CN112763988B - Anti-interference waveform design method based on self-adaptive binary particle swarm genetic algorithm - Google Patents
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Abstract
The invention discloses an anti-interference waveform design method based on a self-adaptive binary particle swarm genetic algorithm, which comprises the following steps: 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; performing maturation operation on parent individuals in the population by using a binary particle swarm algorithm with self-adaptive inertia weight; performing crossover and mutation operations on chromosomes in the population by using an adaptive binary genetic algorithm; performing elite reserving operation; and continuing to evolve, and taking the chromosome of the current generation population as an initial value for generating the chaotic sequence when the evolution algebra reaches the set maximum evolution algebra. The method has the capabilities of local searching and global searching, can improve the searching efficiency under the condition of maintaining population diversity, and can generate the chaotic sequence with good anti-interference performance.
Description
Technical Field
The invention belongs to the technical field of signal processing, and particularly relates to an 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 and other information of a target by transmitting and receiving electromagnetic waves, so that all-weather detection, identification and tracking of the target all the day are realized. With the increasing complexity of the battlefield electromagnetic environment and the development of radar interception technology, the performance and the viability of radar detection targets face serious tests, so that the requirements on the anti-interception capability, the anti-interference capability, the resolution, the action distance and the measurement accuracy of the radar are higher and higher. 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 bandwidth product, the phase coding signal has larger main side lobe ratio, good pulse pressure performance, and the fuzzy graph is a thumbtack type, which receives more and more 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 coding sequence of a phase-coded signal has a great influence on radar performance, so that a series of algorithms are used for waveform design to obtain a phase-coded signal with excellent performance, which is more and more important. In the case of shorter codes, the code pattern meeting the requirement can be obtained usually by adopting a traversing search mode. But the way to traverse the search can significantly reduce efficiency when the code is longer. Therefore, the code sequence of the phase code signal is generated by an optimized searching method, so that the anti-interference performance of the radar signal is improved and becomes a research hot spot.
In 2007, li Ming proposes a design of a quadrature-phase code waveform based on a hybrid genetic algorithm, wherein the algorithm adopts a method of combining a simulated genetic algorithm and a genetic algorithm, and specifically comprises the steps of randomly generating a group of code sequences as an initial population, and generating a group of code sequences with better orthogonality after searching, crossing, mutation and other operations on the population. However, the method has the main defects of low algorithm efficiency, long optimization time consumption, long iteration time for solving the coding sequence when the number of the transmitted waveforms is large, poor orthogonality and inapplicability to the waveforms with large number of designed waveforms or large number of coding bits. In 2012, niu chao et al used chaotic sequences with good randomness, auto-correlation and cross-correlation properties as the code sequences, and the method did not require random optimization, thus having significant advantages in terms of algorithm efficiency and allowing the design of any number of orthogonal waveforms. However, the method is sensitive to the initial value, the initial value is different, and the phase code signal cross correlation normalized peak value phase difference generated can reach more than 5 dB.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides an anti-interference waveform design method based on a self-adaptive binary particle swarm genetic algorithm. The technical problems to be solved by the invention are realized by the following technical scheme:
The invention provides an anti-interference waveform design method based on a self-adaptive binary particle swarm genetic algorithm, which comprises 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 the steps S2-S5, continuing to evolve by using the next generation population, stopping evolution when the evolution algebra reaches the set maximum evolution algebra, and taking the chromosome of the current generation population as the initial value for generating the chaotic sequence.
In one embodiment of the present invention, the S1 includes:
s11: parameter initialization: setting an algebraic counter initial value g=1, and setting the maximum evolution algebra G, evolution early algebra G', population size Popsize, cross 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 and minimum values w of adaptive inertial weights min 、w max 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,for binary coding corresponding to initial value, 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 Is carrier frequencyRate f d Is the doppler frequency.
In one embodiment of the present invention, the S2 includes:
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 ) For 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 ) Is the second pulse period echo signal autocorrelation function value.
In one embodiment of the present invention, the S3 includes:
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.
In one embodiment of the present invention, in updating the speed and position of an individual using a binary particle swarm algorithm with adaptive inertia weights, the evolution formula of the binary particle swarm algorithm with adaptive inertia weights is:
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 For 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:
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.
In one embodiment of the present invention, the crossover operator and mutation operator of the adaptive binary genetic algorithm are:
wherein k is 1 And k 2 Is the crossover probability, k 3 And k 4 For the 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.
In one embodiment of the present invention, the S5 includes:
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.
Compared with the prior art, the invention has the beneficial effects that:
the anti-interference waveform design method based on the self-adaptive binary particle swarm genetic algorithm takes the self-adaptive genetic algorithm as a basic framework on the basis of adopting elite retention strategy, introduces the binary particle swarm algorithm using self-adaptive inertia weight to replace early genetic selection operation, has local searching capability and global searching capability, is suitable for solving the combination optimization problem of chaotic sequence anti-interference waveform design, and improves searching efficiency under the condition of maintaining population diversity. Simulation results show that the method can still converge to a high-quality solution with a larger probability when the code length of the chaotic sequence is longer, and the anti-interference performance of the anti-interference waveform design method for obtaining the waveform 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 block flow diagram of an 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 an 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 illustration of an invalidation crossover;
FIG. 4 is a graph of the anti-interference performance results using a Logistic chaotic sequence as a phase encoding sequence;
FIG. 5a is a graph showing the variation of the optimal fitness value and the average fitness value of each generation of individuals with the number of evolution algebra during the iteration of the adaptive binary particle swarm genetic algorithm;
FIG. 5b is a graph of the correlation and normalization of two periodic phase encoded echo signals generated using the optimal initial value of the obtained Logistic chaotic sequence;
FIG. 6 is a graph of the performance of the search versus interference resistance of a genetic algorithm to a 100 bit Logistic sequence phase encoded Signal using the method of an embodiment of the present invention;
FIG. 7 is a graph of another search performance versus result of the anti-interference capability of a genetic algorithm on a 100-bit Logistic sequence phase encoded signal using the method of an embodiment of the present invention.
Detailed Description
In order to further explain the technical means and effects adopted by the invention to achieve the preset aim, the following describes in detail an anti-interference waveform design method based on the adaptive binary particle swarm genetic algorithm according to the invention with reference to the attached drawings and the specific embodiments.
The foregoing and other features, aspects, and advantages of the present invention will become more apparent from the following detailed description of the preferred embodiments when taken in conjunction with the accompanying drawings. The technical means and effects adopted by the present invention to achieve the intended 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 intended to limit the technical scheme of the present invention.
It should be noted that in this document relational terms such as first and second, and the like are 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. Moreover, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that an article or apparatus 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 one … …" does not exclude the presence of other like elements in an article or apparatus that comprises the element.
Referring to fig. 1 and fig. 2, fig. 1 is a flow chart of an 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 an anti-interference waveform design method based on an adaptive binary particle swarm genetic algorithm according to an embodiment of the present invention. The anti-interference waveform design method comprises 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;
the chaotic sequence is a pseudo-random sequence generated by random motion in a determined system, and has certainty and randomness. The certainty means that the iterative relation of the chaotic sequence is determined, the randomness means that different chaotic random sequences can be generated for different initial values, and different mapping relations can also generate different chaotic sequences. The initial value sensitivity of the chaotic mapping is utilized to easily obtain a plurality of mutually orthogonal sequences, and each group of sequences corresponds to one initial value and one mapping relation, so that the chaotic sequence has good agility and orthogonality characteristics.
Further, the step S1 specifically includes:
s11: parameter initialization: setting an initial value g=1, a maximum evolution algebra G and a preliminary evolution algebra G', namely the evolution algebra of genetic selection operation, the population size Popsize and the cross probability coefficient k 1 、k 2 Variation ofProbability coefficient k 3 、k 4 Learning factor c 1 、c 2 Population number N g And maximum and minimum values w of adaptive inertial weights min 、w max The particle (i.e., individual in the population) velocity is limited to v max ＝5,v min ＝-5。
S12: initializing a population: 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 numbers, normalizing the decimal numbers to obtain an initial value of the chaotic sequence, and performing interval [ v ] min ,v max ]Generating a set of random numbers of size pop ize as the velocity of the individual (individual particles) in the initial population;
s13: encoding: usingAs chromosome, binary coding is carried out on the initial value of the chaotic sequence, namely binary number is converted into decimal number and normalized, and the binary number is used as the initial value of the chaotic sequence, wherein, i is more than or equal to 1 and less than or equal to pop ize,>for binary coding corresponding to initial value, f i Is the fitness of the chromosome.
In this embodiment, the initial value is binary encoded, i.e., chromosome Ch i ：
Wherein,for the initial chromosome value, f i Is the fitness of the chromosome. The chromosome is converted into decimal and normalized to obtain the initial value of the chaos sequence, and the initial value is generated into X through the Logistic chaos sequence i . n-bit binary chromosome structure Ch i (g) The g generation population of (1.ltoreq.i.ltoreq.Popsize) is P (g), whichIn (2), pop is the number of individuals in the population.
P(g)＝{Ch i (g)},i＝1,2,3...,Popsize
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 Phase-encoding echo signals for chaotic sequences with distance shielding, f 0 For carrier frequency, f d Is the doppler frequency.
S2: individual evaluation: and calculating the fitness of the initial register values of the individuals in the initial population according to the fitness function.
In particular, use is made ofCalculating 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 ) Is the self-phase of the echo signal of the second pulse periodThe off function value. The adaptation degree f i The magnitude indicates the anti-interference capability of the phase encoded signal.
According to the formula of the fitness function, calculating the fitness value of each individual in the population P (g), and in order to avoid unreasonable distribution of the fitness value or difficulty in embodying individuality, the fitness value is adjusted according to actual conditions, wherein the adjustment method mainly comprises linear change, power exponent change, exponential change, goldberg linear stretch change and the like. And recording the maximum value f of fitness in the population max Corresponding chromosome Ch max 。
S3: and (3) utilizing a binary particle swarm algorithm with self-adaptive inertia weight to mature parent individuals in the population.
Judging the relation between the current algebra counter G and the originally set pre-evolution algebra G ', if G is smaller than G', calculating the individual extremum and the global extremum of the particles (namely the individuals in the population), and then updating the speed and the position of the particles (the individuals) by adopting a formula with self-adaptive inertia weight; if g=g', making the individual extremum of the particle (individual) as the individual of the current generation population; if G > G', the selection operation in the traditional adaptive genetic algorithm is adopted to generate offspring, specifically, the proportion of individuals with large initial value of the next generation population adaptation degree value is generated according to the proportion of the adaptation degree value of each individual in the whole population adaptation degree value sum, so that the individuals with large initial value of the next generation population adaptation degree value are more easily selected and directly copied into the next generation individuals. In the embodiment, in the early stage of evolution, a binary particle swarm algorithm with adaptive inertia weight is used for maturing a parent individual; later in evolution, individuals surviving the next generation were selected in a "roulette" fashion.
Specifically, in the particle swarm algorithm, each particle (i.e., an individual in the population) has a position and a velocity, the position representing the code of the particle, and the velocity determining the distance and direction of the particle search. All particles are searched based on the particle with the largest current fitness value. Every time the optimal particle is searched, the optimal particle changes, other particles follow the new optimal particle to search, and the iteration is repeated. At the beginning of an iteration, each particle initializes its velocity and position in space by means of a random way, during an iteration the particle changes its position and velocity in solution space by tracking two extremums, one extremum being the optimal position of the individual particle itself during the iteration, called the individual extremum of the particle, and the other extremum being the optimal position of all particles in the population during the iteration, called the global extremum.
The evolutionary formula of the particle swarm algorithm is:
wherein v is id 、x id The d-th dimension component of the i-th particle velocity and position, respectively, w being the inertial weight, c 1 And c 2 Is two non-negative learning factors which determine the influence of the empirical information of the particle itself and other particles on the particle search trajectory, pos id And pos gd For the individual extremum and the global extremum, rand () is [0,1]Random numbers on the same.
Aiming at the discrete space constraint problem, a binary particle swarm algorithm is provided, and the binary particle swarm algorithm is different from the particle swarm algorithm in that: the particle can only take two values of 0/1 in the state space, and each bit of the velocity represents the possibility that the bit corresponding to the position of the particle takes the value of 0/1, so that in the binary particle swarm algorithm, the updating formula of the velocity of the particle is kept unchanged, the position of the particle is updated in a probability mapping mode, and the velocity is mapped to [0,1 ] by using a sigmoid function]The interval is taken as the probability s (v id ) This probability is the probability that the next position of the particle becomes 1:
the updated formula for the particle location is:
among the adjustable parameters of the binary particle swarm algorithm, the inertia weight w is an important parameter because it is used to control the global searching capability and the local searching capability of the algorithm, a larger w will enhance the global searching capability of the algorithm but weaken the local searching capability of the algorithm, and a smaller w will be beneficial to enhance the local searching capability of the algorithm but weaken the global searching capability of the algorithm. The conventional binary particle swarm algorithm adopts a fixed weight method, namely, a fixed inertial weight is used. In the present embodiment, in order to balance the global searching capability and the local searching capability of the binary particle swarm algorithm, the velocity v id The self-adaptive inertia weight is adopted, and the expression is as follows:
wherein w is min 、w max Respectively represent the minimum value and the maximum value of w, f max Is the maximum fitness value of all particles in the particle swarm, f avg The average fitness value of all particles in the particle swarm is f, and the fitness value of the current particle is f.
As can be seen from the expression of the adaptive inertial weight, when the fitness value of the particle is larger than the average fitness value, the particle has smaller inertial weight, so that the particle has smaller speed, and the particle is protected from being damaged; conversely, when the fitness value of the particle is smaller than the average fitness value, the particle has larger inertia weight, so that the particle has larger speed and can trend to a better search area. Therefore, the self-adaptive inertia weight can dynamically calculate the inertia weight of each particle according to the overall state of the current particle, so that the searching capability of the algorithm is globally improved.
The selection operation is to generate a population of the next generation according to the proportion of the fitness value of each individual in the total sum of fitness values of the whole population. The operation imitates the survival rule of the adaptation in the nature, the individuals with large fitness values can be directly copied into next generation individuals, so that the individuals with large fitness values can be repeatedly selected with large probability, the operation is favorable for rapid convergence of the algorithm in the later period of evolution, the operation can lead to reduced population diversity in the earlier period of evolution, the population evolution is unfavorable, and the individuals themselves are not changed due to the fact that the parent individuals are directly changed into child individuals, so that the searching efficiency of the algorithm can be reduced.
Aiming at the defects, the improved binary particle swarm algorithm with self-adaptive inertia weight is used for maturing parent individuals in the early stage of evolution, so that offspring individuals are generated, the reduction of population diversity caused by directly copying the parent individuals is avoided, individuals with small fitness values can be moved to individuals with large fitness values, and the searching efficiency of the algorithm is effectively improved. However, as the randomness of the binary particle swarm algorithm becomes stronger and stronger in the later period, the algorithm is not beneficial to converging on the global optimal solution, the selection operation of the adaptive genetic algorithm is still adopted in the later period of evolution to generate offspring individuals, so that the rapid convergence of the algorithm is facilitated. The method replaces the original selection operation, not only ensures that the population can be quickly closed to the global optimal solution in the early stage of evolution, but also ensures that the individuals in the population can be quickly converged in the later stage of evolution.
S4: and performing crossover 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 step length, 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 If the set Z is an empty set, the crossover operation is not performed, otherwise, the self-adaptive crossover probability of two chromosomes is calculated, whether the crossover operation is performed or not is judged according to the crossover probability, and if the crossover operation is performed, one N or less is generated Z Is crossed as a crossing bit number.
Traversing chromosomes in the population by taking 2 as a step length, calculating self-adaptive mutation probability, judging whether mutation operation is carried out according to the mutation probability, and randomly selecting one bit in the current chromosome binary code to carry out mutation if the mutation operation is carried out.
In particular, the tradition is inheritedThe traditional algorithm adopts a mode of fixing a crossover operator and a mutation operator, and the crossover probability and the mutation probability can not reflect the evolved state and can cause random roaming or premature phenomenon. The algorithm for solving the optimization problem should have two capabilities at the same time: the method has the advantages that the method has global searching capability, namely, a new solution space can be opened up in the process of searching a global optimal solution; and secondly, the local searching capability can be converged to an optimal solution in the area containing the optimal solution. In genetic algorithms, the balance of these two capabilities is determined by the crossover probability P c Probability of variation P m Determined, wherein the crossover probability P c Determining the frequency of crossing of individuals, P c The larger the frequency of creating new individuals, the faster, when P c When the size is too large, the possibility of damage to the individual is increased, so that the individual with high adaptability is quickly damaged, but when P c Too small, slow or even stagnant search speed may result; probability of variation P m Determining the frequency of individual variation, when P m If it is too large, the genetic algorithm will become a completely random search algorithm, but when P m If the time is too small, new individuals are not likely to occur. For complex optimization problems, it is difficult to find the best crossover probability and mutation probability for each individual, so this embodiment adopts crossover operators and mutation operators of the adaptive genetic algorithm:
wherein k is 1 And k 2 As cross probability coefficient, k 3 And k 4 As the coefficient of variation probability, k 1 、k 2 、k 3 And k 4 Is [0,1]A value of 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 in the crossed individuals, and f the fitness value of the variant individuals. In particularThe crossing operation is to randomly select two chromosomes, judge whether to cross according to the crossing probability, and f' is one of the two chromosomes with larger adaptability.
From the crossover operator and mutation operator of the above formula, in the adaptive genetic algorithm, P c And P m The adaptation varies according to the fitness value of each individual. When the population is more divergent, the P is properly increased c And P m The method comprises the steps of carrying out a first treatment on the surface of the When the population is more concentrated, P is suitably reduced c And P m . At the same time, for individuals with fitness values higher than the population average fitness value, a lower P is adopted c And P m So that the method has higher probability of entering the next generation; for individuals with fitness values lower than the average fitness value of the population, a higher P is adopted c And P m So that the probability of the solution is improved to be a better solution. Therefore, the adaptive genetic algorithm not only ensures the convergence capacity of the algorithm, but also maintains the diversity of population individuals and improves the optimization capacity of the genetic algorithm.
The crossing operation is to randomly select two chromosomes, judge whether to cross according to the crossing probability, and randomly select a position to realize the crossing operation if crossing is performed, wherein common crossing modes include single-point crossing and multi-point crossing. In the early stages of evolution, the chromosomes are very low in similarity, most crossover operations are effective, but in the later stages of evolution, the chromosomes become increasingly similar, and many ineffective crossover operations are performed, as shown in FIG. 3, chromosome Ch i And Ch k If these positions are selected to cross, no new chromosome is generated, and if these positions are selected to cross, a new chromosome can be generated only if 4 to 6 positions, i.e., positions different from the gene, are selected to cross.
Aiming at the problem of ineffective crossing, consider that validity judgment is added before crossing operation is carried out on two chromosomes, 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 Z Then determine if set Z is an empty set, i.e., N Z Whether or not it is 0, if N Z 0, do not go intoLine cross operation, if N Z If not 0, then generate a value less than or equal to N Z The random number of (2) is used as the crossing bit number to perform the crossing operation. The above operation is 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 retention
Calculating fitness value of each individual after mutation and maximum value f 'of fitness in population' max If f' max <f max The individual Ch with the largest fitness value before the maturation operation is made max Instead of individuals Ch 'with minimal fitness in the population after mutation operations' min Wherein f max Representing 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 elite individuals caused by the randomness of the algorithm is avoided. After maturation, crossover, mutation and elite retention, a new generation population P (g+1) is generated.
S6: repeating the steps S2-S5, and stopping the evolution when the evolution algebra reaches the set maximum evolution algebra.
Specifically, let g=g+1, repeat steps S2-S6, and perform iterative evolution; judging whether the current evolution algebra G reaches the set maximum evolution algebra G, if G<G, go to S2 until g=g, or the optimal fitness value f max If the continuous generations have no larger change, stopping calculation, and obtaining chromosomes of the current generation population as optimal initial values for generating the chaotic sequence.
Then, performance simulation and comparative analysis are performed on the adaptive binary particle swarm genetic algorithm provided in this embodiment. The Logistic sequence is one of chaotic sequences, and the Logistic sequence is used as a coding sequence to test the anti-interference performance of echo signals. Specifically, the mapping relationship of the Logistic sequence is:
x(k+1)＝λx(k)(1-x(k))
wherein x (k) is a chaos sequence iteration result value, k is the iteration number, when k=0, x (0) is an initial value for generating a chaos sequence, and the value range is 0< x (0) <1. Lambda is a system parameter and the value range is 3.5699456.
The chaotic phase coding is to take a binary sequence obtained by quantization of a chaotic sequence as a phase coding sequence. Mean value E of chaotic sequence n The method comprises the following steps:
the method comprises the following steps of performing binary quantization treatment on a chaotic sequence obtained by chaotic mapping to obtain:
the phase sequence of the chaotic two-phase coded signal is as follows:
it is found from experiments that when λ=4, the obtained sequence has the best chaos property with the initial value unchanged. The choice of a suitable initial value x (0) is therefore the core for generating a high agility and orthogonality logic sequence.
In this embodiment, a logic sequence initial value is selected, and a phase encoded signal with a code length of p=100 and a symbol pulse width t=0.1 μs is generated, and a simulation result thereof is shown in fig. 4. From the graph, the interference immunity of the randomly selected Logistic sequence echo signal with the code length P=100 is 9.3704dB.
Under the same condition, 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 adaptive binary particle swarm genetic algorithm parameter table
The adaptive binary particle swarm genetic algorithm according to the embodiment of the present invention simulates a Logistic sequence with a code length p=100 by using parameters shown in table 1, and when the target speed v=0m/s and the echo signal is not blocked, the simulation results refer to fig. 5a and fig. 5b, wherein fig. 5a is a graph of the change of the optimal fitness value and the average fitness value of each generation of individual with the evolution algebra during the iteration of the adaptive binary particle swarm genetic algorithm, and fig. 5b is a graph of the 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 searching method provided by the embodiment of the invention is used, the maximum adaptability value is 15.9176dB, the anti-interference performance result obtained by carrying out Logistic sequence anti-interference waveform design by using the searched result is shown in FIG. 5b, the maximum peak value is 16.4782dB, and the anti-interference performance is improved by 7.3788 dB compared with that before the phase encoding searching. As can be seen from the optimal fitness value curve of each generation in FIG. 5a, the method has good global searching capability in the early stage, can quickly converge to a better solution, has good local searching capability in the later stage, can continuously jump out a local optimal solution and gradually converges to the searched optimal solution, so that the algorithm has both global searching capability and local searching capability.
The adaptive binary particle swarm genetic algorithm of the embodiment is suitable for solving the combination optimization problem, the optimal initial value of the Logistic sequence is searched and generated by using the algorithm, the objective function is the ratio of the current pulse period of the Logistic sequence echo signal to the cross-correlation peak value of the jacket pulse period to the auto-correlation peak value of the current pulse period, the fitness value is normalized again by the ratio of the cross-correlation peak value of the current pulse period to the auto-correlation peak value of the jacket pulse period to the auto-correlation peak value of the current pulse period, 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, a radar using a transmitting/receiving common antenna cannot receive a signal during a signal transmission period, and thus, echoes of some targets cannot be completely received, which is called distance blocking, which is also called echo cutting or echo blocking. In the case of distance occlusion, pulse compression is partially correlated, which not only deteriorates the side lobe performance of pulse compression and has a certain influence on the detection target, but also has a certain loss of signal energy. And the echo signal is often accompanied by a doppler effect, so that the modulation phases of the echo signal and the transmission signal are not matched, which causes loss of pulse compression and even cannot compress the target, and therefore the doppler shift and the distance shielding should be taken into consideration.
The performance of the Genetic Algorithm (GA) in the prior art and the performance of the binary particle swarm genetic algorithm (AGABPSO) in the invention are respectively simulated and compared under the conditions of no Doppler frequency shift, no distance shielding, doppler frequency shift and distance shielding. Because the two algorithms are required to generate initial values in a random mode, the running results of each time are not identical, the result of a certain time is not representative, the actual problem cannot be described, the simulation result presented in the part is the result with the maximum frequency of running each algorithm for fifty times under different conditions, the result can effectively reflect the performance of each algorithm, and the simulation result has a certain practical significance. Five algorithms are used for respectively simulating the Logistic sequence with the code length of P= [100,500,1000,5000], wherein the simulation result of the Logistic sequence with the code length of 100 is presented in a graph form, and the simulation results of the Logistic sequences with the rest code lengths are presented in a table form.
(1) Echo signal has no Doppler shift and no distance shielding
Simulation results for a 100-bit Logistic sequence using two algorithms are shown in FIG. 6. As shown in FIG. 6, two algorithms are used to simulate a 100-bit Logistic sequence under the condition that echo signals have no Doppler frequency shift and no distance shielding, the anti-interference performance obtained by adopting a binary particle swarm genetic algorithm is about 16.5dB, and the anti-interference performance obtained by adopting the genetic algorithm is about 15.5dB, so that the optimal fitness value obtained by adopting the binary particle swarm algorithm is higher, the anti-interference performance is better, and the overall optimal solution is easier to converge through a series of improvements. The genetic algorithm converges faster than the present example algorithm, but is not a globally optimal solution.
The optimal fitness value obtained by simulating the Logistic sequence with the code length of P= [100,500,1000,5000] by 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 two algorithms without Doppler shift and distance occlusion
| Code length | GA(dB) | AGABPSO(dB) | Anti-interference performance is improved (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 were used to simulate the Logistic sequence with the code length p= [100,500,1000,5000] without doppler shift and distance occlusion of the echo signal. 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 to obtain a globally optimal solution through a series of improvements.
(2) The echo signal has Doppler frequency shift and distance shielding
Simulation results for a 100-bit Logistic sequence using two algorithms are shown in FIG. 7. As can be seen from fig. 7, two algorithms are used to simulate 100-bit Logistic sequences respectively under the conditions that the target speed v=50m/s and the echo distance shielding is 30%, and the anti-interference result is affected to a certain extent. The self-correlation peak value is reduced due to the sensitivity characteristic of the phase coding signal to the speed, so that the anti-interference performance is reduced by about 1dB compared with the previous case. However, from comparison in the figure, the example proposes that the algorithm 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 two algorithms for Doppler shift and distance occlusion
| Code length | GA(dB) | AGABPSO(dB) | Anti-interference performance is improved (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 simulate the Logistic sequence of the p= [100,500,1000,5000] bit, 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 anti-interference performance, so as to solve the initial value of the Logistic sequence corresponding to the optimal fitness value. From the above table, the phase encoded signal after the addition speed and occlusion is degraded in anti-interference performance, which is determined by the characteristics of the phase encoding itself. However, in this case, the algorithm can still obtain a globally optimal solution, which minimizes the speed and occlusion effects.
In summary, the embodiment of the invention provides an anti-interference waveform design method based on a self-adaptive binary particle swarm genetic algorithm, which is verified to have local searching capability and global searching capability by taking a Logistic chaotic sequence as an example in experiments, is suitable for solving the problem of combination optimization of the anti-interference waveform design of the chaotic sequence, and improves searching efficiency under the condition of maintaining population diversity. Simulation results show that: the method can still converge to a high-quality solution with a larger probability when the code length of the chaotic sequence is longer, and effectively improves the performance of the anti-interference waveform design method for obtaining the waveform when the code length is longer.
The 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 optimal value by improving the offspring maturation method and adaptively changing the crossover and mutation probability. In addition, the orthogonal characteristic of the chaotic sequence is adopted, so that the algorithm can more easily search an initial value with optimal anti-interference performance on the basis, the optimization consumption is greatly reduced, and the anti-interference performance can be ensured to be maintained in a higher range when the number of coding 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 further detailed description of the invention in connection with the preferred embodiments, and it is not intended that the invention be limited to the specific embodiments described. It will be apparent to those skilled in the art that several simple deductions or substitutions may be made without departing from the spirit of the invention, and these should be considered to be within the scope of the 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.
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