Collaborative Jamming Resource Scheduling Method Based on Improved Sparrow Search Algorithm

Abstract

The present invention relates to a collaborative interference resource scheduling method based on an improved sparrow search algorithm, and belongs to the field of collaborative interference technology. The method comprises the following steps: 1) constructing an interference decision matrix and a power allocation matrix; 2) constructing a first suppression probability model for a networked radar based on the principle of uniform distribution of jammer beam power, and using a sparrow search algorithm to solve the interference decision matrix corresponding to the maximum first suppression probability; 3) constructing a second suppression probability model based on the solved interference decision matrix, and using a sparrow search algorithm to solve the power allocation matrix corresponding to the maximum second suppression probability; in the finder position update step of the sparrow search algorithm, if the warning value is greater than the safety value, a random crossover operation is performed on the coded and sorted finders. Finally, a collaborative interference resource scheduling scheme is obtained. The scheduling method of the present invention has high scheduling efficiency and a more reasonable scheduling scheme. Under the condition of limited interference resources, it can form the best interference effect on the networked radar.

Description

Technical Field

[0001] The present invention belongs to the technical field of coordinated interference, and in particular relates to a coordinated interference resource scheduling method based on an improved sparrow search algorithm. Background Art

[0002] In recent years, due to the increasing complexity of battlefield electromagnetic environments, modern electronic warfare has evolved from single-action operations to system-of-systems confrontation. Networked radars, due to their superior "four-way jamming" capabilities, have been widely deployed, posing a significant threat to target penetration missions. To enhance jamming against networked radars, multiple jammers can be used to implement coordinated jamming. Given limited jamming resources, optimizing their allocation to achieve optimal jamming against networked radars has become a key military research topic.

[0003] The optimal allocation of collaborative jamming resources is the process of rationally scheduling jamming resources to achieve optimal jamming effectiveness, given the known operating parameters of each radar. Currently, there are two main approaches to optimizing jamming resource allocation: classical combinatorial optimization algorithms and intelligent optimization algorithms. Traditional algorithms such as 0-1 integer programming, proximity, and fuzzy multi-attribute dynamic programming, used in the papers "Research on Radar Jamming Resource Optimization Based on 0-1 Programming" (by Shen Yang et al., Journal of the Chinese Academy of Military Engineering, 2007, No. 5, pp. 528-532), "Collaborative Electronic Jamming Resource Allocation Method Based on Fuzzy Multi-Attributes" (by Luo Juanjuan et al., Journal of Electronic Information Countermeasures Technology, 2019, Vol. 34, No. 5, pp. 65-70), and "Research on Radar Jamming Resource Allocation Strategy Based on Proximity" (by Lü Yongsheng et al., Journal of Systems Engineering and Electronics, 2005, No. 11, pp. 79-80, 160), suffer from significant performance degradation as the scale of jamming resource allocation increases, due to the discrete and non-convex nature of the optimization problem, making them difficult to solve.

[0004] Genetic algorithms are used to solve the problem of optimizing the allocation of interference resources. While improving the probability of finding the optimal solution, the running time also increases accordingly, and it is not real-time. The paper "Application of Improved Cuckoo Algorithm in Collaborative Interference Resource Allocation" (author: Liu Xiang et al., journal: Modern Radar, 2019, Vol. 41, No. 2, pp. 84-90) applies the cuckoo algorithm to the interference resource allocation problem, improving the convergence stability at the expense of the convergence speed, and only considers the case where the number of radars is equal to the number of jammers.

[0005] In summary, current jamming resource optimization allocation methods generally have problems such as slow convergence speed and weak optimization ability, which cannot meet the needs of practical problems. At the same time, the problem of beam power allocation of jammers has not received widespread attention. The paper "Joint Optimal Allocation Method of Multi-Jammer Resources for Networked Radar Jamming Tasks" (author: Zhang Dalin et al., journal: Journal of Radar, 2021, Vol. 10, No. 4, pp. 595-606) uses detection probability as the interference evaluation index, establishes a joint optimization model for jammer beam allocation and power allocation, and solves it using the PSO algorithm, but does not take into account the allocation of interference patterns. Summary of the Invention

[0006] The purpose of the present invention is to provide a collaborative interference resource scheduling method based on an improved sparrow search algorithm to solve the problems of slow convergence speed and weak optimization ability of existing interference resource optimization allocation methods, which lead to poor interference effect.

[0007] The present invention provides a technical solution for solving the above technical problems by providing a method for collaborative interference resource scheduling based on an improved sparrow search algorithm. The method comprises the following steps:

[0008] 1) Construct an interference resource allocation model based on the networked radar sets, jammer sets, jamming pattern sets, and power allocation of each jammer beam. The interference resource allocation model includes an interference decision matrix and a power allocation matrix.

[0009] 2) setting the power allocation matrix in the interference resource allocation model based on the principle of uniform power distribution of each jammer beam, constructing a first suppression probability model of the networked radar based on the interference resource allocation model, taking the first suppression probability model as the first objective function, and using the sparrow search algorithm to solve the interference decision matrix corresponding to maximizing the first objective function;

[0010] 3) Based on the optimal interference decision matrix obtained in step 2), a second suppression probability model of the networked radar is constructed, and the second suppression probability model is used as the second objective function. The power allocation matrix corresponding to the maximum value of the second objective function is solved using the sparrow search algorithm to obtain the optimal power allocation matrix;

[0011] When solving the first and second objective functions using the sparrow search algorithm, in the finder position update step of the sparrow search algorithm, if the warning value is greater than the safety value, the finders after coding sorting are randomly grouped in pairs, forming parent chromosomes and then cross-generating offspring individuals;

[0012] 4) Perform collaborative interference resource scheduling based on the obtained optimal interference decision matrix and optimal power allocation matrix.

[0013] The present invention has the following beneficial effects: For multi-jammer coordinated interference scenarios, the present invention uses the probability of suppressing networked radars as the objective function, establishes an interference benefit model, and solves the transmit power allocation result based on the optimal allocation method. The improved sparrow search algorithm adds a crossover operation to the genetic algorithm, ensuring the feasibility of the solution while enhancing the algorithm's iteration speed and optimization capabilities. The scheduling method based on the improved sparrow search algorithm has high scheduling efficiency and more reasonable scheduling schemes. Under the condition of limited interference resources, the rational allocation of interference resources can achieve the optimal interference effect on the networked radar.

[0014] Furthermore, in the finder position update step of the sparrow search algorithm, if the warning value is greater than the safety value, a code is assigned to the interference object, and the sorted finders are randomly grouped in pairs to form parent chromosomes. The arithmetic crossover operator is used to generate offspring individuals through linear recombination. The formula is: in and is the offspring individual produced by linear recombination, c is the crossover parameter, and its value range is (0,1). and is the parent chromosome, and t is the current iteration number.

[0015] Furthermore, in the finder position update step of the sparrow search algorithm, if the warning value is greater than the safety value, the interference pattern is selected to encode, and the parent chromosomes are subjected to multi-point crossover processing in the genetic algorithm to obtain offspring individuals.

[0016] Furthermore, during the sentinel position update step of the sparrow search algorithm, adaptive mutation of individual positions is performed after the sentinel position is updated, with the mutation probability increasing with the number of iterations. By introducing adaptive mutation in the sentinel stage, a higher mutation probability increases population diversity and enhances optimization capabilities.

[0017] Furthermore, the formula for the adaptive variation is: Among them, P m (t) is the mutation probability of the current iteration stage, T is the total number of iterations, t is the current number of iterations, P m is the maximum variation value.

[0018] Furthermore, in the initialization step of the sparrow search algorithm, the tent chaotic sequence is used to initialize the population. Using the tent chaotic sequence to initialize the population makes the initial individuals as evenly distributed as possible in the solution space, maintains the diversity of the population, and enhances the global optimization ability.

[0019] Furthermore, the expressions of the first suppression probability model and the second suppression model of the networked radar are respectively: and Among them, C1 and C2 are the first suppression probability and the second suppression probability of the networked radar, R is the distance between the jammer and the radar, F is the jamming decision matrix, and F 最优 is the optimal interference decision matrix, P is the power allocation matrix, P 均匀 Ps is the power distribution matrix set up based on the principle of uniform distribution of power among the jammer beams. net (R,F,P 均匀 ) represents the first detection probability of the networked radar, Ps net (R,F 最优 ,P) represents the second detection probability of the networked radar, ω(R) represents the weight corresponding to the suppression probability when the distance between the jammer and the radar is R, R min 、R max are the minimum and maximum distances between the jammer and the radar, respectively.

[0020] Furthermore, the weight is calculated as follows: Among them, the penetration process of the jammer is divided into Q segments with an interval of ΔR, q represents the qth segment, α is the weight factor, α∈(0,1), and the value of α is related to the distance interval and the setting of R.

[0021] Furthermore, the constraints of the objective function are:

[0022]

[0023] Among them, P max is the maximum power of the interference beam, P min Expressed as the minimum power of the interference beam, is the total power of the interference beam emitted by the jammer.

[0024] Furthermore, the interference decision matrix F is:

[0025] Where D represents the interference object allocation matrix, D mn Indicates whether the jammer m interferes with the radar n. If so, D mn =1, otherwise D mn =0; Y represents the interference pattern selection matrix, Y mk Indicates whether jammer m selects jamming pattern k. If so, Y mk =1, otherwise Y mk = 0, m, n, k are the numbers of the jammer, radar, and jamming pattern respectively, m = 1, 2, 3, ..., M, n = 1, 2, 3, ..., N, k = 1, 2, 3, ..., K;

[0026] The power allocation matrix P is: Among them, P m,nRepresents the power allocated by jammer m to radar n, where m and n are the numbers of the jammer and radar respectively, m = 1, 2, 3, ..., M, and n = 1, 2, 3, ..., N. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 Schematic diagram of a cooperative interference model according to an embodiment of the present invention;

[0028] Figure 2 Schematic diagram of an interference decision matrix model according to an embodiment of the present invention;

[0029] Figure 3 A schematic diagram of a networked radar countermeasure model according to an embodiment of the present invention;

[0030] Figure 4 Schematic diagram of the multi-point crossover process in the discoverer phase of the SSA algorithm according to an embodiment of the present invention;

[0031] Figure 5 This is a flow chart of solving interference resource allocation using the ISSA algorithm according to an embodiment of the present invention;

[0032] Figure 6 Schematic diagram of a radar countermeasure model according to an embodiment of the present invention;

[0033] Figure 7 This is a comparison chart of the single convergence of the ISSA algorithm and the SSA algorithm of the present invention;

[0034] Figure 8 This is a comparison chart of multiple convergence situations of the ISSA algorithm and the SSA algorithm of the present invention;

[0035] Figure 9 This is a comparison diagram of the convergence error between the ISSA algorithm and the SSA algorithm of the present invention;

[0036] Figure 10 It is a convergence curve diagram of the objective function value in power optimization under the ISSA algorithm of the present invention;

[0037] Figure 11 Schematic diagram of the beam power distribution of jammer 1 under the ISSA algorithm of the present invention;

[0038] Figure 12 Schematic diagram of the power distribution results of each jammer beam under the ISSA algorithm of the present invention;

[0039] Figure 13 Schematic diagram of radar network detection probability under different interference conditions using the ISSA algorithm of the present invention. DETAILED DESCRIPTION

[0040] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0041] The technical concept of the present invention is to construct an interference resource allocation model, where each interference resource allocation method corresponds to a set of suppression probability values. The suppression probability values throughout the entire penetration process are combined to obtain the suppression probability C corresponding to the entire penetration process. This probability C is used as the objective function. An improved sparrow search algorithm is used to find the interference decision matrix corresponding to the maximum value of the objective function, maxC, i.e., the optimal allocation object and interference pattern. Based on the optimal interference decision matrix, the improved sparrow search algorithm is used to find the power allocation matrix corresponding to the maximum value of the objective function, maxC, to obtain the final interference resource allocation strategy. The improved sparrow search algorithm is an improvement on the standard sparrow search algorithm, with three major improvements: 1) introducing a tent chaotic map to initialize the population; 2) incorporating the crossover operation of the genetic algorithm into the position update of the discoverer; and 3) incorporating the adaptive mutation operation of the genetic algorithm into the position update of the sentinel. Any of these three improvements enables the sparrow search algorithm to improve its iteration efficiency and optimization probability while ensuring the feasibility of the solution. Scheduling collaborative interference resources based on the improved sparrow search algorithm can achieve optimal interference results.

[0042] 1. Construction of interference resource allocation model.

[0043] The interference resource scheduling problem can be understood as a multi-constrained nonlinear discrete integer programming problem, which mainly includes three aspects: the allocation of interference objects, the selection of interference patterns, and the power allocation of interference beams. Figure 1 A cooperative jamming model for networked radars is presented.

[0044] Assume that the jammer set is J={J1,J2,…,J M}, the radar set of the network is R={R1,R2,…,R N}, the set of interference patterns that can be selected is S={S1,S2,…,S K}, the power distribution of each jammer beam is G={G1,G2,…,G L}.

[0045] Establish the interference object allocation matrix D, D mn Indicates whether the jammer m interferes with the radar n. If so, D mn =1, otherwise D mn =0.

[0046]

[0047] Establish the interference style selection matrix Y,Y mk Indicates whether jammer m selects jamming pattern k. If so, Y mk =1, otherwise Y mk =0.

[0048]

[0049] The final interference decision matrix can be used m,n,k =F{D mn ,Y mk} indicates that its interference decision matrix model is as follows: Figure 2 As shown. m,n,k =1 means jammer m selects jamming pattern k to jam radar n; F m,n,k =0 means that the jammer m does not interfere with the radar n or the jamming pattern k is not selected.

[0050] The entire interference decision matrix can be expressed as:

[0051]

[0052] In order to express the power distribution of each beam of the jammer, the interference power distribution matrix is further defined:

[0053]

[0054] If jammer m allocates beams to jam radar n, then P m,n >0; otherwise P m,n =0.

[0055] Therefore, when performing collaborative jamming on networked radars, the jamming decision matrix F and the power allocation matrix P can be used to describe the entire jamming system.

[0056] 2. Construct a suppression probability model for networked radar.

[0057] The search and warning of the target is the most basic and important processing link of the radar. Only after the target signal is detected, the next step of positioning, tracking and fire guidance will be carried out. Figure 3 shown.

[0058] In the absence of interference, the target echo signal signal-to-noise ratio can be obtained according to the radar equation:

[0059]

[0060] Among them, P t is the radar transmission power, G t (θ), G r (θ) are the antenna transmission and receiving gains, λ is the radar signal wavelength, σ is the target RCS (radar cross section), Pc is the radar matching pulse compression gain, R t is the distance between the radar and the target, k is the Boltzmann constant, T0 is the effective noise temperature, B is the receiver bandwidth, N f is the receiver noise figure, Lt is the total radar loss.

[0061] When the jammer selects different jamming patterns, the signal-to-noise ratio (SNR) will be different due to the large energy differences in time, frequency, space, and processing domains. Therefore, according to the interference equation, the interference signal JNR can be obtained by considering the influence of various interference factors:

[0062]

[0063] Among them, P j , G j are the jammer transmit power and antenna gain respectively; γ j is the polarization mismatch factor; L j is the comprehensive loss of the jammer, E j =E t E f E s E p , are the relative energy differences of the interference signal in time, frequency, space and processing domains, E t is the time domain energy difference of the interference signal, E f is the energy difference of the interference signal in the frequency domain, E s is the spatial energy difference of the interference signal, E p It is the energy difference in the interference signal processing domain, which is related to the interference pattern.

[0064] Therefore, when the same radar is interfered by multiple jammers, assuming that the interference signals of each jammer are independent of each other, the total power of the interference signal received by the radar is equal to the sum of the power of the interference signals of each jammer. Combining the above formula, the signal-to-interference ratio of the target echo of the nth radar under interference can be obtained:

[0065]

[0066] Among them F m,n,k and E m,n,k They represent the interference decision value of jammer m selecting interference pattern k for radar n and the interference signal gain, R m,n represents the distance between the jammer m and the radar n, P m,n represents the power allocated to radar n by jammer m, G m,n represents the antenna gain of jammer m.

[0067] According to the radar detection principle, the detection probability of the radar to the target is related to the signal-to-interference-noise ratio of the target echo and the false alarm probability. In the case of a Swerling II target, the detection probability of the radar to the target is given by the following formula:

[0068]

[0069] Where V TRepresents the detection threshold, and the false alarm probability P fa About, n p represents the pulse accumulation number, Γ I represents the incomplete gamma function, defined by DiFranco and Rubin as:

[0070] In a jamming environment, the signal-to-interference ratio (SJR) can be replaced by the SNR to obtain the probability of the radar detecting a target when jammed. Generally speaking, the weaker the radar's detection capability after jamming, the better the jamming effect. The probability of suppressing a radar in a jamming environment can be expressed as:

[0071] Ps=1-Pd (9)

[0072] Obviously, the greater the interference intensity, the faster the radar detection probability decreases and the greater the suppression probability. Therefore, the suppression probability Ps can be used to evaluate the suppression effect on networked radars under coordinated interference.

[0073] For the nth radar:

[0074]

[0075] It can be seen that the suppression probability Ps n With F m,n,k and P m,n Therefore, the joint optimization of the jammer's interference decision matrix F and power allocation matrix P can effectively enhance the probability of cooperative interference suppressing the networked radar and maximize the benefits of limited jamming resources.

[0076] From the above analysis, we can see that the detection probability of the networked radar is related to the interference signal power received by each radar, so the detection probability Pd of the networked radar is net It can be expressed as:

[0077] Pd net =f(Pd1(SJR1),Pd1(SJR2),…,Pd n (SJR N )) (10)

[0078] f represents the membership function from the detection probability of a single radar to the probability of network suppression, Pd n Represents the membership function of the interference signal SJR received by the nth radar to the detection probability, n = 1, 2, ..., N.

[0079] During the penetration process of the jammer and the target aircraft, the positions of both are changing at any time, resulting in changes in the probability of suppression. netThe value is not reasonable as the suppression effect of the whole process, so the penetration process can be discretized into several segments, and several track points are selected. The suppression probability values of each track point are weighted and summed to obtain the final function value. Different weights are assigned according to the distance between the route segment and the attack destination. Considering that the closer the target is to the destination, the greater the threat, so the weight of each point decreases with the increase of distance, and it is a nonlinear function. If the penetration process [R min ,R max ] is divided into Q segments with ΔR as the interval, and the weight change relationship is:

[0080]

[0081] Where α∈(0,1), the specific value is related to the distance interval and R setting, so the final suppression probability of the networked radar, that is, the objective function is:

[0082]

[0083] The constraints on the battle relationship are set as follows:

[0084]

[0085] Constraint (1) means that each jammer can generate at most L beams and select one jamming pattern.

[0086] Constraint (2) indicates that the radar may be free from interference or may be interfered with by multiple jammers at the same time.

[0087] Constraint (3) means that the total number of jammers assigned to each radar does not exceed the number of existing jammers.

[0088] Constraint (4) indicates that the interference beam has maximum and minimum power constraints and the total power must be constant.

[0089] Constraint (5) indicates that the elements of the interference decision matrix are defined.

[0090] Each interference resource allocation method corresponds to a set of suppression probability values. By integrating the suppression probability values in the entire penetration process, the suppression probability C corresponding to the entire flight segment is obtained and used as the objective function. The interference resource allocation strategy corresponding to the maximum value maxC of the objective function is found.

[0091] There are several difficulties in optimizing equations (12) and (13):

[0092] (1)F m,n,k is a ternary variable, which is non-convex.

[0093] (2) Interference decision matrix F m,n,k With the power allocation matrix P m,nThe mutual coupling is in the form of a product, and the simultaneous solution is too complicated.

[0094] Therefore, to solve the above optimization problem, we first consider the optimal interference decision matrix F corresponding to maxC under the condition of equal beam power distribution. m,n,k On this basis, power optimization is performed to obtain the power allocation matrix P corresponding to the maximum objective function value m,n .

[0095] 3. Use the improved sparrow search algorithm to find the interference resource allocation strategy corresponding to the maximum value maxC of the objective function.

[0096] Interference resource allocation is a discrete integer programming problem with multiple constraints, dimensions, and choices. As the allocation scale increases, classic combinatorial optimization algorithms are no longer applicable, requiring intelligent algorithms for optimal solution. The SSA algorithm (Sparrow Search Algorithm) optimizes the problem by updating the positions of the discoverer and joiner and incorporating a reconnaissance and early warning mechanism.

[0097] 1. Theoretical framework of standard SSA algorithm.

[0098] In the standard SSA algorithm, it mainly includes three parts: discoverer, joiner and guard.

[0099] (1) The discoverer can provide foraging location information for the joiner, and the location update formula is:

[0100]

[0101] Where: t is the current iteration number, T is the total iteration number, x id is the d-dimensional information of the i-th individual, a is a random number between (0,1], and QL is a id A random matrix of the same dimension between [0,1]; R2∈[0,1], ST∈[0.5,1], where R2 and ST are the warning and alert values, respectively. When R2<ST, the population has not detected any danger, and the discoverer can search a wider area to obtain a higher fitness value; conversely, if danger is detected, the population shrinks to a safe area.

[0102] (2) The position change of the joiner is related to the discoverer, and its position update formula is:

[0103]

[0104] where X best and X worst are the best and worst position information at the current stage, Num represents the number of populations, L j The meaning is a matrix with 1 row and d columns, all 1s. + represents a d-dimensional vector with random values of 1 and -1, and A+ =A T (AA T ) -1 , i>Num / 2 indicates that individuals with low fitness need to find a new food location and search further; otherwise, at the current optimal location X best Find a place nearby to forage.

[0105] (3) Sentinels refer to individuals in a population that are aware of the threat of predators, generally accounting for 10% to 20% of the population. They sense danger and quickly alert the population to counter predation. Their position is updated as follows:

[0106]

[0107] Where W and β are both step-size control parameters, W∈[-1,1], β obeys a normal distribution with a mean of 0 and a variance of 1, ε is a minimum value, and f i is the current individual fitness value, f b and f w are the optimal and worst fitness values of the current population respectively.

[0108] 2. Improved sparrow search algorithm (ISSA).

[0109] While retaining the overall framework of the standard sparrow search algorithm, this paper introduces a tent chaotic map to initialize the population and incorporates the crossover and mutation evolution operations of the genetic algorithm into the standard SSA algorithm, resulting in an improved sparrow search algorithm (ISSA). The improved sparrow search algorithm generates effective feasible solutions while balancing the algorithm's diversity and directionality, further improving the algorithm's iteration speed and optimization capabilities.

[0110] According to the model conditions of cooperative interference resource allocation constraints, the adaptive ISSA algorithm is set mainly from the following key aspects.

[0111] (1) Initialize the population.

[0112] In the standard SSA algorithm, the population is randomly initialized, and the uniformity of the population position distribution will affect the convergence accuracy. Chaotic variables are widely used in optimization problems due to their randomness, ergodicity, and regularity. The population is initialized using the Tent chaotic sequence, so that the initial individuals are distributed as evenly as possible in the solution space, maintaining the diversity of the population and enhancing the global optimization ability. Its sequence expression is

[0113]

[0114] Where: N is the number of particles in the chaotic sequence, z i Represents the chaotic sequence number of the current state, z i+1 The chaotic sequence number of the next state.

[0115] (2) Discoverer stage

[0116] For discrete integer allocation problems such as interference resource allocation, when R>ST, the position of the discoverer basically does not change, and the search is stagnant. The main purpose of the discoverer is to conduct neighborhood search and adopt the crossover operation in the genetic algorithm to increase population diversity while improving the optimization ability.

[0117] For the assignment of codes to interference objects, the sorted discoverers can be randomly grouped in pairs to form parent chromosomes, and the arithmetic crossover operator is used to generate offspring individuals through linear recombination.

[0118]

[0119] in and is the offspring individual produced by linear recombination, c is the crossover parameter, and its value range is (0,1). and is the parent chromosome, and t is the current iteration number. For interference pattern selection coding, since the number of solutions is small, chromosome multi-point crossover can be adopted. The crossover process is as follows: Figure 4 shown.

[0120] (3) Joiner stage

[0121] For individuals with low fitness, best Randomly forage nearby, and for other joiners, observe the discoverer in order to compete for food or find a position near it, increase the cross processing with the global optimal solution to update the position, and randomly select some subscripts of the global optimal solution to replace the subscripts of this part of the joiners, so as to enhance the development performance of the algorithm and the global optimization ability.

[0122] (4) Vigilant Stage

[0123] Adaptive mutation is introduced in the vigilant stage. When the mutation probability is large, the population diversity increases, the optimization ability is enhanced but the convergence speed slows down. Conversely, the convergence speed is accelerated but it is easy to fall into the local optimum. By introducing the sigmoid function, the mutation probability gradually increases with the number of iterations:

[0124]

[0125] Among them, P m (t) is the mutation probability of the current iteration stage, T is the total number of iterations, t is the current number of iterations, P m is the maximum variation value.

[0126] Mutation rule: Select a gene segment at a random position of the individual for mutation, that is, reverse the chromosome.

[0127] The improved ISSA algorithm operation steps are as follows:

[0128] Step 1: Choose an encoding strategy

[0129] The interference decision matrix is divided into two coding segments: interference object allocation and interference style selection. p =[x1,…,x M ] Τ represents the distribution of interference objects, Y p =[y1,…,y M ] Τ Represents the selection of interference style. Where 0≤x i ≤2 N -1 and is an integer. After conversion to binary, it corresponds to the allocation of interference objects. If x1=52, y1=3, after conversion to binary, it is 110100, that is, jammer 1 selects jamming pattern 3 to jam radars 1, 2, and 4.

[0130] Step 2: Initialize the population

[0131] The population is initialized using the Tent chaotic sequence and then encoded. The fitness of the individuals is evaluated and sorted using the solved objective function (12), and the optimal fitness value and its corresponding position are stored.

[0132] Step 3: Discoverer Phase

[0133] The selected discoverers are updated according to the warning value R2. If R2 is less than ST, the discoverer can search in a larger range to obtain a higher fitness value. If R2 is greater than ST, the search strategy needs to be adjusted. At this time, information can be shared with other discoverers, and the sorted discoverers are randomly grouped in pairs to form parent chromosomes and then cross-group to produce offspring chromosomes.

[0134] Step 4: Joiner Phase

[0135] Update the position of the joiner. For individuals with i>n / 2, in X best Randomly search for locations nearby for foraging, and for other joiners, add cross processing with the global optimal solution to update the position, and randomly select some subscripts of the global optimal solution to replace the subscripts of this part of the joiners.

[0136] Step 5: Vigilant Stage

[0137] Several sparrows are randomly selected for reconnaissance and alert, and their positions are updated according to formula (19) and then adaptively mutated.

[0138] Step 6 Elite Retention

[0139] Calculate the fitness value, compare the fitness value of the sparrows generated in step 5 with the previous generation of sparrows, retain the best ones, and update the optimal individual position and fitness at the current stage.

[0140] Step 7: Terminate the judgment

[0141] If the maximum number of iterations has been reached, the algorithm is terminated. Otherwise, step 3 is continued until the iteration ends to determine the optimal interference allocation decision F. m,n,k .

[0142] Similarly, determine the optimal interference allocation decision F m,n,k After that, continue to solve the optimal power allocation matrix P through the ISSA algorithm m,n The ISSA-based coordinated interference resource optimization allocation flow chart is as follows: Figure 5 shown.

[0143] The following takes the example of four jammers surrounding a target aircraft to penetrate six enemy radars to further illustrate the specific implementation process of the technical solution of the present invention.

[0144] Given the operating parameters and location information of the radar, target, and jammer, the radar's location coordinates (unit: km) are (-8,-2,0), (8,2,0), (-12,-6,0), (12,-6,0), (-16,-12,0), (16,-12,0), the target's flight azimuth angle θ = 30°, and the pitch angle The radial distance from the origin ranges from 10 to 100 km. Four jammers fly alongside the target at a distance of 2 km, with a total jammer power of 30W. The penetration route is a straight line. Three jamming patterns can be selected for coordinated jamming: noise frequency modulation jamming, smart noise convolution, and intermittent sampling and retransmission jamming. Radar operating parameters, target, and jammer route parameters are shown in Tables 1 and 2.

[0145] Table 1 Radar operating parameters

[0146]

[0147] Table 2 Target and jammer flight path parameters

[0148]

[0149] After investigation, the energy difference matrix of each jammer's interference pattern matching to each radar is as follows:

[0150]

[0151] Given the working parameters and location information of the target and jammer, the JSR of each radar at different positions is obtained by combining the jammer interference pattern matching energy difference matrix. The network radar positioning error C is obtained by weighted summation of the Ps value of each track point. net The confrontation between the two sides is as follows. Figure 6 shown.

[0152] Simulation parameter settings: Set the population size to 50, the maximum number of iterations to 200, the ratio of discoverers to joiners to 2:8, the warning value ST = 0.6, the number of alert sparrows to 0.2 of the population, and the mutation probability to 0.1; use the ISSA algorithm to run 100 independent times, and the interference decision matrix allocation results are shown in Table 3:

[0153] Table 3 Interference decision matrix allocation results

[0154]

[0155] Since radar 1 is interfered with by jammer 3 using jamming pattern 3, the jamming effect is better, so other jammers can better interfere with other radars that need to be interfered with. There are three jammers to coordinately suppress and interfere with radars 3 and 6 respectively, so it can produce a better jamming effect on the networked radars. The above allocation plan is in line with the actual situation.

[0156] At the same time, the ISSA algorithm is compared with the SSA algorithm. In order to compare the effectiveness of the above algorithms in more detail, the simulation parameters are kept consistent and run independently 100 times. The convergence of each algorithm in single and multiple runs is shown in the figure. Figure 7 、 8 As shown:

[0157] Depend on Figure 7 As can be seen, this optimization problem is a nonlinear multimodal function. The ISSA algorithm initializes the population using the Tent chaotic map, resulting in a higher average fitness of the initial population than the SSA algorithm. In a single run, the ISSA algorithm converged to the global optimal solution after 42 iterations, while the SSA algorithm converged to the global optimal solution after 123 iterations. Over multiple runs, the ISSA algorithm converged faster and more steadily, and its final convergence value was higher than that of the SSA algorithm, demonstrating stronger optimization capabilities and faster convergence speed.

[0158] The difference between the single-run optimization solution and the global optimal solution is considered to be the global optimal solution if it is within 1‰. The performance comparison of the two algorithms is shown in Table 4.

[0159] Table 4

[0160]

[0161]

[0162] At the same time, the difference between the global optimal solution and the convergence value of each run in the two algorithms is obtained, and the convergence error is as follows: Figure 9 shown.

[0163] It can be seen that in 100 runs, the number of optimal solutions and the worst convergence error of the ISSA algorithm are 72 times and 0.0063 respectively, and the convergence error of the ISSA algorithm is below 0.01, while the number of optimal solutions and the worst convergence error of the SSA algorithm are 60 times and 0.0208 respectively. In comparison, the ISSA algorithm proposed in this invention has better global optimization ability and convergence stability, and has obvious advantages.

[0164] Regarding the issue of optimizing the allocation of interference beam power, further analysis and discussion are conducted. When determining the optimal allocation object and the optimal interference pattern under uniform power distribution, by reasonably allocating the power of each beam, the probability of detecting the target by the networked radar can be more effectively reduced, and the collaborative interference suppression capability of multiple jammers can be improved.

[0165] The optimization problem now becomes:

[0166]

[0167] The ISSA algorithm is also used to solve the above problem. When the interference decision matrix is known, the power of each beam is optimized to obtain the optimal power allocation of the corresponding interference beam. The objective value function in the optimization process is as follows: Figure 10 shown.

[0168] The optimization results show that the initial optimization of the objective function value was carried out in multiple stages. This not only demonstrates that the objective function for power allocation is a nonlinear, multimodal function, but also demonstrates the ISSA algorithm's strong global optimization capabilities. After 13 iterations of a single run, the objective function value converged to the global optimal solution of 0.5507, a significant improvement over the maximum objective function value of 0.4679 for equal power distribution. This demonstrates that properly allocating beam power can more effectively implement interference.

[0169] Take jammer 1 as an example, Figure 11 Displays the corresponding beam power distribution of the jammer during each iteration, with different colors representing different power values. Figure 12 The figure shows the power distribution results of each jammer after optimization. Different colors and sizes represent different power values.

[0170] For radar 1, jammer 3 adopts jamming style 3 for interference. Due to the better interference effect, only part of the power needs to be allocated. For radar 3, jammer 2 with better interference effect is allocated more power, while jammers 1 and 4 are allocated less power to radar 3 to interfere with other radars that need interference more, which meets actual needs.

[0171] Next, the detection probability of the radar network under different interference conditions is calculated, and the interference effect after optimizing the interference resources is verified. Figure 13 The radar network monitoring probability under the following four conditions is obtained. The four conditions are divided into:

[0172] (1) Without interference.

[0173] (2) Random allocation of interference resources (power sharing).

[0174] (3) Optimal allocation of interference resources (power sharing).

[0175] (4) Optimal allocation of interference resources (power optimization).

[0176] from Figure 13 The simulation results show that after the jammer performs coordinated interference, the detection probability of the radar network is greatly reduced. The effective detection distance of the random interference strategy is 120km. After optimizing the interference decision allocation matrix, the effective detection distance of the networked radar is shortened to 45km. After jointly optimizing the interference beam power, the effective detection distance is shortened to 35km. Therefore, the ISSA algorithm is used to optimize the interference decision matrix F. m,n,k With the power allocation matrix P m,n The solution of jointly optimizing jamming resources is feasible, which can realize the rational allocation of resources and achieve better jamming effect.

[0177] In summary, for multi-jammer coordinated jamming scenarios, the networked radar suppression probability Ps is selected as the objective function, a mathematical model of coordinated jamming effectiveness is constructed, and an improved sparrow search algorithm is used to optimize the solution. Simulations compared the ISSA algorithm with the SSA algorithm show that the ISSA algorithm has stronger optimization capabilities and faster convergence. Based on the optimal allocation method, the transmit power allocation result is further solved to achieve the optimal jamming effect, improving the coordinated jamming capability of multiple jammers.

Claims

1. A collaborative interference resource scheduling method based on an improved sparrow search algorithm is characterized in that: The method comprises the following steps: 1) Construct an interference resource allocation model based on the networked radar sets, jammer sets, jamming pattern sets, and power allocation of each jammer beam. The interference resource allocation model includes an interference decision matrix and a power allocation matrix. 2) setting the power allocation matrix in the interference resource allocation model based on the principle of uniform power distribution of each jammer beam, constructing a first suppression probability model of the networked radar based on the interference resource allocation model, taking the first suppression probability model as the first objective function, and using the sparrow search algorithm to solve the interference decision matrix corresponding to maximizing the first objective function, thereby obtaining the optimal interference decision matrix; 3) Based on the optimal interference decision matrix obtained in step 2), a second suppression probability model of the networked radar is constructed, and the second suppression probability model is used as the second objective function. The power allocation matrix corresponding to the maximum value of the second objective function is solved using the sparrow search algorithm to obtain the optimal power allocation matrix; When solving the first and second objective functions using the sparrow search algorithm, in the finder position update step of the sparrow search algorithm, if the warning value is greater than the safety value, the finders after coding sorting are randomly grouped in pairs, forming parent chromosomes and then cross-generating offspring individuals; 4) Perform collaborative interference resource scheduling based on the obtained optimal interference decision matrix and optimal power allocation matrix.

2. The method for cooperative interference resource scheduling based on the improved sparrow search algorithm according to claim 1, characterized in that: In the finder position update step of the sparrow search algorithm, if the warning value is greater than the safety value, the interference object is assigned a code, and the sorted finders are randomly grouped in pairs to form parent chromosomes. The arithmetic crossover operator is used to generate offspring individuals through linear recombination. The formula is: in and is the offspring individual produced by linear recombination, c is the crossover parameter, and its value range is (0,1). and is the parent chromosome, and t is the current iteration number.

3. The method for cooperative interference resource scheduling based on the improved sparrow search algorithm according to claim 1, characterized in that: In the discoverer position update step of the sparrow search algorithm, if the warning value is greater than the safety value, the interference pattern is selected to encode, and the parent chromosomes are processed by multi-point crossover in the genetic algorithm to obtain the offspring individuals.

4. The method for cooperative interference resource scheduling based on the improved sparrow search algorithm according to any one of claims 1 to 3, characterized in that: In the sentinel position update step of the sparrow search algorithm, the individual position is adaptively mutated after the sentinel position is updated, and the mutation probability increases with the increase of the number of iterations.

5. The method for cooperative interference resource scheduling based on the improved sparrow search algorithm according to claim 4, characterized in that: The formula for the adaptive mutation is: Among them, P m (t) is the mutation probability of the current iteration stage, T is the total number of iterations, t is the current number of iterations, P m is the maximum variation value.

6. The method for cooperative interference resource scheduling based on the improved sparrow search algorithm according to any one of claims 1 to 3, characterized in that: In the population initialization step of the sparrow search algorithm, the tent chaotic sequence is used to initialize the population.

7. The method for cooperative interference resource scheduling based on the improved sparrow search algorithm according to claim 1, characterized in that: The expressions of the first suppression probability model and the second suppression model of the networked radar are respectively: and Among them, C1 and C2 are the first suppression probability and the second suppression probability of the networked radar, R is the distance between the jammer and the radar, F is the jamming decision matrix, and F 最优 is the optimal interference decision matrix, P is the power allocation matrix, P 均匀 Ps is the power distribution matrix set based on the principle of uniform distribution of power of each jammer beam. net (R,F,P 均匀 ) represents the first detection probability of the networked radar, Ps net (R,F 最优 ,P) represents the second detection probability of the networked radar, ω(R) represents the weight corresponding to the suppression probability when the distance between the jammer and the radar is R, R min 、R max are the minimum and maximum distances between the jammer and the radar, respectively.

8. The method for cooperative interference resource scheduling based on the improved sparrow search algorithm according to claim 7, characterized in that: The weight is calculated as follows: Among them, the penetration process of the jammer is divided into Q segments with an interval of ΔR, q represents the qth segment, α is the weight factor, α∈(0,1), and the value of α is related to the distance interval and the setting of R.

9. The method for cooperative interference resource scheduling based on the improved sparrow search algorithm according to claim 1, characterized in that: The constraints of the objective function are: Among them, P max is the maximum power of the interference beam, P min Expressed as the minimum power of the interference beam, is the total power of the interference beam emitted by the jammer, D mn Indicates whether the jammer m interferes with the radar n. If so, D mn =1, otherwise D mn =0, Y mk Indicates whether jammer m selects jamming pattern k. If so, Y mk =1, otherwise Y mk =0,P m,n represents the power allocated to radar n by jammer m, m, n, k are the numbers of the jammer, radar, and jamming pattern respectively, M is the total number of jammers, N is the total number of radars, K is the total number of jamming patterns, and L is the maximum number of beams generated by each jammer.

10. The method for cooperative interference resource scheduling based on the improved sparrow search algorithm according to claim 1, characterized in that: The interference decision matrix F is: Where D represents the interference object allocation matrix, D mn Indicates whether the jammer m interferes with the radar n. If so, D mn =1, otherwise D mn =0; Y represents the interference pattern selection matrix, Y mk Indicates whether jammer m selects jamming pattern k. If so, Y mk =1, otherwise Y mk = 0, m, n, k are the numbers of the jammer, radar, and jamming pattern respectively, m = 1, 2, 3, ..., M, n = 1, 2, 3, ..., N, k = 1, 2, 3, ..., K; The power allocation matrix P is: Among them, P m,n Represents the power allocated by jammer m to radar n, where m and n are the numbers of the jammer and radar respectively, m = 1, 2, 3, ..., M, and n = 1, 2, 3, ..., N.

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