into decimal and normalize them as the initial value of the chaotic sequence, and generate a set of random numbers as the speed of individuals in the initial population;

S2: Calculate the fitness of individuals in the initial population according to the fitness function;

S3: Use the binary particle swarm algorithm with adaptive inertia weights to perform mature operations on the parent individuals in the population;

S4: Use adaptive binary genetic algorithm to perform crossover and mutation operations on chromosomes in the population;

S5: Calculate the fitness value of each individual after mutation and the maximum fitness value in the population, and perform elite retention operations to obtain the next generation population;

S6: Repeat steps S2-S5 and use the next generation population to continue evolution. When the number of evolution generations reaches the set maximum number of evolution generations, the evolution will be stopped and the chromosomes of the current generation population will be used as the initial value to generate the chaotic sequence.

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

S11: Parameter initialization: set the initial value of the algebra counter g=1, the maximum evolution generation G, the early evolution generation G', the population size Popsize, the crossover probability coefficients k ₁ and k ₂ , the mutation probability coefficients k ₃ and k ₄ , and the learning factor c ₁ , c ₂ , population number N _g , maximum and minimum values of adaptive inertia weight w _min , w _max and particle speed limits v _max , v _min ;

S12: Randomly generate a set of binary codes with a size of Popsize to form the initial population P(0), convert the binary codes into decimal and then normalize them as the initial value of the chaotic sequence, and set them in the interval [v _min , v _max ] Generate a set of random numbers of size Popsize as the speed of individuals in the initial population;

S13: Use As a chromosome, where 1≤i≤Popsize, is the binary code corresponding to the initial value, _fi is the fitness of the chromosome;

S14: Generate a chaotic sequence with a length of 2N. The first N are used as the encoding sequence of the first periodic phase encoding signal, and the last N are used as the encoding sequence of the second periodic phase encoding signal, and an echo signal is generated:

Among them, s(t,X _i ) is the phase encoding signal of the chaotic sequence, _Xi is the chaotic sequence, s _rn (t,X' _i ) is _the phase encoding echo signal of the nth period chaotic sequence, There is a chaotic sequence with distance occlusion, f ₀ is the carrier frequency, and f _d is the Doppler frequency.

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

use Calculate the fitness of the initial value in the initial population as a fitness function and record the maximum value of fitness f _max in the population and the corresponding chromosome Ch _max , where s _r1 (t,X' _i ) and s _r2 (t, X' _i ) represent the first pulse period echo signal and the second pulse period echo signal respectively, R(s _r2 (t,X' _i ),s _r1 (t,X' _i )) are the first The cross-correlation function value between the pulse period echo signal and the second pulse period echo signal, R(s _r2 (t,X' _i ),s _r2 (t,X' _i )) is the second pulse period echo Signal autocorrelation function value.

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

Determine the size relationship between the current generation counter g and the initially set early evolution generation generation G'. If g<G', use the binary particle swarm algorithm with adaptive inertia weight to update the individual's speed and position; if g=G ', then let the individual extreme value of the individual be the individual of the current generation population; if g>G', then generate the initial value of the next generation population based on the proportion of each individual's fitness value in the total fitness value of the entire population. .

In one embodiment of the present invention, in the process of updating an individual's speed and position using a binary particle swarm algorithm with adaptive inertia weights, the evolutionary formula of the binary particle swarm algorithm with adaptive inertia weights is:

Among them, v _id and x _id are the d-dimensional components of the velocity and position of the i-th individual respectively, c ₁ and c ₂ are two non-negative learning factors, pos _id and pos _gd are the individual extreme value and the global extreme value respectively. , rand() is a random number on [0,1], w is the adaptive inertia weight, w _min and w _max represent the minimum and maximum values of w respectively, f _max is the maximum fitness value of all individuals in the population, f _avg is the average fitness value of all individuals in the population, f is the fitness value of the current individual,

In one embodiment of the present invention, the S4 includes:

Traverse the chromosomes in the population and find the different positions of the genes on the two chromosomes. Let the set of different gene positions be Z, and the number of elements in the set be N _Z ;

Determine whether the set Z is an empty set. If so, no crossover operation is performed. If not, the adaptive crossover probability of the two chromosomes is calculated, and then it is determined whether to perform the crossover operation based on the adaptive crossover probability. If the crossover operation is performed, then Generate a random number less than or equal to N _Z as the number of crossover bits for crossover operation;

Traverse the chromosomes in the population, calculate the adaptive mutation probability, and determine whether to perform a mutation operation based on the adaptive mutation probability. If a mutation operation is performed, randomly select one bit in 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:

Among them, k ₁ and k ₂ are crossover probabilities, k ₃ and k ₄ are mutation probabilities, f _max is the maximum value of fitness in the population, f _avg is the average fitness in the population, and f' is the average value of fitness in the population. The larger fitness value, f is the fitness value of the mutated individual.

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

Calculate the fitness value of each individual after the mutation operation and the maximum fitness value f' _max in the population. If f' _max <f _max , then replace the individual with the largest fitness value before the mature operation with the fitness value in the population after the mutation operation. The individual with the smallest value, where f _max represents the maximum fitness value among all individuals in the initial population.

Compared with the prior art, the beneficial effects of the present invention are:

The anti-interference waveform design method of the present invention based on the adaptive binary particle swarm genetic algorithm adopts an elite retention strategy, takes the adaptive genetic algorithm as the basic framework, and introduces the binary particle swarm algorithm using adaptive inertia weights to replace the early genetic selection. Operation, it has both local search capabilities and global search capabilities, and is suitable for solving the combinatorial optimization problem of chaotic sequence anti-interference waveform design, improving search efficiency while maintaining population diversity. The simulation results show that this method can still converge to a high-quality solution with a high probability when the chaotic sequence code length is long, which effectively improves the anti-interference performance of the waveform obtained by the anti-interference waveform design method when the code length is long.

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

Description of drawings

Figure 1 is a flow chart of an anti-interference waveform design method based on an adaptive binary particle swarm genetic algorithm provided by an embodiment of the present invention;

Figure 2 is a detailed flow chart of an anti-interference waveform design method based on an adaptive binary particle swarm genetic algorithm provided by an embodiment of the present invention;

Figure 3 is a schematic diagram of an invalid crossover;

Figure 4 is a diagram of the anti-interference performance results of using a Logistic chaotic sequence as a phase encoding sequence;

Figure 5a is a graph showing the changes in the optimal fitness value and average fitness value of each generation of individuals with the number of evolutionary generations during the iteration of the adaptive binary particle swarm genetic algorithm;

Figure 5b is the result of cross-correlation and normalization of two periodic phase-encoded echo signals generated using the optimal initial value of the obtained Logistic chaos sequence;

Figure 6 is a graph showing the comparison results of the anti-interference ability search performance of a 100-bit Logistic sequence phase encoding signal using the method of the embodiment of the present invention and the genetic algorithm;

Figure 7 is another search performance comparison result of the anti-interference ability of the 100-bit Logistic sequence phase encoding signal using the method of the embodiment of the present invention and the genetic algorithm.

Detailed ways

In order to further elaborate on the technical means and effects adopted by the present invention to achieve the intended invention purpose, an anti-interference waveform design method based on the adaptive binary particle swarm genetic algorithm proposed by the present invention is described below in conjunction with the accompanying drawings and specific implementation modes. Detailed description.

The foregoing and other technical contents, features and effects of the present invention can be clearly presented in the following detailed description of the specific embodiments in conjunction with the accompanying drawings. Through the description of the specific embodiments, we can have a more in-depth and specific understanding of the technical means and effects adopted by the present invention to achieve the intended purpose. However, the attached drawings are only for reference and illustration, and are not used to explain the technical aspects of the present invention. program is restricted.

It should be noted that in this article, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply that these entities or operations are mutually exclusive. any such actual relationship or sequence exists between them. Furthermore, the terms "comprises," "comprises," or any other variation are intended to cover a non-exclusive inclusion, such that an article or device including a list of elements includes not only those elements, but also other elements not expressly listed. Without further limitation, an element defined by the statement "comprises a..." does not exclude the presence of additional identical elements in an article or device including the stated element.

Please refer to Figures 1 and 2. Figure 1 is a flow chart of an anti-interference waveform design method based on an adaptive binary particle swarm genetic algorithm provided by an embodiment of the present invention; Figure 2 is a flow chart of an anti-interference waveform design method based on an adaptive binary particle swarm genetic algorithm provided by an embodiment of the present invention. Detailed flow chart of anti-interference waveform design method adapted to binary particle swarm genetic algorithm. The anti-interference waveform design method includes:

S1: Randomly generate a set of binary codes to form the initial population, convert the binary codes into decimal and normalize them as the initial value of the chaotic sequence, and generate a set of random numbers as the speed of individuals in the initial population;

Chaos sequence is a pseudo-random sequence generated by irregular motion in a certain system, which is both deterministic and random. Determinism means that the iteration relationship of the chaotic sequence is certain, randomness means that different initial values can produce different chaotic random sequences, and different mapping relationships can also produce different chaotic sequences. Using the initial value sensitivity of chaotic mapping, multiple mutually orthogonal sequences can be easily obtained. Each set of sequences corresponds to an initial value and a mapping relationship, so chaotic sequences have good agility and orthogonal properties.

Further, the S1 specifically includes:

S11: Parameter initialization: Set the initial value of the algebra counter g=1, the maximum evolutionary generation G, the early evolution generation G', that is, the evolutionary generation of the genetic selection operation, the population size Popsize, the crossover probability coefficients k ₁ and k ₂ , and the mutation probability coefficient k ₃ , k ₄ , learning factors c ₁ , c ₂ , population number N _g , and the maximum and minimum values of adaptive inertia weight w _min , w _max , the speed of particles (ie, individuals in the population) is limited to v _max = 5, v _min =-5.

S12: Population initialization: Randomly generate a set of binary codes of size Popsize to form the initial population P(0). This set of binary numbers is converted into decimal numbers and normalized to become the initial value of the chaotic sequence, and in the interval [v _min , v _max ] generate a set of random numbers of size Popsize as the speed of individuals (each particle) in the initial population;

S13: Encoding: Use As a chromosome, the initial value of the chaotic sequence is binary encoded, that is, the binary number is converted into a decimal number and normalized as the initial value of the chaotic sequence, where 1≤i≤Popsize,/> is the binary code corresponding to the initial value, and _fi is the fitness of the chromosome.

In this embodiment, the initial value is binary encoded, that is, chromosome _Chi :

in, is the value of the initial chromosome, and _fi is the fitness of the chromosome. The chromosome is converted into decimal and normalized to become the initial value of the chaotic sequence, which is generated as _Xi through the Logistic chaotic sequence. The g-th generation population of n-bit binary chromosome structure Ch _i (g) (1≤i≤Popsize) is P(g), where Popsize is the number of individuals in the population.

P(g)＝{Ch _i (g)},i＝1,2,3...,Popsize

S14: Generate a chaotic sequence with a length of 2N. The first N are used as the encoding sequence of the first periodic phase encoding signal, and the last N are used as the encoding sequence of the second periodic phase encoding signal, and an echo signal is generated:

Among them, s(t,X _i ) is the phase encoding signal of the chaotic sequence, _Xi is the chaotic sequence, s _rn (t,X' _i ) is _the phase encoding echo signal of the nth period chaotic sequence, Chaos sequence phase encoding echo signal with distance occlusion, f ₀ is the carrier frequency, f _d is the Doppler frequency.

S2: Individual evaluation: Calculate the fitness of the individual initial register value in the initial population according to the fitness function.

Specifically, use Calculate the fitness of the initial value in the initial population as a fitness function and record the maximum value of fitness f _max in the population and the corresponding chromosome Ch _max , where s _r1 (t,X' _i ) and s _r2 (t, X' _i ) represent the first pulse period echo signal and the second pulse period echo signal respectively, R(s _r2 (t,X' _i ),s _r1 (t,X' _i )) are the first The cross-correlation function value of the pulse period echo signal and the second pulse period echo signal, R(s _r2 (t,X' _i ), s _r2 (t,X' _i )) is the second pulse period echo signal. The autocorrelation function value of the wave signal. The size of the required fitness _fi represents the anti-interference ability of the phase-encoded signal.

Calculate the fitness value of each individual in the population P(g) according to the formula of the fitness function. In order to avoid the unreasonable distribution of fitness values or difficulty in reflecting personality, the fitness value is adjusted according to the actual situation. The adjustment method is mainly Including linear changes, power exponential transformations, exponential changes, Goldberg linear stretch changes, etc. And record the maximum fitness value f _max in the population and the corresponding chromosome Ch _max .

S3: Use the binary particle swarm algorithm with adaptive inertia weights to mature the parent individuals in the population.

Determine the relationship between the current algebra counter g and the originally set early evolution algebra G'. If g<G', calculate the individual extreme value and global extreme value of the particles (i.e. individuals in the population), and then use adaptive inertial weights The formula updates the speed and position of the particle (individual); if g=G', let the individual extreme value of the particle (individual) be the individual of the current generation population; if g>G', use the traditional adaptive genetic algorithm The selection operation in generates offspring. Specifically, according to the proportion of each individual's fitness value in the total fitness value of the entire population, the proportion of individuals with a larger initial value of the next generation population's fitness value is greater. , so it is easier to be selected and directly copied to become the next generation of individuals. In this embodiment, in the early stage of evolution, the binary particle swarm algorithm with adaptive inertia weights is used to mature the parent individuals; in the late stage of evolution, a "roulette" method is used to select individuals that survive in the next generation.

Specifically, in the particle swarm algorithm, each particle (ie, an individual in the population) has a position and speed. The position represents the encoding of the particle, and the speed determines the distance and direction of the particle search. All particles are searched based on the particle with the largest current fitness value. Each time the search is performed, the optimal particle will change, and other particles will follow the new optimal particle to search, and so on. At the beginning of the iteration, each particle initializes its speed and position in the space in a random manner. During the iteration process, the particle changes its position and speed in the solution space by tracking two extreme values, one of which is an extreme value. is the optimal position of a single particle itself during the iterative process. This extreme value is called the individual extreme value of the particle. The other extreme value is the optimal position of all particles in the group during the iterative process. This extreme value is called Global extreme value.

The evolution formula of particle swarm algorithm is:

Among them, v _id and x _id are the d-dimensional components of the speed and position of the i-th particle respectively, w is the inertia weight, and c ₁ and c ₂ are two non-negative learning factors, which determine the behavior of the particle itself and other particles. The impact of empirical information on the particle search trajectory, pos _id and pos _gd are individual extreme values and global extreme values, and rand() is a random number on [0,1].

For the problem of discrete space constraints, the binary particle swarm algorithm was proposed. The difference between the binary particle swarm algorithm and the particle swarm algorithm is that the particles can only take two values 0/1 in the state space, and each bit of the speed represents the corresponding bit of the particle position. The possibility of taking a value of 0/1, so in the binary particle swarm algorithm, the update formula of the particle speed remains unchanged, its position is updated using probability mapping, and the sigmoid function is used to map the speed to the [0,1] interval As probability s(vi _id ), this probability is the probability that the particle’s next position will become 1:

Then the update formula for particle position is:

Among the adjustable parameters of the binary particle swarm algorithm, the inertia weight w is a very important parameter because it is used to control the global search capability and local search capability of the algorithm. A larger w will enhance the global search capability of the algorithm, but will Weakening its local search ability, while a smaller w is beneficial to improving the local search ability of the algorithm, but will weaken its global search ability. The traditional binary particle swarm algorithm uses a fixed weight method, that is, a fixed inertia weight is used. In this embodiment, in order to balance the global search capability and local search capability of the binary particle swarm algorithm, the velocity vi _id adopts an adaptive inertia weight, and its expression is:

Among them, w _min and w _max represent the minimum and maximum values of w respectively, f _max is the maximum fitness value of all particles in the particle swarm, f _avg is the average fitness value of all particles in the particle swarm, and f is the current particle fitness value.

It can be seen from the expression of adaptive inertia weight that when the fitness value of a particle is greater than the average fitness value, it has a smaller inertia weight, causing the particle to have a smaller speed, thus protecting the particle from being destroyed; otherwise , when the fitness value of a particle is less than the average fitness value, it has a larger inertial weight, so that the particle has a larger speed and can tend to a better search area. Therefore, the adaptive inertia weight can dynamically calculate the inertia weight of each particle based on the current overall state of the particle, so that the search capability of the algorithm can be globally improved.

The selection operation is based on the proportion of each individual's fitness value in the total fitness value of the entire population to generate the next generation population. This operation imitates the law of survival of the fittest in nature. Individuals with large fitness values will be directly copied to become the next generation of individuals. Then individuals with large fitness values will be repeatedly selected with a high probability. In the later stages of evolution, this operation is beneficial to The rapid convergence of the algorithm. In the early stage of evolution, this operation will lead to a reduction in population diversity, which is not conducive to the evolution of the population. Since the parent individual directly becomes the offspring individual, the individual itself does not change, which will reduce the search efficiency of the algorithm. efficiency.

In view of the above shortcomings, it is proposed to use an improved binary particle swarm algorithm with adaptive inertia weights to mature the parent individuals in the early stage of evolution to generate offspring individuals. This avoids the loss of population diversity caused by directly copying the parent individuals. Reducing the fitness value will make individuals with small fitness values move in the direction of individuals with large fitness values, effectively improving the search efficiency of the algorithm. However, since the randomness of the binary particle swarm algorithm becomes stronger and stronger in the later stage, which is not conducive to the algorithm converging to the global optimal solution, the selection operation of the adaptive genetic algorithm is still used to generate offspring individuals in the later stage of evolution, which is beneficial to the algorithm. Convergence quickly. Using the above operation to replace the original selection operation not only ensures that the population can quickly move closer to the global optimal solution in the early stage of evolution, but also ensures that individuals in the population can quickly converge in the late stage of evolution.

S4: Use adaptive binary genetic algorithm to perform crossover operations and mutation operations on chromosomes in the population.

Traverse the chromosomes in the population with a step length of 2 to find the different positions of the two chromosome genes. Let the set of different gene positions be Z, and the number of elements in the set be N _Z. If the set Z is an empty set, then no Perform a crossover operation, otherwise calculate the adaptive crossover probability of the two chromosomes, and then determine whether to perform a crossover operation based on the crossover probability. If a crossover operation is performed, a random number less than or equal to N _Z is generated as the number of crossover digits for crossover.

Traverse the chromosomes in the population with a step size of 2, calculate the adaptive mutation probability, and determine whether to perform a mutation operation based on the mutation probability. If a mutation operation is performed, a random bit in the binary code of the current chromosome is selected for mutation.

Specifically, traditional genetic algorithms use fixed crossover operators and mutation operators, and their crossover probabilities and mutation probabilities cannot reflect the state of evolution, leading to random roaming or premature maturation. The algorithm for solving the optimization problem should have two capabilities at the same time: one is the global search capability, that is, it can open up a new solution space in the process of searching for the global optimal solution; the other is the local search capability, that is, it can converge to the optimal solution. The optimal solution in the solution region. In the genetic algorithm, the balance of these two abilities is determined by the crossover probability P _c and the mutation probability P _m . Among them, the crossover probability P _c determines the frequency of individuals crossing. The larger P _c , the frequency of generating new individuals. The faster, when P _c is too large, it will increase the possibility of individuals being destroyed, so that individuals with high fitness will be destroyed quickly, but when P _c is too small, it will cause the search speed to be slow or even stagnant; mutation probability P _m determines the frequency of individual mutation. When P _m is too large, the genetic algorithm will become a completely random search algorithm. However, when P _m is too small, it is difficult for new individuals to be generated. For complex optimization problems, it is difficult to find the optimal crossover probability and mutation probability suitable for each individual. Therefore, this embodiment uses the crossover operator and mutation operator of the adaptive genetic algorithm:

Among them, k ₁ and k ₂ are crossover probability coefficients, k ₃ and k ₄ are mutation probability coefficients, k ₁ , k ₂ , k ₃ and k ₄ are values between [0,1], and f _max is the adaptation value in the population. The maximum value of degree, f _avg is the average fitness value in the population, f' is the larger fitness value in the crossover individual, and f is the fitness value of the mutant individual. Specifically, the crossover operation randomly selects two chromosomes, and determines whether to perform crossover based on the crossover probability. f' is the one with greater fitness among the two chromosomes.

It can be seen from the crossover operator and mutation operator in the above formula that in the adaptive genetic algorithm, P _c and P _m adaptively change according to the fitness value of each individual. When the population is relatively divergent, increase P _c and P _m appropriately; when the population is relatively concentrated, decrease P _c and P _m appropriately. At the same time, for individuals whose fitness value is higher than the average fitness value of the population, lower P _c and P _m are used to give them a greater probability of entering the next generation; while for individuals whose fitness value is lower than the average fitness value of the population, , using higher P _c and P _m so that it has a greater probability of evolving into a better solution. Therefore, the adaptive genetic algorithm not only ensures the convergence ability of the algorithm, but also maintains the diversity of individuals in the population, improving the optimization ability of the genetic algorithm.

The crossover operation is to randomly select two chromosomes, and determine whether to perform crossover based on the crossover probability. If crossover is performed, a position is randomly selected to implement the crossover operation. Common crossover methods include single-point crossover and multi-point crossover. In the early stages of evolution, the similarity of chromosomes is very low. At this time, most crossover operations are effective. However, in the later stages of evolution, the similarity of chromosomes becomes higher and higher. At this time, many invalid crossover operations will be performed, as shown in the figure. As shown in 3, positions 1 to 3 and positions 7 to 10 of chromosomes Ch _i and Ch _k are the same. If these positions are selected for crossover operation, no new chromosome will be generated, which is an invalid crossover. Only positions 4 to 6 are selected, which means the genes are different. Only by performing a crossover operation at the position can a new chromosome be generated.

To solve this problem of invalid crossover, consider adding a validity judgment before performing a crossover operation on two chromosomes. First, find out the different positions of the genes of the two chromosomes to be crossed. Let the set of different gene positions be Z, and the number of elements in the set. The number is N _Z , and then determine whether the set Z is an empty set, that is, whether N _Z is 0. If N _Z is 0, no crossover operation will be performed. If N _Z is not 0, a random number less than or equal to N _Z will be generated. Perform crossover operations as crossover bits. Adding the above operations before the crossover operation can effectively avoid the occurrence of invalid crossovers and improve the search efficiency of the algorithm.

S5: Elite reserved

Calculate the fitness value of each individual after mutation and the maximum fitness value f' _max in the population. If f' _max <f _max , then let the individual Ch _max with the largest fitness value before the mature operation replace the fitness value in the population after the mutation operation. The individual with the smallest fitness value Ch' _min , where f _max represents the maximum fitness value among all individuals in the initial population. Using the above operations can ensure that the best individuals directly enter the next generation and avoid the loss of elite individuals caused by the randomness of the algorithm. After maturation operation, crossover operation, mutation operation and elite retention, a new generation population P(g+1) is generated.

S6: Repeat steps S2-S5, and stop evolution when the number of evolution generations reaches the set maximum number of evolution generations.

Specifically, let g=g+1, repeat steps S2-S6, and perform iterative evolution; determine whether the current evolution generation g reaches the set maximum evolution generation G, if g<G, go to S2 until g=G, or If the optimal fitness value f _max does not change significantly for several consecutive generations, the calculation will be stopped and the chromosomes of the current generation population will be obtained as the optimal initial value for generating chaotic sequences.

Next, perform performance simulation and comparative analysis on the adaptive binary particle swarm genetic algorithm proposed in this embodiment. Logistic sequence is a kind of chaotic sequence. Logistic sequence is now used as the encoding sequence to test the anti-interference performance of its echo signal. Specifically, the mapping relationship of the Logistic sequence is:

x(k+1)=λx(k)(1-x(k))

In the formula, x(k) is the iteration result value of the chaotic sequence, k is the number of iterations, when k=0, x(0) is the initial value of the chaotic sequence, and the value range is 0<x(0)<1. λ is a system parameter, the value range is 3.5699456...<λ≤4.

Chaotic phase coding is to use the binary sequence obtained by quantization processing of the chaotic sequence as a phase coding sequence. The mean E _n of the chaotic sequence is:

By performing binary quantization processing on the chaotic sequence obtained by the chaos mapping, we can get:

The phase sequence of the chaotic two-phase encoded signal is:

Through experiments, it can be seen that when the initial value remains unchanged, when λ = 4, the obtained sequence has the best chaos. Therefore, choosing an appropriate initial value x(0) is the core of generating a high agility and orthogonality Logistic sequence.

In this embodiment, the initial value of the Logistic sequence is selected to generate a phase-encoded signal with a code length of P=100 and a symbol pulse width of T=0.1 μs. The simulation results are shown in Figure 4. It can be seen from the figure that the anti-interference performance of the randomly selected Logistic sequence echo signal with code length P=100 is 9.3704dB.

Under the same conditions, the performance of the anti-interference waveform designed by the adaptive binary particle swarm genetic algorithm is simulated. The parameter settings of the adaptive binary particle swarm genetic algorithm are shown in Table 1.

Table 1 Parameter table of adaptive binary particle swarm genetic algorithm

The adaptive binary particle swarm genetic algorithm of the embodiment of the present invention uses the parameters shown in Table 1 to simulate the Logistic sequence with code length P=100. When the target speed v=0m/s and the echo signal is unobstructed, the simulation results are as follows: See Figure 5a and Figure 5b. Figure 5a is a diagram of the optimal fitness value and average fitness value of each generation of individuals during the iteration of the adaptive binary particle swarm genetic algorithm. Figure 5b is the optimal fitness value obtained using The two periodic Logistic sequence echo signals generated by the initial value are cross-correlated and the result map is normalized.

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

The adaptive binary particle swarm genetic algorithm in this embodiment is suitable for solving combinatorial optimization problems. This algorithm is used to search for the optimal initial value to generate a Logistic sequence. Its objective function is the cross-correlation peak value between the current pulse period of the Logistic sequence echo signal and the upper pulse period. The fitness value is then normalized by the ratio of the cross-correlation peak between the current pulse period and the top pulse period and the autocorrelation peak of the current pulse period. The individual with the largest fitness value is the optimal initial value, the Logistic sequence corresponding to the individual is the optimal Logistic sequence. In real life, for radars that use shared transmitting and receiving antennas, since the signal cannot be received during the transmission period, the echoes of some targets cannot be completely received. This problem is called distance occlusion, also called echo truncation, echo Occlusion. In the case of distance occlusion, pulse compression is partially correlated, which will not only worsen the side lobe performance of pulse compression and have a certain impact on the detection target, but also cause a certain loss of signal energy. And the echo signal is often accompanied by the Doppler effect, which causes the modulation phase of the echo signal and the transmitted signal to not match, which will cause the loss of pulse compression and even fail to compress the target. Therefore, the Doppler frequency shift and distance occlusion should be considered. Go in.

Currently, the performance of the two algorithms, the genetic algorithm (GA) in the prior art and the binary particle swarm genetic algorithm (AGABPSO) of the present invention, is respectively in terms of no Doppler frequency shift, no distance occlusion and Doppler frequency shift, with distance. Simulation comparison is performed under occlusion conditions. Since both algorithms need to generate initial values in a random manner, the results of each operation will not be exactly the same. The results of a certain time are not representative and cannot explain the actual problem. The simulation results presented in this section are for each algorithm. Run fifty times under different circumstances to obtain the most frequent results. This result can effectively reflect the performance of each algorithm and has certain practical significance. Five algorithms are used to simulate Logistic sequences with code lengths P = [100, 500, 1000, 5000]. The simulation results of the Logistic sequence with a code length of 100 are presented in the form of graphics, and the simulation results of the Logistic sequences with the remaining code lengths are Presented in table form.

(1) The echo signal has no Doppler frequency shift and no distance obstruction

The simulation results of a 100-bit Logistic sequence using two algorithms are shown in Figure 6. As shown in Figure 6, two algorithms are used to simulate a 100-bit Logistic sequence when the echo signal has no Doppler frequency shift and no distance occlusion. The anti-interference performance obtained by using the binary particle swarm genetic algorithm is approximately 16.5dB. The anti-interference performance obtained by the genetic algorithm is about 15.5dB. Therefore, the optimal fitness value obtained by using the binary particle swarm algorithm is higher and the anti-interference performance is better. After a series of improvements, it is easier to converge to the global optimal solution. . The genetic algorithm converges faster than the algorithm in this example, but it is not the global optimal solution.

The optimal fitness value obtained by simulating a Logistic sequence with code length P = [100,500,1000,5000] using two algorithms and the optimal initial register obtained by the adaptive binary particle swarm genetic algorithm are shown in Table 2.

Table 2 Simulation results of the two algorithms without Doppler frequency shift and distance occlusion

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, two algorithms are used to simulate a Logistic sequence with a code length of P=[100,500,1000,5000] when the echo signal has no Doppler frequency shift and no range obstruction. When the Logistic sequence code length is P=[100,500,1000,5000], the anti-interference performance of the Logistic sequence obtained by the binary particle swarm genetic algorithm is better than that of the genetic algorithm. Compared with the genetic algorithm, this algorithm is more likely to jump out of the local optimum and obtain the global optimal solution after a series of improvements.

(2) The echo signal has Doppler frequency shift and distance obstruction

The simulation results of a 100-bit Logistic sequence using two algorithms are shown in Figure 7. It can be seen from Figure 7 that when the target speed v=50m/s and the echo distance occlusion is 30%, two algorithms are used to simulate the 100-bit Logistic sequence, and the anti-interference results are affected to a certain extent. Due to the sensitivity of the phase-encoded signal to speed, the autocorrelation peak has decreased, resulting in a decrease in anti-interference performance of about 1dB compared to the previous case. However, from the comparison in the figure, the algorithm proposed in this example converges to a better solution than the genetic algorithm, and the anti-interference performance is about 0.7dB better than the genetic algorithm.

The optimal fitness value obtained by simulating a Logistic sequence with a code length of P=[100,500,1000,5000] using two algorithms is shown in Table 3.

Table 3 Simulation results of the two algorithms with Doppler frequency shift and distance occlusion

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 v=50m/s and the distance occlusion is 30% of the front occlusion, two algorithms are used to respectively analyze the Logistic sequence of P=[100,500,1000,5000] bits. After simulation, in terms of anti-interference performance, this algorithm is easier to jump out of the local optimum and reach the global optimal solution than the genetic algorithm, thereby solving the initial value of the generated Logistic sequence corresponding to the optimal fitness value. It can be seen from the above table that when speed and occlusion are added to the phase encoding signal, the anti-interference performance decreases. This is determined by the characteristics of phase encoding itself. However, this algorithm can still obtain the global optimal solution in this case, minimizing the impact of speed and occlusion.

In summary, the embodiment of the present invention proposes an anti-interference waveform design method based on the adaptive binary particle swarm genetic algorithm. The experiment took the logistic chaotic sequence as an example and verified that the adaptive binary particle swarm genetic algorithm has both local search capability and The global search capability is suitable for solving the combinatorial optimization problem of chaotic sequence anti-interference waveform design, and improves search efficiency while maintaining population diversity. The simulation results show that this method can still converge to a high-quality solution with a high probability when the chaotic sequence code length is long, which effectively improves the performance of the anti-interference waveform design method in obtaining waveforms when the code length is long.

The adaptive binary particle swarm genetic algorithm proposed in the embodiment of the present invention overcomes the shortcomings of genetic algorithms that easily fall into local convergence and cannot obtain the global optimal value by improving the method of offspring maturation and adaptively changing the crossover and mutation probabilities. In addition, the orthogonal characteristics of the chaotic sequence itself make it easier for this algorithm to search for the initial value with the best anti-interference performance, which greatly reduces the time-consuming optimization and can also be used when the number of coding bits is large. Ensure that its anti-interference performance remains within a high range. In summary, the anti-interference performance of the anti-interference waveform designed by this method is better than that of existing methods.

The above content is a further detailed description of the present invention in combination with specific preferred embodiments, and it cannot be concluded that the specific implementation of the present invention is limited to these descriptions. For those of ordinary skill in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, and all of them should be regarded as belonging to the protection scope of the present invention.

Claims (7)

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

S1: randomly generating a group of binary codes to form an initial population, converting the binary codes into decimal codes, normalizing the decimal codes to serve as an initial value of a chaotic sequence, and generating a group of random numbers to serve as the speeds of individuals in the initial population;

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

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

s4: performing crossover operation and mutation operation on chromosomes in the population by using an adaptive binary genetic algorithm;

s5: calculating the fitness value of each individual after mutation and the maximum value of fitness in the population, and carrying out elite retention operation to obtain the next generation population;

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

the S1 comprises the following steps:

s11: parameter initialization: setting an initial value g=1, a maximum evolution algebra G, an evolution early algebra G', a population size pop ize and a crossover probability coefficient k ₁ 、k ₂ Coefficient of variation probability k ₃ 、k ₄ Learning factor c ₁ 、c ₂ Population number N _g Maximum value w of adaptive inertial weight _max And a minimum value w _min 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 codes, normalizing the decimal codes to be used as an initial value of a chaotic sequence, and carrying out interval [ v ] _min ,v _max ]Generating a set of random numbers of size pop size as the speed of individuals in the initial population;

s13: usingAs a chromosome, wherein 1.ltoreq.i.ltoreq.Popsize,binary corresponding to the initial valueCode making, f _i Fitness for the chromosome;

s14: generating a chaotic sequence of length 2N, the first N being the code sequence of the first periodic phase encoded signal, the last N being the code sequence of the second periodic phase encoded signal, and generating an echo signal:

wherein s (t, X) _i ) For phase encoding signals of chaotic sequence, X _i Is a chaotic sequence, s _rn (t,X′ _i ) For the phase encoding echo signal of the nth period chaotic sequence, X' _i For the chaotic sequence with distance shielding, f ₀ For carrier frequency, f _d Is the doppler frequency.

2. The method for designing an anti-interference waveform based on the adaptive binary particle swarm genetic algorithm according to claim 1, wherein said S2 comprises:

UsingCalculating the fitness of the initial values in the initial population as a fitness function and recording the maximum value f of the fitness in the population _max Corresponding chromosome Ch _max Wherein s is _r1 (t,X′ _i ) And s _r2 (t,X′ _i ) Respectively represent 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 the cross-correlation function value 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 ) For the second pulse period echo signalAutocorrelation function values of the numbers.

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

judging the magnitude relation between the current algebra counter G and the initial set pre-evolution algebra G ', and if G is less than G', updating the speed and the position of the individual by using a binary particle swarm algorithm with self-adaptive inertia weight; if g=g', making the individual extremum of the individual as the individual of the current generation population; if G > G', generating the initial value of the next generation population according to the proportion of the fitness value of each individual in the total sum of fitness values of the whole population.

4. The method for designing an anti-interference waveform based on an adaptive binary particle swarm optimization according to claim 3, wherein in the process of updating the speed and the position of an individual by using the binary particle swarm optimization with adaptive inertia weight, the evolution formula of the binary particle swarm optimization with adaptive inertia weight is as follows:

Wherein v is _id 、x _id D-th dimension component, c, of the i-th individual velocity and position, respectively ₁ And c ₂ Is two non-negative learning factors, pos _id And pos _gd The individual extremum and the global extremum are respectively, and the rand () is [0,1 ]]The random number on the self-adaptive inertial weight, w _min And w _max Respectively represent the minimum value and the maximum value of w, f _max Is the maximum fitness value of all individuals in the population, f _avg Is the average fitness value of all individuals in the population, f isThe fitness value of the current individual,

5. the method for designing an anti-interference waveform based on an adaptive binary particle swarm genetic algorithm according to claim 3, wherein said S4 comprises:

traversing chromosomes in the population, finding out different positions of two chromosome genes, setting a set of 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 adaptive cross probability of two chromosomes, judging whether to perform cross operation according to the adaptive cross probability, and if so, generating a value less than or equal to N _Z Performing cross operation by taking the random number of the random number as the cross bit number;

traversing chromosomes in the population, calculating adaptive mutation probability, judging whether mutation operation is carried out according to the adaptive mutation probability, and randomly selecting one bit in the current chromosome binary code to carry out mutation if the mutation operation is carried out.

6. The method for designing an anti-interference waveform based on an adaptive binary particle swarm genetic algorithm according to claim 3, wherein the crossover operator and the mutation operator of the adaptive binary genetic algorithm are:

wherein k is ₁ And k ₂ As cross probability coefficient, k ₃ And k ₄ As a coefficient of variation probability, f _max Is the maximum value of fitness in the population, f _avg The average value of fitness in the population is f' the larger fitness value of two crossed individuals, and f the fitness value of a variant individual.

7. The method for designing an anti-interference waveform based on an adaptive binary particle swarm genetic algorithm according to any one of claims 1 to 6, wherein S5 comprises:

calculating fitness value of each individual after mutation operation and maximum value f 'of fitness in population' _max If f' _max <f _max The individual with the largest fitness value before the maturation operation replaces the individual with the smallest fitness value in the population after the mutation operation, wherein f _max Representing the maximum fitness value among all individuals in the initial population.