CN109039974B - PSO-GA hybrid algorithm-based directional modulation signal synthesis method - Google Patents

PSO-GA hybrid algorithm-based directional modulation signal synthesis method Download PDF

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CN109039974B
CN109039974B CN201810912971.1A CN201810912971A CN109039974B CN 109039974 B CN109039974 B CN 109039974B CN 201810912971 A CN201810912971 A CN 201810912971A CN 109039974 B CN109039974 B CN 109039974B
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王伶
刘峰
谢坚
陶明亮
粟嘉
张兆林
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Abstract

The invention provides a PSO-GA (particle swarm optimization-genetic algorithm) -based directional modulation signal synthesis method, which constructs a low-complexity multi-objective function based on signal synthesis of a quaternary phased array directional modulation communication system, and designs a PSO-GA-based hybrid algorithm by combining the characteristics of high convergence speed of a particle swarm optimization algorithm and strong global search capability of a genetic algorithm, so that the defect of a single optimization algorithm is overcome, and the effectiveness of the method is verified by a simulation result.

Description

PSO-GA hybrid algorithm-based directional modulation signal synthesis method
Technical Field
The invention relates to a direction modulation signal synthesis method.
Background
The traditional wireless communication transmitter signal is modulated at baseband, then up-converted and power amplified to the radio frequency domain. The transmitted signal is only power-different in each direction and the constellation format remains substantially unchanged. Therefore, an eavesdropper can easily recover information in an undesired direction by using a highly efficient and sensitive receiver, which is very disadvantageous for the physical layer secure transmission. Directional modulation is considered as a promising secure transmission technology, and is an effective approach to wireless communication security.
The direction modulation technology transmits digital modulation information along a pre-designated direction, and simultaneously causes a constellation diagram to be seriously distorted in other directions, and the signal has strong directivity, thereby effectively improving the safety of wireless transmission. In conventional transmitters, the radiation pattern beamwidth represents the power directivity of the beam; in a directional modulation transmitter, the information beam width represents the information directivity of the beam.
In document 1, "m.p.daly, j.t.bernhard.directional modulation technique for phased arrays.ieee trans.antennas propag., vol.57, No.9, pp.2633-2640, sep.2009", a phased array antenna is introduced, and a directional modulation signal is synthesized based on a single target function using a genetic algorithm, but this synthesis method only considers that the baseband modulation signal maintains the same constellation format in the transmission direction, and does not consider the distortion degree of the constellation diagram in an undesired direction.
Document 2, "Hong Tao, Song Maozhong, Liu yu. design of direct modulation signal based on multi-objective genetic algorithm for physical layer communication, journal of Applied sciences.vol.32, pp.51-56,2014," applies a genetic algorithm based on a multi-objective function to synthesize a directional modulation signal, but does not consider the convergence rate of the optimization algorithm.
Document 3 "Ding Y, Fusco v.directional modulation transmitter synthesis using a specific sampling timing, ieee Antennas and processing reference, vol.9, No.6, pp.500-503,2014" sets a phase shift value according to the system error rate performance, and synthesizes a directional modulation signal using a particle swarm optimization algorithm, but does not consider the global search capability of the optimization algorithm.
The above documents use different objective functions and optimization methods to synthesize the directional modulation signal, each having advantages and disadvantages.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a direction modulation signal synthesis method based on a PSO-GA (particle swarm optimization-genetic Algorithm), which is characterized in that a multi-objective function and a hybrid optimization algorithm are constructed on the basis of a phased array direction modulation technology to realize direction modulation signal synthesis, and the complexity of the objective function is reduced by combining the characteristics of high convergence speed of a particle swarm optimization algorithm and strong global search capability of a genetic algorithm, so that the direction modulation has better safety performance.
The technical scheme adopted by the invention for solving the technical problem comprises the following steps:
step one, in a direction modulation communication system based on a quaternary phased array, an electric vector of an ith QPSK symbol transmitted by a direction modulation transmitter and reaching a far-field receiver is
Figure BDA0001762243000000021
Wherein, anIndicating the amplitude of excitation of the antenna element n, psin(i) Representing the excitation phase of an antenna element n, theta being the azimuth angle about the z-axis, k-2 pi/lambda being the electromagnetic wave propagation constant, lambda being the carrier wavelength, the target receiver being located in the far field, and R being approximated in terms of amplituden≈R0The phase of the signal, in terms of phase,
Figure BDA0001762243000000022
the distance of the term is approximately Rn≈R0-ndsin θ; assuming that the amplitude excitations of all array elements are the same and normalized to a0＝a1＝a2＝a31, the antenna directivity function of each array element is represented by fe(theta, phi) represents, the radiation of the directional modulation transmitter at the P point and the field intensity are represented as
Figure BDA0001762243000000023
The constellation points of QPSK modulation are represented as
Figure BDA0001762243000000024
In order to maintain the desired direction thetasUpper constellation diagram, defining an objective function
Figure BDA0001762243000000025
Defining an objective function
Figure BDA0001762243000000026
Wherein, thetacIs a constant, with a value of 10 °, step is a step, with a value of 0.01;
therefore, the multi-objective optimization model is designed as
Figure BDA0001762243000000027
For comparing the performance of the algorithm, another multi-objective optimization model is established
Figure BDA0001762243000000031
Defining a search area as a 16-dimensional space, setting the value range of each dimensional space to be-180 degrees, setting the search precision to be 0.01 degrees, and adopting 16-bit coding as a chromosome; PSO employs global optimization model xid k+1＝xid k+vid k+1，
vid k+1＝ω·vid k+c1·rand1()·(pbest_id k-xid k)+c2·rand2()·(gbest_id k-xid k) Wherein v isidIs the velocity, x, of the particle iidIs the position of the particle i, pbest_id kIs the best position that the particle i has experienced, gbest_id kIs the global best position that particle i has experienced; superscript k denotes the kth iteration and subscript d denotes the d-th dimension; rand1() And rand2() Is a random variable, uniformly distributed over [0,1 ]]；c1And c2Is an acceleration factor, and the value is 1.5; omega is an inertial weight and has a value ranging from 0.9 to 0.4;
the particle swarm size K is set to 10000, and the maximum iteration number is set to 100; the population size used by the genetic algorithm is consistent with the population scale of the PSO;
the selection operator design of the genetic algorithm uses a mixed strategy of proportion selection and optimal storage, and the probability of selecting an individual i is
Figure BDA0001762243000000032
Wherein, FiIs the fitness of the individual i;
the crossover operator of the genetic algorithm adopts single-point crossover, and firstly, a crossover position is randomly generated; then, the two father chromosomes take the crossing position as a boundary and mutually exchange chromosomes at the front section of the crossing position; probability of inter-process crossing PcIs set to 0.8, PcDetermining whether to implement the crossover operation;
generating a mutation operator of a genetic algorithm, namely randomly generating two mutation positions; then the values at the two variant positions are exchanged; probability of variation in processThe ratio is set to PmIs 0.05, PmDetermining whether mutation operation is performed;
the hybrid optimization algorithm is specifically realized by the following steps:
(1) the parameters are initialized. Randomly generating N individuals according to a coding rule of a problem to form an initial population, and substituting each individual into a target function to obtain corresponding fitness;
(2) evaluating the fitness function and recording the optimal solution p of the particlesbest_idAnd the current optimal solution g of the populationbest_id；
(3) According to vid k+1＝ω·vid k+c1·rand1()·(pbest_id k-xid k)+c2·rand2()·(gbest_id k-xid k) Update the particle velocity according to xid k+1＝xid k+vid k+1Updating the particle positions, and outputting an initial optimized population after the maximum iteration times are reached;
(4) according to the formula
Figure BDA0001762243000000041
Selecting individuals according to the cross probability PcPerforming cross operation to generate a new individual;
(5) with a mutation probability PmPerforming mutation operation to generate new individuals to be added into the offspring population;
(6) stopping when the set iteration condition is met, outputting the optimal individual as an optimization result, otherwise, jumping to the step (4);
and step three, solving the multi-objective function by using a hybrid algorithm to obtain a global optimal solution.
The invention has the beneficial effects that: a low-complexity multi-target function based on signal synthesis of a quaternary phased array directional modulation communication system is constructed, a PSO-GA-based hybrid algorithm is designed by combining the characteristics of high convergence speed of a particle swarm optimization algorithm and strong global search capability of a genetic algorithm, the defect of a single optimization algorithm is overcome, and the effectiveness of the method is verified by a simulation result.
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FIG. 1 is a direction modulation transmitter based on a quaternary phased array;
FIG. 2 is a block diagram of an implementation of a PSO-GA based hybrid optimization algorithm;
FIG. 3 is a constellation diagram of the optimal and worst solutions at 60, 55, and 65 orientations;
FIG. 4 is a graph of bit error rate at different azimuth angles for a directionally modulated signal synthesized by four different methods;
fig. 5 is a graph of the convergence of the three optimization algorithms.
Detailed Description
The present invention will be further described with reference to the following drawings and examples, which include, but are not limited to, the following examples.
The invention provides a PSO-GA hybrid algorithm-based directional modulation signal synthesis method, which combines the characteristics of high convergence speed of a particle swarm optimization algorithm and strong global search capability of a genetic algorithm to complement the advantages, constructs a hybrid algorithm, realizes the synthesis of directional modulation signals and enables the directional modulation to have better safety performance.
The invention uses a direction modulation transmitter based on a quaternary phased array, and the schematic block diagram of the direction modulation transmitter is shown in figure 1. The antenna array is a four-element linear microstrip plate-shaped antenna array, and the array element interval is half wavelength. The transmitted signal is QPSK modulated. It is assumed that the target receiver is located in the far field region of the antenna array. The i-th QPSK symbol transmitted by the transmitter reaches the far-field electric vector of the receiver to be
Figure BDA0001762243000000051
Wherein, anIndicating the amplitude of excitation of the antenna elements, #n(i) Which represents the excitation phase of the antenna element, i.e. the nth phase shift. θ is the azimuth angle about the z-axis. k 2 pi/λ is an electromagnetic wave propagation constant, and λ is a carrier wavelength.
In most applications, only the far-field signal is considered, so some approximation can be done. In the vector of the electric fieldIn terms of amplitude, the difference in distance between different antenna elements to a target receiver is negligible and is approximately represented as Rn≈R0. Meanwhile, the target receiver is limited to be positioned in an x-z plane, so that the electric field vector is independent of phi, and the phi can be an arbitrary value.
Figure BDA0001762243000000052
The distance in the term can be approximately expressed as
Rn≈R0-nd sinθ (2)
For a quaternary uniform linear array, assuming that the amplitude excitations of all array elements are the same and normalized, then there are
a0＝a1＝a2＝a3＝1 (3)
The antenna directivity function of each array element is defined by feAnd (theta, phi) are uniformly expressed, and meanwhile, the coupling among array elements is ignored, and the normalization is 1.
In summary, the field strength of the directional modulation transmitter at the point P can be regarded as the mutual superposition of the electric vectors of the transmitted signals of the 4 array elements. Thus, the combined field strength at P can be expressed as
Figure BDA0001762243000000053
Therefore, by setting an appropriate phase shift value ψ0(i),ψ1(i),ψ2(i),ψ3(i) In a desired direction thetasThe conventional baseband modulation signal is synthesized.
Constellation points for QPSK modulation are represented as
Figure BDA0001762243000000054
In order to maintain the desired direction thetasThe above constellation, an objective function is defined as follows
Figure BDA0001762243000000055
The target function only considers that the constellation diagram in the expected direction is in a standard format, no constraint is made on the distortion degree of the constellation diagram in the unexpected direction, and the single target optimization result may cause the approximate standard constellation format to appear in some unexpected directions, so that the safety of directional modulation is reduced. Therefore, in order to obtain the maximum information beam width and increase the directional modulation security, the degree of constellation distortion in a certain range near the undesired direction is considered to be as maximum as possible, and in order to reduce the computational complexity and facilitate the hardware implementation, another objective function is defined as follows
Figure BDA0001762243000000061
Wherein, thetacIs a constant, with a value of 10 °, step is a step, with a value of 0.01. .
Therefore, the multi-objective optimization model is designed as
Figure BDA0001762243000000062
A pareto optimal solution of the multi-objective function (8) is defined as a multi-objective function optimal solution. In order to compare the performance of the algorithm, another multi-objective optimization model is established
Figure BDA0001762243000000063
And simultaneously defining the pareto optimal solution of the multi-objective function (9) as a multi-objective function worst solution.
Because the optimization task is a multi-objective and highly non-linear problem, classical optimization algorithms tend to result in locally optimal solutions that are no longer suitable for the solution of the problem. In order to better realize global convergence, the invention designs a PSO-GA-based hybrid optimization algorithm. The method comprises the steps of firstly, carrying out optimization in the previous stage by utilizing the rapid convergence characteristic of a particle swarm optimization algorithm to obtain an initial population evolved to a certain degree; and then, carrying out the optimization of the later stage by using a genetic algorithm to obtain a global optimal solution. A block diagram of an implementation of the hybrid optimization algorithm is shown in fig. 2.
For the synthesis of the direction modulation signals of the quaternary phased array, the parameters of the hybrid optimization algorithm are designed as follows.
The search area is a 16-dimensional space, and the value range of each dimensional space is-180 degrees to 180 degrees. The search accuracy was set to 0.01 °. Therefore, each dimensional space adopts 16bit encoding as one chromosome and corresponds to a particle in the particle swarm optimization.
Aiming at PSO, the invention adopts a global optimization model, and the specific form is as follows:
vid k+1＝ω·vid k+c1·rand1()·(pbest_id k-xid k)+c2·rand2()·(gbest_id k-xid k) (10)
xid k+1＝xid k+vid k+1 (11)
wherein v isidIs the velocity, x, of the particle iidIs the position of the particle i, pbest_id kIs the best position that the particle i has experienced, gbest_id kIs the global best position that particle i has experienced. The superscript k denotes the kth iteration and the subscript d denotes the d-th dimension.
rand1() And rand2() Is a random variable, uniformly distributed over [0,1 ]]。c1And c2Is an acceleration factor, and takes a value of 1.5. ω is the inertial weight, which varies linearly with the number of iterations, with a value in the range of 0.9 to 0.4.
vidAnd xidMay evolve large enough to fly the particle out of the solution space. Thus, v is definedidMaximum value of vmax，xidMaximum value of (2) is xmax。
The size K of the particle group was 10000, and the maximum number of iterations was 100.
For GA, in order to maintain continuity of algorithm interfaces, the population size used by genetic algorithms is designed to be consistent with the population size of PSO.
The selection operator design of the genetic algorithm uses a hybrid strategy of proportional selection and optimal preservation. The probability that the individual i is selected is
Figure BDA0001762243000000071
Wherein, FiIs the fitness of the individual i.
The crossover operator of the genetic algorithm adopts single-point crossover, and the implementation steps are as follows:
(1) randomly generating a crossing position;
(2) the two parents are bound by the crossing position, and the chromosomes at the front section of the crossing position are mutually exchanged.
(3) Cross probability PcIs set to 0.8, PcIt is determined whether or not the interleaving operation is performed.
The mutation operator of the genetic algorithm is realized by the following steps:
(1) randomly generating two variation positions;
(2) swapping values at two variant positions;
(3) the mutation probability is set to PmIs 0.05, PmIt is determined whether mutation operations are performed.
In summary, the hybrid optimization algorithm is implemented as follows:
(1) the parameters are initialized. Randomly generating N individuals according to a coding rule of a problem to form an initial population, and substituting each individual into a target function to obtain corresponding fitness;
(2) evaluating the fitness function and recording the optimal solution p of the particlesbest_idAnd the current optimal solution g of the populationbest_id；
(3) Updating the particle speed according to the formula (10), updating the particle position according to the formula (11), and outputting an initial optimization population after the maximum iteration times are reached;
(4) selecting individuals according to equation (11) with a crossover probability PcPerforming crossover operation to generate new oneA body;
(5) with a mutation probability PmPerforming mutation operation to generate new individuals to be added into the offspring population;
(6) and (4) stopping when the iteration condition is met, outputting the optimal individual as an optimization result, and otherwise, jumping to the step (4).
In step (3), when the particle position is updated according to equation (11), the particle position may become a decimal, which does not conform to the encoding definition, and the decimal needs to be set to the nearest integer.
Table 1 phase shift values of QPSK symbols integrated in the desired direction (60 °) using a hybrid optimization algorithm
Figure BDA0001762243000000081
The phase shift values of the QPSK symbols integrated in the desired direction (60 °) according to the above optimization procedure are shown in table 1. The constellation of the best and worst solutions in the directions 60 °, 55 ° and 65 ° is shown in fig. 3. As can be seen from fig. 3, the constellation in all directions except the desired direction 60 ° is distorted to a different extent. The constellation of the best solution transmitter has severe distortion in the direction of 55 degrees, while the constellation of the worst solution transmitter has less distortion in the direction of 55 degrees, and an eavesdropper can easily recover information by using a high-sensitivity receiver. Thereby showing the effectiveness of the hybrid optimization algorithm.
The bit error rate performance at different azimuth angles of the directional modulation signal integrated by the four different methods is shown in fig. 4. The four comprehensive methods used for simulation are a directional modulation transmitter optimized by a genetic algorithm, a directional modulation transmitter optimized by a particle swarm optimization algorithm, a directional modulation transmitter optimized by a hybrid algorithm and the directional modulation transmitter of the document [2 ]. It can be seen from fig. 4 that the error rates of the four transmitters in the desired direction are almost the same at 60 °, and the error rate degradation degree of the direction modulation transmitter in the hybrid optimization algorithm in the vicinity of 60 ° is obviously better than that of the other transmitters, the information beam width is narrower, and the security is higher.
The direction modulation signals are respectively synthesized by adopting a standard genetic algorithm, a particle swarm optimization algorithm and a hybrid optimization algorithm, and the convergence curves of the three algorithms are shown in figure 5. From fig. 5, the convergence rate of the hybrid optimization algorithm is superior to the genetic algorithm, and inferior to the particle swarm optimization algorithm. From the overall result, the hybrid algorithm has better optimization performance.
The invention has been described in detail for the purpose of enabling those skilled in the art to understand the invention, but it is contemplated that other changes and modifications may be made without departing from the scope of the invention encompassed by the claims.

Claims (1)

1. A PSO-GA hybrid algorithm-based directional modulation signal synthesis method is characterized by comprising the following steps:
step one, in a direction modulation communication system based on a quaternary phased array, an electric vector of an ith QPSK symbol transmitted by a direction modulation transmitter and reaching a far-field receiver is
Figure FDA0002929868470000011
Wherein, anRepresents the excitation amplitude of an antenna array element n, phi represents the pitch angle of a far-field target point relative to the x-axis of the antenna array, phin(i) Representing the excitation phase of an antenna element n, theta being the azimuth angle about the z-axis, k-2 pi/lambda being the electromagnetic wave propagation constant, lambda being the carrier wavelength, the target receiver being located in the far field, and R being approximated in terms of amplituden≈R0The phase of the signal, in terms of phase,
Figure FDA0002929868470000017
the distance of the term is approximately Rn≈R0-nd sin θ; assuming that the amplitude excitations of all array elements are the same and normalized to a0＝a1＝a2＝a31, the antenna directivity function of each array element is represented by fe(theta, phi) represents, the radiation of the directional modulation transmitter at the P point and the field intensity are represented as
Figure FDA0002929868470000012
d represents the distance between adjacent array elements in the uniform linear array, and the constellation points of QPSK modulation are represented as
Figure FDA0002929868470000013
In order to maintain the desired direction thetasUpper constellation diagram, defining an objective function
Figure FDA0002929868470000014
Defining an objective function
Figure FDA0002929868470000015
Wherein, thetacIs a constant, with a value of 10 °, step is a step, with a value of 0.01;
therefore, the multi-objective optimization model is designed as
Figure FDA0002929868470000016
For comparing the performance of the algorithm, another multi-objective optimization model is established
Figure FDA0002929868470000021
Defining a search area as a 16-dimensional space, setting the value range of each dimensional space to be-180 degrees, setting the search precision to be 0.01 degrees, and adopting 16-bit coding as a chromosome; PSO employs global optimization model xid k+1＝xid k+vid k+1，
vid k+1＝ω·vid k+c1·rand1()·(pbest_id k-xid k)+c2·rand2()·(gbest_id k-xid k) Wherein v isidIs the velocity, x, of the particle iidIs the position of the particle i, pbest_id kIs the best position that the particle i has experienced, gbest_id kIs the global best position that particle i has experienced; superscript k denotes the kth iteration and subscript d denotes the d-th dimension; rand1() And rand2() Is a random variable, uniformly distributed over [0,1 ]]；c1And c2Is an acceleration factor, and the value is 1.5; omega is the inertia weight and has the value range of 0.4 to 0.9;
the particle swarm size K is set to 10000, and the maximum iteration number is set to 100; the population size used by the genetic algorithm is consistent with the population scale of the PSO;
the selection operator design of the genetic algorithm uses a mixed strategy of proportion selection and optimal storage, and the probability of selecting an individual i is
Figure FDA0002929868470000022
Wherein, FiIs the fitness of the individual i;
the crossover operator of the genetic algorithm adopts single-point crossover, and firstly, a crossover position is randomly generated; then, the two father chromosomes take the crossing position as a boundary and mutually exchange chromosomes at the front section of the crossing position; probability of inter-process crossing PcIs set to 0.8, PcDetermining whether to implement the crossover operation;
generating a mutation operator of a genetic algorithm, namely randomly generating two mutation positions; then the values at the two variant positions are exchanged; setting mutation probability as PmIs 0.05, PmDetermining whether mutation operation is performed;
the hybrid optimization algorithm is specifically realized by the following steps:
(1) initializing each parameter, randomly generating N individuals according to a coding rule of a problem to form an initial population, and substituting each individual into a target function to obtain corresponding fitness;
(2) evaluating the fitness function and recording the optimal solution p of the particlesbest_idAnd the current optimal solution g of the populationbest_id；
(3) According to vid k+1＝ω·vid k+c1·rand1()·(pbest_id k-xid k)+c2·rand2()·(gbest_id k-xid k) Update the particle velocity according to xid k+1＝xid k+vid k+1Updating the particle positions, and outputting an initial optimized population after the maximum iteration times are reached;
(4) according to the formula
Figure FDA0002929868470000031
Selecting individuals according to the cross probability PcPerforming cross operation to generate a new individual;
(5) with a mutation probability PmPerforming mutation operation to generate new individuals to be added into the offspring population;
(6) stopping when the set iteration condition is met, outputting the optimal individual as an optimization result, otherwise, jumping to the step (4);
and step three, solving the multi-objective function by using a hybrid algorithm to obtain a global optimal solution.
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