Distributed signal synthesis power distribution method based on improved particle swarm optimization

Abstract

The invention discloses a distributed signal synthesis power distribution method based on an improved particle swarm algorithm, and belongs to the technical field of signal synthesis. The method comprises the following steps: firstly, determining the number of array elements to be optimized, the position of each array element, a distribution power limiting condition, an antenna gain and the position of a target synthesis point, and constructing a constrained optimization problem which takes a field intensity value of the target synthesis point as a target and takes the distribution power of each array element as an independent variable through a distributed signal field intensity three-dimensional synthesis principle; a PSO algorithm is taken as a main body, and an optimal solution of an independent variable is obtained by fusing Bernoulli chaotic mapping initialization, a nonlinear random decline inertia weight based on a population separation degree and a Cauchy disturbance strategy. The method is high in convergence speed and high in convergence precision, and can meet the requirement of improving the synthesis effect of the target synthesis point when distributed signal coherent synthesis is carried out under the condition that the array element power is limited.

Description

Technical Field

[0001] The invention belongs to the technical field of signal synthesis, and in particular relates to a distributed signal synthesis power allocation method based on an improved particle swarm algorithm. Background Art

[0002] In designing solutions for distributed spatial power synthesis, the main obstacle is how to solve the optimization design of the main parameters in such solutions, that is, how to solve the problem of extreme value optimization of such multi-extreme, multi-dimensional, nonlinear multi-objective functions. Traditionally, intelligent optimization algorithms such as PSO and GA are used to solve such problems. However, the standard PSO algorithm is prone to slow convergence and falling into local optimality when dealing with function optimization problems involving high-dimensional independent variables and complex combinatorial optimization problems. Some scholars proposed the DMS-PSO algorithm using the dynamic neighborhood topological structure as the learning sample of the particle swarm. The large population is divided into small populations through the topological structure, which to a certain extent avoids the algorithm from falling into the local optimal problem. However, this method also sacrifices some global search capabilities, making it not strong in convergence when dealing with high-dimensional problems with low correlation between decision variables. Some scholars also divided the particle evolution state into four stages of exploration, mining, convergence and jump out to speed up the convergence speed of PSO and try to avoid the algorithm from falling into the local optimal state, and adopted elite Gaussian learning to adaptively control the inertia weight and acceleration coefficient and proposed the APSO algorithm. This type of algorithm can accelerate the convergence of the algorithm through parameter adaptive control, and help the population escape from the local optimum through elite learning, and has achieved good results in a specific set of benchmark functions. However, the algorithm effect is highly sensitive to the parameter elite learning rate. How to find the best adjustment strategy for the elite learning rate in different problems and environments needs further study.

[0003] In addition, the inertia weight in the standard PSO is mostly linearly decreased or cosine decreased. An obvious defect of these two methods is that the iterative update of the inertia weight is not strongly associated with the state of the population in the iteration. However, there is still a lack of algorithm design for power allocation scheme that can effectively solve the above problems in the prior art. Summary of the invention

[0004] The purpose of the present invention is to propose a distributed signal synthesis power allocation method based on an improved particle swarm algorithm to solve the above problems. The present invention improves the particle swarm optimization (PSO) algorithm by using chaotic mapping, nonlinear dynamic adaptive inertia weight and Cauchy perturbation, and uses it for node power allocation of distributed signal synthesis, which can effectively improve the signal field strength of the target synthesis point.

[0005] The technical solution adopted by the present invention is:

[0006] A distributed signal synthesis power allocation method based on an improved particle swarm algorithm is applied to a distributed array with dispersed arrays to allocate the power value of each array element during signal coherent synthesis; wherein, the number of array elements is N, and a rectangular coordinate system of the northeast sky is established, then the array element position is L i (x i ,y i z i ), i = 1, 2, ..., N, the position of the target synthesis point C is C (x0, y0, z0), the position of any point M in the synthesis area is M (x, y, z), R ic is the distance from the ith array element to point C, R i is the distance from the ith array element to point M; the directional patterns of all array elements are the same and their centers all point to point C;

[0007] The method comprises the following steps:

[0008] Step 1: Control the initial phase of the transmit signal of the i-th array element to be:

[0009]

[0010] Where, λ is the signal wavelength;

[0011] The phase of the transmitted signal of the i-th array element arriving at point M is calculated as:

[0012]

[0013] The field strength generated by the transmitted signal of the i-th array element at point M is calculated as:

[0014]

[0015] in, P i represents the power allocated to the i-th array element, G T represents the antenna gain of the array element; f i (θ i ,α i ) represents the array antenna pattern function of the i-th array element, the elevation angle θ i is the angle between the line from the ith array element to point M and the xOy plane, and the direction angle α i is the angle between the projection of the line from the ith array element to point N on the xOy plane and the x-axis, k is 2ω / λ;

[0016] Step 2: Decompose the signal intensity at point M into intensity components in three spatial directions:

[0017]

[0018] Therefore, the signal intensity at point M is expressed as the superposition of the intensity components in three directions:

[0019]

[0020] in, They respectively represent the x-direction, y-direction, and z-direction components of the field strength generated by the transmit signals of all array elements at point M;

[0021] Step 3: Construct a constrained optimization problem with the field strength value at point C as the target and the power value allocated to each array element as the independent variable:

[0022]

[0023] in, It represents the field strength generated by all array element transmission signals at point C. They respectively represent the x-direction, y-direction, and z-direction components of the field strength generated by the transmit signals of all array elements at point C;

[0024] The power limit condition imposed on the array element is:

[0025]

[0026] Among them, P sum The upper limit of the total power allocated to each array element, P i is the allocated power of the ith array element, P min , P max Assigning upper and lower limits of power to a single array element;

[0027] Step 4: Use the allocated power value of each array element as the particle population and initialize it using Bernoulli chaotic mapping:

[0028] Set the control parameter λ B , loop iterates the Bernoulli definition:

[0029]

[0030] Among them, z k Indicates the sequence value generated for the kth time;

[0031] The generated chaotic sequence is converted into the restricted range of formula (10), and the initialization population P = [p 1, p2,…,p N ];

[0032] Step 5, setting the nonlinear dynamic adaptive inertia weight w(t) based on population separation to keep the particles inertia;

[0033] Step 6: Apply disturbance to the particle population that falls into premature convergence, and define the judgment criterion of premature convergence as:

[0034]

[0035] f mi =max(1,|f i -f avg |) (13)

[0036] Among them, f i represents the fitness value of the i-th particle in the current iteration, f avg represents the average fitness value of the entire population in the current iteration, f mi is an intermediate variable;

[0037] Setting Δ 2 The threshold value of Δ 2 With the size of the threshold, when Δ 2 When it is less than the threshold, the population is considered to have fallen into premature convergence;

[0038] Step 7: After judging that the population has converged prematurely, sort the population in descending order according to the fitness value, take out the top 20% of particles, and apply velocity perturbation as follows:

[0039]

[0040] Among them, v id (t) is the particle velocity of the current generation, c1 and c2 are learning rates, and p id (t) is the optimal value of the individual in the current generation, g best is the global optimal value currently searched, x id (t) is the position of the particle of the current generation, r1(t), r2(t), and rand are random numbers between [0,1]. Indicates that the mean is 0 and the variance is p id (t) the Cauchy distribution function value;

[0041] Step 8: Apply position disturbance to the population after applying velocity disturbance:

[0042]

[0043] Step 9, iterate steps 5 to 8 for a total of T times, and output the optimal population, which is the optimal power allocation solution g best .

[0044] Furthermore, the specific method of step 5 is:

[0045] The population separation d(t) is expressed as:

[0046]

[0047] Among them, varfit(t) represents the variance of the fitness value of the t-th generation population;

[0048] Combining the population separation d(t) with the Tanh activation function, we get the nonlinear dynamic adaptive inertia weight w(t):

[0049]

[0050] Among them, W max , W min are the upper and lower limits of the inertia weight, T is the maximum number of iterations, and b is the damping factor.

[0051] Compared with the prior art, the present invention has the following advantages:

[0052] 1. The present invention adopts Bernoulli chaotic map initialization, designs nonlinear dynamic adaptive inertia weight and Cauchy perturbation strategy based on population separation, which can effectively accelerate the algorithm convergence speed, improve the algorithm convergence accuracy, and effectively improve the target synthesis point signal synthesis effect.

[0053] 2. The present invention can be applied to distributed signal synthesis scenarios of distributed arrays with arbitrary linear / planar array arrangements in a plane, and has a wide range of applicability. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 This is a flow chart of a distributed signal synthesis power allocation method based on improved particle swarm algorithm.

[0055] Figure 2 Schematic diagram of the transmitting array elements and the locations of points in the spatial region.

[0056] Figure 3 This is a schematic diagram of the semicircular array position.

[0057] Figure 4 This is a top view of the field strength on the xOy surface after optimization.

[0058] Figure 5 This is the three-dimensional distribution map of the field strength in the optimized synthesis area. DETAILED DESCRIPTION

[0059] In order to make the objectives, technical methods and advantages of the present invention more clear, the present invention is further described in detail below in conjunction with the implementation modes and the accompanying drawings.

[0060] A distributed signal synthesis power allocation method based on an improved particle swarm algorithm is completed in two parts. The first part is to determine the field strength formed by the dispersed array to be optimized at the target synthesis point as the goal, and the power value allocated to each array element as the independent variable. This part designs the initial phase of the transmitted signal according to the phase difference caused by the distance difference between each transmitting array element and the target synthesis point, and determines the expression of the optimization problem through vector decomposition and constraints imposed on the array element power; the second part is to design an improved PSO algorithm to optimize the above optimization problem, integrate Bernoulli chaotic mapping, improve the PSO algorithm based on the nonlinear dynamic adaptive inertia weight of population separation and the Cauchy perturbation strategy, and use the optimization problem expression obtained in the first part as the objective function of the improved algorithm to seek the optimal power allocation solution. Specifically, it includes the following steps:

[0061] (1) Establish the northeast sky rectangular coordinate system. The number of array elements to be optimized is N, and the position of each element is L. i (x i ,y i z i ), i = 1, 2, ..., N. The target synthesis point position is C (x0, y0, z0), let the position of any point M in the synthesis area be M (x, y, z), R ic is the distance from the ith array element to point C, R i is the distance from the ith array element to point M. The directional patterns of all array elements are the same and their centers all point to point c. T is the maximum number of iterations of the improved algorithm.

[0062] (2) The initial phase of the transmitted signal of the ith array element is determined based on the distance from point c, and the field strength generated by the transmitted signal of the ith array element at point M is thereby determined.

[0063] (3) Decompose the signal field strength generated by the i-th array element signal at point M into three spatial direction field strength components.

[0064] (4) Combined with the constraints imposed on the array element power, a constrained optimization problem is constructed with the field strength value at point C as the target and the power value allocated to each array element as the independent variable.

[0065] (5) The power value assigned to each array element is used as the particle population and initialized using the Bernoulli chaotic map.

[0066] (6) Design a nonlinear dynamic adaptive inertia weight based on population separation to enable particles to maintain their motion inertia.

[0067] (7) Apply perturbations to the particle population that falls into premature convergence and first define the judgment criteria for premature convergence.

[0068] (8) After judging that the population has converged prematurely, it is sorted in descending order of fitness value, the top 20% of particles are taken out, and velocity perturbation is applied.

[0069] (9) Apply position disturbance to the population after velocity disturbance.

[0070] (10) Iterate steps (6) to (9) T times and output the optimal population, i.e., the optimal power allocation scheme.

[0071] Here is a more specific example:

[0072] A distributed signal synthesis power allocation method based on improved PSO, referring to Figure 1 , including the following steps:

[0073] Step 1: Establish the northeast sky rectangular coordinate system. The number of array elements to be optimized is N, and the position of each element is L. i (x i ,y i z i ), i = 1, 2, ..., N. The target synthesis point position is C (x0, y0, z0), let the position of any point M in the synthesis area be M (x, y, z), R ic is the distance from the ith array element to point C, R i is the distance from the ith array element to point M. The directional patterns of all array elements are the same and their centers all point to point C, such as Figure 2 As shown in Figure 2. T is the maximum number of iterations of the improved algorithm.

[0074] Step 2: Control the initial phase of the transmit signal of the i-th array element to be:

[0075]

[0076] Where, λ is the signal wavelength;

[0077] The phase of the transmitted signal of the i-th array element arriving at point M is calculated as:

[0078]

[0079] The field strength generated by the transmitted signal of the i-th array element at point M is calculated as:

[0080]

[0081] in, P i represents the power allocated to the i-th array element, G T represents the antenna gain of the array element; f i (θ i ,α i ) represents the array antenna pattern function of the i-th array element, the elevation angle θ i is the angle between the line from the ith array element to point M and the xOy plane, and the direction angle αi is the angle between the projection of the line from the ith array element to point M on the xOy plane and the x-axis, k is 2π / λ;

[0082] Step 3, decompose the signal field strength at point M into field strength components in three spatial directions:

[0083]

[0084] Therefore, the signal intensity at point M is expressed as the superposition of the intensity components in three directions:

[0085]

[0086] in They respectively represent the x-, y-, and z-direction components of the field strength generated by the transmitted signals of all array elements at point M.

[0087] Step 4: Construct a constrained optimization problem with the field strength value at point C as the target and the power value allocated to each array element as the independent variable:

[0088]

[0089] in, It represents the field strength generated by all array element transmission signals at point C. They respectively represent the x-direction, y-direction, and z-direction components of the field strength generated by the signals transmitted by all array elements at point C.

[0090] The power limit condition imposed on the array element is:

[0091]

[0092] Among them, P sum The upper limit of the total power allocated to each array element, P i is the allocated power of the ith array element, P min , P max Assigning upper and lower limits of power to a single array element;

[0093] Step 5: Use the allocated power value of each array element as the particle population and initialize it using Bernoulli chaotic mapping:

[0094] Set the control parameter λ B , loop iterates the Bernoulli definition:

[0095]

[0096] Among them, z k Represents the sequence value generated for the kth time.

[0097] The generated chaotic sequence is converted into the restricted range of formula (10), and the initialization population is obtained: P = [p 1, p2,…,p N ];

[0098] Step 6: Design a nonlinear dynamic adaptive inertia weight based on population separation to keep the particles inertia. The population separation d(t) is expressed as:

[0099]

[0100] Among them, varfit(t) represents the variance of the fitness value of the t-th generation population.

[0101] Combining the population separation with the Tanh activation function yields the nonlinear dynamic adaptive inertia weight w(t):

[0102]

[0103] Among them, W max , W min are the upper and lower limits of the inertia weight w, T is the maximum number of iterations, and b is the damping factor.

[0104] Step 7: Apply perturbations to the particle population that falls into premature convergence, and define the judgment criterion of premature convergence as:

[0105]

[0106] Among them, f i represents the fitness value of the i-th particle in the current iteration, f avg Represents the average fitness value of the entire population in the current iteration;

[0107] Setting Δ 2 The threshold value of Δ 2 With the size of the threshold, when Δ 2 When it is less than the threshold, the population is considered to have fallen into premature convergence;

[0108] Step 8: After judging that the population has converged prematurely, sort the population in descending order according to the fitness value, take out the top 20% of particles, and apply velocity perturbation as follows:

[0109]

[0110] Among them, v id (t) is the particle velocity of the current generation, c1 and c2 are learning rates, and p id (t) is the optimal value of the individual in the current generation, g best is the global optimal value currently searched, x id(t) is the position of the particle of the current generation, r1(t), r2(t), and rand are random numbers between [0, 1]. Indicates that the mean is 0 and the variance is P id (t) the Cauchy distribution function value;

[0111] Step 9, apply position disturbance to the population after applying velocity disturbance:

[0112]

[0113] Step 10, iterate steps 6 to 9 for a total of T times, and output the optimal population, i.e., the optimal power allocation scheme g best .

[0114] The effect of the present invention can be illustrated by the following simulation experiment:

[0115] 1. Experimental environment and conditions.

[0116] The number of transmit elements in the array to be optimized is 10, arranged in a semicircle with a radius of 2000m on the xOy plane, i.e., on the ground at an elevation of Om, and all elements are on the positive half axis of the y axis. The target synthesis point is located at 1000m on the z axis. The array elements are arranged at equal central angles, that is, the angle difference between two adjacent elements relative to the origin O(0, 0, 0) of the xOy plane is 18°, and the distance difference is 694.595m. Figure 3 As shown. Set the signal transmission frequency to 100MHz and the gain of the transmitting antenna to 2.5dB. The total transmission power of all array elements is P sum =10kW. The simulation parameters are shown in Table 1:

[0117] Table 1 Simulation parameters

[0118] parameter value Number of array elements 10 Array Radius 2000m Distance between adjacent elements 694.595m Target synthesis point (0，0，1000) / m Signal frequency 100MHz

[0119] The improved particle swarm algorithm proposed in the present invention is used to optimize the power of each element of the semicircular array, and the algorithm parameters are set as follows:

[0120] Population size N p = 1000, number of iterations T = 200. Learning rate c1 = c2 = 1.5, the maximum and minimum values ​​of the speed parameter are V max =3, V min =-3. Inertia weight W max =0.8,W min =0.4.

[0121] Also set constraints:

[0122] The maximum power of a single array element is X max =6kW, X min =150W. The upper limit of the total power of all array elements is Psum =10kW. Activation function damping factor b = 0.2, penalty coefficient afa = -2. Bernoulli mapping control parameter λ B =0.479.

[0123] The particles that update their positions after the population enters premature convergence are the first 20% of particles sorted in descending order of fitness values. The algorithm parameter settings are shown in Table 2:

[0124] Table 2 Improved PSO parameter settings

[0125] parameter value Population size 1000 Iterations T＝200 Learning Rate <![CDATA[c1=1.5,c2=1.5]]> Particle Speed <![CDATA[V max =3,V min =-3]]> Inertia Weight <![CDATA[W max =0.8,W min =0.3]]> Upper limit of single array element power <![CDATA[X max =6kW]]> Single array element power lower limit <![CDATA[X min =150W]]> Total power <![CDATA[P sum =10kW]]> Penalty coefficient afa=2 Damping factor b＝0.2

[0126] 2. Experimental content and results.

[0127] Figure 4 This is a top view of the xOy plane of the target synthetic point field strength obtained by applying the power allocation value of each array element after optimization by the improved algorithm to the example array.

[0128] Figure 5 To synthesize the three-dimensional distribution map of the field intensity in the region, the selected isosurface threshold is 0.1 to 0.5.

[0129] In summary, the present invention takes the PSO algorithm as the main body, integrates the Bernoulli chaotic map initialization, and obtains the optimal solution of the independent variable based on the nonlinear random decreasing inertia weight and the Cauchy perturbation strategy of population separation. The method has a fast convergence speed and high convergence accuracy. It can perform signal coherent synthesis on a distributed array with any linear / surface array arrangement in a plane, and can provide a distribution scheme for the power value of each array element, effectively improve the field strength of the target synthesis point, and meet the needs of improving the synthesis effect of the target synthesis point when performing distributed signal coherent synthesis under the condition of limited array element power.

Claims

1. A distributed signal synthesis power allocation method based on improved particle swarm algorithm, characterized in that: Distributed arrays used for dispersed arrays are used to allocate the power value of each array element during signal coherent synthesis; where the number of array elements is N, and the rectangular coordinate system of the northeast sky is established, then the array element position is L i (x i ,y i z i ), i = 1, 2, ..., N, the position of the target synthesis point C is C (x0, y0, z0), the position of any point M in the synthesis area is M (x, y, z), R ic is the distance from the ith array element to point C, R i is the distance from the ith array element to point M; the directional patterns of all array elements are the same and their centers all point to point c; The method comprises the following steps: Step 1: Control the initial phase of the transmit signal of the i-th array element to be: Where, λ is the signal wavelength; The phase of the transmitted signal of the i-th array element arriving at point M is calculated as: The field strength generated by the transmitted signal of the i-th array element at point M is calculated as: in, P i represents the power allocated to the i-th array element, G T represents the antenna gain of the array element; f i (θ i ,α i ) represents the array antenna pattern function of the i-th array element, the elevation angle θ i is the angle between the line from the ith array element to point M and the xOy plane, and the direction angle α i is the angle between the projection of the line from the ith array element to point M on the xOy plane and the x-axis, f is 2π / λ; Step 2: Decompose the signal intensity at point M into intensity components in three spatial directions: Therefore, the signal intensity at point M is expressed as the superposition of the intensity components in three directions: in, They respectively represent the x-direction, y-direction, and z-direction components of the field strength generated by the transmit signals of all array elements at point M; Step 3: Construct a constrained optimization problem with the field strength value at point C as the target and the power value of each array element as the independent variable: in, It represents the field strength generated by all array element transmission signals at point C. They respectively represent the x-direction, y-direction, and z-direction components of the field strength generated by the transmit signals of all array elements at point C; The power limit condition imposed on the array element is: Among them, P sum The upper limit of the total power allocated to each array element, P i is the allocated power of the ith array element, P min , P max Assigning upper and lower limits of power to a single array element; Step 4: Use the allocated power value of each array element as the particle population and initialize it using Bernoulli chaotic mapping: Set the control parameter λ B , loop iterates the Bernoulli definition: Among them, z k Indicates the sequence value generated for the kth time; The generated chaotic sequence is converted into the restricted range of formula (10), and the initialization population P = [p 1, p2,…,p N ]; Step 5, setting the nonlinear dynamic adaptive inertia weight w(t) based on population separation to keep the particles inertia; Step 6: Apply disturbance to the particle population that falls into premature convergence, and define the judgment criterion of premature convergence as: f mi =max(1,|f i -f avg |) (13) Among them, f i represents the fitness value of the i-th particle in the current iteration, f avg represents the average fitness value of the entire population in the current iteration, f mi is an intermediate variable; Setting Δ 2 The threshold value of Δ 2 With the size of the threshold, when Δ 2 When it is less than the threshold, the population is considered to have fallen into premature convergence; Step 7: After judging that the population has converged prematurely, sort the population in descending order according to the fitness value, take out the top 20% of particles, and apply velocity perturbation as follows: Among them, v id (t) is the particle velocity of the current generation, c1 and c2 are learning rates, and p id (t) is the optimal value of the individual in the current generation, g best is the global optimal value currently searched, x id (t) is the position of the particle of the current generation, r1(t), r2(t), and rand are random numbers between [0,1]. Indicates that the mean is 0 and the variance is p id (t) the Cauchy distribution function value; Step 8: Apply position disturbance to the population after applying velocity disturbance: Step 9, iterate steps 5 to 8 for a total of T times, and output the optimal population, which is the optimal power allocation solution g best .

2. The distributed signal synthesis power allocation method based on improved particle swarm algorithm according to claim 1 is characterized in that: The specific method of step 5 is: The population separation d(t) is expressed as: Among them, varfit(t) represents the variance of the fitness value of the t-th generation population; Combining the population separation d(t) with the Tanh activation function, we get the nonlinear dynamic adaptive inertia weight w(t): Among them, W max , W min are the upper and lower limits of the inertia weight, T is the maximum number of iterations, and b is the damping factor.

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